Infrared Detectors (Semiconductors and Semimetals: v. 5)

SEMICONDUCTORS AND SEMIMETALS VOLUME 5

Infrared Detectors

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SEMICONDUCTORS AND SEMIMETALS Edited by R. K . WILLARDSON BELL AND HOWELL ELECTRONIC MATERIALS DIVISION PASADENA, CALIFORNIA

ALBERT C. BEER BATTELLE MEMORIAL INSTITUTE COLUMBUS LABORATORIES COLUMBUS, OHIO

VOLUME 5 Infrared Detectors

1970

ACADEMIC PRESS New York and London

COPYRIGHT @ 1970, BY ACADEMIC PRESS, INC. ALL RIGHTS RESERVED NO PART OF THIS B O O K MAY BE REPRODUCED IN ANY FORM, BY PHOTOSTAT, MICROFILM, RETRIEVAL SYSTEM, OR ANY OTHER MEANS, WITHOUT WRITTEN PERMISSION FROM THE PUBLISHERS.

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Uniied Kingdom Edition published by ACADEMIC PRESS, INC. (LONDON) LTD Berkeley Square House, London Wl X 6BA

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PRINTED IN THE UNITED STATES OF AMERICA

List of Contributors Numbers in parentheses indicate the pages on which the authors' contributions begin.

F. R. ARAMS, Airborne Instruments Laboratory, A Division of Cutler-Hammer, Inc., Melville, New York (409) T. C. HARMAN, Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, Massachusetts (1 11) R. J. KEYES,Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, Massachusetts (32 1) PAULW. KRUSE,Honeywell Corporate Research Center, Hopkins, Minnesota (15) HENRYLEVINSTEIN, Physics Department, Syracuse University, Syracuse, New York (3) DONALD LONG,Honeywell Corporate Research Center, Hopkins, Minnesota (175) IVARSMELNGAILIS, Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, Massachusetts (1 11) F. P. PACE,Airborne Instruments Laboratory, A Division of Cutler-Hammer, Inc., Melville, New York (409) B. J. PEYTON, Airborne Instruments Laboratory, A Division of Cutler-Hammer, Inc., Melville, New York (409) M. B. PRINCE,' Electro-Optical Systems, Inc., A Xerox Company, Pasadena, California (85) E. H. PUTLEY, Ministry of Technology, Royal Radar Establishment, Malvern, Worcestershire, England (259) T. M. QUIST,Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, Massachusetts (32 1) E. W. SARD,Airborne htruments Laboratory, A Division of Cutler-Hammer, Inc., Melville, New York (409)

' Present address: Solid State Radiations, Inc., Los Angeles, California. V

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LIST OF CONTRIBUTORS

L. SCHMIT, Honeywell Corporate Research Center, Hopkins, Minnesota (1 75) ROBERTSEHR, Solid State Electronics Branch, McDonnell Douglas Astronautics Company, Western Division, Santa Monica, California (467) H . S. SOMMERS, JR., RCA Laboratories, David Sarnofl Research Center, Princeton, New Jersey (435) NORMAN B. STEVENS, Santa Barbara Research Center, Subsidiary of Hughes Aircraft Company, Santa Barbara, California (287) M. C. TEICH,Department of Electrical Engineering, Columbia University, New York, New York (361) RAINERZULEEG, Solid State Electronics Branch, McDonnell Douglas Astronautics Company, Western Division, Santa Monica, California (467) JOSEPH

Preface The extensive research that has been devoted to the physics of semiconductors and semimetals has been very effective in increasing our understanding of the physics of solids in general. This progress was made possible by significant advances in material preparation techniques. The availability of a large number of semiconductors with a wide variety of different and often unique properties enabled the investigators not only to discover new phenomena but to select optimum materials for definitive experimental and theoretical work. In a field growing at such a rapid rate, a sequence of books which provide an integrated treatment of the experimental techniques and theoretical developments is a necessity. The books must contain not only the essence of the published literature, but also a considerable amount of new material. The highly specialized nature of each topic makes it imperative that each chapter be written by an authority. For this reason the editors have obtained contributions from a number of such specialists to provide each volume with the required detail and completeness. Much of the information presented relates to basic contributions in the solid state field which will be of permanent value. While this sequence of volumes is primarily a reference work covering related major topics, certain chapters will also be useful in graduate study. In addition, a number of the articles concerned with applications of specific phenomena will be of value to workers in various specialized areas of device development. Because of the important contributions which have recently resulted from studies of the III-V compounds, the first few volumes of this series have been devoted to the physics of these materials: Volume 1 reviews key features of the III-V compounds, with special emphasis on band structure, magnetic field phenomena, and plasma effects. Volume 2 emphasizes physical properties, thermal phenomena, magnetic resonances, and photoelectric effects, as well as radiative recombination and stimulated emission. Volume 3 is concerned with optical properties, including lattice effects, intrinsic absorption, free carrier phenomena, and photoelectronic effects. Volume 4 includes thermodynamic properties, phase diagrams, diffusion, hardness, and phenomena in solid solutions as well as the effects of strong electric fields, hydrostatic pressure, nuclear irradiation, and nonuniformity of impurity

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Viii

PREFACE

distributions on the electrical and other properties of 111-V compounds. The present volume differs in scope from its predecessors in that, being devoted to infrared detectors, it becomes the first of a number of volumes to deal specifically with applications of semiconductor properties. Many chapters in the volume emphasize the exploitation of unique characteristics in certain materials; other chapters are concerned with special detection techniques. Because of time and space limitations, a number of articles had to be postponed for a later volume. In addition to further chapters on infrared detection, subsequent volumes of Semiconductors and Semimetals will be devoted to other applications such as high-temperature diodes and power rectifiers, field-effect transistors, IMPATT diodes, tunnel diodes, and applications of bulk negative resistance. Volumes will also deal with such fundamental phenomena as charge-carrier injection, lattice dynamics, galvanomagnetic effects, luminescence, and nonlinear optical phenomena. The editors are indebted to the many contributors and their employers who made this series possible. They wish to express their appreciation to the Bell and Howell Company and the Battelle Memorial Institute for providing the facilities and the environment necessary for such an endeavor. Thanks are also due to the U.S. Air Force Offices of Scientific Research and Aerospace Research and the U.S. Navy Office of Naval Research and the Corona Laboratories, whose support has enabled the editors to study many features of compound semiconductors. The assistance of Rosalind Drum, Martha Karl, and Inez Wheldon in handling the numerous details concerning the manuscripts and proofs is gratefully acknowledged. Finally, the editors wish to thank their wives for their patience and understanding. R. K. WILLARDSON ALBERTC. BEER

Contents . . . PREFACE . . . . . CONTENTS OF PREVIOUS VOLUMES . LISTOFCONTRIBUTORS

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v vii xiii

INTRODUCTION Chapter 1 Characterizationof Infrared Detectors

Henry Levinstein I. Introduction . . . . 11. Characterization of Detectors .

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111-V COMPOUNDS Chapter 2 Indium Antimonide Photoconductive and PhotoelectromagneticDetectors

Paul W. Kruse I. Introduction .

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11. Electrical Properties, Optical Properties, and Lifetime Values of Importance to

the Design of lnSb Infrared Detectors . . . . . 111. Theoretical Detector Design . . . . . . . IV. Preparation of Photoconductive and Photoelectromagnetic Detectors V. Performance of Photoconductive and Photoelectromagnetic Detectors

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Chapter 3 Narrowband Self-Filtering Detectors

M . B. Prince 1. Introduction . . 11. Theoretical Discussion 111. Experimental Data . 1V. Summary . .

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CONTENTS

X

IV-VI AND 11-VI ALLOYS

Chapter 4 Single-Crystal Lead-Tin Chalcogenides Ivars Melngailis and T. C . Harman I. Introduction .

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. . 111. Photovoltaic Detectors . 11. Crystal Preparation

IV. Photoconductive Detectors V. Summary . . .

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Chapter 5 Mercury-Cadmium Telluride and Closely Related Alloys Donald Long and Joseph L. Schmit I. Introduction .

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11. Basic Material Properties

111. IV. V. VI.

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. . . 218 Basic Infrared Detector Theory Applicable to These Materials Crystal Preparation . . . . . . . . . . 233 Detector Fabrication and Properties . . . . . . . . 244 Conclusion . . . . . . . . . . . . 251 253 Appendix. Intrinsic Carrier Concentration versus Temperature in Hg,-.Cd,Te.

THERMAL DETECTORS

Chapter 6 The Pyroelectric Detector E. H . Putley I. The Pyroelectric Effect . . . 11. The Pyroelectric Detector . . 111. Construction ofPyroelectric Detector . Appendix. Electrode Geometry . . . Note Added in Proof

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283

Chapter 7 Radiation Thermopiles Norman B. Stevens I. 11. 111. IV. V.

Introduction . . . . . . Theoretical Background . . . . . Thermopiles as Radiation Detectors . Properties of Thermopile Radiation Detectors Conclusion . . . . . . List ofSymbols . . . . .

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CONTENTS

HETERODYNE DETECTION AND OTHER SPECIAL TECHNIQUES Chapter 8 Low-Level Coherent and Incoherent Detection in the Infrared R. J . Keyes and T. M . Quist I. Introduction .

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11. Low-LevelIncoherent Detection

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111. Low-Level Coherent Radiation Detection . . . . . Appendix. Thermal Generation-Recombination Noise in Photoconductors

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Chapter 9 Coherent Detection in the Infrared

M . C. Teich I. 11. 111. IV. V. VI . VII.

Introduction . . . . . . . . . . Quantum Theory of Infrared Coherent Detection . . . Measurement of the Signal-to-Noise Ratio . . . . . . . . Detection from a Moving Diffuse Reflector An Infrared Laser Radar . , . . . . . . Photoconductors and Photodiodes in the Infrared: A Comparison Conclusion . . . . . . . . . .

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361

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Chapter 10 Infrared Heterodyne Detection with Gigahertz IF Response F. R. Arams, E. W. Sard, B. J. Peyton, and F. P. Pace I. 11. 111. IV. V. VI. VII.

Introduction . . . . . . . . . . . . Design Formulas for Photoconductive Mixers . . . . . . . . . . . Mixer Response Measurements Using Ge:Cu . IF Preamplifier . . . . . . . . . . . . . Prediction of Performance from Mixer I-V Characteristic . Results on Heterodyne Detection in Ge:Cu . . . . . . Effects of Bias Voltage and Operating Temperature on Mixer Response. . Appendix A. Derivation of Design Equations . . . . . . Appendix B. Effective IF Noise Temperature under Mismatched Conditions . Appendix C. Analysis of Mixer Performance from Mixer I-V Characteristics.

409 410 415

419 420 421 426 429 431 432

Chapter 1 1 Microwave-BiasedPhotoconductive Detector H . S. Sommers. Jr. I. 11. 111. IV.

Introduction . . . . Limitations of Ohmic Contacts Response of Detector-Theoretical Design Details . . .

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xii

CONTENTS

V. VI. VII. VIII.

Performance Factors for Broadband Detectors . . Response of Various IR Photoconductors-Experimental Comparison of Sensitivity with Representative Broadband Areas for Further Research . . . . .

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Detectors

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Chapter 12 Imaging and Display Robert Sehr and Rainer Zuleeg .

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11. Beam-Scanned Imaging Devices

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I. Introduction

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111. Electronically Scanned Photodetector Arrays IV. Image Readout Methods for Photodetector Arrays V. Imaging Characteristics of Photodetector Arrays V1. Array and Scanning Circuit Integration . . VII. Display Devices . . . . . . VIII. Parallel Readout Image Converters . . . AUTHORINDEX. SUBJECTINDEX .

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461 470 483 497 . 505 . 508 . 508 . 520

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Semiconductors and Semimetals Volume 1 Physics of 111-V Compounds C . Hilsum, Some Key Features of 111-V Compounds Franco Bassani, Methods of Band Calculations Applicable to 111-V Compounds E. 0. Kane, The k . p Method V. L. Bonch-Bruevich, Effect of Heavy Doping on the Semiconductor Band Structure Donald Long, Energy Band Structures of Mixed Crystals of Ill-V Compounds Laura M . Roth and Petros N . Argyres, Magnetic Quantum Effects S. M . Puri and T . H. Geballe, Thermomagnetic Effects in the Quantum Region W. M . Becker, Band Characteristics near Principal Minima from Magnetoresistance E. H . Putley, Freeze-Out Effects, Hot Electron Effects, and Submillimeter Photoconductivity in InSb H . Weiss, Magnetoresistance Betsy Ancker-Johnson, Plasmas in Semiconductors and Semimetals

Volume 2 Physics of 111-V Compounds M . G. Holland, Thermal Conductivity S. I . Nooikoua, Thermal Expansion U. Piesbergen, Heat Capacity and Debye Temperatures G. Giesecke, Lattice Constants J . R . Drubble, Elastic Properties A . U. Mac Rae and G. W . Gobeli, Low Energy Electron Diffraction Studies Robert Lee Mieher, Nuclear Magnetic Resonance Bernard Goldstein, Electron Paramagnetic Resonance T. S. Moss, Photoconduction in 111-V Compounds E. Antdncik and J. Tauc, Quantum Efficiency of the Internal Photoelectric Effect in lnSb G. W . Gobeli and F. G. Allen, Photoelectric Threshold and Work Function P. S. Pershan, Nonlinear Optics in Ill-V Compounds M . Gershenzon, Radiative Recombination in the Ill-V Compounds Frank Stern, Stimulated Emission in Semiconductors

Volume 3 Optical Properties of III-V Compounds Marvin Hass, Lattice Reflection William G. Spitzer, Multiphonon Lattice Absorption D. L. Stierwalt and R. F. Potter, Emittance Studies H . R . Philipp and H . Ehrenreich, Ultraviolet Optical Properties Manuel Cardona, Optical Absorption above the Fundamental Edge Earnest J . Johnson, Absorption near the Fundamental Edge John 0. Dimmock, Introduction to the Theory of Exciton States in Semiconductors B. Lax and J . G. Maurozdes, Interband Magnetooptical Erects

xiv

CONTENTS OF PREVIOUS VOLUMES

H . Y. Fan, Effects of Free Carriers on the Optical Properties Edward D . Palik and George B. Wright, Free-Carrier Magnetooptical Effects Richard H . Bube, Photoelectronic Analysis B. 0. Seraphin and H . E . Bennett, Optical Constants

Volume 4 Physics of 111-V Compounds N . A . Goryunova. A . S. Borshchevskii, and D . N . Tretiakou, Hardness N . N . Sirofa,Heats of Formation and Temperatures and Heats of Fusion of Compounds A"'BV Don L . Kendall, Diffusion A . G . Chynowerh, Charge Multiplication Phenomena Robert W .Keyes, The EfFects of Hydrostatic Pressure on the Propertiesof IIILV Semiconductors L . W . Aukerman, Radiation Effects N . A . Goryunova, F. P . Kesamanly, and D . N . Nasledov, Phenomena in Solid Solutions R. T. Bute, Electrical Properties of Nonuniform Crystals

Introduction

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CHAPTER 1

Characterization of Infrared Detectors Henry Levinstein

I . INTRODUCTION.. 11.

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CHARACTERIZATION OF

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3 3

I. Introduction Infrared detectors may be characterized by three basic parameters : the spectral range over which they respond, speed with which they respond, and the smallest radiant power they can detect. Some of these parameters arc not absolute quantities, but may depend on the conditions of measurement and on the environment in which the detectors are used. Thus the minimum detectable power, frequently referred to as noise equivalent power (NEP), may vary with the energy distribution of the source; it will also depend on the amount of extraneous radiation which reaches the detector from the thermal background. The parameters may be an inherent property of the detector material, or they may depend on fabrication techniques and on the geometrical design. It is important in the characterization of detectors that measurement techniques are clearly specified, so that they may be reproduced at will. In addition, the physical processes responsible for detector action should be sufficiently well understood that their behavior under conditions other than those prevailing during parameter measurement may be anticipated. 11. Characterization of Detectors

A determination of the parameters may require the measurement of several detector properties, or a single measurement by several techniques. In particular, evaluation of noise equivalent power requires measurement of two quantities: the signal produced by the detector when it is exposed to modulated radiation from a blackbody source, and the detector noise when it is shielded from the blackbody radiation. Among the conditions of measurement which must be specified are the temperature of the radiation

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HENRY LEVINSTEIN

source, the modulating frequency, and the amplifier bandwidth. Standardization of blackbody temperature is required because the spectral distribution of the emitted radiation will determine the amount of radiation the detector “sees.” A blackbody at 500°K is usually employed as a radiation source for detectors with response beyond 2p. Since both detector signal and noise may be frequency-dependent, the modulating frequency must be specified. The amplifier bandwidth must be known because it determines the magnitude of the measured noise. In order to minimize the noise variations within the frequency interval over which noise is measured, the amplifier bandwidth must be made as narrow as practicable (usually 4 or 5 Hz, the bandwidth of commercially available harmonic analyzers). The noise equivalent power (NEP) expressing a particular set of measurement conditions may be written as follows : P A NEP(500°K, 900 Hz,5 Hz) = D. (1) SIN

The quantities in parentheses refer to the blackbody temperature, modulating frequency, and amplifier bandwidth, respectively ; S and N represent signal and noise under the conditions of measurement, A the detector area, and PD the radiant power density which reaches the detector from the blackbody. As a matter of convenience the reciprocal of NEP, the detectivity D (in reciprocal watts), is often specified. In order to make possible comparison among detectors, detectivity is often normalized to an amplifier bandwidth of 1 Hz and a detector area of 1 cm’. This yields the parameter D* such that’

The normalization is based on evidence that noise varies as the square root of amplifier bandwidth and that D varies inversely as the square root of detector area. The first assumption is usually well justified, since detectors are generally measured at a frequency where noise is frequency-invariant, or at a sufficiently narrow bandwidth that the frequency variation of noise is insignificant. The second assumption is sometimes not entirely justified and may lead to considerable error in the normalization process. Yet its convenience usually justifies its use, especially where its shortcomings are understood. Infrared detectors are used in a spectral range where they “see,” in addition to the radiation from a given source, considerable radiation from thermal background. The amount and type of background to which the detector is exposed must be specified, since it may affect detector characteristics rather drastically. Unless otherwise specified D* is given for a field R. C. Jones, Proc. I.R.E. 47, 1495 (1959).

1 . CHARACTERIZATION

OF INFRARED DETECTORS

5

of view of 2n sr and a background temperature of 300°K. It is usually possible to calculate what effect different background conditions will have on D*.2 On the other hand, effects on other characteristics, such as the speed of response, may not always be estimated. While D* provides a useful means of comparison among detectors, it is of little value to the system designer who must construct amplifiers to be used in conjunction with detectors. Since the design of the amplifier depends on the magnitude of the signal, usually specified in terms of responsivity (signal voltage per watt incident power) and the nature of the detector noise, information on both quantities must be available. Both noise and responsivity are frequency-dependent. Several types of noise are observed in detectors. Johnson noise3 is the limiting noise in all conductors. It is frequency-invariant in the audio- and radio-frequency regions and is independent of the magnitude of current passing through the detector. It is given by the expression

vj

=

(4KTRAf)”2,

where R is the resistance ofthe conductor in ohms, K the Boltzmann constant (1.38 x l o p z 3J/deg), T the temperature of the detector in OK, and A,f the amplifier bandwidth in hertz. A type of noise known as llfnoise is present in all detectors containing semiconductor elements. This type of noise has a spectrum whose noise voltage varies as llf”. where n is approximately i,but may deviate somewhat from that value.4 Noise due to fluctuations in the generation and recombination of charge carrier^,^ just as llf noise, varies linearly with current. It may be due to the random arrival of photons from the background (photon noise) or to fluctuation in the density of charge carriers as produced by lattice vibration (g-r noise). Its frequency spectrum is determined by the free-charge carrier lifetime. Temperature noise is produced by fluctuations in the temperature of the surroundings, especially the surface on which the detector element is mounted. Information on the speed of response of a detector may be obtained from two types of measurements: the observation of the signal rise and decay times as the detector is exposed to square pulses of radiation having sufficient duration for equilibrium to be established in the detector element, and the determination of the frequency response of the detector as the modulation

* P. Bratt, W. Engler. H. Levinstein, A. U. MacRae. and J. Pehek, lnfrared

Phys. 1. 27 (1961). P. W. Kruse, L. D. McGlauchlin, and R. B. McQuistan, “Elements of Infrared Technology.” Wiley, New York, 1962. A. U. MacRae and H . Levinstein, Phys. Rev. 119. 62 (1960). K. M. Van Vliet, Proc. I.R.E. 46, 1004 (1958).

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HENRY LEVINSTEIN

frequency of the incident power is varied. If the signal rise and decay characteristics have an exponential behavior, as expressed by a single time constant, both methods give the same value of time constant. Frequently, detector response to a square radiation pulse consists of a rapid rise, designated by a short time constant, followed by a more slowly increasing signal. Under these conditions the detector speed may be given by the fraction which each behavior contributes to the total signal. For this type of behavior and the even more complicated rise and decay characteristics often observed, a detailed description of measurement techniques accompanied by oscilloscope traces and frequency response curves is usually required. A mere statement of the detector response time may then represent only an order of magnitude estimate. In addition, rise and decay characteristics will depend on the amount of radiation reaching the detector, both from the signal source and from the background. Occasionally, they may vary with the spectral distribution of the signal source. It is thus quite clear that specifications of the speed of response of a detector are only really meaningful if the conditions of measurement are clearly specified and if the data can be extrapolated to the conditions under which the detector is actually being used. The spectral response of a detector may be given in either relative or absolute units. If one is merely interested in the shape of the response, i.e., a comparison of the response of the detector a t several wavelengths, it is sufficient to vary the wavelength of radiation incident on the detector by means of a monochromator and to compare the detector response with one of known response. Absolute response determination requires that the comparison detector be calibrated or that calibration of the unknown be performed with the aid of a standard blackbody source. When this has been accomplished Da*, the detectivity at a particular wavelength, may be specified. The value of D,* at spectral peak, where one exists, is usually more meaningful than D* referred to a blackbody, since it does not require specification of blackbody temperature and gives some indication of the general shape of the spectral response. Of course, Da* and D* are identical for wavelength-invariant response and have a calculable relation when the shape of the spectrum is known. The case where the response rises linearly with wavelength and then drops abruptly represents a large group of detectors. Figure 1 shows the ratio of D* at spectral peak to D* for a 500°K blackbody as a function of long-wavelength threshold (or wavelength for detector peak response).6 In order to present more specific information about detectors, the mechanism responsible for the detector action must be considered.

‘ H. Levinstein, in “Applied Optics and Optical Engineering” Chap 9. Academic Press, New York, 1965.

(R. Kingslake, ed.), Vol. 2,

1, CHARACTERIZATION OF INFRARED DETECTORS

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A (microns)

FIG.1. Ratio of detectivity at spectral peak to the value for a 500°K blackbody as a function of detector threshold wavelength. The curve assumes ideal photon detectors, where the response for constant energy rises linearly with wavelength and then drops abruptly to zero.

Infrared detectors had their beginning with the blackened thermometer used by Hershel when he discovered infrared in 1800. All infrared detectors for the next century were, like the thermometer, of the thermal type. Radiation incident on an absorbing layer warms the layer. This in turn warms the temperature-sensitive material in contact with the absorber. Incident radiant power is then measured by the changes in the characteristics of the temperature-sensitive material. Many types of thermal detectors have been developed and a large variety of them are commercially available. If it were possible to produce materials with wavelength-invariant absorption, these devices would respond uniformly to equal amounts of incident power over all regions of the electromagnetic spectrum. In practice, no uniform “black” exists, and thus the spectral response of thermal detectors is usually not wavelength-invariant. Since these detectors frequently serve as standards for other detectors with a more rapidly varying spectral response, great care is required in their calibration, especially over a wide spectral range. Because of their slowly varying response with wavelength, blackbody detectivity measurements do not require precise specification of blackbody temperature as long as the incident power is known. Since the response time is determined by the rate at which the element warms and cools, its size, specificheat, and the degree of isolation from the environment determine response time. These factors also influence the minimum detectable power

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HENRY LEVINSTEIN

in such a way that the devices which respond more rapidly usually have lower detectivity. Among the physical phenomena which have been applied in the construction of thermal detectors are the generation of thermal voltages (thermocouples and thermopiles), temperature variation of the resistance of metals and semiconductors (metal and thermistor bolometers), pyroelectric effects, and the variation of gas pressure with temperature (Golay cell). While originally most thermal detectors were operated at ambient temperatures, the development of a variety of semiconductors whose electrical properties change more rapidly in the vicinity of liquid helium temperatures, providing at the same time lower thermal capacities, has led to the development of cooled thermal detectors, most of them of the bolometer type. Conventional thermal detectors operated at ambient temperature have values of D*, when this is applicable, in the range from lo8 to lo9 cm H Z ’ ’ W-’ ~ and a time constant in the millisecond range. Semiconductor bolometers designed for liquid helium temperatures may have detectivities several orders of magnitude larger and time constants in the microsecond range. In contrast to thermal detectors are photon detectors, where the incident photons interact with the electronic energy states. In most conventional photon detectors this interaction results in the liberation of charge carriers and increased conductivity or a photovoltage. Photoconductivity was first observed in selenium in the late 18003, but construction of infrared photon detectors did not progress rapidly until the 1940’s. In contrast to thermal detectors, these devices have a well-defined spectral cutoff, depending on the energy required to free charge carriers in a particular material. The shape of the ideal spectral response, assuming constant quantum efficiency rather than being wavelength-invariant for constant incident energy as in the case of thermal detectors, is wavelength-invariant for constant photon flux up to the threshold wavelength. For constant energy, of course, the ideal response increases linearly with wavelength up to the threshold. Real detectors do not have such idealized response curves. The spectral peak will usually occur near, but not at, the threshold wavelength. The decrease in response after the spectral peak may not be abrupt, and the linear rise with wavelength may show considerable deviation. The relationship shown in Fig. 1 should thus be considered merely as a guide. The response time, rather than being determined largely by geometrical considerations as in the case of thermal detectors, is dependent on free charge carrier lifetimes, a characteristic of the material. Because of the various types of recombination mechanisms, rise and decay characteristics may be rather complex and require careful analysis. The emphasis in the development of photon detectors has been toward response to ever longer wavelengths and shorter time constants. At the same time there has been

1. CHARACTERIZATION OF INFRARED DETECTORS

9

a concerted effort to achieve increased detectivity up to the theoretical limit. The earliest photon detectors consisted of evaporated or chemically deposited layers which required trial-and-error sensitizing techniques. Unfortunately, physical processes responsible for the success or failure of these techniques are still not well understood, even though many of these detectors have been prepared for more than 20 years. The first of the infrared film detectors was TI,&, with a response to 1 . 2 ~ .It finds little application today. It was followed rapidly by the use of PbS, responding to about 3 p ; PbTe, to 6 ,u ; and PbSe, to about 7 p. Advances in semiconductor technology, especially the purification and crystal growing techniques employed for Ge and Si, have led to an entirely new group of infrared photon detectors. Not only was it possible to produce detectors of Ge and Si in the near infrared, but also Ge detectors whose response could be extended to beyond loop by the addition of selected impurities with a variety of activation energies. These extrinsic detectors have two superimposed spectral curves, one due to the host crystal, and the other due to the particular impurity added to germanium. When

L

1010,

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5

WAVELENGTH

610

30

50

( rn icro ns)

FIG.2. Dependence of DA* at spectral peak on long wavelength threshold for several background temperatures. Calculations assume ideal photoconductive detectors having a 2s-sr field of view.

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HENRY LEVINSTEIN

semiconductor technology was applied to the synthesis of new compounds, such as InSb or InAs, single-crystal detectors for the intermediate IR region (4-6 p) could be constructed with highly-reproducible characteristics and well-understood behavior. In most recent developments the alloying of compounds, such as HgTe and CdTe or PbTe and SnTe, one with a small energy gap and the other with a larger gap, has made possible the construction of detectors whose long wavelength threshold is dependent on the fractional composition of the compounds and has thereby resulted in detectors with a tailor-made spectral response. While extrinsic single crystal detectors are always used in the photoconducting mode, intrinsic single crystal detectors

lo9

190°K

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\I 6

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FIG. 3. Spectral response curves of various intrinsic detectors and their temperature of operation (field of view 1 8 O O ) .

1. CHARACTERIZATION

OF INFRARED DETECTORS

11

such as InSb may be constructed to be either photoconductive or photovoltaic. The functioning of photon detectors depends critically on the detector temperature. As the response extends to longer wavelengths, increased cooling is required to reduce competition between carriers liberated by incident signal photons and those generated thermally. Detectors with response in the 1-3p region may be operated at room temperature; those with response beyond 100 p require liquid helium temperature. Between these extremes cooling requirements vary, depending on, in addition to the spectral cutoff, the type of detector-intrinsic detectors generally require less cooling than extrinsic detectors. Since IR detectors respond to signals in a wavelength range where there is an appreciable photon flux from the background and thus a competition in the liberation of charge carriers between signal and background photons, the distribution and amount of background photon flux affects the detectivity and must be specified. If one assumes under ideal conditions unity quantum efficiency and noise due only to fluctuations in the arrival of background photons, one can evaluate the upper limit of detectivity for various amounts

Theoretical limit (60" angular field)

IGe : Cu Cooled

I

2

5

10

20

30

Wavelength (microns)

FIG.4. Spectral response curves of various extrinsic germanium detectors and their operating temperature (field of view -60').

12

HENRY LEVINSTEIN

and distribution of background photonse2 Such an ideal detector (BLIP) represents an upper bound to the detectivity which may be achieved. Figure 2 shows how DA* at spectral peak for ideal detectors depends both on the long wavelength threshold of the detector and the temperature of the background to which it is exposed. These curves are for a 21r-sr field of view. The detectivity increases as l/sin)6 as the angle 6 subtended at the detector by the background is reduced below 180". The background limited condition requires that the detector be cooled to the extent that thermally generated charge carriers are reduced considerably below those generated by the background. Thus as the background radiation is reduced, the detector will have to be cooled to even lower temperatures. Photon detectors with a 2n-sr field of view and a 300°K background have detectivities at spectral peak above 10'0cmHz''2 W-' and time constants in the microsecond and nanosecond ranges. Figures 3 and 4 show the spectral response curves of some commercially available IR detectors and their cooling requirements.

111-V Compounds

This Page Intentionally Left Blank

CHAPTER 2

Indium Antimonide Photoconductive and Photoelectromagnetic Detectors Paul W.Kruse

I . INTRODUCTION

.

.

.

. .

.

. . . . . .

.

. .

.

15

11. ELECTRICAL PROPERTIES, OPTICAL PROPERTIES. AND LIFETIME VALUES OF IMPORTANCE TO THE

DESIGN OF INSB~ N F R A R E DDETECTORS . .

.

. . . . . . . . . . . . . 2 . Optical Properties . . . . . . . . . . . . . . 3 . Electron and Hole Lifetimes . . . . . . . . . . . 111. THEORETICAL DETECTOR DESIGN . . . . . . . . . . . 4. Photoconductivity . . . . . . . , . . . . . . 5 . Photoelectromagnetic Effect . . . . . . , . . . . I V . PREPARATION OF PHOTOCONDUCTIVE AND PHOTOELECTROMAGNETIC DETECTORS. . . . . . . . . . . . . . . . . 6 . Purification and Crystal Growth . . . . . . . . . . 7. Fabrication ofthe Sensitive Element . . . . . . . . . 8 . Detector Housing Design . . . . . . . . . . . . 1. Electrical Properties .

V , PERFORMANCE OF PHOTOCONDUCTIVE AND PHOTOELECTROMAGNETIC DETECTORS . . . . . . . . . . . . . . . . . 9. Properties of Selected High-Performance Photoconductive and Photoelectromagnetic Detectors . . . . . . . . . . 10. Comparison of Measured Performance with Theory . . . . . 11. Statistical Distribution of the Properties of Large Numbers of 77'K Photoconductive Detectors . . . . . . . . . .

18 18 27 31

39 41 57 62 63 64 67 70 71 74 77

I. Introduction Indium antimonide, InSb, is a direct, small energy gap semiconductor whose semiconducting properties were first revealed by H. Welker in 1952.' Detailed studies of its properties were soon initiated on a worldwide basis, and in the middle and late 1950's it was the subject of numerous scientific investigations. It was soon discovered that InSb had the smallest energy gap of any semiconductor known at that time; its application as a long wavelength infrared detector became obvious, The gap of 0.17 eV at H.Welker, Z . Naturforxh. 7a, 744 (1952); 8a, 248 (1953).

15

16

PAUL W . KRUSE

room temperature indicated it would have a long wavelength limit of approximately 7 p. When cooled with liquid nitrogen the gap increased to 0.23 eV, resulting in a long wavelength limit of 5.5 p. The interest in InSb as an infrared detector stemmed not only from its small energy gap, but also from the fact that it could be prepared in single crystal form by conventional means. Although lead selenide, PbSe, was also a small gap semiconductor, infrared detectors made from it were in the form of thin films prepared by either vacuum evaporation or chemical deposition. The technique of preparing and oxidizing these films was in the nature of an art, rather than a science. Furthermore, the performance of PbSe detectors could not be inferred from a study of the bulk crystal properties. Thus the interest in InSb as an infrared detector material stemmed also from the realization that it was a classical semiconductor whose properties could be analytically determined, leading to the rational design of a high-performance infrared detector. Three modes of operation have been of interest : photoconductivity, the photovoltaic effect, and the photoelectromagnetic effect. Interest in the photoelectromagnetic (PEM) effect was novel ; no infrared detectors had previously been made which operated by this effect. It can be shown that for materials having a high electron mobility and a low direct lifetime the PEM effect is capable of giving rise to a photosignal larger than that from photoconductivity for reasonable values of magnetic field and electric field. Thus early interest existed in the study of the PEM effect in InSb and the fabrication of PEM detectors. The first practical InSb detectors were grown junction photovoltaic ones.’ Techniques of purifying semiconductors require years before purities in the range of 10’4cm-3 or less required for high performance photoconductors are developed. On the other hand, photovoltaic detectors require p-n junctions having majority carrier concentrations on either side of the junction in the lO”-lO’* cm-3 range, Thus in the early stages of development of a new semiconductor, high performance photovoltaic detectors are usually prepared before photoconductive detectors of comparable performance. The first high performance InSb detectors employed grown junctions, followed soon after by the development of a diffused junction detector. S. W . Kurnick e t a ! . , Electrochem. Soc. Spring Meeting (May 1955); G. R . Mitchell, A. E. Goldberg, and S. W. Kurnick, Phys. Rev. 97, 239 (1955); D. G. Avery, D. W. Goodwin, and A. E. Rennie, J. Sci. Instr. 34, 394 (1957). Unpublished work on diffused junction detectors at Texas Instruments, Inc., Dallas; S. J. Nicolosi, L. H . DeVaux. and A. J . Straws. EIectronics(Eng1ish ed.)31,48 (1958); M. E. Lasser, P. Cholet, and E. C. Wurst, Jr., J . Opt. SOC.Am. 48,468 (1958).

2.

INDIUM ANTIMONIDE DETECTORS

17

InSb photovoltaic detectors are to be the subject of another chapter in a forthcoming volume of this series. In this chapter only the photoconductive and PEM modes of operation will be studied. Photoconductive detectors4 have been designed for optimum performance at room temperature (300"K), dry ice temperature (195"K), and liquid nitrogen temperature (77°K). PEM detector^,^ designed to operate only at room temperature, require use of a small permanent magnet having pole pieces which direct the magnetic induction through the sample. To obtain a sufficiently high field, the sample must be narrow, approximately 1 mm or less, and the pole pieces must nearly touch the sample edges. If the detector is to be cooled, one of two geometries must apply: The entire magnet can be placed within the vacuum space, necessitating a clumsy Dewar design with a large heat capacity, or an extremely narrow Dewar can be used which is capable of fitting between the pole pieces of an uncooled magnet. In the latter, the problem is one of constructing a double-walled Dewar with an extremely small clearance between the walls. Neither approach is satisfactory. Thus this chapter deals with InSb photoconductive detectors operating at room temperature, dry ice temperature, and liquid nitrogen temperature, and with PEM detectors operating at room temperature. To lay the basis for a prediction of detector performance, the following part discusses those electrical properties, optical properties, and excess-carrier lifetime values of InSb which are of importance to detector design. This is followed by a part concerned with theories of the photoconductive and PEM effects in InSb, in which expressions are derived for the spectral responsivity and detectivity for each detecting mode and operating temperature. Part IV deals with the practical aspects of detector preparation, including growth of high-purity InSb crystals, sensitive element fabrication by such methods as photolithography, and design details of detector housings. Finally, Part V considers the measured performance of representative detectors of each type, compares performance with theory, and ends with information on the statistical distribution of the values of the performance parameters of two large groups of 77°K photoconductive detectors. Among the earliest papers are: D. G. Avery, D. W. Goodwin, W. D. Lawson, and T. S. Moss, Proc. Phys. SOC.(London)B67,761(1954);D. W .Goodwin, J . Sci. Instr. 34,367 (1957);Awry et al.'; Nicolosi et al.3;L. H. DeVaux and A . J. Strauss, Electrochem. SOC.FuNMeeting (October 1957); H. P. R. Frederikse and R. F. Blunt, in "Photoconductivity Conference" (R.G. Breckenridge, B. R. Russell, and E. E. Hahn, eds.), p. 414. Wiley, New York, 1956; S. W. Kurnick and R. N. Zitter, J. Appl. Phys. 27, 278 (1956). Early papers include: Nicolosi et aL3; Kurnick and Zitter4; C. Hilsum and I. M. Ross, Nature 179, 146 (1957); C. Hilsum, Instr. Prac. 12, 857 (1958);P. W. Kruse, J. Appl. Phys. 30. 770 (1959);P. W. Kruse, Electronics33,62 (1960).H. P. R. Frederikse and R.F. Blunt, Proc. I.R.E. 43, 1828 (1955) summarize studies of all three modes of operation in InSb prior to 1955.

18

PAUL W . KRUSE

11. Electrical Properties, Optical Properties, and Lifetime Values of Importance to the Design of InSb Infrared Detectors Proper design of an infrared detector which will operate in a specified mode at a given temperature requires a detailed knowledge of the properties of the semiconductor from which it is made. The equations to be found in Part I11 relate figures of merit such as the responsivity and detectivity to the internal parameters of the semiconductor, including electron and hole concentrations, mobilities, and lifetimes. In general, these internal parameters are dependent upon the purity of the semiconductor. Therefore it is not sufficient to tabulate, say, the electron mobility at 77°K. Instead, the dependence of mobility upon purity must be displayed graphically. The material in this section has been selected from the many publications and review articles in the literature of InSb.6-’ Of particular value has been the work of Hilsum and Rose-Innes,* who succinctly summarize much information on the electrical properties of InSb containing shallow donors and acceptors. 1. ELECTRICAL PROPERTIES

a. Dependence of the Forbidden Energy Gap and Intrinsic Carrier Concentration upon Temperature Indium antimonide is a direct gap semiconductor whose conduction band minimum and valence band maximum are located at k = 0. Because of the small energy gap, the conduction band follows the nonparabolic behavior postulated by Kane.I4 The forbidden energy gap exhibits the conventional negative temperature coefficient as illustrated in Fig. 1, which is from the “Semiconductors and Semimetals” (R. K. Willardson and A. C. Beer, eds.), Vol. 1, Physics of

111-V Compounds, 1966; Vol. 2, Physics of 111-V Compounds, 1966; Vol. 3, Optical Properties of 111-V Compounds, 1967. Academic Press, New York. K. F. Hulme, in “Materials Used in Semiconductor Devices” (C. A. Hogarth, ed.), p. 115.

’

Wiley (Interscience), New York, 1965. C. Hilsum and A. C. Rose-Innes, “Semiconducting 111-V Compounds.” Macmillan (Pergamon), New York, 1961. 0. Madelung (translated by D. Meyerhofer), “Physics of 111-V Compounds.” Wiley, New York, 1964. l o H. Welker and H. Weiss, Sdid State Phys. 3, 1 (1956). F. A. CunneH and E. W. Saker, Prog. Semicond. 2, 35 (1957). T.S. Moss, Prag. Semicond. 5, 191 (1961). l 3 T. S. Moss, “Optical Properties of Semiconductors.” Academic Press, New York, 1959. l4 E. 0. Kane, J . Phys. Chem. Solids 1, 249 (1957).

’’ ’’

2.

19

INDIUM ANTIMONIDE DETECTORS

o‘ -320

I

\

O

> (3

U 2

0.20

I w

t

I

F,C

th P

data (circles) of Roberts and Q~arrington.’~ The data (squares) compiled by Long16 represent values believed to be most accurate at 0, 77, and 300°K.

data of Roberts and Quarringt~n,’~ with additional points from Long’s review paper. The intrinsic carrier concentration as a function of temperature” is illustrated in Fig. 2. The room temperature value is 1.6 x 10’6cm-3. Because of the steep dependence of the intrinsic concentration upon temperature at low temperatures, the exact value at 77°K has not been established. It is most probably in the 10” cm-j range. V. Roberts and J. E. Quarrington, J . Electron. 1, 152 (1955). The curve is that listed as E&, representing the value of photon energy at which the measured absorption coefficient equals 100cm l 6 D. Long, in “Semiconductors and Semimetals” (R. K. Willardson and A. C. Beer, eds.), Vol. 1, Physics of 111-V Compounds, p. 143. Academic Press, New York, 1966. ” C . Hilsum and A. C. Rose-Innes,’ p. 122. The data have been compiled from D. J. Howarth, R. H. Jones, and E. H. Putley, Proc. Phys. Soc. (London)70, 124 (1957); and from C. Hilsum and R. Barrie, Proc. Phys. Soc. (London) 71, 676 (1958). l5

’.

20

PAUL W . KRUSE

b . Dependence of the Hall Coefficient, Electrical Conductivity, and Carrier Mobilities of InSb Containing Shallow Donors and Acceptors upon Temperature and Carrier Concentration

Most of the electrically active impurity atoms in InSb, whether donors or acceptors, have shallow activation energies (see Table I, after Hulme'). At 77°K or above-the temperature range of interest for photoconductive and photoelectromagnetic InSb detectors-these impurity centers are thermally ionized. Data pertinent to InSb containing these shallow centers are discussed in this section. Because one approach to preparing InSb detectors operating in the photoconductive mode at 77°K is to compensate residual donors with Ge-a deep lying acceptor-the following section will briefly discuss the electrical properties of InSb containing Ge. lo'*

(0''

?-

I 2

16

10

.-

c

IS

I0

I 0l4

200

300

400

so0

T (DEG K )

FIG.2. Oependence of the intrinsic concentration ni of InSb upon temperature. (After Hilsum and Rose-Innes.'')

2.

INDIUM ANTIMONIDE DETECTORS

21

TABLE I ENERGIESIN INSB"

IMPURITY IONIZATION

Element

Na, (Li?)

cu

Electrical effect

Donor Double acceptor

Separation of level from conduction (valence) band edge for donor (acceptor) (ev)

Lower level : 0.023 (Hall effect) 0.026 (photoconductivity) Upper level : 0.056 (photoconductivity)

Double acceptor

Lower level : 0.023 (Hall effect) 0.028 (photoconductivity) Upper level : 0.039 (photoconductivity)

Au

Double acceptor

Lower level: 0.032 (Hall effect) 0.043 (photoconductivity) Upper level : 0.066 (photoconductivity)

Mg, Zn. Cd, Hg

Acceptor

A1 Ga

Acceptor Neutral

Si

Acceptor

Ge

Acceptor

Sn

Donor

Pb

Donor or neutral?

S, Se, Te

Donor

Mn

Acceptor

a

0.0075 Zn(?) (Hall effect)

0.10

Usually merged with conduction band at low magnetic fields

After compilation by Hulme.'

Figures 3 and 4 (from Hilsum and Rose-Innes*) illustrate typical Hall coefficient and conductivity data on reasonably pure n- and p-type InSb samples over the temperature interval between room temperature and 77°K. The temperature independent portions of the Hall curves indicate that the samples are thermally ionized in that interval. Figure 5 illustrates the temperature dependences of the electron and hole mobilities of samples of

22 PAUL W . KRUSE

FIG.3. Dependence of the Hall coefficient R , upon temperature for n-type and p-type samples of InSb. (After Hilsum and RoseInnes. *)

FIG.4. Dependence of the electrical conductivity c upon temperature for the n-type and p-type samples of Fig. 3. (After Hilsum and Rose-Innes.')

2. I.

23

INDIUM ANTIMONIDE DETECTORS

n = 2 x 10'4CM-3

loGI 2. n = 101SCM-3

3.n = i0'6CM-3

1.0

4. p

.

3x 10'4CM-3

5. p = 4x 1015CM-3 6. p = 3x 10'bCM-3

10

I00

I 000

T (OEG K )

FIG. 5. Dependence of the electron and hole mobilities upon temperature for n-type and p-type samples of InSb. (After Hilsum and Rose-Innes.8)

n- TYPE SAMPLES \

\

8-

\ \

\rn-

TYPE

\

\

6-

-

I

I0''

H6

@

F6

813 S2 p-TYPE SAMPLES

Q

%'"b,

p TY >:p

0-

PI

@

0

B

'\

2-

GI

0

8 c4

fi

4-

8

I

6

ZI

- -*Wsp , --s-@--+T-+ I

I0l5 1o16 1018 1 0 ~ ~ IMPURITY CONCENTRATION (CM-'1 FIG.6. Dependence of the electron mobility pn at 77°K upon purity in n-type and p-type InSb. (After Hilsum and Rose-Innes.*)

24

PAUL W . KRUSE

l0,OOO

-

c4 FI 8 F7 0 H3 A H6 8 PI s2 x

+

8.000-

C)

W

v)

6,000-

Nz

I

0

0

-$

a\

@\

zI

4,000-

2,000-

0

\ I

I

--------. ..

~

FIG.7. Dependence of the hole mobility / I , , at 77°K upon purity in p-type InSb. (After Hilsum and Rose-Innes.8)

varying purity.8 The maximum mobility of both carriers occurs in the 50-100"Krange. Figures 6 and 7 illustrate the dependence of the electron and hole mobilities, respectively, upon impurity concentration at 77°K.' Similar data for the electron and hole mobilities at room temperature8 are illustrated in Figs. 8 and 9. If the electron and hole mobilities were equal at a given temperature, the maximum resistivity would occur for intrinsic material. Because the electron 8 x lo4

-Y

6x104

u)

> 'N

-3

THEORY FOR p-TYPE /"", SAMPLES

+

\'\ 'b,

@, '

',a

\

4x104

Li 2 x 1 0 ~ C

d4

dS

i0l6

ide

10"

IMPURITY CONCENTRATION (CM-')

FIG.8. Dependence of the electron mobility pE at room temperature upon purity in n-type and p-type InSb. (After Hilsum and Rose-Innes.')

2.

2s

INDIUM ANTIMONIDE DETECTORS

cI

600

-

V W

m

>

I

\

\

a x

K1

s2

4

0

10'~

l0l5

lo1'

l0l6

l0l8

IMPURITY CONCENTRATION ( C M 3 )

FIG.9. Dependence of the hole mobility p, at room temperature upon purity in p-type InSb. (After Hilsum and Rose-Innes.')

0*051

n

0.04

1.0

0.75

0.5

0.2 5

0

(y)

FIG. 10. Dependence of electrical resistivity p o upon acceptor concentration N , at room temperature in InSb; n,/p is the intrinsic concentration to free hole ratio. (After Hilsum.")

mobility in InSb at room temperature is roughly two orders of magnitude greater than the hole mobility, maximum resistivity is found in p-type material. Figure 10 (from Hilsum") illustrates the dependence of the roomtemperature resistivity upon acceptor concentration.

'* C . Hilsum, Solid

State Phys. Electron. Telecornmun., Proc. Intern. Conf: Brussels, 1958 2 (1960); "Semiconductors, Part 2" (M. DCsirant and J. L. Michiels, eds.), p. 733. Academic Press, New York, 1960.

26

PAUL W . KRUSE

The large electron mobility and mobility ratio give rise to pronounced transverse magnetoresistance effects at low magnetic fields in InSb at room temperature. Room temperature magnetoresistance data18 are illustrated in Fig. 11.

0

5000

10,000

MAGNETIC FIELD (GAUSS)

FIG. 11. Dependence of the magnetoresistivity ratio A p / p o upon magnetic field and hole concentration p o at room temperature. (After Hilsum.")

c. Dependence of the Hall Coeficient and Mobility of Ge-Doped InSb upon Temperature Cunningham et ~ 1 . 'have ~ shown that Ge in InSb introduces a shallow donor level and a shallow acceptor level, both of which are thermally ionized at 77°K and above, and a deep acceptor level whose ionization energy with respect to the valence band is about 0.1 eV. By introducing Ge into n-type InSb shallow donors can be compensated, resulting in InSb having resistivities at 77°K in the 1-100 ohm-cm range. The temperature dependences of the Hall coefficient and electron and hole mobilities for InSb containing Ge are illustrated in Figs. 12 and 13, respectively. l9

R. W. Cunningham, E. E. Harp, and W. M. Bullis, Proc. Intern. Con$ Phys. Semicond., Exeter, 1962, p. 732. Inst. ofPhys. and Phys. Soc., London, 1962.

2.

21

INDIUM ANTIMONIDE DETECTORS

Io6

-

lo5

-1

3

0

u

\

n

5

-u 1

P -

4

10

SAMPLE

lo3

lo2

4

6

N A - N ~ ( C ~ - N,,(c~-~) ~)

0

187T

2 . 5 0 ~l0l2

1.30~loi4

A

187M

2.80

o

1878

6 . 2 5IOl3 ~ 2 . 3 6 ~IOl4

8

10

12

loi4

6.65~10'~

14

16

1 0 ~(DEG 1 ~K-'1

FIG.12. Dependence of the Hall coefficient R , upon temperature for Ge-doped InSb having the stated excess acceptor concentrations (NA-ND).The solid curves were computed assuming a deep acceptor ionization energy of 0.106eV and the deep acceptor concentrations N,, shown. (After Cunningham et a1.")

2. OPTICALPROPERTIES a. Dependence of the Optical Absorption Coeficient upon Energy, Temperature, and Purity The dependence of the optical absorption coefficient of InSb upon photon energy at 298"K, 90"K, and 5°K is illustrated in Fig. 14 (after

28

PAUL W . KRUSE

TIDEG K l

FIG.13. Dependence of the electron and hole mobilities upon temperature for the Ge-doped InSb samiles shown in Fig. 12. The electron mobilities indicated by the ordinate scale are 0.1 times the actual value. The mobility ratios of samples 187T, (bT),and 187B, (b,) are included. (After Cunningham et a!.”)

Gobeli and Fan2’). Details of the temperature dependence of the lowenergy portion of the absorption edge are displayed in Fig. 15 (from Roberts and Quarrington”). Because of the very small effective mass ratio of free electrons (0.0155 at liquid helium temperature’ 6), the conduction band density of states is small. Since the effective mass ratio of free holesI6 is approximately 0.4, the Fermi level lies in the conduction band at room temperature for InSb whose free electron concentration is greater than about 5 x lo1 cm- Intrinsic absorption of a photon requires an energy sufficient to cause excitation

’.

2o

’

G . W. Gobeli and H. Y. Fan, Semiconductor Research, Second Quarterly Report, Purdue University, 1956. [Quoted by E. J. Johnson, in “Semiconductors and Semimetals” (R. K. Willardson and A. C. Beer, eds.), Vol. 3, Optical Properties of 111-V Compounds, p. 153. Academic Press, New York, 1967.1 See Roberts and Quarrington.”

29

2. INDIUM ANTIMONIDE DETECTORS

lo4 3 10

-

2 10

-

-

1

I

5 Y

0

-T

a 5°K

I

10

+

\

I

T

- 90°K I

I

I

I

I

FIG.14. Dependence of the optical absorption coefficient a of pure InSb upon photon energy hv and temperature. (After Gobeli and Fan.”)

from the top of the valence band to the Fermi level in such degenerate material. Thus the optical absorption edge shifts to shorter wavelengths with increasing free electron concentration, as illustrated in Fig. 16 (see Hrostowski et ~ 1 . ~ ~ ) . b. Dependence of the Refractive Index and Extinction Coefficient upon Wavelength Seraphin and Bennettz3 have tabulated values of refractive index and extinction coefficient of InSb over the wavelength interval from 0.049 p

‘’ H. J. Hrostowski, G. H. Wheatley, and W. F. Flood, Jr., Phys. Rev. 95, 1683 (1954). 23

B. 0. Seraphin and H. E. Bennett, in “Semiconductors and Semimetals” (R. K. Willardson and A. C. Beer, eds.), Vol. 3, Optical Properties of 111-V Compounds, p. 499. Academic Press, New York, 1967.

30

PAUL W . KRUSE

WAVELENGTH ( p )

Fic. 15. Dependence of the optical absorption coefficient a of InSb upon photon wavelength and temperature. (After Roberts and Quarrington2l)

to 12.06~.Table I1 lists the values compiled by them from the data of Philipp and E h r e n r e i ~ hMoss , ~ ~ et and Kurnick and which apply to the 1-8 p interval. c. Dependence of the Quantum EfiEciency ofthe Internal Photoefect upon Energy

Tauc and Abrahamz7have determined the quantum efficiency for intrinsic photoexcitation at room temperature, i.e., the number of free hole-electron pairs produced per absorbed photon. Their data are illustrated in Fig. 17 for a sample containing 6.4 x c m - j acceptors. The rise in quantum efficiency with increasing energy for energies greater than 0.5 eV is attributed to the generation of additional hole-electron pairs by impact ionization, i.e., the interband Auger effect, Gibson et ~ 1 . ~have ~ ‘ observed photoconductivity at 1 0 . 6 ~using a Qswitched CO, laser. They attribute the effect to a two-photon absorption process. 24

H. R. Philipp and H. Ehrenreich, Phys. Rev. 129, 1550 (1963).

’’ T. S. Moss. S. D. Smith, and T . D. F. Hawkins, Proc. Phys. SOC.(London) 870, 776 (1957). 26

*’

S. W. Kurnick and J. M. Powell, Phys. Rev. 116, 597 (1959). J. Tauc and A. Abraham, Czech. J. Phys. 9.95 (1959). [Quoted by E. AntonEik and J. Tauc, in “Semiconductors and Semimetals” (R. K. Willardson and A. C. Beer, eds.), Vol. 2, Physics of 111-V Compounds, p. 245. Academic Press, New York, 1966.1 A. F. Gibson, M. J. Kent, and M. F. Kimmit, Brit. J . Appl. Phys. Ser. 2, I, 149 (1968).

2.

INDIUM ANTIMONIDE DETECTORS

31

TABLE IT WAVELENGTH DEPENDENCE OF REFRACTIVE INDEXn AND EXTINCTION COEFFICIENT k IN INSB‘

1.03 1.24 1.55 1.60 1.80 2.00 2.07 2.50 3.00 3.50 4.00 4.50 5.00 6.00 6.10 6.20 6.30 6.40 6.50 6.60 6.70 6.80 6.90 7.00 7.50 7.87 8.00 a

n

k

Reference

4.24 4.15 4.08

0.32 0.26 0.20 0.18 0.17 0.17

24 24 24 25 25 25 24 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 26 26 25 25

4.03 0.15 0.13 0.12 0.11 0.10 0.09 I 0.074 0.072 0.070 0.068 0.066 0.063 0.059 0.055 0.049 0.037 0.025 5.2 x 10-3 4.001 3.995

After Seraphin and Bennett.23

3. ELECTRON AND HOLELIFETIMES A knowledge of the dependence of electron and hole lifetimes upon purity and temperature is important to proper detector design, since the lifetime values can affect not only the photosignal, but also the response time and noise. In general, the determination of the proper model of the recombination mechanisms which limit the lifetimes is a difficult task. Those interested in a detailed review of the recombination processes operable in semiconductors are referred to Blakemore.28 As pointed out in Part 111, following the analysis of Zitte~-,~’ the photoconductive response time zpc and the photoelectromagnetic response time 28

29

J. S. Blakemore, “Semiconductor Statistics.” Pergarnon Press, New York, 1962. R. N. Zitter, Phys. Rev. 112, 852 (1958).

32

PAUL W . KRUSE

tpEM in general have differing dependences upon the electron lifetime t, and the hole lifetime tp.Thus, for example, determination of the frequency response of the photoconductive signal reveals zpc, but not tpEM, z,, or t p .In

2

3

c

0.010'

4

0.0075'

3

4

5

WAVELENGTH

6

7

8

(pl

FIG.16. Dependence of the optical transmission of n-type InSb upon wavelength A'at room temperature. The free electron concentration ranges from 5 x loL5cmU3for curve 1 to about 10'' ~ r n for - ~curves 4 and 5. The sample thicknesses in inches are shown. (After Hrostowski et dzz)

only two special cases are tpc and tpEM equal. The first is when z, equals tp, in which event zpEMand tpc are both equal to t, and tp.The second is when the electron concentration multiplied by the mobility ratio equals the hole concentration, in which event tpEM and tpcare equal to each other but not to z, and tp.

2.

0.5

33

INDIUM ANTIMONIDE DETECTORS

0.4

0.8

0.6 Ef

1.0

[eq

FIG.17. Dependence of the quantum efficiency of the internal photoeffect upon photon energy E , in InSb at room temperature. (After Tauc and Abraham2’)

I

b

t*

TPEM 0

TPC

+ O

I.

I I I I

I

a

I I I

I 11

a

INTRINSIC CONCENTRATION

I I I 1

I I

FIG.18. Dependence of zK and rPEMupon hole concentration po in p-type InSb at 300°K. (After Zitter er a / . 3 2 )

34 PAUL W . KRUSE

FIG. 19. Dependence of T~ upon hole concentration po in p-type lnSb at 200°K. (After Zitter et aL3')

FIG. 20. Dependence of zpCand tpEM upon hole concentration p o in p-type InSb at 77°K. (After Zitter et ~ 1 . ~ ' )

2.

'.

\

35

INDIUM ANTIMONIDE DETECTORS

T = 84°K

-Nt

a

14

-3

0 . 8 x l O cm

'

1

FIG.21. Fermi level dependence of electron and hole lifetimes for n- and p-type samples of InSb at various carrier concentrations at 84°K. Solid curves are carrier lifetimes calculated by using the model of two level centers. The dashed curves show the variations of the carrier concentration p or n and effective impurity concentration ( N A-ND)or (N,- N A ) . (After Lag and Fan.")

Wertheim,30 who studied recombination in n-type and p-type InSb over the temperature interval from 130 to 250"K, pointed out that the recombination mechanism at the lower and middle portions of the temperature interval was of the low level Shockley-Read3' type in which the electron and hole lifetimes were equal. Zitter et aL3' showed that the dominant recombination mechanism in n- or p-type InSb of reasonable purity at room temperature is a direct Auger process. Thus the data of Wertheim and of Zitter et al. showed that the electron and hole lifetimes were equal in InSb at room temperature, down to temperatures of the order of 130°K. Figure 18 illustrates the dependences of s~~~ and zpc upon hole concentration at 300°K. G . K. Wertheim, Phys. Rev. 104,662 (1956). W. Shockley and W. T. Read, Phys. Rev. 87, 835 (1952) 32 R. N. Zitter, A. J. S t r a w , and A. E. Attard. Phys. Rev. 115,266 (1959). 30

31

36

PAUL W . KRUSE

c /-

10-

i

t

1 0 ~ (1D E ~ G K-’)

FIG.22. Dependence of spc. rPEM,I,, and tP upon temperature in a sample of p-type InSb having 3 x 10” cm-3 excess acceptors. (After Zitter et ~ 1 . ’ ~ )

Figure 19 shows the dependence of zpc upon free hole concentration at 200°K. In p-type InSb at 77°K the hole and electron lifetimes are far different (see Fig. 20). It can be seen that zpc depends inversely upon the free hole concentration p o , whereas zPEMis much less and is independent of the hole concentration. The data are indicative of unequal minority and majority carrier lifetimes. On the other hand, in n-type InSb of moderate to high purity the lifetimes are equal. Figure 21 (after Laff and Fan33) shows the dependence of z, and zp upon purity at 84“K, assumed to be representative of the 77°K data. The abscissa is the energy of the Fermi level with respect to the valence band edge (left side) and conduction band edge (right side). Thus in p-type InSb at 84°K the hole lifetime t pincreases as p o is reduced (ie., as the Fermi level moves toward the right from the extreme left), but the electron lifetime t, remains constant. In n-type InSb at 84°K the two

’’ R. A. Larand H. Y. Fan, Phys. R w . 121, 53(1961).

2.

37

INDIUM ANTIMONIDE DETECTORS

CONC ENT RAT10N OF ACC E PTOR S

N14 ~ x I O : ~ C M - ~ ' N 5 1.2~10 CM-3 N19 10'4CM'3

N 4 4 2x10"CM-3 N 2 2 8 x 1012CM-3* N 2 3 4 X 1013CM-3 N I O 2 n 10'4CM-3

lrsJ -

HOLE CONCENTRATION AT 7 7 ' K . SINCE ACCEPTORS WERE NOT COMPLETELY IONIZED AT 77.K

2 -

1 2-

z X 1tg1

I 6

I

5

4

I

I

1

1

1

7

8

9

10

II

103/TCOEG K - ' )

FIG. 23. Dependence of zK upon temperature and acceptor concentration in p-type InSb. (After Nasledov and Smetannikova.")

v W ro N13

U

N16 CONCENTRATION OF DONORS N4 2 x 1013~m-3

N15

Id8

4

N13

3 . 8 x IOl3&i3

~

N16 8 I

I

5

6

~

N3

~

I . I x 10'4c63

1 . 7 ~d 4 c m 3

~

~

n

i

I

I

1

1

1

7

e

9

10

I1

~

1 0 ~ (1 DEG ~ K-')

FIG.24. Dependence of rpc upon temperature and donor concentration in n-type InSb. (After Nasledov and S m e t a n n i k o ~ a . ~ ~ )

w

lo6 L

a,

I

10' -

-u

IP-

-

w ln

-e

10

V W

cn

u

lo9-

b

lo9

-10

10

-

-LO

10 0

2

4

6

E

1 01 2

14

IO~/T(DEG.K-')

- q l , 10 0

2

4

6

8

10

I

I

I

I2

14

16

1 0 ~(DEG 1 ~K - I )

FIG.25. Dependences of zPc and rpEMupon temperature for Gedoped InSb. Curves 1'-6': ipcfor samples 1 4 . Curves 1-7: rPEM for samples 1-7. Free hole concentrations at 77°K are as follows :Sample 1 : 5.6 x 10l~Cm-3;2: 1.9 x 1014cm-3; 3: 3.4 x 10'4cm-3; 4: 7.1 1 0 ' 4 ~ m - 3 ; 5 : 6.3 x 1 0 ' 5 ~ m - 3 ;6: 1.0 x 1016cm-3; 7 : 1.7 x 1 O I 6 ~ m - (After ~ . Gulyaeva et d3')

FIG.26. Dependences of rpc (curves I) and T~~~ (curves 11) upon temperature for InSb with Ge and Au impurities. Sample 8, Ge-doped, has a free-hole concentration at 77°K of 1.7 x IOl3 Sample 9, Au-doped, has a free-hole concentration at 77°K of4.9 x 10" cm-j. (After Gulyaeva et al.")

2.

INDIUM ANTIMONIDE DETECTORS

39

lifetimes are equal, having a value of 8 x IO-’sec. The recombination mechanism at 77°K (or 84°K) in n-type InSb is the low level Shockley-Read type in which the recombination center concentration is far less than the majority carrier concentration. In p-type InSb, however, the recombination center concentration is greater than the majority carrier concentration, leading to unequal lifetimes. The general temperature dependences of zpc, z ~ z, ~and~ z p in , p-type InSb are shown in Fig. 22. Data on p-type samples of higher purity, and on n-type samples (after Nasledov and Smetannik~va’~)are illustrated in Figs. 23 and 24, respectively. Hollis el aL,35extending the analysis of Laff and Fan,33 believe such data can be interpreted in terms of two sets of single level, donorlike recombination centers. On the other hand, Volkov and G a l a ~ a n o vbelieve ~ ~ that a single level recombination center model applies at these temperatures in p-type InSb. From studies of tpCand zpEMbetween 77°K and 170°K in Ge-doped and Au-doped InSb (see Figs. 25 and 26), Gulyaeva et af.37found that these impurities do not introduce recombination centers. Thus their data tend to confirm the structural defect recombination center mechanism postulated by Laff and Fan.33

111. Theoretical Detector Design The previous part has presented values of parameters pertinent to the performance of InSb infrared detectors. The present part will employ these values to determine the optimum design of detectors operating at 3 W K , 195”K, and 77°K. Equations will be derived illustrating the dependences of spectral detectivity and responsivity upon the purity of the InSb. The design equations for the photoconductive and photoelectromagnetjc effects can be exceedingly complex if all the parameters which play a part in the effects are included. Thus all who employ the equations make one or more simplifying assumptions. For example, Kurnick and Zitter3’ assume the optical absorption coefficient is infinite, the sample is thick, and the electron and hole lifetimes are equal. Kruse et ~ 2 1 also . ~ ~assume the absorption coefficient to be infinite and the lifetimes equal, but take into account D. N. Nasledov and Y u . S . Smetannikova, Fiz. Turrd. Tela 4, 110 (1962) [Souiet Phys-Solid State (English transl.) 4, 78 (1962)l. 35 J. E. L. Hollis, S. C. Choo, and E. L. Heasell, J . Appl. Phys. 38, 1626 (1967). 3 6 A. S. Volkov and V. V. Galavanov, Fiz. Tekh. Poluprou. 1, 163 (1967) [Soviet Phys.-Semicond. (English transl.) 1, 129 (1967)l. 37 A. S. Gulyaeva, V. S. Ivleva, and M. I . Iglitsyn, Fiz. Tuerd. Tela 8, 2472 (1966) [Soviet Phys.Solid State (English transl.) 8, 1972 (1967)l. S. W. Kurnick and R. N. Zitter, J . Appl. Phys. 27, 278 (1956). 39 P. W. Kruse, L. D. McGlauchlin, and R. B. McQuistan, “Elements of Infrared Technology.” Wiley, New York, 1962. 34

40

PAUL W . KRUSE

sample thickness and unequal front- and back-surface recombination velocities. ZitterZ9assumes infinite absorption and thick samples, but considers the case in which trapping occurs so that the carrier lifetimes are not equal. D e V ~ r e , ~ who ’ considers only photoconductivity, removes the restriction on infinite optical absorption, but assumes both lifetimes are equal. Moss?’ who also considers only photoconductivity, also includes finite values of the optical absorption coefficient, but assumes both lifetimes to be equal and the sample to be thick compared to a diffusion length. Laff and Fan33 remove the restriction on the value of the optical absorption coefficient and allow unequal carrier lifetimes, but restrict the analysis to samples whose thickness is large compared to an ambipolar diffusion length, and assume the front and back surface recombination velocities to be equal. Nearly all authors assume the sample dimensions to be infinite in the plane of the incident, normal radiation, and the quantum efficiency to be unity. Of the authors mentioned above, only Kruse et introduce expressions for noise and solve for the detectivity. The present discussion will not attempt to derive or employ the most rigorous expressions for the photoconductive or PEM signals. Rather, the most simple of the expressions which reasonably describe InSb will be used, namely, those of Zitter.29 His expressions permit unequal values of the hole and electron lifetimes, the case which applies to the most important of the InSb infrared detectors, namely, the p-type photoconductive one operating at 77°K. The purpose of the derivations of the spectral responsivity and detectivity, which begin with Zitter’s expressions, is to determine the manner by which the one material parameter under direct control, namely, the material purity, influences these derived quantities. Thus it will be possible to determine the optimum purity for operation in the photoconductive and PEM modes at 300”K, and the photoconductive mode at 195°K and 77°K. Operation in the PEM mode at these lower temperatures will not be considered because it offers no performance advantage and entails means for cooling the magnet. The derivation of the spectral detectivity, given the proper expression for the spectral responsivity, hinges upon the proper choice of noise expression. Since no electrical bias is employed in the PEM effect, only thermal (Johnson) noise is found. The mechanisms operable in photoconductive detectors are thermal, generation-recombination (g-r), and l/f power-law noise. Of these, llfpower-law noise shall be ignored because it is not presently possible to write an expression for the magnitude of the noise which explicitly depends upon material parameters. In addition, this noise usually disappears in thermal or g-r noise at the higher electrical frequencies. 40 41

H. B. DeVore, Phys. Rev. 102, 86 (1956). T. S. Moss. in “Semiconductors and Scmimetals” (R. K. Willardson and A. C. Beer. eds.), Vol. 2. Physics of 111-V Compounds. p. 205. Academic Press, New York, 1966.

2.

INDIUM ANTIMONIDE DETECTORS

41

As Long42 has pointed out, it is important that the proper form of the several g-r noise expressions be employed. Thus the analyses for operation in the photoconductive mode at 77°K will employ differing expressions for n-type and p-type materials because of their differing recombination mechanisms. Since the mechanism is the same for n- and p-type InSb at 195"K, a single expression will suffice. Finally, the question of the transition from g-r limited performance to background limited (BLIP condition) will not be treated analytically. It is not at all clear that the phonon induced g-r noise and photon induced background noise are statistically independent and therefore can be added in quadrature. This problem becomes particularly acute when the recombination process is other than direct radiative, for example, of the Shock1ey-Read3' type. In his review of noise in solid state photodetectors Van Vliet43 derives expressions for the background limited detectivity and the g-r noise limited detectivity, but not for the transition between the two. The present analysis will do likewise. 4. PHOTOCONDUCTIVITY ZitterZ9has shown thati,,pc, the photoconductive short-circuit current per unit sample width, is given by is,,, = qNPnZPC(1 + l/b)J%, (1) where q is the electronic charge, N is the number of absorbed photons per unit surface area per unit time which produce intrinsic holeeelectron pairs with unit quantum efficiency, p,, is the electron mobility, b is the ratio of electron mobility to hole mobility, E x is the applied electric field strength, and tpC is the photoconductive response time. The principal assumptions upon which Eq. (1)is based include the following. Recombination in the bulk only is allowed; i.e., the front and back surface recombination velocities are assumed to be negligible.43" Optical absorption is assumed to take place entirely at the irradiated surface. Intrinsic excitation of the holeeelectron pairs is assumed to take place with unit quantum efficiency. That the last assumption is reasonable for InSb is illustrated by the quantum efficiency data of Taw2' (see Fig. 17). The photoconductive response time is shown by Zitter29 to be given by

D. Long, Infrared Phys. 7, 169 (1967). K. M. Van Vliet, Appl. Opt. 6, I145 (1967). 43"Rittner436has shown that for intrinsic processes where the radiation is strongly absorbed, photoexcitation may be considered to be uniform throughout the sample if the effective diffusion length is much greater than the sample thickness. 43bE. S. Rittner, in "Photoconductivity Conference" (R. G. Breckenridge, B. R. Russell, and E. E. Hahn, eds.), p. 215. Wiley, New York, 1956. 42

43

42

PAUL W . KRUSE

Here t, is the electron lifetime and t pis the hole lifetime. For monochromatic radiation of wavelength A, N is related to the irradiance H , (radiant power per unit area) by

(3)

N = H,A/hclw,

where h is Planck’s constant, c is the speed of light, 1 is the sample length between electrodes, and w is the width. Thus the open circuit voltage uovPc is given by V0,PC

=

is,,cwR

*

where R is the sample resistance. The spectral responsivity

(4)

is therefore

where d is the sample thickness, and po, the electrical resistivity, is given by P o = b/qP”(nob

+ Po).

(6)

Here no is the concentration of free electrons and p o is the concentration of free holes. Equation (5) shows that the spectral responsivity depends linearly on the applied electric field. In practice, an upper limit for the responsivity exists which depends upon the Joule heating produced in the sample by the applied basis. Expressing Eq. (5) in terms of Pn, the power dissipation per unit surface area, results in :#n,pc

=

qAP.[l

+ (1/~)1~PcP;/2w h~wd~‘~

(7)

In general, photoconductive detectors will be limited by thermal noise, u,,, , and/or generation-recombination noise, ug+. Because these add in

quadrature, the total noise voltage uT is given by

The expression for the thermal noise voltage is

where Ajis the electrical bandwidth within which the noise is measured, k is Boltzmann’s constant, and T is the absolute temperature. Because the form of the g-r noise expression depends upon the conditions under which the detector operates, the expressions appropriate to each condition will be introduced where needed.

2.

INDIUM ANTIMONIDE DETECTORS

43

The spectral detectivity D,* is given by

DA* =

( l ~ ) " ~ % ' ~ (' IA2 f ) VT

where Af is the noise bandwidth. and D,* expressions is In practice, the wavelength /z employed in the the long wavelength limit lo,which is related to the forbidden energy gap E, by /zo = hc/E,.

(11)

The spectral peak responsivity 9,0and detectivity D t are related to the 500°K blackbody values a(50WK) and D*(500°K) by

B(50WK) = 2I0G(500"K)

(14

D"(500"K) = D~oC(5000K),

(13)

and where the G function is defined by Kruse et aL44 Appropriate values of G(500"K) and loare listed in Table 111. TABLE 111 VALUES OF

a.

AND

~ ( 5 0 0 0FOR ~ ) INSB

AS

FUNCTIONS OF TEMPERATURE TemperaturevK) l o( p ) 300

6.6 6.0 5.2

195

I1

G(500"K) 2.8 3.9 5.7

a. Operation at Room Temperature have shown that the recombination process in p-type InSb Zitter et of moderate or high purity at room temperature is of the direct Auger type. Thus the electron and hole lifetimes are equal. The mobility ratio at room temperature, which can be determined from Figs. 8 and 9, lies between 60 and 105, depending upon purity. The expression for zpc, Eq. (2),thus becomes Zpc % 5,.

(14)

The dependence of zpc upon hole concentration in p-InSb at 300°K is shown in Fig. 18. 44

See Kruse et a ~ , ~p. '362.

44

PAUL W . KRUSE

The intrinsic concentration ni at room temperature is 1.6 x loi6~ m - ~ . Since ni2

= n o ~ 3o

(15)

the electrical resistivity po, Eq. (6),can be written as Po =

no Po d n o 2 p n + ni2pp) dni2pn + PO'CCJ

(16) '

From the dependences of pn and p p upon purity shown in Figs. 8 and 9 the dependence of p o upon no in n-type InSb and upon p o in p-type InSb at 300°K has been calculated (see Fig. 27). These data should be compared to Fig. 10, which relates to p-type material only. The data of Fig. 27 will be employed in the calculation of the responsivity and detectivity. From the dependence of tpC upon purity (Fig. 18) and the dependence of po upon purity (Fig. 27), the dependence of spectral responsivity upon purity can be determined from Eq. (7). The results of the calculation are illustrated

Id' 5 -

2 -

-

Id2-

I

v

f0 e

1

5 -

2-

lo3

-

5-

cn

z

(L

I-

2-

z 1.6

,041

I'

I

I

I

I

I

I

FIG.27. Dependence of resistivity po at 300°K upon majority carrier concentration in n-type and p-type InSb.

45

FIG.28. Dependence of spectral responsivity for photoconductive operation at 300°K upon majority carrier concentration in n-type and p-type InSb, assuming AD = 6.6 p, PD = 5 W/cmZ, d = l o p , and w = 1 mm.

in Fig. 28, assuming 1 = lo= 6.6 p (Table III), w = 1 mm, d = 10 p, and PD = 5 W/cm2. The dimensions are typical of photoconductive InSb detectors operating at room temperature. The maximum allowable value of the power dissipation obviously depends upon the manner by which the sensitive element is bonded to the heat sink ;the value of 5 W/cm’ is believed to be a representative one. Figure 28 shows that the optimum spectral responsivity of room temperature InSb photoconductive detectors is found in p-type material having free. theoretical hole concentrations of approximately 1 x 10’’ ~ m - ~The maximum value for the given values of thickness, width, and power dissipation per unit area is approximately 6 V/W at 6.6 p wavelength. Since the derivation of gA0 assumes complete absorption of the incident radiation and zero surface recombination velocity, values for real detectors will be substantially less. Determination of the spectral detectivity requires knowledge of the limiting noise mechanism. As stated previously, llf power-law noise will be neglected because no analytic expression exists for the amplitude of the noise

46

PAUL W . KRUSE

loi6

2

I

I

I

5

,017

2

5

MAJORITY CARRIER CONCENTRATION (CM-’I FIG. 29. Dependence of spectral detectivity for photoconductive operation at 300°K upon majority-carrier concentration in n-typc and p-type InSb, assuming lo= 6.6 p, P, = 5 W/cm2, d = l O j t , and w = 1 mm.

voltage. In any event, it has been established experimentally that roomtemperature InSb photoconductors are limited by thermal noise at all bias values below that at which excessive heating occur^.^^-^^ Thus the expression for the spectral detectivity [from Eqs. (5), (9), and (lo)] is Figure 29 illustrates the dependence of D t upon purity for n-type and p-type InSb at 300”K, assuming the same values of the parameters used for determining gA0 in Fig. 28. In contrast to the responsivity, the detectivity is relativeiy independent of purity for p-type samples in the range from intrinsic to 1 x lo” cmP3holes, achieving a slight maximum of 9 x lo8 cm Hz’’’/W at 7 x 1 O I 6 holes. As was true for the responsivity, the detectivity for

‘’ T. S. Moss, in “Photoconductivity 46 47

48

Conference” (R. G. Breckenridge, B. R. Russell, and E. E. Hahn, eds.), p. 427. Wiley, New York, 1956. G. H. Suits, W. D. Schmitz, and R. W. Terhune, J . A p p l . Phys. 27, 1385 (1956). R . E . J.KingandB.E.Bartlett, PhilipsTech. Reu.22,217(1961). D. G. Avery, D. W. Goodwin, and A. E. Rennie, J . Sci. Instr. 34,394 (1957).

2.

INDIUM ANTIMONIDE DETECTORS

47

n-type material is far less than for p-type of comparable purity. Again, real detectors will exhibit values of D,* well below the theoretical maximum. Two comments should be made with regard to Figs. 28 and 29. First, the derivations of BL0and OX, assume that the detector is operated in the opencircuit voltage condition, which is easier to realize experimentally than the short-circuit current one. Second, because no experimental information is available concerning the dependence of zpc on purity in n-type material, the calculations upon which Figs. 28 and 29'are based have assumed that dependence to be the same as in p-type material. In other words, the 300°K value of zpc for 1 x 1017cm-3 n-type InSb is assumed to be the same as that for 1 x 1017cm-3 p-type material. In general, the Auger lifetime for n-type semiconductors is less than or equal to that for p-type ones. Thus the values of gA0 and 0%in n-type InSb shown in Figs. 28 and 29 are upper limits. b. Operation at 77°K

The discussion in Section 3 , supported by Fig. 20, showed that in p-type InSb at 77°K the photoelectromagnetic response time zPEM is independent of purity. ZitterZ9 has shown that in general zpEM is given by ZPEM

= (z,

+ czp)/(f + c),

(18)

where c = noIP0.

In p-type InSb at 77°K c is much less than unity, because the intrinsic , less than the majorityconcentration, of the order of 10'' ~ m - is~ much carrier concentration in the purest samples. Thus in p-type InSb at 77°K 7pEM

= z,

=2 x

sec

(p-type),

(19)

where the value shown in Fig. 20 has been introduced. On the other hand, Fig. 20 shows that the photoconductive response time 7pcin p-type InSb at 77°K varies reciprocally with the purity. From Zitter's expression for zpc, Eq. (2), it can be seen that ZPC

= rplb = lC/P,b

(P-tYPe),

(20)

where b is no greater than 50 (see Figs. 6 and 7). Zitter et indicate IC = 1 x 109cm-3 sec, Laff and Fan33 state K = 1.5 x lo9 ~ r n sec, - ~ and G ~ o d w i nfeels ~ ~that K = 4 x lo8 cmP3sec is the most appropriate value. In n-type InSb the electron and hole lifetimes are equal to each other and independent of purity, having a value of 8 x sec (see the right hand 49

D. W. Goodwin, J . Phys. Chem. Solids 22,401 (1961).

48

PAUL W. KRUSE

side of Fig. 21). It is assumed that these data at 84°K also represent the data at 77°K. Thus zpc z 5, = zp = 8 x lo-’ sec (n-type). (21) Recombination in InSb at 77°K is by means of recombination centers, which Hollis et believe to be of a simple nature. Thus the appropriate recombination model is the Shockley-Read3, one. In the simplified case in which the density of recombination centers is low the Shockley-Read model requires the majority and minority carrier lifetimes to be equal to each other, given by T ~ where ~ ,

here T ~ and , T~ , , ~ are the minority carrier lifetimes when the Fermi level is at the conduction band edge or valence band edge, respectively, and n, and p1 are the electron and hole concentrations, respectively, when the Fermi level is at the recombination center energy level. Since the recombination mechanism in n-type InSb at 77°K is of the Shockley-Read type, and since the lifetimes are equal, Eq. (22) applies. From Eqs. (21) and (22) it can be seen that in n-type InSb at 77°K the expression for the Shockley-Read lifetime becomes

zSR z T ~ = ,8 x~ sec (n-type). (23) On the other hand, in the general case in which the recombination-center concentration is so high that it exceeds no, p o , nl,andp,, which amounts to exceeding the majority carrier concentration, then the majority and minority carrier lifetimes are unequal and Eq. (22) does not apply. Because the recombination mechanism at 77°K in p-type InSb is Shockley-Read, but the lifetimes are unequal, the recombination center concentration is large in that material compared to the majority carrier concentration for the range of hole concentrations considered by the various authors. Consider now the expression for the spectral responsivities of n-type and p-type detectors under conditions of similar doping and similar power dissipation. From Eqs. (6), (7), and (20) the spectral responsivity of p-type detectors at 77°K is given by T, = z p =

where it has been assumed that po 9 no&.From Eqs. (61, (7), and (21)

where it has been assumed that nob 9 po.

2.

I' 0 1(!13

49

INDIUM ANTIMONIDE DETECTORS

;

; ; 1;l5 ;

loo

MAJOR IT Y CAR R I E R CONCENTRATION ( C M-

FIG.30. Dependence of spectral responsivity for photoconductive operation at 77°K upon majority-carrier concentration in n-type and p-type InSb, assuming 1, = 5.2 p, Po = W/cm2, d = 5 p, and w = 1 mm.

Figure 30 illustrates the dependence of the spectral responsivity at the peak wavelength upon majority-carrier concentration in n-type and p-type InSb at 77"K, based upon Eqs. (24) and (25). Here it has been assumed that the peak wavelength ;lo is 5.2 p, that a power per unit area PDof 10- W/cm2 can be dissipated equally well by either type, that the detector width w is 1 mm, and that the thickness d is 5 p. Values for pn and b have been obtained from Figs. 6 and 7. For p-type InSb the value of IC = 1 x lo9 cmP3sec has been assumed to be the best compromise between the three reported v a l ~ e s . For ~ ~ n-type * ~ ~ InSb ~ ~ T, ~ = 8 x lO-'sec, as pointed out previously. From Fig. 30 it can be seen that the spectral responsivity at 5.2 ,u of p-type InSb detectors theoretically can be well above lo6 V/W. Again, much lower values will be obtained in practice. The values for n-type detectors can be seen to be about two orders of magnitude lower than for p-type at lOI4 cm-

50

PAUL W . KRUSE

majority carrier concentration. The discrepancy becomes even greater for samples of higher purity. Consider now the expressions for the spectral detectivity of n-type and p-type InSb detectors at 77°K. The appropriate noise mechanisms must first be determined. Again, llf power-law noise will be ignored. Since the recombination mechanisms differ in n- and p-type InSb at 77°K-two variants of the Shockley-Read mechanism-it follows that the g-r noise expressions also differ. In p-type InSb, for which the electron and hole lifetimes are vastly different, the density of recombination centers is much higher than the hole concentration. Since the electron concentration is many orders of magnitude below the hole concentration, the recombination centers are almost completely empty of electrons. Because the acceptor levels are completely ionized, the instantaneous concentration of free holes is governed by the generation and recombination rate fluctuations between the valence band and the recombination centers. Furthermore, the conductivity is totally dominated by the holes. Thus, as Van Vliet” shows, the proper g-r noise expression for p-type InSb at 77°K is that of excitation and recombination of a single type of carrier from a single type of center, i.e., Vg+ =

2ib‘T;’’R(Af) ”’/(polWd)

”’

(p-type),

(26)

where ib is the bias current. G ~ o d w i nhas ~ ~experimentally verified the application of this expression to p-type InSb at 77°K. In n-type InSb, however, a different expression applies. Here the electron and hole lifetimes are equal, although their concentrations differ greatly. Van Vliet5’ has shown that the appropriate expression is

Introducing Eq. (23) causes Eq. (27) to become

In n-type InSb thermal noise must also be considered. Combining Eqs. (6), (8), (9), and (28) results in the expression for the total noise voltage: VT

51

=

2ib(b + l)b(nop0)1’2~~iZ11/2(Af)1~zb b o b + ~ ~ ) + ~P ~ () ’ n~ ’ ~( W ~ ) ~ ~ ‘ ~ P ~

Van Vliet,43 Eq. (145), in which See Van Eq. (126).

T~

< T,, and n, 9 (po + pi).

2.

INDIUM ANTIMONIDE DETECTORS

51

Consider now the spectral detectivity of p-type detectors. From the general expression for the detectivity, Eq. (lo), the responsivity of p-type detectors, Eq. (24), the noise voltage of p-type detectors, Eq. (26), and the majority carrier lifetime in p-type material, Eq. (20), the spectral detectivity of p-type detectors at 77°K is found to be

Dk*= ( A / 2 h ~ p ~ ) ( ~ / d ) ' /(p-type). ~

(30)

On the other hand, the spectral detectivity of n-type detectors is, from Eqs. (lo), (21), (2.9, and (29),

where

Since in n-type InSb at 77°K no

+ p o , Eq. (31) becomes (33)

or

"(?!I

112

D,* = 2hcni d

(1 +

r)-li2

(n-type).

(34)

Equations (30) and (34) illustrate the major difference between p-type and n-type InSb photoconductive detectors operating at 77°K. In p-type detectors the spectral detectivity increases as the majority carrier concentration po is reduced. In n-type detectors the spectral detectivity increases as the majority carrier concentration is increased, provided that is much less than unity. This somewhat surprising behavior for n-type detectors arises because the g-r noise is reduced as the majority carrier concentration is increased [see Eq. (2811. In order to achieve the highest performance in n-type detectors, it is necessary to reduce r to well below unity, equivalent to requiring the g-r noise voltage to greatly exceed the thermal noise voltage. For n-type detectors for all reasonable values of purity, i.e., no > 10" ~ r n - the ~ , expression for r reduces to

r =kTno4w2d2qp, ib2ni2Tn Obviously,

(35)

r can be made small by going to high bias currents. However,

52

PAUL W. KRUSE

lo'2

5

1013 2

5

10'4 2

ELECTRON CONCENTRATION

5

,d5

no (CM-3)

FIG.31. Dependence of r upon majority-carrier concentration no in n-type InSb at 77"K, assuming ni = 1 x 1 0 " ~ m - ~cn, = 8 x lO-'sec, d = 5 p , and Po = W/cm'.

above some threshold value of power dissipation, excessive heating will occur. In terms of power dissipation per unit area PD,Eq. (35) becomes

Figure 31 illustrates the dependence of I7 on majority carrier concentration no in InSb at 77"K, assuming n, = 1 x 10'' ~ r n - z~, , = 8 x lO-'sec, d = 5 p , and PD = lop3W/cm2. It can be seen that at this power dissipation, for all reasonable values of purity, r is never small compared to unity. In this event Eq. (34) reduces to

2.

53

INDIUM ANTIMONIDE DETECTORS

t t

a

3

c'

I

N

I

I 0 * r0

n

> k i

1

I0 W IW

n 2

U

BLIP LIMITPHOTOCONDUCTIVE MODE ; 300.K BACKGROUND; 2 7 1 STER. FOV; A. 5.2pM

2t

u

FIG. 32. Dependence of spectral detectivity for photoconductive operation at 77°K upon majority-carrier concentration in n-type and p-type InSb, assuming lo = 5.2 p, ni = 1 x 10” W/cm2. ~ m - 7,~ =, 8 x IO-’sec, 1c = 1 x lo9 sec, d = 5 p, and Po =

Consider now the relative values of spectral detectivity for p-type and n-type detectors, Eqs. (30) and (34). The values at the peak wavelength of 5.2 p are illustrated in Fig. 32, assuming the values of the parameters listed above and IC = 1 x lo9 cm-3 sec. Over the entire range of majority-carrier concentration shown, from 1 x 10” cm-3 to 1 x 1015~ r n - the ~ , detectors offer equivalent performance. However, the photon noise limit (BLIP) for a 300°K hemispherical background imposes an upper limit at a value of D t ( 5 . 2 ~of) about 1.2 x 10” cm H Z ~ J * / W Thus , ~ ~the higher responsivity of the p-type detector provides the decisive advantage in most applications. Were it possible to increase PD over the chosen value, n-type detectors would offer the higher detectivity, making them superior to p-type when operated under reduced background conditions. 5z

See Kruse et

p. 360.

54

PAUL W . KRUSE

c. Operation at 195°K As discussed in Section 3, Wertheirn3O found the recombination mechanism in both n-type and p-type InSb in the range from 130°K to 250°K to be of the Shockley-Read type. These results were confirmed by Zitter, Strauss, and Attard3’ for p-type InSb, and Nasledov and S m e t a n n i k ~ v for a ~ ~both n-type and p-type material. Wertheim found that the Shockley-Read lifetime, Eq. (22), reduced to

+ PO)

(37) was found to be constant over for both n-type and p-type material, where tp,O . =~ ~ the temperature range studied. According to Zitter et ~ 1 zp,o 8x sec. On the other hand, the data of Hollis et aL3’ indicate a value sec. in the range 4.0-5.5 x The photoconductive response time at 195”K, obtained from Eqs. (2) and (37), is therefore zSR =

zn = z p = z p , O n O / ( %

~ P = C 7, =

zp =

zSR

= zp.ono/(no

+

PO).

(38)

Assuming again that the limiting factor is the allowable power dissipation, the spectral responsivity is found from Eqs. (7) and (38) to be

In terms of the intrinsic concentration ni, the spectral responsivity, from Eqs. (16) and (39), is

or

Figure 33 depicts the dependence of the spectral responsivity at 195°K upon majority carrier concentration, based upon Eqs. (40)and (41). The value of n,, from Fig. 2, is 1 x 10’’ ~ m - From ~ . the data of Hollis et al.35 a value for zp,o of 5 x sec has been selected. The wavelength Lo at . value of PD is which the spectral response peaks at 195°K is 6 . 0 ~ The assumed to be lo-’ W/cm2. Values of thickness d and width w are assumed to be 10 p and 1 mm, respectively. Values of pn and p p at 195°K as functions of sample purity have been taken from Fig. 5. Figure 33 shows that the optimum purity for maximizing the responsivity is slightly p-type, about 2 x ~ r n - The ~ . responsivity remains reasonably

2.

55

INDIUM ANTIMONIDE DETECTORS

5 x lo2

2

;

Ioo 21 0 ' ~

2

5

10'6

2

5

10'~

FIG.33. Dependence of spectral responsivity for photoconductive operation at 195°K upon majority-carrier concentration in n-type and p-type InSb, assuming I , = 6 . 0 ~ PD . = lo-' W/cmZ, d = 10 p , and w = 1 mm.

high to about 5 x 10'5cm-3 p-type, but then falls off precipitously. The responsivity for n-type samples falls off rapidly with decreasing purity. Consider now the appropriate noise expression. Again, llf power law noise will be ignored. Because the recombination mechanism is ShockleyRead, with both lifetimes equal in both n-type and p-type material, the proper g-r noise expression is the same as in n-type InSb at 77°K. In other words, Eq. (27) properlj. describes g-r noise in both n-type and p-type InSb at 195°K. Introducing the expression for z ~ Eq. ~ (37), , gives rise t o

Expressing the resistance R in terms of the carrier concentrations and mobilities, and including the expression for the thermal noise voltage

56

PAUL W. KRUSE

[Eq. (9)], gives the expression for the total noise voltage in n-type and p-type InSb at 195°K : 2ibnop~/zb(b + l)11~2~~!~(Aj)1'z (no + po)(bn0 + p o ) 2 ~ ~ . ~ 3 / 2 d 3 / 2 kT(no po)'(bn0 p o ) 3 q p . ~ 2 d 2 1/2 x [I+ (43) i,2n02pob(b 1 ) 2 ~ p , o Combining Eqs. (lo),(39), and (43) results in the expression for the spectral detectivity : VT

=

+

+ +

1.

or

where

or

As was true for n-type InSb at 77"K, the value of DA*at 195°K is maximized by causing A to approach zero by employing high bias currents. Figure 34 illustrates the dependence of A on majority carrier concentration in InSb a t 195"K, assuming n, = 1 x 10'' cmP3, d = lop, PD = lo-' W/cmZ, and tp,O = 5 x lo-' sec. The value of b, determined from Fig. 5, is approximately 80 for the concentrations of interest. Figure 34 shows that A is small in intrinsic material, but becomes important in n-type material at majority carrier concentrations greater than about 2 x 10lscm-3, and in p-type material for concentrations greater than about 5 x 10'scm-3. The value of DA* at A,, = 6.0 p is illustrated in Fig. 35, assuming the same values of the parameters given above. Whereas the maximum responsivity is found in p-type material, the maximum detectivity is found in n-type, because the g-r noise in n-type material is less than that in p-type. The maximum detectivity is found at an electron concentration of about 2 x 10l5 cm- '. For material somewhat less pure the detectivity decreases rapidly

2.

INDIUM ANTIMONIDE DETECTORS

,C?l

I

,o15

2

I 5

l

I

lo16 2

l

s

l

I

,017 2

s

l

57

MAJORITY CARRIER CONCENTRATION (CMm3)

FIG.34. Dependence of A upon majority-carrier concentration in InSb at 195"K,assuming T , , ~ = 5 x lO-'sec, ni = 1 x 1015~ m - PD ~ = , lo-' W/cm2, d = lop, and w = 1 mm.

with increasing carrier concentration as thermal noise becomes dominant. Even at the optimum carrier concentration the photon noise limit is not attained.

5. PHOTOELECTROMAGNETIC EFFECT The other photoeffect to be considered is the photoelectromagnetic, or PEM, effect. As stated in the introduction, PEM detectors have been designed only for operation at room temperature. When cooled, they offer no advantage over photoconductive or photovoltaic ones, and suffer the cooling problems associated with the use of the magnet. Thus the analysis of the PEM effect will be confined to only room temperature operation. As was true for the analysis of the photoconductive effect, the analysis of the PEM effect begins with the expression of ZitterZ9for the short-circuit

58

PAUL W . KRUSE

P

-I-I= - o [l 2l

Id"

22

,ne

l0lS

5

2

2

,016

5

10"

MAJORITY C A R R I E R CONCENTRATION ( C M - 3 )

FIG.35. Dependence of spectral detectivity for photoconductive opcration at 195°K upon majority-carricr concentration in n-type and p-type InSb. assuming 1, = 6 . 0 p z,,,~ = 5 x l o - ? sec, n, = I x l o t 5~ r n - ~P,,, = 10 W/crn2. and d = lop.

current per unit sample width, jS,PEM

=

4N&BLD*[1

+

5

(48)

where B is the magnetic induction and LD*,the effective ambipolar diffusion length in the magnetic field, is given by

+

+

Here c = n,/po, and z ~ E M= (7, C T ~ ) , / ( ~ c) as in Eq. (18). Because the recombination process at room temperature is of the direct Auger type, the

2.

59

INDIUM ANTIMONIDE DETECTORS

electron and hole lifetimes are equal. Thus TpEM = 7, =

(50)

zp.

Comparing this to Eq. (14), it can be seen that the PEM and photoconductive response times for InSb at room temperature are equal. Thus zpEMdepends upon hole concentration in p-InSb at 300°K in the same manner as zpc does, as illustrated in Fig. 18. The open circuit voltage v ~ is given , by~ ~ ~ UO,PEM

=

iS.PEMWRB

(51)

9

where w is the sample width. Here R B represents the resistance of the sample in the magnetic field, given by RB = (PB/PO)(POl/Wd)

(52)

9

and

+ c)/b(bc + l)] P B - 1 + j.if12B2[(b _ 1 + j.if12B2[(1 ~)/(1+ bc)]' PO

(53)

is the magnetoresistivity ratio. The dependence of the magnetoresistivity ratio upon majority-carrier concentration in InSb at 300°K is illustrated in Fig. 36. The intrinsic concentration, needed to determine c as a function of majority-carrier concentration, is 1.6 x l O I 6 cm-3. Values for the mobility ratio b, which lies between 60 and 105, depending upon purity, can be determined from Figs. 8 and 9. The magnetic induction B is assumed to be

l0l6

2

5

10'~

2

5

id8

MAJORITY CARRIER CONCENTRATION ( C M - 3 )

FIG. 36. Dependence of magnetoresistivity ratio upon majority-carrier concentration in InSb at 300"K, assuming ni = 1.6 x 10l6~ r n and - ~ B = 7000 G.

60

PAUL W. KRUSE

0.7 Wb/m2 (7000 G), a value attainable in the small magnets employed for InSb PEM detectors. Figure 36 shows that the magnetoresistivity ratio has its maximum value of approximately 2.5 in p-type InSb having a hole concentration of about 7 x 10'6cm-3, a conclusion supported by the data of Fig. 11. Figure 27 shows that p o , the resistivity in the absence of the magnetic field, also attains its maximum value in p-type material of slightly higher hole concentration. Thus the maximum resistance in the magnetic field is found in p-type InSb having a hole concentration of approximately 1 x lo" cm-'. Consider now the spectral responsivity BA.Because N is given by Eq. (3), N = H,rl/hcEw, the expression for BAis therefore

The dependence of W Aupon majority-carrier concentration according to Eq. (54) is illustrated in Fig. 37. Here it has been assumed that B = 7000 G, Lo = 6.6 p, w = 1 mm, and d = 20 p. Values of pn as a function of purity are those of Fig. 8. The dependences of p o and p B / p o upon purity are taken

10-2

9

,o'6

2

5

(0'7

2

5

2

5

MAJORITY CARRIER C O N C E N T R A T I O N (CM-3)

FIG.37. Dependence of spectral responsivity for PEM operation at 300'K upon majoritycarrier concentration in n-type and p-type InSb, assuming A, = 6.6p, B = 7000G, and d = 20p.

2.

INDIUM ANTIMONIDE DETECTORS

61

from Figs. 27 and 36, respectively. The dependence of z~~~ upon purity in p-InSb is the same as that of zpc (see Fig. 18). It has been assumed that 7pEM depends upon electron concentration in n-InSb in the same manner as it does upon hole concentration in p-InSb. Figure 37 shows that the highest responsivity is found in p-type InSb ~ . the assumed values having a hole concentration of about 8 x 1 O I 6 ~ m - For of the parameters, the highest value of spectral responsivity is approximately 5V/W. By comparing this with data on the room temperature photoconductive detector (see Fig. 28) the optimum purities for the two modes are seen to be approximately equal. The maximum responsivity for the PEM detector is slightly less than that for the photoconductive detector, based upon the assumed values of magnetic induction of 7000G and electrical power dissipation of 5 W/cm2. The spectral detectivity of the room temperature PEM detector can be calculated, based upon a thermal-noise mechanism, the only one operable in the absence of electrical bias. Here the appropriate resistance is that in the magnetic field. Thus Eq. (9) is modified to become

The expression for the spectral detectivity Da* determined from Eqs. (lo), (54), and ( 5 5 ) is thus

Note that high values of resistivity and magnetoresistivity ratio are desirable for maximizing Da*. Figure 38 illustrates the dependence of D,* upon majority carrier concentration from Eq. (56).The values of the parameters assumed are the same as those above. The highest spectral detectivity is found in p-type material having a hole concentration of approximately 7 x loi6~ m - The. ~ . maximum detectivity value is about 6 x lo8 cm Hz’/’/W. Comparing again the photoconductive mode (Fig. 29) with the PEM mode (Fig. 38), the optimum purity is found in each instance in p-type ~ concentration. For the material of approximately 1 x l O ” ~ m - hole assumed values of electrical power dissipation and magnetic induction the photoconductive mode appears slightly superior. It should be borne in mind that the calculations are based upon measurement of the open-circuit voltage, which is proportional to the resistance. If instead the short circuit current were measured, the optimum purity would no longer be near that which gives rise to the maximum resistance, but would be expected to be near or equal to the intrinsic value.

62

PAUL W . KRUSE

1

l0l6

2

5

I

I

1

2

5

2

3

MAJORITY C A R R I E R CONCENTRATION ( C t ~ l - ~ )

FIG. 38. Dependence of spectral detectivity for PEM operation at 300°K upon majoritycarrier concentration in n-type and p-type InSb, assuming I , = 6 . 6 ~B ~ = 7000G, and d = 20u.

IV. Preparation of Photoconductive and PhotoelectromagneticDetectors The previous part considered the theoretical aspects of the performance of photoconductive and photoelectromagnetic InSb detectors. This part will present details of the method by which the detectors are prepared, and the next will consider the experimentally realized performance, contrasting it to the theoretical predictions. The preparation of detectors can be divided into three major categories : (1) purification and crystal growth, (2) fabrication of the sensitive elements from the crystals, and (3) design of the housing into which the elements are placed. It is not the intent of this part to dwell in detail on any of these aspects, since the growth and fabrication aspects are standard methods employed in semiconductor technology, and the housing design is straightforward. Therefore each of these shall be discussed only in moderate detail.

2.

INDIUM ANTIMONIDE DETECTORS

62

6. PURIFICATION AND CRYSTAL GROWTH

The preparation of high purity single crystals of InSb has been reviewed by many authors, for example, L i a ~ ~ Hulme g , ~ ~and M ~ l l i nand , ~ ~Hulme.7 Commercially available, high purity (six nines) indium and antimony are reacted above the compound melting point of 523°C to form InSb. Because the partial pressures of indium and antimony are low, the reaction can proceed at atmospheric pressure. A reducing atmosphere is employed to prevent formation of indium and antimony oxides which react with the quartz ampoule. Horizontal zone refining of the compound in a reducing atmosphere is employed to remave foreign atom impurities, the dominant ones, as H a r m a showed, ~ ~ ~ ~ being zinc, an acceptor having a segregation coefficient greater than unity, and tellurium, a donor having a segregation coefficient less than unity. Because that of the latter differs only slightly from unity. zone refining to remove Te is tedious. Indium antimonide which has been extensively zone refined is n-type. The ionization energies of nearly all the foreign atoms, Ge excepted, are sufficiently small for the atoms to be ionized at 77°K and above (see Table I). Most workers have attributed the residual donor to Te, believing that deviations from stoichiometry are negligible. However, H ~ l m ereferring ,~ to Stocker’s datas6 on indium vacancies, considers the residual donor to be a lattice defect. Although the early photoconductive detectors of Frederikse and Blunt4 were n-type, and n-type detectors operating at 77°K theoretically are equivalent to p-type (see Fig. 32), normal practice is to prepare p-type ones because of their higher responsivities, which make them more easy to use. Thus it is necessary to compensate the residual donor, usually with zinc or cadmium, to form p-type material. Hole concentrations in the 10” cmrange at 77°K can be attained in this manner.57 Because the 300°K photoconductive and photoelectromagnetic detectors exhibit optimum detectivity and responsivity when slightly p-type, zinc or cadmium doping is also employed for them.57 Published information is lacking on the dopant for the 195°K photoconductive detectors. Because the optimum purity is only slightly n-type, it is probable that intrinsic material is used. In order to minimize the compensation problem in the high puritj material required for the 77°K photoconductive detectors, the use of the

’

S. C. Liang, in “Compound Semiconductors” (R. K. Willardson and H. L. Goering, eds.), Vol. I, Preparation of 111-V Compounds, p. 227. Reinhold, New York, 1962. 5 4 K. F. Hulme and J. B. Mullin, Solid-Srare Electron. 5,21 I (1 962). 5 5 T. C. Harman, J . Electrochem. Soc. 103, 128 (1956). 5 6 H. J. Stocker, Phys. Rev. 130, 2160 (1963). ” T. J. Davies. nersonal communication 53

64

PAUL W. KRUSE

deep acceptor germanium has been explored. Because germanium acceptors are deionized at 77°K due to their midgap position (see Table I), they can be introduced in a concentration sufficient to compensate the residual donors at a concentration much higher than is possible with a shallow acceptor. Single crystals of InSb are formed from the zone-refined polycrystalline ingots either by the Czochralski method or by zone leveling. Where attaining compensation is a problem, the zone-leveling approach is preferred for the greater yield of useable material.s7 As in the zone-refining process, growth is accomplished in a reducing atmosphere in a quartz ampoule or boat. Hulme and M ~ l l i nshowed ~ ~ that a faceting effect exists in which the segregation coefficients of selected impurities depend upon the growth axis. To minimize the faceting effect, growth along the [ill], and [lo01 axes should be avoided; acceptable axes are (311) and (1 10). Routine evaluation of the single crystal InSb is accomplished in several ways. Thermoprobing reveals the n- and p-type regions. The majority carrier concentration and mobility are established through measurement of the Hall coefficient and resistivity. An etch pit count reveals the dislocation density. By evaluating samples at selected intervals along the crystal, a “profile” or “map” is established which indicates the regions from which the sensitive elements should be selected.

[in]

7. FABRICATION OF THE

SENSITIVE

ELEMENT

In its final form the sensitive element consists of a thin InSb layer with attached electrical leads mounted on an electrically insulating substrate. The steps in preparing the element from the single crystal of InSb are discussed below. Because the process may differ in detail from one manufacturing group to another, the steps should be considered typical rather than unique. Except where noted, the processing details for photoconductive elements and photoelectromagnetic elements are the same. The single crystal of InSb which galvanomagnetic measurements have revealed to have the desired electrical properties is mounted on a ceramic block with quartz cement. Transverse cuts by means of a diamond saw or a wire saw are used to remove slabs 1-2 mm thick. The wire saw, preferred because it introduces less damage to the crystal, employs a slurry of glycerine and Sic to lubricate the wire. Each slab is degreased in warm trichloroethylene, rinsed in warm methanol, and dried by means of a nitrogen gas jet. Each slab is then lapped on silk with 600 mesh Sic, rinsed, lapped with lo00 mesh Sic, and rinsed again. At this point the processing of the photoconductive elements differs from that of the photoelectromagnetic elements.

2.

INDIUM ANTIMONIDE DETECTORS

65

Whereas photoconductive detectors require a low surface-recombination velocity on both the front surface (upon which the radiation is incident) and the back surface, photoelectromagnetic detectors require a low recombination velocity on the front surface and a high recombination velocity on the back. * Since lapping leaves the surface with a high recombination velocity, the back surface of the PEM detector is not etched in the manner described below. To prepare the front surface of the PEM detector and both surfaces of the photoconductive detector for etching, the surfaces are lapped to a mirror finish with a 0.1 p alumina powder. No scratches should be visible to the naked eye. After again cleaning the slabs thoroughly, they are etched in a mixture of equal volumes of undiluted HF. H N 0 3 , and CH3COOH. The etchant is rinsed away with distilled water and the slabs are dried in a nitrogen jet. Next the slabs are epoxied to substrates. The requirement which the substrate for a 300°K photoconductive or photoelectromagnetic detector must meet is that of sufficiently high resistivity in the event that the electrical contacts inadvertently touch the substrate. This is minor; the usual substrate material is glass in the form of a microscope slide. The photoconductive detectors operating at 195°K and 77°K not only impose more severe requirements on resistivity, but have the additional one of a thermal expansion coefficient which is in reasonably close agreement with that of InSb. For these reasons the usual choice of substrate for the cooled detectors is either high resistivity Ge or Irtran 2. To prepare the slabs for the “dicing” operation in which they are serrated into the individual detector elements, a protective coating of polystyrene dissolved in toluene is applied to the exposed surface and allowed to become firm but not hard. The slabs are then cut into “rectangles,” i.e., rectangular parallelepipeds, having dimensions sufficient to allow for placement of the electrical contacts. Each rectangle is etched in the etchant again until the desired final thickness is attained. For the 300°K photoelectromagnetic detector the optimum thickness is about 2 5 p , whereas that for the 300°K photoconductive element is 5-10 p. The optimum thicknesses for the 195°K and 77°K photoconductive elements are also about 25 p. Platinum wire electrical contacts are applied to the sensitive elements by means of indium solder. For better delineation of the sensitive area the indium is evaporated onto the sensitive elements and the platinum leads applied by thermocompression bonding. An underlying evaporated gold layer is sometimes employed for better bonding. Figure 39 illustrates the final form of the photoconductive or photoelectromagnetic sensitive element.

’’See Kruse et

(Chap. 9).

66 PAUL W . KRUSE

tn c W

W

d

-

b c:

FIG.40. lnSb four-element array. (After Williams.60)

Q

a

(L

C

n

v)

I

w

t t

2

cn

v)

w

0

L

FIG. 39. Final configuration of sensitive element.

2.

INDIUM ANTIMONIDE DETECTORS

67

An alternative approach to the use of a wire saw for removal of the sensitive elements from the slab employs photolithographic technique^.^^ Here the slab is mounted on a turntable rotating at 1500rpm, and 3-4 drops of KMER (Kodak Metal Etch Resist) are placed on the center of the slab. Radial forces spread the KMER in a uniform film over the slab. The coating is allowed to dry at room temperature, then baked at 80°C. The KMERcoated slab is then dipped in KPR (Kodak Photo Resist), allowed to dry, then baked at 80°C. The KPR-KMER-coated slab is then exposed to a high intensity ultraviolet-rich radiation source through a mask whose transparent and opaque regions correspond to the geometrical requirements of the sensitive element. Since the KPR-KMER coating when exposed to ultraviolet radiation becomes resistant to the subsequent chemical etching solutions, the mask pattern should allow radiation to fall on the coating overlying the desired shape of the sensitive element and block radiation from falling in those regions where it is desired to serrate the elements. The coating is then developed by spraying it with KPR developer, flushed with distilled water, sprayed with KMER developer, and again flushed with distilled water. The remaining coating, overlying those areas which it is desired to protect from etching, is then baked at 80°C. The HF-HN0,-CH,COOH etchant is then applied to remove the unprotected areas of InSb. A wire saw is then employed in the etched regions to serrate the substrate as desired. This photolithographic method is of great value for the formation of multielement arrays of complex shapes on a common substrate. An example of a four-element photoconductive array6’ is illustrated in Fig. 40. 8. DETECTOR HOUSINGDESIGN

The housings, mountings, or envelopes of the InSb detectors fall into three categories : those for the 300°K photoconductive detector, those for the 195°K and 77°K photoconductive detectors, and those for the 300°K photoelectromagnetic detectors. Details of the designs will vary according to the manufacturer and application ; what is presented here can be considered to be typical. CI.

300°K Photoconductive Detector

The term “housing” for the 300°K photoconductive detector is a misnomer; the sensitive element is simply mounted on a copper block which also serves as a heat sink (see Fig. 41). Because of the low resistivity of InSb 5y

6o

For further information, see Introduction to Photofabrication Using Kodak Photosensitive Resists, Kodak Industrial Data Book P-79, Eastman Kodak Co., Rochester, New York ( 1967). D. B. Williams. Injrared Phys. 5, 57 (1965).

SAPPHIRE WINDOW

I n S b SENSITIVE ELEMENT

I-& O T!/

I n S b ELEMENT

AL UMI FORM N IZ EFOV D INTERIOR LIMITING APERTURE

SOLDER CONTACT TO ELEMENT AND LEAD

COPPER MOUNTING

SILVER PAIN LEADS

! M

r K O V A R RINGS

? w

P

sm

FINAL SEAL HELIARC WELDSPACE FOR COOLANT

FIG.41. Mounting for 300°K photoconductive detector. (After King and Bartlett.47)

FIG.42. Dewar for 195°K and 77°K photoconductive detectors. (After Kruse et ~ 1 . ~ ' )

2. INDIUM

ANTIMONIDE DETECTORS

69

56°AVERAGE FIE1.D-OF-VIEW

/

\ 3 . 5 - 5 . 0 ~SPECTRAL BANDPASS FILTER

COLD SHIELD ASSEMBLY

FIG. 43. Dewar for 77°K four-element array photoconductive detector incorporating background limiting cold shield and filter. (After Williams.60)

at 300"K,it is desirable to have a long, narrow element if the application will allow it. A problem with this design is the lack of protection for the sensitive element. b. 195°K and 77°K Photoconductive Detectors

The housing design for the 195°K and 77°K detectors shown in Fig. 42 is basically a vacuum Dewar, the coolant dry ice or liquid nitrogen being contained within the central well. The sensitive element (see Fig. 39) is mounted on the interior (vacuum) surface of the well, viewing the surroundings through a sapphire window. The interior surface of the external wall of the Dewar is aluminized to minimize coolant loss. The reflecting properties of this surface, together with those of an annular aluminized ring on the sapphire window, provide a limitation to the field of view of the detector which increases the background photon noise limited detectivity. Electrical leads, which can be either silver paint or wires embedded in glass, run along the interior surface of the sensitive well to Kovar pins penetrating the glass. Kovar weld rings are employed to ease assembly problems. A more complex design employed with a four-element array reported by Williams6' is shown in Fig. 43. Here a cold shield assembly is provided in the form of an interior cap over the array having an aperture which defines the field of view to 56", thus increasing the background photon noise limited detectivity62by a factor of approximately two. A 3.5-5.0 p spectral bandpass filter mounted over the aperture provides an additional enhancement in the detectivity by rejecting background photon noise outside of the 3.5-5.0 p interval. The Dewar design requires five electrical leads, one to each element and one common to all. 6 1 See Kruse et Chap. 10. "See Kruse et ~ f . , ~Fig. ' 9.13.

70

PAUL W . KRUSE

HIGH PERMEABILLTY

POLE PIECES

BRASS MOUNTING PLATE

I n S b SENSITIVE EL EMENT BRASS CASE

BRASS BASE PLATE TWO- PIN SHIELDED

CONNECTOR

FIG.44.Housing for 300°K photoelectromagnetic detector. (After Kruse

ct

db1)

c. 300°K Photoelectromagnetic Detector The housing design of the 300°K photoelectromagnetic detector (Fig. 44) incorporates an Alnico V U-shaped permanent magnet within a brass case.61 High permeability pole pieces direct the magnetic flux through the sensitive element. The requirement for a high flux density within the sample restricts the sample width to a value of about 1 mm or less in order that the pole piece separation not be excessive. As was true for the 300°K photoconductive detector, it is desirable to have a long, narrow sample if the application allows in order to have a high resistance and responsivity. A CaF, infrared transmitting window is mounted within the brass case, which incorporates a two-pin shielded electrical connector. Obviously, the photoelectromagnetic detector is much more bulky than the 300°K photoconductive one ;however, the sealed housing of the former affords far more protection for the sensitive element. V. Performance of Photoconductive and PhotoelectromagneticDetectors

Part I11 analyzed theoretically the performance of InSb photoconductive and photoelectromagnetic detectors. In this final part the actual measured performance of detectors is compared to the theoretical predictions. It would be most desirable to present data on detectivity and responsivity as

2.

INDIUM ANTIMONIDE DETECTORS

71

functions of purity for each of the temperatures and modes of operation, in order to determine whether the experimental points fall along the theoretical curves. Unfortunately, such data are not available in the literature. Instead, this part will present performance data on detectors which are assumed to be prepared in an optimum manner. The data fall into two categories. First, the performance of a single detector for each operating mode and temperature will be reported. The data on this representative detector will include spectral detectivity, frequency response, noise spectrum, frequency dependence of peak spectral detectivity, and, for the photoconductive mode, signal and noise as functions of bias current. The spectral detectivity, spectral responsivity, and response time values will be compared to the values predicted in Part 111. Second, information will be presented on the statistical distribution of the values of detectivity, response time, and resistance of a large number of 77°K photoconductive detectors made using supposedly identical processing parameters. Information of this type is especially valuable for systems requiring multielement arrays, where uniformity is of paramount importance. It would be desirable to have similar information on detectors operating at 300°K and 195°K;such information is not available in the literature. 9. PROPERTIES OF SELECTED HIGHPERFORMANCE AND PHOTOELECTROMAGNETIC DETECTORS

PHOTOCONDUCTIVE

The selection of data which truly represent high performance state-of-theart detectors is difficult. The available sources include manufacturers’ specifications and published literature. With either of these the accuracy and completeness of the data may be areas of concern. One source of information stands above all, namely, the reports of the Infrared Division, U.S. Naval Ordnance Laboratory Corona, Corona, California (now the Infrared Technology Division of the Naval Electronics Laboratory Center, San Diego). This facility, formerly part of the National Bureau of Standards, has been measuring the performance of infrared detectors supplied to it from worldwide sources for approximately two decades. The data are presented periodically in so-called “NOLC Reports.” By employing a standard format, the reports allow an easy comparison between detectors. There are two problems connected with the use of the NOLC reports, namely, military security and information selection. It was obviously necessary to choose only unclassified data for presentation herein. This is not a serious problem for the InSb detectors, since much of the data are unclassified. In reviewing the data it was necessary to select one set for each operating mode and temperature which best represented the state of the art. This is a subjective judgment with which it is hoped most readers will agree.

72

PAUL W . KRUSE

TABLE IV PROPERTIES

OF

SELECTED DETECTORS" ~

~

~~

Detector 300°K Photoconductive

300°K Photoelectromagnetic

195°K Photoconductive

5.5

5.4

1.9 x 10'

1.7 x lo*

5.9

1.9 x 10'

1.7 x 10'

8.6 x lo9

6.5 x 10"

7.1 x 107

5.8 x lo7

1.5 x 109

7.5

109

1.96

1.1

140

1.1

105

35

1.9

104

0.7

0.38

flat 1.01 x 0.1

> 75 0.128 x 0.106

109

5.16 x

41

60

(wc)


<1


4 x 104

557, No. 710

-

557, No. 716

4.3

1010

I 104 1 W 2 0.043 x 0.052

I x lo4

117

i, (PA) NOLC reference

5.3

5.0

R (ohms) T

77°K Photoconductive

8 x lo3 551, No. 704

2.9

104

<2 15

557, No.708

'After NOLC reports.63I, is wavelength at which spectral response peaks, D&, is detectivity at optimum wavelength and modulation frequency, fmod is modulation frequency at which detectivity peaks, and i, is bias current for 90 Hz data.

The data63are presented in Figs. 4 5 4 9 and Table IV. Figure 45 illustrates the spectral detectivities as functions of wavelength, with modulation frequencyfas an independent parameter. The spectral detectivities of the 300°K photoconductive and photoelectromagnetic detectors have similar values, with peaks of approximately 2 x 10' cm Hz'/'/W, for frequencies greater than 20 Hz and 75 Hz, respectively. The 195°K photoconductive detector has a peak detectivity of approximately 5.9 x lo9 cm Hz'/'/W at 90 Hz. At frequencies greater than lo4 Hz the peak detectivity increases to 8.6 x lo9 cm Hz'"/W. The highest detectivity is found in the 77°K photoconductive detector, which has a spectral detectivity at 5 . 3 ~of 4.3 x 10" cm HZ'/~/Wat 90 Hz. At frequencies greater than lo4 Hz the peak spectral detectivity is 6.5 x 10" cm Hz'/'/W. The 290°K background photon noise 63

Data sheets 708,710, and 716 of NOLC Rept. 557, and data sheet 704 of NOLC Rept. 551.

2. INDIUM ANTIMONIDE DETECTORS

7 I0

II

13

I

I

I

I

I

I

2

3

4

5

6

7

WAVELENGTH

k (p)

FIG.45. Spectral detectivities of 300, 195, and 77°K photoconductive detectors and 300°K photoelectromagnetic detector at the indicated modulation frequencies. (After NOLC Repts. 551 and 557, data sheets 704,708,710, and 716.)

limit for a detector having a 5.3 p long wavelength limit is also illustrated in Fig. 45. The data show that for modulation frequencies greater than lo4 Hz the spectral detectivity of the 77°K detector is approximately 55% of the background limit for a 27c sr field of view. Figure 46 illustrates the modulation frequency responses of the four detectors. The fastest response is found in the 300°K detectors. Table IV lists response times of less than 1 psec for all but the 77°K photoconductive detector, for which the response time is less than 2 psec. Figure 47 illustrates the noise spectra of the four detectors. Only the data for the 300°K photoconductive detector lack a frequency-dependent component. The appearance of the component in the data for the 300°K photoelectromagnetic detector is puzzling, since there is no bias current.

74

PAUL W . KRUSE

FREQUENCY ( H Z )

FIG.46. Frequency responses of 300, 195, and 77°K photoconductive detectors and 300°K photoelectromagnetic detector. (After NOLC Repts. 551 and 557, Data sheets 704, 708, 710, and 7 16.)

Figure 48 illustrates the frequency dependence of the spectral peak detectivity, with bias current appearing as an independent parameter for the three photoconductive detectors. Figure 49 depicts the dependence of signal (left-hand ordinate) and noise (right-hand ordinate) voltages upon bias current. Data for the 300°K photoelectromagnetic detector of course do not appear in Fig. 49. 10. COMPARISON OF MEASURED PERFORMANCE WITH THEORY

It is instructive to compare these experimental data with the theoretical values derived in Part 111, keeping in mind the approximations involved in those derivations. This comparison of the detectivity, responsivity, and response time values is found in Table V. Since the DA*values derived in Part I11 relate to the optimum modulation frequency, they are compared with the D:,,, values of the NOLC reports. Note that two rows represent the calculated values of peak spectral detectivity and responsivity taken from the listed figures of Part 111. Since the NOLC data list the bias current and detector dimensions, it is possible to normalize the calculated values to the same power dissipation per unit area and same detector width as

7 ? ' K , PC

.

N -

5 c

2

Id8 5

I 6 MA

300 O K , PC

2

1"9t-

\

300° K , PEM 3 0 0 ' K . PC

40 MA 3 0 0 " K , PEM I

2

I

5

16'O1

10

1

I

I

I

I

I

I

I

5

102

2

5

103

2

5

FREQUENCY ( H Z )

FIG.47. Noise spectra as functions of bias current of 300, 195, and 77°K photoconductive detectors and 300°K photoelectromagnetic detector. (After NOLC Repts. 551 and 557, Data sheets 704, 708, 7 10, and 7 16.)

I lo2

I

I

2

5

1

lo3

I

I

2

5

lo4

FREQUENCY (Hi!)

FIG.48. Frequency dependence of peak spectral detectivity of 300, 195, and 77°K photoconductive detectors and 300°K photoelectromagnetic detector at the indicated bias currents. (After NOLC Repts. 551 and 557, Data sheets 704. 708, 710, and 716.)

76

PAUL W . KRUSE

TABLE V COMPAR[SON OF PREDICTED PERFORMANCE

WITH

NOLC DATA

Detector 300°K Photoconductive

300°K Photoelectromagnetic

195°K Photoconductive

77°K Photoconductive

Calculated D,* (cm HZ'/~/W)

9 x lo8 (Fig. 29, p o = 7 x 10l6 cm-')

Normalized Calculated D,' (cm Hz'/'/W)

5.5 x lo8 (Po = 1.86 W/cm ')

6.2 x 10"

1.0 x 1 0 ' O

1.2 x 10"

1.9 x 10"

1.7 x 10'

8.6 x lo9

6.5 x 10"

NOLC Or, (cm Hz'l'jW) Calculated

W/W) Calculated normalized Ye, W/W)

6.2 x 10" 1.0 x 1 O ' O (Fig. 35, no = (Fig. 38, p o = 7x ~ r n - ~ ) PO = nil

6.4 (Fig. 28, po = 7 x 1016cm-3)

4.8 160 (Fig. 33, no = (Fig, 37, po = Po = nil 7 10'6cm-3)

3.9 (Po = 1.86 W/cm2)

(w

NOLC 9,(V/W)

1.96

Assumed z (psec)

6.5 x 1 0 - 3 (Fig. 18, po = 7 x 10l6crn-')

4.5 = 0.10fjcm)

1.1

1.2 x 10" (Fig. 32, p o = 5 x 1013 C T I - ~BLIP) ,

1.1 x lo6 (Fig. 30, p o = s x 1013 cm-Y

61 3.6 x lo6 (PD = 7.43 X (Po = 2.92 X 10-2W/cmZ; LO-' W/cmZ; w = 2.27 x w = 5.2 x 10- cm) 1O-'cm) 140 1.1 x 105

6.5 x lo-' 2.5 x lo-' (Fig. 18, p o = (zp.o = 5 x 7 x 1 0 l ~ c m - ~ ) lo-'sec; no PO = nil

(K =

4 x 10-1 = 1 x loq

cm-3 sec; po=5x 1013

ern-3;

h = 50) NOLCr (psec)

<1

il


<2

the NOLC data. These values labeled "normalized calculated DA*" and "normalized calculated BA''are also listed. Comparison of the NOLC data with the normalized calculated values shows reasonable agreement throughout. (Compare the second row with the third, and the fifth with the sixth.) With the exception of the responsivity for the 195°K photoconductive mode, the calculated values are higher than the measured. This is certainly to be expected in light of the approximations made in the derivations. No correction was made for the reflectance of the

2.

77

INDIUM ANTIMONIDE DETECTORS

o9

I

6 '

I

lo-* BIAS o

300'K

,PC

CURRENT lo-' (MILLIAMPERES) I 6

10

SIGNAL

- 10

I6 01 20

FIG.49. Bias dependences of signal and noise voltages of 300,195, and 77°K photoconductive detectors. (After NOLC Repts. 551 and 557, Data sheets 704, 708, and 710.)

surface of incidence due to the high refractive index. Carrier recombination at the surfaces was neglected. The optical absorption was assumed to be complete. The derivation of the photoelectromagnetic effect assumed the signal voltage to depend linearly upon the magnetic induction, an assumption which is invalid at p B > 1. Thus the agreement between the NOLC data and the calculations based upon the simplifying assumptions is felt to be reasonable. 1 1 . STATISTICAL DISTRIBUTION OF THE PROPERTIES OF LARGENUMBERS OF 77°K PHOTOCONDUCTIVE DETECTORS

Lennard64 has presented in histogram form the statistical spread in the properties of 100 InSb photoconductive detectors operating at 77°K. Williams6' has presented statistical data on an additional 74 detectors in the form of four-element arrays which operate in the photoconductive mode at 77°K. These data are discussed below. 64

J. K. Lennard, unpublished work (1964).

78

PAUL W. KRUSE

t-

u w

301

THEORETICAL BLIP L I M I T SPECIFIC DETECTIVITY

20

CI

I ‘\

m

z

0.9

1. I

1.3

I .5

I .7

2. I

1.9

D ” ( ~ O O O K ,iooo,i,go~),( IO’OCM HZ”*/WATT)

FIG. 50. Histogram of blackbody detectivities of 100 77°K-photoconductive detectors. (After Lennard.h4)

According to Lennard,64 the 100 photoconductive detectors were produced by the same manufacturing techniques, all having a sensitive.area of 0.5 x 0.5mm2 and a 90” field of view. The detectors were individually mounted in Dewars similar to that illustrated in Fig. 42. Histograms of the detectors’ properties are displayed in Figs. 5@-52. That of Fig. 50 represents the values of D*(50O0K,1000,1), obtained by rounding off the measured values to two significant figures and adding the number of occurrences of a given detectivity value. As indicated in Table 111, the values of DL*(5.2p,

A ,

/

I I

\

,‘\

\

/

4

6

L 12

8

PHOTOCONDUCTIVE TIME CONSTANT

10 (p

SEC 1

FIG.S1. Histogram of photoconductive response times of 100 77°K photoconductive detectors. (After L e n n i ~ r d . ~ ~ )

2.

79

INDIUM ANTIMONIDE DETECTORS

DETECTOR RESISTANCE (OHMS

I

lo3)

FIG. 52. Histogram of resistance values of 100 77°K photoconductive detectors. (After Lennard.64)

1000,l) can be obtained by multiplying the D*(500°K,1000,1) values by 5.7. The most probable value of DA*(5.2p,1000,1)can be seen to be approximately 7 x 10" cm Hz'/'/W. The distribution in photoconductive response times is illustrated in Fig. 51; the most probable value is 8psec. Finally, Fig. 52 illustrates the distribution in resistance. A value of 4000 ohms per square is most probable. TYPE 1

I

- I6 DETECTORS

SIN

TYPE

P

- 47 DETECTORS

SIN

BOO- IOOOp AMPS

0

300 500 BIAS CURRENT, *AMPS

TYPE m-I0 DETECTORS SIN

0

300 BIAS CURRENT,

500 p

AMPS

I

1 1

0

300

500

BIAS CURRENT, p AMPS TYPE

IX - 25

DETECTORS

SIN

BIAS CURRENT, p AMPS

FIG.53. Dependences of detectivity (proportional to SIN) upon bias current for 77°K photoconductive detectors. (After Lennard.64)

80

PAUL W . KRUSE

P.C.InSb SPECIFIC SPECTRAL RESPONSE AFTER INCORPORATION OF 3.5 5 . 0 ~COLD FILTER AND 56’ FIELD-OF-VIEW DEFINING

\

2.01

\

-

WAVELENGTH FOR PHOTOCONDUCTOR WITH 180’

SPECIFIC SPECTRAL

2.0

3 0

40

5,O

6.0

WAVELENGTH ( p )

FIG.54. Average spectral detectivity of 74 77°K photoconductive detectors with and without cold shields and cold filters. (After Williams.60)

Lennard64 also found that the dependence of the detectivities upon bias current fell into the four categories illustrated in Fig. 53. The optimum bias current range common to all except the 25 categorized as Type IV was

*O v)

t

W I T H 180’ UNOBSCURED FIELD-OF- VIEW V I E W I N G A 56. BACKGROUND

t

I5 w

S P E C T R A L BANDPASS FILTER

+ W

n LL

0

10

a

w m

s 5 2

0 0.8

1.0

1.2

1.4

1.6

1.8

D“(500.840.11~10-lo(CM

2.0

2.2

HZ”*/WATT

2.4

2.6

1

FIG.55. Histogram of blackbody detectivities of 74 77°K photoconductive detectors with and without cold shields and cold filters. (After Williams.60)

2.

INDIUM ANTIMONIDE DETECTORS

n

81

0 180' UNOBSCUREO FIELO-OF-VIEW 1 3.5 - 5.0 + BANDPASS FILTER 56* AVERAGE FIELD -OF-VIEW

W

I-

W 0

W

L

i 0.8

0.4

1.0

1.2

I

i.4

1.6

18

2.0 2.2 2.4 2.6

D: (4.6p,840,1) x IO-"(CM H Z 1 ' h A T T )

FIG.56. Histogram of 4.6 p spectral detectivities of 74 77°K photoconductive detectors with and without cold shields and cold filters. (After Williarn~.~')

200-300pA. At 200pA the responsivity was stated to be well above 5000 v/w. Williams6' reported upon the properties of 74 photoconductive detectors arranged in four-element arrays as illustrated in Fig. 40.The dimensions of each of the long, narrow sensitive elements were 0.94 x 0.050mm2. Each array was evaluated initially in a test Dewar similar to that illustrated in Fig. 42, but without the silvered interior surfaces, and later in pairs (eightelement linear array) in a second test Dewar incorporating a cold shield and

40

0

180°UNOBSCURED FIELD-OF-VIEW 5 6 O FIELD-OF-VIEW 3.5 - 5 . 0 ~ BANDPASS FILTER

u)

C 30

z

3 LL

0

a

20

W

m

$

10

0 20

40

60

80

100 120 140 160 180 200 220 240

RESISTANCE ( K OHMS)

FIG. 57. Histogram of resistance values of 74 77°K photoconductive detectors with and without cold shields and cold filters. (After Williams.60)

82

PAUL W . KRUSE

a 3.5-5.0~cold filter, as shown in Fig. 43. The effective background flux density in the former case was 1.4 x 1 0 I 6 photonscm-2 sec-', and was 2.0 x 1015photons cm-' sec- in the latter. The average spectral detectivity of the 74 unshielded, unfiltered 'detectors, and the improvement attendant upon cold shielding and filtering, is^contrasted to the room temperature background limited spectral detectivity in Fig. 54. Histograms illustrating the blackbody and spectral detectivities, resistances, and optimum bias currents, all'with and without cold shielding and filtering, are shown in Figs. 55-57'. Figure 55 shows the distribution in values of D*(500°K,840,1)before and after cold shielding and filtering. The improvement in detectivity with cold shielding and filtering is clearly evident in the shift in distribution toward higher values. Figure 56 illustrates the distribution in spectral detectivity, 0,*(4.6,840,1), with and without cold shielding and filtering. Here the improvement is marked ; no overlap exists between the two distributions. Figure 57 illustrates the resistance increase attendant upon cold shielding and filtering, indicating that the major portion of the carriers present in the unshielded detectors are produced by photoexcitation by the room temperature background radiation. The last histogram, Fig. 58, shows that the optimum bias current distribution is shifted toward lower values following cold shielding and filtering. As L e n n a ~ - ddid, ~ ~ Williams6' also categorizes the dependence of detectivity upon bias current, as illustrated in Fig. 59. Note that cold shielding and filtering has a moderate effect upon the distribution of detectors among the three shapes.

0

40

180°FIELD-OF-VIEW

v)

a

0

COLD 3 . 5 - 5 . 0 ~SPECTRAL EANDPASS FILTER AND 56" FI ELD -OF - V I E W

30

W

I-

W

n

lL

20

0

a W

g

10

3

z

0

10

20

30

40

50

60

70

00

90

BIAS CURRENT ( p A M P S ) FIG.58. Histogram of optimum bias currents of 74 77°K photoconductive detectors with and without cold shields and cold filters. (After Williams.60)

2.

83

INDIUM ANTIMONIDE DETECTORS

SHAPE I

SHAPE 2

20

20

SHAPE 3

I

40 BIAS CURRENT ( p AMPS)

40

20

40 BIAS CURRENT (pAMPS)

BIAS CURRENT (pAMPS)

SHAPE I

74 DETECTORS VIEWING

I

SHAPE 2

1

SHAPE 3

UNOBSCURED 160' FIELD - O F - V I E W

56" F I E L D - O F - V I E W AND COLD SPECTRAL FILTER

FIG.59. Dependences of detectivity upon bias current for 74 77°K photoconductive detectors. (After Williams.60)

Finally, Table VI illustrates the uniformity within a single eight-element array incorporating a cold shield and filter. The range in detectivity values is k 18% ; that in resistance is k 15%. All detectors operate at the same bias current with similar dependences of detectivity upon bias. TABLE VI PROPERTIES OF AN EIGHT-ELEMENT PHOTOCONDUCTIVE ARRAYOPERATED AT 77°K WITH 560-FIELD-OF-VIEW COLDSHIELD A N D 3.5-5.0-p COLDFILTER' Cell number Characteristic 1

Bias current (pA) Resistance(ohms x Signal (pV) Noise (pV) D*(500,840,1) (cmHz"*/W x lo-'') DA*(4.6,840,1) (cmHz"'/W x lo-")

" After Williams.60

2

3

4

5

6

7

8

10 10 10 10 10 10 10 10 73 76 72 75 66 82 62 69 145 130 125 148 115 135 135 135 0.86 0.73 0.74 0.80 0.70 0.80 0.73 0.74 1.64 1.64 1.64 1.84 1.32 1.56 1.70 1.67 1.57

1.57

1.57

1.77

1.27

1.50

1.63

1.60

This Page Intentionally Left Blank

CHAPTER 3

Narrowband Self-Filtering Detectors M . B . Prince

. . . . . . . . . . . . . . 2 . Requirement of Direct Semiconductors . . . . . 3 . Tuning Techniques . . . . . . . . . . . 4. Binary III-V Materials . . . . . . . . . 5. Ternary 111-V Materials . . . . . . . . . 111. EXPERIMENTAL DATA. . . . . . . . . . . 6. Spectral Measurement Technique . . . . . . . 1. Binary Maierials-GaAs . . . . . . . . . 8. Ternary III-V Materials--lnAs,P, . . . . . . IV. SUMMARY . . . . . . . . . . . . . . I. JNTRODUCTION.

11. THEORETICAL DISCUSSION . . . . . . . . . 1. General Solution of Photovoltaic Detector Response

. . . . . . . . . . . .

. . . . . . . . . . . .

. . . . . . . . . . . .

. . . . . . . . . . . .

85 87 81 92 93 94 94 97 91 98 102 106

I. Introduction This chapter reviews a relatively new type of photovoltaic detector'.' that is of interest for infrared radiation detection. Such devices make use of the unusual absorption coefficient versus wavelength characteristics of a special group of III-V compounds and mixtures of compounds. When properly fabricated with these materials, p-n junction devices with a relatively narrow spectral response can be made. Narrow response does not depend upon a narrow-band filter (such as a multilayer thin-film filter) placed in front of the device, but depends rather upon the optical absorption of the material itself for filtering purposes. Thus these devices are called narrowband self-filtering detectors (NBSFD). In addition to improved reliability due to mechanical simplicity and a relaxing of the cooling requirements needed for use of external filters,narrowband self-filtering detectors have a very broad field of view and a spectral response which is relatively insensitive to the angle of incidence of the radiat ion being detected.

' A. Lopez and R. L. Anderson, Solid-State Electron. 7 , 695 (1964). D. B. Medved and S. Kaye, Bull. Amer. Phys. SOC. Series II,9,714 (1964).

86

M. B . PRINCE

Several of the applications' for solid-state detectors that require some restrictions on the wavelength span of their response functions are : (1) detection of fluorescence spectra from the nitrogen first positive band at 8911 A ; (2) detection of injection luminescent diode outputs from gallium arsenide devices ; and (3) detection of laser emission at 1.06 p. The design principles of the NBSFD are quite simple. Two requirements must be met :(1) a direct-gap semiconductor must be used, and (2) the device must be illuminated through a relatively thick base region, rather than through the thin diffused region as is the usual practice. Figure 1 illustrates the geometry requirements. The spectral response functions of p n junction devices are usually determined by the interaction of two distinct mechanisms. Free carriers are produced by the absorption of incident radiation at energies in excess of the band gap. These charge carriers may then be transported to the junction by diffusion or drift or by a combination thereof. Those pairs which reach the junction are separated by the field, and an external current or voltage is generated. Direct gap semiconductors usually have a rapidly varying absorption coefficient in the vicinity of the long wavelength cutoff. It can change by an order of magnitude in a wavelength interval spanning less than 100 A. If diffusion lengths for the minority carriers are much less than the thickness of the base region, only radiation within a very narrow band of energy will be absorbed close enough to the p-n junction for the resulting carriers to be collected. Part I1 provides a quantitative analysis of predicted spectral response functions for the geometries of the type shown in Fig. 1. Criteria for selection of specific material combinations are also formulated in this section. In Part I11 experimental results are described for two different materials

INCIDENT

RADIATION

X =W (JUNCTION PLANE)

X=d

LOIFFUSED REGION ( 5 0 - 7 5 8 ) FIG. 1. Geometry for narrowband detector.

3.

NARROWBAND SELF-FILTERING DETECTORS

87

demonstrating the general applicability of the concept : gallium arsenide for 8850 A, and indium-arsenide-phosphide solid solutions exhibiting narrow spectral response at 1.06 p. 11. Theoretical Discussion

I . GENERAL SOLUTION OF PHOTOVOLTAIC DETECTOR RESPONSE The theoretical spectral response characteristics are obtainable from solutions of the steady-state continuity equations with suitable boundary conditions. The steady-state equations for the minority carriers ( p , n ) in the regions of Fig. 1 for radiation impinging on the surface are p _ aN d 2 p_ _ -tax = 0,

+

dx2

L,

d2n dx2

Ln2

D,

n + -aN e-=x

__-__

=

D,,

0

The boundary conditions for these equations are

D,dp/dx = spp at x

=

0,

p(w) = n(w) = 0 at x = w ,

D, dnjdx

=

s,n

at x

=

d,

where the symbols are defined following Eq. (3). Since 1954 various paper^^-^ have been published relating to the spectral response of photovoltaic devices. These papers were primarily concerned with energy conversion with devices such as solar cells and nuclear batteries. One of the first of these papers was by Pfann and van Roosbroeck3. They have given an expression for the quantum efficiency [their Eq. (23)] which is relatively complex but does not take into account all the parameters for the device under consideration here. Wolf4 has derived equations for the contributions from both sides ofthe p-n junction to the quantum efficiency. In this chapter short-circuit conditions will be assumed in the operation of the narrowband self-filtering detectors. Thus Wolf's Eqs. (4) and ( 5 ) can be converted into the following equations for the contribution to quantum efficiency W. G. Pfann and W. van Roosbroeck, J . Appl. Phys. 25, 1422 (1954). M. Wolf, Proc. I.R.E. 48, 1246 (1960). D. A. Kleinman, Bell System Tech. J . 40,85 (1961). M. B. Prince and M. Wolf, J . Brit. IRE 18, 583 (1958).

88

M. B. PRINCE

from the two sides of the p-n junction :

Q, =

Q

=

2

e-aW

= aL,

+

+-spLp{exp[(l DP

- aL I?] LP

3

aLp+ 1

Qn+Qp.

where Q, is the quantum efficiency contribution from the base region, Q , is the quantum efficiency contribution from the diffused region, Q is the total quantum efficiency, J,, is the charge carrier flux in the base region, J , is the charge carrier flux in the diffused region, N is the photon flux, a is the absorption coefficient, L, is the hole diffusion length, L, is the electron diffusion length, s, is the front surface recombination velocity, s, is the rear surface recombination velocity, D, is the diffusion constant for holes, and D, is the diffusion constant for electrons.

In this discussion it is assumed that the geometry of Fig. 1 prevails with a bulk base region of n-type material and a rear diffused region of p-type material. This structure was chosen for the analysis because the experimental devices have this configuration. Since the diffused region has a concentration gradient of impurities, there is a drift field set up which should contribute to an improved quantum efficiency from this p-region. Kleinman5 has shown that the built-in field can be eliminated from the calculation by reducing the surface recombination velocity for the region of interest. This will be done in the calculations in this section. Equations (1) and (2) have been solved for

3.

NARROWBAND SELF-FILTERING DETECTORS

89

two special cases. These cases were chosen to be consistent with the experimental data using gallium arsenide devices. The values chosen are given below. Detectors have been fabricated by diffusion of zinc into n-type gallium arsenide. The base material employed for device fabrication had a range of carrier concentration from 2 x loi6 to 5 x 1017cm-3. The optical and electrical properties of n-type gallium arsenide have been extensively studied for doping concentrations in this range. It is possible to obtain acceptable values from the literature for all the parameters in the expression for quantum efficiencyfor gallium ar~enide.’-’~Of these, Hill,7 Braunstein et d.,’ Turner and Reese? and Kudman and Vieland” treat the optical properties of the n-type and p-type materials. Kudman and Seidel“ restrict the discussion to degenerate p-type gallium arsenide,and Sturge” and Hobden and SturgeI3 describe the semi-insulating variety. Figure 2 shows room temperature absorption spectra of n-type gallium arsenide as obtained from Hill’ and Braunstein et a/.* for the doping range of interest. Unless otherwise specified,the optical values in Hill’s work7 have been utilized. For N , E 2 x 10l6cm-3 the diffusion length (L,) should be of the order of 10-15 p. The surface recombination velocities were chosen for the n-type surface based on reported data14; for the p-type surface the infinite recombination velocity (due to the ohmic contact on the back of the device) was reduced to lo4 cm/sec in the light of Kleinman’s discussion. Equations (1)and (2) have been calculated as quantum efficiency (Q)versus absorption coefficient (ct) curves for two cases. Case 1 is the configuration of Fig. 1 with W = 50 p or 5 x l o v 3cm, and case 2 has W = 1OOp or cm. In both cases the other parameters are fixed : s p = i04cm/sec, = i0-3cm, = 10 cm2/sec, = 1W3cm, = 10 cm2/sec, and s, = - lo4 cm/sec.

L,, D, L, D,

In both cases the diffused region is 50 p thick.

’ D. E. Hill, Phys. Rev. 133, A866 (1964). R. Braunstein, J. 1. Pankove, and H. Nelson, Appl. Phys. Lerrers 3, 31 (1963). W. J. Turner and W. E. Reese, J . Appl. Phys. 35,350 (1964). l o 1. Kudman and L. Vieland, J . Phys. Chem. Solids 24,437 (1963). 1. Kudman and T. Seidel, J . Appl. Phys. 33, 771 (1962). ” M. D. Sturge, Phys. Rev. 125,768 (1962). l 3 M. V. Hobden and M. D. Sturge, Proc. Phys. Soc. (London) 78, 615 (1961). I 4 K. L. Ashley and J. R. Baird, IEEE Trans. Electron Devices 14, 429 (1967).

M. B . PRINCE

'I

1,000

-

-w+-z6

n = 5.3X 10 ~

0

0 LL

100-

0-DATA CALCULATED FROM NBSFD

0 0

z

0 + a

/i1 / I

I1I

/'j/l

0 m

m a

-_-_----' 10

/

I

/

/

n = 2.5 X d7

I '

1.30 9530

/

0

I

1.35 9175

I

1.40 eV0050

A-

1Y

A

FIG.2. Absorption coefficient for n-type GaAs (dashed curves after Braunstein et d.,* solid curves after Hill').

Case 1 curves for quantum efficiency versus absorption coefficient are given in Fig. 3. Curve A represents the contribution due to the front base region, curve B represents the contribution due to the diffused rear region, and curve C is the total response curve. From these curves two points should be noted: (1) Practically all the spectral response is due to those photons having a wavelength such that the absorption coefficient lies between 10 and 200Ocm-'; and (2) the front base region contributes more to the total response than the diffused region and its peak response is shifted toward higher values of alpha. (The quantum efficiency is defined as the number of electrons crossing the junction per photon incident into the device. These calculations do not take into consideration the surface reflectivity properties.) Figure 4 gives similar curves for Case 2 (which has the junction twice as deep as in Case 1). In this case several points should be observed: (1) The total peak response has been cut in half; (2) the pass band has been reduced to 10-500 cm- ; and (3) the peak response has shifted from an alpha value of 200 to 100 cm- These points will be considered later under the discussion of tuning techniques.

3.

I4

-

A CURVE = BASE REGIONB CURM:DIPFUSED REGION t CUR#= TOTAL RESPONSE

-

13 12 I1 -

-

10

91

NARROWBAND SELF-FILTERINC DETECTORS

-

-

-

ABSORPTION COEFFICIENT, a (cm-1)

FIG.3. Curves showing Case 1 response of base and diffused regions.

Solutions of Eqs. (1-3) under the extreme cases of letting (a) s, = sp + 0, and (b) s, = s p -+ 00 for Cases 1 and 2 yield curves that match those of Figs. 3 and 4 within & on the ordinates. This is as expected, since the diffusion lengths for these cases are small compared to the base region or diffused region thicknesses. 8

I

7 -

I

I

c/ ,/-/

6 -

/

\

.

I

CASE 2 CURVE A = BASE REGION CURVE B * DIFFUSED REGION CURVE C ' TOTAL RESPONSE

\

\

\

/

/ 57 5 -

/ /

\ A

\

ABSORPTION COEFFICIENT, a (ern-') FIG.4. Curves showing Case 2 response of base and diffused regions.

92

M. 8 . PRINCE

A simple approximation can be developed for the case where W % L, and surface recombination is neglected. The generation term g(x) for photon to electron-hole pairs is

g(x) = aN,e

-IIx,

(4)

where N o is the photon flux in photons/cm2 sec. In this case the variable g(x)is relatively constant over a diffusion length in the vicinity of the junction for values of wavelength where g(x) has a relatively large value at W. It becomes g = tlNoe-IIW. Under this approximation the particle current J is J

=

aNOLpe-uW,

(5)

and the quantum efficiency Q is

Q = J/N,

=

aLpe-uW.

(6)

The maximum value of the quantum efficiency is

Q,,,

=

(L,/W)e-

’.

(7)

The values of quantum efficiency in Eqs. (6) and (7) must be doubled to take into consideration both sides of the junction. 2. REQUIREMENT OF DIRECT SEMICONDUCTORS From the above general discussion it was noted that as the junction is moved further from the front surface both the total spectral response and the bandwidth are reduced. The bandwidth of interest is that for which M ranges from 10 to approximately lOOOcm-’. In order for this bandwidth to be narrow, the absorption coefficient should vary rapidly with wavelength (A) in this range. It so happens that this occurs with direct semiconductors. To show this, Fig. 5 presents a plot of c( versus 1 for a collection of several semiconductors. It is observed that the indium compounds and gallium arsenide have very steep slopes in the absorption-coefficient region of interest. These are all direct semiconductors, i.e., materials in which electrons and holes can recombine without the assistance of a phonon or by direct radiative recombination with the emission of a photon. It is not known whether or not all direct semiconductors have this steep slope (for example, the early data on GaSb as shown do not meet this requirement), but the recombination cross section should be relatively high in the narrow spectral region of the energy band gap compared to indirect semiconductors, in which recombination must be assisted with a phonon. In “indirect” semiconductors recombination takes place nonradiatively with the help of multiple recombination levels and the emission of many phonons into the crystal lattice.

3.

93

NARROWBAND SELF-FILTERING DETECTORS WAVELENGTH ( p )

310

62 124

413

207 I55 124 103 08 0775 248 177 138 113 0953 0826 0730

-

-

01 3 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9

10

I I

I 12

I 13

i

l

i

14

15

16

_ 17

ENERGY ( e V ) FIG 5 Absorption coefficient vs energy/wavelength

3. TUNINGTECHNIQUES

There are four methods by which the response characteristics ofthe NBSFD can be modified or tuned. The most obvious and the grossest technique is the selection of the material. From Fig. 5 it is observed that the wavelength of interest can be changed from approximately 0.9 ,u to approximately 4.0 p by changing from GaAs to InAs. Finer changes can be obtained by using ternary mixtures of 111-V materials. This technique for tuning is called compositional tuning. More will be given about this technique later in the chapter. A second technique, temperature tuning, allows for changing the spectral response by adjusting the operating temperature of the device. This technique can most readily be understood by using Fig. 6, a plot of the absorption coefficient versus wavelength for several temperatures for InAs.' At room temperature (298°K) the response will peak at about 3.7 p. By reducing the temperatuie to liquid nitrogen temperatures (77°K) the peak wavelength will shift to 3.0 p, and upon heating the device to 388°K the peak wavelength will shift to approximately 4.1 p. Similar shifts are expected for other materials. A third technique, which depends upon the depth of the junction below the surface impinged by radiation, has been described essentially in Section 1 of Part I1 where it was shown theoretically that as the junction depth is l5

H. Welker and H. Weiss, Solid

Stute Phys.

3, 56 (1956).

94

M . B. PRINCE

FIG.6. The behavior of the absorption constant of InAs at different temperatures.

increased the peak spectral response occurs at longer wavelengths. This technique is called junction depth tuning. Reverse biasing, the fourth tuning technique, depends upon the fact that when a p-n junction is reverse-biased by an external voltage supply the space-charge region is increased ; this increase occurs primarily in the more lightly doped side of the junction. In the case of the structure of Fig. 1 practically the entire increase takes place in the original base material and moves the effective junction closer to the radiation-impinged surface. Thus the effective junction depth can be changed after fabrication of the device, and the spectral response can be modified by changing the reverse bias. Specific data on these various methods of tuning will be presented in Part 111.

4. BINARY111-V MATERIALS As shown in Fig. 5, there are several binary 111-V materials that have the proper rapid change in absorption coefficient with wavelength for use in the NBSFD concept. These include most of the direct semiconductors (GaAs, InAs, InSb, etc.). The spectral response peak of an NBSFD is determined essentially by the energy gap of the material from which it is fabricated. For typical NBSFD geometries in gallium arsenide the peak occurs at photon energies approximately 0.05 eV greater than the band gap. 5. TERNARY 111-V MATERIALS

There are a number of specific wavelengths for which NBSFD’s would be useful, but for which there are no elemental or compound semiconductors

3.

NARROWBAND SELF-FILTERING DETECTORS

95

having the requisite energy gap. In these cases one must resort to solid solutions of various direct gap semiconductors. There is usually more than one solid solution of appropriate energy gap. In this subsection some criteria upon which a selection can be based are discussed. Of prime importance is the crystallographic structural quality that can be achieved in the solid solution. In considering various possible combinations of the III-V compounds, only those cases involving the mixing of two compounds which have one element in common will be considered, rather than the general quaternary systems, The liquid-solid equilibrium phase diagrams will not be discussed for two reasons: these have already been considered in the literature,16 and the work reported here involved growth of the solid solutions from the vapor phase only. There are eighteen systems among the nine III-V compounds formed with the elements Al, Ga, In, P, As, and Sb, considering only the ternary systems. In the early work on solid solutions between pairs of these compounds the conclusion was reached that the compounds were mutually soluble only over a very limited range.”*’* Later it was found that, in the cases of InAs-InP and GaAs-Gap, solid solution could be achieved through the whole composition range.’ 9*20 The suggestion was made2’ that solid solution could be achieved if the group V elements were mixed, but not if group I11 elements were mixed. Further studies, which have included eight of the quasibinary systems, indicate solid solubility through the entire range of composition ; however, in most cases single-phase material is obtained only after months of annealing if the solution is prepared from a melt.22~23 If the annealing is done on powder samples (as for X-ray powder photographs), single-phase material has been achieved by anneals over periods as short as two weeks. Homogeneous singlephase material is required for good p-n junction devices. A number of rules have been devised for predicting solubility in the case of binary substitutional alloys of simple metals, the most important being Hume-Rothery’s rules of atomic size and of electron-atom ratio. There is no rule which is generally applicable for combinations of the III-V compounds. Predictions have been made based on atomic sizes. The zincblende lattice (the lattice of interest) consists of two interpenetrating fcc lattices with groupJ. C. Woolley, “Compound Semiconductors” (R. K. Willardson and H. L. Goering, eds.), Vol. I, Chap. 1. Reinhold, New York, 1962. l 7 C. Shih and E. A. Peretti, J. Am. Chem. SOC. 75,608 (1953). W. Koster and B. Thoma, Z . Metallk. 46, 291 (1955). 0.G. Folberth, Z . Naturforsch. 10a, 502 (1955). 2o H. Weiss, Z . Naturforsch. ll a , 430 (1956). P. Baruch and M. Desse, Compt. Rend. 241,1040 (1955). 2 2 N. A. Goryunova and N. N. Fedorova, Zh. Tekhn. Fiz. 25, 1339 (1955). 2 3 J. C. Woolley and B. A. Smith, Proc. Phys. SOC.(London)72,214 (1958). l6

‘’

’*

96

M. B . PRINCE

I11 atoms on one and group-V atoms on the other. Since only those compounds having one element in common will be mixed, the mixing will take place in the form of substitution on one or the other of the fcc lattices, but not both. The effect of a difference in radius if a small atom such as A1 is substituted into the group-I11 fcc lattice on InAs will be to decrease the tetrahedral bond distance at the A1 sites, and it may be expected that there would also be an increase in the second-nearest-neighbor bond distance with distortion in the bond angles. This distortion can be minimized and the possibility of forming homogeneous single-phase solid solutions enhanced by choosing solutions in which the radii of the solvent and solute atoms are comparable. The effect of the radius ratios can be made more apparent by considering the actual nearest-neighbor distances in the compounds of interest.24These are simply the sum of neighboring radii. The difference in the nearestneighbor distances is of interest when two compounds with a common element are mixed, since this results in the lattice distortions at solute sites TABLE 1 THE18 POSSIBLE SYSTEMS OF THE MORE-COMMON 111 v COMPOUNDS, THE POSSIBLE WAVELENGTH RANGESFOR NBSFD’s. AND DIFFERENCE AETWEEN NEAREST-NEIGHBOR DISTANCES ANNIN THE TERMINAL COMPOUNDS

System In<Sb, P) In<Sb, As) In4As, P) Ga<Sb, P) GadSb, As) Ga
Wavelength range (PI

ANN

6.25-0.94 6.25-3.5 3.5 -0.94 I .65-O.54 1.65-0.84 0.84-0.54 0.75-0.4 0.75-0.54 0.54-0.4 6.25-0.75 6.25- 1.65 1.65-0.75 3.5 -0.54 3.5 -0.84 0.840.54

0.26 0.18 0.08 0.27 0. I9 0.08 0.28 0.20 0.08 0.16 0.17 0.01 0.18 0.18 0.00

0.94-0.4

0.18 0.18 0.00

0.94-0.54 0.54-0.4

(‘4

Linus Pauling, “The Nature of the Chemical Bond,” 3rd ed., p. 248. Cornell Univ. Press, Ithaca. New York, 1960.

3.

97

NARROWBAND SELF-FILTERING DETECTORS

TABLE I1 COMPARISON OF PERTINENT CHARACTERISTICS OF POSSIBLE 1II-V 1.06 p NBSFD

Crystal

SOLID SOLUTIONS FOR

Energy gap

Solute concentration x (assuming direct gap)

Direct Direct

0.07 0.09 0.69 0.28 0.30 0.48 0.54 0.18

9

Direct ? ?

? Direct

0.26 0.08 0.27 0.19 0.16 0.01 0.18 0.18

discussed above. These differences, A", are listed in Table I for the eighteen systems, together with possible wavelength ranges for NBSFD's. As indicated in Table I, A" for arsenide-phosphide combinations are 0.08 A and are essentially zero for gallium-aluminum. All other combinations are worse than the arsenide-phosphide combination by at least a factor of two. These considerations must be borne in mind in selecting a solid solution for a specific wavelength, since the lattice distortions at the solute sites not only make it difficult to prepare single crystals, but also have a deleterious effect on the electrical characteristics. In addition to the above, the solute concentration required to reach a specified wavelength must also be considered. Very dilute solutions should be used where possible. Such considerations guided selection of a material for the fabrication of NBSFD's operating at 1.06 p. Specifically, these are : (1) the energy gap should be direct, (2) the solute concentration x should be close to zero or unity (with 0.5 being the worst case), and (3) the difference in nearest-neighbor distances should be as small as possible. From Table I it can bc seen that there are eight solid solutions which could be used to obtain the energy gap required for 1.06p. These are listed in Table 11, together with data on the three important properties just discussed. It would appear that the second material, In(As,P, -J,is easily the best choice for 1.06p. 111. Experimental Data

6. SPECTRAL MEASUREMENT TECHNIQUE A modified Perkin-Elmer Model 13-U spectrometer was used in making the spectral response measurements discussed below. For detector spectralresponse measurements one source beam and two detectors are utilized, one

98

M. B . PRINCE

of the latter being the detector under test and the other a thermocouple reference detector. The thermocouple was used in the slit-servo system for the purpose of maintaining the emerging energy constant as the wavelength range of interest was scanned. The signal from the detector under test was fed to a Princeton Applied Research phase-sensitive amplifier, and the output was recorded as a function of wavelength. The amplifier input impedance was 10 megohms, so that the measurements were essentially open-circuit voltage measurements. All measurements were made under zero bias conditions, and a tungsten ribbon filament was used as the light source. There is a source of error in this measurement system which has not been corrected in the measurements reported below. Since the reflectivity of the beam splitter varies slightly with wavelength, the energy reflected by the beam splitter to the reference thermocouple varies slightly with wavelength, and this variation will obviously differ from the wavelength variation of the energy transmitted to the detector under test. In view of the relatively narrow response characteristics of the GaAs and InAs,P, - x devices, however, the error is small and has been neglected.

7. BINARYM 4TERIALS-GaAS a. Device Fabrication

Detectors were fabricated from n-type gallium arsenide with a carrier concentration range extending from 2 x 1016 to 5.3 x 10'' atoms/cm3. The variation in resistivity over this impurity range appears to have no significant effects on the position of the peak response wavelengths. Electrical properties ofthe junctions were affected by the choice of starting resistivity; for example, zero bias capacitance was appreciably lower for the higher-resistivity devices. In addition, the quantum yield of the higher resistivity detectors was consistently larger. It was found empirically that the impurity concentration for optimum electrooptical properties was in the area of 3 x loi6atoms/cm3. Total detector thicknesses of the order of 150p were typically utilized. The junction depth of the diffused region was 50 to 75 p , corresponding to diffusion times varying from 6 to 24 hours. The detectors were fabricated by processing single-crystal n-type gallium arsenide slices 60CL750 p thick. Closed-capsule techniques for diffusion at 850°C were employed. Finished slices were ultrasonically cut to produce circular detectors about 1.2 cm in diameter. Contacts and antireflection coatings of silicon monoxide were applied by evaporation. An optimum thickness of the coating was determined by monitoring the output of the detector exposed to a tungsten lamp during the evaporation process.

3.

NARROWBAND SELF-FILTERING DETECTORS

99

ENERGY (eV)

WAVELENGTH

(dJ

FIG 7. Spectral response of gallium arsenide as function of base-layer thickness.

b. Spectral Response Curves with Junction Depth Tuning

Figure 7 shows typical results obtained for gallium arsenide with the radiation normally incident on the base layer. The curve labeled 0 was obtained with a base layer thickness of approximately 250 p. Approximately equal increments of material were then removed by chemical etching in three successive controlled etches, spectral response data being obtained after each etch. These data are shown in Fig. 7 as curves 1,2, and 3. The base thickness of the device after the last etch was about 60 p. The data of Fig. 7 are normalized to the peak response after the last etch. The peak response before etching was 54% of that after the last etch, and the peak shifted from 8915 A to 8864 A. For the device of Fig. 7 the half-width was 135 A and did not change. It should be noted that the peak response wavelength corresponds to a photon energy (1.39-1.40 eV) that is 0.04 to 0.05 eV greater than the forbidden band gap for GaAs at 300°K (1.35 eV). c . Field-of-View Vuriutions

The shift in the position of the peak response for off-axis illumination is negligibly small. Figure 8 shows this. For radiation at an angle of incidence of 80" the high index of refraction of GaAs, 3.5, leads to an angle of refraction less than 17", so that the optical thickness of the base layer is increased by only 3%. This is not sufficient to cause an appreciable shift, thus allowing the detector to be used in applications requiring a wide field of view.

100

M . B. PRINCE

142

141

140

ENERGY ( e V ) 139 I38

I37

I36

I35

NORMAL INCIDENCE

5“ OFF-AXIS

8700

8800

8900 WAVELtNGTH

9000

9100

9200

(d)

FIG.8. Spectral response of gallium arsenide detector with angle of incidence as parameter.

d. Temperature Tuning At the time of this writing, no data are available for response of GaAs NBSFD’s as a function of temperature. e. Reverse-Bias Tuning

Detectors have been made on high resistivity gallium arsenide wafers.” These detectors do not have good diode characteristics, but they exhibit photocurrents under light; when tested in the monochromator they have a spectral response that varies with the bias. The variation of spectral response for one of the better diodes is shown in Fig. 9, where several points should be noted. First, the peak response wavelength has been displaced to a shorter wavelength by 240A upon applying a reverse bias of 10 V. Second,the peak response amplitude has increased for this device by a factor greater than ten with the applied bias. Finally, the spectral response characteristic has broadened considerably. All three of these effects qualitatively follow from the discussion of Part 11, Section 1. The quantitative changes are more difficult to predict, primarily since high resistivity (semi-insulating)gallium arsenide is frequently highly compensated and consequently subject to change in resistivity upon heat treatment. In fact, an investigation of the capacity of these high resistivity GaAs diodes as a function of bias shows the depletion region to be less than anticipated from the uncompensated resistivity by up to two orders of magnitude. For the diode of Fig. 9 (carrier concentration of lo9 to 10” ~ r n - ~it) ,is a good approximation to use the abrupt junction formulas and assume that the space charge (depletion)region extends entirely into the very high resistivity region

’’ D. B. Medved and G. P. Rolik, Appl. Phys. Letters 10, 213 (1967).

3.

NARROWBAND SELF-FILTERING DETECTORS 8

I A -,-

7500

I 0 VOLTS

8oOo

I

101

I

BIAS

8500

WAVELENGTH

9ooo

9500

(8)

FIG.9. Reverse-bias tuning of GaAs NBSFD.

of the diode.25 Assuming minimal thermal effects, the 1OV reverse bias extends the. space-charge region approximately 180 p, or almost to the front surface of a 250 p thick device. Thus not only does the reverse-biased device lose its narrow-band response properties, but it becomes much more efficient in collecting the electron-hole pairs generated (due to the high electric fields in the space-charge region). It also shifts its peak response to the shorter wavelength in relative agreement with the data of Fig. 7.

f: Quantum EfJiciency Measurements The absolute integrated response was measured using a standard lamp calibrated by the National Bureau of Standards, and the quantum efficiency was calculated from the measurements. In computing the quantum efficiency the area under the spectral response curves was integrated and the response was assumed to be a constant, uniform value in the response band and zero outside this band. This leads to an effective width of the response band.

102

M . 9. PRINCE

At a wavelength of 9000 I% the standard lamp used had a spectral irradiance of 55.24 W/sr-nm-mm2 of source. It was assumed that the lamp had a constant irradiance over the narrow spectral band of the detector. This assumption led to slightly pessimistic values of quantum yields, since the lamp irradiance at the peak response wavelength of the detector is slightly lower than the above figure. The geometry of the system was controlled by placing suitable apertures between the lamp and the detector. Under the conditions employed the spectral flux density F falling on the detector was 23.9 x lo-'' W/cm2 A. The average quantum efficiency determined for a group of 50 gallium arsenide detectors was 22.9%. The average peak response wavelength for these diodes was 8870 A. g . Signal-to-Noise Datu

Noise measurements have been made on several NBSFD diodes made of gallium arsenide (0.89~).The diodes were shunted by a l-megohm load resistor R,, and the rms noise measured in the frequency interval between 1 and 2 kHz. There was no excess noise above the Johnson noise of the resistor R , when the diode was in the dark. When illuminated, the excess noise could be attributed to the shot noise of the current. Since iN2 = (4kTAf/R,)

+ 2ql A f ,

where i , is the noise current, k is Boltzmann's constant, Af is the frequency interval, I is the diode current (in this case, light generated), T is the absolute temperature, and q is the charge of electron.

This implies that the detectivity D*,or signal-to-noise ratio at the wavelength of peak response, is equal to the theoretical maximum multiplied by the square root of the conversion efficiency.26The above is correct as long as the lightgenerated current is large compared to the leakage current. When this relation does not hold, the shot noise term must contain the leakage current as a term in I . 8. TERNARY II1-v

MATERIALS-hAS,P,

-,

a . Material Preparation

The only method of crystal growth attempted was growth from the vapor phase by a halogen transport reaction in evacuated, sealed quartz capsules. 26

H. S. Sommers, Jr. and E. K.Gatchell, Proc. IEEE 54, 1553 (1966).

3.

NARROWBAND SELF-HLTERING DETECTORS

103

The solid solution was first prepared in fine-grained polycrystalline forms in one transport reaction. The resulting material was then used in subsequent crystal growth runs in a second quartz capsule. This method produced larger single crystals than could be obtained when the elements were used as the starting material. Four different halogen sources were used during the work : InCI,, HCl, C1, ,and I,. The use of I, proved most convenient, and all of the results given here refer to crystals grown with I2 added to the growth capsule. It was mentioned in connection with the GaAs results that the spectral response peak occurred at photon energies 0.05 eV greater than the band gap. This would indicate that a band gap of 1.12 eV would be required in order to have a response peak at 1.17 eV (1.06 p). O ~ w a l d found ,~ that the energy gap of solid solutions of InAs and InP varies linearly with the phosphorus concentration. It follows that the composition of the solid solutions should be InAso.lSPO.8s~ The quartz crystal growth capsules were 15 cm long, with a bore of 2 cm. A side arm leading through the capsule wall was used to facilitate the distillation of I, from a reservoir into the capsule. It was found experimentally that an iodine concentration of 3.6 x lo-' gm-atoms/cm3 yielded the best results. Higher concentrations led to excessive transport and nucleation at the temperatures used ; lower values made the transport rate unnecessarily slow. The growth capsule was sealed and loaded into a resistance-heated tube furnace. For crystal growth the furnace (and temperature gradient) was caused to move bodily with respect to the growth capsule. This was accomplished by mounting the furnace on a carriage driven by a lead screw, the combustion tube being independently supported. The rate of travel of the furnace in the early growth runs was 6mm/day, but this was later reduced to 2mm/day, the slower speed giving the better results. At the beginning of the run, the capsule was positioned in the hot zone such that the temperatures at its ends were the same, usually 910°C. The crystal growth was allowed to proceed for from two to three weeks, at the end of which time the source end would still be in the flat hot zone at 910"C, but the cooler end would be at a temperature from 885 to 895"C, depending on the time allowed for growth. These temperature differences, ranging up to 25", resulted in growths such as that shown in Fig. 10. The larger facets are planes of type { 111>.The circular spots on these facets are water spots; the capsules were broken open under water because phosphorus often condensed in the yellow form when a capsule was quenched. X-ray powder patterns revealed only one zincblende lattice, indicating that a single-phase solid solution was being obtained. The composition of the

*'

F. Oswald. Z . Naturforsch. 14a, 374 (1959).

FIG.10. InAs,P,-, crystal as grown.

solid solution (determined from the lattice constant on the assumption that Vegard’s law applied) did not, however, correspond with the weights of the elements used in the initial preparation. Vegard’s law for the solution InAs,P, --x has been verified by Folberth,” and it may be concluded that the ratio of As to P changed during the two transports (preparation and growth). It was found that the mole fraction of InAs invariably increased from the planned 15% to approximately 20%. This was borne out by the fact that the peak response of NBSFDs was correspondingly long. NBSFDs peaking at 1.06 p required the use of weights corresponding to InAso,,,Po,9, in the preparation runs. These weights could be used repeatedly to produce material of the same composition from one growth run to the next. The InAs, PI - crystals as grown were invariably n-type, although no doping agent was added. The residual impurity has not been determined. The small size of the crystals, several millimeters, precluded accurate Hall measurements, but resistivities of the material were of the order of 0.01 ohm cm. 6. Device Fabrication

P-n junction diodes were prepared from small chips cut from theInAs,P, - x crystals. The junctions were prepared by diffusion, and since the as-grown material was n-type, zinc was used as the diffusant. The zinc source was ZnAs,. In addition to the ZnAs,, small quantities of free arsenic and phosphorus were sealed in the evacuated quartz diffusion capsule to prevent out-

3.

NARROWBAND SELF-FILTERING DETECTORS

105

ENERGY (eV)

09

1.0

1.1

WAVELENGTH ( p ) FIG.11. Spectral response of InAs,P,-, NBSFD.

gassing of these elements from the InAs,P,-, wafers. The diffusion was carried on for two hours at 800°C. After diffusion the p-type layer was lapped off one surface. The chips were then mounted, diffused side down, on transistor headers. Gold-germanium eutectic alloy was used to contact the header, and a gold wire lead was bonded to the base layer. The diodes normally showed a reverse breakdown of 5 V or more at room temperature. c. Spectral Response Curves

Figure 11 shows the response of a typical InAs,P,-, NBSFD around 1.06 p with the radiation normally incident. The precise composition of the material has not been established, but the starting elements were in the ratios indicated by the formula InAs,, The crystal, however, is presumably richer in As, as discussed previously. Three different diodes fabricated of material from the same growth run had response peaks at 1.063p, 1.064 p , and 1.065p, all measured at 30°C. This variation may well be due to variations in base layer thickness rather than composition, since the base thickness was not precisely controlled. The half-widths of the InAs,P, - x NBSFD’s varied from 225 8, to 250 A when the radiation was normally incident.

d. Field-of- View Variations Off-axis response measurements also were made on three InAs,P, -, diodes. In one case the response peak shifted from 1.068p at normal incidence

106

M. B. PRINCE

to 1.070p at an angle of incidence of 75". This is negligible for most applications. In the other two cases the shift in the peak response wavelength was not measurable for 75" off-axis radiation. Similarly, changes in the halfwidth of the spectral response, if any, were within the experimental error of the measurement system for radiation from normal incidence to 75" off-axis. e. Tuning Techniques for InAs,P,

-x

Devices

As of this writing no data are available for clearly demonstrating the various fine tuning techniques for diodes made from InAs,P, -,. These would include junction depth variations, temperature variations, and reverse-bias variations.

f. Quantum EJJlciencyMeasurements The quantum efficiencies of a number of InAs,P, - x NBSFD's were also measured using the technique described for GaAs. The resulting efficiency percentages of five diodes were 12.6, 10.3,9.5, 18.6,and 32. These values were determined on diodes having no antireflection coatings. No attempt has been made to use antireflective coatings with the InAs,P, - x units. g . Signai-to-Noise Data

Measurements on these InAs,P, - x diodes were identical to those for the GaAs devices, except that the wavelength of interest was shifted to 1.06 p. There was no excess noise above the Johnson noise of the load resistor when the diodes were in the dark ;when illuminated excess noise could be attributed to the shot noise of the current. The diode peaking at a wavelength of 1 . 0 6 5 ~was measured in greater depth" and was found to have a detectivity of 2.1 x 10" cm Hz"' W that is flat over a frequency range from 20 Hz to 10 kHz at a temperature of 296°K for 1.05p incident radiation. IV. Summary

Using the data of Fig. 2, together with the total response curves of Figs. 3 and 4, one can calculate theoretical response curves for GaAs NBSFD's with Wvalues of 50 and 100 p. These curves, plotted in Fig. 12, compare favorably with the experimental curves of Fig. 7. The 50 p theoretical curve has its peak response at 8830b;, which compares with experimental curve number 3 (W 60 p) peaking at 8864 A. Similarly, the 100 p theoretical curve peaks at 8860 A, which compares with experimental curve number 2 (W z 125 p) peaking at 8890 A. The theoretical curves are extremely sensitive to the 28

D. Stierwalt, Naval Ordnance Laboratories, Corona. California (private communication).

3, NARROWBAND

107

SELF-FILTERING DETECTORS

WAVELENGTH

(A)

FIG.12. Calculated responses of GaAs NBSFD.

absorption coefficient data ;thus it is possible to calculate the latter data from experimental spectral response curves of NBSFD’s. As an example, this has been done by using curve 3 of Fig. 7 and the total response curve of Fig. 3, resulting in the circled points shown in Fig. 2. These data agree with the other experimentaldeterminations of the spectral variation ofabsorption coefficient. Table 111 compares experimental measurements for four typical GaAs devices with the theory developed in this chapter as a function of detector properties. The theoretical data for the first three devices are obtained from interpolation of Fig. 12, and the theoretical data for the last device derive from Eq. (7).As the quantum efficiency is increased, there is a shift in the peak spectral response to shorter wavelengths. Since the analysis matches with experiments for these GaAs devices, it should be possible to obtain semiquantitative estimates of diffusion lengths TABLE 111 COMPARISON OF EXPERIMENTAL RESULTSWITH PREDICTED RESULTS ~

FOR

~~~

GAASDEVICES

~~

~-

Response functions Detector parameters

2.8 2.0 2.0 2.0

50 90 90 250

Theory

Experimental

8861 8876 8872 8915

25 12.6 14.3 Not measured

8830 8855 8855 8900

15 8.9 8.9 3

108

M. B. PRINCE

in direct semiconductors by fabricating narrow-band detector structures and evaluating the peak spectral response shift as a function of base thickness. In employing the theory of Part 11, Section 1, care must be exercised in employing bulk material properties (such as the mobility in characterizing the device). Fabrication of a p-n junction in such materials usually produces some changes in this and other parameters for the base region. The theoretical data for the InAs,P,-, devices are not given, since the optical parameters for this material are not available.

ACKNOWLEDGMENTS Most of the efforts described in this chapter are the results of the work of a team of scientists at Electro-Optical Systems, Inc. in Pasadena, California. S. Kaye and D. B. Medved have conceived the concept of the class of devices: J. W. Burns has carried out the materials development: H. Flicker has contributed to fruitful discussions concerning some of the analysis: and L. Garasi and G. P. Rolik have been responsible for the fabrication of the devices. The author wishes to acknowledge and thank his colleagues for their contributions.

IV-VI and 11-VI Alloys

This Page Intentionally Left Blank

CHAPTER 4

Single-Crystal Lead-Tin Chalcogenides Iuars Melngailis AND

T . C . Harman I . INTRODUCTION

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. . . . . 2 . Materials Properties . . . . II . CRYSTAL PREPARATION . . . . 3 . Crystal Growrh . . . . . 4 . Annealing. . . . . . . 5 . Drffusion . . . . . . . 6 . Discussion . . . . . . I11 . PHOTOVOLTAIC DETECTORS . . . 7 . Theory . . . . . . . 8 . Experimental Results . . . IV . PHOTOCONDUCTIVE DETECTORS . . 9 . Sample Preparation . . . . 10. Lifetime . . . . . . . 1 1. Detectivity . . . . . . V . SUMMARY . . . . . . . . 1 . Band Structure

APPENDIXA . APPENDIXB .

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111 112 114 116 116 128

137

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142 144 144 151 163 163 165 169 170

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171 172

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. . . . . . . . . . . . . .

1. Introduction The binary semiconductors Pb. -.Sn. Te and Pb. _.Sn. Se have composition-dependent energy gaps which. according to the proposed band model. can be made arbitrarily small. The unique structure of the energy bands together with the ease in producing single crystals with excellent homogeneity and good quality has made these alloys particularly usefu1 for long wavelength infrared detectors as well as lasers. The purpose of this chapter is to review the present understanding of the band structure of these alloys. the materials’ properties and crystal preparation techniques. and the fabrication and properties of intrinsic infrared detectors .

212

IVARS MELNCAILIS AND T . C. HARMAN

I . BAND STRUCTURE The model for the energy bands in Pb,-,Sn,Te and Pbl-,Sn,Se was originally proposed’ to explain the variation of the energy gap with composition and with temperature in Pbl -,Sn,Te, which was inferred from laser emission at low temperatures,’’2 from optical absorption data at room t e r n p e r a t ~ r e , and ~ , ~ from the results of tunneling experiment^.^ According to the model, which to date appears to be consistent with all experimental results, the energy gap first decreases with increased Sn content as the conduction and valence band states (& and L6 +,respectively6)approach each other, goes through zero at an intermediate composition, and then increases as the states cross over and separate. The model for the bands in Pb, -,Sn,Te is represented schematically in Fig. 1. Since the L6+ and L6- states each have only a twofold spin degeneracy, the alloy can be a semiconductor on both sides of the crossover. This variation of the energy gap with composition can be explained on the basis of the difference in the relativistic effects’ in Pb and Sn. An estimate of the magnitude of the relativistic effects is in satisfactory agreement with the observed shift with composition of the L6+ and L6states.’ Figure 2 shows the variation of the energy gap with composition in

v SnTe

PbTe

V L6

AT E g = O

7-

t

E =0.18 eV 9

L i AND

FIG.1. Schematic representation of the valence and conduction bands at 12°K for PbTe, for the composition at which the energy gap is zero, and for SnTe. (After Dimmock et u L ’ )

’ J. 0.Dimmock, I. Melngailis, and A. J. Strauss, Phys. Rev. Letters 16, 1193 (1966).

’

J. F. Butler and A. R. Calawa, in “Physics of Quantum Electronics” (P. L. Kelley, 9. Lax, and P. E. Tannenwald, eds.), p. 458. McGraw-Hill, New York, 1966. P. M. Nikolic, Brit. J . Appl. Phys. 16, 1075 (1965). E. G. Bylander, Muter. Sci. Eng. 1, 190 (1966). L. Esaki and P. J. Stiles, Phys. Reo. Letters 16, 1108 (1966). J. B. Conklin, Jr., L. E. Johnson, and G. W. Pratt, Jr., Phys. Rev. 137, A1282 (1965). F. Herman and S . Skillman, “Atomic Structure Calculations.” Prentice-Hall, Englewood Clitfs, New Jersey, 1963.

4.

SINGLE-CRYSTAL LEAD-TIN

CHALCOGENIDES

0 LASER EMISSION

0.3

113

i4

0 TUNNELING

I

I

FIG.2. Energy gap of Pb,-,Sn,Te

as a function of x, the mole fraction of SnTe.

Pbl -,Sn,Te at 12°K and 77°K as determined from laser wavelength^,'^^^^^^ photovoltaic cutoffs," and from tunneling data for SnTe.5 In accord with the crossover of the two states, the tunneling experiment shows that the temperature coefficient of the energy gap in SnTe has a sign opposite to that in PbTe. On the basis of the difference between the relativistic shifts in Pb and Sn similar variations in band structure with composition could be expected in

n,L

0

LASER EMISSION

A PHOTOVOLTAIC

EFFECT

2

0.1

+--+it

&

PbSe 0.1

0.4

[r

w

5

0.4

12OK

FIG.3. Energy gap cf Pb, -,Sn,Se as a function of y, the mole fraction of SnSe.

J. F. Butler, A. R. Calawa, and T. C . Harman, Appl. Phys. Letters 9,427(1966).

' J. F. Butler and T. C . Harman, Appl. Phys. Letters 12,347 (1968). 'O

I. Melngailis and A. R. Calawa, Appl. Phys. Letters 9,304 (1966).

114

WARS MELNGAILIS AND

T. C.

HARMAN

the Pbl -,Sn,Seand Pb, -,Sn,S alloys with rock salt structure. In Pbl -,Sn,Se which can be grown with the rock salt structure" in the range 0 < y < 0.43, this variation has been demonstrated by means of laser and photovoltaic effects,13as shown in Fig. 3, as we11 as by optical absorption in thin filrns.l4The observation of laser emission out to a wavelength of 28 p in Pb, -.Sn,Te and to 34 p in Pbl - ,Sn,Se provides evidence that the energy gap remains direct at least down to 0.046 eV and 0.036 eV in the two alloys, respectively. In addition, the observation of laser emission in Pbl -,Sn,Se for a number of compositions in the range 0 < y < 0.3 provides evidence that the gap remains direct on both sides of the band inversion.'* in the range In Pb,-,Sn,S, which has the rock salt s t r ~ c t u r e ' only ~ 0 < z < 0.10, preliminary data of photoluminescence at low temperatures for z up to 0.05 are also consistent with a decrease in energy gap with increased Sn content. 2 . MATERIALS PROPERTIES Lead and tin combine with tellurium and selenium to form the binary compounds PbTe, PbSe, SnTe, and SnSe. There is no evidence for the formation of any other compounds in the cases of the Pb-Te, Pb-Se, and Sn-Te systems. PbTe, PbSe, and SnTe possess the cubic rock salt or NaCl crystal structure of type B1, whereas SnSe possesses the orthorhombic B29 structure. The temperature-composition phase diagram for PbTe is shown in the upper part of Fig. 4. According to the phase diagram a compound exists at very nearly the 50% chalcogenide composition. The composition range within which this compound can exist as a single solid phase is very narrow and is usually represented as a single line at 50 at. %. Although this solidus line is narrow in Pb and Sn chalcogenides, its width is very important because an excess of metal contributes electrons and an excess of chalcogenide contributes holes to the electrical conduction processes. The lower part of Fig. 4 is a schematic diagram of a greatly magnified solidus range of PbTe and Pbl _.Sn,Te. Single crystals of rock salt structure Pb,-,Sn,Te and Pb, _,Sn,Se have been grown by the Bridgman techniqueI6 and by a closedH. Krebs, K. Criin, and D. Kallen, Z . Anorg. Allgem. Chem. 312,307 (1961). T. C. Harman, A. R. Calawa, I. Melngailis, and J. 0. Dimmock. Appl. Phys. Letters 14, 333 (1969); also A. R. Calawa, J. 0. Dimmock, T. C . Harman, and I . Melngailis, Phys. Rev. Letters 23, 7 (1969). l 3 A. R. Calawa, I. Melngailis, T. C . Harman, and J. 0. Dimmock, unpublished work (1967); also Solid Slurp Res. Rept., Lincoln Laboratory, MIT (1967: 3), pp. 1-2, DDC 661275; (1967: 4). pp. 1-5, D D C 665465. l4 A. J . Strauss, Phys. Rev. 157,608 (1967). l 5 W. Albers, C. Haas, H. Ober, G. R. Schodder, and J. D. Wasscher, J. Phys. Chem. Solids 23, 215 (1962). l 6 A. R. Calawa, T. C. Harman, M. Finn, and P. Youtz, Tritns AIME 242, 374 (1968).

"

4.SINGLE-CRYSTAL

115

LEAD-TIN CHALCOGENIDES

1oo P b Te

L

200 0

Pb

20

I I I 60 80 ATOMIC PERCENT T E L L U R I U M 40

I 1O(

Te

n -TYPE (excess r n e t a l ) y ( excess Te) I

FIG. 4. The upper part of the figure is the binary phase diagram of Pb and Te; the lower part is a greatly expanded view of the Pb-Te phase diagram in the vicinity of the stoichiometric composition.

tube vapor-growth16process. Pbl -,Sn,Te crystals have also been grown by the Czochralski technique.” Although the as-grown carrier concentrations are of the order of 1019/cm3,carrier concentrations as low as 101S/cm3have been measured in crystals which have been extensively annealed. In the case of Pb, -xSn,Te,’8 n-type crystals with carrier concentrations in the 10’5/cm3 to IOl7/cm3 range have been achieved for x = 0.17 to x = 0.20, and p-type I’

J. W. Wagner and R. K. Willardson, Trans. A l M E 242,366 (1968).

’* 1. Melngailis and T. C. Harman, Appl. Phys. Letters 13, 180 (1968).

116

WARS MELNGAILIS AND T. C. HARMAN

carrier concentrations have ranged from 1015/cm3to 1020/cm3for the same values of x. For Pb, -ySn,Se,16 n-type crystals with carrier densities in the 1016/cm3to 10'9/cm3 range and p-type densities in the 1016/cm3to IO2'/cm3 range were prepared for y z 0.06. The carrier mobilities have ranged up to 800,000cm2/V-sec and 46,000 cm2/V-sec at 4.2% and 77"K, respectively. The combination of relativelylow carrier concentration, high carrier mobility, and low energy gap results in materials of special interest for intrinsic infrared detectors. The primary purpose of Part I1 will be to discuss the background information pertaining to materials preparation of the pseudobinary Pb-Sn telluride and selenide alloy systems with the rock salt structure. Some of the aspects of investigations in the areas of crystal growth, annealing, phase diagram studies, and electrical measurements will be discussed.

11. Crystal Preparation 3. CRYSTAL GROWTH

Early work on the vapor growth of PbSe was carried out by Prior.'' He used small chips of Bridgman-grown single crystals as the source material and frequently converted the whole charge of a few grams into one crystal. Zlomanov et d2' have prepared lead selenide single crystals weighing 15-30g from the vapor by a closed-tube method. In recent work' on Pb,-,Sn,Te and Pb,-,Sn,Se the following vapor growth technique was used. A schematic diagram of the special growth and diffusion-annealingampoule used to grow crystals and form junctions of the alloys is shown in Fig. 5(a). The fused silica ampoule consists of a tubular section about 1.8 cm i.d. and 14 cm long, tapered to a point at the bottom, and with three indentations about 4cm from the tip. The evacuated (lo-' Torr) ampoule is suspended it? a vertical tubular furnace, which has the temperature profile depicted in Fig. 5(b). In order to enhance the thermal stability of the system, a stainless steel liner is also inserted in the furnace. The temperature difference between the source material and vapor grown crystals was about 1°C. The temperature gradient is approximately 0.25"C/cm. The source material is prepared by placing a 100gm charge containing (metal),, (~halcogenide),,~,proportions or (metal)o~4,(chalcogenide),,. proportions of the as-received elements in chunk form in a 2.5 cm id., 15 cm long, high purity silica ampoule. After the ampoule is loaded it is evacuated C. Prior, J. Electrochem. Soc. 108,82 (1961). V. P. Zlornanov. 0. V. Matreev, and A. V. Novoselova, Zh. Neorgun. Khim. 10, 1753 (1 967) [Russ. J . Inorg. Chem. (English Trans].) 10, 957 (196511.

" A. 2o

4.

SINGLE-CRYSTAL LEAD-TIN CHALCOGENIDES

117

SOURCE MATERIAL

- 54

800

810

820

830

"C

(a 1

(bf

FIG.5. (a) Schematic diagram of special vapor growth and diffusion-annealing quartz tube (there are three indentations in the outer ampoule which are spaced 120" apart). (b) A section of the furnace temperature profile (the overall length of the vertically positioned furnace is 60 cm). (After Butler and Harman.')

with a diffusion pump and sealed. The sealed ampoule is placed in the center of a vertical resistance furnace. The region containing the ampoule is heated to about 5O"C.abovethe liquidus temperature for the particular composition used. After about four hours at temperature, the elements are reacted and the molten material homogenized. The ampoule is quenched quickly in water. The quenched ingot is crushed to a coarse powder for vapor-growth experiments, and to a fine powder for the isothermal annealing experiments which are discussed in a later section. The quenched coarse powder is contained in the inner quartz or source tube shown in Fig. 5, which has a 1.0cm id. and is 6.5 cm long. The crystals usually grow on the walls of the ampoule in the conical tip region. However, device grade crystals have grown also in the source tube. After a growing time of approximately 20 hours, the tube is air-cooled. Crystals with very smooth and highly reflecting (100) surfaces 1 mm2 or larger in area and of composition up to x = 0.27 for Pb, -,Sn,Te and y = 0.13 for Pb, -,Sn,Se have been obtained by this method. The rapidly cooled, as-grown crystals have bulk interior carrier concentrations which are given approximately by the points on the metal-saturated solidus lines (to be discussed in the section on annealing) corresponding to the growth temperature.

118

IVARS MELNGAILIS AND T. C. HARMAN

TABLE I SOME ANNEALING; PARAMETERS FOR

~

X

0.12 0.15 0.17 0.20 0.22 0.24 0.21

~~

JUNCTION FORMATION IN Pb, _,Sn,Te VAPOR-GROWN CRYSTALS ~

Annealing temp. ("C)

~-

450 450 450 400

-

~

Annealing time (days) None None 2 3 7 14

Annealing schedule: 4 hr at 7WC, 6 days at 650°C. 7 days at 450°C, and 21 days at 400°C.

N-type layers of thickness equal to or greater than 25 p were diffused by isothermally annealing the crystals in a horizontal furnace in the unopened growth ampoule and thus in the presence of the remaining source ingot. This method of preparing junctions utilizes the property16 that, at least for values of x up to x = 0.27, metal-saturated crystals change from p-type to n-type conductivity as the temperature is decreased. From isothermal metal-saturation experiments, type conversion temperatures for Pb, -,Sn,Te of 580,525, and 425°C are estimated for x = 0.17,0.20, and 0.27, respectively. For x < 0.27, annealing parameters for junction formation are given in Table I. For x = 0.27 the annealing schedule for preparing junctions was 4 hours at 700"C, 6 days at 650°C 7 days at 450"C, and 21 days at 400"C, giving an n-region approximately 30 p deep. Annealing studies indicate the surface electron concentration of annealed undoped Pb,,,,Sn,,2,Te to be < 1016/cm3.From the annealing schedules followed, we expect that the hole concentration in the p-type substrate will be less than the surface n-type carrier density for a distance beyond the n-p junction essentially equal to the junction depth. Hence p-n junction phenomena in these diodes may occur in a region of relatively low carrier concentration. Crystals have also been vapor-grown with the source material at various temperatures between 700 and 825°C using a 10gm powdered charge of various compositions. For Pbl -,Sn,Te with 0.16 < x < 0.20, p-type crystals were grown using metal-saturated source powders. After an air quench an n-type skin was observed on the crystal due to the preferential loss oftellurium from the surface during the cooling process. For x < 0.10, only n-type crystals were grown from metal-saturated sources. For metal-rich sources with x = 0.20, the following observations were noted: (a) for growth at 745"C, only a few spots on the crystals and the sintered source ingot were n-type;

4.

SINGLE-CRYSTAL LEAD-TIN CHALCOGENIDES

119

(b) for growth at 795"C,about 10% of the surface of the material was n-type; and (c) at 825"C, about 90% of the total material in the capsule possessed n-type layers on the surface. Long wavelength infrared diode detectors have been fabricated from these vapor-grown crystals using the junctions which were formed upon air cooling. The above procedure was used also to vapor grow Pb, -,Sn,Se crystals. However, the carrier concentrations achieved were about 10'9/cm3 p-type for y = 0.05-0.07. As discussed in Section 4, the high carrier densities are consistent with the solidus lines for this system. In order to achieve a low carrier density, the crystals were grown from the vapor in a two-zone system. For this case, the quenched powder and a selenium pellet are placed in a diffusion pump evacuated quartz tube. The powder is placed in a high temperature zone set at typically 825"C, while the selenium pellet is positioned in the low temperature zone at typically 220°C. Crystals up to 1 mm in length grow on the walls of the tube at intermediate temperatures. Room temperature thermoelectric power measurements have yielded values as high as 380pV/"K on the vapor-grown crystals for y N 0.05, corresponding to carrier concentrations of about 10' '/cm3. However, the electrical properties usually varied considerably from crystal to crystal. In the case of the selenide, p n junctions were not formed on cooling and could not be prepared without opening the quartz vapor growth capsule and replacing the metal-saturated powder with Se-saturated powder. A diffused p-type layer was produced by heating the crystals for I hour at 400°C with the vapor source of Se-saturated Pb, -,Sn,Se for y = 0.065. Single crystals of Pb-Sn chalcogenides have also been grown by the Bridgman techniqueI6 and have exhibited a surprisingly high degree of homogeneity in their Pb-Sn ratio. Electron microprobe analysis has shown that the Pb-Sn ratio is constant across the surface of crystal slices cut perpendicular to the growth direction, within the experimental error of the microprobe of Ax z f0.005. The'composition along the length 1 of a typical Pb,-,Sn,Te Bridgman-grown crystal varies from x = 0.127 for 1 = 0 to x = 0.140 for 1 = 5 cm. The Pb, -,Sn,Se Bridgman-grown crystals have exhibited the same high degree of P b S n ratio homogeneity as the telluride. The growth techniques used will now be described in detail. Alloy ingots are prepared by the Bridgman method from semiconductorgrade lead, tin, selenium, and tellurium obtained from commercial suppliers. For both the selenides and tellurides a 400 gm charge containing stoichiometric proportions of the as-received elements in chunk form is placed in a fused silica ampoule which has been coated with graphite produced by pyrolysis of acetone. The ampoule consists of a lower tubular section about 1.5 cm i.d. and 7.5 cm long, tapered to a point at the bottom, and an upper section of about 2.5cm i d . and 42.5cm long. A schematic drawing of the

120

IVARS MELNGAILIS AND T. C . HARMAN

1

MOTOR DRIVE (fcrn/day)

[ i

HEATERS

.

INGOT

CAPILLARY

FIG.6. (a) Schematic diagram of Bridgman crystal growing apparatus for Pb,-.Sn,Te and Pb, -,Sn,Se. (b) Temperature profile for growing crystals with a solidus composition of Pb,,,,Sn,,,,Te. (After Calawa et ~ 1 . ' ~ )

crystal growing apparatus and a typical temperature profile are shown in Fig. 6. After the ampoule is loaded, it is evacuated with a diffusion pump and sealed. In preparing the selenide alloys this ampoule is placed inside a fused silica protection tube (not shown in Fig. 6),which is flushed, back-filled with argon to a pressure of about 0.25 atm, and sealed. The protection tube is used to prevent oxidation of the ingot, since the inner ampoule usually cracks when the ingot is being cooled after solidification. A fused silica support tube is then sealed to the top of the protection tube. Protection tubes are not needed in preparing Pb,-,Sn,Te ingots, which do not crack the ampoules. For these ingots the support tube is sealed directly to the top of the ampoule. The sealed ampoule (with its protection tube, if used) is placed in a horizontal furnace setupwhich is obtained by butting two 60cm furnaces together, with the bottom of the ampoule near the center of the higher temperature furnace. To melt the charge, the center of the furnace containing the material is heated to about 50°C above the liquidus temperature for the particular alloy composition used. The liquidus temperatures,20a'2 along with the ZoaForPbl -,Sn,Te, the liquidus and solidus lines were drawn using the data of Table Ila and assuming symmetrical liquidus and solidus lines. 2 1 A. J. Straws, Trans. A I M E 242,354 (1968).

4.

121

SINGLE-CRYSTAL LEAD-TIN CHALCOGENIDES

8oo

t

700 I

0 PbTe

I

1

I

I

0.2

0.4

0.6

0.0

S

X

FIG.7. Temperature-composition phase diagram of the pseudobinary Pb, -,Sn,Te system. (After Calawa et d L b )

1100-

LIQUIDUS (after Strauss) W LT

3 W LL

SOLIDUS

a I

p

9001\

I

800 0

I 0.2

I

I 04

I

I 06

I

I

0.8

I 1.0

FIG. 8. Partial temperature-composition phase diagram of the Pbl -,Sn,Se system. (After Calawa el a l l 6 )

122

WARS MELNGAILIS AND T. C . HARMAN

TABLE IIa

LIQUIDCOMPOSITION, SOLIDCOMPOSITION, CARRIER CONCENTRATION, A N D HALLMOBILITY OF B R I D G M A N - G R O W N CRYSTALS OF Pb, -.Sn,Te ~~

~

~

Liquid composition x

First to freeze, solid composition

0.0 0.20 0.25 0.30 0.35 0.70

0.0 0.127 0.168 0.20 0.25 0.62

X

First to freeze, hole concentration at 77°K ( ~ m - ~ ) 3 3.1 2.8 2.4 1.2 3

x 10IS x 10i9 x 1019

10i9 x 10i9 x 10ZO

Hall mobility at 77°K (cm2/V-sec) -

940 1260 240 2740 60

TABLE IIb

LIQUIDCOMPOSITION,

SOLID COMPOSITION. AND CARRIER CONCf'NTRATION OF BRIDGMAN-

GROWNCRYSTALS OF Pb, _,Sn,Se

Liquid composition Y

0.12 0.13 0.14 0.16 0.18 0.40 0.50

First to freeze, solid composition Y

0.064 0.074 0.078 0.088 0.095 0.241 0.308

First to freeze, hole concentration at 77°K ( ~ m - ~ ) 3.9 1.8 2.2 4.2 5.2 3.2

x 10" x loi9

X

10i9

7

X

1019

1019 x 10i9 x 10"

Hall mobility at 77°K (cm'jv-sec) 220 1850 920 629 795 3820 260

solidus points determined in this work, are shown in Figs. 7 and 8 for Pbl -,Sn,Te and Pb,-,Sn,Se, respectively. It is-seen that the separation of solidus and liquidus lines is relatively narrow, particularly for Pbl -,Sn,Te. The center of the other furnace is simultaneously heated to about 50°C below the liquidus temperature. The furnace setup is then rotated into the vertical position, with the ampoule suspended in approximately the position shown in Fig. 6 by means of the support tube, which extends out of the top of the furnace. The furnace is generally rotated after it has been at the operating temperature overnight, but satisfactory ingots have also been obtained in several cases where it was rotated as soon as the operating temperature was reached.

4.

SINGLE-CRYSTAL LEAD-TIN CHALCOGENIDES

123

After the furnace is in the vertical position, the molten alloy is solidified directionally by slowly lowering the ampoule. Lowering rates in the vicinity of 1 cm/day are used. In some cases the entire ingot is frozen in this manner, while in others the furnace is turned off as soon as the capillary section of the ampoule is below the melting point. The alloy liquid composition, first-to-freeze solid composition, carrier concentration at 77"K, and the Hall mobility at 77°K are shown in Tables IIa and IIb for Pb, -,Sn,Te and Pb, -,Sn,Se. The ratio of tin content in the first-to-freeze solid to that of the liquid alloy composition is approximately 0.5 for Pb, -,Sn,Se and varies between 0.65 and 0.9 for Pb,-,Sn,Te. The solidus composition data for the two alloy systems are displayed in Figs. 7 and 8. The first-to-freeze solidus composition was measured with the electron microprobe. The liquidus composition was determined from the weight of the elements. The Hall coefficient R and electrical resistivity p of the crystals cut from the first-to-freeze section of the ingots were measured at 77°K. The electrical measurements were carried out by standard techniques using the van der Pauw configuration. A magnetic field strength of 6 kG was used for the Hall measurements. From the results of the electrical measurements the carrier concentration and carrier mobility were determined from n = 1/Re and p = Rip. From Tables IIa and IIb it is seen that the as-grown crystals are p-type with high hole densities. By analogy with work on the binary lead salt crystals, it is believed that the excess selenium or tellurium concentration of the Bridgman-grown crystals is greater than the hole carrier density due to the presence of electrically neutral selenium or tellurium microprecipitates. In some crystals, metal inclusions and low angle grain boundaries22 have been revealed by microscopic examination of samples electrolytically etched in a solution of 20 gm of KOH, 45 ml of H 2 0 , 35 ml of glycerol, and 20 ml of ethanol. This is a well-known polishing etch for PbTe.23 The samples are biased anodically and are thoroughly rinsed in distilled water after etching. The stirred etch solution is maintained at room temperature. At a current density of 0.5A/cm2 the Pb,-,Sn,Te crystal is polish-etched at a rate of approximately 30 ,u/min, while metallic inclusions, if present, acquire an orange film but otherwise remain intact. They remain as protuberances on the deeply-etched semiconductor surface. The lower half of Fig. 9 shows an extreme example of metallic inclusions in a Pb,,,Sn,,,Te Bridgman-grown crystal etched at the higher current density. The upper half of Fig. 9 shows a section of a second Bridgman-grown crystal without inclusions. It was etched using the same current density as for the crystal shown in the lower half of Fig. 9. The crystal containing inclusions was grown from a metal-rich 22

23

J. F. Butler and T.C. Harman J . Electrochem. Soc. 116, 260 (1969).

M.K.Norr, J . Electrochem. Soc. 109,433 (1962).

124

WARS MELNGAILIS AND T. C. HARMAN

melt with a metal/Te ratio of 0.506/0.494, whereas the inclusion-free sample was grown from a Te-rich melt with a metal/Te ratio of 0.49/0.51. The observed inclusions ranged in size from a few microns to over 0.1 mm in

FIG.9. The lower part of the figure shows an electrolytically etched sample of Pbo,,Sno,2Te containing an unusually large number of metallic inclusions. This is contrasted with the electrolytically etched section from an inclusion-free crystal shown in the upper figure.

4. SINGLE-CRYSTAL

LEAD-TIN CHALCOGENIDES

125

diameter. At a current density of approximately 0.05 A/cmZ the solution is suitable for obtaining dislocation density measurements or showing low angle grain boundaries. A photomicrograph of the surface of a specimen obtained near the first end to freeze of the Pbo,,Sno.2Tecrystal grown from the metal-rich melt is shown in Fig. 10. The sample was etched at the slower rate to reveal the low angle grain boundaries. Table I11 lists the presence or absence of metallic inclusions and low angle grain boundaries in several crystals of Pb,,,Sn,,,Te. Bulk metal

FIG.10. Photomicrograph of the surface of a crystal of Bridgman-grown Pbo.a%o ,Te from the first-to-freeze part of the crystal. The sample was etched using a current density of about 0.05 A/cm2 in order to produce the low angle grain boundaries.

126

WARS MELNGAILIS AND T. C. HARMAN

TABLE 111 PRESENCE O R

AHSENCE OF METAI I.1C INCLUSIONS AND LOW CRYSTALS OF Pbo,,Sn,.,Te Liquid composition

Technique

a

AN1iI.E

G R A I NBOUNI>AHIES IN

Bulk inclusions

Surface inclusions

Low-angle grain boundaries

Present Present Present Present Absent

Prcsent Present Present Present Present

Present Present Present Present Absent

Absent

Present

Absent

Source composition.

inclusions, when present, varied in number from essentially zero at the first end to freeze to a maximum at the opposite end of each crystal. The density of inclusions decreased as the composition was shifted to the Te-rich side. Surface inclusions were distributed rather uniformly over the exterior surfaces of the crystals. A second M0,49Te0,51 crystal was grown which was free of both bulk and surface inclusions. When present, the low angle grain boundaries were found throughout a crystal. The bulk metal inclusions and low angle grain boundaries are believed due to constitutional supercooling.The mechanism of constitutional supercooling has been previously used to explain cellular growth and other

t

STOICHIOMETRIC

I I

Te-SATURATED

METAL-SATUR~TED,~ SOLIDUS

(excess metal)

'I

I

SOLlDUS

(excess Te) c

COMPOSITION (excess metal or Tel

FIG.1 I . Schematic of the equilibrium phase diagram of Pbl _,Sn,Te near the stoichiometric composition. (After Butler and Harman.22)

4.

SINGLE-CRYSTAL LEAD-TIN

I

CHALCOGENIDES

127

INTERFACE DISTANCE (a)

TWO POSSIBLE ACTUAL TEMPE RAT URE GRADlE NTS

EQUILIBRIUM FREEZING POINT REGION OF INSTABILITY’

LIQUID-SOLID INT E R FACE DISTANCE

(b)

FIG.12. (a) Schematic diagram of the metal/Te ratio near the freezing interface of a growing crystal of Pbl -,Sn,Te. Here C L , C,, and Cs are the metal/Te ratios in the liquid far from the interface, in the liquid at the interface, and in the solid, respectively. (b) Schematic diagram of equilibrium freezing temperature variation near freezing interface, along with two possible gradients of the actual temperature and a region of instahility. (After Butler and Harman.z2)

defects in various crystal^.'^ In the case of a three component system such as the Pb-Sn-Te ternary system, we believe two kinds of constitutional supercooling are possible. One kind may be thought of as constitutional supercooling with respect to the Pb/Sn ratio and results from the relative buildup of SnTe at the liquidus-solidus interface. A second possible kind of constitutional supercooling may be thought of as constitutional supercooling with respect to the metal/Te ratio and will result in a buildup of excess metal at the liquidus-solidus interface of a growing crystal if the liquidus composition is richer in metal than the maximum melting point composition. The 24

See for example, W. Bardsley, J. S. Boulton, and D. T. J. Hurle, Solid-State Electron. 5, 395 (1 962).

128

WARS MELNGAILIS AND T. C. HARMAN

latter type is illustrated in Figs. 11 and 12. Figure 11 shows an idealized equilibrium phase diagram for Pb, -,Sn,Te near the stoichiometric composition. For x = 0.2 the maximum melting temperature is approximately 890"C, and intersection of the solidus line with the stoichiometric line occurs at about 525°C. Figure 12a shows schematically how the metal/Te ratio varies across the interface between the melt and solid of a growing crystal. The liquid buildup of the ratio at the interface depends on the growth rate and would be absent for an infinitesimally slow rate. The pertinent compositions are shown at the liquidus and solidus temperatures in Fig. 11. It is evident that the freezing temperature in the liquid will vary with position as a result of the varying metal/Te ratio. The variation of freezing temperature is shown schematically in Fig. 12(b). Also shown are two possible actual temperature gradients. For the less-steep line there is a region of instability where liquid is locally supercooled. Rapid quenching will occur in this region, causing spurious nucleation and leading to low angle grain boundaries. In addition, the rapidly quenched material should contain metal-rich liquid as a second phase at the higher temperatures and two solid phases at lower temperatures, i.e., Pbl -,Sn,Te and metal. The metal phase is manifested in the crystal as metallic inclusions. The qualitative explanation for the macroscopic defects suggests some practical methods of avoiding them. As may be seen in Fig. 11, C,, CL,and Cs are identical at the maximum melting point composition; hence growth from a melt of this composition will eliminate constitutional supercooling. We believe the Mo.49Teo,51 crystals mentioned previously were grown from a melt at approximately the maximum melting point composition. These were free of bulk metal inclusions and low angle grain boundaries. However, a detailed analysis of constitutional supercooling of a pseudo-binary material would require a rather complete knowledge of the ternary phase diagram since the PbTe/SnTe ratio, metal/Te ratio, and melting point change as an appreciable fraction of the melt is converted to solid. According to Fig. 12(b),constitutional supercooling can also be prevented by imposing a steep enough temperature gradient or by reducing the slope of the freezing ternperature curve by decreasing the growth rate. 4. ANNEALING In order to reduce the carrier concentration of as-grown material, the crystals must be annealed. In the case of Pbl -,Sn,Te, the isothermal annealing techniqueI6 has been found effective. For Pb, -,Sn,Se, the two-zone technique16 is used. The annealing techniques will not be described in detail. The Bridgman-grown crystals are sliced with a 1.25 x lo-' cm diameter nichrome wire saw using an abrasive slurry of light oil and 8 p silicon carbide powder. This technique was found to be less damaging than either using an

4,SINGLE-CRYSTAL

LEAD-TIN CHALCOGENIDES

129

abrasive wheel or spark-cutting techniques. By observing dislocation patterns formed by standard etching techniques as a function of distance from the crystal surface it was found that the wire-cutting damage extended to about 60p. To remove this damage, about 2 0 p were removed with a slurry of water and 6 p powder and 20 p removed with a slurry containing 4 ,upowder. For the Pb,-,Sn,Te crystals, the remaining 20p of damage was removed by polishing on a felt covered wheel saturated with a solution of 2gm of iodine crystals in 100 ml methanol. In the case of Pbl -,Sn,Se (or PbSe used in diffusion experiments described below), the remaining 20 p of damage was removed by polishing on a felt covered wheel saturated with a solution of 10 volumes ethylene glycol, 10 volumes KOH saturated in water at 25°C and 1 volume of H,O,. The surfaces appeared highly polished, but also had slight evidence of etch-pit formation. In general, unoriented crystals were used for annealing experiments, However, the smoothest surfaces were obtained on {loo} oriented crystals. It was found that a thin film on the surface of the crystals was formed during the chemical polishing. To ensure that the film was removed, the above procedure was followed by a very slight abrasive polishing using 0.2 p diamond dust wetted with methanol. The samples were then thoroughly rinsed in methanol before proceeding with the diffusions or annealing experiments. It is well known that excess lead and excess nonmetal defects introduce donor and acceptor levels, respectively, in the lead salts. The defect concentration can be altered by the isothermal annealing technique which was first used by Brebrick and Al1gaierz5on PbTe. The solidus lines on the metalsaturated side and chalcogenide-saturated side of the solidus fields of some Pb, -,Sn,Te and Pb, -,Sn,Se alloys have been studied. As described in detail below, the technique involves the equilibration under isothermal conditions of an alloy powder of known composition outside the solidus field with a crystal of arbitrary initial defect concentration. The small diameter, first-to-freeze part of the large 400 gm Bridgmangrown single crystals were cut into 4 x 12 x 0.75 mm parallelepiped-shaped wafers. The specimens were polished as described above to a typical thickness of 0.25mm and were sealed in quartz ampoules with the metal-rich (Mo,51Co.49)or chalcogenide-rich (M0,49C0.51) powder of the same Pb/Sn ratio. For annealing runs below 600°C the ampoules were evacuated to less than mm Hg. For runs above 600°C the ampoules were evacuated and backfilled with 300 mm of argon to minimize thermal etching of the specimens. In order to keep the powder and crystal wafers separate during heat treatment, two types of tubes have been used with equal success, One is a “shelf” tube consisting of a 2.3 cm 0.d. vial 7.5 cm long with a 5 cm long inner shelf 25

R.F. Brebrick and R. S. Allgaier, J. Chern. Phys. 32, 1826 (1960).

130

WARS MELNGAILIS AND T. C. HARMAN

situated toward one end of the tube. As many as eight wafers or as few as two small quartz test tubes of 5 mm i.d. each containing one sample are placed on the shelf and up to 10 gm of powder is placed below the shelf. The second is a “tube within a tube.” The outer tube has a 10 mm o.d. and is 7.5 cm long, whereas the inner tube, open at one end, has a 8 mm 0.d. with a 2.5 cm length. One crystal is placed in the inner tube and the powder is placed in the outer tube. The shelf tube is useful for the preparation of a large number of samples, whereas the second tube is more convenient for annealing one specimen. The crystals were annealed for various times at various temperatures and quenched in water. Usually, a surface layer up to 25 1.1 deep of higher concentration n-type or lower concentration p-type formed on cooling, which was removed before carrying out electrical measurements. Electrical resistivity, Hall coefficient, and Seebeck coefficient c( were measured on the annealed samples. A commercial liquid metal alloy containing Hg, In, and Te was used to attach the copper lead wires to the sample for the electrical resistivity and Hall coeficient measurements, whereas pressure contacts were used for the Seebeck-coefficient measurements. In the case of only partially equilibrated specimens, it has been found that the carrier concentration calculated from the Hall coefficient is largely determined by the carrier type and concentration of the outer or surface regions of the sample, whereas the carrier concentration estimated from the Seebeck coefficient is a weighted average of the entire bulk. Samples are judged equilibrated if the carrier concentration calculated from the Seebeck coefficient and Hall coefficient measurements are in approximate agreement. In the several cases checked thus far, agreement has been obtained with Henry’sz6 diffusion result that for Dt/hz 2 1 (where D is the diffusion coefficient, t is the time, and h is the thickness of the sample) equilibration is obtained and no measurable macroscopic inhomogeneity is present. The details of diffusion experiments in these materials are considered later. The results of isothermal annealing experiments on the metal-rich side of the Pb, -,Sn,Te solidus field are shown in Table IV for x = 0.13,0.17,0.20, and 0.27. The results are also displayed graphically in Fig. 13. At 77°K the electron carrier mobility ranges up to 40,000 cm2/V sec whereas the hole mobility ranges up to 30,000 cmZ/V sec. By annealing for various times, these samples were shown to be equilibrated. It should be noted that the solidus field for Pb, -,Sn,Te shifts considerably toward the tellurium side of the stoichiometric composition with increasing SnTe content in the alloy. This has resulted in at least three significant differences in the device fabrication process from that for the binary PbTe. First, the metal-saturated edge of the solidus field crosses the stoichiometric composition at reasonably low

’‘ P. S. H . Henry, Proc. Roy. Soc. (London)171,231 (1939).

4. SINGLE-CRYSTAL

131

LEAD-TIN CHALCOGENIDES

TABLE IV RESULTSOF ISOTHERMAL, METAL-RICH, SATURATION ANNEALING OF Pb, -,Sn,Te Sample temp. ("C)

Annealing time (days)

thickness (mm)

Composition x 750 700 650 600 650 550 650 525

4 2 5 8

I 4

0.30

6.2 x 1OZ7(P)

0.27

3.5 x 10'7(P)

14

10 14 23

x

10'9(P)

x 1oi9(p) x lO'*(P) x 10IH(P)

= 0.20

7.7 x 10'8(P) 1.7 x 10i8(P) 1.1 x 10'8(P) 6.4 I O ~ ~ ( P ) 4.8 x 1 o t 7 ( p ) 2.7 x 1oi7(p)

0.26 0.25 0.29 0.27 0.25 0.28 0.27

23 6:

)

0.28 =

9.2 x 10I6(N) 0.17

4

0.25

3.8 x lO"(P)

7

0.26

2.2 x 10'8(P)

1.0 0.23

6.5 x lo'? (P) 2.6 x 1 o i 7 ( p )

0.25

7

10 13

10 14 4}

ComDosition 750 750 700 750 680 750 650

0.27 2.5 I 3 1.5

Composition x 750 750 700 650 600 650 575

=

~~~

Carrier concent rat ion" (cmO3)

0.56 0.31 0.30 0.30

Composition x 750 650 625 600 590 565 750 650 550 650 500

-

~~

~

Sample

.Y =

x 10i6(N)

0.13

5

0.25

2.2 x 10'8(P)

'>

0.25

9.5 x lO"(P)

0.28

3.4 x 1oi7(p)

0.28

2.1 x 10'6(N)

10

:>

132

IVARS MELNGAILIS AND T. C. HARMAN

TABLE IV (continued) Annealing time (days)

Sample temp. (“C) 7 50 650 600 a

Carrier concentration” (~m-~)

Sample thickness (mm)

2.3

0.28

x

10”(N)

P represents p-type, N denotes n-type specimens, 77°K.

temperatures, making it possible to obtain both p - and n-type low carrier concentration material by the relatively simple and more easily controlled isothermal annealing procedure. Second, the metal-saturated solidus line does not appear retrograde with respect to concentration (i.e., the concentration becomes more n-type, or less p-type, as the temperature is reduced), at least in the temperature range where device diffusions are feasible. This greatly reduces the probability of metal precipitation during quenching. In the third place, n-p junctions can be made by metal-saturation annealing the

,~~~~ 750

Temperature (“C)

700

550

600

670

0

A 0

57

x = 0.i3 ~2017 X’O.20 x = 0.27

-p-tw

_._. n-type

-0

b 10’6

0 95

I 4 05

I

i15

I25

lo3/T -K FIG.13 Carrier concentration at 77°K as a function of isothermal annealing temperature for metal-saturated Pb, _,Sn,Te.

4.

SINGLE-CRYSTAL LEAD-TIN

CHALCOGENIDES

133

material to p-type above the stoichiometric crossover, then reducing the temperature to below the crossover, where the n-diffusion takes place. If the sample were first annealed n-type followed by a tellurium-rich isothermal diffusion, the p-side of the resulting p-n junctions would have an extremely high surface-hole concentration (- 1019/cm3 for a diffusion temperature of 400°C). Thus it appears that the rather peculiar shape of the solidus field may prove advantageous in forming p-n junctions for device use. The results of the tellurium-rich saturation annealing experiments are shown in Table V and in Fig. 14. It is seen that the hole carrier concentrations are very large. At the higher temperatures there is evidence that the quenching was too slow to avoid precipitation. As seen in Table V, the equilibration times are relatively short. This results from the relatively fast effect of precipitating out a second phase of Te, which does not contribute charge carriers TABLE V

RESULTSOF

ISOTHERMAL,

Sample temp. (“C)

TELLURIUM-RICH, SATURATION ANNEALING OF Pb,_,Sn,Te

Annealing time (days)

Sample thickness (mm)

Carrier concentrationo (cm-’)

ComDosition Y = 0.27 0.30

1.4 x lo2’

550

0.29

1.4 x 10’’ 1.4 x 10’’

500 450 400

0.19 0.30

650 600

0.31

9.5 1019 6.9 loi9 5.1 x 10”

Composition x = 0.20 0.28

650 600 550 500

0.18

0.30 0.18

1.4 x 10’’ 1.2 x lozo 1.05 x 10’’ 7.0 x 1 0 1 ~

Comoosition x = 0.13 650 600 500 450

1 2 3 3 7

400 600 350 600 300 ~

‘p-type specimens. 77°K.

0.27 0.26

0.28

8.8 x loi9 7.2 x 10” 4.5 101~ 3.0 10i9 2.1 x 10lY

0.31

1.1 x 1019

0.33

6.2 x 10”

~

134

WARS MELNGAILIS AND T. C. HARMAN

to the crystal. Thus the measured carrier concentration is directly proportional to the amount of excess Te dissolved in the Pb, -,Sn,Te lattice. Due to the very high rate of precipitation, the tellurium saturation concentration above about 550°C is expected to be even larger than the measured values of carrier concentration shown in Fig. 14 for x = 0.20 and x = 0.27. Isothermal annealing experiments were also performed on the Pb, - ,Sn,Se system. Results for y = 0.07 are summarized in Table VI and in Fig. 15. It is seen that high concentration n-type material is obtained by metal-rich isothermal annealing, whereas high concentration p-type material is prepared by selenium-rich isothermal annealing. In these experiments a concerted effort was made to quench the samples rapidly enough to prevent appreciable precipitation. Thc samples were placed in intimate contact with the exterior wall (bottom) ofa flattened ampoule. The ampoule was suspended in a vertical muffle furnace by a nichrome wire. After saturation the wire was cut and the ampoule fell into a salt brine cooled to 0°C. Since the results shown in Fig. 15 are consistent with the usual exponential behavior, further evidence for equilibration is indicated. In order to obtain material with low defect and low precipitate concentrations, experiments were carried out using the two-zone annealing technique. Temperature ("C) 400

650 600

300

0 0

x.013 x = 0.20

-20

I 1.05

1

1

1.25

I

I

1.45

1 1.65

i03/T O K

FIG.14. Carrier concentration at 77°K as a function of isothermal annealing temperature for Te-saturated Pb, -,Sn,Te.

135

4. SINGLE-CRYSTAL LEAD-TIN CHALCOGENIDES TABLE VI RESULTSOF ISOTHERMAL SATURATION ANNEALING EXPERIMENTS FOR Pb I .,Sn,Se Sample temp. (“C)

Annealing time (days)

Thickness (mm)

Metal-rich, y 750 700 650 650 600

550 550 550 500 450

=

0.065

3

1

1 5

0.25 0.9 0.25 0.25 0.26 0.26 0.5 0.5 0.54

2 5 4 4 13 32 365

Selenium-rich, y

=

7.2 8.5 4.1 4.8 4.1

x 10l8(N) x 10”

(N)

x lO’*(N) x 10i8(N) x

10’*(N)

1.9 x 10’*(N)

1.8 x 2.1 x 6.6 x 7.1 x

10’’ (N) 10‘8(N) IOi7(N) 10’7(~)

0.07

0.30 0.30 0.26 0.26 0.25

700 650 550 500 450

Carrier concentrations (~m-~)

6.5 x lO”(P) 6.5 x 101’(P) 6.1 x 1019(p) 4.5 x 1o19(p) 4.4 x lO”(P)

N indicates n-type specimens, P indicates p-type. 77°K.

The carrier concentrations discussed in this section were determined from the Hall coefficient. It is also possible to calculate the carrier concentration in the following manner from Seebeck coefficient measurements for samples in the extrinsic conduction region (for n or p > 1 x at 300°K). For the case of polar scattering due to optical p h o n o n ~ ~ ~ CI

= -86.3[(3FJ2F,) - U , ] ,

where F2 and F , are Fermi-Dirac integrals and UF = EF/kTis the reduced Fermi level energy relative to the band edge. Upon determining UF from the above expression using measured values of CI the carrier concentrationz7 is calculated from n = 4n(2m,*kT/h2)3‘2Fl,2(UF), where the density-of-states effective mass md*is estimated from PbTe values. The agreement in carrier concentrations calculated from measured values of 27

See for example, T. C. Harman and J. M. Honig, ”Thermoelectric and Thermomagnetic Effects and Applications.” McGraw-Hill, New York, 1967.

136

IVARS MELNGAILIS AND T. C. HARMAN

with the carrier concentrations calculated from measured values of Hall coefficient is satisfactory and verifies the homogeneity of the crystals annealed above 600°C. The two-zone annealing of Pb, -,Sn,Se was carried out by controlling the vapor pressure of selenium or of the metal in a second temperature zone. It was shown that the two-zone technique yields a lower carrier concentration in Pbl-,Sn,Se at a given temperature than can be achieved by isothermal annealing. Thus useful crystals for device studies should result when the composition within the solidus field is properly adjusted. Our best results with regard to low carrier concentration and high mobility are given in Table VII. It is seen that carrier concentrations are lower and carrier mobilities are generally higher than the corresponding values obtained by isothermal annealing. However, at present the two-zone annealing results for the lower c1

Temperature

iOZ0

t

0.9

750 [ I

("C)

550

650

450 I

I

Selenium-saturated, y

= 0.07

I

I

I

t .3

1.1

1.

{O~ITOK

FIG.15. Carrier concentration at 77°K as a function of isothermal annealing temperature for both metal-saturated and Se-saturated Pb, -,Sn,Se.

4,SINGLE-CRYSTAL

137

LEAD-TIN CHALCOGENIDES

TABLE VII TWOZONEANNEALING OF BRIDGMAN-GROWN Pb,,,,Sn,,,,Se Sample temp. (“C)

Selenium temp. (“C)

Annealing time (days)

Sample thickness (mm)

650 650 592 550 500

160 170 149 I30 100

6 3.2 5.7 13 15

0.44 0.50 0.47 0.23

1 .o

CRYSTALS Carrier concentration“ (cm-,) 2.9 9 1.5 1.5 5

x

1017(~)

x 10’6(P) x 10i7(~) x

x

1oi7(p) 10’6(P)

N indicates n-type specimens, P indicates p-type. 77°K

carrier concentration material (c5 x 10”/cm3) have been difficult to reproduce. 5 . DIFFUSION Early work on interdiffusion in the lead salt crystals was carried out by Brebrick and Scanlon.28 Natural n-type PbS crystals were exposed to sulfur vapor of various pressures at about 500°C and then quenched. An interdiffusion constant of 2 x 10-6cm2/sec at 550°C was calculated from the various pn junction depths and diffusion times. An investigation of interdiff~sion‘~ in PbSe and Pb, - ,Sn,Se was initiated in order to establish some useful diffusion parameters necessary to fabricate p-n junction devices in a controllable manner. Detector fabrication requires obtaining shallow junctions with both p - and n-type diffused layers and some knowledge of the impurity concentration and profile in these layers. The same is true for the fabrication of diode lasers, except for the possibility of requiring deeper junctions. Also, since the saturation annealing process is a diffusion process, it is possible to calculate minimum times required for the samples to reach equilibrium in the annealing experiments if the related interdiffusion coefficients are known. The method used to study the interdiffusion process was to form a p-n junction in a crystal and to measure its motion as a function of time and temperature. The experiment is identical to the isothermal annealing experiments except that the sample has a known initial concentration which is opposite in type to that of the source powder, and the diffusion times are long enough to convert a layer of the sample to the opposite conductivity type, but not long enough to convert the type of the entire sample. The boundary value problem is then one of diffusing from a constant source C, into an isotropic medium having an initial concentration C o . If the material is thick

** R. F. Brebrick and W. W. Scanlon, Phys. Rev. %, 598 (1954).

138

IVARS MELNGAILIS AND T. C. HARMAN

enough to be considered a semi-infinite medium, i.e., the concentration Co in the center of the sample remains essentially unchanged after the diffusion, then the solution to this problem may be ~ r i t t e n * ~ , ~ ”

where C(X,t) is the net concentration of charge carriers at any distance from the sample surface x at a time t , and D is the diffusion coefficient. The p-n junction occurs where C(x, t ) = 0. Since Co is opposite in type to the surface concentration C,,C, is taken to be a negative quantity. To obtain an accurate value of C,, the samples are isothermally annealed to a known uniform concentration. Considerable care was taken to process the as-grown samples in such a manner as to minimize or eliminate precipitates in the crystal to be diffused. Since the diffusion depth is determined by the total density of excess metal or excess chalcogenide present in the P b S n chalcogenide crystal lattice as well as in microprecipitates rather than only the excess atoms dissolved in the P b S n chalcogenide lattice, C, was determined for samples in which the density of precipitates was believed to be negligible. For p-type substrates the p-type as-grown crystals were isothermally annealed and equilibrated initially in the presence of metal-saturated vapor and subsequently isothermally annealed and equilibrated in the presence of chalcogenidesaturated vapor. For n-type substrates the as-grown p-type crystals were isothermally annealed and equilibrated only in the presence of metal-saturated vapor. For diffusion under isothermal conditions C, is the saturation concentration at the diffusion temperature. Since the annealing time is proportional to the square of the sample thickness, it is desirable in this respect to use as thin a sample as possible. As is shown below, the diffusion coefficients can be large, and with thin samples (thickness of 0.2 to 1.0 mm) the approximation of a semi-infinite solid is not always valid, and diffusion from opposite boundaries of the sample must be considered. The solution in this case is given C(X, t ) -

co = (C,- C,) ‘

29 30

”

“p[

-(2k

]

+b21)2n2Dt

sin

(2k

+ 1)nx

R. F. Brebrick, J . Appl. Phys. 30,811 (1959). J. F. Butler, J. Electrochem. Soc. 111, 1150(1964). B. I. Boltaks, “Diffusion in Semiconductors,” p. 112. Academic Press, New York, 1963.

(4)

4.

SINGLE-CRYSTAL LEAD-TIN CHALCOGENIDES

139

where k is an integer and b is the sample thickness. For Dt/bz > 4.5 x the first term of the rapidly converging series can be used with a resultant error of less than 1% in C(x,t).31 For this case, Eq. (4) reduces to C(x,t)

- c,

cs - c o

n

In our isothermal annealing experiments, where we used Dt/b2 = 1, at xJb = 0.5, C(X,t ) = O.99993Cs. As noted above, Eq. (3) can be used if C(x,t ) = C, at x / b = 0.5. This condition is satisfied within less than 1 % error if Dt/h2 < 0.015. The function in braces in Eq. (4) has been tabulated" as a function of x/b for different values ofthe parameter Dt/b2. Both Eqs. (3) and (4) are derived using the assumption that D is independent of concentration. The following procedure, although referred to PbSe, is applicable to Pb,-,Sn,Se. The sample preparation procedures are the same as for the isothermal annealing experiments. For PbSe diffusions the source of excess lead or selenium is prepared by mixing the elements using Pbo.51Seo,49 or Pbo,49Seo.51 and placing them in a quartz tube which is evacuated, sealed, and heated to 1050°Cfor one hour. The elements used are 0.99999 pure Se and 0.999999 pure Pb. Upon removal from the furnace the tube is quenched in water. A 4 g m piece of the ingot is crushed into fine powder immediately before it is placed into the diffusion ampoule. The diffusion ampoule is the same as the shelf tube previously described. The small inner tubes mentioned in the annealing section were not used for these experiments. The diffusions were performed isothermally in a temperature zone controlled to within 1°C. The junction depths were determined using a thermoelectric microprobe. To magnify the probed region and improve the resolution, the diffused samples were lapped at an angle of 3.82" relative to the diffused surface. This provided a magnification of 15 :1. Using a micromanipulator to position the probe it was possible to determine junction depths to within 1 p. Thermoelectric measurements were made both at 300 and 77°K. For the short, high temperature diffusions no difference was found in the junctiondepth measurements made at 300°K and those made at 77°K. The junction in these cases was considered abrupt. For the diffusions which resulted in a more gradual change from p-type to n-type a difference in junction-depth measurement of as much as a factor of two was observed in going from 300 to 77°K. The reason for this is that the number of intrinsic carriers in the lightly doped regions is comparable to the extrinsic carrier density at 300"K, and since the electron mobility is greater than the hole mobility, a lightly doped p-type region appears n-type. The 77°K junction-depth measurements were used in our determinations of the diffusion coefficients.

+

140

IVARS MELNGAILIS A N D T. C. HARMAN

To calculate the diffusion coefficient D, it is important to have accurate values of initial excess-metal or nonmetal concentration Co in the sample and the surface concentration C , , which is the solubility limit of excess lead or selenium in PbSe at the diffusion temperature. The resultsI6 of several saturation experiments are shown in Fig. 16. The saturation values on the Pb side of the solidus field are in good agreement with the values of Brebrick and Gubner.j2 However, the selenium saturation values are somewhat higher. As was pointed out by Brebrick and G ~ b n e r , ~precipitation ’ of the excess selenium occurs much more rapidly than that of excess lead. Consequently, to keep the selenium from precipitating out of lattice sites, it is necessary to establish a special rapid-quenching procedure. In fact, it has been observed that there is a limiting temperature above which samples cannot be quenched without internal p r e ~ i p i t a t i o n This . ~ ~ temperature is dependent on the thermal conductivity, heat capacity, and dimensions of the

700 I

_

c

l

’

TEMPERATURE (“c) 50C 400

600 l

I

I

I

12

I

I

I

I

I

I 14

I

1

16

IO~/TOK

FIG.16. Carrier concentration at 77°K as a function of isothermal annealing temperature for Se-saturated and Ph-saturated PhSe. (After Calawa ef 32 33

R. F. Brebrick and E. Guhner, J . Chem. Phys. 36,170 (1962). W . Albers, C . Haas, and H. J. Vink, Philips Res. Rep. 18,372 (1963).

4. SINGLE-CRYSTAL

141

LEAD-TIN CHALCOGENIDES

sample. The method used for quenching in these experiments was the same as that used for Pbl -,Sn,Se saturation annealing experiments. The surface concentrations C, for all of the diffusions were taken from the saturation curves shown in Fig. 16. The concentration values given in Fig. 16 were obtained from Hall measurements at 77°K. To ensure that the initial concentration Co was accurately known, the samples used in the diffusion experiments were saturation-annealed and quenched in the manner described above. Figure 17 is a plot of the diffusion coefficients versus 103/T.The diffusion coefficients can reasonably be described by a normal exponential dependence on temperature. However, note that there is about an order-of-magnitude difference between the diffusion coefficients for diffusing from an excess selenium vapor into lead-saturated PbSe and those for diffusing from an excess lead vapor into selenium-saturated material. This suggests that the diffusion coefficient for this interdiffusion process may be dependent on the carrier concentration. In the diffusion from the metal-rich vapor into p-type samples, two different sample concentrations were used, 5.4 x lo1' and TEMPERATURE ("C) 600

-12

500 I

I

I 13

400

0

I

I

I

I

I

1.5

!

I 17

~O~/TOK

FIG. 17. Temperature dependence of interdiffusion coefficients for PbSe. (After Calawa et a/.'6 ,

142

WARS MELNGAILIS AND T. C. HARMAN

1.5 x 10i9/cm3.At least in this concentration range the diffusion coefficient was insensitive to concentration changes. For the n-type substrates, only the 5.7 x 10'8/cm3 concentration was used. The slopes for the two types of diffusion are very nearly equal and correspond to an activation energy of approximately 1.15 eV. It should be noted that in the course of these experiments several anomalous nonreproducible results were obtained. These results were attributable to three principal factors : (1) a surface film acting as a diffusion barrier, (2) a nonuniform source ingot, and (3) lack of knowledge about the probable absence or presence of metal or selenium internal precipitates in the substrate material. Diffusion experiments were performed in Pb,,,,Sn, o,Se in the same manner as that described for PbSe. The surface concentrations C, were taken from an extrapolation of the saturation curves shown in Fig. 15. For the diffusion of excess selenium into n-type Pb, 93Sn,,,,Se two substrate concentrations were used, n = 4.8 x 1018/cm3and n = 9.2 x lOl8/crn3. Both groups of samples were obtained by isothermal saturation annealing. The diffusion coefficients derived from these interdiffusion experiments are shown in Fig. 18. These preliminary results indicate that the interdiffusion coefficients are smaller than the corresponding coefficients for PbSe in the temperature range studied, but that the activation energy is larger. In view of the scarcity of selenium saturation data for Pbo,93Sn,,,Se it is quite possible that the temperature dependence of the selenium saturation concentration is different from that shown in Fig. 15. Since the slope of the curve in Fig. 18 is very sensitive to changes in the temperature dependence of C,, the extrapolation used to obtain C, at the lower temperatures could possibly explain the difference in diffusion activation energy. For diffusing from excess metal into p-type Pbo.93Sn,.07Se preliminary results indicate that the diffusion coefficients are smaller than those shown in Fig. 18. This is consistent with the PbSe results. 6 . DISCUSSION It is concluded that very large single crystals of Pbl-,Sn,Te and Pbl -,Sn,,Se of a predetermined composition with a high degree of homogeneity can be grown by the Bridgman technique. High quality single crystals of Pb,-,Sn,Te and Pbl-,Sn,Se, which exhibit (100) facets, can be grown from the vapor phase. Single crystals of Pb,-,Sn,Te can be grown by the Czochralski or pulling technique. The high carrier concentration samples, which are obtained by melt-grown methods, must be annealed under rather stringent conditions in order to obtain device grade material. In order to achieve the low carrier concentration crystals, which are required for photoconductive devices, Pb, -,Sn,Te can be annealed by the

4.

SINGLE-CRYSTAL LEAD-TIN

143

CHALCOGENIDES

TEMPERATURE ( " C ) 0

FIG. 18. Temperature dependence of interdiffusion coefficients for Pb,~,,Sn,,,,Se. (After Calawa et ~ 1 . ' ~ )

isothermal one-temperature-zone technique, whereas Pb, - ,Sn,Se requires the two-temperature-zone technique. The latter method is inherently more difficult to control. A second advantage of the Pb, -,Sn,Te system is that the melting points are lower and hence the possibilities of foreign-impurity contamination are diminished. A third advantage is that the separation between the liquidus and solidus curves is less for Pb, -,Sn,Te than for Pb, -,Sn,Se. Thus the possible effects of inhomogeneities with respect to the Pb/Sn ratio due to constitutional cooling should be reduced. Calculated diffusion parameters are quite useful for annealing and device studies. However, the absolute values of the diffusion coefficients must be regarded as tentative for the following reasons. The concentrations Co and C , were calculated assuming Co or C , = l / R e , where R is the Hall coefficient measured at 77°K and e is the electron charge. Actually, n or p = ?-/Re,where I is a complex function dependent on the anisotropy of the band or bands, the charge carrier scattering mechanism, and the Fermi level. Usually, r is

144

WARS MELNGAILIS AND T. C . HARMAN

near unity, but it can range from approximately 0.5 to 2.0. In addition, we have assumed that one hole or electron is equivalent to one defect, i.e., n or p = C. The ratio of carrier density to defect density is not established in these materials. At very low carrier concentrations, the carrier density is determined in part by foreign impurity atoms. Excess metal or selenium present as a second phase in the form of precipitates does not contribute charge carriers to the conduction processes in the crystal. Since the presence of the precipitates does affect the motion of the p-n junction, it is important to heat treat the sample so that one type of precipitate is absent and the other type is of known density. In the vicinity of the p-n junction, where the net carrier concentration is low, the carrier density due to foreign impurities may be sufficiently greater than the defect concentration, and may significantly influence junction depth measurements. Foreign impurities may also affect the temperature at which the carrier type changes sign in the isothermal annealing experiments in Pb, -.Sn,Te. However, this effect would be small, since the active foreign-impurity density level is most likely below 101'/cm3. It is concluded that there is a significant degree of uncertainty associated with the determination of defect density from electrical measurements. 111. Photovoltaic Detectors

7. THEORY The most widely used photovoltaic detector consists of a shallow p-n junction formed by diffusion. The incident radiation is directed normal to the plane of the junction as shown in Fig. 19, and is absorbed in a thin layer adjacent to the surface, typically 1 p thick in the case of direct-gap semiconductors. The photoexcited carriers diffuse toward the p-n junction where, in the open-circuit case, they produce a change in the junction potential as a result of an increase in the minority carrier density on both sides of the junction. If the junction is externally shorted, a photocurrent flows such that the minority carrier densities on each side of the junction change back to their equilibrium values and the external junction voltage is reduced to zero. In case of reverse bias the photocurrent adds to the normal reverse diode current. The open-circuit case will be of primary concern here. In the design of sensitive photovoltaic detectors it is important that as many as possible of the photoexcited carriers reach the p n junction. This is synonymous with the requirement of a low recombination velocity at the front surface and a junction depth (distance from the surface) which is smaller than the diffusion length of the carriers. In order to maximize the open-circuit photovoltage, it is also important to maximize the incremental resistance of the junction. As shown below, the sensitivity of a photovoltaic detector can be completely specified by two parameters, the efficiency q, defined as the number of carriers reaching the junction per incident photon, and the incre-

4. SINGLE-CRYSTAL

LEAD-TIN CHALCOGENIDES

145

RADIATION

n JUNCTION

P

FIG.19. Structure of a photovoltaic detector.

mental junction resistance R. Since the subject of most interest here is the optimization of detector parameters, we shall assume the absence of any background radiation, both as a noise source and as a source of bias on the detector. An analysis of photovoltaic detectors subjected to background radiation is given elsewhere.34 The questions to be answered are: In the absence of background radiation what is the maximum detectivity obtainable at any temperature and wavelength, and what determines the speed of response? a. Detectivity

The current in a diode detector I , can be expressed as the sum of a photocurrent I , and a current I ( V )which flows in the absence of incident radiation as a result of an applied voltage V, I, = - I ,

+ I(V).

(6)

In an ideal diode in which all of the current is due to injection

w’) = I,[exp(qV/W - 11, where I, is the diode saturation current. However, since photovoltaic diodes often do not obey this relationship, as a result of additional conduction mechanisms we shall retain the general form of Eq. (6).The photocurrent I , can be expressed as I , = qv]N, (7) where N is the number of incident photons per second and v] is the quantum efficiency defined as the number of light-generated carriers crossing the junction per incident photon. 34

G . R. Pruett and R. L. Petritz, Proc. I.R.E. 47, 1524 (1959).

146

IVARS MELNGAILIS AND T. C . HARMAN

For small voltages I ( V )can be assumed to be linear : I, = -Ip

+ (l/R)V,

(8) where R is the incremental diode resistance R = (dV/dI)lv=,. For the diode operated as a photovoltaic detector I, = 0. Then V = R I P = q q N R = (qqR/E,)P,,

(9)

where V is the open-circuit photovoltage, P, is the power of the incident photons (P, = NE,), and E , is the energy per photon at the wavelength A. The voltage responsivity at the wavelength , Ican be expressed as V/P, = qqR/E,.

9v.A

(10)

This relationship is useful for evaluating the efficiency from measured quantities. The noise voltage of the unbiased open-circuit junction is simply given by the Johnson noise of the incremental diode resistance,

V 2= 4kTR A f .

(11)

Both contacts and surfaces in diodes are often known to be sources of the so-called llfnoise. Since this noise is predominant at low frequencies only and can generally be reduced by improved fabrication techniques, it will not be considered here. we equate the signal voltage To evaluate the noise-equivalent-power to the rms voltage in a 1 Hz bandwidth using Eqs. (9) and (1 1): (qqR/EI)PN.I.= (V2)l12= (4kTR)'12 PN,,

=

2E,(kT)'i2/qqR"2

and the detectivity D,*,defined as D," area, can be expressed as

D,*

=

(1 2)

= A1'2/PN.I, where A is the detector

qq(AR)'/2/2E,(kT)'i2,

(13)

Thus the detectivity is proportional to the efficiency and to the square root of the diode resistance. This relationship is useful even if the diode is not an ideal p-n junction. If in addition to minority-carrier injection there are other conduction mechanisms, such as surface leakage, the diode resistance and hence the detectivity will be degraded. The conduction mechanisms in present Pb, -,Sn,Te and Pb,.-,Sn,Se diodes are not known with any degree of certainty. There are indications, however, that most of the mechanisms which are responsible for high reverse currents (and low zero bias impedances) can be eliminated with improved crystal perfection and with improved surface treatment. To assess the more

4.

SINGLE-CRYSTAL LEAD-TIN

CHALCOGENIDES

147

fundamental limitations on the detectivity of these diodes, we therefore consider the case of the ideal injection diode. In an injection diode in which I ( V ) = Z,[exp(qV/kT) - 11 the resistance becomes R = kT/ql,. (14) The shot noise current in this case can be expressed as35

i2 = 2q[I, + 21,] A f .

(15)

For the open-circuit operation, where I , = 0, E2 = 4q1,Af and the noise voltage V 2 = i2R2 = 4ql,R2 Af, Substituting I, from Eq. (14) we again obtain Eq. (11): V 2 = 4kTR Af; i.e., the shot noise of an ideal diode in the special case of zero bias reduces to the Johnson noise, as expected. Using Eq. (14), the detectivity becomes

DA* = V ~ ‘ ~ ~ / ~ E , J : ‘ ~ ,

(16)

where J , is the saturation current density36

=‘s = Pn,0(4kTPhP2 ’

A

+

n,o(qkTPe)1’2 t y

zy2

(17)

Here pn,o is the equilibrium density of holes in the n-region, ph is the hole mobility, and zh is the hole lifetime, with nP,@,pe and z, the respective parameters for electrons in the p-region. In deriving Eq. (17) contacts and surfaces have been assumed to have no influence on the junction current by virtue of being sufficiently remote (at least several carrier diffusion lengths from the junction). This assumption will be examined below. Besides open-circuit operation, another case of interest is that of reverse bias, for which I , z -I,. The noise current from Eq. (15) becomes f2 = 2ql, Af. In this case it is simplest to express the signal as a photocurrent according to Eq. (7) : 1,

=

qVN

=

4‘1P,/EA.

(18)

To obtain the detectivity, the signal and noise currents are then equated, as was done for the voltages in Eqs. (12) and (13). Then

i.e., the detectivity of a reverse-biased diode is higher than that of an opencircuit unbiased diode by the factor $. 35

36

A. van der Ziel, “Noise.” Prentice-Hall, Englewood Cliffs, New Jersey, 1954. W. Shockley, “Electrons and Holes in Semiconductors,” pp. 309-318. Van Nostrand, Princeton, New Jersey, 1950.

148

IVARS MELNGAILIS AND T. C . HARMAN

According to Eq. (16) the reverse saturation current density J , has to be made small in order to maximize the detectivity. This means reducing the minority carrier densities on both sides of the junction by increasing the densities of the majority carriers. In practice this means choosing the maximum majority-carrier concentrations at which the dominant conduction mechanism still is minority carrier injection. As the carrier density is increased, other mechanisms, such as tunneling, will eventually predominate and will bring about a decrease in the diode resistance and hence in the detectivit y. h. Eflcicncy

The efficiency 9 is determined by reflection of the radiation at the surface (at x = 0 in Fig. 19), by the surface recombination velocity, and by recombination of the carriers in the region between the surface and the p-n junction (0-region in Fig. 19). To evaluate the efficiency, it is necessary to solve the problem of minority carrier diffusion from the surface into the bulk. We assume that at the junction all of the current is due to the diffusion of minority carriers, as is the case in ideal junctions. The steady-state distribution of excess minority carriers (Ap and An) on both sides of the p-n junction is shown schematically in Fig. 20 for opencircuit, short-circuit, and for reverse-bias operation. In the open-circuit case minority carriers are stored on both sides of the p n junction. The carrier gradients at the junction are such that the hole diffusion rate from the n-region into the junction is equal to the electron diffusion rate from the junction into the p-region, thus making the total current equal zero. For short-circuit operation the excess carrier densities at the junction must be zero in order to satisfy JUNCTION

FIG.20. Schematic representation of the distribution of added minority carriers in a photovoltaic detector under open-circuit (O.C.),short-circuit (S.C.),and reverse-bias (R.B.) conditions.

4.

SINGLE-CRYSTAL LEAD-TIN

CHALCOGENIDES

149

the requirement of zero external voltage. Consequently, the only excess carriers are holes in the n-region, and the diffusion current is due to holes only. In the case of reverse bias, carriers are depleted on both sides in the vicinity of the junction. For the purpose of evaluating the efficiency we need only to consider the short-circuit case, for which V = 0 and I, = - I , = - qqN, according to Eqs. (7) and (8). Then I , can be found by equating it to the hole diffusion current at the junction. However, for the sake of completeness and in order to determine the effect of the front surface and back contact on the reverse saturation current, we consider the general case where an arbitrary junction voltage Vis present. We first obtain the excess hole distribution in the n-region by solving the continuity equation subject to boundary conditions at the front surface and the junction, and the excess electron distribution in the p-region subject to boundary conditions at the junction and at the back contact. We then express the total current in terms of electron and hole diffusion currents at the junction. From the solution, which is carried out in Appendix A, we obtain the efficiency as

'

I - r ____ = COSh(d/Lh) f (SZh/Lh) Sinh(d/&,) '

(20)

where r is the reflection coefficient at the surface, s is the surface recombination velocity, Lh is the hole diffusion length, and d is the depth of the junction. To maximize the efficiency, we desire a low surface-recombination velocity such that sq,,/Lh << 1 and a junction depth small compared to the hole diffusion length d < Lh. The reverse saturation current [the expression in brackets in Eq. (37) of Appendix A] is increased by the presence of the back contact and may be increased or decreased by the presence of the front surface, depending on the junction depth and the value of the surface recombination velocity. T o minimize the saturation current (for maximum D*),we first require that the back contact be at least several electron diffusion lengths from the junction, i.e., b 9 L,, so that coth(b/l,) + 1, where b is the distance between the junction and the back contact. This minimizes the electron contribution to the saturation current. If we impose the conditions of low surface recombination and of a shallow junction, which were required to maximize the efficiency, we find that the hole current is thereby minimized. In fact, according to Eq. (37) the hole current in a shallow junction can be smaller than in a deep junction.

c. Response Speed The response speed of photovoltaic diodes can be limited either by the effective lifetime of the photoexcited carriers or by circuit parameters,

150

IVARS MELNGAILIS AND T. C. HARMAN

particularly by the junction capacitance. For the capacitance-limited case, the simple equivalent circuit of Fig. 21 is generally applicable. Here I, is the photocurrent (represented as a current source), C is the diode capacitance, R is the diode resistance, and RL is the load resistance. The time constant is then simply t, = RTC, where RT is the parallel combination of R and RL. The junction capacitance for an abrupt junction is given by3’

where c is the dielectric constant, A V is the barrier potential, and n, and p p are the majority electron and hole concentrations on the n- and p-sides of the junction, respectively. To reduce the capacitance, we can decrease the majority carrier concentration adjacent to the junction, increase A V by means of a reverse bias, or decrease the junction area. The R,C time constant can also be reduced by lowering either the diode resistance or the load resistance. Except for the application of a reverse bias, all of these changes will degrade the detectivity. Reducing the majority carrier concentration will increase the reverse saturation current of an ideal diode and lower the detectivity to Eq. (16). If the load resistance is at the same temperature as the diode, then R in Eq. (13) can be simply replaced by RT in order to compute the detectivity of the circuit. The trade-off between speed and detectivity is thus apparent. For a fixed capacitance D* is proportional to the square root of the time constant z,. In case the response time is determined by the storage time of the photogenerated excess carriers, the response can also be expected to be different for each mode of operation. Depending on the magnitude of various parameters, the response time may be dominated either by the bulk lifetime or by the transit time of the carriers to the junction or to the surface where their recombination is fast. From the carrier distributions for the three cases shown

FIG.21. Equivalent circuit of a photovoltaic detector showing the signal current source I,, the diode capacitance C, the shunt resistance R , and the load resistance R , . 3’

See for example, E. Spenke, “Electronic Semiconductors,” pp. 107-1 13. McGraw-Hill, New York, 1958.

4.

SINGLE-CRYSTAL LEAD-TIN

CHALCOGENIDES

151

in Fig. 20 we can intuitively expect that the response will be faster for shortcircuit and reverse biased operation than for open-circuit operation because of the presence of added minority carriers on the p-side of the junction in the latter case. This is found to be true for a large number of photovoltaic detectors; however, we should recall that the response speed also increases in the RC-limited case as the load resistance is reduced and as the capacitance is decreased by reverse bias. To identify the mechanism which limits the speed, an independent determination of the time constant z, by a direct measurement of C and R can be helpful. In order to find what diode parameters determine whether the response is limited by bulk lifetime or by carrier diffusion, it is instructive to calculate the response time for the short-circuit case. The calculation is carried out in Appendix B. The results show that for junctions sufficiently shallow so that d2/Dh 4 zh, the response will be diffusion-limited. In this case the response time can be reduced by decreasing the junction depth. In addition, the response time can be up to four times longer in a diode with a low surface recombination velocity as compared to a diode with a high surface recombination velocity. Remembering, however, that an increased surface recombination velocity degrades the efficiency, we cannot accept this as a practical means for reducing the response time for most applications. The frequency response of alloyed photodiodes has been calculated for the general case of a finite absorption coefficient by Sawyer and re dike^-.^* Their conclusions are in agreement with the ones reached here in the case of a large absorption coefficient. 8 . EXPERIMENTAL RESULTS

a. Diode Fabrication Sensitive detectors for the 8-14 p wavelength range operating at 77°K have been fabricated from both Pbl _,Sn,Te’* and Pb, -,Sn,Se’4 single crystals, grown from a vapor or by the Bridgman technique. However, as a result of the more favorable metallurgical properties of Pbl -,Sn,Te, which were discussed above, most of the recent work has been focused on this alloy system. Diodes from both alloys have been fabricated by means of the diffusion techniques described. In most cases the stoichiometry adjacent to the surface is altered to produce an n-type layer of the order of 10 p thick on a p-type substrate. In the case of Pbl _,Sn,Se the starting material was Bridgman-grown and annealed to a p-type carrier concentration of about 10”/cm3. The active area of the diode can be defined by a SiOz diffusion mask. A 1000 A pyrolytic Si02 layer is first deposited on the surface of the annealed slice by 38

D. E. Sawyer and R. H. Rediker, Proc. I.R.E. 46, 1122 (1958).

152

WARS MELNGAILIS AND T. C. HARMAN

reacting silane and oxygen on the surface of the sample, which is kept at 300°C on a graphite heater strip in a hot stage. Then a photoresist etch mask is formed and 0.5 or 1.0mm diameter circular holes are opened in the oxide using a buffered hydrofluoric acid etch. To produce a thin n-type layer on a p-type substrate, a crushed metal-rich ingot of the same Pb-Sn composition as the substrate is used as a source. The diffusion is done in an evacuated shelf tube (about 15 cc) in a single-temperature zone, typically at 400”C, for three hours. This produces junction depths of about 10 p. A small circular contact about 100 p in diameter is either evaporated or electroplated on the n-layer, and a large area contact covering the entire back surface is made to the p-region. Before electroplating the small contacts, the front surface was masked either with alkydol wax or with photoresist. Contacts to the n-region generally had a low resistance, regardless of the metal used, whereas some metals made high-resistance contacts to the p-layer. Some contacts, e.g., silver, showed a marked deterioration (increase in resistance) with time. In our experience plated gold contacts were relatively “ohmic” to both n- and p-type crystals of both Pb, -,Sn,Se and Pb, -,Sn,Te and showed no noticeable deterioration. A heavy layer of indium is plated on the gold layer of both contacts and the wafer is then diced either by cleaving or by a wire saw. The complete device (shown schematically in Fig. 22) is then mounted in a modified microwave diode package (Fig. 23) which has a window cut in the ceramic insulator. The diode can be mounted by pressing the indium-plated contact on the p-side to an indium plated copper heat sink located inside I. R. loooH

\’

sio27

JI r Au

FIG.22. Structure of a photovoltaic diode

4.

SINGLE-CRYSTAL LEAD-TIN CHALCOGENIDES

153

FIG.23. Photovoltaic detector mounted in a microwave diode package

the package. This makes an indium-indium bond at room temperature. An indium plated wire can then be pressure bonded to the small circular contact. The highest sensitivity detectors in the 8-14p wavelength raqge so far have been fabricated from vapor-grown Pb, -.Sn,Te. Here the combined operation of vapor-growth, annealing, and junction formation discussed in Section 3 has been particularly successful. The vapor-grown crystals, which have an n-type skin of 10 to 50p, are generally diced by cleaving prior to contacting and mounting them in the diode package. A number of etches have been used to reduce the surface recombination in the active area, to reduce the junction depth, and to improve the currentvoltage characteristics of diodes. For Pb, -,Sn,Te diodes the electrolytic etch23consisting of 20 g of KOH, 45 ml of H 2 0 , 35 ml of glycerin, and 20 ml of ethanol has been found most successful. In order to avoid surface contamination, the etch is applied by means of a continuous stream to the diode mounted in the package. A current density of 0.1 A/cm2 is applied at the diode surface. This results in an etch rate of about 10p/min. The etch is followed by a rinse of a few seconds in a 1% nitric acid solution followed by a

154

IVARS MELNGAILIS AND T. C. HARMAN

thorough rinse in distilled water. Particularly for diodes in which the junction is bounded by cleaved faces, the etch almost invariably increases the zero-bias impedance of the diodes, presumably as a result of the removal of a damaged layer. A chemical etch consisting of a concentrated solution of KOH, H,Oz, and ethyleneglycolJ9has also been used with some success. For Pbl -,Sn,Te the volume ratio of the ingredients was 10: 1 : 10, respectively, and for Pb,_,Sn,Se 10:2:10. The efficiency of the detectors is significantly reduced by surface reflection. Assuming that Pb, -,Sn,Te-like PbTe has an index of refraction n l of about 6,40 we estimate a reflection coefficient [r = ( n , - l)’/(nl + l)’] of 0.5. Consequently, by antireflection coating we can then expect to gain a factor of two in efficiency. This has been accomplished by evaporating a coating of selenium on the active surface of assembled detectors. The thickness of the selenium, which has an index of refraction of about 2.4, was chosen to correspond to a quarter wavelength at lop, i.e., about 1 p. The thickness was monitored during evaporation with the aid of a 1.7 p infrared source. h. Detectittity

Responsivity spectra were measured with the diodes in the unbiased opencircuit condition using a globar source and a KBr or Csl prism spectrometer.

M I

L

rn

0

n 0.1 r n w

n

1

10

100

WAVELENGTH

FIG, 24. Responsivity spectra of a Pb0,936Sn0.0h4Se diode. (After Calawa rt ~ l . ’ ~ ) 39 4(’

D. G. Coates, W. D. Lawson, and A. C. Prior, J . Ekctrochem. SOC.108, 1038 (1961). J . N. Zemel, J. D. Jensen, and R. B. Schoolar, Phys. Rev. 140, A330 (1965).

4.

SINGLE-CRYSTAL LEAD-TIN CHALCOGENIDES

155

To determine the values of responsivity and efficiency, a calibrated blackbody source, chopped at 900cps, was used. The responsivity spectra of a Pbo,g36Sno,064Sedetector shown in Fig. 24 for 12, 77, and 195°K have cutoff wavelengths of 15, 12, and 8.5 p for the three temperatures, respectively. The peak in responsivity just prior to cutoff is attributed to an increase in the number of photoexcited carriers reaching the junction as the radiation begins to penetrate the n-type layer in the vicinity of the band gap absorption edge of the crystal. When the surface recombination velocity and the junction depth are reduced on etching, the overall efficiency can be enhanced and the peaking prior to cutoff eliminated. The spectra of a Pbo,9&ho,o64Se diode shown in Fig. 25 have a nearly 45" slope up to the peak wavelength, as expected for an ideal photon detector. Some detectors were made from Pbl -,Sn,Se wafers which had a graded band gap near the surface resulting from a change in the Sn content in the process of annealing. Figure 26 shows the responsivity of a detector made from a graded-gap material in which the SnSe content (y)varies from 0.087 at the surface to 0.125 at a depth of 13 p. The resulting band gap variation at 77°K is from 0.09 eV at the surface to 0.07 eV in the bulk. The cutoff wavelength, which is determined by the band gap energy near the junction, is 15 p at 77°K and 20 p at 12°K. The junction depth is approximately 8 p and the surface is unetched. The responsivity of this detector has a peak prior to cutoff, but the peak is considerably broader and the cutoff more gradual than for the detector of Fig. 24, which does not have a graded band gap. This reflects one of the possible advantages of a graded gap structure, in which the gap at the surface is larger than at the junction. Radiation whose photon energy lies between the two values of energy gap is absorbed in the region between the surface and the junction, where the photogenerated carriers are less likely to suffer from surface recombination. This can produce an enhancement in efficiency over the corresponding wavelength range, as seen in the spectra of Fig. 26. Although external quantum efficiencies of about 15% have been observed in Pbl-,Sn,Se diodes, the peak responsivity was generally between 1 and lOV/W at either 77" or 12°K and about 0.1 V/W at 195°K. These low responsivity values resulted from low values of zero bias resistance, typically 1-10 ohms. In most Pb,-,Sn,Se diodes the resistance and hence the responsivity was lower at 12°K than at 77°K. Considerably higher values of zerobias resistance and of responsivity have been obtained in Pbl -,Sn,Te diodes fabricated from vapor-grown crystals. The responsivity spectra of a Pbo~,lSno,lgTediode before and after application of a selenium antireflection coating are shown in Fig. 27. The antireflection coating increases the responsivity by about a factor of two over a relatively wide wavelength range, as expected. Photovoltaic cutoff

156

WARS MELNGAILIS AND T. C. HARMAN

10

L 10

-10.0 i

2

3

5

15

20

3

WAVELENGTH ( p ) FIG.25. Responsivity spectra of a Pbo.936Sno,064Se diode which exhibits nearly ideal photondetector characteristics.

4.

SINGLE-CRYSTAL LEAD-TIN

CHALCOGENIDES

157

12OK

,Fl, 77OK

,

0.01 1

100

10

WAVELENGTH (p)

FIG. 26. Responsivity spectra of a graded-gap Pb,_,Sn,Se diode. (After Calawa et d L 3 )

i

1.5

2

5

10

( 5 21

WAVELENGTH ( p )

FIG. 27. Responsivity spectra of a Pb,,, ISn,,,gTe diode at 77°K before and after application of a selenium antireflection coating.

158

IVARS MELNGAILIS A N D T. C. HARMAN

wavelengths as long as 2 0 p at 77°K and 3 0 p at 12°K have been observed in Pb, -,Sn,Te diodes with a higher Sn content. Noise measurements were made using a Princeton Applied Research type B low noise preamplifier, which is preceded by a built-in 1 : 100 or 1 : 350 step-up input transformer. The lock-in amplifier can be used as a simple wave analyzer. With the 1 :350 transformer the preamplifier has a rated noise figure of 1 dB at frequencies near 1 kHz for source impedances between 1 and 10 ohms. With this arrangement it was possible to observe the thermal noise of resistors of several ohms at 77°K. The detector noise voltage measured at an operating frequency of 900 Hz was, in all cases, in good agreement with the thermal noise voltage V, = (4kTRAf)'I2 calculated for the zero bias incremental diode resistance R. The detectivity of these detectors is thus limited by the expected thermal noise rather than by noise sources associated with contacts or surfaces, as has often been the case in polycrystalline film lead salt detectors. Detector parameters of a few representative diodes are summarized in Table VIII. The efficiency, which was defined as the number of carriers reaching the p-n junction per incident photon, is limited by the loss of about 0.5 due to reflection at the surface and by losses due to recombination at the surface and in the bulk of the n-type layer. To optimize the efficiency, the TABLE VlIl PROPERTIES OF PHOTOVOLTAIC DETECTORS

Crystal

Area (mm2)

Cutoff IncrePeak Temperawave- mental Peak detectivity ture Efficiency responsivity (OK) length resistance (cmjWP/W) sec"2j (PI (ohms)

Pb0.936Sn0.064Se 0.78

{ ::

Pbo.8Sno.2Te

2.5

3

11.5 8.5

-

-

17 13

18 1.3

0.4 0.01

110 0.15

4 x 10'0 3 x 10'

180

0.14

190

5.3 x

109

109

0.15

3.5 0.13

109 -

P ~ O . E,,Te ~ S ~ ~0.1 .

77

Pbo.8,Sno.f9Te0.1

77

12

16

0.37

70

7.5

Pbo,,,Sno,,sTe

0.17

77

10

25

0.32

64

8

0.18

12 12

10

Pb0,81Sn0.19Te

8

0.19 0.43

18 32

3.7 109 6.8 x 199'

Pb0,86Sn0,14Te

0.4

10

0.60

45

1.1 x 1 0 ' O U

a

{ 7'; 77

After antireflection coating with Se.

9.5

9.5

x

lo9

159

4, SINGLE-CRYSTAL LEAD-TIN CHALCOGENIDES

junction depth has been made smaller than the carrier diffusion length, the surface recombination velocity has been reduced by etching, and for some of the detectors the reflection has been reduced by antireflection coating with selenium. The efficiencies of 0.37 and 0.4 for the uncoated diodes are close to the theoretical limit of 0.5. Thus according to the expression for Johnson noise limited detectivity [Eq. (13)], a significant further improvement in detectivity can be expected only from an increase in the incremental diode resistance. Considering the case of an ideal injection diode, we can estimate the highest obtainable R A product from Eqs. (14) and (17). For this purpose we can assume that the diode current is predominantly due to electron injection. In that case R A z (kTz,)”2/q312npp,‘/2.In order to determine the minority carrier density n,, for a given density of majority carriers, the intrinsic carrier densityz7 n, must first be calculated. In case the energy gap E , kT

+

n, = 2(271kT/h2)312(rn~,em~,,)314 exp( - E$2kT),

(22)

where rnt, and r n t h are the density-of-states effective masses of electrons and holes, respectively. For the lead-tin chalcogenides we can obtain the densityof-states effective masses from the longitudinal and transverse mass components according to rnd* = N$’3(mI*m3’3, where Nv is the number of equivalent band extrema. By observing laser emission corresponding to transitions between magnetic levels in Pb, -,Sn,Te diodes at 12°K the effective masses have been found to be approximately proportional to the gap energy, as expected, at least down to an energy gap of about 0.07eV.41 Using the values for the mass components of the valence and conduction bands in PbTe given by Cuff et ~ l . , ~ ’we can then estimate the density-ofstates masses for any value of Pb, -,Sn,Te energy gap. For E , = 0.1 eV (peak photoresponse at about 12 p ) rnXe z m2.h z 0.07 rn, where rn is the free electron mass. At 77°K the total n, for the four equivalent extrema is 3.3 x 1013/cm3. Assuming a majority carrier density of 5 x 1016/cm3 adjacent to the junction, npis about 2 x lO1O/cm3. For a typical mobility of 2 x lo4 cm2/V-sec and a lifetime of sec, estimated from photoconductivity measurements, R A = 20 ohm cmz. This gives an estimate of 7 x 10’ crn/W-sec’‘’ for the maximum achievable detector-noise limited D,* if the quantum efficiency is assumed to be unity. (The detectivity limited by noise due to the photon flux of a room temperature background for a 271 sr aperture is about 5 x 10” cm/W-sec”’ in this wavelength range.) J. F. Butler, Solid State Comm. 7,909 (1969). See also I. Melngailis, Proc. Intern. Colloq. IV-VI Compounds, Paris, 1468, in J . Phys. (Frame) 29, Suppl. Colloq. C-4, 84 (1968). 4 2 K. F. Cuff, M. R. Ellett, C. D. Kuglin, and L. R. Williams, in “Physics of Semiconductors” (Proc. 7th Intern. Conf.), pp. 677-684. Dunod, Paris and Academic Press, New York, 1964.

41

160

WARS MELNGAILIS AND T. C . HARMAN

-0.2$

i

-0.4

FIG.28. Current-voltage characteristic of a 0.2 mm2 Pbo.s5Sno.,STediode at 77°K

The highest resistance diode in Table VIII has an RA of 0.18 ohm cm'. Although the conduction mechanisms responsible for the reverse current are not certain at present, there is evidence that at least in some cases a shunt conductance is created by metallic inclusions in the crystal, which were discussed earlier. The highest value of incremental resistance at 77"K, corresponding to an R A of about 2, has been observed in a Pbo.s5Sno.,,Te laser diode, for which the current-voltage characteristic is shown in Fig. 28. Although the structure of this diode was not suitable for photodetection, the relatively low reverse current indicates that large improvements in the detectivity of photovoltaic detectors should indeed be possible. Using Eq. (22), we can calculate ni for different temperatures and energy gap values and obtain an estimate of the maximum detectivity at any temperature for a specified cutoff wavelength. Since the detectivity varies only as the +-power of the ratio of lifetime to mobility, we neglect changes in these parameters. (The mobility increases by about one order of magnitude as the temperature is lowered from 77 to 4.2"K, and the lifetime, according to photoconductivity measurements, increases by about two orders of magnitude; thus ( T J ~ ~ ) 'increases ' ~ only by a factor of 1.8 for the same temperature change.) Assuming a linear variation of effective masses with energy gap, izi can be expressed as

ni = 2.9 x 10'5(TE,)3/2exp -(E,/1.72 x

T) ( ~ m - ~ ) , (23)

where E , is in electron-volts and T is in degrees Kelvin. Using Eq. (23), we have plotted ni as a function of energy gap for a number of temperatures, as

4. SINGLE-CRYSTAL

Id0

0.04

0.06

008

LEAD-TIN CHALCOGENIDES

010

012

0.14

161

16

FIG. 29. Intrinsic carrier concentration ni in Pb, _,Sn,Te as a function of energy gap E, for various temperatures.

shown in Fig. 29. We have then calculated the detectivity corresponding to these values of ai for a constant majority-carrier density of 5 x l0I6/cm3. The values given in Fig. 30 should be considered as estimates of the upper limit of detector-noise limited detectivity. For energy gap values smaller than 0.1 eV tunneling may well begin to contribute to the conduction in diodes. This could result in appreciably lower detectivities. c. Response Speed

The speed of response of detectors was measured by observing the photovoltage due to a light pulse at 0.84 p from a GaAs diode laser. The laser was mounted in a separate liquid nitrogen Dewar and was pulsed using a mercury relay. When the pulser was properly terminated with a 50 ohm resistor in series with the laser the light pulses had rise and fall times less than 1 nsec. The Pb, -,Sn,Te detector was connected directly to a properly terminated

162

WARS MELNGAILlS AND T. C . HARMAN

10'~

ld4

h

d3

N

I0 0) v)

5

1d2

E

0 Y

*0 lo"

ldO #

9

10

# 0

20

15

12

10

9

8

FIG.30. Maximum detectivity of Pb, .Sn,Tc photovoltaic detectors as a function of cutoff wavelength (energy gap) for various temperatures.

50 ohm line, and the output was observed either on a sampling oscilloscope or a fast risetime conventional oscilloscope. The detector response times ranged from between less than 10 to 100 nsec both for Pb,-,Sn,Te and Pb, -,Sn,Se diodes. The photovoltage pulse from a Pb,_,Sn,Se detector, shown in Fig. 31, has a rise (and fall) time of about

4. SINGLE-CRYSTAL LEAD-TIN CHALCOGENIDES

163

I1

+ +- 5 0 n s e c

FIG. 31. Response of a Pb0.936Sn0,064Se diode at 77°K to a GaAs laser pulse.

f

TIME

15 nsec. To determine the mechanism which limits the speed, the capacitance ofa number of diodes was measured by using a capacitance bridge at 20 MHz. The zero bias capacitance was generally about 2000 pF/mm2. In most diodes the RTC time constant estimated from the measured capacitance and from the parallel combination of the 50 ohm load resistance and the incremental diode resistance was no more than half of the measured photovoitage time constant. Hence circuit effects and lifetime effects appear to be of comparable size in these devices. In some diodes the response time was significantly increased after the active surface was etched. This is consistent with a decrease in surface recombination velocity.

IV. Photoconductive Detectors 9. SAMPLE PREPARATION

Photoconductivity at wavelengths up to 15 p at 77°K and up to 20 p at 4.2"K has been observed in Bridgman-grown and subsequently annealed TABLE IX ANNEALED BRIDGMAN-GROWN Pb, _,Sn,Te

Crystal No.

.Y

Sample temp.

Annealing Sample time thickness (days) (mm)

YC)

Hall carrier concentration' (cm-3)

Hall carrier mobility at 77°K (cm'/V-sec)

66-16A

0.17

500 450

22 38

0.29

2.3 x lO"(P)

3.1 x 104

66-16B

0.17

650 450

4 50

0.27

5.8 x 1015(p)

2.6 x 104

67-41

0.20

600 450

8 56

0.25

7.5 x 1 0 * 5 ( ~ )

3.2 x 104

67-3R

0.17

600 450

5 14

0.06

2.6 x lO"(N)

2.9 x 104

~

a

P indicates p-type specimens, N indicates n-type. 77°K.

~

~

164

WARS MELNGAILIS A N D T. C. HARMAN

crystals of Pb, -,Sn,Te.'* The annealing parameters and the resulting carrier concentrations and mobilities of the crystals used for photoconductors are shown in Table IX. The two compositions x = 0.17 and 0.20 are of particular interest for detectors because the photoconductivity of the 0.17 alloy at 77°K peaks very close to the 10.6,~CO, laser wavelength, whereas for the 0.20 alloy the peak is at 14 p, i.e., detectors of this composition cover the 8-14 p atmospheric window.

4

-

50 nsec

FIG.32. Response of a Pbo.,,,Sno.,,Te photoconductor at 77°K (crystal No. 66-16) to a GaAs diode laser pulse for (a) a photoconductor bias current of +20 mA, (b) zero bias, and (c) a bias of -20 mA.

4. SINGLE-CRYSTAL

LEAD-TIN CHALCOGENIDES

165

After annealing, the samples were chemically etched both to reduce their thickness and to lower the surface recombination velocity. The etch39 consisted of ten parts of concentrated K O H solution, one part of H , 0 2 , and ten parts of ethylene glycol. Contacts were made by electroplating gold. In order to ensure uniform cooling and to avoid thermal stresses, the samples were suspended by the lead wires and immersed directly in the liquid refrigerant in preference to mounting them on a heat sink. 10. LIFETIME

To ensure that photoconductivity, rather than slow thermal effects (bolometer effect or thermoelectric effect), is observed, the response speed was measured by using a pulsed GaAs diode laser. Figure 32 shows the response of a Pbo,,,Sno,,,Te sample (crystal No. 66-16B) at 77°K for positive bias, I

4.2'K x = 0.17

/i

f 77OK x = 0.2(

x=O.17

I

1

t

r

2

I

I

I

5

I

1

7

/

1

1

10

I

1

20

z

WAVELENGTH (pL)

FIG. 33. Responsivity spectra of Pb, -,Sn,Te Harman. '*)

photoconductors. (After Melngailis and

166

IVARS MELNGAILIS AND T. C . HARMAN

TABLE X LIFETIME

T

(“W 300 I98 77 4.2

MEASIJKEMENTS I N Pbl -,Sn,Te

Crystal 66-168 4 3 1.5 1.2

x lo-* x lo-@ x lo-’ x

PHOTOCONDUCTOKS

Crystal 67-41 -

2 x 1.5 x lo-’ 0.7 x 10-6

zero bias, and negative bias. The 15nsec response time corresponds to the effective carrier lifetime. According to the photoconductive response spectra of Fig. 33, the cutoff wavelengths at 77°K are 11 and 15 p for the 0.17 and 0.20 alloys, respectively, and 15p for the 0.17 alloy at 4.2”K. Peaking in the response spectra of the type seen in Fig. 33 prior to cutoff may occur as the radiation begins to penetrate into the bulk, where the lifetime of carriers is longer than near the surface. Another source of irregularities in the spectrum may be the optical interference of a transparent film on the surface of the sample which occasionally forms as a result of etching. The increase in the responsivity of the 0.17 alloy by about two orders of magnitude in going from 77 to 4.2”K is largely due to longer lifetime at the lower temperature. This was verified by directly observing the decay of the photocurrent following a 0.84 p GaAs diode laser pulse. As shown in Table X the photoconductive lifetime is close to sec at 77°K and higher temperatures and about low6sec at 4.2’K. For the crystals for which both responsivity and lifetime measurements were available the lifetime calculated from the responsivity (BV)according t 0 43 =

9i?vE,12/2q~clopR2

was in agreement with the measured lifetime. Here 1 is the length of the sample, qc is the external quantum efficiency defined as the number of electron-hole pairs produced per incident photon, lo is the bias current, R is the sample resistance, and p is the carrier mobility, which for Pbl -,Sn,Te has been assumed to be the same for electrons and holes. The photoconductive lifetime in general provides a lower limit to the bulk lifetime, due to the possibility of enhanced recombination at the surface. It 43

The relationships for responsivity and effective lifetime in an intrinsic photoconductor can be derived from elementary considerations which are discussed for example by E. S. Rittner, in “Photoconductivity Conference” (Proc. Atlantic City Conference) (R.C. Breckenridge, B. R. Russell, and E. E. Hahn, eds.), pp. 215-268. Wiley, New York and Chapman & Hall, London, 1956.

4.

SINGLE-CRYSTAL LEAD-TIN CHALCOGENIDES

167

can be shown that zeff is related to the bulk lifetime o by the expression43 Teff -

z

+

[sinh(b/L)] (sz/L){[cosh(b/L)] - l } [1 + (s2zz/L2)][sinh(b/L)]+ 2(so/L)cosh(b/L)’

(25)

where b is the thickness of the sample, L is the carrier diffusion length, and s is the surface recombination velocity, which is assumed to be the same for

both surfaces. The radiation which is incident on one surface is assumed to be absorbed within a distance much smaller than the thickness b and the diffusion length L. The width and length of the sample are assumed large compared to the thickness. For the two lifetimes to be approximately equal we require a sufficiently low surfacearecombination velocity so that ST/L6 1. From estimates of sz/L at 77 and 4.2”K we can expect that the photoconductive lifetime at 77°K is a good measure of the bulk lifetime, whereas at 4.2”K the bulk lifetime may be as much as a factor of two longer than the photoconductive lifetime. This is consistent with the spectra of Fig. 33, where the peaking prior to cutoff, which may be associated with surface recombination, is very small at 77”K, but becomes somewhat more pronounced at 4.2”K. The radiative recombination lifetime can be estimated from the radiative recombination rate given by van Roosbroeck and S h ~ c k l e yin~the ~ form of an integral over all values of energy E

where c1 is the absorption coefficient, n1 is the index of refraction, and U = E/kT. For direct allowed transitions between the valence and conduction band states, c1 can be expressed as45 c1=

e2(2m,*,,,/m)3’2 ( E - E,)I’2Jf n ch2mEo

=o

E > E, E < E,

where m;,, is the reduced density of states effective mass

since mXe % mz,h in the lead-tin chalcogenides. E, is the energy gap andA, is 44 45

W. van Roosbroeck and W. Shockley, Phys. Reo. 94, 1558 (1954). J . Bardeen, F. J . Blatt, and L. H. Hall, “Photoconductivity Conference” (Proc. Atlantic City Conference) (R. G . Breckenridge, B. R. Russell, and E. E. Hahn, eds.), p. 149. Wiley, New York and Chapman & Hall, London, 1956.

168

WARS MELNGAILIS A N D T. C . HARMAN

the oscillator strength of the transition. 2 (P.1'

m m,"

m mh*'

fI f =-If--%-

m E, where is the momentum matrix element; me* and inh* are the electron and hole effective masses, respectively. The approximate expression for hf holds for me* 4 1. Because of the large effective mass anisotropy in these crystals and because of the multiple band extrema, m& and me* will differ. The density-of-states effective mass was defined in connection with Eq. (22). me* can be expressed in terms of the longitudinal and transverse mass components ml* and m,* as I -1 2 ,r* - I ( .):

ler(

6

+

mZe can be expressed in terms of the anisotropy ratio K number of equivalent band extrema as N, as

= mr/mt and the

Substituting Eq. (27) into Eq. (26) and assuming that the index of refraction and the effective mass are independent of energy over the relatively small energy range above the energy gap for which the integral of Eq. (26) is appreciable, we have

s

( U - Ug)1/2U2dU $3= 8nrr2n,(kT)712(2m~,,/m)3'2~~ h5me,c3 e"-1

(28)

u,

For the cases of interest here E, $ kT; hence, e"

$

1 , and the integral of nl/2

Eq. (28) can be shown to have the approximate value --ULTgze-"g. The 2 minority carrier lifetime in n-type material is given by

Substituting Eqs. (22) and (28) yields

where kT and E , are in electron volts, n, is in cm-3 and where N , = 4 for

169

4. SINGLE-CRYSTAL LEAD-TIN CHALCOGENIDES

these crystals. Since Boltzmann statistics have been used in deriving Eq. (30), its validity is limited to cases where the carriers are statistically nondegenerate. Thus, low temperatures and high carrier concentrations are excluded. For Pb, -,Sn,Te with an energy gap of 0.1 eV at 77"K, an effective mass m,* = 0.019 obtained by extrapolating from the mass values given for PbTe by Cuff et a K value of about 10 (assumed the same as that for PbTe), a carrier density of 5 x 1015cm-3, and an index of refraction of about 6, Eq. (30) gives a radiative recombination lifetime of about sec, i.e., two orders of magnitude longer than the photoconductive lifetime measured at 77°K. Since Auger recombination has previously been found to be insignificant in the lead salts,46 the shorter measured lifetime is probably due to dislocations or other crystalline imperfections. 1 1. DETECTIVITY Properties of a number of photoconductors are summarized in Table XI. At 77°K the noise measured at 900 Hz at the bias current used was generally less than twice the Johnson noise calculated for the sample resistance. The TABLE XI PROPERTIES OF Pb, -,Sn,Te

Crystal No.

PHOTOCONDUCTORS

Dimensions length Tempera- ResisBias Peak cutoff Peak width ture tance current responsivity wavelength detectivity thickness ( O K ) (ohms) (mA) (V/W) (p) (cm/W-sec"2)

(mm) 66-168

4.0 2.0 0.05

66- 16B

4.0 2.0 0.03

67-41

1.5 1 .0 0.05

67-41

1.5 I .o 0.01

4h

77

4.2

77

4.2

42

10

52

4

13

30

10

30

0.7

80

0.6

130

11

3

15

1.7 x 10''

15

1

x loM

x loM

20

E. R. Washwell and K. F. CuK, in "Radiative Recombination in Semiconductors" (Proc. 7th Intern. Conf.), pp. 11-20. Dunod, Paris and Academic Press, New York, 1965.

I70

WARS MELNGAILIS AND T. C. HARMAN

excess portion of the noise increased with the bias current and decreased with frequency. For the first sample of Table XI the measured noise at 900 Hz was only 50% higher than the Johnson noise for the 42-ohm resistance at 77°K. At frequencies higher than 4 kHz the noise approached the limiting thermal value, with a resulting increase in peak detectivity to 4.5 x lo8 cm/ W-sec’I2. Thus in the present devices the noise is largely dominated by thermal fluctuations. The magnitude of the excess l/f noise strongly depended on the metal and the application technique used for the contacts. Plated gold contacts have so far given the lowest values of excess noise. The generationrecombination noise for an extrinsic n-type semiconductor with pe % ph can be shown to be4’ Vn,g = 41,~i[:R A,f1/Zpf’2/nn~1‘2,

(31)

where v is the volume of the sample. For the samples tested the g-r noise at 77°K calculated using the measured values of lifetime is about three orders of magnitude lower than the Johnson noise. With the present rate of improvement in the quality of Pb,-,Sn,Te crystals we anticipate that carrier concentrations of 1014/cm3and lifetimes of sec at 77°K may be possible as the crystalline imperfection density is reduced. For this value of lifetime the noise will begin to be dominated by the g-r noise, in which case the detectivity for a photoconductor with an illuminated area A can be expressed as

using Eqs. (24) and (31). For the above values of II, and T e f f , for a sample thickness b of 10 p and unity quantum efficiency qc we estimate a detectivity of about lo’* cm/W-sec’’’ which can be realized in a sample with an energy gap of 0.1 eV operating under reduced background conditions at 77°K. V. Summary At the present stage of development the lead-tin chalcogenide infrared detectors are already of practical use. Photovoltaic detectors at present have operated to wavelengths of about 20 ,u at 77°K and 30 p at 12°K. External quantum efficiencies are close t o the reflection-limited maximum of 0.5, and detectivities at 77°K up to 1.1 x 10” cm/W-sec’’2 have been measured in diodes with cutoff wavelengths in the 8-14 p atmospheric window. Response speeds are of the order of sec. Photoconductivity has been studied in Bridgman-grown and 47

D. Long, Infrared Physics 7, 12 (1967).

4.

171

SINGLE-CRYSTAL LEAD-TIN CHALCOGENIDES

subsequently annealed Pb, -,Sn,Te crystals with carrier concentrations between 2 x and 8 x 10’’ cm-3 and mobilities of about 3 x lo4 cm2/ V-sec at 77°K. In samples etched down to a thickness of 10to 50p, detectivities range from lo8 to lo9 cm/W-sec”’ at wavelengths up to 15 p at 77°K. Lifetimes of approximately IO-’sec at 77°K and lop6sec at 4.2”K have been measured by direct observation of the photoconductivity decay. For a large number of applications, especially for heterodyne detection, the photovoltaic detectors are particularly advantageous, since they combine good sensitivity and high speed. The excellent homogeneity of the crystals holds a great deal of promise for the fabrication of large detector arrays on a single crystal wafer with the aid of the oxide masking techniques described. Although most of the work presented in this chapter has concentrated on detectors for the 8-14 p wavelength range, the band structure of the materials makes them potentially useful for the development of intrinsic detectors operated at temperatures below 77°K with cutoff wavelengths beyond 100 p. Finally, the results on the lead-tin chalcogenides point out the potential superiority of the single crystal approach to the intrinsic detector problem as opposed to the polycrystalline film approach. Appendix A. Efficiency and Saturation Current in Photovoltaic Detectors

To obtain Ap(x) in the region 0 < x < d in Fig. 20 we solve Dhd2(Ap)/dx2

=

hp/Th

(33)

for Ap

=

p,,,[exp(qV/kT) - 13 at x = O+

and J h = - qDh d(Ap)/dx

= -[qN(1

- r)/A] + qs hp

at

x

= d.

The last boundary condition expresses the hole current J h at the front surface as the difference between a current due to photoexcitation and a current due to surface recombination; Y is the reflection coefficient of the radiation at the surface and s is the surface recombination velocity. Similarly, for electrons An(x) in the region - b < x < 0 D, d2(An)/dx2

=

An/z,

(34)

with

x = 0-

An

=

n,,o{[exp(qV/kT)] - 1)

at

An

=

0

at x = -6,

and

172

IVARS MELNGAILIS AND T . C. HARMAN

assuming a high recombination surface at the back contact. The results are

[(

cosh

x

hp =

(cosh

y)+

t)+ Lh STh

Lh

sinh d

L

(35)

O<x
The total current is expressed as

_-

(cosh

t)+ Lh

Lh

srh sinh . d

AqDhPn,O

(sinh

e)

sTh

+ L,cosh

d

(37)

We recognize the terms here as the photocurrent I , and the dark current I ( V ) of Eq. (6),and by comparison with Eq. (7) we obtain the efficiency

'

1-r = [COSh(d/Lh)] + (STh/Lh) sinh(d/Lh)'

(38)

Appendix B. Carrier Lifetime in a Short-circuited Photovoltaic Detector

In the short-circuit mode only excess holes are stored in the n-region, as shown in Fig. 20, so that we only need to solve the continuity equation for holes

4.

SINGLE-CRYSTAL LEAD-TIN

CHALCOGENIDES

173

Considering that a constant signal which has created a steady-hole distribution in the n-region is reduced to zero at t = 0, we can express the boundary conditions as Ap=O

at x = 0 , at x = d ,

Dh a(Ap)/dx = -s Ap

(40)

Assuming a solution Ap =

C Aie-Pt sin(a,x), i

we have, from the differential equation,

From the boundary condition at x a&,cos(aid)

=

d

=

- s sin(aid),

(43)

or (tan yi)/yi = - Dh/sd where y i

=

aid. Then

which can be fitted to the boundary condition at t = 0. A graphical solution of the transcendental equation is sketched in Fig. 34. The effective lifetime zi of the termsin the summation can be defined by

Unless Dhyiz/d2@ 1/Th, in which case the response is simply limited by the bulk lifetime, we see that higher-order terms of the summation decay more rapidly with time than the first, and we can consider z1 as the effective lifetime. Then for large values of s, for which &/Sd @ 1, y1 tends to the value y1 = n, and we have

174

IVARS MELNCAILIS AND T. C. HARMAN

1

I

I

I

I

I

l

l

I

I

I I

1 I

l

l

l

37T -2

Zrr

0

I

_-

I

X

I Q

"2

I

7

T

z 2

Y FIG.34. Graphical solution of the transcendental equation tan yi

=

-(D,/sd)yi.

For small values of s, such that DJsd % 1, y1 tends to the value 71

=

n/2, and

From these results we can conclude that the response will be diffusionlimited when d 2 / D h 4 T,,, and in that case the response time can be up to four times longer for a low recombination surface than for a high recombination surface. Ac K NOw LEDGMENTS The authors would like to express their appreciation to J. 0. Dimmock, R. H. Rediker, A. J. Strauss, A. R. Calawa, and J. F. Butler for reading the manuscript and offering many helpful comments and suggestions.

CHAPTER 5

Mercury-Cadmium Telluride and Closely Related Alloys* Donald Long and Joseph L . Schmit

. . . . . . . . . . . . . . . . i75 I . INTRODUCTION 177 1 . Semiconductor Alloy Approach . . . . . . . . . . . 2 . Historical Reoiew . . . . . . . . . . . . . . 178 180 3 . Scope of the Chapter . . . . . . . . . . . . . 180 11 . BASICMATERIAL PROPERTIES. . . . . . . . . . . . 180 4 . Crystul (Lattice) Properties . . . . . . . . . . . . 189 5 . Setniconducting (Electronic) Properties . . . . . . . . THEORY APPLICABLE TO THESEMATERIALS 218 111. BASICINFRARED DETECTOR 6 . Photoconductive Mode . . . . . . . . . . . . . 219 7 . Photovoltaic Mode . . . . . . . . . . . . . . 227 IV . CRYSTAL PREPARATION . . . . . . . . . . . . . . 233 233 8 . Sources and Pur$ca!ion of’Constiturnt Elements . . . . . . 234 9 . Solidification from the Melt . . . . . . . . . . . . 235 10. Vapor Phase Deposition: Epitaxial Growrh . . . . . . . 240 1 1 . Annealing of Crystals . . . . . . . . . . . . . 241 12. Junction Formation . . . . . . . . . . . . . . 13 . Crysral Evaluation Techniques . . . . . . . . . . . 242 V . DETECTOR FABRICATION AND PROPERTIES . . . . . . . . . 244 245 14. Deterlor Element Fabricazion . . . . . . . . . . . 15 . Encapsulation . . . . . . . . . . . . . . . 246 . . . . . . . 249 16. Typical Defector Response Characteristics VI . CONCLUSION . . . . . . . . . . . . . . . . . 251 APPENDIX . . . . . . . . . . . . . . . . . . 253

.

I Introduction An intrinsic infrared detector is basically a very simple semiconductor device. Incident infrared radiation excites electrons from states near the top of the valence band of the semiconductor across its energy gap into states near the bottom of the conduction band. producing excess electron-hole

* Some of the Honeywell results reported in this chapter were obtained under contract support by the U.S. Air Force and the Advanced Research Projects Agency.

175

176

DONALD LONG AND JOSEPH L. SCHMIT

pairs, which change the electrical properties of the material. The form in which this change appears depends on the properties and configuration of the material. For example, for a photoconductive sample it is detected as an increase of electrical conductivity, whereas for a p-n junction or a sample designed as a photoelectromagnetic sensor it is detected as a photovoltage. The semiconductor is chosen or “designed” to have an energy-gap width E , related to the longest wavelength 2 of the radiation to be detected by

where h is Planck’s constant and co is the speed of light in vacuum. The semiconductor must also have other properties satisfactory to permit a photoconductive, photovoltaic, or photoelectromagnetic effect large enough to be useful, but the main criterion is that its energy gap correspond to the longest wavelength to which the detector must respond, i.e., the cutoff wavelength. The material will respond to radiation of all wavelengths shorter than the

-

0.7

-

0.5

-

0.3

2

0.2-

3 > (3

5

0.1-

z 0.070.05 -

-

0.03

0.021 I

I

2

I

3

I

I

I

5 7 1 0

I

20

I

30

I

50

(@

FIG.1. Energy gap versus maximum detector wavelength, including points representing a number of common semiconductor materials. The important 3-5 p and 8-14 p detector wavelength ranges, corresponding to atmospheric “windows” of high infrared transmission, are indicated by hash marks.

5. MERCURY-CADMIUM

TELLURIDE AND CLOSELY RELATED ALLOYS

177

cutoff, so that one could in principle use any semiconductor with an energy gap narrower than that corresponding to the longest wavelength to be detected, but for practical reasons the best response occurs when the gap width and cutoff wavelength are related by Eq. (1). In Fig. 1 we have plotted the energy gap versus wavelength from Eq. (l),and have included points representing the gaps of a number of well-known semiconductors suitable for intrinsic infrared detectors. The gap widths of these semiconductors all vary with temperature. The points plotted in Fig. 1 are for the gap at 77”K,’ which is perhaps the most common operating temperature for high-performance intrinsic detectors. The 1-8 p wavelength range is fairly well covered by well-developed elemental and compound semiconductors, but there is no such material with an energy gap suitable for an intrinsic detector responding at wavelengths longer than 8 p. Furthermore, in the 1-8 p range the known materials have gaps which fall at discrete points randomly along the Eg versus L line, so that even this shorter wavelength range is not fully covered by semiconductors having optimum responses.’” Thus there is a need for new materials suitable for intrinsic infrared detectors which have a greater range ofknergy gaps. One can use mixed crystals (alloys) of two or more semiconductor elements or compounds to satisfy this need. This chapter deals with the Hg, -,Cd,Te alloy system, which has been extensively studied and developed as a variable-energy-gap intrinsic infrared detector material, and with its close relatives in the IJ-VI compound mixedcrystal family. The formula Hg, -,Cd,Te represents a mixed crystal of HgTe and CdTe in which x denotes the mole fraction of CdTe.

1 . SEMICONDUCTOR ALLOYAPPROACH Let us consider the basic idea of the semiconductor alloy approach to the development of designable-gap intrinsic detector materials. Suppose an energy gap of 0.1 eV is needed. One can conceive of simply mixing a semiconductor having E , > 0.1 eV with one having E , < 0.1 eV to make an alloy with the desired gap width, because experiments have shown that there is a continuous variation of the gap width with composition throughout a semiconductor alloy system (assuming mutual solubility of the constituents at all compositions). In most alloy systems the gaps of all compositions lie between those of the “endpoint” elements or compounds, although the Pb, -,Sn,Te and Pb, -,Sn,Se systems discussed elsewhere in this volume are notable exceptions, in which for some alloy compositions the gaps are narrower than that of either constituent compound.

’ D. Long, “Energy Bands in Semiconductors.” Wiley, New York, 1968. This is an up-to-date review which includes discussion of the electronic energy bands in the materials of interest, and which gives references to original publications on band structure. l a M. Srnollett, Infrared Phys. 8, 3 (1968).

178

DONALD LONG AND JOSEPH L. SCHMIT

Experiments on a number of mixed-crystal systems have shown that these alloys have well-defined band structures, in which the energy gaps (and other band parameters) vary continuously with composition between their values in the constituent compounds. These results are also consistent with theory. Specific effects of the lattice disorder, such as spreading of band edges or tailing of states into the forbidden gap, appear to be negligible. Therefore, these materials can be treated simply as ordinary semiconductors having parameters which vary continuously with alloy composition, instead of being fixed as in the normal elemental and compound semiconductors. The mixed crystals under consideration are single-phase, disordered substitutional alloys, composed of pairs of 11-VI compounds which have the same type of crystal structure and chemical formula and are mutually soluble in all compositions. The alloy crystals exhibit lattice periodicity like that of either constituent of the alloy system. There is long-range order in that each regular lattice site is occupied by an atom, but the two species of atom or molecule are distributed over the sites in a disordered, random manner; however, this lattice disorder produces no important specific effects. We can think of mixed crystals simply as a class of semiconductors in which the parameters vary continuously with alloy composition, and are thereby designable and controllable insofar as the alloy composition can be controlled. The alloy system of special interest in this chapter, Hg, -.Cd,Te, consists of a mixture of the wide-gap semiconductor CdTe ( E g = 1.6eV) with a semimetallic compound, HgTe, that can be thought of as a semiconductor having a “negative energy gap” of about 0.3 eV. The negative gap in HgTe is generically related to the 1.6 eV gap in CdTe; the gap in the alloys varies nearly linearly with x between the two endpoint values, so that it passes through zero at an intermediate composition (x E 0.15) and is 0.1 eV, e.g., at x x 0.2 at 77°K. Materials suitable for intrinsic infrared detectors can be obtained simply by mixing HgTe and CdTe. 2. HISTORICAL REVIEW It should be helpful to an understanding of this chapter to review briefly the short history of research on Hg, -,Cd,Te as an intrinsic infrared detector material. The initial incentive for this research was provided around 1960 by the need for better detectors sensitive in the important 8-14 p atmospheric transmission “window.” Previously, only extrinsic detectors, notably Hgdoped Ge, had been available with high performance in this wavelength interval, but they required very low operating temperatures, below 30°K. An intrinsic photoconductive or photovoltaic detector offered the possibility of higher operating temperatures because of the well-known fact that relatively little thermal excitation of carriers across an energy gap occurs at

5. MERCURY-CADMIUM

TELLURIDE AND CLOSELY RELATED ALLOYS

179

temperatures high enough for substantial excitation from an impurity level of the same energy to take place. The basic problem was to find a suitable semiconductor having an energy gap of about 0.09 eV, corresponding, through Eq. (I), to the desired 14p long-wavelength cutoff of detector response. No elemental or compound semiconductor with this gap width was known, so that it was necessary to develop the technology of an alloy system, the properties of which could be “tuned” to the 8-14 p interval by adjusting the alloy composition. Hg,-,Cd,Te with x % 0.2 was found to be a promising material, and the subsequent intensive effort on this alloy has yielded both photoconductive and photovoltaic detectors operable at 77°K with very high performance. The Hg, - ,Cd,Te crystals from which the best photoconductive detectors have been made are among the most nearly pure semiconductor materials available, often having (uncompensated) extrinsic carrier concentrations below 10’’ cm- ’. Most of the effort on Hg,-,Cd,Te to date has been on the x % 0.2 alloy and on 77°K photoconductive and photovoltaic detectors based on it; therefore, relatively little is known about other alloy compositions, operating temperatures, and modes of detection. The original interest in Hg, -,Cd,Te really had nothing to do with its being an alloy: the practical objective was simply to get a semiconductor with the narrow energy gap needed for an 8-14 p intrinsic infrared detector. However, the fact that the original objective did require the development of an alloy system with its variable properties permitted using it for a much wider range of detector wavelength responses. Recent research has in fact been emphasizing alloy compositions away from x = 0.2, for the purpose of making high-performance detectors of Hg, - ,Cd,Te having response peaks both shorter than 8 p and longer than 14 p. Several research groups throughout the world have been deeply involved in the work on Hg,-,Cd,Te. W. D. Lawson and co-workers at the Royal Radar Establishment in England initiated the effortin this field by discovering in 1958 the potentialities of Hg, -,Cd,Te as an infrared detector material, but they did relatively little research on this system later. Two other groups have done most of the subsequent development of infrared detectors based on Hg, -,Cd,Te: the French investigators at the Laboratoire de Magnktisme et de Physique du Solide, CNRS, Bellevue, including M. Rodot and others, have contributed many important results on the basic properties of the alloy system and emphasized photovoltaic detectors; the group at the Honeywell Corporate Research Center in Minnesota, consisting of P. W. Kruse and co-workers, has concentrated on photoconductive detectors. Important research programs of a basic nature leading to a good understanding of Hg,-,Cd,Te have been carried out at the Lincoln Laboratory in Massachusetts by Strauss and Harman and others, at the Institute of Physics,

180

DONALD LONG AND JOSEPH L. SCHMIT

Warsaw, Poland, and at several locations in the Soviet Union. There have been other researchers in this field, but the above groups obtained most of the results pertinent to our interests. 3. SCOPEOF

THE

CHAPTER

This chapter will concentrate almost entirely on the Hg, -,Cd,Te alloy system, because it has received far more attention to date as an intrinsic infrared detector material than any other 11-VI compound alloy system. Reproduction and review of experimental results will be limited to Hg, -,Cd,Te. Related material will be mentioned only in those few places where relevant information is available, and in those cases the information will be given only through references to the original publications. However, Hg, -,Cd,Te offers an excellent prototype for discussion and is adequately representative of the 11-VI compound alloy class. The basic material properties are reviewed in Part I1 of the chapter. Then a discussion is given in Part 111 of the important aspects of intrinsic infrared detector theory applicable to these materials. The methods used to prepare crystals suitable for infrared detectors are reviewed in Part IV, followed by a description in Part V of the fabrication and properties of typical detectors. The conclusion summarizes the present status of the detectors covered in this chapter and indicates the prospects for their future development. There are a few minor inconsistencies in this chapter in the use of certain parameter values in calculations. For example, values for the average effective mass of holes in the valence band ranging from 0.3 m to 0.4 m are used (m is the mass of a free electron). These inconsistencies arise because different parameter values were used in the various original calculations reviewed here. For two reasons it would not be worthwhile to attempt to correct the resultant small quantitative inconsistencies: First, the results need not be highly accurate quantitatively for our purposes. Second, research on the alloy systems is still in progress, so that “final” values of these parameters are not yet established. 11. Basic Material Properties

4. CRYSTAL (LATTICE) PROPERTIES a. Crystal Structure and Brillouin Zone

The materials considered in this chapter, including the binary-compound constituents of the mixed crystals as well as all compositions of the mixed crystals themselves, crystallize in the zincblende cubic structure. The zincblende crystal is composed of two interpenetrating face-centered cubic

5. MERCURY-CADMIUM

TELLURIDE AND CLOSELY RELATED ALLOYS

181

sublattices displaced by (&ao,$uO,*ao) along the cubic body diagonal, where a, is the lattice constant. If we represent the 11-VI compounds generically as AB, the A atoms (cations) occupy the sites on one of these fcc sublattices and the B atoms (anions) the sites on the other. The structure is illustrated in Fig. 2. Each cation has two valence electrons outside filled inner shells, and each anion six such electrons. The crystal bonding is mainly covalent, the valence electrons being shared between adjacent atoms to form tetrahedrally-directed bonds. There is also an ionic contribution to the bonding because of the different nuclear charges of the A and B atoms. Each primitive unit cell of the zincblende lattice contains two atoms, an A and a B. In an alloy or mixed crystal of the type involved here the cations are of two different species, and the material may be represented generically as A; -,A",B. The A' and A" species are distributed randomly over the A lattice sites in the crystal, so that the overall character of the zincblende structure is maintained. The point group of the zincblende lattice is &. The zincblende Brillouin zone is the familiar truncated octahedron which applies to most well-known semiconductors. It is shown in Fig. 3. The

FIG. 2. Zincblende crystal lattice, illustrating the tetrahedral bonding, the cubic symmetry, the lattice constant a,. and the two different species of atom, A and B. The spheres represent the atoms and the bars the covalent bonds between them. (After Long'.)

182

DONALD LONG AND JOSEPH L. SCHMIT

FIG. 3. First Brillouin zone of the zincblende lattice. (After Long.’)

principal directions are indicated by directional indices, which are numerically equal to Miller indices in a cubic lattice. The most important types of symmetry point and line are designated by the usual group-theoretical notation. b. Lattice Constant and Density us Composition

Woolley and Ray’ confirmed experimentally that solid solution occurs at all compositions in the alloy systems of interest. References to earlier work are given in their paper. Using X-ray techniques, Woolley and Ray’ determined the dependences of the lattice constant a. on composition x for the alloy systems Hg,-,Cd,Te and Hg, -,Zn,Te, and Blair and Newnham3 also made measurements of this type on Hg,-,Cd,Te. The resulting curve for Hg, -,Cd,Te is plotted in Fig. 4. It is interesting that in both alloy systems there is a deviation from Vegard’s law, i.e., a nonlinearity of the a, versus x variation ;however, the deviations are small. The density versus composition curve of Hg, -,Cd,Te, determined gravimetrically by Blair and N e ~ n h a m , ~ is plotted in Fig. 4 ; Blair and Newnham showed also that their experimental densities agreed well with those calculated from the lattice constant versus composition data. See p. 243 for a discussion of density determination. J. C. Woolley and B. Ray, J . Phys. Chem. Solids 13, 151 (1960). J. Blair and R. Newnham, in “Metallurgy of Elemental and Compound Semiconductors,” Vol. 12, p. 393. Wiley (Interscience), New York, 1961.

5. MERCURY-CADMIUM

6.460L

0

TELLURIDE AND CLOSELY RELATED ALLOYS

1

I

I

0.1

0.2

0.3

I

0.4

I

0.5

I

0.6

I

0.7

I

I

0.8 0.9

183

‘5.5 1.0

Y

FIG.4. Lattice constant and density versus alloy composition x in Hg, -.Cd,Te. The triangles represent the values of Woolley and Ray*: the circles represent the values of Blair and Newnhani.3

c. Phase Diagram

The (7; x) phase diagrams of Harman4 and of Ray and Spencer5 are compared here, and a (P, T ) diagram for Hg,&do.,Te is presented.6 The ( P , T ) diagram reconciles the two (T,x) diagrams by showing how liquidus and solidus temperatures depend on the mercury pressure for one x value. Also given are data on segregation coefficient obtained by measuring x on the first-to-freeze tips of several ingots, which data help identify the most useful solidus and liquidus lines. Throughout this section Hg, -,Cd,Te is considered as an alloy of HgTe and CdTe; therefore, no ternary phase diagram discussion is presented. Until recently very few phase diagram data wereavailable for Hg, _.Cd,Te. The work of Harman and Strauss, done in 1964, was first published in 1967 by H ~ m a nThe . ~ work of Ray and Spencer was published in 1967,5 but does not appear to agree with that of Harman and Strauss. Figure 5 reproduces the data of both papers in a single plot. The upper solidus line is due to Harman and Strauss4 and the upper liquidus line to Blair and Newnham,3 while the lower solidus and liquidus lines are the work of Ray and S p e n ~ e r . ~ Neither reference 4 nor 5 mentions the Hg pressure maintained during the ( T ,x) phase determination. The cross-hatched areas in Fig. 5 represent the range of uncertainty in the liquidus and solidus lines found in the literature.’ In Fig. 5 the circled plus signs represent the solidus and liquidus

’

‘T. C. Harman, in “Physics and Chemistry of 11-VL

Compounds” (M. Aven and J . S. Prener, eds.), p. 784. Wiley (Interscience), New York, 1967. ’ B. Ray and P. M. Spencer. Phys. Starus Solidi 22, 371 (1967). (’ J. L. Schmit and C. J. Speerschneider, Infiarrd Phys. 8, 247 (lY68).

184

DONALD LONG AND JOSEPH L. SCHMIT

I

I

0.1

I

I

I

I

I

I

0.2 0.3 0.4

I

I

0.5

I

I

I

0.6

I

0.7

1

I

0.8

I

I

0.9 1.0

MOLE F R A C T I O N C d T e

FIG. 5. (7; x) phase diagram for Hg,-,Cd,Te. (After Schmit and Speerschneider.6)

points taken from the (P, diagram presented in Fig. 6 for x = 0.20 & 0.02 material maintained above 2.5 atm Hg pressure. This liquidus point agrees well with the liquidus curve drawn by Ray and Spencer, while the solidus point agrees well with the solidus line of Harman and Strauss. The circled x’s represent the liquidus and solidus points from Fig. 6 for that same material maintained at 0.36 atm Hg pressure, which is the pressure that gives a solidus point agreeing with the data of Ray and Spencer. Thus both solidus lines and one of the liquidus lines can be fitted at x = 0.20 & 0.02 by using Hg pressure as an adjustable parameter. The ( T ,x) data thus support the liquidus line of Ray and Spencer, at least at x = 0.2. Figure 6 is not consistent with the data of Blair and Newnham, but differs by only a few mole percent. The melting point of CdTe is from the work of DeNobel.’

’ D. DeNobel, Philips Res. Rept. 14, 361 (1959).

5. MERCURY-CADMIUM

TELLURIDE AND CLOSELY RELATED ALLOYS

185

Segregation coefficient data6 are plotted in Fig. 5 as I's at temperatures dictated by the two liquidus lines for the starting material. They show that the solidus line of Harman and Strauss best represents Hg,-,Cd,Te for low x values when a high Hg pressure is maintained. Figure 6 is a (P, T ) phase diagram for Hg,-,Cd,Te with x = 0.20 0.02, measured by Schmit and Speerschneider.6 A series of curves obtained at various Hg partial pressures was used to plot the Hg pressure versus 1/T phase diagram for Hg,-,Cd,Te. This is shown in Fig. 6 with liquidus points marked with a circle and solidus points with a square. The region to the left of the liquidus line is liquid, the region between the liquidus and solidus lines is liquid plus solid, and the region to the right of the solidus is completely solid. The

o 0

+

LlOUlDUS POINTS SOLIDUS POINTS Hgo.e Cd0,*Te DISSOLVED I N Hg

A

Hgg.eCdo.2T6 SOLID, p-TYPE

v

HgTe DISSOLUTION LINE

i o o h

I O ~ I T(OK-')

FIG. 6. ( P , T ) phase diagram for Hgo,,Cdo,2Te.(After Schmit and Speerschneider.6)

186

DONALD LONG AND JOSEPH L. SCHMIT

liquidus line in solidification represents the point for any specific composition at which the first solidification occurs, while the solidus temperature indicates where it is completed. The triangles and plus signs represent annealing data taken on samples of Hg,,,Cdo,,Te. Each symbol refers to a sample which was annealed for 24 hours at the temperature and Hg pressure indicated. The triang1,es represent the samples which remained solid throughout their anneals. Hall data on one of these showed an extrinsic hole concentration of 10" cm- ; all of them were p-type by thermoelectric probing at 77°K. The plus signs represent the samples which absorbed Hg vapor until a solution of Hg,-,Cd,Te in Hg resulted which was liquid at room temperature. The line drawn between the plus signs and triangles is the dissolution line for Hg,,,Cd,,,,Te. This line is arbitrarily assumed to be continuous with the dissolution line of HgTe determined by Brebrick and Strauss' and represented by the two inverted triangles. A likely position of the intrinsic line, based on data taken at 300 and 400"C, is also dashed in. Since the solidus and liquidus lines are not parallel at low pressures, we must conclude that the segregation coefficient has a pressure dependence as well as an x dependence. Note that both the solidus and liquidus temperatures are lowered by reducing the mercury pressure below 2.5 atm. Schmit and Speerschneider6 postulate that this shift to lower temperatures with decreasing pressure is what causes the large discrepancy in the solidus line of Fig. 5. Taken together, the segregation coefficient data and the ( P , T ) phase diagram presented in Fig. 6 support the use of the solidus line of Harman and Strauss for low x values.

d. Diffusion The studies of diffusion in Hg,-,Cd,Te made to date have been restricted to the interdiffusion of HgTe and CdTe and the atomic diffusion' of Hg. Nothing is known experimentally about the diffusion of impurities. Rodot and Henoc" originated the method of obtaining Hg, -,Cd,Te structures of variable composition by means of the interdiffusion of HgTe and CdTe, and Bailly et ul." then made the first detailed study of the parameters of this interdiffusion process. Later results have been reported by Marfaing et ~ 1 . 'and ~ by Bailly.I3 Almasi and Smith" have studied the R. F. Brebrick and A. J. Strauss, J . Phys. Chem. Solids 26, 989 (1965). H. Rodot, Thesis. Univ. of Paris, 1964 (unpublished). H. Rodot and J. Henoc, Compt. Rend. 256,1954 (1963). I ' F. Railly, G. Cohen-Sulal, and Y. Marfaing, Cornpt. Rend. 257, 103 (1963). '' Y. Marfaing, G. Cohen-Solal, and F. Bailly, in "Physics of Semiconductors" (M. Hulin, ed.), Vol. I , p. 1245. Dunod. Paris and Academic Press, New York, 1964. F. Bailly, Compf. Rend. B262,635 (1966). '' G. S. Alrnasi and A. C. Smith, J . Appl. Phys. 39, 233 (1968).

5. MERCURY-CADMIUM

TELLURIDE AND CLOSELY RELATED ALLOYS

187

solid-state diffusion from mixtures of HgTe and CdTe powders into singlecrystal CdTe wafers, and have found results consistent with those of the above investigators. Reference can be made to these papers for plots of data on the interdiffusion coefficient versus temperature and alloy composition. e. Thermal Properties

The thermal properties of interest are the thermal conductivity and the coefficient of thermal expansion : Both can influence the method of mounting an infrared detector in a cooler. The thermal conductivity of CdTe has been studied in some detail, but much less is known about this property for the other compounds and the alloy^.'^" The thermal c o n d ~ c t i v i t y of ' ~ pure single-crystal CdTe is 0.4 W cm- ' OK- at 77"K, and it varies approximately as T - 1 . 3 between -30 and 300°K. Measurements on heavily p-type polycrystalline (- 10I8cm-3 acceptor concentration) HgTe gave about 0.15 W cm-' OK-' for the thermal conductivity16 at 77"K, with a variation of roughly T - l between this temperature and 300°K; these values for HgTe are only indicative of the probable behavior, because careful measurements on high-purity single crystals have not been made.I6" Experiments by Chasmar et a1.17 on several Hg,-,Cd,Te alloy samples suggest that the thermal conductivity passes through a shallow minimum for Hgo,,Cdo,zTe, but their results are not very quantitative. LaddI8 found the linear thermal expansion coefficient a of hot pressed disks of CdTe to be about 5.5 x lop6 per "C in the 25-100°C temperature range. Blair and Newnham3 obtained a value for HgTe single crystals of a=4 x per "C in the 25-50°C range. Quartz dilatometer determinations of a for HgTe as a function of temperature were made both by Novikova and Abrikosov several years ago" and by Alper and Saunders recently.20 The results of these two studies are plotted in Fig. 7. The overall agreement is poor, although the curves happen to meet at a value of a = 2x at the important temperature of 77°K. It is difficult to be sure which curve is more nearly correct, but very recent X-ray measurements 14'F. Kelemen, A. Neda, E. Cruceanu, and D. Niculescu, Phys. Status Solidi 28,421 (1968), give data for Hg, -,Zn,Te. G. A. Slack and S. Galginaitis, Phys. Rev, 133, A253 (1964). l 6 R. 0. Carlson, Phys Rev. 111,476 (1958). '"D. A. Nelson and C. R. Whitsett, Bull. Am. Phys. SOC.Ser. II 14,353 (1969), report very recent results. R. P. Chasmar, E. W. Durham, and A. D. Stuckes, Proc. Intern. Con$ Semicond. Phys., Prague, 1960, p. 1018. Czech. Acad. Sci., Prague, and Academic Press, New York, 1961. L. S. Ladd, Infrared Phys. 6, 145 (1966). S. I. Novikova and N. Kh. Abrikosov. Fiz. Tuerd. Tela 5, 2138 (1963) [Soviet Phys.-Solid State (English Trans/.)5, 1558 (1964)l. 2o T. Alper and G. A. Saunders, J . Phys. Chem. Solrds 28, 1637 (1967).

''

188

DONALD LONG A N D JOSEPH L. SCHMIT

Y Y

U

c 2

wu

Ew s

7

1

6-

54-

-

z 0 3-

-

v)

2

2-

X W

I -

J

a

0-

U

-

a a

I

W

-I

/ 1

/

/ I I

3

c U

-2-

a u -3-

z J

-4

I

-

-

I

’;‘

I

I

I

I

I

TEMPERATURE (“K)

FIG.7. Linear thermal expansion coefficient of HgTe versus temperature. The dashed curve is after Novikova and Abrikosov”; the solid curve is after Alper and Saunders.”

of the lattice constant versus temperature (120-300”K) by Sniadower et dZoa agree with the results of Novikova and Abrikosov. The thermal expansion coefficients of the HgTe-rich Hg, -,Cd,Te alloys of interest are presumably similar to that of HgTe.

f.Miscellaneous Properties Measurements of the elastic constants of HgTe have been made over the 4.2-290°K temperature range by Alper and Saunders2’ and at room temperature by Mavroides and Kolesar.’l The results are plotted in Fig. 8. Alper and Saunders found that the elastic constants changed slightly upon annealing the HgTe crystals in Hg vapor. Alper and Saunders obtained their data from annealed samples because they believed that their annealed crystals were more nearly free of structural defects than samples obtained directly from as-grown crystals. The discrepancy seen in Fig. 8 between the room temperature results of the two pairs of investigators may be due to differences in crystal preparation and history, involving different effective annealing treatments. The corresponding elastic constants” for CdTe, in ’OaL. Sniadower,M. Psoda, and R. R. Galazka, Phys. Sfatus Solidi 28, K121 (1968). J. G . Mavroides and D. F. Kolesar, Solid State Comrnun. 2, 363 (1964). H. G. McSkimin and D. G. Thomas, J. Appl. Phys. 33.56 (1962).

’’

’*

5 , MERCURY-CADMIUM

- :

TELLURIDEAND CLOSELY RELATED ALLOYS

I

5.60 5.40

CI I

189

I

-

5 20-

5.00

0

FIG.8. Elastic constants of HgTe versus temperature. The curves represent the results Of Alper and Saunders,20 and the open circles are the room temperature results of Mavroides and Kolesar.’’

units of 10“ dyn/cm2, are cI1 = 5.35, c12 = 3.681, and c44 = 1.994. One can probably assume that the elastic constants of the Hg,-,Cd,Te alloys vary linearly with composition between these endpoint values. Several other parameters are of some importance, and their values’ 1,23--26 as known for HgTe and CdTe are listed in Table I. Some parameter values from those presented earlier are also included in Table I. A linear interpolation between the values in Table I can be assumed for alloys in the Ng, -,Cd,Te system; the interpolated values for Hg0,,Cdo.,Te are included in the table. 5 . SEMICONDUCTING (ELECTRONIC) PROPERTIES a. Energy Band Structure

A conventional account of the research on the II-VI compound alloys would deal chronologically with the observed optical, electrical, and other 23 24 25

26

0. G. Lorimor and W. G. Spitzer, J . AppE. Phys. 36, 1841 (1965). D.H.Dickey and J. G. Mavroides, Solid State Commun. 2,213 (1964). L. Sniadower, V. I. Ivanov-Omskii, and E. Z. Dziuba, Phys. Starus Solidi 8, K43 (1965). R. E. Halsted, M. R. Lorenz. and 8. Segall, J. Phys. Chem. Solids 22, 109 (1961).

190

DONALD LONG AND JOSEPH L . SCHMIT

TABLE I PHYSICAL PARAMETERS OF HGTE A N D CDTE

Parameter

Static dielectric constant, co Optical (high frequency) dielectric constant, E, Longitudinal optical phonon energy at zone center, k," (ev) Transverse optical phonon energy at zone center, hw,., (eV) Thermal conductivity (W cm-' O K - ' ) Lineal thermal expansion coefficient (x

Temperature

Experimental values HgTe CdTe

20 14

10.6 & 0.5 7.05 _+ 0.05

Interpolated Hg, ,Cdo,,Te 18.1 12.6

References 21,23,24 23 -25

0.0161

0.21 3

0.055

23.26

0.0143

0.173

0.046

23,24

77°K

0.15

0.4

0.2

16,15

77°K 25°C

2 4

5.5

4.3

19,20. 20a 3. 18

5.35 3.681 1.994

5.39 3.78 2.04

20.22 20.22 20.22

OK-')

Elastic constants

300°K 300°K 300°K

5.4 3.8 2.05

properties first, showing how their measurement graduaiiy helped lead to an understanding of the electronic energy band structures of the materials. For our purposes, however, it is better to describe the band structures first, mentioning only those experimental results needed to establish them, and then to review later the optical and electrical properties pertinent to the use of these materials in infrared detectors. The band structures are fairly well known now" and form the basis for much that follows in this chapter. We will continue to concentrate on the Hg, -,Cd,Te alloy system. There is a close generic relationship among the electronic energy band structures of all the materials crystallizing in the zincblende cubic structure. Their band structures are also analogous in many respects to those of the diamond cubic semiconductors silicon and germanium because of the basic similarities of these two crystal structures. The band structures of Si and Ge and of the 111-V compounds are already well understood,' and much can be learned about the less well-known materials under consideration here by comparison with these better-known semiconductors. We will be concerned mainly with the energy bands in the vicinity of the r point (k = 0), where the 27

See T. C. Harman. in "[I-VI Semiconducting Compounds" (Proc. Inrern. CoqL, Brown Uniu., 1967), p. 982. Benjamin, New York and Amsterdam, 1967, for an up-to-date review of band structure and other parameters in the materials or interest.

5 . MERCURY-CADMIUM TELLURIDE AND

CLOSELY RELATED ALLOYS

191

extrema of the valence and conduction bands occur in the Brillouin zones of the materials of interest. The valence electrons in the zincblende structure semiconductors form the covalent bonds which hold the crystal together, and the quasicontinuum of energy levels which they occupy is the valence band. Each atom in the lattice is connected directly to the four adjacent atoms by hybridized tetrahedral orbitals, each of which contains two valence electrons. Since there are six valence electrons per anion and two per cation, and one anion and one cation per primitive unit cell, the valence band contains eight electrons per unit cell. The four tetrahedral orbitals form a basis for a reducible representation of the r point group. One of the irreducible representations is r6(in

r

4-L

t

W

*

(3

rs A

a W

z

W

2

InSb

7

Eg = 0.2350'4

0

a I-

V

w

J

W

q 1hv

b"r0.0 rv

-

-0.5

0.5

1.0

k (107CM-') [I I I]

[I 001 -c

FIG.9. Energy band structure of InSb. The values shown for the energy gap E , and valence band spin-orbit splitting energy A are for -0°K. The important I- point levels are indicated in double group notation. (After Long.')

192

DONALD LONG AND JOSEPH L. SCHMIT

double group notation), which accounts for the s contribution to the hybridized orbitals; this level lies at the bottom of the valence band, is twofold spin degenerate, and is occupied by two electrons per unit cell. The remaining six electrons occupy a level derived from the p orbitals; this level would be sixfold degenerate at (including the double spin degeneracy associated with each of the three p orbitals) except for the spin-orbit interaction, which splits it into a fourfold degenerate level made up of the two p3/’ states and a twofold degenerate plI2 level. The p3,’ level lies higher than the pIlt and marks the top of the valence band at r. The irreducible representation corresponding to the p3,’ level is Ts, and that for the pliZ level is r,. The absence of inversion symmetry in the zincblende crystal lattice permits an additional detailed splitting of the valence band edge originating from the spin-orbit interaction, so that the absolute maxima of the valence band may occur at points in the Brillouin zone away from k = 0. The general characteristics of the valence band structure around k = 0 of a zincblende cubic crystal, described in the preceding paragraph, are shown in the lower half of Fig. 9. This figure happens to be the energy E versus wave vector k diagram for InSb, but its qualitative features represent those of any narrow-gap zincblende structure semiconductor. Note the detailed splittings away from k = 0 at the top of the valence band and also the division of the valence band into the so-called “heavy-hole,’’ “lighthole,” and “split-off’’ branches, labeled hhv, lhv, and sov, respectively, in Fig. 9. The conduction band minimum in the materials of interest is a Ts state, at k = 0 (see Fig. 9). Of great importance is the fact that the conduction band is nonparabolic; i.e., the electron energy E does not vary as k2. This nonparabolicity is caused by the well-known k p interaction,’*’* which also determines the effective masses at the edges of the conduction band and of the light-hole valence band. The k p theory for the types of band structure shown in Fig. 9 gives the following approximate E(k) relationships for the four bands of Fig. 9 : a

Ehhv= h 2 k 2 / 2 m ,

E,,,

=

- A -t

ii’k’ 2m

Elh” = __

h2k2 2m

__ -

(2)

k2P2 3(E, A)’

+ E , - [E,’ +2(8k’P’/3)]”2 + + [EgZ+2(8k2P2/3)]”’

h2k2 E , E, = 2m 28

M. Cardona, J. Phys. Chem. Solids 24, 1543 (1963).

(3)

+

9

(4) (5)

5. MERCURY-CADMIUM

193

TELLURIDE AND CLOSELY RELATED ALLOYS

The energies in Eqs. (2t(5) are measured from the valence band edge. These equations assume that kP and the energy gap E , are both much smaller than A, the spin-orbit splitting energy; here P is the momentum matrix element, which has the empirical value of about 9 x lo-' eV cm for the 11-VI compounds,28 and m is the mass of a free electron. The nonparabolic shapes of the conduction and light-hole valence bands are evident in the forms of Eqs. (4) and (5). Note that the surfaces of constant energy are spherical in this model ; inclusion of k p interactions with higher-lying conduction bands would lead to the warping of the valence-band constantenergy surfaces known to exist in the zincblende-structure materials. Cardona has published a useful paper on this subject,28 to which the reader should refer for the more nearly complete k * p analysis. When k z 0 the nonparabolic band equations simplify to

-

h2k2 2k2P2 Elh"= __ - -, 2m 3E, E , - h2k2 + -k2Pz( 2 2m 3 E,

+

1

___

E,

+A

)

(7)

Using Eqs. (6) and (7) and the usual prescription for the effective mass,

m*

= h2(d2E/dk2)-1,

(8)

we find that m/m$,, = 1 - (4mP2/3h2E,)

(9)

and

When these effective masses are small (m* 4 m) and when E, 4 A, conditions which always hold for our narrow-gap materials, Eqs. (9) and (10) reduce further to the following simple expressions for the effective masses : I(m$,,/m)l x 3h2E,/4mP2

(1 1)

and

m,*/m

%

3h2E,/4mP2.

Equations (1 1) and (12) illustrate two important general results for these narrow-gap materials : first, the light-hole valence band and conduction band edge effective masses are approximately equal, and second, they are both approximately proportional to the energy-gap width. Let us now discuss the band structures of the compounds which are the components of the alloy systems of interest,' viz., CdTe, ZnTe, and HgTe. These must be understood first, so that we can consider later how they blend

194

IIONALD LONG AND JOSEPH L. SCHMIT

t

CdTe

Eq = 1.605eV

W

i

W

z

W

z 0

a Iu W

-1

W

hhv7 T+ /hv

, -3

A = O.BeV

?;s -2

-I 1 k (IO’CM-’)

2

3

4

FIG. 1 0 Fnergy band structure of CdTe. The values 5hown for E, and A are for -O”K. Thc importan1 r point levels are indicated in double group notation. (After Long.’)

to give the band structures of the mixed crystals. A plot of the E vs k curves for CdTe in the vicinity of its energy gap at k = 0 is shown in Fig. 10. The valence band maximum is Ts and the conduction band minimum r,, as in most zincblendc structure semiconductors ; hence CdTe has a divrct cnergy gap at k = 0. The detailed structure of the valence band edge, indicated in Fig. 9, although possibie in these materials, has not been observed clearly in CdTe, and is thereforc not shown in Fig. 10. Several different types of experiment agree in giving a gap width of 1.605eV at -0°K in CdTe. ZnTe has a band structure qualitatively analogous to that of CdTe, but its energy gap is 2.39 eV at -0°K. The temperature dependence of the CdTe energy gap is plotted in Fig. 11, including data points from the different experiments which have established the curve. The curve in Fig. 11 has the shape which is normal for semiconductors, and it has been explained

5. MERCURY-CADMIUM

TELLURIDE AND CLOSELY RELATED ALLOYS

1.62 I

1

I

195

I

c

1.56 W

&

1.54

U

o OPTICAL ABSORPTION

W W

1.48’

I

100

0

I

200

300

TEMPERATURE (DK) FIG. 1 I .

Temperature dependence of the energy gap in CdTe. (After Long.‘)

theoretically in terms of a narrowing of the gap with increasing temperature owing to electron-phonon interactions. The E , versus T curve for ZnTe is similar to that for CdTe. The valence band spin-orbit splitting energies are about 0.8 eV in CdTe and 0.9 eV in ZnTe. No reliable experimental information is available about the valence band effective masses in CdTe or ZnTe, but Cardona has estimated values of these parameters using the k p theory.2*The conduction band edge effective mass of CdTe has been measured fairly accurately, and its -0°K and room temperature values are listed in the first row of Table 11. The corresponding mass for ZnTe at -O”K, for which the only available value is that calculated by the k p method, is given in the second row of Table 11. A plot of the E versus k curves for HgTe in the region of interest is shown in Fig. 12. One can see from Fig. 12 that HgTe is actually a semimetal rather than a semiconductor,’*29because the r6 state, which is normally the conduction-band minimum in zincblende structure compounds, happens to lie lower in energy than the Ts valence band maximum. The energy “gap,” or T6-Te energy difference, is thus negative in HgTe. The k p interaction causes an inversion, or reversal of curvature, of the conduction and lighthole valence bands in HgTe because of the negative Ts - Tsenergy ; hence, what is usually the light-hole valence band becomes a conduction band tied by symmetry to the heavy-hole valence band at T, while what is usually the

-

-

-

*”

T. C. Harman, W. H. Kleiner, A. J. Strauss, G. B. Wright, J. G. Mavroides, J. M. Hoiiig, and D. H. Dickey, SolidStafe Cummun. 2, 305 (1964); S. H. Groves and W. Paul, in “Physics of Semiconductors” (M. H u h , ed.). Vol. I , p. 194. Dunod, Paris, and Academic Press, New York, 1964.

196

DONALD LONG AND JOSEPH L. SCHMlT

TABLE I1 k = 0 CONDUCTION BAND ELECTRON EFFECTIVE MASS RATIO, THE ZINCBLENDE STRUCTURE 11-VI COMPOUNDS'

VALUES OF ffl.*/m, THE IN

Effective mass (in units of free electron mass)

-0°K Compound

Measured

Calculated

CdTe

0.096 f 0.005

(0.11)

ZnTe HgTe

0.029 & 0.003

(0.17) (0.026)

Experimental methods

300°K 0.11 & 0.01

Cyclotron resonance, Faraday rotation Oscillatory magnetoresistance

-.

"The values in parentheses, calculated using the k p theory in Cardona's formulation, agree quite well with the corresponding experimental values, which come from publications listed by Long.'

r

-c

X--

BAND EDGE

t

W

i W

a W 2 W

B a

I

&-

V

w -I w

A m i eV

HgTe

-1.5

-

-1.0 -0.5

0

0.5

k ( lo7 CM-' 1 [Ill]

1.0

1.5

[loo]

2.0

-

FIG.12. Energy band structure of HgTe. The values shown for the "negative energy gap" and A are for -0°K. (After Long.')

5. MERCURY-CADMIUM TELLURIDE AND CLOSELY RELATED ALLOYS

197

conduction band becomes a light-hole valence band separated from the heavy-hole valence band at r. There is no actual energy gap in HgTe. The conduction and light-hole valence bands have reversed their usual roles in HgTe, but they still have nearly equal band edge effective masses and nonparabolic shapes due to the k p interaction, just as in the ordinary zincblende structure semiconductors. One can deal with the band structure in HgTe in a straightforward way simply by treating the Ts - Ta energy difference as a “negative energy gap.” This “gap” is about -0.30eV at -0°K from the results of interband magnetoreflection experiments. It apparently shrinks to about -0.15 eV at room temperature, although the analyses of the room temperature data may not be correct. They are based on the assumption that the temperature shift of the gap can be incorporated directly in the k - p theory; this may be a bad assumption since, strictly speaking, the k . p theory is valid only for a rigid lattice, a situation best approximated by -0°K data. The semimetallic band structure of HgTe is analogous to that of a-Sn (gray tin).‘ s 3 0 It was thought originally that HgTe was a semiconductor with a very narrow energy gap of only about 0.01 eV, but many recent experiments have verified the semimetallic model of Fig. 12. Determinations of the electron effective mass from reflectivity and other measurements, and application of the k p theory to the results, showed that the gap must be much wider than the above value of 0.01 eV. Studies of the effects of pressure on the electrical properties of HgTe and of the properties of Hg, -,Cd,Te alloys as functions of composition x gave results consistent with the semimetallic model, but not with the very-narrow-gap semiconductor band structure. Incidentally, the detailed structure of the valence band edge permitted by symmetry has been shown for HgTe in Fig. 12, but several experiments have suggested that the maxima along the (1 11) axes are less than 0.003 eV above the rpoint energy and therefore practically unobservable. The valence band spinorbit splitting energy has not been measured reliably, but it should be roughly 1 eV by analogy with other zincblende structure materials. A value of mu* z 0.35 m has often been used for the average effective mass of holes near the valence band edge in HgTe, but recent experiments suggest values up to 0.7m.30a*30b The -0°K electron effective mass at the conduction band minimum has been determined from oscillatory magnetoresistance and other experiments, and the result is listed in Table I1 together

-

.

S. H. Groves and W. Paul, Phys. Rev. Letters 11, 194 (1963). ’OaV. I. Ivanov-Omskii, F. P. Kesamanly, B. T. Kolomiets, A. Sh. Mekhtiev, and V. A. Skripkin, Phys. Status Solidi 27, K 169 (1968). 30bV.I. Ivanov-Omskii, B. T. Kolomiets, A. A. Mal’kova, Yu.F. Markov, and A. Sh. Mekhtiev, Fiz. Tekh. Poluprov. 2, 1340 (1968) [English Transl.: Soviet Phys.-Semiconductors 2, 1122 ( 1969)l. 30

198

DONALD LONG AND JOSEPH L. SCHMIT

with the value calculated from the k p theory, using Cardona’s formulation28 and the measured 0.30 eV “negative energy gap.” Let us now consider the consequences in terms of energy band structure of mixing two of the IT-VI compounds together to form an alloy. The alloy systems of interest are those which can yield material with relatively narrow energy gaps, in the range corresponding t o intrinsic electron-hole pair excitation by infrared radiation. We noted in the introduction that these mixed crystals can be treated simply as ordinary semiconductors which have continuously variable, adjustable energy gaps, so that we need not be concerned with any special properties due to their alloy nature. Furthermore, in the case of a mixture of two materials having qualitatively similar band structures the energy gap and other band parameters should vary smoothly, and in fact nearly linearly, with composition. The procedure to obtain gaps in the range of zero to -0.5 eV (corresponding to typical infrared wavelengths) is then to mix a material having a gap wider than 0.5 eV with onc having a virtually zero gap to obtain the desired gap width in some alloy 9

0

1NTERBANO MAGNETOREFLECTION AT 77’K

x INTERBAND MAGNETOREFLECTION AT 4 * K OPTICAL ABSORPTION AT 300’K

A,A

I .4

1.2 -

V

PHOTOVOLTAIC STUDIES AT 7 7 ’ AND 300°K PHOTOLUMINESCENCE AT 12’K

;1.0-

-% 0

o.8-

W

*

w 0.6a w

2

w 0.4-

1 - ‘,. 0’

- 0.2

K

r

- 0.4 1

H g Ta

I

1

1

X

I

CdTe

FIG. 13. Energy gap versus composition in Hg, .,Cd,Te. The solid line represents the dcpcndcncc at -0°K. and the dashed line is for 300°K. The types of experiments giving the data point$ are indicated. (After Long. ’)

5 , MERCURY-CADMIUM TELLURIDE AND CLOSELY RELATED ALLOYS

199

composition. For the compounds of this chapter, the obvious mixtures (alloy systems) are Hg, -,Cd,Te and Hg, -,Zn,Te. We will discuss Hg, -,Cd,Te below. Good data giving information about the energy gap versus x are not available for Hg, -,Cd,Te over the entire range of alloy compositions, but there are some reliable experimental results for the compositions in the vicinity of x = 0.2-0.4 which have been of the most interest in the development of infrared detection and emission devices. These better r e ~ u l t s1-36 ,~ combined with the well-established gap values for the HgTe and CdTe “endpoints” of the system,’ fit well with the linear r e l a t i ~ n s h i p ~ between ’,~~ E, and x assumed in Fig. 13. The data plotted in Fig. 13 have been chosen mainly from relatively recent experiments done by groups long engaged in research on this alloy system because some of the earlier data are inconsistent and probably unreliable ; it is difficult to prepare uniform crystals of an alloy and to determine its composition correctly, so that care must be taken in choosing data from which to draw conclusions. Note that the band structure shown in Fig. 9 should represent quite accurately a Hg, -,Cd,Te alloy with x z 0.27, as well as InSb. Also, all the narrow-gap semiconducting compositions of Hg, - ,Cd,Te have band structures qualitatively analogous to that in Fig. 9. The energy gap can be considered direct, both band extrema being at the same point in k-space, because the detailed structure permitted at the valence band edge is negligible with respect to most physical processes. T h e ~ r e t i c a l l y the , ~ ~ energy gap of an alloy system should vary slightly nonlinearly with composition. The deviation from linearity should reduce the gap below the linear dependence by an amount proportional to x2, i.e., the E, vs x curve should be slightly “bowed” downward. This type of Eg vs x curve seems to apply to several of the 111-V compound alloy systems, but the absence of data spread over all compositions of Hg, -,Cd,Te keeps T. C. Harman, A. J. Strauss, D. H. Dickey, M. S. Dresselhaus, G. B. Wright, and J. G . Mavroides, Phys. Rev. Letlers 7, 403 (1961). 32 A. J. Strauss, T. C. Harman, J. G. Mavroides, D. H. Dickey, and M. S. Dresselhaus, Proc. Intern. ConJ Phys. Semicond., Exeter, 1962, p. 703. Inst. Phys. and Phys. SOC.,London, 1962. 33 M. D. Blue, Phys. Reo. 134, A226 (1964); in “Physics of Semiconductors” (M. H u h , ed.), Vol. I, p. 233. Dunod. Paris, and Academic Press, New York, 1964. 34 C. Verii. and R. Granger, Cornpt. Rend. 261, 3349 (1965). 3 5 I. Melngailis and A. .I.Strauss, Appl. Phys. Letters 8, 179 (1966). 3 6 C. Vcrie and J. Ayas, Appl. Phys. Letters 10, 241 (1967). 3 7 This linear relationship was proposed first by D. Long (unpublished results presented at Infrared Information Symposium Detector Specialty Group Meeting, Dayton, Ohio, March, 1967). 38 C. VCrie. in ‘‘TI -VT Semiconducting Compounds” (Proc. Intern. Con$ Brown Uniu., 1967), p. 1124. Benjamin, New York and Amsterdam, 1967. 39 M. Cardona, Phys. Rev. 129,69 (1963). 31

200

DONALD LONG AND JOSEPH L. SCHMIT

4 n

HQ0.83cd0.1TT' ( PHOTOCONDUCTIVITY 1

I

L!

{ MAGN€TOOPTICAL\

-0.30

-0.321 0

1

20

I

1

40 60 TEMPERATURE ('K)

I

80

I

I00

FIG. 14. Energy gap versus temperature in HgTe, and in Hg,-,Cd,Te with x z 0.17. The magnetooptical data of Pidgeon and Groves4' and the photoconductivity data of Saur4I are shown.

one from noticing it in Fig. 13. In any case, the deviation from linearity should be small (<0.1 eV at x z 0.5 by analogy with the 111-V compound systems39).Very recent optical absorption measurements by and photoconductivity data of Schmit and S t e l ~ e rsuggest ~ ~ ~ a downward bowing of the curves of Fig. 13, so that the gap at x z 0.5 is about 0.1 eV narrower than in Fig. 13. Energy gap versus x lines have been plotted in Fig. 13 for both -O"K and room temperat~re.~' It is apparent that the temperature dependence changes the gap width by a large fraction in the narrow-gap alloys, so that the temperature variation of E, is an important factor in the use of these alloys in infrared detectors. Of special interest is the fact that the temperature dependence (aE$U),,, reverses sign at x x 0.5 and is positive in the narrow-gap semiconductors with x < 0.5, i.e., the gap widens with increasing temperature. This positive (dEJaTf,,, is anomalous in that nearly all other semiconductors have negative dependences. Figure 14 reproduces recent experimental results of Pidgeon and Groves4' (magnetooptical experiments) and of Saur4' (photoconductivity), which show the positive temperature dependence of the gap in HgTe and the low-x alloys at low temperatures; this figure also 39aM.W. Scott, Bull. Am. Phys. SOC.Ser. I1 14,416 (1969); J . Appl. Phys. 40,4077 (1969). 39bJ. L. Schmit and E. L. Stelzer, J. Appl. Phys. 40,4865 (1969). 40 C. R. Pidgeon and S. H. Groves, in "11-VI Semiconducting Compounds" (Proc.Intern. Con$? Brown Univ., 1967). p. 1080. Benjamin, New York and Amsterdam, 1967; S. H. Groves, R. N. Brown, and C. R. Pidgeon, Phys. Rev. 161,779 (1967). 4 ' W. D. Saw, Infrared Phys. B, 255 (1968); also unpublished results and ref. 39b.

5. MERCURY-CADMIUM

TELLURIDE AND CLOSELY RELATED ALLOYS

201

I

I

INTERBAND MAGNETOREFLECTION AT ? ? O K x INTERBAND MAGNETOREFLECTION AT 4 * K 0 CYCLOTRON RESONANCE AT 4" 0

0.010

-

0.005

-

0 HgTo

0.1

0.2

0.3

I

FIG. 15. Conduction band edge effective mass at k = 0,in units of the free electron mass, versus composition in Hg, _,Cd,Te, calculated for 0°K by the k * p method. (After Long.') The magnetoreflection and cyclotron resonance data are from Harman e t aL3*and Strauss et aL3' ; the magnetoresistancedata are from Giriat.42

-

demonstrates the interesting and peculiar result that the gap apparently The electronvaries linearly with temperature all the way down to O°K.39a,39b phonon interactions lead inherently to a narrowing of the gap with temperature, while the lattice expansion contribution to the gap shift is known from high pressure experiments on HgTe and Hgo,8Cdo.zTeto contribute also to a narrowing of the gap, so that the anomalous (aE$aT),,, in these low-x alloys cannot be understood on the basis of the mechanisms normally considered. The variation of (BE$dT)v,Pwith x in the Hg,-,Cd,Te alloy system is probably a specific crystal lattice potential effect, having to do with the gradual change of the crystal potential and a possible variation in the lattice vibrational properties with x. An analogous situation seems to occur in the Pb, - .Sn,Te alloy system.' We have used the E, versus x dependence of Fig. 13 in Cardona's formulation of the k . p theory2' to calculate the curve of the conduction band edge effective mass versus x shown for Hg, -,Cd,Te in Fig. 15. The few existing data are plotted there also, and they agree rather well with the 42

W. Giriat, in "11-VI Semiconducting Compounds" (Proc. Intern. Con$, Brown Unio., 1967), p. 1058. Benjamin, New York and Amsterdam, 1967.

202

DONALD LONG AND JOSEPH L. SCHMlT

I LL

W

0

u

I

0

i

0

0

to3

2X1OL‘

0

8

0.05

I

0.10

I

I

I

I

0.15 0.20 0.25 0.30 PHOTON E N E R G Y ( e V )

I

0.35

I

0.40

FIG. 16. Fundamental optical absorption edge versus composition in Hg, -,Cd,Te. (After Blue.33)Data points for seven different samples are shown, and the value of the composition parameter .v for each sample is given in parentheses. The curves represcnt calculated absorption edges for material with energy gaps of 0,0.03,0.09,0.16,0.20, and 0.24 eV from left to right.

theoretical Recent results of Sosnowski and Galazka lend further ~erification.~~ One would expect the Hg,-,Zn,Te system to have energy gap and effective mass versus x curves qualitatively like those of Figs. 13 and 15, and available data appear to support this expectation.43a 6. Optical Properties

We will concentrate in the remainder of this review of semiconducting properties mainly on Hg, -,Cd,Te alloy compositions giving energy gaps suitable for long-wavelength intrinsic infrared detectors (0.15 5 x 5 0.4); we will deal with other compositions and with the properties of the “endpoint” compounds only when they aid the understanding of these narrowgap alloys. The optical properties to be considered include absorption, photoconductivity, luminescence, and magnetooptical effects, as they are determined by the energy gap and by the properties of the free electrons and holes. Optical properties determined by the lattice were covered in Section 4. D. Wiley and R. N. Dexter, Phys. Rev. 181, 1181 (1969). L. Sosnowski and R. R. Galazka, iu “IT-VI Semiconducting Compounds” (Proc. Inrrm. Con$, Brown Unro., 1967), p. 888. Benjamin, New York and Amsterdam, 1967. 43aE.2. Dziuba, D. Niculescu, and N. Niculescu. Phys. Status Sofidi 29, 813 (1968). 42aJ. 43

5. MERCURY-CADMIUM

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203

Lawson et were the first to report results of a detailed study of the Hg, ,Cd,Te alloys ; their experiments included measurements of the fundamental optical absorption edge as a function of alloy composition. Other absorption-edge studies were carried out by Kruse and Blue,45by Kot et by Kolomiets and Mal’k~va:~by Blue,33 by Shneider and Zhmurko,48 by Marfaing et ul.,” and by Ivanov-Omskii et aL4’ All of the results show a gradual, apparently smooth shift of the absorption edge to longer wavelengths as x -, 0 in the Hg,-.Cd,Te crystals, but the alloy compositions were seldom well enough known or uniform enough, or the absorption edges clearly enough defined, to permit accurate determination of the energy gap versus x from these data. The measurements and analysis by Blue33 are the most extensive in the composition range of interest; we have already used some of his data in Fig. 13. He measured the fundamental absorption edges of several Hg, -,Cd,Te samples ranging from pure HgTe to Hgo,6,Cdo,,2Te, and compared the results with absorption edge shapes calculated from the k . p theory for several energy gaps. His data and calculated curves, plotted in Fig. 16, are in fair agreement, but one probably cannot make definite conclusions about the band structure from this type of experiment alone ; however, we have already seen that other experiments combine to indicate that the Hg, -,Cd,Te alloys in this range have an InSb-like band structure of the type to which the calculated curves in Fig. 16 apply. We will use these calculated curves later in the discussion of excess-carrier lifetimes in Hg, -,Cd,Te. More recent measurements on much better samples are available. Lawson et ~ 1were . the ~ first ~ to report photoconductivity in narrow-gap Hg, -,Cd,Te alloys, while Kruse et al. first demonstrated these effects c o n ~ l u s i v e l yOther . ~ ~ groups of invcstigators have also studied the intrinsic photoconductivity in this alloy s y ~ t e m , ~ ~ especially ~ , ~ ~ *the~ wave~ * ~ ~ - ~ ~ length of the photoconductive peak as a function of sample composition, and -

W. D. Lawson, S. Nielsen, E. H. Putley, and A. S . Young, J . Phys. Chern. Solids 9, 325 (1959). P. W. Kruse and M. D. Blue (unpublished results). 46 M. V. Kot, V. G. Tyrziu, A. V. Simashkevich, Yu. Y. Maronchuk, and V. A. Mshenskii, Fiz. T i ~ d Tela . 4, 1535 (1962) [Sovier Phys.-Solid State (English Trunsl.)4, 1128 (1962)l. 4 7 B. T. Kolomiets and A. A. Mal’kova, Fiz. T w r d . Tela 5, 1219 (1963) [Soviet Phys.-So[id Stare (English Transl.) 5, 889 (1963)l. 4R A. D. Shneider and 1. S . Zhmurko, Ukr. Fiz.Z h . 9, 32 (1964). 49 V. I. Ivanov-Omskii, B. T. Kolomiets, and A. A. Mal’kova, Fiz. Tuerd. T e f a 6, 1457 (1964) [Soi’iet Phys.-Solid State (English Transl.) 6, 1140 (1964)l. P. W. Kruse, M. D. Blue, J. H. Garfunkel, and W . D. Saur, Infrared Phys. 2-53 (1962). 5 1 P. W. Kruse, Appl. Opt. 4,687 (1965). 5 2 J. C. Ayache and Y . Marfaing, Compt. Rend. B265, 363 (1967). 53 G. Cohen-Solal, Y. Marfaing, and P. Kamadjief, in “11-VI Semiconducting Compounds” (Proc. Intern. Conf, Brown Univ., 1967),p. 1304. Benjamin, New York and Amsterdam, 1967. 44

45

204

DONALD LONG AND JOSEPH L. SCHMIT

have found general correlation of the results with the absorption-edge measurements ; however, once again the samples were often not trustworthy enough to allow accurate conclusions. Photoelectromagnetic47.49.52.53 and p h o t o v o l t a i effects ~ ~ ~ have ~ ~ ~also ~ ~been ~ ~observed ~ ~ ~ ~in~ Hg, -,Cd,Te; some of the photovoltaic data appear in Fig. 13. Several other optical and magnetooptical effects have been studied in narrow-gap Hg, -,Cd,Te samples. Both spontaneous and coherent (laser) photoluminescence have been observed by Melngailis and S t r a u ~ s and ,~~ the results give quite accurate energy-gap values for samples with x x 0.3-0.4. Injection electroluminescence in p-n junctions has been studied by VeriC. and c o - w o r k e r ~ . ~Relatively ~ * ~ ~ early low-temperature magnetoreflectivity measurements by Harman and Strauss and c o - ~ o r k e r s on ~~,~~ Hg,-,Cd,Te samples with x near 0.15 gave narrow gaps of only a few hundredths of an eV, and also very small values of the electron effective mass, consistent with the requirements of the k p interaction (see Figs. 13 and 15). Cyclotron resonance corresponding to a very small electron effective mass was observed in a Hgo,,3Cdo.,7Tesample3’ (see Fig. 15). c . Electrical Properties

In their pioneering study of Hg, -,Cd,Te Lawson and c o - ~ o r k e r s ~ ~ measured the electrical conductivity and Hall effect of several alloy samples as functions of temperature. Since then, further experimental work on the electrical properties of crystals in the range of alloy compositions of interest has been done by others. Early measurements by Harman and Strauss and co-workers3’ yielded high electron mobility values at low temperatures in the narrow-gap alloys. Studies of the electrical properties of a few samples were also carried out by Kot et a1.,46 by Shneider and G a v r i ~ h c h a k ,by ~~ Malis6 and by VCrie.57Kruse, Schmit, and co-workersS8have made extensive measurements of the electrical properties of alloys of compositions near Hgo.,Cdo.,Te. A few reports also exist of the electrical properties of Hg,-,Cd,Te outside the 0.15 5 x 5 0.4 and they may aid an understanding of the alloy compositions of specific interest here. J. Fourny, S. Martinuzzi, and J. Decque, Compt. Rend. 261,4713 (1965). A. D. Shneider and I. V. Gavrishchak, Fiz. Tuerd. Tela 5, 1208 (1963) [Soviet Phyx-Solid State (English Trunsl.) 5, 881 (1963)l. 5 h M. Mali, Phys. Status Solidi 13, 21 5 (1966). 5 7 C. Verie, Phys. Status Solidi 17, 889 (1966). ‘’P. W. Kruse and J. L. Schmit (unpublished results). 5 9 R . R. Galazka, Acta Phys. Poton. 24,791 (1963). 6 o M. Rodot, H. Rodot, and C. VtriC, in “Physics of Semiconductors” (M. H u h , ed.), Vol. 1, p. 1237. Dunod, Paris, and Academic Press, New York, 1964. R. R. Galazka and L. Sosnowski, P hys. Status Solidi 20, 1 1 3 (1967). 6 2 R. R. Galazka and T. Zakrzewski, Phys. Starus Solidi 23, K39 (1967). 54

55

’

5. MERCURY-CADMIUM

to2 1 0

TELLURIDE AND CLOSELY RELATED ALLOYS

I

I

I

I

20

40

60

80

I

100

I

205

*.

120'

240

1 0 ~( O 1 K - ' )~

FIG.17. Hall Coefficientversus temperature for an n-type sample of Hgo,,Cdo.,Te.

Data on the Hall coefficient R, and the resistivity p versus temperature T for a typical sample with the approximate composition Hgo,,Cdo,,Te are The sample was taken directly plotted in Figs. 17 and 18, re~pectively.~~ from a crystal grown by solidification from a melt prepared with highly pure elements. The Hall coefficient versus temperature curve has the shape expected for a narrow-gap InSb-like semiconductor. It is n-type at low temperatures because an excess of donors dominates the extrinsic conduction, and remains n-type in the intrinsic range at higher temperatures because the electron mobility is greater than the hole mobility. There is no evidence for carrier freeze-out onto discrete impurity or defect donor levels at the lowest temperatures in Figs. 17 and 18; this behavior is consistent with the very low effective mass of conduction band electrons given by the band structure described in Section 5a and with the consequent probable absence of any bound states for electrons near the conduction band edge. That is, the donor levels must be merged with the conduction band, so that the extrinsic electron concentration remains constant at all temperatures. The extrinsic electron concentration no calculated from the low-temperature Hall coefficient of Fig. 17 assuming no = (e0RH)-'is about 6 x l O I 4 crnp3.

206

DONALD LONG AND JOSEPH L. SCHMIT

I

I

I

I

c

5 0 I

0

I

I

I

I

20

40

60

80

I

100

I

120

,.

'

240

IO3/T (-K-')

p i c . 1 R Electrical resistivity versus temperature for the n-type sample of Hg, ,Cd, ,Te of Fig 17

The intrinsic slope of the In R , versus 1/T curve in Fig. 17 corresponds to an energy gap, extrapolated linearly to O'K, of about 0.1 eV. The intrinsic carrier concentration n, in Hg, -,Cd,Te for the composition t ~ temperatures ~ range 0.15 < x ,< 0.25 has been calculated by S ~ h m i for between 40 and 300°K. The type of band structure shown in Fig. 9 and the energy gap versus x curve of Fig. 13 were assumed, and full account was taken of the nonparabolicity of the conduction band due to the k - p interaction. Schmit's calculations are described in detail in the appendix; the results are especially useful for analyses of intrinsic infrared detector properties for various alloy compositions, and thereby wavelength responses. The calculated curves of n, versus x for a number of temperatures are shown in Fig. 19. Also ptotted in Fig. 19 are experimental values of izi for several samples of compositions around Hg,.,Cdo 2Te, deduced by Vkrie3' for 300°K and by Schmit and c o - ~ o r k e r sfor ~ ~77 and 300°K from Hall curves similar to that of Fig. 17 [assuming n, = (eoR,J1 in the intrinsic range]. Although the agreement in absolute values between the data points and theoretical curves does not appear very good, the dependences on alloy composition do agree wcll. In view of the assumptions required in the calculations about values of parameters not then accurately known, the overall understanding of the intrinsic electrical properties of Hg, -,Cd,Te represented in Fig. 19 is probably satisfactory. An alternative representation of the calculated ni is given in Fig. 20 by curves of ni versus 1/T for various values of x. The Hall coefficient and resistivity data of Figs. 17 and 18 can be combined in the usual way to give a Hall mobility (pH = R d p ) , and the resulting mobility vs temperature curve is plotted in Fig. 21 ; it should represent the mobility of the conduction band electrons because of the strongly n-type nature of the sample. Few quantitative analyses of mobility data and

'' 1. L. Schmit (unpublished results)

5. MERCURY-CADMIUM

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207

mechanisms have been published for Hg, -,Cd,Te, but the typical electron mobility versus temperature curves for material in the composition range of interest, like that of Fig. 21, can be understood qualitatively. The rapid drop of the mobility with increasing temperature above 50°K undoubtedly results from the dominance of lattice scattering mechanisms at the higher temperatures. At the lower temperatures (4to -50°K) the electron mobility is nearly constant with temperature. This behavior can be explained by scattering by singly charged ionized impurity or defect centers having a 10'

IdZ

1:

10 n-

'f

-u.E

I4

10

10''

12

10

016

0.17

018

0.19

0.20

0.21

0.22

0.23

x (MOLE FRACTION CdTe)

FIG. 19. Intrinsic carrier concentration versus x in Hg,_,Cd,Te at several important temperatures. The solid curves are theoretical, and the points represent values of n,determined from Hall effect data for the following temperatures: 0-77°K,63 A-300aK,"3 0-300°K.3*

208

DONALD LONG AND JOSEPH L. SCHMIT

population equal to the extrinsic electron concentration n o . A quantitative analysis has been made by Long64 of the very-low-temperature (-4°K) electron mobility in Hg,-,Cd,Te in the 0 S x 6 0.3 range, assuming that the scattering limiting the mobility is of the type just described and that the Born approximation applies; full account was taken of the conduction band nonparabolicity due to the k. p interaction, and complete statistical degeneracy was assumed. A detailed presentation of the analysis is given in T(*K)

300

10°F'

4

200

150

110

90

77

70

I

I

I

1

1

1

6

e

10

12

14

60

16

IO3/T ( * K - ' )

FIG.20. Intrinsic carrier concentration versus temperature in Hg,-,Cd,Te for various alloy compositions x of interest. The curves are theoretical, based on best available parameter values for Hg, -,Cd,Te.

'' D. Long, Phys. Reo. 176,923 (1968).

5.

MERCURY-CADMIUM TELLURIDE AND CLOSELY RELATED ALLOYS

TEMPERATURE

(OK

209

1

FIG. 21. Hall mobility of electrons versus temperature for the sample of Hgo.,Cdo ,Te of Figs. 17 and 18.64

reference 64, and its results are plotted in Fig. 22. Also plotted in Fig. 22 are 4°K electron Hall mobility data points from several representative samples, includingthe value from Fig. 21 which is the sample being used as an example here. We make no distinction between the Hall and conductivity mobilities because they are equal for the spherical energy surfaces and degenerate statistics involved. The data points agree well with the theoretical curves, considering the difficulties of obtaining perfectly uniform samples, of taking highly accurate data, and of accounting theoretically for a parameter such as mobility which can vary over several orders of magnitude as a function of temperature or scattering center concentration. Therefore, the lowtemperature electron mobility in Hgo&do.,Te and other alloys in this range is explained satisfactorily by the simple ionized-impurity scattering model employed to calculate the curves in Fig. 22. We conclude also from the good theory-experiment agreement that the mobility samples must have been largely uncompensated (virtually free of any defect-type scattering center other than the ionized defects which donate the no electrons to the conduction band); thus the low-temperature mobility data show that these are quite pure crystals in which the extrinsic electron concentration provides a true measure of the concentration of electrically effective impurities or lattice defects in the material. The slight increase of mobility with temperature above 4°K seen in Fig. 21 is probably caused by a gradual transition of the conduction band electron distribution away from complete statistical degeneracy.

210

DONALD LONG AND JOSEPH L. SCHMIT 5

I

I

I

0.05

0.10

0.15

I

I

I

1

0.25

0.30

0.35

10

0

0.20

FIG. 22. Hall mobility of electrons versus composition of Hg,-,Cd,Te at -4°K.h4 The curves are theoretical, and most of the points represent mobility values calculated from --4"K Hall effect and resistivity data for samples with no % l O I 5 ~ m - The ~ . circles represent unpublished Honeywell data; the upright triangles represent the data of Harman e/ d3'The inverted trianglc is from recent helicon propagation and nonresonant cyclotron absorption measurements of Wiley and D e ~ t e r . ~ ' "

So far in this discussion of electrical properties we have used as an example the resistivity and Hall effect data for an n-type sample of Hg,,,Cd,,2Te because most existing experimental results are for samples of this type. Crystals grown from the melt are usually n-type, probably because of a "natural" deviation from stoichiometry in that direction (see Section 44. However, a few results for p-type samples do exist. Shneider and Gavrish~ h a have k ~ reported ~ data for a pair of samples in the 77400°K temperature range. Kruse and c o - ~ o r k e r smeasured ~~ the electrical properties of some p-type samples from 4-3WK, and Hall coefficients and resistivity versus temperature data for one of their typical samples are plotted in Figs. 23 and 24; the exact composition of this sample is uncertain, but it is probably near Hgo.,Cdo,,Te. The Hall coefficient versus temperature curve of Fig. 23 has the shape expected for a p-type InSb-like sample: R , is positive in the low-temperature, extrinsic range, and reverses sign to become negative in the intrinsic range because of the higher mobility of the 65

P. W. Kruse (unpublished results).

5 . MERCURY-CADMIUM

TELLURIDE AND CLOSELY RELATED ALLOYS

211

i I

0

I

I

1

I

1

I

20

40

60

80

I00

A.

120"

1 0 ~ ('K-') 1 ~

FIG.23. Hall coefficient versus temperature for a p-type sample of Hg,,,Cd,,,Te, measured in a relatively weak magnetic field. The sign of the Hall coefficient is indicated on both sides of the sign reversal.

electrons. Once again, as in the n-type material, there is no evidence for carrier freeze-out onto what would be discrete acceptor levels in this case ; however, the reason now must be that the sample is effectively quite heavily doped p-type, so that the acceptor levels have merged with the valence band [Po = (e0RH)-' = 8 x l O I 7 ~ m - ~ ]The . hole effective mass is not small enough to give this effect in lightly doped material as in the n-type case. The Hall mobility vs temperature curve for this p-type sample, obtained by I

I

I

I

I

I

I

i---0

I

I

I

1

20

40

60

80

I

100

I

120

.,

' 240

lo3/ T ( O K - ' )

FIG.24. Electrical resistivity versus temperature for the p-type sample of Hg,.8Cd,,,Te of Fig. 23.

212

DONALD LONG AND JOSEPH L. SCHMIT

combining the R, and p data of Figs. 23 and 24, is plotted in Fig. 25. Only at the lowest temperatures ( ~ 3 0 ° Kdoes ) the mobility in this plot directly characterize the valence band holes. Its magnitude is quite low and is almost independent of temperature. This mobility is undoubtedly limited by ionized-impurity scattering, but the Born approximation is probably not valid in this case, so that we cannot readily calculate a theoretical value for comparison.

d . Impurities and Their Efects Very little is known experimentally about the properties and effects of impurities in Hg, -,Cd,Te, but some tentative conclusions can be drawn by analogy with what is known about impurities in HgTe, and also to some extent in HgSe. Harman4 has recently reviewed the properties of impurities in these compounds. For the 11-VI compounds the usual arguments about hydrogenlike impurity energy levels suggest that elements from groups I and V of the periodic table could act as acceptors by substitution for the cations and anions, respectively, in the crystal lattice, and that elements from groups I l l and VII could act as donors by similar substitution. In practice, however, not all of these theoretical possibilities actually work in HgTe. Harman4 and Tufte66 say that Cu, Ag, and Au are effective as p-type dopants in HgTe. Tufte66 and Strauss6' have been able to achieve n-type HgTe crystals with carrier concentrations in the 1018-10'9 cm-3 range by doping a melt with either Ga or In prior to crystal growth and then annealing the grown crystal in Hg vapor; Verie has achieved similar concentrations by A1 doping.38 The as-grown crystals have high concentrations of Hg vacancies which act as compensating acceptors, and the Hg anneal reduces the vacancy concentration to permit the Ga or In dopant to determine the carrier concentration. Galazka and Sosnowski6' followed an analogous procedure and found similar results for Ga in Hgo,,Cdo,,Te. All of the above dopants are probably electrically effective also in the Hg, -,Cd,Te alloys of interest, since the alloys are HgTe rich, but experimental verification of this prediction is not yet available. Incidentally, these dopants all seem to give singly-ionized impurity centers in the lattice. Other impurities have been tried in HgTe and in a few cases also in Hg, -,Cd,Te, including Si, As, Na, and I, but they have not been successful. As a general rule, one can apparently dope these crystals with elements from groups I and 111, which substitute for the cations in the lattice and act as acceptors and donors, respectively, but elements from groups V and VII are not electrically effective in substituting for the anions. 66 67

0. N. Tufte (private communication). A. J. Straws, Solid State Res. Rept. 2. Lincoln Lab., M.I.T., p. 25 (1962).

5. MERCURY-CADMIUM

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TELLURIDE AND CLOSELY RELATBD ALLOYS

I l l

I

I

I

213

1

TEMPERATURE (' K

FIG.25. Hall mobility versus temperature for the sample of Hg,,Cd0,,Te of Figs. 23 and 24. Above about 60°K the electrons dominate the mobility, and at lower temperatures the holes dominate.

No finite impurity or defect ionization energy has been definitely observed in HgTe or in HgTe-rich Hg, -.yCd,Te, either in a Hall effect experiment or any other type of measurement. We noted earlier that there is no evidence of carrier freeze-out in the low-temperature Hall coefficient, so that the defect levels providing the extrinsic current carriers must not have bound states, and we argued that the absence of such bound states is reasonable under the conditions involved. Actually, the extrinsic carriers in the highpurity Hg, -,Cd,Te crystals grown as intrinsic detector material are believed to derive from stoichiometric deviations rather than from impurities. Mercury atoms which exceed the number needed for stoichiometry and presumably reside interstitially in the lattice act as singly-charged donors and are the source of the extrinsic electrons in virtually all high-purity Hg,-.Cd,Te crystals. On the other hand, a deficiency of Hg, resulting in cation lattice vacancies, leads to p-type extrinsic properties. There is no evidence for electrically effective impurities in Hg, - ,Cd,Te crystals which have not been doped intentionally. e . Excess- Carrier L.fet ime

The lifetimes of optically excited, excess electrons and holes are among the most important parameters of an intrinsic infrared detector material, since they govern the magnitude and frequency response of the signal. Very few lifetime data exist for Hg, -,Cd,Te because the values are generally quite short (less than 1 psec) and are difficult to measure. Nevertheless, there

214

DONALD LONG AND JOSEPH L. SCHMIT

is some knowledge about excess-carrier lifetimes in this material, particularly theoretical, that we will review below. In developing a detector material one usually strives for the longest possible carrier lifetimes so as to achieve the highest possible detectivities. The upper limit to the carrier lifetimes is imposed by the intrinsic recombination mechanisms, radiative recombination and Auger recombination, and the magnitudes of both these mechanisms can be calculated for a semiconductor once its band structure and parameters are known. The lifetimes of excess electrons and holes are equal when limited by these intrinsic recombination mechanisms. Let us now consider the calculations for Hg, -.Cd,Te. The basic theory of radiative recombination in a semiconductor has been formulated by van Roosbroeck and Shockley.68They showed that the rate R , of radiative recombination at a temperature T in a material of index of refraction n is given by

R r = 2.52 x 101 1n 2

~

IOm ::2f (cmp3sec-'),

3

',

where a is the optical absorption coefficient in cm- and u = hw/k,T, with o the angular frequency of the incident radiation in an experiment which measures a. The radiative lifetime T, is given by zr

= ni2/Rr(no

+ PO +

ne)r

(14)

where n, is the intrinsic carrier concentration, no and po are the thkrmal equilibrium electron and hole concentrations, respectively, and n, is the excess-carrier concentration. Highly accurate and reliable optical-absorption data39"were not yet available for Hg, -.Cd,Te, but the calculated absorption edge curves of Blue33 plotted in Fig. 16 of Section 5b can be used in calculating R, from Eq. (13); we recall that these curves incorporate the actual k * p determined band structure of Hg, -,Cd,Te. Curves of R, versus temperature for Hg, _,Cd,Te calculated by Long69 for the energy gaps of 0.09 and 0.24 eV are plotted in Fig. 26. These gaps correspond approximately to material suitable, respectively, for the important 14 and 5 , u cutoff wavelength (Aco) detectors. It should be noted when calculating values of z, from Figs. 20 and 26 that whereas the R, versus temperature curves plotted in Fig. 26 are for fixed energy-gap values, the ni versus temperature curves of Fig. 20 take into account the temperature dependence of the gap in material of a given alloy composition x ; thus in calculating z, at a particular temperature, one must use the E , versus x relationship given in the appendix to determine what x

'' W. van Roosbroeck and W. Shockley, Phys. Rev. 94, 1558 (1954) 69

D. Long (unpublished results).

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215

FIG.4.Lattice constant and density versus alloy composition x in Hg, -,Cd,Te. The triangles represent the values of Woolley and Ray’; the circles represent the values of Blair and N e ~ n h a m . ~

in Fig. 20 corresponds to the desired gap at that temperature. As a numerical example, we find from Figs. 20 and 26 and Eq. (14) that for a Hg, -,Cd,Te sample of 0.09 eV energy gap at 7TK, with no = 10’ cm-3 and p o . n, < no, the radiative lifetime should be about 4 psec. The theory of Auger recombination has been formulated mainly by Beattie and Landsberg” and reviewed by B l a k e m ~ r e . For ~ ’ a simple semiconductor model, excluding such complications as nonparabolic bands,’ l a they give the following formula for the Auger lifetime T ~ in , intrinsic ~ material :

TA,i =

3.8 x 10-’8coz((l + r)’”(t ( m , * / m ) l ~F ~

+ 2r)exp

sec,

(15)

~ I ~ ( ~ ~ ~ ’ / E ~ ) ~ I ~

where E~ is the static dielectric constant, r is the ratio of the electron effective mass to the hole effective mass, and F,F, represents the products of two wave-function-overlap integrals ; the other symbols were defined previously. The actual Auger lifetime zA in a given sample depends upon the extrinsic ’O

A. R. Beattie and P. T. Landsberg, Proc. Roy. Soc. (London) A249,16 (1959).

’’ J. S. Blakemore, “Semiconductor Statistics.” Pergamon Press, Oxford, 1962. ’lap. E. Petersen, Bull. Am. Phys. Sol. Ser. If 13, 1677 (1968), has extended the theory to account for a nonparabolic conduction band.

216

DONALD LONG AND JOSEPH L. SCHMIT

carrier concentration according to the formula

where

In the kind of semiconductor of interest here we have r 6 1, and consequently p 6 1. In an n-type sample, e.g., Eq. (16) simplifies to become TA(no) zz 2ni2~A,i/1102.

(18)

In Fig. 27 we have plotted curves of T ~versus , ~ temperature calculated using Eq. (15) for the 0.09 and 0.24 eV cases considered above in connection with the radiative lifetime. The values of c0 needed in Eq. (15) were found by linear interpolation between the values given for HgTe and CdTe in Table I

lo -8

1 4

6

8

10

12

14

16

1 0 3 1(OK-') ~

FIG.27. Intrinsic Auger lifetime versus temperature for two Hg, -,Cd,Te alloy compositions having different energy gaps.

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of Section 4f; r was given by the ratio of the conduction band edge electron effective mass plotted for Hg,-,Cd,Te in Fig. 15 t o a valence band edge hole effective mass of 0.35m; m,*/m was obtained from Fig. 15; and the value of lF,Fzl has been estimated to be roughly 0.1 for this type of semiconductor. Figure 27 actually gives only the order of magnitude of T ~ because there is considerable uncertainty in the value of JFlF2J and also because of the simplifications in the theoretical model. As a numerical example, we find from Figs. 20 and 27 and Eq. (18) that for a Hg, -,Cd,Te sample of 0.09 eV energy gap at 77"K, with no = 10l5 and p o , n, .g no (the same conditions as for the numerical example used above for the radiative lifetime), the Auger lifetime should be about 2.7 psec. Thus the radiative and Auger lifetimes are roughly equal in this example. For lower extrinsic electron conccntrations, howevcr, the radiative recombination would become dominant because z, increases as no', whereas the Auger lifetime increases as n,'. Measurements of both the steady-state photoconductivity and its frequency dependence on samples of Hg,-.Cd,Te of the composition and properties used in the above examples have yielded lifetime values as high as 1 psec at 77°K'a,72These results indicate that the observed lifetime has sometimes approached order-of-magnitude agreement with the theoretically predicted intrinsic lifetime. Nonintrinsic recombination mechanisms are then weak, since 1 Tabs

-

1 t r

1

1

f-+---, zA

'j

in general, where T~ represents any nonintrinsic recombination mechanisms. Ayache and M a r f a i ~ ~have g ~ ~reported the results of measurements of the photoconductive and photoelectromagnetic effects in an n-type Hg,,,7Cdo.23Tesample, from which they deduced the curve of the excesscarrier lifetime versus temperature plotted in Fig. 28. The sample had an energy gap E , = 0.16 eV at 77°K and an extrinsic electron concentration no = 4 x 10l5cm-3. The results in Fig. 28 can be understood on the basis of the well-known Shockley-Read expression7'

Equation (20) gives the (equal) lifetimes of electrons and holes limited by

'' Unpublished Honeywell 73

results.

J. C. Ayache and Y. Marfaing, Compf. Rend. B265, 568 (1967).

,

~

218

DONALD LONG AND JOSEPH L. SCHMIT

0

5

10

15

103/r( O K - ‘ ) FIG. 28. Excess-carrier lifetime versus temperature in an n-type sample of Hgo 77Cdo2,Te, drawn from data of Ayache and Marfair~g.’~

recombination through a concentration of discrete recombination centers which is small compared to the majority-carrier concentration ; here T ~ and 7 p , o are constants, no and po are the equilibrium electron and hole concentrations, respectively, and nl and pl are exponential functions of the energy level of the recombination centers. From Fig. 28, z,,,~ = lo-’ sec for this sample, and the energy level of the recombination centers is 0.055 eV. The positive slope of the lifetime versus temperature curve at the highest temperatures in Fig. 28 is probably due to an intrinsic recombination mechanism. These lifetime results of Ayache and Marfaing can be considered generally representative, although not necessarily typical of the best possible material. 111. Basic Infrared Detector Theory Applicable to These Materials

The theory of the major mechanisms of infrared detection has been given elsewhere in detail, notably in the book by Kruse et at.74 Our purpose is not to repeat that treatment ; it is simply to review those parts of the theory which must be understood clearly in developing high-performance intrinsic detectors from a semiconductor such as Hg,-,Cd,Te. We will follow a simple approach, which, while sometimes lacking full mathematical rigor, l4

P. W. Krusc, L. D. McGlauchlin, and R . B. McQuistan, “Elements of Infrared Technology: Generation, Transmission, and Detection,” Chap. 9. Wiley, New York, 1962.

,

~

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219

and not dealing quantitatively with such details as the nonuniform absorption of the radiation through the sample thickness, does account for the essential physics. We will emphasize deriving the relationships between the detector performance and semiconducting material parameters, to show how one must “design” and prepare the material to achieve optimum detector performance. We will treat the two mechanisms that have been the most important for Hg, -.Cd,Te, the photoconductive and the photovoltaic. 6. PHOTOCONDUCTIVE MODE

The model of an intrinsic photoconductive detector and its output circuitry that we will consider is shown in Fig. 29. The detector is a parallelepiped of semiconductor crystal (Hg, -.Cd,Te) with the dimensions indicated and with electrical contacts on its ends, and it is used in a constantcurrent circuit because of its low electrical resistance. Excitation of current carriers in the crystal arises in general from three sources. Thermal excitation provides the thermal equilibrium carriers which give the crystal its “dark” conductivity. There will usually be electromagnetic (largely infrared) radiation falling on the detector from a warm background to which it is exposed, and this radiation will excite some excess carriers (electron-hole pairs) above the thermal equilibrium concentration, thereby increasing the conductivity. (It is common for a detector to be mounted on a flat base which holds it at the operating temperature and to be exposed to a 2 r s r field of view of a background with a temperature of -300”K, although narrower fields of view which reduce the amount of background radiation received may be used.) The “signal” radiation from the infrared-emitting object to be detected excites additional excess carriers, and it is chopped to give a periodically fluctuating component of the conductivity, which can be STEADY-STATE RADIATION FROM BACKGROUND

ELECTRICAL OUTPUT

SIGNAL RADIATION

PC DETECTOR

I

T I

0

FIG.29. Basic circuitry for an intrinsic photoconductive infrared detector. Symbols for the detector dimensions are indicated. The capacitor C blocks the dc from the output.

220

DONALD LONG AND JOSEPH L. SCHMIT

distinguished from the dark and background-radiation-induced dc conductivities by ac methods. The photoconductor detectivity is limited by whatever noise voltage appears with the signal voltage V, at the output. a. Responsivity

The voltage across the photoconductor in the absence of signal radiation is VO = jo[i/(ad

+ ob)wt].

(21)

Equation (21) includes the dimensions defined in Fig. 29, the dark conductivity ad,and background-induced photoconductivity ab. Signal radiation changes the conductivity by an amount cs,resulting in an ac signal voltage of magnitude

v, = (a,/o)Vo.

(22)

where a represents the total conductivity in the presence of the background and signal radiation. We will almost aIways be concerned only with small signals (a, < ad cb),so that Eq. (22) can be approximated as

+

Thus the magnitude of the photoconductive signal voltage equals the product of the photoconductivity os/(ad + cb)and the bias voltage Vo. The dark conductivity of an intrinsic photoconductor is ad = E O ( n O h

+ POPp)?

(24)

where e0 is the electronic charge, n , and p o represent the therinaf equilibrium electron and hole concentrations, respectively, and ,unand ,up are their mobilities. The background-radiation-induced photoconductivity is Ob =

eOnb(pn + , u p ) ,

(25)

where nb represents the steady-state excess concentration of electron-hole pairs maintained by the background radiation. The signal photoconductivity (for small signals) can be shown to be 6s

= [dvs)Js/tleo(~u,tn +

~ p z p ) ,

(26)

where ~ ( v , )represents the quantum efficiency (number of electron-hole pairs created by a given number of absorbuble photons), which may vary with the radiation frequency v,; J , is the number of signal photons arriving per unit area per unit time which have enough energy to create electron-hole pairs (i.e., are absorbable); and T,, and T~ are the lifetimes of the excess electrons and holes, respectively. Combining Eqs. (24)-(26), we get the following expression for the photoconductivity involving both background and signal

5. MERCURY-CADMIUM

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221

radiation :

The signal photon flux density is related to the radiant power PAat wavelength ,i incident on the detector by the expression74

PA 2 J =--,

lw hco

where h is Planck’s constant and co is the speed of light in vacuum. Substitution of Eq. (28) into Eq. (27) and use of Eq. (23) lead to the following equation for the spectral responsivity 9,, which is an important detector performance parameter giving the signal voltage per unit of incident radiant power at the wavelength II :

W,is usually expressed in volts/watt. Approximations can often be made to simplify Eq. (29). In Hg, -,Cd,Te one can usually assume that pn 9 ,up and that zn z z p . Photoconductive detectors have been made typically of n-type material, so that no 9 p o ; also, bb -g od in many practical situations. Under these conditions Eq. (29) reduces to

g Ax ~(v,),izVo/hcolwtno,

(30)

where 7 = 7,. This simplified expression shows clearly the basic requirements for high photoconductive responsivity at a given wavelength : one must have high quantum efficiency, long excess-carrier lifetime, the highest possible bias voltage, the smallest possible piece of crystal, and a low thermal equilibrium carrier concentration. Only in more complex cases requiring a less simplified version of Eq. (29) might the carrier mobilities become explicitly relevant parameters. b. Noise Mechani~rns’~

There are two distinct types of noise associated with the photoconductor material which determine the fundamental limits of its detectivity, Johnson (sometimes called thermal) noise and generution-recombinatian (g-r) noise. Let us review the dependences of these noise voltages on material 75

See K . M. Van Vliet, Appl. Opt. 6, 1145 (l967), for an up-to-date review of noise mechanisms in photodetectors and for references to earlier papers on noise.

222

DONALD LONG AND JOSEPH L. SCHMIT

parameters. We will ignore such other noise mechanisms as those arising from electrical contacts or associated circuitry, because even though they may sometimes be the major detectivity-limiting mechanisms, they are really extraneous to the detector itself. These include the so-called l/fnoise, for example. The development of "good" detector fabrication technology should generally reduce these extraneous noise sources and make them negligible. The well-known expression for the Johnson noise voltage of a resistance R is V, = (4kBTRAf)"2, (31) where R = l/(od+ o,)wt. (32) Equation (32) gives the resistance of the photoconductor in the presence of background radiation (the general case), and Af represents the electrical frequency bandwidth. The proper g-r noise voltage expression for Hg,-.Cd,Te is probably normally that for the so-called near-intrinsic semiconductor, in which the energy-level structure of the material consists simply of the conduction and valence bands, and possibly also a discrete level within the energy gap due to a relatively small concentration of Shockley-Read recombination center^.'^ The Hg, -,Cd,Te crystals from which high-performance photoconductive infrared detectors have been made are nearly always n-type, and the donors providing the extrinsic electrons are believed to be excess Hg atoms. N o evidence has been found for bound states (within the energy gap) associated with these donors, so that they simply provide a constant, temperature-independent conduction band electron concentration no. Crystals like these should satisfy the requirements of the near-intrinsic model, including the condition that the electron and hole lifetimes be equal, i.e., T , = T~ = T . This is probably a realistic assumption in practice. One generally does not become concerned with the g-r noise until the detectivity is quite high; the carrier lifetimes are then likely to be limited mainly by intrinsic recombination processes or by a small number of Shockley-Read recombination centers, so that T~ = t p . We will assume that the nearintrinsic model applies at least approximately to Hg, -,Cd,Te, noting however that this has not been proven experimentally in all cases. Under the above conditions the magnitude of the g-r noise voltage is given by

76

D. Long, Infrared Phys. 7, 169 (1967)

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223

where b represents the ratio of the electron and hole mobilities (b = p,Jpp); also n = no nb (34) and

+

P

PO

+ nb.

(35)

Here n b is the concentration of excess electron-hole pairs (above the thermal equilibrium concentrations no and po) maintained by the steady-state radiation absorbed by the photoconductor, in this case the background radiaDynamic equilibrium between generation and recombination determines the steady-state electron and hole concentrations n and p. From the “g-r theorem” of Burgess” and Van Vliet7* one can show that

in general for the near-intrinsic model, where n and p are given by Eqs. (34) and (35), respectively. In Eq. (36) q(vJJ, represents the creation of electronhole pairs in thermal equilibrium, and t and z are the sample thickness and excess-carrier lifetime defined previously. One often finds in practice that no & ti,, & p o , and it should almost always be true for Hg, -,Cd,Te that h p 1. Using these inequalities to simplify Eq. (33), we obtain

For negligible background radiation simplified form of Eq. (33),

(nb

< po < no) one has the alternate,

Both simplified forms, Eqs. (37) and (3X), illustrate the important fact that Jha

Equation (33) is definitely valid when’n = no and p = p o . it., when the material is in thermal equilibrium, and also when the direct radiative recombination process is dominant in limiting the steady-state concentration nb of background-radiation-generated excess electron hole pairs. We arc not aware, however, of a clear discussion in the literature of its validity (at least as an approximation) when Shockley-Read recombination is important. Nevertheless, we will use Eq. (33) for all these cases, lacking knowledge of any better formulation. We believe it is clear physically that Eq. (33)cannot be too poor an approximation when ShockleyRead recombination is not very strong, which is apparently the situation in better crystals of Hg, -,Cd,Te. 7 7 R. E. Burgess, Proc. Phys. Soc. (London) B68,661 (1955);B69, 1020 (1956). 78 K . M. Van Vliet, Pruc. I.R.E.46, 1004 (1958).

224

DONALD LONG AND JOSEPH L. SCHMIT

the g-r noise voltage is proportional to the square root of the minoritycarrier concentration, whether it is provided by steady-state background radiation or is simply the thermal equilibrium concentration. Equations (37) and (38) are companions to the simplified expression for the spectral responsivity, Eq. (301, in that all three equations apply to essentially the same type of photoconductor material. The different specific assumptions leading to Eqs. (37) and (38) for the g-r noise are not relevant to the responsivity, however, since they involve only the minority-carrier concentration ; the photoconductor responsivity depends only on the majority-carrier concentration. Expressions for the g-r noise voltage for other cases, such as p-type Hg, -,Cd,Te, could be derived, but they are often more complicated and are not worth presenting here. The references should be consulted for those cases. We recall finally that the total noise voltage V, due to a combination of mechanisms is given by the square root of the sum of the squares of the noise voltages of the individual mechanisms. In the present discussion we have V” = ( v , 2

+

v y 2 .

(39)

c . Detectivity

The usefulness of an infrared detector depends mainly on its detectivity, representing its ability to produce an electrical signal observable above the noise level. The spectral detectivity D,* is given by DA*

=

~,(lw)’”(AJ)’’2/V,,

(40)

in terms of parameters defined previously ; the ratio of the spectral responsivity 9, to the total noise voltage V, is a measure of the signal-to-noise ratio. The general expression for the spectral detectivity of our intrinsic photoconductor could be obtained by substituting the general expressions for the spectral responsivity and the noise voltages stated earlier into Eq. (40);however, the result would be very complicated. For clarity we will use the simplifying assumptions applied above to the responsivity and noise voltage expressions. Also, we will assume that only one noise mechanism is important in each case. In the first case treated, that of the Johnson noise-limited detectivity, we again assume for Hg,_.Cd,Te that p,, % pp and that z, = tp = t. Also, we let cr, 4 crd, so that no 9 nbr where nb is the excess electron-hole pair concentration maintained by the background radiation. Substitution of Eqs. (30) and (31) into Eq. (40) then gives the following expression for the spectral

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225

detectivity : D,*

=

q(v,),?zeAi2p:u,”2Vo 2 h ~ ~ n ~ ~ ~ t ” ~ .l ( k , T ) ’ ~ ~

In order to maximize the detectivity at a given wavelength A in this Johnson noise-limited case, one therefore wants to maximize 7 and p,,, minimize no, use a thin sample, operate at a low temperature, and apply a large bias field Vo/l. However, as the applied voltage is increased a limit will be reached: either Joule heating of the sample will become excessive, or the g-r noise voltage, itself proportional to V,, will surpass the Johnson noise voltage. Let us treat next the detectivity limited by g-r noise only. We assume as above that p,, 9 p p and 7, = z p = 7, and also at first that no, tq, p o , i.e., that both the majority thermal equilibrium and the background-induced carrier concentrations are much larger than the thermal equilibrium minority-carrier concentration. One can show from Eqs. (29), (33)-(39, and (40) that the spectral detectivity is then given by

+

Equation (42) may be simplified further. When no 9

nb

9 p o , it becomes

using Eq. (36). When nb 9 no 9 p o it becomes

using the appropriate approximate form of Eq. (36). The final forms of Eqs. (42a) and (42b), which are identical because they represent the fundamental background-noise limit, are independent of photoconductor material parameters (except insofar as the quantum efficiencies depend on the material); the detectivity is limited only by background radiation noise under the assumed conditions. Any detector satisfying Eqs. (42) is a socalled BLIP (Background-Limited Infrared Photoconductor) detector, and values of D,* versus A for various background conditions are given in the 1iteratu1-e.’~In the general situation of exposure of the detector to the background radiation Eqs. (42) give the maximum possible detectivity. For another simplified g-r noise-limited case let us assume finally that nb po 4 no, i.e., that there are almost no steady-state excess carriers in the material. Equation (38) then applies, and its substitution together with

+

226

DONALD LONG AND JOSEPH L. SCHMIT

Eq. (30) into Eq. (40) gives

D,* = ~ ( ~ , ) ~ ~ ” ~ / 2 h ~ o t ” ~ p ~ ’ ~ . (43) Equation (43) refers to reduced-background-radiation detector operation when the bias voltage is high enough that the Johnson noise is negligible compared to the g-r noise.79 Here the spectral detectivity does depend upon some material parameters : to maximize Dn*a t a given 2, one wants to maximize T and use a thin sample. One also wants the lowest possible minoritycarrier concentration p o ; however, there is a limit imposed by such considerations as having a responsivity high enough to overcome system noise, keeping the sample resistance high enough that the Joule heating will be tolerable at the required bias voltage, and so forth. Each of the above spectral detectivity expressions applies only to a special case. In practice, one must take all possible noise mechanisms, the responsivity magnitude, Joule heating, and other such factors into account in attempting to “design” the detector crystal material for a particular application because these performance parameters usually interact in ways that require the choice of compromise values of the material parameters to achieve optimum detector performance.

d. Quantitative Example As a hypothetical quantitative example, let us consider what performance may be expected of a photoconductive detector fabricated from a typical good crystal of n-type Hg,-,Cd,Te having the alloy composition (x x 0.2) appropriate to the important 8-14 ,u wavelength interval. We assume that the detector has a 14p long-wavelength limit of response and operates at the common temperature of 77°K. We assume further that the crystal electrical properties are like those in Figs. 17 and 18 of Section 5c, so that no = 6 x 10’4cm-3 and ,un(77OK)% 3 x 1OScm2V-’sec-’. Experience has shown that the photoconductive response time (excess-carrier lifetime in our model) is generally several hundred nanoseconds in this type of material; let us use T = 5 x lO-’sec for this example. We will deal with the important standard configuration in which the detector is exposed to radiation from a 300°K (blackbody) background through a hemispherical (271s~)field of view, for which one can show that J , x 1.15 x 10l8

-

7 9 D. Long, In/rured Phys. 7.121 (1967), shows that high D,* values are possible in principle in this case. R. L. Williams, 1nfrarrdPhy.s. 8,337 (1968). has extended the theory, implicitly assuming ohmic contacts and dc bias, to show that minority-carrier sweep-out by high bids fields limits the attainable D,*; however, D,* need not be so limited if the minority carriers are held or replaced in the photoconductor somehow : for example, by using an ac bias, by having replenish. case ( I ) . ingcontacts suchas those discussed by R. H. Bube, “Photoconductivityof S o l i d s , ” ~75, Wiley, New York. 1960, or by trapping the minority carriers.

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227

sec-'. The other (representative) parameter values to be used are:

v(vJ = v(vb) = 0.5, 1 = w = 5 x cm, and t = cm. Using these values Eq. (36) yields iib x 4 x loL4c m - j for the steady-state electron-hole pair concentration maintained by the background radiation. For the material under consideration we assume that no % p o , p , 3-p p , and z, = z = -. z, so that simplified versions of the general equations for responsivity, noise voltages, etc., may be employed. The photoconductor sample resistance is found from Eqs. (24), (25), and (32) to be 21 ohms. In a typical detector mounting one is limited to about W of electrical power dissipation, so that the tolerable maximum bias voltage on this detector should be -0.14V. Equation (29) then gives a spectral responsivity for this voltage of 1.0 x lo3 V/W. The Johnson noise voltage calculated from Eq. (31) is 3.0 x lo-'' V, while the g-r noise voltage calculated from Eqs. (33H35) is 2.1 x V, both per unit frequency interval Af Using these values and Eq. (40), we find that D,* x 2.35 x 10" cm Hz''' W - ' , This theoretical result is about 0.8 of the BLIP value of the spectral detectivity for this case calculated from Eq. (421, so that the type of Hg,-,Cd,Te crystal under consideration should be able to yield nearly a BLlP detector if the near-intrinsic g-r noise model applies. Slight improvements of the carrier lifetime and equilibrium carrier-concentration properties of the material would theoretically permit full BLIP performance according to this model.

7. PHOTOVOLTAX MODE A photovoltaic detector consists of a p-n junction, the electrical properties of which are sensitive to infrared radiation8' We will treat the case of an open-circuited junction which develops a voltage by absorption of incident radiation. One could also consider a p--n junction photodiode to which a bias voltage is applied to move its operating point to some desired place on the current-voltage characteristic, a mode of operation often used, but the essential results would not be different enough to warrant treating that case also. Thus our photovoltaic detector will be open-circuited and simply produce a photovoltage upon absorption of infrared radiation. We assume as a model of the p-n junction detector the structure shown in Fig. 30. The detector is a p-n junction with a thin n-type layer on top of a slab of p-type material. This configuration conforms with a common practical situation ; the essentials of the results would not be changed by assuming a p-type layer next to the surface. The important sample dimensions are indicated in Fig. 30, and electrical contacts are made to the n- and p-type regions as shown. Once again thermal excitation provides the thermal

'"G. R. Pruett and R. L. Petritz, Proc. I.R.E. 47, 1524 (1959).

228

DONALD LONG AND JOSEPH L. SCHMIT

CHOPPED SIGNAL RADIATION

STEADY -STATE RADIATION FROM BACKGROUND

n P

FIG.30. Basic configuration of a p n junction photovoltaic infrared detector. Symbols for the detector dimensions are indicated.

equilibrium concentrations of carriers in both regions, and they give the p--n junction its “dark” electrical properties. The background radiation generally will cause the steady-state electrical properties to be dependent upon the background conditions. In the present discussion we assume, both for convenience and to correspond to a practical situation to be explored later, that the n-type layer in Fig. 30 is enough more heavily doped than the p-type region that only the contribution of the diffusion current due to the minority electrons from the p-type region need be considered in accounting for the dark electrical properties of the device. We also assume that the background and signal radiation excite excess electron-hole pairs only in the p-type region within a diffusion length of the junction; thus the n-type layer is nearly transparent, both by virtue of being very thin and for another reason to be discussed later. The excess electron-hole pairs diffuse to the junction and are separated at it to create a photovoltage. The essential physics of the detector does not require the assumption of excitation in both the n- and p-type regions. The signal voltage due to the chopped signal radiation is detected above the steady-state junction voltage by ac methods. The detectivity of the photovoltaic detector is limited by whatever noise voltage appears with the signal voltage V , at the output. u . Rrsponsivity

The current-voltage curve of the p-n junction in the absence of radiation (the “dark” characteristic) is given by I, =

- I]

[(expg)

= lweODnnp Ln

- 11

(44)

5. MERCURY-CADMIUM TELLURIDE AND CLOSELY RELATED ALLOYS 229 in terms of the dimensions defined in Fig. 30: here Id represents the junction current, carried only by diffusion of the minority electrons in the p-type region in the present model: D, and L, are the diffusion coefficient and diffusion length, respectively, of these electrons, and np is their thermal equilibrium concentration in the p-type region: Vis the voltage appearing across the terminals in Fig. 30; the junction resistance is so high in practice that this voltage is almost equal to that across the junction itself (i.e., ZR voltage drops in the n- and p-type regions are negligible), and it will be exactly so in our open-circuit case. The background radiation causes an additional current by exciting excess electron-hole pairs. The background-induced current is 1, = lwte,n,/r, (45) in terms of symbols defined in Section 6. The signal radiation generates a current (for small signals) 1, = lWeoY(lJs)J,, (46) in terms of symbols defined in Section 6. Under open-circuit conditions a photovoltage must appear across the junction to drive a diffusion current which opposes and balances the photocurrents to make the net current zero, i.e., I,

+ I, = I , .

(47)

Substitution of Eqs. (44)-(46) into Eq. (47) (with t replaced by L,) and use of the expression for the (small) signal-radiation-excitedconcentration, ?I,

= Y(vs)Jsz/Ln,

148)

combine (with some manipulation) to give the following general expression for the total junction voltage :

Since for small signals n, << np, it follows that the signal photovoltage is given by

an equation analogous to Eq. (23) for the photoconductor. Use of Eqs. (28) and (48) in Eq. (50)leads to the following expression for the spectra1 responsivity :

230

DONALD LONG AND JOSEPH L. SCHMIT

an equation similar in form to Eq. (29) for the photoconductor. Here the responsivity is proportional to kRT/eo rather than to an applied voltage. Equation (51) can be written as

since

in general. It is obvious in Eqs. (51) and (52) that if the background radiation is negligible, the responsivity is inversely proportional to the thermal equilibrium minority-carrier concentration, so that the p-type region should be rather heavily doped; however, the doping is limited by the fact that the carrier lifetime is shortened with increasing majority carrier concentration. When the background radiation is intense enough that f l b 9 np (although n,, -=$p p , the majority-carrier concentration in the p-type region), the responsi vi t y equation becomes

h. Noise Mechani~m.s’~

The noise in a photovoltaic detector originates from microscopic physical processes similar to those contributing to the noise in a photoconductive detector, but it is convenient to treat the photovoltaic detector in terms of the concept of shot noise. Once again we assume that all other extraneous noise mechanisms are negligible. For a p-n junction having the current-voltage characteristic of Eq. (44) one can show that the magnitude of the shot-noise voltage is given by VSh

= [&,(I

+ 210 + Ip)Af]li2R,

(55)

where I is the net junction current, I , represents the photocurrent (Ip = I, + I, in our case), and R is the (dynamic) junction resistance. Under our assumed open-circuit condition 1 = 0; also, for small signals I , 4 I , . With these approximations and with the resistance given by

5 . MERCURY-CADMIUM TELLURIDE AND

since I , =

CLOSELY RELATED ALLOYS

231

at the open-cjrcuit operating point, Eq. (55) becomes

Substitution of Eqs. (36), (44), and (45)into Eq. (57),combined with some manipulation, gives

This is the general expression for the shot noise voltage analogous to the g-r noise voltage expression for the photoconductor, Eq. (33); the similarities between the two equations are noteworthy. When the background radiation is intense enough that flb 9 n p , Eq. (58) reduces to

For negligible background radiation (fib G np) one has the alternate simplified form of Eq. (58),

2k,T Vsh

eo(I W L , ) ’ ’z

2”2(Af)”2

nk”

’

Equations (59) and (60) are analogous to Eqs. (37) and (38), respectively, for the intrinsic photoconductor. Equation (60)gives the pure Johnson noise of the p-njunction, because it applies when no net junction current is flowing. c. Detectivity

The general expression for the spectral detectivity of our photovoltaic detector in the presence of background radiation is obtained by substituting Eqs. (51) and (58) into Eq. (40). The result is

D,” =

q(Vs)lt”2

2hc0L9p[1

+ (n,/2n,)]”2

’

When nb B np Eq. (61) simplifies to

where we have used Eq. (36). This is the well-known expression for the background noise-limited detectivity of a photovoltaic detector, which has a

232

DONALD LONG AND JOSEPH L. SCHMlT

d2

value higher than the corresponding detectivity of a photoconductive detector [see Eqs. (42)]. When nb < np Eq. (61) simplifies to

This expression is analogous to Eq. (43) for the intrinsic photoconductor, and it therefore applies to reduced-background-radiation detector operation.

d . Quantitative Example As a hypothetical quantitative example, let us consider what performance may be expected of a photovoltaic detector fabricated from a crystal of p-type Hg, -,Cd,Te like that described in Section 5c and having the configuration of Fig. 30. The alloy composition is again x ;t: 0.2, the long-wavelength cutoff is assumed to occur at 14 p, and the detector is to operate at 77°K. We assume that the p-type region electrical properties, which dominate the detector characteristics in the present model, are like those in Figs. 23 and 24 of Section 5c, so that p o ;t: 8 x l O " ~ m - ~ the ; minority electron concentra, Fig. 19 and the general tion must then be n,, z 1.1 x 1 0 ' ~ r n - ~using statistical relationship nope = ni2. It is impossible to calculate with confidence the minority-electron mobility in the p-type region because the Born approximation is probably not valid in this case; let us assume ~ " ( 7 7 ° K= ) 104cm2V - ' sec-' as a rough order of magnitude value estimated from Fig. 25 and the electron-to-hole effective mass ratio in Hgo,,Cdo,2Te. We assume also that the minority-carrier lifetime is limited by direct radiative recombination in this rather heavily doped material; using Eq. (14) and Figs. 20 and 26, we find 7 zz 3 x lO-'sec. One can show that the Auger lifetime is much higher in p-type material,74 so that Auger recombination can be ignored in this case. We will assume the same background radiation conditions as in Section 6d. The other parameter values to be used are: ~ ( v J= g(vb) = 0.5 and 1 = w = 5 x 10-2cm. For the above values nb n p , so that the spectral responsivity can be calculated using Eq. (54); the result is 1.6 x 10' V/W. The shot noise voltage calculated from Eq. (59) is 2.5 x lO-'OV per unit frequency interval Aj: Finally, we find from Eq. (61a) that D,* = 3.2 x 10" cm Hz"' W-', which is the background-limited spectral detectivity. However, it would be virtually impossible to achieve this level of performance in practice, because the internal noise voltage of the photovoltaic detector is lower than the usual system noise. One would have to use less heavily doped p-type material to lengthen z, and perhaps a sample of smaller area, to achieve background noise-limited performance in practice.

+

5. MERCURY-CADMIUMTELLURIDEAND CLOSELY RELATED ALLOYS

233

For the p-n junction structure of Fig. 30 the Burstein-Moss effect would help to make the n-type layer almost transparent to the longest wavelength infrared radiation to which the photovoltaic detector responds. The Burstein-Moss effect’ consists of the filling up of the low density of states conduction band in a semiconductor like InSb or Hg,,,Cd,.,Te by the carriers in rather heavily doped n-type material, so that the Fermi level lies within the conduction band. This effect permits fundamental optica4 absorption only for energies wider than the energy gap by the height of the Fermi level above the conduction band edge. Thus incident photons of energies only slightly larger than the gap are not absorbed.

IV. Crystal Preparation A major problem in the use of the alloys of interest as intrinsic infrared detector materials is the preparation of single crystals of high quality. We have seen in the preceding sections that high detector performance places stringent demands on crystal purity in terms of carrier concentration. The crystals must also be nearly free of structural imperfections so that such parameters as the excess-carrier lifetime can reach optimum values. In the sections to follow we will review the methods which have been developed to prepare high-quality single crystals of Hg, -,Cd,Te; similar approaches would presumably apply also to such alloys as Hg,-,Zn,Te. The crystal preparation techniques include purification of the constituent elements, growth of the single crystals from the melt or from the vapor phase, annealing and other post-growth methods of modifying the crystal properties, and techniques for the evaluation of crystal quality. 8.

SOURCES AND PURIFICATION OF CONSTITUENT

ELEMENTS

The alloy crystals must be prepared from highly-pure elements. The mercury used in Hg, -,Cd,Te and other Hg-containing alloys can be obtained from suppliers who certify the material to have as little as eight parts per billion of foreign-atom impurities, so that it is not usually necessary to purify this element further. Cadmium is available which contains about 200 parts per billion of impurities, but this element is the minor constituent in low-x Hg, -,Cd,Te and therefore generally need not be purified further either. The best grade of tellurium known to be available commercially has about one part per million of metallic impurities. Direct use of this material would result in an alloy crystal impurity concentration of about lo” ~ m - ~ .

234

DONALD LONG AND JOSEPH L. SCHMIT

Some of these impurities may not be electrically active and some may compensate each other, resulting in a lower carrier concentration, but such other important parameters as excess-carrier lifetime may still be degraded : therefore the Te is generally zone refined by standard procedures before it is used in preparing an alloy crystal. A few zone passes through a Te ingot are usually sufficient to reduce the impurity concentration in the purified region below the limits of detection by spectrophotometric trace analysis. 9.

SOLIDIFICATION FROM THE

MELT

The crystals of Hg, -,Cd,Te used for detectors have usually been grown by solidification from a molten charge of the alloy. Well-known, rather straightforward melt-growth methods can yield the high quality single crystals needed for detectors provided that careful laboratory procedures are followed. Hg,-,Cd,Te is an alloy of the two binary compounds HgTe and CdTe, and so could be prepared by starting either with the three individual elements or with the two compounds. Woolley and Ray' mixed the compounds CdTe and HgTe, melted the mixture to form an alloy, solidified it, and then annealed it for two days at 600°C to homogenize the alloy. Blair and Newnham3 started with the elements sealed in a carbonized thick-walled quartz tube, heated the ingot to above its melting point very gradually to prevent explosion due to unreacted Hg, homogenized the melt by rocking for 8-12 hours, and lowered the ingot through a temperature gradient at 2.5 mm/hr. Harman4 started with the elements plus excess Hg, heated slowly with a lower temperature sidearm to prevent excessive Hg pressure, and finally lowered the ingot through a temperature gradient at 0.5 mm/hr. Faster solidification rates resulted in gross gradients in alloy composition x due to constitutional supercooling, since in this system there is wide separation of the liquidus and solidus lines (see Section 4c). Kruse" started with the elements plus excess Hg sealed in an evacuated, heavy-walled quartz tube, and reacted the elements by heating slowly and rocking the capsule through an angle of k20". The capsule was rocked for 24 hours, solidified rapidly using a moving temperature gradient, and transferred to a second furnace for crystal growth. Several methods of crystal growth were used including Bridgman,"" vertical zone melting,80b freezing from a large volume to avoid the segregation problem, and high temperature annealing similar to that used by Woolley and Ray.' The last method yielded the most nearly uniform material. When the melt is solidified 'OaB. E. Bartlett, J. Deans, and P. C. Ellen, J . Materials Science4,266 (1969). *ObE. Z. Dziu ba, J . Electrochem. SOC. 116, 104 ( I 969).

5. MERCURY-CADMIUM

TELLURIDE AND CLOSELY RELATED ALLOYS

235

rapidly, a dendritic crystal structure results, but gross macroscopic segregation is avoided. The subsequent high temperature anneal effectively eliminates the dendritic structure of the alloy, yielding large crystals having a longitudinal x gradient of only -0.002 mole fraction/cm and a vertical gradient of 0.03 mole fraction/cm. These remaining compositional gradients are due to thermal segregation upon solidification, rather than to either lack of mixing or gravitational segregation.

-

10. VAPORPHASEDEPOSITION : EPITAXIAL GROWTH Methods of depositing single-crystal layers epitaxially from the vapor phase are of interest for many semiconductors. By an epitaxial layer we mean a smooth, continuous single-crystal film growth on a substrate, such that the film crystal structure corresponds to and is determined by that of the single-crystal substrate. More generally, epitaxial growth could refer to any situation in which crystallites grow onto a crystalline substrate in conformance with the structure of the substrate, but since for practical applications one needs continuous single-crystal layers of uniform thickness and properties, we use the more restricted definition of the term epitax y. The development of epitaxial growth techniques for Hg, -,Cd,Te has been pursued recently as a straightforward means of preparing the thin layers of high alloy uniformity needed for infrared detectors, and especially for two-dimensional detector arrays. Epitaxial growth of Hg, -,Cd,Te could be carried out using vapor transport of the three constituent elements to a substrate with compound and alloy formation at that point, and the vapor transport could involve additional materials as transport agents, such as the halogens used with some 111-V compounds. However, this rather conventional approach to epitaxial growth has not been followed for Hg, -,Cd,Te in most of the work done to date.*l Instead, a basically simpler approach, involving an evaporation-diffusion mechanism without the use of any additional materials as transport agents, has been emphasized because of its simplicity and its potential for satisfying the demands of the detector application intended for the epitaxial layers. In addition, transport agents are not necessary since all three elements have high vapor pressures. Any epitaxial growth technique must be able to yield thin layers of single-crystal material of high purity and very good alloy compositional uniformity, and the entire epitaxial growth procedure must be simple enough to offer the possibility of very low cost preparation of detector material, otherwise epitaxial growth would have no advantage over melt growth. "

An exception is the work of P. S. McDermott (unpublished)

236

DONALD LONG AND JOSEPH L. SCHMIT

/ OUARTZ

SUSPENSiON LOOP

FUSED SEAL

FLAT BOTTOM QUARTZ TUBES

EVACUATED ( I x

KPTORR \

CdTe SUBSTRATE OUARTZ SPACER

HgTe OR Hg,-nCdnTe SOURCE

FIG.31. Experimental arrangement used in the close-spaced Hgl -,Cd,Te epitaxial growth method.

The method of epitaxial growth emphasized to date involves the evaporaIn this method a singletion-diffusion mechanism mentioned crystal wafer of CdTe is used as the substrate, and either HgTe or Hg,-.Cd,Te as the source. The source and substrate are placed close together in an evacuated chamber (see Fig. 31). If the source material is also a wafer (which need not be a single crystal), the setup is then something like a parallel-plate capacitor, although one may use instead a powder of source material in a suitable crucible. At a high enough temperature the material evaporates from the source and migrates in the vapor phase to the CdTe substrate, on which it deposits epitaxially. The transport of material from source to substrate can be driven by applying a temperature gradient AT 0. N. Tufte and E. L. Stelzer, J. Appl. Phys. 40,4559 (1969). G. Cohen-Solal, Y. Marfaing, F. Bailly, and M. Rodot, Compt. Rend. 261,931 (1965). 8 4 G . Cohen-Solal, Y. Marfaing, and F. Bailly, Rev. Phys. Appl. 1, 1 I (1966). 8 5 C. Sella, G. Cohen-Solal, and F. Bailly, Compt. Rend. B264, 179 (1967). 86 Y. Marfaing, G. Cohen-Solal, and F. Bailly, J. Phys. Chem. Solids Suppl. No. 1, 549 (1967). ” F. Bailly, Y. Marfaing, G. Cohen-Solal, and J. Melngailis, J . Phys. 28, 573 (1 967).

82 83

5. MERCURY-CADMIUM TELLURIDE AND CLOSELY RELATED ALLOYS 237 between the two, the source temperature being the higher, but it is found experimentally that transport and epitaxial growth of source material on the substrate occur even when AT = 0. Let us now consider this isothermal case in some detail before returning to the temperature-gradient case. When AT = 0 and the source material is pure HgTe, transport of HgTe to the CdTe substrate and epitaxial growth thereon will take place when the system is held at a temperature between about 550°C and the melting point of HgTe (670°C). The difference in chemical potentials between HgTe and CdTe must therefore provide the driving force for net material transfer. As soon as HgTe begins depositing on the CdTe, interdiffusion of the two compounds starts (see Section 44. This interdiffusion is the rate-limiting process in the growth of the epitaxial layer because there must always be some CdTe at the surface of the layer to maintain a difference of chemical potential between source and substrate and thereby permit further material transfer. If the epitaxial layer surface became pure HgTe, there would no longer be a chemical potential difference, and consequently there could be no more net transfer of HgTe from source to substrate until some CdTe diffused to the epitaxial layer surface to recreate the chemical potential difference. (There have been suggestions that one can achieve a net transport of pure HgTe from source to substrate in the isothermal setup at relatively high temperatures, apparently because the deposited HgTe has a high vacancy concentration or some other such means of maintaining a difference in the material and thereby a chemical potential difference between

-3

I 500-

u)

I

1

I

I

SOURCE -SUBSTRATE SEPARATION T - 550%

I

8

I

I

508p

$ 300z

FIG. 32. Epitaxial layer thickness versus deposition time in the isothermal close-spaced growth of Hg, -,Cd,Te. (After Cohen-Solal et

238

DONALD LONG AND JOSEPH L. SCHMIT

source and substraten6; however, this effect is not discussed here.) The rate-limiting effect of the interdiffusion process is illustrated by the plot in Fig. 32, taken from data of Cohen-Solal, Marfaing, Bailly, and Rodota3;the layer thickness varies approximately as the square root of the deposition time in the manner characteristic of a diffusion process. Other parameters of this isothermal epitaxial growth method, including mercury pressure, temperature, and source-to-substrate spacing, have also been studied by the French investigator^^^-^' and by Tufte and co-workers.82 A Hg, -,CdxTe alloy sample may be used instead of HgTe as the source material, in which case some of the Cd in the alloy is transported and deposited. Hg, _,Cd,Te alloy composition profiles for layers typical of those prepared by Tufte and co-workers,82 using the isothermal method, are plotted in Figs. 33 and 34. The composition profiles were determined by means of an electron beam microprobe (see Section 13 below). The results in Fig. 33 represent four epitaxial layers, each grown during an 88 hr time period, but under different capsule pressures achieved by adding extra Hg to the system; it is evident that increasing the Hg pressure inhibits the rate of buildup of the layer thickness, although the compositional profiles of the four layers are virtually identical over equivalent distances from the CdTe substrate. The results in Fig. 34 illustrate the fact that for a given set of conditions of temperature, source material, source-to-substrate spacing, and excess-Hg pressure, the alloy composition at the layer surface becomes asymptotic to a particular value regardless of the deposition time.

HQTe POWDER SOURCE T = 600 "C 5 m m SPACING 88 HR DEPOSITION T I M E

0.8

(1_1 0.6

0.2

0 ATM I

0 0

I I

40

80

120

,

I

, ~ , I

I

,

I

,

160 200 240 280 320 360 400 440 480 THICKNESS ( M I C R O N S )

FIG.33. Alloy composition profiles of Hg, -,Cd,Te epitaxial layers deposited under four different added-Hg pressures using the isothermal close-spaced technique. (After Tufte and Stelzer.* 2 ,

5 . MERCURY-CADMIUM TELLURIDE AND CLOSELY RELATED ALLOYS

239

HgTe POWDER SOURCE

MERCURY PRESSURE

T = 6OO0C 5 m m SPACING

-

3 ATMS X

-

4

I

0 0

I

"

40

'

I

I

I

"

I

I

I '

'

I

I

'

200 THICKNESS ( MlCRONSl

80

I20

160

I

240

260

FIG. 34. Alloy composition profiles of Hg, -,Cd,Te epitaxial layers deposited for three different times using the isothermal close-spaced technique. (After Tufte and Stelzer.")

The results described in the preceding paragraph can be understood in the following qualitative way: The thickness and profile of the epitaxial layer are determined by the interplay between the interdiffusion rate and the rate of transfer of HgTe from the source to the substrate. At a given temperature the transfer rate is a function of several parameters: it is reduced by increasing the excess-Hg pressure, is reduced at least slightly by increasing the source-to-substrate spacing, appears to be lower for a Hg, -,Cd,Te source than for pure HgTe, and, finally, is proportional to the difference of chemical potential between the surfaces of the source and substrate. Thus, all other parameters being fixed, the layer thickness attained in a given deposition time is greater the lower the Hg pressure, as in Fig. 33, because the transfer rate is greater. On the other hand, the final alloy composition reached at the surface of the epitaxial layer is lower for the lower-pressure (thicker-layer) cases because the limited diffusion rate prevents as much CdTe from diffusing to the relatively rapidly advancing layer surface as in the higher-pressure cases. However, for given values of the excess Hg pressure, the spacing, and the source composition, an equilibrium must ultimately be reached in which the chemical potential difference has become small enough that the transfer rate is balanced by the diffusion rate, so that a constant alloy composition is maintained at the layer surface. This situation is illustrated in Fig. 34, which shows that nearly the same final surface composition is reached in different deposition times, when the other growth parameters are held constant. Thus in the isothermal method

240

DONALD LONG AND JOSEPH L. SCHMIT

the combination of the interdiffusion mechanism and of the transfer rate, with its dependence on several controllable parameters, permits one to achieve a range of alloy compositions at the surface of the epitaxial layer by controlling these parameters. A more quantitative analysis of results like those in Figs. 33 and 34 has been made by Tufte and co-workers.82 This isothermal epitaxial growth method can also be used for other combinations of materials. We pointed out earlier that a practical epitaxial growth technique must be capable of yielding thin layers with a high degree of lateral composition uniformity. Electron beam microprobe studies of Hg, -,Cd,Te layers like those of Figs. 33 and 34 have shown that the alloy composition is constant over an area of the order of 1 cm2 to within 0.5 mole 9% ; i.e., x varied by less than 0.005 over that area. On the other hand, these layers are inherently nonuniform through their thickness because of the diffusion profile, and this property may sometimes limit their use as photoconductive detector material. By imposing a temperature gradient between the source and substrate, one can enhance the transfer rate and make the layer growth at least partly independent of the interdiffusion process, so that layers more nearly of uniform composition through their thickness should be possible. However, metallurgical problems occur in layers prepared by this “gradient-growth’’ technique, so that they are not suitable for detector applications ; some of these problems are discussed by Speerschneider et The gradient-growth variation does not appear at this time to be a practical method for the epitaxial growth of Hg, -,Cd,Te. Ludeke and Paul” have grown epitaxial films of Hg,-,Cd,Te onto single-crystal BaF2 substrates by flash evaporation in vacuum. Their purpose was mainly to prepare samples for studies of optical properties. This approach is probably not practical for the preparation of detector material. Kraus et aLY0 have deposited films of Hg, _,Cd,Te onto single-crystal substrates of NaCl, Ge, and sapphire by means of cathodic sputtering, but the resulting films were amorphous as deposited and became crystalline only upon subsequent annealing ; this does not appear promising as a practical approach either. Foss9*’ has formed Hg, -,Cd,Te films by Hg ion bombardment of CdTe single crystals. 11. ANNEALING OF CRYSTALS

Crystals of Hg,-,Cd,Te and analogous alloys can be annealed to modify their stoichiometry. This section deals only with the annealing of crystals as a C. J. Speerschneider (to be published). R. Ludeke and W. Paul, J . Appl. Phys. 37, 3499 (1966). 90 H. Kraus, S. G . Parker, and J. P. Smith, J . Electrochem. Sac. 114,616 (1967). ““N. A. Foss, J . Appl. Phys. 39, 6029 (1968). 88

89

5. MERCURYXADMIUM

TELLURIDE AND CLOSELY RELATED ALLOYS

241

means of adjusting stoichiometry ; it does not include the high-temperature anneals mentioned in Section 9 for removing microscopic alloy-compositional gradients. Hg, -,Cd,Te is a defect solid3 in which deviations from stoichiometry provide donor and acceptor sites, at least in the vicinity of x % 0.2. Interstitial Hg atoms appear to act as donors and Hg vacancies as acceptors. The extrinsic semiconducting properties of a crystal, determined either by thermoprobing or from the Hall coefficient, can be converted from n-type to p-type and back again by adjusting the Hg pressure during annealing. The French w o r k e r ~have ~ ~ employed ~ ~ ~ this method to produce p-n junctions for photovoltaic detectors. In general, post-crystal-growth annealing treatments provide a way of adjusting the stoichiometry and thereby the electrical properties of a crystal to improve them toward the requirements of infrared detectors. The intrinsic line in the phase diagram of Fig. 6 is based on thermoprobe data taken after annealing crystals at 300 and 400°C under various Hg pressures. Hall data for annealed samples indicated that annealing can yield samples with n-type carrier concentrations of the order of only 1014cm-3; however, the low value of the electron mobility in the extrinsic range of such samples suggests that compensation may exist. Strangely shaped Hall coefficient versus temperature curves having dips and reversals of sign are often observed in annealed samples. A possible explanation of these curves is that as a sample is cooled after annealing, Hg, a fast diffuser, redistributes itself, giving rise to carrier concentration gradients. No method of quenching has yielded normal Hall and mobility curves like those in Figs. 17 and 21, but annealing and cooling a large mass of crystal sometimes does. With a large mass, gradients are probably set up only near the surface, leaving the interior material uniform. Unfortunately, large masses of crystal require long annealing times, sometimes as long as two months to establish equilibrium, In any case, when annealing one must avoid creating samples of highly nonuniform stoichiometry. 12. JUNCTION FORMATION One can prepare both n- and p-type Hg, -,Cd,Te, and p-n junctions can be formed in crystals of the semiconductor alloys in this system. Such p-n junctions are the basis for photovoltaic Hg, -,Cd,Te infrared detectors. “Natural” p-n junctions are observed occasionally in crystals grown from the melt, but of greatest practical interest is the intentional preparation of p n junctions by methods such as diffusion. All of the published work on p-n junctions in Hg, -,Cd,Te has involved their preparation by diffusion of Hg. The diffusion of Hg into a p-type crystal produces an n-type layer on the surface, because the Hg atoms compensate the acceptors and provide an excess of donors; we noted

242

DONALD LONG AND JOSEPH L. SCHMIT

0.6

I-

z

w

0.2

I

1

I

I

I

I

1

1

I

I

I

-

a

‘0

-0.2-

l-c

0 i ,

2 -0.4-

3 3

0.2 APPLIED BIAS (VOLTS)

-0.3 -0.2 -0.1

0

0.1

I .

0.3

FIG. 35. Current-voltage characteristics of p n junctions in Hg, -.Cd,Te of three different alloy compositions (drawn from results of Verie and A y a ~ ’ ~ )The . numbers in parentheses represent samples of cornpositions having the following energy gaps: ( 1 ) 0.072 eV, (2) 0.086 eV, (3) 0.192 eV.

previously that excess Hg can reside interstitially in the lattice and act as a donor impurity. The diffusion of Hg out of an n-type crystal leads to a p type surface layer due to the resulting deficiency of Hg near the surface ; Hg vacancies act as acceptors. A few years ago Verie and Granger34 reported the preparation of p-n junctions in p-type Hgo,,,Cdo~,,Te alloy by Hg in-diffusion. Their p-type crystal contained about 2 x 1017cm-3 electrically active acceptors. An anneal under controlled Hg vapor pressure created an n-type surface layer varying in depth from 10 to 40p. Verie and A y a ~ ,later ~ extended these techniques to the preparation of p-n junctions in alloys having compositions in the range 0.15 < x < 0.28. Current-voltage characteristics obtained by of three different alloy compositions, and Vkrik and A y a ~in ~crystals ~ thereby different energy gaps, are plotted in Fig. 35. 13. CRYSTAL EVALUATION TECHNIQUES

a. Alloy-Composition Determination Two methods for x determination in Hg,-,Cd,Te are in common use. The first involves measurement of the density of samples using a standard lost-weight method. Since the density change with x is relatively small in Hg,-,Cd,Te (see Fig. 4), one must use a high density, low volatility fluid and a microbalance, making the usual corrections for air buoyance. The precision of the method used at Honeywell permits the density to be measured to 0.001 gm/cm3 for a 0.1 gm sample, corresponding to an error in x of less

5. MERCURY-CADMIUM

TELLURIDE AND CLOSELY RELATED ALLOYS

243

INGOT X

0

2

4

9

0.23

6

8

0.22

10

0.2 I

12 14 CM FROM TIP

0.20

16

18

20

22

TOP

lx

13mm

SLAB

FIG.36. Composition profiles of a typical ingot of Hg, -,Cd,Te prepared from the melt by the Bridgman method, and composition profiles of a typical slab cut from such an ingot.

than 0,001mole fraction. The density varies linearly with x (see Section 4b2*3*s9), but the absolute value of x for a given density has an uncertainty of about 0.01 mole fraction due to uncertainties in the original standards. Thus the density method yields x values with an absolute accuracy of fO.O1 mole fraction and a precision or repeatability of 0.001 mole fraction. In an attempt to establish a standard for comparison of compositions measured by the density method, we propose the following density versus x relationship used at Honeywell : x[Hg, _.Cd,Te] = 3.6280 - 0.44924p,

(62)

where p is the density in gm/cm3. This is in essential agreement with Blair and Newnham3 and assumes a linear relationship between the end points of 8.076 gm/cm3 for HgTe and 5.850 gm/cm3 for CdTe, as in Fig. 4.Figure 36 shows a typical composition profile of an ingot and of a slab of Hg, -,Cd,Te grown at Honeywell and determined by density measurements. Typically, 20 samples are cut from such a melt-grown ingot and measured to yield the interpolated curves shown. The slab indicates that lateral gradients are small, and the ingot profile demonstrates that longitudinal gradients are small, at least in the nonseed half of the ingot. Thus large-area planks of material having virtually no x gradient can be cut from ingots of this kind. The second method used to determine alloy composition is the electronbeam microprobe. In this method a beam of electrons is focused on a spot of material, which then emits X rays. Characteristic X rays of each element

244

DONALD LONG AND JOSEPH L. SCHMIT

are detected and counted, yielding a measure of the composition. Since the reabsorption of emitted X rays depends on the composition, and day-to-day changes in the characteristics of the beam and detector can occur, one normally uses a secondary standard having a composition near the expected value as reference. The absolute accuracy can be no greater than that of the standard used, which is about 0.01 mole fraction, and the precision when using a 30 p diameter, 0.1 pA beam counted for 1 min is limited by statistical fluctuations in the count to about k0.006mole fraction near x = 0.2. This method is used primarily on very small samples or to detect microscopic composition gradients. When using a 5 p diameter, 0.01 pA beam for detailed work, however, the statistical fluctuations limit the precision to approximately fO.O1 mole fraction near x = 0.2. b. Stoichiometry Determination

Since Hg, -,Cd,Te is a defect solid wherein deviations from stoichiometry can act as donors and acceptors, the normal way of measuring stoichiometry is by means of the Hall effect. Typical material taken from melt-grown crystals has Hall, resistivity, and mobility curves like those shown in Figs. 17, 18, and 21, with n-type carrier concentrations of below 1015cmP3as determined from the relationship no = (e0RH)-'. Samples with carrier concentrations much below 5 x 1014cm- usually show a drop in the low-temperature carrier mobility, indicating that compensation is taking place. These results then imply that present crystals typically deviate from stoichiometry by less than 30 ppb. c. Crystal Perfection Determination

Large-angle grain boundaries can be seen readily with the naked eye on either lapped or polished surfaces of Hg,-,Cd,Te. However, if one wants more detailed knowledge of the crystal structure, X-ray techniques must be employed. Three backscattering X-ray techniques are used at Honeywell to evaluate crystals : the Laue, Lang, and divergent beam reflections. The Laue patterns obtained from crystal material grown by several methods show clear patterns from the cubic lattice, indicating a lack of strains or of a second phase ; however, both the Lang and the divergent X-ray beam reflections show that most of the present melt-grown material contains lowangle subgrains. There has been no indication that these are detrimental for use as an intrinsic infrared detector material.

V. Detector Fabrication and Properties

'

For the most part intrinsic infrared detectors can be fabricated from Hg, -,Cd,Te using rather standard solid-state technology. However, certain

5. MERCURY-CADMIUM

TELLURIDE AND CLOSELY RELATED ALLOYS

245

special considerations do apply to this material, and they will be reviewed below. We will also present some representative Hg, -,Cd,Te detector data. 14. DETECTOR ELEMENT FABRICATION a. Element Preparation Most of the detector work on Hg,-,Cd,Te

is on crystals with 0.15 <

x < 0.40. This alloy material has physical properties similar to those of

HgTe: it is relatively soft and laps and cuts easily. Since it is soft, however, one must use special precautions when making detectors or other samples to prevent the introduction of dislocations and strains. Normally, a slurry wire saw is used to cut slabs and samplesfrom melt-grown ingots. Either a saw or etching techniques are used to cut individual detector elements from melt-grown or epitaxial slabs. A final etch removes any surface material cutting damage. Since the Hg, -,Cd,Te is used in the intrinsic detection mode, a detector element has a large absorption coefficient and need only be several microns thick to absorb the incident radiation. Photoconductive detectors made from melt-grown crystals are normally epoxied to a substrate and made 5-20 i.( thick by lapping and etching before being cut or photolithographically etched into individual detectors or arrays. Epitaxial layers are usually grown of the proper thickness initially and need only be cut and etched before lead attachment. Photovoltaic detectors are made by diffusing excess Hg into a p-type substrate to form a junction; the n-type face is then mounted to a metal contact, and the p-type side is lapped and etched to within 10-2Op of the junction.36 An alternate approach not requiring a thin sample is to use a graded-gap configuration with radiation entering from the thick, wide-energy-gap, p-type side. An intrinsic detector material such as Hg, -,Cd,Te is especially well suited to the fabrication of detector arrays, both one- and two-dimensional. Each detector element need be only several microns thick as mentioned above. Thus photolithographic techniques similar to those used for mesa transistors can be employed to delineate detector elements. An array of Hg, -,Cd,Te detectors can be made with small elements and very small separations between adjacent elements in the array. Examples of arrays already fabricated include'' : a six-element linear array, each element of which is 0.2 mm square and separated by 10 p from its nearest neighbors ; a 20-element array of 0.8 mm square elements ; and a six-element array having six different sizes ofelements. Lead attachment to the elementsin such arrays is by thermocompression bonding or parallel-gap microwelding onto evaporated layers of indium. Unpublished work, Honeywell Radiation Center, Lexington, Massachusetts.

246

DONALD LONG AND JOSEPH L. SCHMIT

b. Surjace Treatment Hg,-,Cd,Te with x 5 0.4 is soft and easy to damage; therefore, it is essential that a chemical etch be used to remove any damaged surface material after cutting or lapping. The normal polishing etch is a room temperature solution of 20% bromine in methyl alcohol. This etch usually leaves a mirrorlike surface suitable for electrical contacting by any of the means listed below. Acid etches have been used to reveal the presence of crystal grain boundaries, dendrites, flaws, and even alloy compositional gradients. The best of these revealing etches consists of a mixture of 1 :2:3::HCl:HN0,:H20 used for 30 seconds at room temperature. A Hg,-,Cd,Te detector can be passivated by evaporating a ZnS antireflection coating onto its surface. The passivation can reduce ILfnoise due to surface states and increase the tolerance of adverse environmental conditions. The antireflection qualities of the layer can increase the effective quantum efficiency by reducing the reflection of incident radiation. When multilayer coatings are used on BLIP detectors to allow only a narrow spectral band of radiation to reach the detector, the detectivity at the allowed wavelength increases due to the reduction of the total background flux. No definite experimental evidence is available to support the above statements for Hg, -,Cd,Te. c. Electrical Contacts

In narrow-band-gap semiconductors, such as Hg, -,Cd,Te with small x, it is difficult to make good rectifying contacts (such as those required for Schottky barrier diodes). It is only in wide-band-gap semiconductors that one must resort to doping surface layers in order to make low-resistance ohmic contacts. Conversely, ohmic contacts can be made to this narrowenergy-gap material by several means, including soldering, evaporating, and electroplating. Individual-element photoconductive detectors have generally been made by soldering directly to the Hg, -,Cd,Te with indium, or by evaporating an indium contact pad to the element and bonding to that. Arrays of detectors have been contacted almost exclusively using the evaporation method. Photovoltaic detectors have used electroplated gold contacts.36 Some evidence of rectification has been seen in Hg,-,Cd,Te, but this is believed to be due to energy-gap gradients, as described by Kruse.” Typical photoconductive detectors show contact rectification of only a few percent, which is negligible. 15 . ENCAPSULATION

a. Envelopes Detectors are normally operated in a vacuum, both to provide thermal isolation and to prevent detector deterioration due to surface contamination

5. MERCURY-CADMIUM

TELLURIDEAND CLOSELY RELATED ALLOYS

247

and oxidation. For 77°K operation either a metal Dewar with an O-ring sealed window or a glass Dewar with a fused or epoxied window is used, with the detector cemented to the cold well. For temperatures other than 77"K, the bare detector element is mounted in a variable temperature cryostat for experimental use, while for operational use it is mounted in a small vacuum chamber which can be attached to a cold finger of a closed cycle refrigerator or other cold source. Schematic diagrams of these envelopes are shown in Fig. 37. KOVAR LEADS VACUUM T I P - OFF ~

u

GLASS - KOVAR LEAD SEAL

1 1 7-

VACUUM SPACE

KOVAR RING SEAL

GLASS DEWAR

LlOUlD NITROGEN KOVAR LEAD WIRE GLASS WELL GLASS BARREL

e

4

-

DETECTOR KOVAR RADIATION SHIELD I R T R A N WINDOW

FOV

-O-RING

VACUUM SEAL

M ETA L WELL METAL BARREL VACUUM SPACE

METAL DEWAR

LIQUID NITROGEN IRTRAN WINOOW DETECTOR LEAD THROUGHS

c

DETECTOR IRTRAN WINDOW

QETECTOR PACKAGE FOR COLD- FINGER

METAL VACUUM BOTTLE LEAD THROUGHS

F~G. 37. Typical envelopes for Hg, -xCd,Te and similar infrared detectors.

248

DONALD LONG AND JOSEPH L. SCHMIT

-3:

100

5

5

80 60 40

20

: o

2

4

6

8

10

12 14 16 I8 20 WAVELENGTH IN MICRONS(p1

22

24

26

28

30

FIG.38. Infrared transmittance versiis wavelength of IRtran window rnaterials9’

b. Windows

Kodak IRtran materials are used widely as infrared transmitting windows. These materials are polycrystalline binary compounds with excellent chemical inertness. They have long-wavelength cutoffs ranging from 9 to 31 p. IRtran 2, made of ZnS, has a 14-p long-wavelength cutoff and is normally used with the 8-14 p detectors. Figure 38 is a transmittance versus wavelength plot taken from Kodak product literature.’, The materials used for IRtran 1 through 6, along with the long-wavelength cutoff of each, are : MgF,, 9 p ; ZnS, 14 p ; CaF,, 1 1 p ; ZnSe, 22 p ; MgO, 9 p ; and CdTe, 3 1 p, respectively. Applications for infrared detectors vary and require that care be taken to choose the best set of conditions for each specific use. A figure of merit of a detector is the detectivity D*,which is proportional to the signal-tonoise ratio. When the dominant noise is due to fluctuations in the number of carriers generated by radiation from the background, reducing the number of background photons will reduce the noise and increase the signal-to-noise ratio and the detectivity. The background radiation can be reduced in at least two ways. By placing a small diameter aperture in front of the detector its field of view (FOV)is reduced, thus excluding some background radiation. In some cases the effective background radiation is coming not from the background of the scene being viewed, but from the collecting optics. In this case reducing the FOV would exclude signal as well as noise, yielding a net loss in detectivity; signal depends on the first power of the source-generated carrier concentration, while noise depends only on the square root of the background-generated carriers. The solution in this case is to leave the field of view large enough to view the entire objective lens, but to cool the optics so that they will emit fewer photons. Cooling the effective background from 300 to 200°K will reduce the photon flux an order of magnitude, while cooling it to 77°K will reduce the flux five orders of magnitude. Reducing the background flux by reducing the field of view or cooling the optics only helps so long as the detectivity is background noise limited (BLIP). This point has been covered in detail in Section 6. 92

Kodak Pamphlet No. U-71 (1967).

5 . MERCURY-CADMIUM TELLURIDE AND CLOSELY RELATED ALLOYS 249 .-. v) t

ia

1

2

I)

a

> a a

’

t

5

m

a a w

v)

z 0

a v)

3

w

a w >

2

l-

0 I) 0

2

0

u

/ i

0 I-

Pa I W

1

+

0.7

4

w

a 0.5 3

I

I

I

I

I

5

7

10

15

20

30

x cp, FIG. 39. Response versus wavelength of four photoconductive Hg, -,Cd,Te different alloy compositions.

detectors of

16. TYPICAL DETECTOR RESPONSE CHARACTERISTICS We close the body of this chapter by presenting several typical Hg, -,Cd,Te detector response curves. a. Photoconductive

Figure 39 shows the photoconductive spectral response curves of four Hg, -,Cd,Te detectors fabricated from crystals having a range of alloy composition^.^^ These curves illustrate the fact that intrinsic detectors with response peaks at different wavelengths in the infrared can be made from Hg, -,Cd,Te. A similar response curve for a photoconductive detector peaking at 11 p has been published by Rodot et al.94Figure 40 shows the photoconductive spectral response curve of a long-wavelength Hg, - ,Cd,Te detector at five different temperature^,^' illustrating the rather strong temperature dependence of the response due to the temperature dependence 93 94

J. L. Schmit et al. (unpublished Honeywell data). M. Rodot, C. Vkrik, Y. Marfaing, and H. Lebloch, I E E E J. Qiiaritum Electron. 2. 586 (1966).

250

DONALD LONG AND JOSEPH L. SCHMIT

i

27'K

a

10

20

30

50

70

A (PI FIG. 40. Response versus wavelength of a photoconductive Hg, _,Cd,Te detector at five different temperatures.

of the energy gap. The temperature dependence of the cutofi wavelength is this large only in the narrow-energy-gap detectors.

b . Photovoltaic Response curves of Hg, -,Cd,Te photovoltaic detectors have been published by the French investigator^.^^*^^*'^*^^ VCrie and A y a show ~ ~ a~ set of photovoltaic response curves peaking at wavelengths betwecn about 4 and 15 which are analogous to those in Fig. 39. Curvcs for a short-wavclength p--n junction photovoltaic detector at 77 and 300°K drawn from published results of VCrit. and Granger,34 are plotted in Fig. 41. These

5. MERCURY+ADMIUM

TELLURIDE AND CLOSELY RELATED ALLOYS

2

3

4

5

7

251

10

x (/A) FIG.41. Response versus wavelength of a photovoltaic Hg, -,Cd,Te detector at two different temperatures. (After Vbrii: and Granger.34)

curves are interesting in showing the relatively small wavelength shift with temperature in this comparatively wide-energy-gap alloy (Hg,.,,Cdo.35Te).

VI. Conclusion Our purpose in this chapter has been to review the present knowledge of 11-Vl compound alloy systems with respect to their use as intrinsic infrared detector materials. We have concentrated almost entirely on Hg, -,Cd,Te because virtually all the useful available information is about that system. Hg,-,Cd,Te is already one of the most extensively studied and best understood semiconductor alloy systems ; probably only GaAs, -,P, has been as heavily investigated. Furthermore, Hg, -,Cd,Te is one of the most nearly pure semiconductors developed, as measured by the extrinsic carrier concentration provided by uncompensated donors or acceptors ; only Si, Ge, Te, InSb, GaAs, and possibly one or two other semiconductors are equal or superior to Hg,-,Cd,Te in this respect. And yet the research on Hg, -,Cd,Te is certainly not finished. For detector purposes, further improvements are needed in crystal growth methods to permit still better

252

DONALD LONG AND JOSEPH

L. SCHMIT

crystal uniformity and purity. A much better understanding of carrier recombination mechanisms is needed. Very little is known about electrically effective impurities in this material. More research on these and other such subjects is warranted. In this chapter we have paid primary attention to photoconductive and photovoltaic Hg, -.Cd,Te detectors developed to operate in the 8-14 p wavelength interval at 77°K because most of the detector work to date has involved these devices. However, as we emphasized in Section 2, the alloy nature of this material permits extending its use over a much wider range of wavelengths, as well as to other operating temperatures both above and below 77°K. Perhaps the greatest strength of Hg,-,Cd,Te as an infrared detector material is the potential it offers for a whole family of compatible detectors, using alloys of a variety of compositions. We have already seen examples of these possibilities in Figs. 39-41. Another possibility offered by Hg, _.Cd,Te, not discussed in the body of this chapter, is that of graded-gap devices. These are structures in which the energy gap varies with position through the crystal due to a variation of alloy composition. Krusesl discussed the properties of graded-gap crystals several years ago. The French investigator^^^*^^ and Almasi and Smithi4 have reported spectral response data for the photovoltaic and photomagnetoelectric effects for graded-gap structures prepared by HgTe-CdTe interdiffusion. Further exploitation of graded-gap Hg, -,Cd,Te can be expected in the One must ask finally whether some other semiconductor alloy system may prove to be a generally better designable intrinsic infrared detector material than Hg, _.Cd,Te. This could conceivably happen, but it seems unlikely. No serious specific limitations of Hg, -,Cd,Te as a high-performance detector material have arisen. For example, there appears to be no fundamental limit to crystal purification or the achievement of perfect stoichiometry in this system. In addition, the band structure of Hg, -,Cd,Te yields a relatively low intrinsic carrier concentration for a given energy gap because the conduction band density of states is so small, and this is a good feature for an intrinsic detector material. Thus experience to date shows that Hg, _,Cd,Te is a “good enough” material. It would probably not be worthwhile to do all the research needed to bring some other alloy system to the point of simply being able to replace Hg,-,Cd,Te. For certain special requirements, however, it may be found that another material is necessary. ACKNOWLEDGMENTS We are indebted to our colleagues at the Honeywell Corporate Research Center and the Honeywell Radiation Center for innumerable contributions to whatever good features this

’’G. Cohen-Solal, F. Bailly, C.V6rit, and Y. Marfaing, Cornpt. Rend. 257,863 (1963). 95aG. Cohen-Sola1 and Y.Marfaing, Solid-Srare Electronics 11, 1131 (1968).

5. MERCURY--CADMIUM TELLURIDEAND CLOSELY RELATED ALLOYS 253 chapter may have. We owe special thanks to P. W. Kruse of the Research Center, who led the Honeywell research and development effort during its formative and most difficult period, and to T. D. Pickenpaugh of the US.Air Force Avionics Laboratory, who supported and advised this effort; without their contributions this review would not have been possible. J. K. Lennard and J. 3. Schlickman of the Radiation Center have been especially helpful also. J. N. Dempsey and C. H. Li, the directors of the Research Center, provided constant encouragement. Finally, we thank Mrs. J. Liset and Mrs. V. Squier for their highly competent work in typing the manuscript and preparing the figures, respectively.

Appendix. Intrinsic Carrier Concentration versus Temperature in Hg, - .Cd,Te

Two assumptions have been combined for these calculations : The first is that the energy gap varies linearly with alloy composition x (see Fig. 13). The second is a quadratic temperature d e p e n d e n ~ eof~ ~ E , based on the known quadratic dependence of E , in CdTe (this assumption is not fully consistent with the latest data given in Fig. 14). Also, the well-known Kane k p giving a nonparabolic conduction band has been incorporated in the calculations. Values of x and T were chosen and the energy gap calculated using the above two assumptions, and then the reduced Fermi energy was varied in the Kane model until a numerical integration yielded n = p = n,, where n, is the intrinsic carrier concentration, These calculations give the intrinsic properties of any Hg, -,Cd,Te alloy with 0.15 < x < 0.25 for temperatures between 40 and 300°K. The semiempirical temperature dependence of the energy gap of Hg, -,Cd,Te was given by S ~ h l i c k m a nas~ ~ E , = E,,o + p T 2 , (All where p = (1.34 - 2 . 4 4 ~ ) 1 0 - ~eV/"K2, (A2) where is the energy gap at O"K, and /3 is the coefficient of quadratic temperature dependence. This assumption is not strictly consistent with Fig. 14, but it does not seriously affect the results here. The linear dependence of E , on x can be written E,,o = 1.875(~- 0.15). (A31 Combining equations (AlWA3) gives the energy gap as a function of x and 7: namely,97a

.

E, = 1 . 8 7 5 ( ~- 0.15) + PT2 = 1 . 8 7 5 ( ~- 0.15)

+ (1.34 - 2 . 4 4 ~ ) 1 0 - ~ T ~ . (A41

96 97

J. J. Schlickman (private communication). E. 0. Kane, J . Phys. Chem Solids 1,249 (1957).

97"Equation (A4) is not precise ; a better e x p r e ~ s i o n ~is~: " * ~ ~ ~

E, = 1.59~- 0.25 + 0 . 3 2 7 ~+~5.233 x 10-4T(l - 2.08~).

254

DONALD LONG AND JOSEPH L. SCHMIT

The equation for the conduction electron concentration n was taken from Harman and Strauss,” who used the Kane model to take into account the effects of nonparabolic bands on the statistical degeneracy, and is as follows : n = 4ni(2) 3 3 1 / 2 ( q 3 T 3 I OX”2(X 4)”*(2X 4) d X , 1 exp(X - q )

+ +

+

where the terms not previowly defined are: P is the Kane matrix element ( = 9 x * l o p 8eV cm)28; X (variable of integration) = [ - E g + (Eg2 + 8pZk2 1/2]/2kB?:with k the wave vector; 4 is the reduced energy gap, E$kBT; 3 ) and q is the reduced Fermi energy measured from the conduction band edge, E,/kBT. The integral in Eq. (A5) cannot be solved explicitly; therefore a computer program was written to solve it numerically. The last expression needed to compute the intrinsic carrier concentration is the standard expression for the density of free holes p in the valence band and is as follows98:

with the Fermi-Dirac functions F,,&

+ #) approximated by for q + + > - 1 ,

z 0.667[(q

+ 4)2+ 1.f1451~’~for

q

+ 4 < - 1.

The symbols not previously defined are as follows : mu* is the effective mass of holes in the valence band = 0.3 m, and B = 4n(2kR/h2)3’2(mu*)3/2 = 8.9537 x 10140K3/2cm- 3. In the range of x and T covered here the holes never become degenerate, so only the first approximation for the Fermi function was used. Starting with the above equations a computer program was written to set up various combinations of x and T, calculate p from Eq. (A2), calculate E, from Eq. (A4), and caIculate the reduced energy gap #. Then starting with an arbitrary q, calculating p from Eq. (A6), and integrating Eq. (A5) to within 0.5% a value of n - p was determined. A root finding program was next initiated which adjusted q and repeated the process until n - p m 0, or n = p = ni, the intrinsic carrier concentration. We have already given plots of n, versus x for various temperatures in Fig. 19, and of ni versus 1/T for various x values in Fig. 20. T.C . Harman and A. J. Strauss, J . Appl. Phys. 32,2265 (1961).

5. MERCURY-CADMIUMTELLURIDE AND CLOSELY RELATED ALLOYS

255

This entire calculation is for intrinsic material, and therefore only degeneracy due to intrinsic carriers is included; however, an estimate of the doping level allowed before these intrinsic results are invalidated can be made by assuming that doping levels as high as the intrinsic carrier concentration are allowed and determining these levels from Fig. 19 and 20.

This Page Intentionally Left Blank

Thermal Detectors

This Page Intentionally Left Blank

CHAPTER 6

The Pyroelectric Detector E. H . Putley

I. THEPYROELECTRIC EFFECT, .

.

.

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 3 . Principal Noise Sources . 4. Total Energy Detector .

. .

. .

.

. . . . . . . . . . . DETECTOR . . . . . . . .

11. THEPYROELECTRIC DETECTOR . .

I , The Thermal Circuit . 2. The Electrical Circuit. 111.

CONSTRUCTION OF PYROELECTRIC

. .

. .

. .

. .

. .

. .

. .

. .

. .

. .

5 . Choice of Material . . . . . . . . . . . . . . 6. Details of Construction . . . . . . . . . . . . . 7. Performance of RRE Pyroelectric Detector. . . . . . . . 8 . Comparison with Other Detectors . . . . . . . . . . APPENDIX . . . . . . . . . . . . . . . . . NOTEADDEDI N PKOOF. . . . . . . . . . . . . .

259 26 1 26 I 263 266 272 213 273 275 276 279 283 284

I. The Pyroelectric Effect Crystals of noncentrosymmetrical structure make up 21 of the 32 types of symmetry. Of the 21 noncentrosymmetric classes, ten (which are all piezoelectric) can exhibit spontaneous electric polarization. However, an external electric field will not normally be observed, since if the material is a conductor, its mobile charge carriers will assume a distribution which neutralizes the internal moment, while if it is an insulator, stray charges will be attracted to and trapped on the surfaces until the surface charge associated with the polarization is neutralized. The charge distribution produced in this way near the surface of an insulator is relatively stable, unable to respond quickly to sudden changes of the internal dipole moment. Thus, in particular, if the temperature of the material is changed, the dipole moment may also change, and this change will produce an observable external electric field. Thus, although the dipole moment is not directly observable, its temperature coefficient is. This temperature coefficient is called the pyroelectric coefficient (Cady’). The purpose of this chapter is to discuss the exploitation of this effect as a means of detecting infrared radiation.

’ W. G. Cady, “Piezoelectricity.” McCraw-Hill. New York, 1946. 259

260

E. H. PUTLEY TABLE 1 THEPROPERTIES OF SOMEPYROELECTRIC MATERIALS AT 300°K

Material ~~

Tourmaline

4

x

BaTiO,

Triglycine sulphate (2-3.5) (TGS) (NH,CH2COOH),.H,SO4 Li,SO,,H,O

x

'O

lo

*

lo-'

1.0 x 10.8

,o

LiNbO, LiTaO, SbSI NaN02

10

~

6 x 2.6 10-7

1.2

x

lo-'

I 60 (11 polar axis) 4100 (Ipolar axis) 25-50 10

OS

0.97 -0.4

30 (11 polar axis) 104

x lo-'

6.0

x

10''

1.69

17 x

lo-'

2.05

6.8

4.64

75 (Ipolar axis) 56 8.0

9

0.29 0.96

8.2 2.1

Table I gives the magnitude of the pyroelectric coefficient (expressed in C c m - Z o K - ') for some typical materials. When it is recalled that a sensitive C it is seen that use of electrometer can detect a charge of about 5 x the pyroelectric effect should enable change in temperature of less than 1pdeg to be detected, and in fact it has been used for this Any sensitive thermometric element can, in principle, be used as a thermal infrared detector. This application of the pyroelectric effect was suggested by Yeou Ta4 and Chynoweth,s and a detailed analysis of the characteristics of the pyroelectric detector was first made by Cooper showed that it should be possible to produce a pyroelectric detector of performance close to the limit set by the surroundings at room temperature. Unfortunately, Cooper was not able to achieve this performance in practice, apparently due to the limitations of the pyroelectric materials then available, Since that time improved materials have been developed. Several laboratories have been studying the development of improved pyroelectric It appears S. B. Lang and F. Steckel, Rev. Sci. Znstr. 36,1817-1821 (1965). S. B. Lang, Natl. Bur. Std. (U.S.),Tech. News Bull. 51, 193 (1967). Yeou Ta, Cornpt. Rend. 207, 1042-1044 (1938). ' A. G . Chynoweth, J . Appl. Phys. 27,78-84 (1956). J. Cooper, Rev. Sci. Instr. 33, 92-95 (1962). ' J. Cooper, J . Sci. Instr. 39,467-472 (1962). * A. L. Stanford, Jr., Solid-state Electron. 8, 747-755 (1965). G. A. Burdick and R. T. Arnold, J. Appl. Phys. 37,3223-3226 (1966). H. P. Beerman, Am. Ceram. SOC.Bull. 46, 737-740(1967). ' I A. Hadni, Y. Henninger, R. Thomas, P. Vergnat, and B. Wyncke, J . Phys. 26,345-360 (1965). L. S. Kremenchugskii, A. F. Mal'nev, and V. V. Samoilov, Prihory i Tekhn. Eksperim. No. 6, 169-171 (1966) [Instr. and Experim. Techniques (English Trans/.)No. 6, 1460 (1966)l. l 3 K. Takdmi, K. Suda, and M. Koga, Oyo Butsuri 37, 147-156 (1968). l4 J . H. Ludlow, W. H. Mitchell, E. H. Putley, and N. Shaw, J. Sci. Instr. 44, 694-696 (1967); J. H. Ludlow, W. H. Mitchell, and E. H. Putley (to be published).

'

6 . THE PYROELECTRIC DETECTOR

261

now that the performances being achieved are beginning to approach the ideal limit. In addition, it has been possible to demonstrate that under certain conditions a useful fast pyroelectricdetector (with an effective response time of less than 1 psec) can be produced.

II. The Pyroelectric Detector When the pyroelectric detector absorbs radiation its temperature rises, changing its surface charge. To calculate its performance, both the thermal and electrical characteristics must be considered in detail and the sources contributing to the detector's noise must be enumerated. These aspects are discussed in detail in the following three sections. In this way the performance of the pyroelectric detector can be calculated. There are three ways in which a pyroelectric detector may be used : (1) To detect a signal modulated at a constant angular frequency w ;(2) by combining a detector operating in this mode with a frequency-equalizing amplifier, a receiver with a very short (less than 1 psec) response time suitable for observing transient signals, such as laser pulses, may be produced ; and (3) the pyroelectric element can be used to store the total charge liberated by a transient signal, Measurement of this charge determines the total energy of the transient. The discussion of the next three sections is concerned primarily with detectors employingthe first two modes of operation, but in the following section the charge storage mode is also discussed. 1 . THETHERMAL CIRCUIT Consider a thin plate of pyroelectric material held in position by supports of low thermal conductance in an evacuated constant temperature enclosure of temperature T"K. Then the thermal conductance coupling the plate to its surroundings will be mainly determined by radiative exchanges. From Stefan's law, if the plate is at a temperature T + 8, the heat flow from the plate to its surroundings is GRe,where GRis the radiative conductance, which for a unit area is GR = 490T3, (1) where q is the emissivity of the surface and (T is Stefan's constant. If the area of the plate is A and both sides radiate with the same emissivity, then GR = 8 v g A T 3 . (2) Since in most cases there will be other significant contributions to the thermal conductivity, GR is the limiting value to which the actual conductance G tends in ideal circumstances. Although this will not apply to all processes M. F. Kimmitt, J. H. Ludlow, and E. H. Putley. Proc. IEEE 56, 1250 (1968).

262

E. H.PUTLEY

contributing to the conductance, we will assume G is proportional to A (i,e., G = gA). If the thickness of the plate is d cm and its specific heat is c J gm-' deg- and its density S gm cmP3, the plate's thermal capacity is

'

H = dAd, (3) where c' = cS is the volume specific heat. If the plate is exposed to a beam of radiation containing a component modulated at angular frequency w, the incident power of the beam can be written

f

=

f,

+

(4)

loejWf,

where 1, > I,. The temperature of the plate is found by solving the equation ?I = H(dB/dt)

+ GB.

(5)

Solving for the amplitude of the component tlo at angular frequency w of the excess temperature gives

+ o2H2)-

ti',

= r71(o(G2

lj2,

(6)

and q5 = tan-'(oH/G) is the phase difference between the radiation and temperature oscillations. Having calculated O w , the corresponding pyroelectric charge appearing on the surface of the element can be obtained at once and the output voltage produced calculated by considering the electrical circuit of the element. Before doing this the thermal circuit will be considered in more detail. The simple calculation just outlined for a,, assumes that the incident radiation is absorbed uniformly throughout the sample. If the material has a large absorption coefficient a cm ' or if its surface is coated with a thin absorbing layer, this assumption may not be justified. In some regions of the infrared spectrum the absorption coefficients of pyroelectric material appear to be greater than 1000 cm-', so that the radiation will be absorbed in a distance less than 10 p , which is likely to be less than the thickness of the plate. Hence the thermal behavior when the absorption is nonuniform must be considered in more detail. An exact calculation is difficult, but a useful insight to the problem is obtained by considering the case where the radiation is absorbed at the surface of a semiinfinite slab, If we consider again the component of excess temperature at the angular frequency w, we find that a damped temperature wave is propagated into the material. The behavior can be calculated by considering the distributed thermal circuit for the plate. An element of thickness dx will have a thermal capacity c'A d x and a thermal resistance d x / K A, where K is the thermal conductivity. This distributed circuit can be treated in exactly the same way as an electrical circuit. Then it is found that the bulk material presents to the absorbing layer a thermal ~

6. THE PYROELECTRIC DETECTOR

263

+ ~)(&oKc’)”~A:

(7)

admittance Y = (1

while the propagation constant for the thermal wave is

y = (I

+j)(~c’/2K)’~~.

Hence if the excess temperature at the surface is written 80 = 8, cos ot ,

(8) (9)

the excess temperature at a distance x below the surface will be

6,

=

6, exp[( - ~ c ’ / 2 K ) ’ / ~cos[ot x]

-

(o~’/2K)’/~x].

(10)

Thus at a depth below the surface

d T = (2K/oc’)1’2

(11)

the amplitude will be reduced to l/e of its value at the surface, while at the ’ ’ ~wave will be in quadrature with the slightly greater depth ~ ( K / ~ w c ’ )the wave at the surface. Hence if the incident radiation is absorbed in a very thin surface layer, the lumped circuit approximation will only be valid if the thickness of the pyroelectric plate is less than 6,. If 6 , is small compared with the thickness of the plate, then the thermal admittance of the thick slab must be included in the thermal circuit. To indicate the magnitudes involved, typical values for c’ and K are 1.5 J c m - j O K - ’ and 5 x l o d 3W cm-’ O K - ’ , respectively, giving 6 , = 3.3 x 10-2f-”2cm, where f is the frequency in hertz Thus for f = 100 Hz, BT = 33 p, while f = 10 kHz gives 6 , = 3.3 p. Hence 6, could become small compared with the thickness of the plate at relatively low frequencies, so that if the absorption coefficient is high, or the surface is blacked, the distributed thermal circuit must be used to calculate the thermal characteristics of the pyroelectric element. 2. THEELECTRICAL CIRCUIT If the pyroelectric coefficient is p and the area of the electrodes A (which for the present will be assumed to be the same as the receiving area; an alternative configuration is discussed in the appendix), the alternating temperature component 8, will produce an alternating charge pA8,. If we represent the element as a capacity C, in parallel with a resistance R,, the alternating charge on the electrodes is equivalent to a current generator i, = o p A 8 , in parallel with the capacity. If the element is connected across the input of an amplifier whose input impedance can also be represented by a capacity and a parallel resistance, the voltage applied to the amplifier is found by calculating the voltage across the equivalent circuit for the combined impedances (see Fig. 1).

264

E. H. PUTLEY

Detector

Arnplif ier inpul

Equivalent circuit

FIG. 1. Equivalent electrical circuit of detector and amplifier input.

Thus I/ =

i,[Zl

=

i,R( 1

+

WZZEZ)

-

,

where zE = RC. Hence V = WpAB,R(l

+ w2rE2)-112.

Substituting for 6 , from Eq. (6) gives 9v

=

V/ZU = q(wpAR/G)(l

+ C U ~ T E ~ ) -+~ w~ ~TT( )~ 2

2 -1/2

,

(13)

where rT = H/G is the thermal time constant. (This result will still apply if the distributed thermal circuit has to be used, provided the correct values are used for H and G.) Bv is the voltage responsivity (output voltage/input radiant power) of the pyroelectric detector.

w

FIG.2. The log-log plots of 0, and W, against w.

265

6. THE PYROELECTRIC DETECTOR

Figure 2 shows the frequency dependence of 8, and Bv.The former is constant at low frequencies, but varies as f - when f % (2mT)- ; the latter is zero when f = 0, is proportional to f when f < (27tTT)- ', (27~7,)- ', and varies asf-' whenf ( 2 7 t t T ) - ' , (27q4-l. Depending on the parameters of particular materials, zTmay be greater or smaller than zE.In the intermediate

'

Frequency (HA

FIG.3. Performance of a TGS detector with an XE 5886 amplifier. The resistance and capacity are measured values. Measured values for the responsivity are plotted, but the curve is calculated from Eq. (13) using the following values for the parameters : = 0.23, p = 2 x lo-* C cm-ZPK, G = 4.3 x JPK, 77. = 150 msec. The noise voltages Ah, AVT, and AVRare calculated from the electrical and thermal parameters of the detector, while AVA and AV, are measured. These noise sources are used with the responsivity to obtain the calculated curve for the NEP which is compared with the directly measured experimental curve.

266

E. H. PUTLEY

frequency region (27n,,J1 < f < (27c~,,,~~)-',W v is independent off: These remarks assume that the quantities p , H , G, C, and R are all independent of frequency. In actual materials some of them will usually show some frequency dependence (see, for example, the results plotted in Fig. 3), but this has not been found to be large enough to alter significantly the behavior of the responsivity from that given by Eq. (13). The order of magnitudes of zEand oT for the type of device we have measured fall within the range 1 0 4 . 1 sec. Since for the majority of applications the frequencies of interest are at least 10 Hz and in some cases are greater than 1MHz, the high frequency approximations of equations (6) and (13) are sufficient most of the time, i.e.,

0,

=

qIJuH,

(14)

qpA/wHC. Expressing (15) in terms of the material parameters, Wv

(15)

=

WV = ( l / ~ E ' ) ( ? P / ~ c ' ) ( ~ / A ) , (16) where E is the dielectric constant and E' the permittivity of free space. Substituting the numerical values given in Table I1 gives

.*"= 2.4 x

103(~~)-1

for A = 10-'cm2

= 2.4 x losf-' = 2400

vjw for f = 100 Hz.

V/W TABLE I1

PROPERTIES OF

THE

PYROELECTRIC MATERIAL ASSUMEDFOR 6

THE

CONSTRUCTION OF FIG. ~

Pyroelcctric coefficient p Resistivity p Dielectric constant c Volume specific heat c' Thermal conductivity K Emissivity q Absorption coefficient c1

~~~

~

2 x 10-*Ccrn-*OK-' 10'* ohm cm 10 1.5 J c m - 3 OK-' 5 x lo-' W cm-' OK-' 1 103 c m - l

3. PRINCIPAL NOISESOURCES The equivalent circuit (Fig. 4) shows the principal noise sources. These are (1) temperature or radiation noise, (2) Johnson noise in equivalent shunt resistance, (3) amplifier current noise, and (4) amplifier voltage noise.

6. THE PYROELECTRIC DETECTOR

AVT AVj

267

AV, AVA

FIG.4. Equivalent noise sources for (a) primary sources, and (b)equivalent voltage generators at amplifier input.

These will be considered in turn and then combined to determine the noise equivalent power or detectivity.

a. Temperature or Radiation Noise If a small body of thermal capacity H is coupled to a large heat sink at temperature T via a thermal conductance G, it will attain the same temperature T, and when thermal equilibrium is established the mean power flow between the body and the sink through the conductance G will be zero. However, it will have a fluctuation spectrum with an rms value16 AWT

=

(4kT2G)”’.

(17)

It is also possible to consider the blackbody radiation incident when the element is placed inside a blackbody enclosure at temperature T. The fluctuation in the radiation power absorbed and emitted can be calculated using radiation statistics. Ifthe element absorbs uniformly throughout the spectrum, the result obtained is similar to Eq. (17) but with G replaced by GR, the radiative conductance given by Eq. (2). Since GRis the minimum value G has when the element is coupled to its surroundings only by radiative exchanges, the radiative fluctuation is the limiting value to which Eq. (17) tends. In an ideal detector only the radiation term would contribute to the noise. I6

R. Clark Jones, Aduan. Electron. 5, 1-96 (1953).

268

E. H. PUTLEY

The temperature noise voltage produced by AWT is calculated by treating A W, the same way as an incoming signal. Hence

A VT

= 9v(A

;

(1st

7 appears in Eq. (18) because gvis defined in terms of the incident power

while Eq. (17) is given in terms of the power absorbed.

b. Johnson Noise There will be a Johnson noise voltage associated with the equivalent circuit resistance R (Fig. 1) given by

Ah = (4kTR)”’

(19)

(for a 1 Hz bandwidth). Referred to the amplifier input (Fig. 4) the corresponding voltage is AVJ = (4kTR)”’(l

+ W’T~’)-’’’.

(20)

At high frequencies this becomes AV,

=

(~~T)”’/UCR’”,

which shows that at high frequencies

(21)

A 5 is reduced by making R large.

c . Amplifier Noise

The noise characteristics of both vacuum tubes and solid-state devices can be represented by the combination of a voltage generator AVA in series with the input and a current generator AiA in parallel. Both these generators may be frequency dependent. Figure 5 shows typical values for some types of amplifier suitable for use with pyroelectric detectors. The voltage generator represents noise sources which are independent of the circuit connected to the input of the amplifier, while the current generator represents sources such as grid current noise whose relative importance depends on the circuit impedance. Thus AV’ appears in Fig. 4, while AiA is replaced by the equivalent voltage generator A y, where AK

=

R &A (1

+ W2~E2)p1/2,

(22)

which at high frequencies becomes

AK = Ai,/wC.

(23)

d . Comparison of Noise Sources-Noise Equivalent Power The four noise generators shown in Fig. 4 can be replaced by an equivalent generator AVN formed by summing the squares : (AV#

= (AV,)’

+ (AK)’ + (A&)2 + (AV,)’.

(24)

269

6. THE PYROELECTRIC DETECTOR

XE 5886 triode connected

1

-----A XE 5886 pentode connected

XE 5886 pentode connected

I

102

I

I0 3 Frequency

I

I0 4

-

J

Io5

(Hz)

FIG.5. Noise characteristics of amplifiers. The frequency dependence of the equivalent current and voltage generators is shown for the X E 5886 miniature electrometer triode and pentode connected and for the BFW 11 FET.

Suppose an incident signal of rms power PNproduces an rms signal voltage V, equal to AVw Then

PN = KJ%v

= AVN/Bv

(25)

is the noise equivalent power (NEP) or signal power required to produce an output voltage equal to the noise voltage. If in addition to knowing the pyroelectric material parameters the four noise generators in Eq. (24) are known or can be measured, the noise equivalent power of the detector can be measured. As defined by Eqs. (18), (21), (23), and (24), the NEP refers to unit amplifier bandwidth. If the bandwidth is B, the NEP will be increased

270

E. H. PUTLEY

by the factor B1/2. It is sometimes convenient to use instead of the NEP the detectivit y

D

=Pi1.

(26)

Often the performance of a detector is expressed in terms of the normalized detectivity D”,

(27) since in many cases AT/, varies as A’/’. However, as the following discussion will show this relationship only applies to pyroelectric detectors if AVT or AV, is the dominant noise source. In many instances either AK or AV’ is found to be the principal source of noise, so that the use of D* to discuss pyroelectric detectors can be misleading. To discuss the relative importance of the four noise sources combined in Eq. (24) and to show how they depend upon the properties of the pyroelectric materials, expressions for the NEP will be written down in which each noise source in turn will be assumed to be so large that the others can be neglected. High frequency operation will be assumed and the results will be expressed in terms of the bulk properties and the detector dimensions. This will show that the relative importance of the different noise sources depends in a different way on both material parameters and dimensions. This makes it difficult, therefore, to write down a single figure of merit for the comparison of pyroelectric materials. However, by making numerical estimates of the quantities involved (as shown in Fig. 3, for example) it is easy to see which parameters are the most important for any particular case. By using equations such as (15), (16), (IX), (21), (23), and (25) the following expressions for the NEP are obtained in the high frequency approximation :

D* = DA’lZ,

PN,(cmp = AV,/.%’v = (l/ll)(4kT’)’’Z(g)1i2A f“,johnson

(28)

= A Y / ~ & V = ( I / ~ ) ( 4 k T ) ” 2 ( ” / ~ ~ ” 2 ) ( A d ) ” 2 , (29)

AK/WV

( l / ~Ai) ( c ’ / ~ ),d

P N , amp current

=

f“,ampvoktage

= A L ‘ C ~ V= ( l / q ) (AVA)(C’E’~:/JI)A. ~

(30) (31)

Figure 6 shows some numerical examples calculated using typical values for a pyroelectric material (see Table 11) similar to lithium sulphate. This shows that for large area detectors and for high enough frequencies, the amplifier voltage noise will be the most important, but for smaller areas and low frequencies the behavior is more complicated. It should be possible to choose an amplifier with sufficiently small current noise to reduce this noise below Johnson and radiation (temperature) noise. Johnson noise can only fall below radiation noise with the parameters chosen if the thickness of the

271

6. THE PYROELECTRIC DETECTOR

16'

10-1

I

10

A (crn2)

FIG.6. Noise equivalent power as a function of area as calculated from Eqs. (28H31)using data from Table 11. These calculations assume that a thickness of the detector of l o p is the thinnest practicable for an unsupported element. The results indicate that the amplifier contributes the main sources of noise determining the NEP. This conclusion seems at first sight inconsistent with the experimental results shown in Fig. 3. However, the resistance of the detector measured for Fig. 3 was lower than has been assumed for this figure; hence the Johnson noise is greater in Fig. 3. To achieve the results predicted in this figure requires material of higher resistivity than was used for the detector of Fig. 3.

element can be reduced below 1 p. Since it is likely to be very difficult to produce elements less than 10 p thick without supporting them on a substrate which would increase the temperature noise excessively, it appears that radiation-noise-limited performance will only be obtained by the discovery of pyroelectric material with superior parameters to those given in Table 11. Nevertheless, taking the minimum practical thickness as about 10 y there

272

E. H. PUTLEY

is a good chance of making a detector that approaches within an order of the ideal limit. Its NEP would then compare quite favorably with that of other room temperature thermal detectors, and as the calculations given in Fig. 6 show, this performance should be attainable with the pyroelectric detector at frequencies well in excess of l/z, Thus the frequency response attainable should be very superior to that obtained with other thermal detectors, and in fact be comparable to that obtained with the slower types of photoconductor. 4. TOTALENERGYDETECTOR Consider a pulse of radiation absorbed near the surface of a relatively thick plate of pyroelectric material attached by its rear surface to a heat sink. The temperature of the surface will rise at once and a temperature wave will propagate into the body of the pyroelectric element. If the duration of the pulse is short compared with the time taken for the temperature rise to reach the rear surface of the element, then the only way energy can leave the element before the pulse is completed is by radiation from the front surface. Comparison of the radiative conductance with the thermal conductance of the slab (cf. Section 1) shows that the radiation loss will be negligible. Hence the pyroelectric charge produced will be proportional to the energy of the pulse. It can also be shown that the total charge is independent of the spatial distribution of the incident energy across the receiving area of the element.’ If the element has an electrical (RC) time constant which is long compared with the duration of the pulse, then the charge leakage will also be negligible. Hence measuring the charge produced using a suitable electrometer circuit will give the total energy of the pulse, independent of the duration of the pulse and of its exact spatial distribution. Study of the thermal circuit shows that if an abrupt increase in temperature occurs at the surface, the time required for the temperature at a distance 1 from the surface to rise to l/e of the surface value is

12c’/K.

(32) Hence if z is the duration of the pulse, the thickness d of the plate must satisfy the condition d 9 (KZ/C’)’/~ if no energy is to be lost during the duration of the pulse. If t x lmsec, then I z low2cm, and thus a relatively thick plate is required to satisfy this condition. Assuming that this condition is satisfied, the output voltage is given by z=

v(t)= (Ap/c’4 (1/C)

sd

d x ) exp[(x

- t ) / t E l dx

9

(33)

where q(t) is the energy flux per unit area absorbed by the detector. This expression simplifies if the electrical time constant is either long or short

6. THE PYROELECTRIC DETECTOR

273

compared with the duration of the incident signal. In the first case the integral is zero except when x x t, so that V ( t )= (Ap/c’d)Rq(t).

(34)

In the second case the exponential term approximates to unity over the range of integration, so that

Thus operation with a long electrical time constant gives a signal output proportional to the total energy of the pulse. Since pyroelectric materials with values of T~ 9 1 msec are commonly used, this condition is easily satisfied. If the time constant is reduced by shunting with a low value resistor, then the signal output will follow the shape of the pulse. Resolving times as short as 1 p e c have been obtained in this way. The total energy mode of operation has been used for measuring the energy of pulses in shock tube^,^.'^ hypersonic wind tunnels,18 and of laser pulse^.'^^^^ Attempts to use the fast mode have been of limited success due to the occurrence of elastic resonances. For this application the detector using frequency equali~ation’~ seems to be more suitable (see Section 7). The difference between the performance of these two detectors is probably due to differences in construction (the frequency-equalizeddetector is made very thin and is not supported at its back) which suppress the 100kHz resonances found when total energy detectors are used with short electrical time constants. 111. Construction of Pyroelectric Detector 5 . CHOICE OF MATERIAL

Examination of Eqs. (28)-(31) shows that suitable material will have a large pyroelectric coefficient, a high resistivity, a small dielectric constant, and a low thermal capacity. In addition, 9 must be made as close to unity as possible, either by using material with a high absorption coefficient or by depositing a suitably chosen absorbing layer on the front surface. The thermal conductance g must be made as small as possible, by careful design of the detector mounting. It is not possible to formulate these requirements by a single combination of the parameters as a figure of merit, since, as the equations for the NEP show, the precise combination for optimum performance ”

l9

A. D. Wood and J. C. Andrews, IEEE Trans. Aerospace Electron. Systems 3,356-367 (1967). C . R. Spitzer. I E E E Trans. Aerospace Electron. Systems 3,349-355 (1967). M. Shimazu, Y.Suzaki, M. Takatsuji, and K. Takami, Japan. J . Appl. Phys. 6, 120 (1967). R. W. Astheimer and R. E. Buckley, Rev. Sci. Instr. 38, 1764-1768 (1967).

274

E. H. PUTLEY

depends upon which noise source is dominant. Thus if we were to focus attention on Eq. (28) only, we might conclude that we need only worry about the design of the thermal circuit to achieve background-radiation-limited performance, which is clearly not the case. The choice of the best parameters for minimizing amplifier noise will depend on the relative values of AVA and A& for a particular amplifier, and this will depend upon the operating frequency. Thus the optimum choice of material and design of detector can only be made by considering each of the four equations for NEP in turn. The values obtained for the NEP also depend on the dimensions. The area A will be determined by the particular requirement. Since PN,temp and PN,Johnson vary as A l”, PN.amp current is independent of A, and PN,ampvoltage is proportional to A, the choice of A will affect the relative importance of these noise sources. Both PN,Johnson and PN,ampcurren, are improved by making the thickness d small. If this is made too small, it will reduce the absorption of the element and will introduce fabrication problems. In addition to these factors, other considerations include the ease of preparation of the material, its long term stability, and its piezoelectric and elastic properties which determine the extent to which microphony is a serious problem and the limitation by mechanical resonances of the high frequency performance. The relevant properties, as far as they are known, of likely materials are summarized in Table I. Although this table shows that promising materials include TGS, Li,S0,.H20, LiNbO,, LiTaO,, NaNO,, and SbSI, most of the recent work on pyroelectric detectors has been based on TGS. The following remarks on detector construction and performance apply primarily to a TGS detector, although most of them would apply to the other materials as well. The optical properties of these materials have certain features in common. Single crystals are transparent in the visible range, but become strongly absorbing at a wavelength of a few microns. Near 10p the absorption is high and remains so until the submillimeter region is reached, where it starts to fall again, Figure 7 shows typical transmission data for TGS. Although the absorption is high near the l o p wavelength, there is finite transmission in samples of thickness 2 0 p or less. Since for other reasons it is very desirable to use thin specimens, careful design of the front surface electrode is required to optimize the absorption. This becomes more important for detectors intended for use at submillimeter wavelengths. In the detectors so far used for submillimeter work this has not been done, so that further improvement in performance can be expected. Similarly, if pyroelectric detectors were required to have optimum performance in the visible or near-infrared, using the front surface layer as a black would enhance the performance.

6. THE PYROELECTRIC DETECTOR

-8

50

-

275

,--.,

7

~

zg 3 0 -

/'

\

/'

c 40-

0

/

//

,/

e t-

/I

20 /

10 -

I

i

/

I

I

,I /

OI

10

I

I00

I000

FIG. 7. Transmission of TGS plate 15 p thick. (The results for A < 15 p were obtained by Mullard (Southampton),20aand the results for I > 33 p are based on an extrapolation of measurements by Dr. G. Chantry,zobN.P.L.)

6. DETAILS OF CONSTRUCTION

Single crystals of TGS are grown by the controlled cooling of an aqueous solution. These crystals exhibit a well-defined cleavage plane normal to the pyroelectric axis. Hence location of this cleavage plane provides a simple method for determining the direction of this axis. Once this has been established, correctly oriented plates about 1 mm thick can be cut from the crystals using a wire saw. Elements of thickness between 10 and 20 pare then prepared from the plates by grinding with BAO abrasive in lapping oil and finally polishing using 0.3 p Linde powder in glycerine. Electrodes are evaporated onto the plates, using a thick deposit of gold for the rear electrode and a semitransparent nichrome electrode (500 ohms per square) on the front surface. The electroded element is then cemented around its edges to a metal plate which forms the heat sink and defines the aperture of the detector. A connecting wire is then attached to one face of the detector using a small blob of cold setting silver paste, while contact to the second face is made via the metal plate and conducting cement. This detector subassembly is then mounted in a case which contains at least the first high input impedance stage of the amplifier, but it is often convenient to include a following integrated circuit amplifier here. The case may be fitted with a rigid window and hermetically sealed or evacuated. Where the highest sensitivity is not required the sealing of the case is not essential. Mullard (Southampton), unpublished data 'ObG. Chantry, unpublished data.

276

E. H. PUTLEY

Reor electrode Heat sink

Solid state amplifier

1

Mylar window

/ Semitransparent front electrode

Pyroelectric

u

1 cm

FIG. 8. Schematic diagram of RRE detector. (After Ludlow et

af.14)

Figure 8 illustrates the type of detector constructed at the Royal Radar Establishment (RRE), while Fig. 9 is the circuit diagram of the amplifier included in the detector unit.

7. PERFORMANCE OF RRE PYROELECTRIC DETECTOR a. Noise Equivalent Power

Figure 3 shows the performance obtained with a pyroelectric detector constructed as described. The figure shows measured values for the responsivity, NEP (using a 500°K blackbody), and the impedance of the detector. These are compared with the responsivity calculated from Eq. (13) and with f

12v

1 FIG.9. Circuit diagram of amplifier (including frequency equalization section) used with R R E detector.

6 . THE PYROELECTRIC DETECTOR

277

calculated values for the NEP obtained by calculating the noise voltages [Eqs. (18), (21), and (23)] and using these in Eq. (24) to calculate the NEP. The calculated values for the various noise voltages are also shown. The impedance was measured using a Wayne Ken- type B221 transformer bridge with external source and detector. The reactive component was found to consist of a capacity (45pF) independent of frequency. The parallel resistive component is plotted in Fig. 3. The thermal characteristics were determined by measuring transient response at very low frequencies (- 1 Hz). All the parameters required to calculate the responsivity were known independently except q. The value of q was chosen (q = 0.23) to fit the experimental points. Since no special steps have been taken to ensure maximum absorption of radiation, the value assigned to q is not an unreasonable one, while at the same time indicating the possibility of a fourfold improvement in performance with more careful design of the front electrode. Considering the noise sources, it appears that Johnson noise A 6 is the dominant one below lOkHz, although the amplifier voltage noise AVA becomes greater above 10 kHz. The amplifier used was an XE 5886 miniature electrometer triode, which gave a slightly better performance than the best available solid-state device (the BFW 11 FET). The next most important source of noise was the temperature-fluctuation noise, while the amplifier current noise A F was smaller still, about the same value as the radiation noise AVRfor an ideal detector of the same area. Having calculated these noise generators using Eqs. (18), (21), or (23) with the data in Fig. 3, the NEP was calculated using Eq. (24). The calculated and measured NEP’s are compared in Fig. 3. At low frequencies the agreement is good, but above 100Hz the measured NEP is superior to the calculated one. Since the Johnson noise is the main noise source, this could imply an error in the measurement of resistance, since if the measured resistance were too small, the calculated Johnson noise voltage would be too large. Since the impedance of the TGS element is somewhat dependent upon the source voltage applied to the bridge and since also the conductive component of the admittance is small compared with the susceptive component, error in this measurement may account for the discrepancy. On the whole, however, the agreement between the measured and calculated NEP is sufficientlygood to indicate that the analysis of the pyroefectric detector given in Part I1 is adequate to account for its behavior and to show what steps are needed to improve the performance still further. In addition to improving the responsivity by improving q, the Johnson noise might be reduced by increasing the resistivity of the material. This might be achieved either by using improved TGS with smaller dielectric loss or by using other pyroelectricmaterials with higher resistivity. Thus preliminary measurements with Li2S0,.H20 detectors indicate that the resistivity of this material is

278

E. H. PUTLEY

about an order of magnitude greater than the TGS we have been using. If the resistivity could be increased two orders of magnitude, the Johnson noise would be reduced below the temperature noise, but this again could be reduced by improvement in the design of the thermal circuit, so that at low frequencies it should be possible to approach within a factor of two or three the NEP of an ideal background-radiation-limited detector. If this performance were achieved, the pyroelectric detector would have a higher detectivity than any other room temperature thermal detector.

b. High Frequency Performance

It is clear from Fig. 3 that although by the use of a frequency equalizing amplifier the overall responsivity can be held at a constant level to frequencies very high compared with l / or ~ l ~/ ~the ~ ,NEP will start falling off above a few hundred hertz. The usefulness of frequency equalization will therefore depend on the extent to which a deterioration in NEP is acceptable. This consideration is one factor which will determine the upper frequency limit. In addition to this there may be other limiting factors. Thus users of the total energy detector in its fast mode of operation',' ',19 have encountered mechanical resonances near 100 kHz which have determined the upper-frequency limit for their detectors. These resonances appear to be associated with elastic compression waves propagating along the length of the detector. Careful tests with detectors constructed as described in Section 6 failed to detect this mode of vibration and, as Fig. 10 demonstrates, a useful performance was

Detection at 10.6 1

0

1 Time ( p s e c )

2

FIG.10. Comparison of the response of a pyroelectric detector and of a Zn:Sn-doped Ge detector to Q-switched CO, laser pulses. (After Kimmitt et ~ 1 . ' ~ )

6. THE PYROELECTRIC DETECTOR

279

still obtained when the frequency equalization was extended to 2 MHz (corresponding to an effective response time of 100 nsec). The construction used appears to suppress the transverse compression resonance, but if this type of resonance occurs along the direction normal to the receiving aperture of the detector, the resonance frequency will be of the order of 100 MHz. Thus far, measurements have not been made at this frequency, so that the existence of this mode cannot be confirmed. Acoustic measurements at lower frequencies have revealed the existence of what appear to be flexural resonances in the 10-20 kHz region. These lower frequency modes do not seem to be excited by pulsed radiation sources, so that with the type of detector described here the limit set by elastic resonances is probably not less than 100 MHz. As an indication of the sensitivity obtainable, the results shown in Fig. 10 were obtained using a Li,S04.H20 detector 7 mm in diameter and 50 p thick with a responsivity of 3 V/W over the frequency range 20 Hz to 2 MHz. The total noise output over this bandwidth was 15 mV rms. Hence a pulse of a few milliwatts peak power could be detected. 8. COMPARISON WITH OTHERDETECTORS

The last two sections have given a detailed account of the construction and performance of the pyroelectric detector constructed at RRE. Although the performance described probably does not represent the ultimate attainable, it is typical of the state of the art for this type of detector, and it is beginning to compare favorably with other types of detector. The NEP attainable at low frequencies is about W, or perhaps slightly better,and this is comparable with the values reported by other workers?,"-' When used as a fast detector, effective response times as short as 100 nsec have been achieved, although it appears that to achieve this result, some care is necessary in the design of the detector element to suppress elastic resonances, In Fig. 11 the NEP of the RRE pyroelectric detector is compared with that ofother detectors operating at room temperature. As there is some uncertainty as to the relation between NEP and area, the results are not normalized to unit area but detectors of area similar to that of the pyroelectric detector have been chosen. The other detectors are all commercially available ones and the performances shown were obtained from the manufacturer's specifications. In Fig. 12 the frequency dependence of the NEP's for these detectors is shown. The pyroelectric detector was operated with a frequency equalizing amplifier, and the deterioration in the NEP at 1 kHz is due to amplifier noise contribution at the higher frequencies. The use of frequency equalization is not advantageous with the Golay cell or thermistor bolometer, nor is it usually required with the photoconductive detectors, so that for the other detectors the falling off of NEP is related to the response time of the detector.

280

E. H. PUTLEY

0.I

I

10

10'

lo3

lo4 10

I Wavelength ( p 1

A (mm)

FIG.11. The detectivity (l/NEP) of a pyroelectric detector compared to those of a Golay cell, a thermistor bolometer, and room temperature PbS and InSb photoconductive detectors. The areas of the detectors compared are given on the figure. The detectivity of an ideal thermal detector at room temperature is shown for comparison.

The data presented in Figs. 11 and 12 show that the pyroelectric detector compares favorably in NEP with the thermistor bolometer and the room temperature InSb photoconductive detector, but is inferior to that of the Golay cell and the PbS detector. The frequency response of the pyroelectric detector is appreciably superior to that of the other thermal detectors. In common with other thermal detectors, the spectral response of the pyroelectric detector extends to very long wavelengths; in fact, a useful performance can be obtained at submillimeter and millimeter wavelengths (although a form of construction more compatible with waveguide circuitry should be adopted for use beyond 1 mm wavelength2'). Results obtained in the submillimeter region with the 337-p CN maser are shown in Fig. 13. 21

D. J. White, J . Appl. Phys. 35,3536-3542 (1964)

6. THE PYROELECTRIC DETECTOR

281

I20 CPY PbS

I06

10

lo3

lo4

Frequency (Hz)

FIG.12. The frequency dependences of the peak detectivities of the detectors shown in Fig. 11.

The results shown in Figs. 11-13 thus demonstrate that where a simple uncooled detector is required the pyroelectric detector has much to commend it. For wavelengths longer than 3 p it has a better sensitivity than most detectors. Its effective response time compares favorably with the photoconductive detectors, while its spectral response can only be matched by liquid helium cooled photoconductors. Where robustness rather than high sensitivity is required, very simple detectors can be made from readily available materials,22 but higher-performance pyroelectric detectors are now becoming available commercially.22" W. W. Duley, J . Sci. Instr. 44,629-630 (1967). ""Manufacturers producing pyroelectric idfrared detectors include : Mullard, London, England ; Barnes Engineering, Stamford, Connecticut ; and Prtcitechnique Dauphin6 Grenoble, France.

22

282

E. H. PUTLEY

FIG.13. Response t o emission from a C N maser. The rcsponse of a pyroelectric detector (lower trace) is compared with that of an InSb submillimeter detector (upper trace). The pyroelectric detector responds to both the visible and the submillimctcr emission from the discharge. but the InSb detector responds only to the submillimeter radiation. This is demonstrated by the use of various filtcrs with the detectors as follows: ( I ) Pyroelectric: n o filtcr: InSb: nu filter. (2) Pyroelcctric: black polythene excluding visible; lnSb : 110 filter. (3) Pyroelectric : glass filter excluding submillimeter; InSb : no filter. (4)Pyroelectric : detuning laser cavity causes double pulsing from laser which pyroelectric detector is too slow to follow. (5) Pyroelectric: no filter; InSb: black polythene excludirig visible. ( 6 ) Pyroelectric: no filter; InSb: clear glass excluding submillimeter.

6. THE PYROELECTRIC DETECTOR

283

Appendix. Electrode Geometry

The electrode configuration assumed so far is that shown in Fig. 14(a), in which the pyroelectric axis is normal to the receiving area of the detector and a partially transparent or absorbing electrode (“face electrode”) is applied to the front surface of the detector. A second configuration, shown in Fig. 14(b), is also possible. In this the pyroelectric axis lies in the plane of the receiving area. Electrodes are applied along the edges of the plate normal to the pyroelectric axis (“edge electrodes”). To compare the two configurations, consider the Eqs. (28H31)for PN, the noise equivalent power associated with the various noise sources. These must first be rewritten to distinguish between A,, the area of the electrode, and A,, the receiving area. Here d is the distance between the electrodes, and for the face electrode configuration AE = AR. Thus we have pN, temp PN. Johnson

= (l/r)(4k T2)1’2 (g)’’2(AR)1/2

(A281

= (1/V)(4kT)1’2(c‘/pp1i2)(AEd)’i2 7

Incident radiation1

I

I

I+ 1 axis

Incident radiation

I electrodes

Pyroelectric axis

FIG.14. Electrode geometries for (a) face electrode, and (b) edge electrodes.

(A29)

284

E. H. PUTLEY

PN.amp current

=

(1h) Ai(c’/~)d

6430)

PN,ampvoltape

=

(l/q)(w AVA)(C’E’E/P)AE.

(A31)

9

Equations (A28) and (A29) are identical to Eqs. (28) and (29), respectively, so that changing the electrode configuration does not alter the temperature or Johnson noise limited value for PN.However, for the same size and shape of detector with edge electrodes d is larger than with face electrodes, and A , is smaller. Hence for edge electrode PN,ampcurrent will be larger and PN,ampvoltage will be smaller than for face electrode. Referring to Fig. 6 shows that at high frequencies, PN, will always limit the performance. Hence there would appear to be some advantage in using edge electrode detectors for high frequency operation. The physical reason for this advantage of edge electrodes is that the electrical capacity of the element is less by a factor which with typical dimensions could be as much as lo4. Since the capacity of a typical face electrode pF, detector is about 50 pF, the capacity of the edge electrode device, 5 x is well below the stray and amplifier input capacities. Hence the improvement with the edge electrode configuration will not be as large as expected from the simple geometry. Equation (3 1) can be written PN,arnpvoltage

= (l/q)(wc AVA)c’d/p‘

(A31‘)

Onlyif the reduction in C (taking into account circuit capacitance) is greater than the increase in d will the edge electrode arrangement be beneficial. With the dimensions we have been considering this appears to be unlikely.

Note Added in Proof Development of the pyroelectric detector is continuing. It is now possible to obtain detectors from commercial sources with NBP’s a factor of 2 to 3 smaller than the value shown in Figs. 3, 11, and 12. This improvement is largely the result of improved fabrication techniques since so far no pyroelectric material superior to TGS has been found. Another factor contributing to the improved performance is the development of better FET’s. The best available now have a voltage noise about one quarter of that shown for the BFW.ll in Fig. 5 and probably also have a somewhat smaller current noise. As a consequence, the dominant noise source in TGS detectors at frequencies up to about 1 kHz is Johnson noise. At higher frequencies, amplifier voltage noise will still be the most important, but with the best available amplifiers, an NEP of about 7 x lo-’ W Hz- 1/2 should be achievable at 1 MHz. There is at present considerable interest in pyroelectric materials. Detailed measurements at RRE on Lipso,. H,O have shown that the best NEP’s obtainable for detectors fabricated from this material are a factor of 2 to 3

6. THE PYROELECTRIC DETECTOR

285

more than the best TGS detectors. has reported encouraging results with strontium barium niobate crystals. Although this material has a larger cm-2 O K - ’ ) , it has a much larger pyroelectric coefficient (-1.1 x dielectric constant (- 1700) and a lower resistivity ( lo9 ohm cm) than TGS. Hence in some low frequency applications i t could be superior to TGS but it appears inferior to TGS for higher frequency applications. Since the best TGS detectors are Johnson noise limited, higher resistivity material is required to obtain further improvement in the NEP. One possible way of obtaining this is the development of better quality TGS having lower dielectric loss. Another approach is to look for newer materials (perhaps among the niobates or tantalates) having higher resistivities. Since the dielectric loss or resistivity is probably determined by impurities or imperfections in the crystal, this search is not likely to succeed unless a systematic study of the preparation and properties of likely materials can be undertaken. Materials which have been studied recently at RRE include EDT, DKT, and GASH, all of which are inferior to TGS. has also measured these, obtaining results in good agreement with our own. Since the NEP of the best pyroelectric detectors is between one and two orders of magnitude worse than that of an ideal room temperature thermal detector, there is a good chance that significant improvement in the performance of pyroelectric detectors will be attained in the near future. Several groups have reported using a pyroelectric detector in a homodyne or heterodyne configuration with a laser local oscillator. Thus Gebbie et aL2’ discuss the use of a TGS detector with a CN maser (337p), Leiba26 has used a TGS detector with a C 0 2 ( 1 0 . 6 ~laser, ) and Abrams and Glass27 have described an experiment with a strontium barium niobate detector and C 0 2 laser. Recent work at Barnes has been discussed by Beerman,28while AstheimerZ9 has described a thermal imaging system using a TGS detector. TGS detectors are being successfully used in submillimeter Fourier transform spectrometers (N. W. B. Stone, private communications) and they are beginning to appear in some commercial instrument^.^' N

A. M. Glass, Appl. Phys. Letters 13, 147-149 (1968). Hadni, Opt. Comm. 1,251 (1969). ” H . A. Gebbie, N. W. B. Stone, E. H. Putley, and N. Shaw, Nature214, 165-166 (1967). 26 E. Leiba, Compt. Rend. 268, 31 (1969). R. L. Abrams and A. M. Glass, Appl. Phys. Letters 15,251-253 (1969). ’* H . P. Beerman, ZEEE Trans. Electron Devices 16, 554-557 (1968). 29 R. W. Astheimer, Photogr. Sci. Eng. 13, 127-133 (1969); R. W. Astheimer and F. Schwarz, Appl. Opt. 7, 1687-1695 (1969). 30 For example Block FTS-14, Fourier transform spectrometer. 23

” A.

*’

This Page Intentionally Left Blank

CHAPTER 7

Radiation Thermopiles Norman B . Stevens

I . INTRODUCTION . I1 .

111.

IV .

V.

. . . . . . . . . . . . . . . . . . . . . . . . .

1 . Historical Background . . . . . . . . . . . . . 2 . Thermopile Radiation Detectors THEORETICAL BACKGROUND . . . . . . . . 3 . Seebeck Coefficient . . . . . . . . . 4 . Peltier Coeficient . . . . . . . . . 5 . Thomson Coeficient . . . . . . . . . 6 . Equations of Eyuilibrium . . . . . . . 7 . Consideration of (T,, - To) . . . . . . . 8 . Parameters Affecting Responsivity . . . . . 9 . Materials Criteria . . . . . . . . . THERMOPILES AS RADIATION DETECTORS. . . . 10. De.yign Criteria . . . . . . . . . . 11 . Device Figure fffMerit . . . . . . . . 12. D* as a Criterion of Merit . . . . . . . 13. M , as a Criterion . . . . . . . . . 14. Profile . . . . . . . . . . . . 15. Spectral Response . . . . . . . . . PROPERTIESOFTHERMOPILE RADIATION DETECTORS. 16. Bulk Material Devices . . . . . . . . 17. Thin Film Devices . . . . . . . . . 18. Evaporated Thermopile Arrays . . . . . . CONCLUSION . . . . . . . . . . . . LISTOF SYMBOLS . . . . . . . . . . .

. . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . .

. . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . .

. 287 . 287 . 288 . 289 . 290 . 290 . 291 . 292 . 294 . 296 . 297 . 299 . 299 . 299 . 301

.

301

. 302 . 302

. . . . . .

304 305 307 312 317 317

I . Introduction 1 . HISTORICAL BACKGROUND Thermocouples and thermopiles have been employed since shortly after the discovery of infrared radiation by Sir William Herschel‘ in 1800. Report was made as early as 1835 of a thermopile fabricated and used by Melloni’ W . Herschel. Phil . Trans. Roy . Soc. (London) 90. 284 (1800); R . A . Smith. F. E. Jones. and R . P. Chasmar, “The Detection and Measurement of Infrared Radiation, ” p . 1. Oxford Univ . Press, London and New York. 1957. M. Melloni. Ann. Chim. Phys . (2) 60.418 (1835); Smith et a/.,’ p . 2.

287

288

NORMAN B. STEVENS

as a temperature sensor for detecting the presence of radiated heat. The early experimenters studying infrared radiation using thermocouples as detectors were not only utilizing the very recently discovered Seebeck effect (1822), but their work falls into appropriate perspective when it is noted that the 12R Joule heating was not even recognized until 1844.3 In 1834 Jean C. A. Peltier4 discovered the heating or cooling of the junction of a current-carrying circuit of two dissimilar metals, the effect depending upon the polarity of the electric current. It remained for William Thomson (Lord Kelvin) to recognize the temperature dependence relationship between the Seebeck (01) and Peltier (H) coefficients, now designated as the second Kelvin relation :

n = Ta,

(1)

where T is the absolute temperature, O K . It was also William Thomson who recognized and predicted the Thomson effect on thermodynamic grounds, and observed it experimentally in 1853.5 Subsequent to the formulation of the second Kelvin relation, practical applications of these discoveries were largely lacking other than for making temperature measurements. With the advent of modern materials research, however, materials of greater utility were developed both for temperature measurement and refrigeration. The status of present day materials development is covered in excellent detail by Cadoff and Miller.6

2. THERMOPILE RADIATION DETECIMS It is important at the outset to describe what is meant by a radiation thermopile. The device includes a collector or absorber of radiant energy, usually for the infrared wavelength region. The collector exhibits a temperature rise over the detector ambient or reference temperature as a result of the absorbed radiation. This characteristic of utilizing a temperature rise as an intermediate process between radiation absorption and electrical response is shared with the radiation bolometer, and classifies it as a thermal rather than a quantum detector. The bolometer is distinguished from the thermopile by the mechanism employed to measure the temperature increment of the collector. Bolometers have a relatively large temperature coefficient of resistance and require a bias current to detect this change of resistance. The thermocouple generates a voltage due to the Seebeck effect, obviating the need for stable bias circuitry. Other thermally variable properties of materials

’ P. H.Egli, “Thermoclectricity,” p. 4. Wiley, New York, 1958. I . B. Cadoff and E. Miller, “Thermoelectric Materials and Devices,” p. 4. Reinhold, New York, 1960. S. P. Thomson, “Life of Lord Kelvin,” Vol. 1, p. 317. Macmillan. London, 1910. See Cadoff and Miller: p. 55.

7. RADIATION THERMOPILES

289

are useful for thermal detectors of radiation (e.g., Golay cells and pyroelectric detectors), but the thermopiles and bolometers enjoy the greatest utility. Two types of thermopile are extensively employed. The first is a fabricated, bulk material device, usually made with fine wires and provided with a thin, black radiation absorber. The second is the thin film thermopile made by vacuum evaporation of the components, permitting the use of photoetch techniques and the attendant high precision in the device assembly. Although this may appear to be an artificial classification, it is a useful one, since the two kinds of device exhibit quite different properties. The extremely small connections and thermal elements provided by evaporation permit the design of devices covering a wide range of impedance and time constant. This allows selection of an impedance which falls near the optimum impedance of modern amplifying transistor circuits. It is true that with careful amplifier development the low impedance fabricated devices are Johnson noise limited, but the circuit usually involves a costly transformer with its attendant magnetic pickup and frequency response problems. Harris7 in 1934 made use of vacuum evaporation techniques in making thermocouples and thermopiles, and developed the theory for the proper design of a couple. He utilized ac amplification and prepared an eightjunction couple. Slightly later (1945) Roess and D a c d adapted the evaporated thermopile design to the requirements of infrared spectroscopy. This chapter will be devoted to consideration of radiation detectors utilizing the Seebeck effect. The operation of these thermoelectric devices is described by much the same theory that applies to refrigeration piles and temperature measuring couples. The theory will be presented briefly and relevant formulas for the radiation couple or thermopile will be given. The character and magnitude of the noise encountered in such a radiation detector will be considered, and finally, typical present day thermopiles of both the bulk material and evaporated types will be shown and properties will be described. 11. Theoretical Background

The conduction electrons in a metal or semiconductor possess thermal energy in addition to electric charge. The thermal energy can be transported physically with the charges either up or down a thermal gradient by the application of an appropriate electric field gradient. Similarly, application of a thermal gradient can transport electric charge along an electric field gradient of either polarity.

’ L. Harris, Phys. Rev. 45, 635 (1934). L. C. Roess and E. N. Dacus, Rev. Sci. Instr. 16, 164 (1945).

290

NORMAN 8 . STEVENS

COUNTER EMF FIG.1. Seebeck effect.

For thermocouples it will be seen that the three thermoelectric effects, designated Seebeck, Peltier, and Thomson, are not equally relevant. The quantities are defined as follows:

3. SEEBECK COEFFICIENT When two metals comprisc a circuit (Fig. 1) and the junctions of these metals are at differing temperatures (i.e., due to the absorption of incident radiation), an electric current flows. Insertion of a counter emf will cancel the current flow, and the magnitude of this emf is the Seebeck voltage. More specifically, the Seebeck coefficient is defined as CL

= lim

AVIAT

=

dVIdT,

AT40

where AV is the emf between the two junctions and AT is the temperature difference between the junctions. The polarity of A V will reverse with reversal of AT. The Seebeck coefficient c( is also known as the thermoelectric power. 4. PELTIER COEFFICIENT

When the circuit of two dissimilar metals is traversed by an electric current, heat is exchanged into or out of the circuit at the two junctions as shown in Fig. 2. Considering first junction number 1, the rate of heat exchange at the junction is proportional to the magnitude of the current as

291

7. RADiATION THERMOPILES

I

dQ HEAT IN = -

dt

:

TI

FIG.2. Peltier coefficient

defined in the following equation :

nI

= dQ/dt

(3)

where the proportionality constant I'l is the Peltier coefficient, I is the electric current, and d Q / d t is the time rate of heat exchange. Reversing the polarity of the current reverses the direction of heat exchange. That is, with one direction of current, heat is evolved at one junction and absorbed at the other junction, while reversing the current direction interchanges the heat exchanging roles of the two junctions. 5 . THOMSON COEFFICIENT

In the course of Thomson's work leading to the formulation of the relationship between Seebeck and Peltier effects the existence of a similar effect in a single homogeneous medium was predicted. If a material carrying electric current possesses a thermal gradient, as shown in Fig. 3, heat is absorbed or evolved reversibly at a rate defined by the equation dQJdx = 7 1 d T / d x .

(4)

Here d Q / d x is the heat absorption rate per unit length, and is positive when I and dT/dx are in the same direction and t,the Thomson coefficient, is positive.

292

NORMAN 6. STEVENS

db dx

dT

1-7- dx

dx

Th

6 =J r r d T TC

FIG.3. Thornson coefficient

It should be recognized that in a circuit of dissimilar conductors in which there are temperature gradients there will be generated emf's due to Seebeck and Thomson effects. The sum of these emf's is the thermal emf of the circuit, or the thermoelectric force E . The Seebeck coefficient or thermoelectric power a is the rate of change of the thermoelectric force E with respect to temperature T , or a = dE/dT, (5) or, expressed in terms of a two material junction or circuit, =

dEiJdT.

(6)

Utilizing the second Kelvin relation [Eq. (I)], this may be expressed as

ll,, = T a l z = T d E , , / d T .

(7)

Before turning to the relevance of these equations to thermopile design it may be noted that the Kelvin relations were derived originally from considerations based upon the second law of thermodynamics. It was recognized by Onsager' that irreversible phenomena were nonetheless present, and more rigorous proofs of Kelvin's relations were sought. Those considerations are well developed and explained in the work of Lucke," and a derivation of Kelvin's relations is presented by Gray" and by Jaumot.

'

6 . EQUATIONS OF EQUILIERIUM Turning now to thermocouple design, it may be noted that most radiation thermocouples are basically similar to the configuration shown in H . J. Goldsmid, "Applications of Thermoelectricity," p. 5. Wiley, New York, 1960. W. H. Lucke, A Brief Survey of Elementary Thermoelectric Theory, US.Naval Res. Lab., Washington, D.C. (NRL Report 5888). May 1963. '' P. E. Gray, "The Dynamic Behavior of Thermoelectric Devices," p. 107. Technology Press of MIT, Cambridge, Massachusetts, 1960. F. E. Jaumot, Jr., Proc. I.R.E. 46,538 (1958). I"

''

7. RADIATION THERMOPILES

293

FIG.4. Thermocouple heat flow schematic

Fig. 4. Here the heat rate balance equation is Qh

=

QGT,~

- 3QJ + QII,

+ QGT,~f

(8)

where Q h is the rate of heat absorption into the junction from the net radiation imbalance; QCT,,and QcT,2are the rates of heat conduction down arms 1 and 2; and are the rates of heat evolution due to Thomson effect in arms 1 and 2 (half appears at the cold sink); QJ is the Joule Thomson heat generation rate in the thermocouple portion of the circuit (due to the presence of two arms, half is absorbed in the cold sink); ando, is the Peltier heat generation rate by the electric current at the hot junction. It is evident that QG+ depends upon the thermal conductance of the arm. This in turn is related to the area A, length 1, and specific thermal conductivity K , so to a first approximation (for small A T )

e,, e,,

QGT = (KA/l)(Th

-

TO).

(9)

Similarly, Qr depends upon the current I and the Thomson coefficient T , and for small temperature differences the rate of evolution of Thomson heat is

Q* =

-

qJ),

(10)

of which half affects the heat balance of the hot j ~ n c t i o n . 'In ~ the case in which I and Th - To are both small the Thomson contribution becomes a second order effect and hence may be neglected. Even in the case of power ' ~ these reasons generating thermocouples the effect is only about 1 5 % ~ For the influence of will not be considered further. l3 l4

See Cadoff and Miller," pp, 28-30. See Gray,' pp. 28 and 39.

294

NORMAN B. STEVENS

The Joule heating QJis simply due to electrical dissipation in the arms, and is given by =

QJ

12Re,ec.

(11)

Half of this thermal power appears at the cold sink’2 as noted in Eq. (8). The magnitude of Relec is composed not only of R , + R,, but also must include a dynamic resistance term due to the Peltier heating of the hot junction, induced by the electric current.” This dynamic resistance R , is always positive, so the temperature change induced by the radiation at the hot junction is always reduced by this Peltier effect. Admittedly, in a thermopile operating into a large load ( R L )the current will be very small and R , will, in practice, be negligible. Its magnitude is

R,

=

nZRT/T= n2/G,IT:

(12)

where RT is the thermal resistance and GT the thermal conductance of the hot junction. Thus the electrical resistance of the circuit becomes

R, should rigorously include a component due to the Thomson effect. It is small, however, so will not be considered in its effect on R,. With a radiation thermopile operating into a large load the I Z R heat source may be neglected, and this permits us to further simplify Eq. (8) by dropping the term QJ. The term Q n [Eq. (S)] is the Peltier heat generation rate at the hot junction by the electric current, and its magnitude is Qn =

nlzi = Z l Z i T h .

(14)

Collecting terms, we may rewrite Eq. (8) as

7. CONSIDERATION OF (T,

-

To)

It will now be illuminating to consider what enters into the determination of the quantity Th - To, or in general, AT. This development is given in If a quantity of heat Q is absorbed by a mass greater detail by Holter et of material, its temperature rise is governed by the equation C, = d Q / d T ,

(16)

’’ See Smith, et a/., ’ pp. 61-63, l6

M. R. Holter, S. Nudelman, G. H. Suits, W. L. Wolfe, and G. J. Zissis, “Fundamentals of Infrared Technology,” p. 228 Macmillan, New York, 1962.

295

7. RADIATION THERMOPILES

where C, is its thermal capacitance. Similarly, if a length 1 of material of area A experiences an overall temperature difference AT, its rate of heat conduction is dQ/dt

=

- K A dT/dx x -(KA/f)AT

(17)

where K is the specific thermal conductivity. If a thermally isolated mass experiences a temperature increment and is connected to a thermal conductor, the rate of loss of thermal energy is obtained using Eqs. (16) and (17): dQ/dt

With T

= CT

dT/dt = - K A dT/dx.

(18)

= Th,Eq. (18) becomes CTdTJdt = - K A AT/l.

Noting that AT

E

(18')

T,, - To and that To is time-independent, we may write

CTd(AT)/dt= - ( K A / I ) AT = -AT/RT

=

-ATGT.

(19)

This can be rewritten as a differential equation

d(AT)/dt + AT/RTCT = 0.

(20)

The solution to this equation is

AT

=

(AT),exp( - t/RTCT).

(21)

If, however, radiant power P is absorbed, Eq. (20) becomes

d(AT)

cT

KA

dti - - 1- A T = P ,

where P is constant for the dc case or P = Podmtfor the sinusoidal case. The solutions in these two cases are

AT

=

RTP

and

However, the passive case of a thermal capacitor and conductor absorbing thermal radiation and exhibiting the familiar exponential temperature distribution developed above can be used in the case of the thermocouple only when the zero electric current case is realized. If this is not the case and current I is generated in a couple circuit by absorption of radiation, the hot junction is cooled by the Peltier effect. This temperature increment is then

296

NORMAN B. STEVENS

But we know that 1 = E / R = a12A T / R = RTPa,2/R

(26)

for the dc case. Thus

A% = RT2ci~2 TP/R, (27) where R is the circuit electrical resistance, which to B first approximation is simply the resistance of the two arms plus the external circuit. Due to this current there is an additional cooling effect A T due to the Thomson effect in the two arms, where

A T = RTQ = $IRT A T ( T I Here again A T

=

+~2).

(28)

RTP in the dc case, and f

=

R,Palz/R,

or

AT

+

=

$(R,Pal2/R)R~P(?, T ~ ) R T

=

RT3p2cxI2(Tl+ z 2 ) / 2 R .

(30)

At first P 2 dependence seems surprising, until it is remembered that the temperature increment to the Thomson effect is dependent upon both the junction temperature increment and the current induced by that temperature increment. Clearly, if we include this Thomson effect, we have an unwieldy

(31) AKffective = RTP - A& - AT,. The solution of the resulting differential equation is not of immediate importance for the case of radiation thermocouples operating into large loads, where both I and AT are small, as noted above. Again it should be noted that this is not the case in thermal refrigeration or power generating devices. 8. PARAMETERS AFFECTING RESPONSIVITY

The responsivity PA of a thermocouple is defined as the open circuit output voltage divided by the input, in radiant watts. We may write from Eqs. (2), (23),and (24) that for this case the steady-state voltage will be AV

=

a12 AT = MlzRTP,

(32)

while for the sinusoidal case we obtain

(33)

7. RADIATION THERMOPILES

297

The power absorbed by the junction has simply been designated P, or Podwt,above. However, the incident radiation Pi contained within the collector surface area normal to the radiation angle of incidence will in fact be larger by that actually absorbed because the emittance E of the absorbing surface is less than unity ; P = EPi. (34) For any reasonably good absorber E will be between 0.9 and 1.0 over the wavelength band of interest. It must be recognized that any window loss will generally contribute a greater degradation than the loss due to nonblackness of the absorber. The responsivity W then becomes

W

== Nl,R=P/Pi =

CtlzER,

(35)

for the steady-state case, or more generally

W = ctl2RT~/[1 + 02RT2CT2]1i2

(36)

9. MATERIALS CRITERIA The performance of a radiation thermocouple is enhanced when - To is maximized with respect to the electrical circuit noise. It is desirable to minimize the electrical circuit resistance while minimizing the thermal conductivity of the two arms of the couple. These are contradictory requirements in view of the Wiedemann-Franz law” relating the thermal conductivity K and the electrical conductivity (T :

V/oC (37) (with L the Lorentz number). This leads naturally to the well-known criterion or figure of merit for materials in which a maximum value of a2rr/K is sought. It is defined” for two materials as follows: K f a T = L x 2.45 x lo-’

+

= ~ t f 2 [ ( K ~ / o ~ () ’K/ ~ / o ~ ) ” ~ ] - ~ .

(38) To have a high figure of merit Z12,the following conditions must obtain: Zl2

1. Thermal conductivity should be small compared to eiectrical conductivity. Usually the factor K/oT, the Lorentz number, is not unrelated to the Seebeck coefficient, so materials with larger values of L tend to exhibit large Seebeck coefficients. 2. The Seebeck coefficient should be large. ” See

Smith, et d . , l p. 7 6 . See Cadoff and Miller,” pp. 21 and 55. It is important to note that this thermoelectric figure of merit is defined in terms of output power delivered into an optimum load resistance, rather than the open-circuit output voltage which enters directly into the definition of the responsivity. The materials parameters affecting this latter quantity were given in Eq. (35).

298

NORMAN 9.STEVENS

Turning briefly to the optimization of the lead configuration, it is known that the thermal conductance of the two arms should be nearly equal. Expressed differently, if the lengths 1 be equal (as is often most convenient) then the cross-sectional areas should be adjusted so the material with greater thermal conductivity will have a correspondingly smaller area to equalize the thermal conductance in the two arms. With the thin film deposited thermopiles discussed later, the thermal conductivity and Seebeck coefficients may not be those published for bulk materials. These properties for deposited thin films may in fact be quite different. Harris and Corrigan” found that for antimony, e.g., the resistivity increased from 58 to 95 x lo8 ohm cm and the Seebeck coefficient declined from 45 to 36 pV “ C - ’ in vacuum deposited layers of 15,350 and 1000 A, respectively. Thermoelectric materials criteria having an influence on a2u/K have been considered in detail by Ioffe.20 His development was based upon the influence of carrier concentration, and did not consider the influence of change in effective mass or mobility from material to material. These material properties and influences are reviewed and summarized by Cadoff and Miller2’ and Egli.22 Ioffe’s conclusions with respect to carrier concentration are of some interest, and are listed here: 1. The Seebeck coefficient CI is inversely related to the carrier concentration by the relationship CI

=W q N ,

(39)

where C,is the specific heat of the charge carriers, N is the number of carriers, and q the charge of each carrier. It has been noted by HadniZ3that for semiconductors N is small compared to metals, giving a larger CI. 2. The electrical conductivity u is approximately proportional to the carrier concentration. 3. The thermal conductivity K consists of a concentration invariant lattice term and an electronic or carrier dependent term, increasing, as does the electrical conductivity, with concentration. 4. Combining these trends in the a2u/K relationship yields a broad maximum at carrier concentration between 3 x 10’’ and 3 x 1019cm-3. l9

L. Harris and F. R. Corrigan, J . Phys. Chem. Solids 26, 307 (1965).

’” A. F. loffe, “Poluprovodnkovye Termoelementy,” Academy Sciences, USSR, 1956 [English

’’ 22 23

Transl. ; “Semiconductor Thermoelements and Thermoelectric Cooling,” Infosearch Ltd., London, 19571. See Cadoff and Miller: pp. 76-83. See Egli,3 pp. &lo. A. Hadni, “Essentials of Modern Physics Applied to the Study of the Infrared,” p. 296. Macmillan (Pergamon),New York, 1967.

7.

RADIATION THERMOPILES

299

111. Thermopiles as Radiation Detectors 10. DESIGNCRITERIA We are now in a position to define the desired properties of an ideal thermopile : 1. Response should be maximum for a given rate of radiant energy absorption, i.e., the responsivity 9 in V/W should be a maximum. 2. The time constant of the device in its response to a pulse of radiation should approximate the minimum dictated by the application, or the design should permit selection of the required time constant. 3. The electrical impedance, which generates Johnson noise, should be designed to provide maximum system signal-to-noise ratio. No simple rule of thumb applies here, since the kind and impedance of the amplifier selected and the electrical noise characteristics of the environment all must be considered. 4. The spectral responsivity should be constant within the wavelength region of interest. 5. The response should be uniform over the entire sensitive area, i.e., the profile should be flat. 6. Secondary properties of practical importance include the following : (a) temperature coefficient of responsivity, (b) resistance to mechanical shock and vibration, (c) permissible temperature extremes, (d) life or permanence of the device as packaged, (e) convenient shape and size of the device as packaged, and (f) electrical impedance compatible with amplifier requirements. These numerous properties are clearly not independent, nor are they simply related. In designing a thermopile for a specific application one generally must maximize responsivity, select a minimum time constant, and provide an impedance near the optimum for a minimal system noise. The other properties must be known to ensure that they are compatible with the environmental demands of the application. Clearly one must first select a pair of materials for the thermocouple which give a maximum figure of merit. Beyond this, the construction details must be determined. As noted earlier, two general types of thermopile are in use today. The first is made with wires of active, bulk material, i.e.,antimony and bismuth, or other alloyed materials, The other utilizes photoetch techniques to provide a vacuum deposited device. In Part IV examples of both types will be described.

11. DEVICEFIGURE OF MERIT In this section we will consider some useful device figures of merit. Although the evaporated devices will be considered, the results are equally applicable

300

NORMAN 8.STEVENS

\

SUBSTRATE FIG.5. Evaporated-thermopile schematic.

to the bulk material designs. Before considering various figures of merit it will be useful to describe a conventional evaporated thermopile, as shown schematically in Fig. 5. Four couples in series are shown, with a sensitive area A = H, x W,. The active metals are evaporated with a width w to a nominal thickness t (adjusted to provide equal heat loss through each side of the couple). In the following equations several reasonable assumptions are made: (1) The major loss of energy from the sensitive area is through the active arms, i.e., radiant heat loss is not large. (2) Conduction loss through the substrate or to a surrounding gas is negligible. (3) Temperature equalization across the sensitive region W, is realized in a time small compared to the device time constant T ~ . (4) The Wiedemann-Franz ratio for the materials is invariant with respect to thickness t. The following empirical relationships describe the properties of this configuration : responsivity

w rx: l/W,t;

(40)

7 . RADIATION THERMOPILES

301

impedance (l/Kt)Nh,

where Nh is the number of hot junctions (four, as shown in Fig. 5 ) ; and time constant

where A is the sensitive area. Before combining these factors into a figure of merit we wish to examine two criteria proposed by Jones,24 D* and M 2 .

12. D” AS

A

CRITERION OF MERIT

The well-known criterion D* proposed by R. Clark Jones has justifiably enjoyed widespread use for comparing detectors. This may be defhed for unit electrical bandwidth as

The multiplying factor A‘‘, permits comparison of detectors of different areas. Underlying the validity of this figure of merit is the assumption that the noise is dependent upon A’/’. In some thermopiles this A’” dependence of the noise is not realized. Examining the schematic of Fig. 5 we see that we can increase the area by inserting a high thermal conductivity metal, e.g., silver, in series with the hot junction, thereby increasing W,. This change, however, does not significantly change the device impedance ; hence the Johnson noise is unaltered even though area has been changed. A similar condition is described by Smith et aLz5 Here, clearly, D* may not be used unambiguously. One additional comment is that, aside from the above precaution to be observed when invoking the use of the D* for thermopile detectors, D* fails to designate the time constant of the device. This parameter must always be one of the boundary conditions to be considered in a thermopile design.

13. M2

AS A CRITERION

Another proposed criterion by Jones,26 M,, is based upon the Havens limit.27*28 It takes the important parameter of time constant into account, R. C. Jones, Proc. I.R.E. 47, 1495 (1959). See Smith et al.,’ p. 251. 26 See Jones,24 p. 1499. 21 R. J. Havens, J. Opt. SOC. Am. 36, 355(A) (1946). 2 s P. W. Kruse, L. D. McGlauchlin, and R. 3.McQuistan, “Elements of Infrared Technology,” p. 385. Wiley, New York, 1962. 24

2s

302

NORMAN B. STEVENS

and is defined as:

M 2 = 6 x 10-" (W seccm-')D,*/rA'2

(44) where Om*is the maximum value of D* with respect to frequency and td is the detector time constant. The constant M , is based upon a Havens limit thermal detector which involves viewing the detector as a thermal engine with 10% efficiency. For this assumption Havens found that the minimum energy (not power) at the receiver to give a unity signal-to-noise ratio was independent of time for a response time shorter than 40 msec, and proportional to the square root of the time constant for longer times. For a 40 msec thermal detector the Havens limit is D* = 5.6 x lo9cm Hz"* W - I . This is about one-fourth the background-limited-noise case. It may be noted that although M 2 assumes the applicability of D* with its A'/' dependence as a valid criterion, the time constant also depends upon A [Eq. (42)]; hence the confusion about area is largely unimportant when using M , . This particular figure of merit is strongly recommended for comparing thermopile detectors. It is dimensionless and it most closely describes the properties of importance to a system designer, who must always consider responsivity, area, noise, and response time. 14. PROFILE

Another parameter of importance to a thermal detector is its profile. This is intimately related to effective area and, as such, must be considered in some detail before any of the criteria suggested above can be used. The response of each couple constituting the thermopile may in some cases be clearly evident in a profile scan.29 Even with thermopiles having a discrete isothermal collector, as shown schematically in Fig. 10, the responsivity is usually not constant over the entire area, particularly at or beyond the chopping frequency corresponding to 0.707 response. Ideally, of course, the responsivity profile should be flat, and fall off abruptly in a manner defined only by the scanning spot size beyond the sensitive area. Similarly, there should be an absence of sensitivity at the cold junctions, since this would contribute a signal of negative polarity to that obtained at the sensitive or "hot" junctions. 15. SPECTRAL RESPONSE

Thermopiles with blackened receivers are usually considered as ideal black receivers far into the infrared. This situation has been abetted by the difficulty of securing standard black receivers for reference measurements in the region of 20-40 p. There now exist good reference^,^' and it is possible 29 30

R. Stair. W. E. Schneider, W. R. Waters, and J. K. Jackson, Appl. Opt 4, 703 (1965). W. L. Eisenrnan, R. L. Bates, and J. D. Merrian, J . Opt. SOC.Am. 53, 729 (1965).

7. RADIATION THERMOPILES

303

to know accurately the spectral response of thermal detectors. Using such a reference detector with well-known properties to approximately 40 p, Bettsj observed a severe decline in the spectral responsivity of thermopiles at wavelengths beyond about 10 p. Thermopiles with blacks of platinum, gold, zinc, and carbon were tested. Measurements of thermopiles relative to a Golay cell were made in the range 1-35 p by Astheimer and Weiner3’ and a small drop in the response, to about 75% of peak value, was observed by them. The author has also observed such a sag in responsivity of the evaporated, thin film thermopiles between 10 and 20 p. To date the cause of this drop has not been determined.

FIG.6. Twelve junction linear thermopile and mount for laboratory radiometric measurement (photo courtesy the Eppley Laboratories, Newport, Rhode Island). 31

D. B. Betts, J . Sci. Instr. 42, 243 (1965).

’’ R. W. Astheimer and S. Weiner, Appl. Opt. 3,493 (1964).

304

NORMAN B. STEVENS

Comparisons of a 2-mm-diameter thermopile with a Gday cell have been ~ ~ a not unexpected decline in thermopile responmade to 3 5 0 in~ which sivity was observed. In this case the relative detectivity was five times greater than that of the Golay cell to 85 p, after which it decayed to comparable performance at 280 p, and to half value at 330 p.

1V. Properties of Thermopile Radiation Detectors It will now be of interest to turn to a comparison of the properties of the bulk, fabricated devices and the evaporated units which usually have a high density of couples in the available space.

FIG. 7. Wire-wound thermopile and mount for high radiant flux density measurements(photo courtcsy the Eppley Laboratories, Newport, Rhode Island).

’’0. Stafsudd and N. Stevens, Thermopile Performance in the Far Infrared, Appl. Opr. 7,2320 (1968).

7. RADIATION THERMOPILES

305

16. BULKMATERIAL DEVICES These devices are made with wires for the active elements, typically silver and bismuth, manganese and constantin, or copper and constantin. Figure 6b shows a mounting that has proved to be very useful in laboratory applications. Figure 6a shows the arrangement of the wires and blackened collector array that constitutes the rectangular receiving area. The rectangular configuration is useful in spectroscopic applications. The cold junctions are provided with thermal mass equal to that of the hot junctions to minimize the effect of temperature drift of the instrument. The “cold” areas are shielded from the incoming radiation. A circular configuration is also available. The devices exhibit impedances of 2-50 ohms, response times (l/e value) of 0.1-2 sec, and sensitivity up to 0.25 pV/pW cm2. A new fabrication technique for bulk material thermopiles is illustrated schematically in Fig. 7. Here the active materials are wrapped around a rectangular support and appropriate blacking is applied on the junction

FIG.8. Thermocouple assembly for spectroscopic instruments (photo courtesy Perkin-Elmer Corporation, Norwalk, Connecticut).

306

NORMAN B. STEVENS

surface, facing the radiation. This design permits the fabrication of large area thermopiles, up to 1 in. square, with sensitivities typically 0.1 V/W cm2. Also shown in Fig. 7 is a typical mounting package. Another mounting for a rectangular (2mm x 0.2mm) thermopile is shown in Fig. 8. This device, which is particularly well known to spectroscopists, is an integral part of a spectrometer. The post which holds the

FIG. 9. Thermopiles as reference detectors in spectroscopic systems require a variety of optical and physical mountings (photo courtesy Charles M. Reeder & Co., Inc., Detroit, Michigan).

7. RADIATION THERMOPILES

307

thermocouple at its terminus offers little obstruction in the optical system. This thermocouple has the following properties : Responsivity 3-6 V/W (at 13 Hz) 20 msec Time constant Resistance 10-12 ohms Minimum detectable power (1.5-0.75) x lO-'OW Target Gold-blacked gold leaf. Some other mountings of spectroscope thermocouples are shown in Fig. 9. A large number of sensitive areas are manufactured, including 0.5 x 1.5 mm, 1 x 3 mm, 6.0 x 6.0 mm, and 10.0 x 1.0 mm, to cite several examples. All are carefully adapted optically and electrically to the system requirements for which they are designed.

17. THINFILMDEVICES Advances in vacuum deposition techniques and improvements in photolithography have facilitated the fabrication of thin film thermopiles. The practical result is that very small devices can be made with a density of 20 or more couples per millimeter, a density far exceeding that achieved with bulk material. This permits much greater design flexibility with respect to responsivity, time constant, and impedance. Referring again to the thermopile schematic shown in Fig. 5, it will be noted that two materials are used, with the darker pattern being deposited first. This is accomplished in a vacuum evaporator chamber which is provided with a source of the desired material. Usually, thermal heating of the material in a metal boat, or electron beam heating of the material is used to provide a stream of atoms of the material, e.g., antimony or bismuth. This material is constrained to the pattern illustrated in Fig. 5 by positioning over the substrate and membrane a mask which is provided with openings where material deposition is desired, The mask is prepared by photoetch techniques from a master typically 50 times larger. This reduction to the mask dimensions permits one to obtain bar widths W of in., placed in proper position with corresponding accuracy. To produce the composite evaporation shown in Fig. 5, the mask may be rotated (or a second mask used) and the second material is evaporated. Clearly, evaporation orders, rates, and general procedures are critical aspects of the technology. The precision of photolithography allows the use of repetitive patterns in thermopile fabrication. This capability greatly reduces the complication usually inherent in detector array fabrication in which repetitive procedures must be employed. Clearly, all thermopiles of an array must perform

308

NORMAN B. STEVENS

BLACKENING

RADIATION E M I T T E D

THERMOELECTRIC MATERIAL N O . l

THERMAL AND ELECTRICAL CONDUCTOR THERMOELECTRIC MATERIAL N 0 . 2

SUPPORTING FILM

FIG.10. Schematic of thermocouple with isothermal collector

similarly, but the important point is that the replication so readily attained with photoetch techniques obviates the need for multiple fabrication steps in making the array. Some interesting thermopile arrays will be shown in the following section. The active materials generally used in making evaporated thermopiles are antimony and bismuth. These evaporate readily and have a high figure of merit.34 The use of alloys is a promising avenue for securing better devices with respect to responsivity alone. However, the difficulty of maintaining a given composition throughout the period of the deposition has delayed the appearance of evaporated alloy thermopiles. Recent developments with electron beam evaporation and sputtering will ease this difficulty and some improved, evaporable alloy materials can be expected to be used in thermopile fabrication. A problem of the thin film thermopile not generally shared by the bulk material devices is flatness or uniformity of profile. This refers to the absence of responsivity peaks and valleys as a small scanning spot is used to explore the receiver or sensitive area of the device. In the case of bulk devices the collector area is thermally massive, with high diffusivity. This condition is not as readily satisfied with an evaporated device. A technique to minimize the unwanted variations in responsivity over the sensitive area is to provide a third material of high thermal diffusivity distributed throughout the sensitive area. The third material is arranged to leave the electrical circuit of the thermopile virtually unaltered and to be of such thickness and thermal conductivity as to permit temperature 34

See Smith rt al.,' p. 78; L. Geiling. Ann. Telecornm. 5,417 (1950).

7. RADIATION THERMOPILES

309

COLLECTOR PATTERN (IMM x 1 MM)

t

t

t

9

A

X-

19

$ s s z RELATIVE RESPONSE

APPROX M A T E SCANNING SPOT S I Z E

u

-

‘*o

SPOT P O S I T I O N , X

FIG.!1. Responsivity profile of thermopile with isothermal collector.

equalization throughout the sensitive area in a time small compared to the device time constant. Thus, it may be considered an isothermal collector. Figure 10 shows one possible arrangement for the isothermal collector, in which it is simply placed in series with the “hot” junction.35 The resulting profile (Fig. 11) shows an absence of responsivity positional structure at scanning frequencies below that corresponding to the device time constant. A typical evaporated thermopile with a sensitive region 1 mm square is shown in Fig. 12. The antimony (Sb) and bismuth (Bi) active elements are evaporated through photoetched masks to provide 15 couples in series. The output leads may be contacted by welding or by a conductive epoxy. The entire device is based on a round sapphire substrate with a groove (as shown) or a circular hole over which is mounted the supporting membrane. The diffusivity and thermal mass of the membrane are small compared to other thermal losses in the structure. The properties of this 1 mm square thermopile and other representative devices, as shown in Table I, point up the major responsivity and impedance 35

See Smith, et ul.,’ p. 86

310

NORMAN B. STEVENS

FIG.12. I mm x 1 mm thermopile with fifteen couples (photo courtesy Santa Barbara Research Center, Goleta, California).

differences between bulk material thermopiles and evaporated thin film devices. Figures 13-15 are illustrations of the other evaporated thermopiles described in Table I. These serve to illustrate the diverse geometries of modern evaporated thermopiles. The 0.25 rnm square thermopile shown in Fig. 13 has been subjected to extensive environmental testing. Throughout temperature changes from 80 to

TABLE I CHARACTERISTICS OF EVAPORATED THERMOPILES Characteristic

1 x I mm (Fig. 12)

0.25 mm x 0.25 mm 2 mm diameter 0.12 mm x 0.12 mm (Fig. 13) (Fig. 14) (Fig. 15)

9, responsivity (vacuum) (V/W) time constant (vacuum) (psec) Z, impedance (K-ohms) NEP (W) D* (cm Hz''~/W)

50

220

160

280

100

75

150

13

T,

M2

6.3 2.1 x 5.0 x 10' 0.10

10 5.9 x lo-" 4.2 x los 0.09

47 1.7 x lo-'' 1.0 x 109 0.15

5 3.3 x 10-" 3.6 109 0.19

FIG.13. 0.25 mm x 0.25 mm thermopile with five junctions (photo courtesy Santa Barbara Research Center, Goleta, California).

312

NORMAN B. STEVENS

FIG.14.2.0mm diameter thermopile with 89 couples (photo courtesy Santa Barbara Research Center, Goleta, California).

400”K the responsivity, time constant, and impedance of this device were measured. These parameters all were found to increase with decreasing temperature. The units survived shock and vibration in all axes as follows : sinusoidal to 40 g at 250-2000 Hz; multiple shocks at 250 g for a duration of 0.7 msec. 18. EVAPORATED THERMOPILE ARRAYS

Figure 16 is an interesting array of thermocouple junctions which provides for detection of the centering of a thermal image. The staggered black areas are underlain by “hot” junctions of reversed polarity. Such a device is useful as the detector of a horizon sensor. An array of eight thermopiles is shown in Fig. 17. Here each 0.4mm x 6.0 rnm thermopile contains 40 junctions connected in series. The external connections between the various thermopiles are readily made by the use of evaporations through photoetch masks.

7. RADIATION THERMOPfLES

313

FIG. 15. 0.12mm x 0.12mm thermopile with five couples (photo courtesy Santa Barbara Research Center, Goleta, California).

A more complex thermopile array is the linear arrangement of 45 thermopiles, each containing 11 couples, shown in Fig. 18. One common lead and 45 separate electrical connections have been provided. These arrays are fabricated on a solid backed substrate and exhibit excellent resistance to both mechanical and thermal A typical spectral coverage of these detectors is shown in Fig. 19. 36

R. W. Astheimer and S. Weiner, Appl. Opt. 3, 500 (1964).

314

NORMAN R. STEVENS

FIG.16. Two 20-element edge detectors on a single substrate (photo courtesy Barnes Engineering Co., Stamford, Connecticut).

7. RADIATION THERMOPILES

315

FIG. 17. Eight thermopile arrays. Each 0.4 mm x 6.0 mm thermopile contains 40 junctions (photo courtesy Barnes Engineering Co., Stamford, Connecticut).

316 NORMAN 9. STEVENS

FIG. 18. Forty-five thermopile arrays of 0.75mm x 3 . 9 m detectors, each with eleven junctions (photo courtesy Barnes Engineering Co., Stamford, Connecticut).

7. RADIATION THERMOPILES

317

WAVELENGTH-MICRONS

FIG. 19. Spectral response of typical thermopile, showing excellent and uniform sensitivity to radiation over a wide band of wavelengths (courtesy Barnes Engineering Co., Stamford, Connecticut).

V. Conclusion

Much recent development has produced thermopile radiation detectors that are sensitive, stable, inherently rugged, and responsive to radiation over a wide range of wavelengths. These properties are realized without cooling and without any electrical bias. Their inability to respond well in submillisecond time is a disadvantage for some systems applications. However, where the information rate is in the domain of greater than one millisecond, where cooling may be a problem, or where wide spectral bandwidth is needed the thermopile detector should definitely be considered.

ACKNOWLEDGMENTS The author wishes to thank L. H. DeVaux and D. D. Errett for many helpful discussions and suggestions. I wish also to thank D. E. Bode for his technical advice during the thermal detector development.

LISTOF a

ll

T V

r E 1

SYMBOLS

Seebeck coefficient or thermoelectric power (V/"C) Peltier coefficient, rate of heat exchange per unit of electrical current absolute temperature ("K) emf(V) Thomson coefficient, rate of heat evolution per unit electrical current, and per unit temperature gradient thermoelectric force, thermal emf (V) length of thermocouple arm

318

Q K

NORMAN B. STEVENS

rate of heat transfer or evolution specific thermal conductivity electrical current electrical resistance area of thermocouple arm thermal conductance electrical specific resistance electrical conductivity thermal resistancc responsivity (V/W) Lorentz number figure of merit, materials specific heat thermal capacitance radiant power, watts height of sensitive area width of sensitive area evaporation thickness device time constant number of hot junctions

Heterodyne Detection and Other Special Techniques

This Page Intentionally Left Blank

CHAPTER 8

Low-Level Coherent and Incoherent Detection in the Infrared R.J . Keyes and T. M . Quisl I . INTRODUCTION .

. . . . . . . . . . . . . . .

11. LOW-LEVEL INCOHERENTDETECTION. . . . . 1 . Our Environmental Radiation and BLIP Detection. 2. Signai and Noise Currents in Photoconductors . , 3 . Minimum Detectable Power in Terms of D1* . .

. . . . . .

32 1 322 322 328 332 336 345 345

. .

350

. . . . . . . . . . . . , . . .

.

.

4 . Copper-Doped Germanium . . . . . . . . . . 111. LOW-LEVELCOHERENT RADIATIONDETECTION . . . . . 5 . Heterodyne Detection and Frequency Response. . . . . 6. Ge:Cu as a Theoretically Perfect Coherent Detector at GHz Frequencies . . . . . . . . . . . . . . I . Discussion . . . . . . . . . . . . . . . APPENDIX . . . . . . . . . . . . . . . .

.

.

. . 353 . .

355

I. Introduction Sensors are now available for the detection of faint coherent and incoherent signals in the infrared region of the spectrum extending from the 1 to 30 p. For the first time the theoretical limits of detection imposed by photon noise are a reality rather than a hypothetical boundary that could only be approached at very high photon noise levels. The barrier to the lower limit of signal detection has switched from the sensor to the environment into which it must operate. It is the intent of this chapter to present those detector and environment parameters which are of first-order importance to the small signal detection problem. A complete treatment of low-level detection, even in the restricted portion of the spectrum dealt with here, should include the vast area of science and technology ranging from quantum mechanics to Dewar design. However, the general tenor of this text lies somewhere between theoretical and pragmatic, reflecting perhaps to a large extent the authors’ experience in the field of infrared detection. It is hoped that the references and other chapters in this volume will help supplement obvious deficiencies.

321

322

K. J. KEYES A N D T. M. QUBT

In practice, one can often utilize the same sensing element to measure both coherent and incoherent signals. In fact, copper-doped germanium photoconductors ideally perform both functions, and for that reason many details concerning preparation, physical properties, and fabrication of such detectors are presented. Although the sensors-the nucleus of both types of low level detection systems-have much in common, the peripheral problems germane to each system are quite different. These differences were felt to be of sufficient importance that each mode of detection (coherent and incoherent) is treated separately in Parts I1 and 111. This separation introduces unavoidable redundancy, for which the authors apologize. 11. Low-Level Incoherent Detection 1. OUR ENVIRONMENTAL RADIATION AND BLIP DETECTION

Because the human eye does not see infrared radiation, one is often not cognizant of the vast quantity of radiation emitted by all the objects of our environment. Every substance (not at absolute zero) emits radiation flux that very closely obeys the well-known Planck equation multiplied by an emissivity factor

whcre Wi is the radiant flux emitted per unit area per unit increment of wavelength (W/cm2/cm AA) of a blackbody of temperature Tand emissivity c ; Wc1n2, and and C, and C 2 are constants, C , = 2 7 ~ ~ 1 13.74 x C, = hc/k zz 1.44 cm O K . The peak in the spectral distribution is accurately described by the Wicn displacement law :

R,

=

a/T,

(2)

with u = 2897.9 p deg, and the total flux radiated per unit area by the surfxctce over all wavelengths is expressed quite simply by the StefanBoltzmann law :

w=

037.4,

(3)

where c = 5.7 x W cm * "K is the Stefan Boltzmann constant. These equations are basic to the calculation of detector performance in the infrared region.a A plot of the Planck distribution for the critical 300°K temperature of our surroundings is shown in Fig. 1 . It is obvious that nearly "Calculations to a first approximation can be handled nicely with the aid of a GE Radiation Calculator 0 1 Autonctics Photon Calculator.

8. LOW-LEVEL

COHERENT/INCOHERENT DETECTlON IN THE INFRARED

323

32t

x

(P)

FIG. 1. Radiant emittance of a 300°K blackbody with the 8-12p atmospheric window indicated.

the entire emission occurs within the I-3Op region. To establish a bench mark for the power densities involved in blackbody emission compared to the more familiar visible emissions of our environment, Fig. 2 is presented. I t may be surprising to note that a 300°K blackbody radiates about six times more power per unit area than is reflected by a white sandy beach on a clear summer day in the visible portion of the spectrum. Even the air we breathe radiates, If we could see in the infrared, the atmospheric emission would produce a sensation analogous to that observed within a sunlit cloud in the visible region : light emanating from all directions. This is the hostile environment in which an infrared sensor must function. It hinders the capacity to detect weak signals by introducing two distinctly different forms of noise. One type of noise stems from the fact that either the emissivity or the temperature of the undesired, but ever-present, background may not be constant in either the space or the time domains. Usually, these variations

324

R. J. KEYES AND T. M. QUIST

Temperature of blackbody

(OK)

FIG.2. Radiant emittance (W/cmZ)as a function of blackbody temperature. Radiances of familiar scenes in the visible region are indicated for comparison.

are only unique to a particular situation and hence are not amenable to a general mathematical formulation. An example of this type of fluctuation is found in atmospheric infrared absorption. Cells of air, because of temperature, pressure, or composition changes in both the spatial and time domains, introduce false signals into a detection system. Usually, these variations display a l/f temporal spectrum which can be effectively discriminated from true signals by frequency selection in electronic circuits.

8. LOW-LEVEL

COHERENT/INCOHERENT DETECTION IN THE INFRARED

325

Space-filtering techniques’ are quite effective in reducing undesirable spatial inhomogeneitiesto a tolerable level. Although these effects are treated lightly here, it requires great effort to eliminate them in practice, and the cure becomes especially difficult in the 5-3Op region when the signal is faint. The atmospheric variations are large at low altitudes and the usual techniques involving moving retical choppers are harassed by the annoying fact that the chopper itself becomes a source of undesirable emission. Nonetheless, solutions to these problems can be found, and this effect is not considered henceforth in this chapter. The second source of noise resulting from background radiation is often called “photon noise.” It establishes the absolute lower limit of detection of any radiation sensor when all other noise sources have been eliminated in comparison to it. The genesis of photon noise lies in the fluctuation phenomenon of a Bose-Einstein ensemble of radiators. The theory of the fluctuations in steady streams of thermal radiation was first presented by Lewis2 The formulation of photon noise can be carried out in a variety of ways depending on one’s purpose, and a number of elegant methods are presented by Jones.3 If pb, an average power level of background photons,3aimpinges on a detector, the mean-square fluctuation of incident photon flux per unit of time is

where hv is the photon energy and is the temperature of the background source. The [l - exp( - hv/kT,)] term is a consequence of the Bose-Einstein nature of thermal radiators. For detectors which have a long-wavelength cutoff such that hv b kTb the effective radiation fluctuations approach a Poisson distribution, and for all practical purposes [l - exp(-hv/k&)] z 1. Unless specifically stated we shall assume this approximation to be valid in the remainder of the text. A perfect sensor, which yields a single unit of charge flow per incident photon, requires an incident signal power =

(2pbhVB)”2

(5)

in order to produce an rms voltage equal to the photon noise generated by the background flux in an electrical bandwidth B. If due to reflection losses,

’ J. A. Jamieson, R. H. McFee, G. N. Plass, R. H. Grube, and R. G. Richards, “Infrared Physics and Engineering.” McGraw-Hill, New York, 1963. W. B. Lewis, Proc. Phys. Soc. (London) 59, 34 (1947). R. C. Jones, Advanc. Electron. 5, 1-96 (1953). ”The background photons include those of the signal as well. For most situations the contribution from the signal is small, but in special situations they must be considered.

326

R. J . KEYES AND T. M. QUIST

transparency, or a noneffective absorption process only a fraction q of the incident photons produces free carriers, Eq. ( 5 ) becomes ps = ( 2 F b y )

(generation noise)

where 11 is the quantum efficiency of the sensor. Photodiodes in which each photon-induced carrier is swept across a p-n junction or a vacuum can be in this category provided all other sources of noise are eliminated. Photoconductors, however, can never achieve the “photon noise” limit, because of the added recombination noise, which is of the same magnitude as photon noise. Recombination noise has its basis in the statistical fluctuation4 in the rate at which photogenerated carriers recombine from an excited to an initial state. The rms signal power required to produce a SIN = 1 in the photoconductive case is

9, = ) ; j2

F,,hvB ‘I2

Scnsars which have a minimum detectable power expressed by Eq. (7) are sometimes referred to as BLIP5 detectors (background limited infrared photoconductor). A rather special case of BLfP operation occurs when the fluctuation in the signal photon stream is the dominant source of noise. For this condition the minimum detectable rms power becomes

P, = 4hvB/q. (8) As will be shown later, this is only a factor of two greater than the minimum detectable power for a perfect heterodyne receiver. Physically, Eq. (8) states that one has a 50% probability of detecting a signal when there are two absorbed photons per measuring time interval. For conditions of BLIP operation the minimum detectable signal is determined by both the magnitude and wavelength of the background flux impinging on the sensor, N6ise equivalent power (NEP) has been widely used as a general figure of merit for weak signal detection. Specifically, it is the amount of incident signal power which will produce an rms response (voltage or current) equal to the rms noise of the detector for a given band pass. Figure 3 shows the NEP of a BLIP detector at 14 p as a function of the conical angular field of view H of the sensor into a unit emissivity background at temperatures of 100 and 300°K. Sets of curves are drawn for the two situations where the maximum wavelength response is 14 and 30 p. K. M. van Vliet, Proc. I.R.E. 46,1004 (1958).

’ See Jamieson et a/.’

8, LOW-LEVEL COHWENT/INCOHERENT DETECTION IN THE INFRARED 327 I0’”I

16”-

-12-

10

10’~-

-

-3 -a

-15-

z 10

1CP-

tot7-

Field of view ( r a d )

FIG.3. The minimum NEP as a function of detector field of view (0 rad) for 300 and 100°K background temperatures. Sets of curves are drawn for two values of detector maximum wavelength response: 1, = 30 and 14 p.

The lower limit of NEP under theoretically perfect conditions is determined by the fluctuations induced by the signal flux as expressed by Eq. (8) when 13 + 0. However, when one considers problems of signal detection within our atmosphere, values of 8 less than lO-’rad are somewhat academic. Collection mirrors which are diffraction limited to rad at 14 p are large (greater than 1.7 m in diameter) and expensive. Even if they are available, the distortions introduced by atmospheric inhomogeneities produce

328

R. I. KEYES AND T. M. QUlST

“dance”6 in target images in excess of rad, which forces the observer to dilate the field of view to ensure that the signal will remain on the detector. In addition to being exposed to the external background radiation, a detector sees the infrared radiation emanating from the cavity in which it is enclosed. For those circumstances where the enclosure temperature is relatively high and the external field of view is small, the NEP may be dominated by the photon noise induced by the cavity blackbody emission. For example, a detector which has a long-wave cutoff of 14 p and an area of 1 cm’ can never achieve an NEP of better than 8.4 x W for a 1 Hz bandwidth when it is surrounded by a cavity at liquid nitrogen temperature. The perfection of sensors toward the ultimate limit is a process of diminishing the excess sources of noise within the detector and its amplifying circuits. These sources of noise are in most instances definable in terms of known parameters. The detailed analysis of these parameters is important to the selection of possible photoconductive materials for low level detection. 2. SIGNALAND NOISE CURRENTS IN PHOTOCONDUCTORS The path to low-signal detection is the process of elimination of all noise currents with respect to the signal. We shall present the mathematical expressions for the pertinent sources of noise and derive an expression of noise equivalent power in terms of D1*which is quite general for all types of photoconductors. The detailed calculations of thermal generationrecombination (g-r) noise, which are very sensitive to the photoconductor parameters, is given in the appendix, but the results are incorporated in the graphs of this section. In photoconductors the total mean-square noise current ’,i can be expressed as a sum of the individual mean-square noise currents, i,2

iI2

+ i22 + i3’ +

+ ’,i

(9) and the desired result is that the square of the rms signal current ( i s 2 ) exceed this sum, i,Z > i n 2 . (10) We shall in our treatment consider only the nearly perfect photoconductors which are void of those noise currents, such as l/f, which have their origin in either contact imperfections, surface, or trapping mechanisms. The noise currents considered are : (1) in,,, the generation-recombination noise induced by the signal flux, (2) i, the generation-recombination noise induced by the background flux in the field of view, (3) i, the generation-recombination noise induced by the photon flux emanating from the detector cavity walls, =

G. N. Plass and H. Yates, in “Handbook of Military Infrared Technology” (W. Wolfe, ed.), Chap. 6, Section 6.6. Office of Naval Res., Washington, D.C., 1965.

8. LOW-LEVEL COHERENT/INCOHERENT DETECTION IN THE INFRARED 329 (4) i,-,, the thermal generation-recombination noise due to the finite temperature of the detector, governed by Boltzmann statistics and the laws of detailed balance, and ( 5 ) it,,, the effective Johnson noise of the sensor and load resistor-amplifier assembly. Four of the five noise currents listed above are the consequence of the statistical fluctuations in the rate of generation and subsequent recombination of free carriers in photoconductors. Individually, each of these currents can be expressed as follows : a. Signal Noise

i& = 4G2e2P,q1B/hc, (11) where e is the charge on the electron, P, is the power in the signal beam of photon energy hc/A, and q is the quantum efficiency of the excitation process ; G is the photoconductive gain, which will be discussed in more detail later. The factor of four would be reduced to two if only generation noise were present. b. Background Noise ib2 = 4G2e2Aii2yA[sin(8/2)]213, (12) where An2 is the mean-square number of photons emitted per unit area by a blackbody in the spectral region to which the detector is sensitive. The [sin(8/2)] term expresses the fractional portion of the background radiation seen by the sensor of area A through a full cone angle 6 (see Fig. 4). From Planck’s law Limperis’ derives the approximate value of Aii2 in terms of the background temperature and maximum wavelength response 1, as :

where hc/;l, kTb, a condition which is applicable to our considerations. We shall make the additional simplification of retaining only the last term within the bracket, 1/AC2. Combining equations, we obtain ib2 =

8G’e’nkTb[ exp hAC2

-

) ( 2”)’

hc q A sinl.,kTb

_ I

B

c. Cavity Noise Using the same approach as that for the background noise, one obtains z,-2

=3

)

j e x p - _hc_ G2e2qAB, A& T,a,

since the cavity at T,,, very nearly surrounds the detector, the sin(B/2) % 1.

’ T. Limperis, in “Handbook of Military Infrared Technology” (W. Wolfe, ed.), Chap. 1 1 . Office of Naval Res., Washington, D.C., 1965.

330

R. J . KEYES AND T. M. QUIST

FIG.4. Detector-cavil y-background configuration.

d. Thermal Generation Recumhination Noise Thc thermal generation-recombination noise current, although quite straightforward, is a complicated relationship between Boltzmann statistics and the parameters which are inherent in the principle of detailed balance of the particular photoconductor at thermal equilibrium. The details of the thermal (g-r) noise current in photoconductors has recently been presented by Long'; a derivation more suitable for our purpose is presented in the appendix. Stating the results of the appendix, we have for a pure intrinsic photoconductor of energy gap E , = hc/R,

where t is the thickness of the material, z is the hole-electron lifetime, and m* refers to the density-of-states mass of the free holes and electrons. HgCdTe and PbSnTe are representative intrinsic photoconductors. For an intrinsic photoconductor which has a donor impurity density that remains ionized at all temperatures of interest, the generationrecombination noise is somewhat modified' and has the form

Here no is the density of low-ionization-energydonor impurities. In impurity photoconductors such as Ge:Cu and Ge:Hg the g-r noise term takes on a slightly different form,

D. Long, Infrared Phys. 7, 121 (1967).

8. LOW-LEVEL

COHERENT/INCOHERENT DETECTION IN THE INFRARED

331

The ionization energy of the acceptor impurity is so chosen that Ei = hc/,?,. The quantities N , and N , refer to the acceptor and donor impurity concentrations, respectively. As usual, T~ represents the lifetime of a photoexcited hole. The effective degeneracy of the acceptor ground state is p, which is 3 for copper in germanium.

e. Johnson Noise qf the Equivulent Load The final noise current to be considered is that due to thermal Johnson” noise in a load resistor and/or the detector. The load resistance is not a unique quantity. Its magnitude is often determined by the value of the detector resistance, which is quite often temperature and background dependent. Normally, one writes the Johnson noise current of a load resistor as i& = (4kTL/RL)B. (17) In order to obtain maximum signal voltage at the input to a preamplifier, it is customary to match the load resistor to the impedance of the photoconductor, which is critically dependent on the material from which it is fabricated and the operating temperature. We shall divide, : i into two components :hi = F(ii-,) (4kTL/RL)B. U8a)

+

The reason for this division is as follows: For low impedance photoconductors the Johnson noise current of the detector or its equivalent load is mathematically similar to its g-r component and can be expressed as a function of i:,. If at low temperatures the impedance of the detector + co, it is unrealistic to consider the thermal noise in an equivalent load. In practice, it has been found, as reported in the section concerning G e : Cu, that the maximum value of commercially available metal film resistors that demonstrate only Johnson noise at low temperatures is in the range of 30meg0hms.~”The introduction of the 4kT‘,B/R, term ensures that the practical value of Johnson noise is always represented in the general treatment when the sample impedance approaches infinity at low temperatures. The F(ii-,) term ensures the proper representation of thermal noise at low detector impedance levels. For intrinsic and impurity photoconductors

J. L. Lawson and G. E. Uhlenbech, “Threshold Signals,” Chap. 4. McGraw-Hill. New York, 1948. ’”Admittedly. values of ideal load resistors in excess of 30 megohms are feasible. The author chose this value to represent the present state of the art. The reader can, if the art improves, utilize values of R , that are appropriate to the existing art.

332

R . J . KEYES AND T. M. QUIST

where p is the mobility of the majority free carriers and I is the distance between electrodes. For extrinsic materials, in which the impurities are all ionized, the expression becomes

At all temperatures of interest the 4kTL/R, term can be omitted. 3. MINIMUMDETECTABLE POWER IN TERMS OF DA* By equating the signal current to the total noise currents we can obtain the signal power required to yield a signal to noise ratio of unit (SIN = 11, namely

9,= (i;)’/’hc/GeAq.

(19)

A figure of merit for the comparison of infrared detectors, DfI, can be expressed as followsgb:

This expression in the mks system thus has the dimension of m Hz”’ W-’ Substituting for in2 the five dominant noise currents, we obtain the complete expression for DXI, for impurity photoconductor (Ge :Hg):

signal

background

cavity

exp -

-)(Z,& k

hc

1

+

)-

thermal g-r

k T , , V W

G2e212

Johnson Idetector)

Johnson (load) ~ - l ) is a widely accepted figure of merit for infrared detectors, it 9bAlthough D,* (cm H Z ” W may be cumbersome to use. Since its units are not consistent, one must exercise caution in the dimensions of the parameters involved in its calculation. With hindsight it seems that if DA* had been defined in units of m Hz”’W- I , a much more sensible and consistent figure of merit would have been obtained, namely, DXI, (m H Z ” ~W-’). We have made our calculations in the latter units: however, in deference to established usage we have plotted our results in terms of DL*.

8. LOW-LEVEL COHERENT/INCOHERENT

DETECTION IN THE INFRARED

Defector Temperature

333

(OK)

FIG.5. Plot of Dt (cm Hz''' W - *) as a function of detector-cavity temperature for PbSnTe (iO'" and 10" cm-3 donor impurities) and Ge:Hg. Also indicated on the graph is the maximum D L as a function of field of view into a 300°K blackbody. The D b limit as a function of cavity temperature is also plotted. A, = 1 4 ~ '

Since the commonly accepted figure of merit Di* has dimensions of cm Hz'l2 W - ', the value obtained from Eq. (21) must be increased by a factor of 100 to conform to the commonly-accepted definition. Theoretical plots of Di* as a function of sensor and of cavity temperature T,,, are given in Fig. 5 for Ge :Hg and PbSnTe when 0 = 0. Curves for two values of impurity content (loll and 10'4cm-3) of PbSnTe are drawn. The value of 10" represents the best purity that can probably ever be obtained, while the concentration of 10'4cm-3 is felt to be representative of the purity obtainable in the near future. Indicated on the right-hand side of each plot is the maximum D,* possible for various fields of view into a unit-emissivity background of 300°K. Also plotted is the limit established by the photons emanating from the cavity walls. For small signals the first term within the bracket of Eq. (21) can be neglected. The photoconductive gain G is expressed in Eq. (22).

334

R. J. KEYES AND T. M. QUIST TABLE 1 Parameter

PbSnTe

Ge:Hg

1.40

1.45 x IO-'" 10 x to x 10-3 1o4

3

x

10-31

10

x

x 10-2 x

I I

x 10

t

1 5 x lo-'

1.4 x 10-5

32

10-.32

2 1.45 x lo-''

lWS

103

10 10 1.45 x lo-'' 1 10-5 10-5 1.4 x 10-5

The values of the photoconductor parameters which were used for the calculations of these graphs are given in Table I. Admittedly, the values of T, p, and t employed for the PbSnTe calculations are optimistically beyond the present state of the art, but because of the infancy of this material compared to the impurity photoconductors, the authors feel that the bias is justifiable. An analysis of D,* equations and graphs leads to some important general conclusions : 1. In uny photoconductive material of the same maximum wavelength cutoff (Ic) the photon induced noise of the signal establishes a minimum detectable power of 4hvB/q. 2. The photon flux from the cavity walls sets another theoretical limit on DA*, but for T,,, < 30°K it is not a contributing factor. At 77°K the maximum D,* possible is 1.2 x 10l3cm Hz'I2 W - ' for & z 14 p, 3. The photon flux reaching the sensor from the thermal radiation in the field of view 0 usually establishes an operational upper limit for D,*. Since background temperatures and emissivities are extremely variable in relationship to a given detection situation, a general analysis is impractical. Typical 0 dependences of Dj,* for background temperatures of 100 and 300°K are indicated in Fig. 3. 4. When the detector and its enclosure are at a very low temperature and the flux from the background is negligible, the major source of noise in both impurity and intrinsic photoconductors is the Johnson noise of the load or

8. LOW-LEVEL COHERENT/INCOHERENT DETECTION IN THE INFRARED 335

the detecting element. In this situation the achievable Dn* is critically dependent on the parameters which regulate the photoconductor gain G. As described by Rose," G is the ratio of the lifetime of an optically-excited carrier to its transit time between electrodes of separation 1. When a photoconductor has ohmic electrodes, which do not inhibit the flow of carriers in and out of the detector, G can be expressed as G =Ep/i, (22) where E is the electric field across the photoconductor, p is the mobility of the excited carrier, and z is the average lifetime of the excited carrier. In photoconductors G can take on values ranging from near zero to above lo3,depending on the parametric values of the material, its dimensions, and the electric field applied. It should be noted, however, that G %- 1 implies that many charged carriers traverse the electrodes for each photon absorbed, and hence for high-gain detection the ohmicity of the contacts becomes very important. Avalanche' gain is an entirely different phenomenon involving impact ionization. A discussion of avalanche multiplication is beyond the scope of this chapter. Let it suffice to say that it is not a useful technique of gain in impurity or one free-carrier photoconductors. It may be very advantageous, however, in intrinsic or two-carrier materials. For impurity photoconductors when thermal noise of the load resistor (3 x lo7 ohms) dominates Da* K GI, and the maximum achievable D,* is obtained when the Epz product is the largest. Only the lifetime in a specific material is amenable to appreciable control. As explained in the section on copper-doped germanium, large values of z are obtained through the elimination of residual donor impurities in the host crystal. 5. Because the absorption coefficient for pair producing radiation in PbSnTe is large (> lo4 cm- '), a reduction of sample thickness to the micron range is effective in increasing DA* when thermal noise predominates. Not only does a decrease of t reduce the total number of thermally generated carriers which introduce noise, but it also raises the sample resistance, which in turn permits larger electric fields to be applied to the detector without undue 12R heating. 6. If the mixed crystals could be deposited in thin layers ( 1 p) of high purity and mobility, Da* performance comparable t o that of the impurity photoconductors would be possible at slightly higher temperatures. A general advantage of intrinsic over impurity photoconductors is their ability to maintain higher Dn* at comparatively elevated temperatures. Although the introduction of low ionization energy impurities into intrinsic materials reduces the maximum Dn* at low temperatures, it extends the N

'' A. Rose, in "Photoconductivity Conference" (Proc.Atlantic City Conf.) (R. G . Breckenridge, ''

B. R. Russell, and E. E. Hahn, eds.), p. 1 1 . Wiley, New York and Chapman & Hall, London, 1956. K. M. Johnson, I E E E Trans. Electron. Devices 12, 55 (1965).

336

R. J . KEYES AND T. M. QUIST

intermediate values of Dn*to a higher temperature. This can be an operationally important factor when D,* is limited by background photon noise and the degree.of cooling is restrictive. As stated previously, for most small signal detection systems the thermal emission of the background in the field of view limits the achievable signalto-noise ratio. Under this condition the designer usually reduces the sensor field of view in order to obtain a more favorable SIN, but he does so at the expense of versatility and acquisition ability of the system. To overcome this lack of versatility an array of sensors might be used. It should be borne in mind that unless the Dn* value of each element in an array or storage tube is comparable to that of a single element device, much of the advantage is lost. For example, if an array or tube has n elements, then each element must have a Dn*value > 1/& times the DA* obtainable from a single element device used in a mechanically scanned mode if the composite structure is to be of advantage in SIN. The larger the number of elements in the array, the less stringent is the requirement on individual performance. For arrays or other devices having lo5 elements, each element has to have a DA* 1/300 of that of a single-element mechanically scanned device in order to obtain comparable performance. From a more optimistic point of view, an array with lo5 perfect elements can detect signals 300 times weaker than a perfect single element used in a scan mode. To this point we have been mainly concerned with the quasitheoretical aspects of low-level incoherent signal detection in the infrared region ; the remaining portion of Part I1 will be more pragmatic, in that it will deal with the actual methods of fabrication and measurement of high-D,* copper-doped germanium detectors for the 1-30 p spectral range. As stated previously, Ge :Cu is not a unique impurity photoconductor, but its problems and performance are representative of those that might be encountered in a host of possible detector materials, of which Ge :Hg, Ge:In, Si :In, Si :A1 are only a few. The authors have selected Ge:Cu as an example because it is the material which they have studied to the greatest extent. An analysis of an intrinsic detector (PbSnTe) is given by Melngailis and Harman in Chapter 4. 4. COPPER-DOPED GERMANIUM

The impurity-photoconductive aspects of Ge :Cu were first reported by Burstein er a/. in 1954.” In the early days of transistor and diode technology this impurity, because of its rapid diffusion and detrimental effect on free carricr lifetime, was considered a tenacious contaminant in semiconductor materials and devices. For infrared detector fabrication the rapid diffusion

‘’ F. Burstein, J. W. Davisson, E. E. Bell, W. J. Turner, and H. Lipson, Phys. Rev. 93,65(1954).

8, LOW-LEVEL

COHERENT~INCOHERENT DETECTIONIN THE INFRARED

337

of copper plus the three acceptor levels associated with each atom permit one to make versatile sensors of different characteristics with a minimum of equipment. Before pursuing the details of infrared detector fabrication and measurements a brief description of the impurity levels of Cu in germanium is in order. Copper introduces three acceptor levels13 in the forbidden band of germanium, one each at 0.04 eV and 0.32 eV above the valence band and one 0.26 eV below the conduction band. Thus, the substitutional copper atom first accepts one, then a second, and lastly a third electron as the Fermi level is increased. It is the 0.04eV level that is of interest when Ge:Cu material is used as a long-wavelength sensor at near liquid helium temperatures. Figure 6 is a schematic band diagram of the copper impurity in germanium. In addition to the copper atoms, other donor or acceptor impurities are present, either as residual or intentionally introduced dopants. For our presentation acceptor atoms other than copper are not considered, but attention is given to donor impurities such as arsenic and antimony which play a vital role in the total photoconductive process. The photoconductive process proceeds as follows : If the temperature of the crystal is below 15"K,thermal excitation of electrons into the copper levels is negligible and all of the copper atoms remain unionized except those that have accepted an electron from a donor impurity atom, in which case the copper atom takes on a net negative charge Cu-. An infrared photon of energy greater than 0.04 eV, upon entering the crystal lattice may excite an electron from the valence band into a Cuo site, producing an additional Cu- level and leaving behind a free hole in the valence band which can move through the lattice by diffusion or under the force exerted by an externally applied electric field. As long as the photon excited hole "lives" photoconduction will persist. Ultimately, the free hole will recombine with an electron from a Cu- site. It is evident from this mechanism that the average lifetime of the hole is inversely proportional to the number of Cuatoms, and is directly related to the density of donor impurities. One can readily see that NDplays a vital role in the photoconductive lifetime zP and hence in the photoconductivity. It is desirable for many applications to make zP as long as possible, which requires ND to be kept very small. Most high sensitivity detectors are obtained from very pure host crystals where ND is the residual impurity remaining in the lattice after maximum purification has been attained. Residual impurity densities in germanium below a concentration of 10'2cm-3 are difficult to achieve. As will be discussed later in the use of Ge :Cu for heterodyne detection, donors are intentionally introduced in order to reduce the lifetime for high frequency operation. In I3

H. H. Woodbury and W. W. Tyler, Phys. Rev. 105,84 (1957).

338

R. J . KEYES AND T. M . QUIST

Conduction band

N,

cu--

cu-

____

~

0 01

O+

O+

O+

0.26

___ 0.32

-

*

0- 0-

*-\

0

! I

I

cuo

-0.04o

o

o

I

c;

-

‘i‘\ I I

o o o

0

0

0

‘I

$;I

I $i-..:’.

/

0

0

0

I & vI

b

E

.

4

Excitation

Recombination Valence band

FIG.6. Energy level diagram of G e at 4°K containing residual donor atoms and showing the triple ionization energies of the Cu atom. The figure illustrates schematically the photoionization of an electron to the 0.04 eV level leaving a free hole and the subsequent recombination of an electron with a free hole in the valcncc band.

view of the impurity photoconductive mechanism of Ge:Cu the first step in the fabrication of detectors is to obtain a very homogeneous germanium host crystal with the desired donor concentration. Many copper-doped germanium detectors have been fabricated from single crystal germanium with a net donor impurity concentration of from ND z 10’’ to 7.4 x 10” atoms/cm3 with a liquid nitrogen temperature mobility p z 4 x lo4 cm2 V - ‘ sec-’ for the purest samples. Prior to indiffusion copper is evaporated or electroplated on to the chemically etched and cleaned surfaces of the germanium wafers. The wafers are then placed inside a quartz tube in a furnace with an 85% argon, 15% hydrogen atmosphere maintained around the sample. The solid solubility of “electrically active” copper in germanium is shown in Fig. 7.13 The maximum

8. LOW-LEVEL COHERENT~NCOHERENTDETECTION IN THE INFRARED 339 TEMPERATURE " C l

I

0.8

~

l

0.9

560

679

838 /

l

l

I0

~

l

I

l

4.1

467 (

l

l

1.2

I

l

l

~

I

\

l

1.3

iOOO/T (OK)

FIG.7. Solid solubility versus diffusion-annealing temperatures for copper in germanium as determined by the density of the 0.04 eV acceptor states. The filled circles represent the data of Fuller et a/. obtained from radiotracer experiments. (The concentration of loi6 cm13 corresponds to an atom fraction of 4.45 x The slope of the solubility curve below the eutectic point is 1.9 eV, while just above this point it is about 1.7 eV. (After Woodbury and Tyler.I3)

solubility of about 2 x 1 O I 6 atoms/cm3 occurs at a temperature of 875°C. The diffusion constant of copper for annealing temperatures in the 700900°C range is fast, about 2.8 x lo-' cm2/sec. This is to be compared to other acceptor impurities in germanium such as gallium and indium, which have diffusion constants in the lo-'' range. The crystals are maintained at the desired temperature for sufficient time to ensure uniform

I

340

R. J. KEY& AND T. M. QWST

distribution of copper, and then removed from the hot furnace and rapidly cooled (usually air quenching is adequate) to freeze in the copper concentration at 8 x 1015atoms/cm3. This is the effective upper limit of usable copper doping due to the occurrence of impurity banding effects at higher concentrations. Material is then lapped from each face to obtain the proper wafer thickness. After the wafers are sawed into 3 mm cubes and chemically etched (CP-4) two indium contacts are soldered to opposite faces of the detector. Care must be exercised when soldering the contacts to keep the temperature low and apply it for as short a period of time as possible in order to prevent the formation of large copper concentration gradients near the contacts due to Cu outdiffusion. The detectors are then cleaned and given a slight chemical etch, one contact is soldered to a copper stud, and a small lead is attached to the other contact. Referring to Fig. 8, we see that the detector when mounted in the Dewar is electrically isolated from the liquid helium heat sink by a sapphire post which is one of the few materials that is a good electrical insulator as well as a good thermal conductor at helium temperature. Electrical isolation of the detector from the Dewar is not necessary, but it allows more versatility in the selection and design of the preamp circuit. The electrical measuring circuit is shown in Fig. 9. A low noise field effect transistor operated as a self-biased source follower is used to transform the high load impedance R , (in some cases 30 megohms) to a more workable

600° C B E SOURCE \

~~

CHOPPER

FIG.8. Physical arrangement for the low background measurement of Cu-Ge photoconductorsat liquid helium temperatures and for the 8-12 p region.

8. LOW-LEVEL COHERENT/INCOHERENTDETECTION IN THE INFRARED 341 LIO He TEMP

LlO N p TEMP

ANALYZER

-

FIG.9. The electrical circuit for the measurement of responsivity and low noise.

value in the kilohm range (15 kilohms). The voltage gain of the source follower circuit is 0.9. The metal film load resistor R, is attached to the helium block to reduce its thermal noise power, while the silicon FET is located on the liquid nitrogen shield to ensure negligible gate current. The dc current through the detector is measured as the voltage across Rc, also located on the helium block. This resistor is located on the helium block for convenience only. Since its resistance is small by comparison to the load resistor, its Johnson noise contribution is negligible even at room temperature. This circuit arrangement permits the measurement of very small noise voltages. For our measurements the limiting noise was the thermal noise of the load resistor R , located at liquid helium temperature. A 600°C blackbody source chopped at various frequencies less than 1OOOHz was used to obtain the detector responsivity. A battery source is used to adjust the bias (positive or negative) of the detector and a high impedance microvoltmeter is employed to measure the voltage across Rc, which is a measure of the dc current through the detector. A low noise preamplifier, used to amplify the output signal from the source follower, is fed to an oscilloscope for measuring the signal voltage and to a wave analyzer which measures the output noise from the detector in a 10-Hz bandwidth, Radiation falling on the detector was limited to the 8-12p wavelength region. Figure 10 is a typical responsivity-electric field (9versus E ) curve for incident radiation in the 8-12p region. The responsivity W is defined as the response per unit of incident radiation. For photoconductors W is usually given in amperes or volts per watt. The responsivity factor used here

342

R. J. KEYES AND T. M. QUIST

c

PI

2 U

5-

0

I00

50

150

E (Volt-cm-‘1

FIG.10. Responsivity versus electric field for the 8-12 /.t region. This curve is symmetrical about the origin, i.e., - E gives the same response as + E. The detector was a 3 mm cube with net donor impurity concentration N D e 7.4 x 10” and Cu concentration of 8 x 1015atoms/cm’.

expresses the detector signal current in amperes (constant detector voltage) as a function of incident power (watts). We feel that the response given as amperes per watt is more closely related to the fundamental photoconductor parameters, namely, W (A/W) = qG(e/hv) = qEpTe/lhv for photoconductors. Within experimental error the responsivity was found to be the same for all values of background and signal intensities measured, and the shape was symmetrical about the origin, i.e., for either polarity of applied voltage. The measured noise equivalent power (NEP) for a 1 Hz bandwidth as a W and about lo-“ W function of background power between 3 x is plotted as a dashed line in Fig. 11. The noise voltage was measured at frequencies of about 300Hz. The theoretical NEP for BLIP detection is the solid line in the same figure; here we have calculated the NEP for BLIP detection to be

NEP

=

~(PJwB/~)”~,

(23)

where Pb is the power incident on the detector, which was deduced from the dc current and the measured responsivity. hv is the average photon energy between 8 and 12 p, B, the electrical bandwidth, is 1 Hz,and q x 0.52 is the quantum efficiency, which includes reflection losses as well as that due to the absorption of the material. The absorption coefficient of 4 cm- for this detector material over the wavelength of interest (8-12 p) was deduced by inserting a 3 mm cube of detector material directly behind the limiting aperture and measuring its transmission at liquid-helium temperature.

8. LOW-LEVEL

COHERENT/INCOHERENT DETECTION IN THE INFRARED

343

P, (Watts)

FIG.11. NEP as a function of background power for the 8- 12 I( region. The solid line is the theoretical limit for BLIP detection and the dashed curve represents the measured values for Cu-Ge.

This absorption coefficient of 4cm-' is in good agreement with that given by Bebb and Chapman,I4 who have reported absorption coefficient data and theory for copper impurity concentrations of 7 x l O I 5 ~ m - A~ com. parison of the experimental and theoretical background-limited curves shows that these detectors exhibit very little extraneous noise for backgrounds as low as about lo-" W or 5 x lo8 photons/sec in the 8-12 p region. Thus any noise contributed by contacts, surface, or other detector parameters is small in comparison to the generation-recombination noise induced by the low background level. This noise equivalent power of 10- W corresponds to an equivalent background temperature of 49"K, but is still about four orders of magnitude above the theoretical minimum detectable signal level of Eq. (8). Extension of noise measurements to lower background levels than shown in Fig. 11 is primarily a problem in decreasing the thermal noise of the load resistor R, or increasing the internal gain of the photoconductor so that the l4

H. B. Bebb and R. A. Chapman, J . Phys. Chum. Solids 28,2087 (1967).

344

R. J. KEYES AND T. M. QUIST

background-induced noise current is dominant. Mathematically, this condition can be expressed in the form ib2 > i&. For the above condition the noise due to the cavity (iza,) and the thermal generation-recombination noise (ii-,) are negligible (KBvnear 4°K). Thus i:h = 4kTLB/R, from Eq. (18b). Multiplying Eq. (23) by the responsivity 2 and squaring gives

Substituting and solving for Pb gives

Pb > kT,hv12/qR,e2E2~Lp2.rp2 as p h + 0. Increasing the load resistance has the additional disadvantage of raising the RC time constant and hence lowering the frequency response of the system. Although it would be desirable to increase the lifetime of the free holes, there seems little hope of significantly raising it beyond the value of 3 x sec which was available in our measurements. At a given temperature below 15°K the hole lifetime can be expressed in terms of the free-hole velocity u p , its capture cross section o p ,and the density of donors N , , i.e.

zp = l/v,a,N,.

(25)

At liquid-helium temperatures T~ z 3 x lO-'sec, corresponding to an ND = 7 x 10" ~ r n - A ~ . significant decrease of N D below this value is beyond present germanium purification techniques. The only parameter of Eq. (22) which is readily adjustable to produce higher gain is the dimension of the detector ( I ) in the direction of the applied electric field. Even with the most advantageous adjustment of the copper doped germanium parameters and load resistance it does not seem plausible that a measured NEP will yield the theoretical minimum of 2hvB. To further investigate responsivity versus temperature, other detectors with higher donor concentrations were checked. Figure 12 is a plot of the normalized photoresponse versus reciprocal temperature for three detectors ~ m - ~ but ), each containing the same copper concentration (-7 x having different donor concentrations (NDNN 7.4 x lo", 1015). AS expected, the relative magnitude of the response is proportional to the reciprocal of the donor densities. There exist two distinctly different slopes for each curve. At low temperatures the slope increases as the donor concentration decreases [slope increases as ( N A - ND)/N,] and when the donor concentration approaches loi5cm-3 the slope approaches zero in this region. For higher temperatures the responsivity increases sharply, as

8. LOW-LEVEL COHERENT~INCOHERENTDETECTION IN THE INFRARED 345 T (OK) 20

15

8

10

0 05

0.10

i/T

7

5

6

0.45

0.20

( O K )

FIG.12. Normalized photoresponse versus l/T for three detectors, each containing the same Cu concentration, but possessing different donor concentrations. The relative magnitude of the response is proportional to the reciprocal of the donor densities.

expected, at about the temperature where thermal generation of free holes begins. The slope of all the curves in this region corresponds to the activation energy of the 0.04 eV copper level. It is felt that the latter increase is due to the increase in z p caused by thermal reemission of the hole captured in an excited state of the neutral copper atom, prior to complete recombination to the ground state. It should be pointed out that responsivity measurements embrace a number of parameters ,up, z p , and u p , all of which can be temperature dependent. Until either the mobility or the lifetime are independently measured as a function of T, one cannot uniquely define the mechanism of the observed responsivity vs temperature data. However, the lack of temperature dependence for highly-compensated crystals is of significance to heterodyne operation, when large amounts of local oscillator power are dissipated in Ge :Cu sensors. The Bat response should permit considerable temperature rise without significantly changing the sensitivity, III. Low-Level Coherent Radiation Detection 5 . HETERODYNE DETECTION

AND

FREQUENCY RESPONSE

The rapid development of single mode, single frequency CO, lasers of high stability and power output has given great impetus to the search for

346

R . J . KEYES AND T. M. QUIST

the ideal heterodyne detector in the middle infrared. The marriage of the COz laser and the heterodyne receiver promises exciting opportunities in the fields of radar,’ communication,’6 and spectro~copy.~’ Heterodyne techniques have been well established in the radio and microwave regions of the electromagnetic spectrum. Over the past decade sensors have been proposed and produced for the optical,’”24 near-IR,2“28 and middle1R29-3’regions, and almost ideal heterodyne receivers using Ge :Cu have been developed for the spectral range of 2-29 p.29In Chapter 9 Teich presents some of lhe more elegant basics of heterodyne detection ; Arams ut al. in Chapter 10 elaborate on the specific problem associated with high frequency operation, and on its application to communications. Again this section approaches the problem of low level coherent detection from a more pragmatic point of view ; emphasizing by example what has been achieved, what the problems are, and what seem to be the greener pastures for the further development of heterodyne devices. By necessity, overlapping areas will be covered by the authors with the certainty that disagreement will result. It is the hope that these differences of opinion will be the most important part of the text. As an appetizer to the main course of heterodyne detectors, it is customary to serve the basic equations which describe the mixing of two parallel electromagnetic waves in the sensor medium. Is

H.A. Bostlck, IEEE J . Quunlum Elwrron. 3, 232 (1967). M. Ross, “Laser Receivers,” pp. 115-118. Wiley, New York, 1966.

K. H. Kingston, Private Communication. A. T. Forrester, J . Opt. Suc. Am. 51, 253 (1961). I ” A E. Sicgman. S E. Harris, and B. J. McMurtry. in “Optical Mascr” (J. Fox, cd.), pp. 5 11-527. Wilcy, New York, 1963. 2 o S. Jacobs, Electronics 36, 29 (1963). 2 1 M . E. Lasscr. Spectrum 3. 73 (1966). 2 2 S. Jacobs and P. Rahinowitz, in “Quantum Electronics 111’’ (P. Grivet and N. Bloembergen, cds.), pp. 481-487. Columbia IJniv. Press, New York, 1963. z3 I,. Mandel. .I. Opt. Soc. Am. 56, 1200 (1966). 2 4 A. E. Siegman, S. E. Harris. and R. .1. McMurtry, in “Quantum Electronics 111” (P. Grivet and N. Bloembergen, eds.), pp. 1651-1658. Columbia Univ. Press, New York, 1964. ” M. I)iIlomenico, Jr.. R. H. Pantell. 0. Svclto, and J . N. Weaver, A p p l . Phys. I d l e r s 1, 77 ( I 962). G . Lucovsky, M. E. Lasser, and R. B. Ernrnons, Proc. I E E E 51, 166 (1963). G. Lucovsky, R. B. Emmons, B. Harned. and J. K. Powers, in ‘Quantum Electronics 111” (P. Grivet and N. Bloembergen, edh.), pp. 1731-1738. Columbia Univ. Press, New York. 1964. ” R. H. Pantell, M. DiIIomenico, Jr., 0. Svelto. and J. N. Weaver, in “Quantum Electronics 111” (P, Grivet and N. Rlnemhergen. eds.), pp, 181 I 1818. Columbia Univ. Press, New York. 1964. 29 M. C. Teich, R. J. Keyes, and R. H. Kingston, Appl. Phys. Letters 9, 357 (1966). 30 C. J. Buczek and C . S. Picus, Appl. Pkys. Letters 11, 125 (1967). F. Arams, E. Sard. B. Peyton, and F. Pace, l E E E J . Quantutn Electron. 3, 484 (1967). I’

’‘ ’’

’’

8. LOW-LEVEL COHERENT/INCOHERENT DETECTION IN THE INFRARED 347 Consider two parallel electromagnetic waves of the same polarization incident on a detector (Fig. 13), a local oscillator wave of frequencyf,, and a signal wave of frequencyf,. If the detector has a linear relationship between response and flux density (photons/sec) of the individual waves, then the two waves will induce a response in the sensor at the difference frequency IfLo - f,l. In theory, the detector can produce outputs at fLo, L , and (fLo + f,), but for all practical purposes, frequencies of these magnitudes are beyond the speed of response of heterodyne receivers. Therefore we shall only consider the difference frequency, which is commonly referred to as the IF frequency in the radio and microwave fields. It has been shown3’ that a perfect heterodyne sensor, which has an average current ,i induced by a local oscillator beam of power P,,, and a corresponding signal current I , induced by a signal power P,, will yield an average current at the difference frequency of the form itF = 2iL0is = [2q2G2e2/(hv)’]PL,P,,

(26)

where q is the external quantum efficiency and G is the gain described in Part 11. It should be noted that in the incoherent detection process the signal current is proportional to the incident signal power ; in heterodyne detection the IF current is proportional to the square root of the signal power. The noise encountered in heterodyne detection is basically the same as that experienced in incoherent systems. Many possible sources of noise exist, but we shall consider only two which are either impossible or tenacious to overcome : (1) generation-recombination noise induced by the local oscillator flux, and (2) the thermal noise associated with the preamplifier loadresistor ensemble. With these restrictions the total mean-squared noise current in terms of measurable parameters can be written as :i

‘

~

PLoB

= 4e2G2q-

:

-

hv

+ -.4kTLB RL

~

-

~

-

FIG.13. Schematic representation of the heterodyne detection circuit. 32

A. E. Siegman, Proc. ZEEE 54, 1350 (1966).

Filters

~

348

R. J. KEYES AND T. M. QUIST

Equation (27) ignores background induced g-r noise because in practice it can always be made much smaller than that introduced by PLo. If it is assumed for thc moment that a nearly perfect amplifier exists and hence the second term on the right of Eq. (27) is small, then by setting i,2 =,:i and solving for P, we obtain the familiar theoretical power detection limit for heterodyne receivers,

Prin= 2hvB/q

photoconductor

(28)

PT"

photoemitter or reverse p-n junction.

(29)

=

hvB/q

At the heterodyne detection limit very small signals are measurable. For example, using a usual bandwidth of 1 Hz and a quantum efficiency of unity the minimum detectable signal (SIN = 1) at 10 p is 2.9 x 10-20W p.c. and 1.45 x 10-" W p.e., which corresponds to one photon per cycle of (IF) bandwidth. It follows from Eq. (28)that the theoretical power detection Iimit improves as the wavelength increases. The results obtained by Teich et on copper-doped germanium are shown in Fig. 14, from which it is obvious that Ge : Cu photoconductors do behave according to theory [Eq. (28)], and yield detectabilities which are much greater than can ever be achieved in the

I0

Ge: Cu DETECTOR '05- HETERODYNE FREQUENCY: 7 0 k H z

a

a ro4-

- 50 - 40

a

%

x

--

-m

U 30 v

a

w Y

20

w

z >-

- 10

0 0

2n


n w Iw

-0

I -

I

I

/

1o-f5 10-44

I

d '

40-43

10-!2

Ps

(o-fl

40-10 40-9

1

-io

(0-8

(Waits)

FIG. 14. The data points, obtained from a typical run, represent the observed signal-to-noise ratio of the heterodyne signal in Ge:Cu. The relation (S/N),,,,, = yPJ2hv Afis in good agreement with data points. (After Teich et d'')

8. LOW-LEVEL COHERENT/INCOHERENTDETECTION IN

THE INFRARED

349

visible region of the spectrum. These experiments were conducted under favorable conditions of low IF frequencies and bandwidths, where the noise contribution of the preamplifier is insignificant. However, for many applications (radar, spectroscopy, and communications) high frequencies and bandwidths are desirable. Under these more adverse conditions the problem of preamplifier load noise becomes more difficult to overcome when the theoretical limit of detectivity is also required. In theory, as indicated by Eq. (27), one needs only to increase the local oscillator power level until its noise contribution overwhelms that from all other sources. By equating the g-r noise introduced by the LO flux to the load amplifier noise and solving for the LO power we obtain PLo> kT,hv/e2G2qRL,

which is the local oscillator power required for the g-r noise to dominate the load amplifier noise. Here T, is the effective noise temperature of the amplifier. It is more instructive to express the gain G in terms of the photoconductor parameters [Eq. (22)], so that Eq. (30) becomes PLo> kT,hv12/e2E2p2T2qRL.

(31)

In order to maintain a flat IF frequency response to some maximum frequencyf,, the lifetime of the excited carriers should be short so that z ,< l/2.nfm is satisfied. In addition, the load resistance should approximate 1/2.nfmC in order to maximize the power transfer and retain flat frequency response to f,, where C represents the effective input capacitance arising from the various circuit elements such as detector, load, and leads. Incorporating these restrictions into Eq. (31), we have

PLo > 8n3kT,hv12fm3C/e2E2p2q.

(32)

Although the above expression contains many parameters which are unique to the specific sensor-amplifier circuit employed, some general statements can be made when the theoretical limit is demanded at high frequencies: The local oscillator power required increases as the cube of the maximum frequency response and as the square of the detector dimension in the direction of the applied field. The PLo required is linearly dependent on the effectivenoise temperature of the preamp and the capacitance of the amplifier input circuitry when it is much larger than the capacitance of the sensing element. This is almost always true for photoconductor detectors, but is rarely true for p-n junction devices. Various workers have reported high frequency operation and noise characteri~tics~l of Ge: Cu used in heterodyne operation. As of this writing the combination of GHz response and theoretical detectivity has been

350

R. J . KEYES AND T. M. QUIST

inferred, but has not been simultaneously achieved. Ge :Cu promises to satisfy both conditions. The problem and techniques are examined below. 6. Ge:Cu AS A THEORETICALLY PERFECTCOHERENT DETECTOR AT GHz FREQUENCIES

The choice of the best germanium crystal from which ideal heterodyne Ge : Cu detectors are to be fabricated is dictated by the maximum desired frequency responsef,. As stated in the previous section the lifetime of an excited hole should satisfy the condition z x 1/2nf,. As pointed out in the section concerning the fabrication of incoherent detectors, T,, is controllable over wide limits by selecting host crystals with the proper donor concentration. Figure 15 is a plot of the maximumjut frequency response as a function of host donor density. Although it is possible to obtain donor concentra-

FIG.15. Maximum pat frequency responseji of Ge:Cu at 4°K as a function of donor concentration ND.Copper density is equal to 1016crn-’. Relative absorption coefficient GI is given as a function of N , for Cuo = ~ 1 1 1 ~ ~ .

8. LOW-LEVEL COHERENT/INCOHERENT

DETECTION IN THE INFRARED

351

tions in excess of 1 O I 8 cmP3, it is self-defeating to approach closely the maximum copper solubility of 1 O I 6 cmV3.The reason for this is illustrated in Fig. 15. Although the frequency response is proportional to the donor concentration ND, as this concentration approaches the density of copper atoms the number of neutral Cuo sites available for the absorption of photons approaches zero, with the result that the quantum efficiency also approaches zero. Techniques to be described later can help to nullify the loss in photon absorption when donor concentrations approach the maximum solubility of copper ; nevertheless a practical upper limit of frequency response for Ge :Cu seems to be in the vicinity of 10" Hz. Once the upper desired frequency is established a uniformly-doped crystal of the proper donor concentration is indiffused with copper by the procedures described in Part 11. The copper diffusion and detector fabrication procedures for heterodyne sensors are similar to those described for the usual incoherent detectors. In the fabrication of high frequency mixers three controllable factors are of prime concern.

-

1. The dimensions of the detector are important (Fig. 16). The distance between electrodes should be kept as small as possible in order to obtain maximum gain and thus impose the smallest demand on local oscillator power as expressed by Eq. (32). The length of the crystal in the direction of the incident power must be such that most of the incident radiation is absorbed. An antireflection coating on the incident face and a reflecting evaporated metal film, insulated by a ZnS layer on the exit face, can yield a quantum efficiency of approximately unity for t z 2 rnm. The width of the detector w, again consistent with operational requirements, should be kept small to ensure minimum cell capacitance.

/x

Heat Sink

FIG.16. Sketch ofGe:Cu heterodyne detector with coatings to improve its quantum efficiency. The nomenclature of the detector dimensions relative to the direction of the impinging radiation and applied electric field is applicable to all equations in this chapter.

352

R. J. KEYES AND T. M. QUIST

2. Effective heat sinking of the detector to the liquid helium bath is critical because of the large local oscillator power which must be dissipated when operating at high frequencies. The total power which must be dissipated into the bath consists mainly of the absorbed PLoplus the I Z R loss, i.e., power dissipated

=

PLo( 1+

Gg)

=

PLO(1 +

")

27Efmhv

.

(33)

To ensure the best possible heat transfer from the detector to the coolant, the entire detector face should be thermally bonded to a large oxygen-free copper base or other high thermal conductivity material with a thin layer of pure, low-melting metal such as indium. Clean, flat contact faces between the mounting studs and heat sink help to eliminate temperature differentials across these boundaries. In the case of liquid helium coolant the interface between the main heat sink and the liquid has a rather large thermal resistance at high power levels, and hence this area should be made as large as possible.

I

I

103

102

I

16'

I oo

Power ( W l

FIG.17. The theoretical local oscillator power PLorequired at 10.6 p to achieve ideal heterodyne detection in Ge:Cu at 4.2"K is given as a function of the maximum IF frequency (f,,): also given is the theoretical power Pddissipated in the detector versusf,, where Pd = PLo+ 1'R. These calculations assume E = 200 V/cm, T, = 600°K. 1 = 0.05 cm, 7 = 1.

8. LOW-LEVEL COHERENT~INCOHERENTDETECTIONIN THE INFRARED 353 3. The stray inductance and capacitance of the detector leads must be reduced to a level that will permit high frequency circuit response.31

Figure 1 7 is a plot of the local oscillator power PLoand the total power Pd dissipated in a Ge :Cu detector as a function of maximum IF operation frequency with the condition that the photon-induced LO noise current equal the current noise of the load-amplifier complex. In making these calculations the following parameters were assumed : E = 200 V/cm, hv = 0.124 eV, T, = 600"K, C = 2 pF, and 1 = 0.05 cm. Up to 1 GHz IF the power dissipated in the sensor is less than 1 W. At this power level the thermal conductivity of germanium is sufficient to prevent temperature rises of more than a degree, but great care must be taken so that the boundary thermal barriers between the various heat-sink components and bath are sufficiently low to handle the 1 W thermal power flow. Pressure contact between clean, flat copper surfaces yields very low thermal barriers. The liquid-helium heat-sink surface area should be at least 10cm2/W of dissipated power33 in order to prevent the formation of an insulating helium gas boundary layer. The spectral peak of our environmental radiation, a good atmospheric window, and the development of high power C O , lasers tend to draw attention to detection capabilities of Ge :Cu in the region of 10 p, but it should be borne in mind that this material is capable of high performance out to 3 0 p . It has been shown that copper-doped germanium and perhaps a host of other impurity photoconductors can achieve the infrared heterodyne detection limit up to mixing frequencies of 1 G H z . ~ Because ~' of the temperature dependence of hole lifetime, Ge :Cu even with the highest possible counterdoping is not capable of retaining a flat frequency response out to 1 GHz above 20°K. If some technique were available to reduce the hole lifetime, then the ideal high frequency heterodyne detection limit might be possible up to 40°K with this material.

7. DISCUSSION Heterodyne receivers exist for the spectral region beyond l o p which perform according to the limits prescribed by theory and are able to maintain this performance out to very high IF at low temperatures. Future developments in the area of coherent infrared detection will most likely follow the rather practical path of raising the operational temperature of these devices. Private communication with H. Kolm, MIT Francis Bitter Nat. Magnet Lab., Cambridge, Massachusetts. have measured the beat frequency of Ge:Cu between a PbSnTe 33"Recently(Hinkley et laser and a C 0 2 laser out to frequencies of 3 GHz. 34 E. D. Hinkley, T. C. Harman, and C. Freed, Appl. Phys. Letters 13,49 (1968). 33

354

R. J . KEYES AND T. M. QUIST

A priovi there is no fundamental law which precludes perfect heterodyne reception at high temperatures, 300°K included. A case in point is that very effective heterodyne receivers are used for radio wavelengths at room temperature. The conditions that must be satisfied in order to achieve ideal GHz detectivity at high operational temperature are : 1. The generation-recombination noise current produced by the incident local oscillator power must exceed the sum of all other noise currents. 2 . The lifetime or transit time of the excited carriers must be short enough to realize flat high frequency response out to the GHz region. 3. The heating produced by the LO must not appreciably raise the detector temperature. 4. The device must have enough gain to overcome load-amplifier noise.

In the search for materials to be utilized as ideal high frequency heterodyne sensors at elevated temperature both back-biased p-n junctions as well as photoconductors should be considered. In spite of the fact that GHz mixing has been observed by DiDomenico et al. in p-n junctions in the near1R and predicted by Lucovsky er al. out to 5 p in InSb diodes, it is difficult to imagine how a flat GHz response can be obtained in the l o p region with p-n junctions of convenient areas. The authors’ pessimism stems from the fact that the materials suitable for p n junction fabrication (PbSnTe) have very high (low frequency) dielectric constants-in the range of 400 for PbSnTe and 16 for HgCdTe. GHz response is only possible by reducing C , i.e., by making devices of very small area. Operationally, when performance approaching the theoretical limit is demanded, diodes have the distinct advantage of requiring less LO power, However, at the present state of the art p-rt junctions are less palatable than photoconductors because the small dimensions required for high frequency response create a geometric problem of keeping the signal and LO radiations on the sensitive area. In addition, the diodes produced to date for the 10 p region exhibit low impedance levels of a few ohms, which makes broadband-high gain coupling to the preamplifier difficult. The most formidable problem to overcome in the utilization of photoconductors for GHz operation at elevated temperatures is to reduce the thermal generation rate of carriers to a level that can be exceeded by a reasonable local oscillator power. The local oscillator power required so that its generation-recombination noise be equal to the thermal noise currents is :

8. LOW-LEVEL

COHERENT~NCOHERENTDETECTION IN THE INFRARED

355

An analysis of Eq. (34) in terms of the photoconductive parameters of PbSnTe suggests that thin films (1 p ) of this material at 150°K could perform as ideal heterodyne receivers for CO, laser radiation at frequencies up to 1 GHz. This same material at room temperature is capable of a flat frequency response out to approximately 20 MHz. Although the latter I F frequency is comparatively low, it is adequate for many device applications. Needless t o say, room temperature operation of both transmitter and receiver would go a long way toward the implementation of infrared heterodyne techniques for nonlaboratory environments. HgCdTe, in spite of its present homogeneity difficulties, is a promising photoconductive material for the extension of GHz response at room temperature. Its main advantage over PbSnTe at 300°K arises primarily from its smaller dielectric constant, smaller electron effective mass, and its orderof-magnitude higher electron mobility at room temperature.

ACKNOWLEDGMENTS The authors are indebted to J. 0.Dimmock for his comments on the text and to R. H. Kingston for many valuable discussions of heterodyne detection. The work reported in this chapter was sponsored by the Department of the Air Force.

Appendix. Thermal Generation-Recombination Noise in Photoconductors

Thermal generation-recombination noise is very similar to photoninduced g-r noise as described in the text. The major difference is that the fluctuations in the rate of generation of free charge carriers have their genesis in lattice phonons rather than a photon stream. Since the expected rate of thermal ionization (and hence its variation) is intimately related to the energy level structure, effective mass, impurity content, volume, and temperature of the crystal, it requires a detailed knowledge of these specific detector parameters in order to calculate quantitatively the thermal g-r noise. As in the case of photon induced g-r noise, the rate of recombination is equal to the rate of generation at equilibrium, and hence the fluctuation in the average free carrier density is mathematically equivalent to multiplying the average generation rate by a factor of two. It should be pointed out, however, that this equality is not strictly true when the measuring interval (l/w) is short compared to the free carrier lifetime z. In this situation the recombination noise term “rolls off” with the characteristic form 1/(1 + ozz2). For all the situations considered in this chapter oz < 1, and hence 1/(1 + w’z’) -, 1. The fluctuations in the density of free carriers for intrinsic and impurity semiconductors have been elegantly derived by Burgess3 from both thermo35

R. E. Burgess, Proc. Phys. SOC.(London) 68B, 661 (1955).

356

R. J . KEYES AND T. M . QUIST

dynamic and purely statistical arguments. Burgess shows that in n-type semiconductors, in which a majority of the donor atoms are ionized, the fluctuation in the free-hole density is far greater than the fluctuation in the majority-carrier density. Long8 has incorporated this fact in the calculation of D,* for HgCdTe sensors. We shall derive the g-r noise currents beginning with the fluctuation of the thermal generation-recombination rate and ending with equations which contain all the pertinent semiconductor parameters. In nondegenerate semiconductors at thermal equilibrium the thermal free-electron and free-hole densities can be expressed in terms of the thermal generation rates (gp,g,) and their corresponding lifetimes (t,,t,,): gp7p =

~(lwt),

Rnrn =

n(lwt),

(‘41)

where p and n refer to the free-hole and free-electron concentrations, respectively, of a crystal of dimensions Iwt. The variance in the generation rate of holes ( j Pis) (g,) = (gp/At)”2 = (2g,BPZ

7

(‘42)

where At is the time interval over which the measurement is performed and = 2/At is the equivalent electrical bandwidth of the measurement. Since the recombination rate and its fluctuation are equal to the generation rate and its fluctuation one can write the total rate of fluctuation of holes (gJpas

B

(EJP

= 42[gp

+ r p ] B ) ” 2 = 2(g,B)”2.

(‘431

The g-r noise current due to @JP is @Jp multiplied by the product of the photoconductive gain G,, and the free carrier charge e is

or

(iipr)p = 4G,’e2gpB.

I f both electrons and holes contribute to the conduction process, then the total rms noise current becomes

+

ii-r = 4e2B(GPZg, Gn2.gn),

(A51

where the subscripts refer to holes and electrons. Incorporating Eq. (A 1) into Eq. (A5) and expressing the photoconductive gain in terms of its crystal parameters, one obtains i:pr

=

+

( 4 e 2 B E 2 w t / l ) [ p p z ~ , pp n 2 t , n ] .

(A61

Unfortunately, all the terms within the brackets exhibit a temperature dependence to some degree in most photoconductive materials. The temperature dependences of mobility and lifetime are seldom completely known,

8. LOW-LEVEL

COHERENT~NCOHERENTDETECTION IN THE INFRARED

357

but their variation is relatively small in comparison to the free-electron and free-hole temperature variation. For the sake of simplicity we shall not incorporate the p and z temperature dependences in our equations, but one should keep this fact in mind when the temperature dependence of these terms is large. The temperature dependence of Eq. (A6) will be evaluated for three specific cases which cover the vast majority of photoconductive materials : (1) Impurity photoconductors in which only one carrier is important to the electrical conductivity; Ge:Hg is an example of this case. ( 2 ) Intrinsic photoconductors where n x p, z p x z,, and ,up x p,; very pure PbSnTe is in this category. (3) Intrinsic photoconductors in which the major impurity (donors or acceptors) are nearly fully ionized at all temperatures of interest and pp % p,, z p x z,; PbSnTe with donor impurities (10’4-1016) is representative of this case. At high temperatures when the intrinsic carrier density exceeds the impurity concentration Case ( 3 ) approaches Case (2). Case 1

The dominant impurity, such as Hg acceptors in germanium, controls the conductivity and the g-r noise. The effect of the electrons on the electrical conduction can be ignored, One can write the thermally ionized free-hole density as

where the newly introduced symbols of this and subsequent equations are as follows: N , is the valence band density of states, N , is the conduction band density of states, NAis the acceptor density, ND is the donor density, ni is the intrinsic free-carrier density, m,* is the effective mass of the holes in the valence band, m,* is the effective mass of the electrons in the conduction band, k is Boltzmann’s constant, h is Planck’s constant, E, = hc/& is the ionization energy of the donor impurity (Case 1)’ E , = hc/& is the energy separation of the valence and conduction band (Case 2), T,,, is the temperature of the detector and cavity, and p is the ground state degeneracy factor of the acceptor impurity. Substituting Eq. (A7) in Eq. (A6) yields

358

R. J. KEYES AND T. M. QlJlST

The reader will recognize this to be identical to Eq. (16c) of the text when the gain and area terms of the latter are fully written out. Case 2

For the intrinsic photoconductor where n = p = ni, p p = pn,and we may write

n

tp = z,

+ p = 2ni = 2(N,N,)1'2exp( -Eg/2kT,,,) = 4(

2zkT,,,

'I2

7) ( ~ n , * r n , * exp( ) ~ ~ ~- E$2kT,,,),

(A9)

which when substituted in Eq. fA6) yields the g-r noise current

ii-r =

(mv*m,*)314exp(- Eg/2kT,,,).

1

(A10)

Case 3

In intrinsic photoconductors of relatively high impurity content the electrical conductivity is controlled by the density of ionized impurities, but the noise current is primarily due to the fluctuation in the minority-carrier density. Consider an n-type semiconductor with a donor density no, where no 9 p over all temperatures of interest. One can express the minoritycarrier density p as P

ni2

c N-v- exp( - EJkT,,,) = --= -N -

no

no

and

- 1 6r2BE2wtpP2t, --(m,*n~,*)~/'(T 2nkT,,, -3) exp(-E,/kT,,,).

$-r

-

(A121

nol

The above equations suggest that in intrinsic photoconductors the thermal g-r noise can be substantially reduced by the addition of low ionization energy impurities. When one analyzes the gross effect of this reduction on sensor detectivity it loses much of its impact. At low temperatures the introduction of free carriers which do not freeze out adds Johnson noise to the system. At high temperatures, where thermal generation across the forbidden gap begins to introduce intrinsic carrier densities that are compa-

8. LOW-LEVEL COHERENT/INCOHERENT DETECTION IN

THE INFRARED

359

rable to the impurity density, the noise equations become nearly identical for doped and for pure materials. These factors are apparent in Fig. 5, where the DA* values for two different impurity contents of PbSnTe can be directly compared.

This Page Intentionally Left Blank

CHAPTER 9

Coherent Detection in the Infrared* M . C.Teich

I. INTRODUCTION.

.

. .

.

.

. . .

.

.

. . . . . .

.

11. QUANTUM THEORY OF INFRARED COHERENT DETECTION. 1. Optical and Infrared Frequencies . . . . . . 2 . Signal-to-Noise Rario . . . . . . . . . 111. MEASUREMENT OF THE SIGNAL-TO-NOISE RATIO . . . 3. Experimental Arrangemen t . . . . . . . . 4. Experiments with Photoconductive Ge :Cu . . . 5. Experiments with Photovoltaic Pb, -,Sn,Se . . .

. . . . . . .. . . . Iv. DETECTIONFROMA MOVINGDIFFUSE REFLECTOR . . . . . 6 . Experimental Arrangement . . . . . . . . . . 7. Power-Spectral-Density ofthe Heterodyne Signal . . . 8. Probability Density o f t h e Signal Envelope . . . . . V. AN INFRARED LASERRADAR. . . . . . . . . . . 9. Doppfer Radar Configuration . . . . . . . . . 10. Radar Resuits . . . . . . . . . . . . . VI.

VII.

PHOTOCONDUCTORS AND PHOTODIODES IN THE INFRARED :A COMPARISON . . . . . . . . . . . . . 11. Signal-to-Noise Ratio . . , . . , . . , 12. Frequency Responxe . , . . . . . , . . 13. Device Responsivity . . . . . . . . . , 14. Temperature of Operation . . . . . . . . CONCLUSION . . . . . . . . . . . , .

.

.

.

,

. . . . . . . .

.

. . . . . . . . . . . . . .

.

.

.

. . . .

36 I 365 366

372 375 375 378 383 389 39 1 391 396 400 400 400

. . 403 . . 403 . . . . 404 . . . . 405 . , . . 405 . , . . 406

I. Introduction Coherent (heterodyne) detection is well known in the radio wave, microwave, and optical 1-6 regions of the electromagnetic spectrum. Recently the * This work was supported in part by the National Science Foundation.

’ A. T. Forrester, R. A. Gudmundsen, and P. 0.Johnson, Phys. Rev. 99, 1691 (1955).

A. E. Siegman, S. E. Harris, and B. J. McMurtry, in “Optical Masers” (J. Fox, ed.), p. 51 1.

’

Wiley. New York, 1963. S.Jacobs, Electronics 36 (28), 29 (1963). M. E. Lasser, Spectrum 3, 73 (1966). S. Jacobs and P. Rabinowitz, in ”Quantum Electronics JII” (P. Grivet and N. Bloembergen, eds.), p. 481. Columbia Univ. Press, New York, 1964. L. Mandel, J . Opt. SOC.Am. 56, 1200 (1966).

361

362

M. C. TEICH

technique has been extended to the middle infrared as This chapter discusses theoretical and experimental considerations related to coherent detection in the middle infrared, particularly at the 10.6 p COz laser wavelength. Coherent detection differs in several significant respects from direct detection, or simple photon counting. In particular, the increased sensitivity available through its use in the infrared allows the detection of far weaker signals than by means of any other technique. The minimum detectable power corresponding to perfect quantum counting is hv AA the detection of one photon in every detector resolution time. Here hv is the photon energy and Af is the receiver bandwidth. The perfect quantum counter will detect each individual photon provided that the inverse photon count rate is large compared to the detector resolution time. For a real photoconductive and photovoltaic coherent detector the minimum detectable power is given by (2/q)hvAL rather than hv Aj; where v is the detector quantum efficiency. Thus a minimum of 2/q photons may be detected. Using a Ge:Cu photoconductive detector as few as five photons have been detected at 10.6 p.’ A plot of the detectable number of photons vs the frequency of electromagnetic radiation from radio waves to X rays has been given by Townes’ and is shown in Fig. 1. The peak in the curve at log,, v z 13.45 (which is just v z 2.83 x IOl3 Hz for the C 0 2 laser) corresponds to the detection of very few photons in this region of the spectrum, and represents the results to be discussed in this chapter. In the submillimeter region an improvement in sensitivity with heterodyne o p e r a t i ~ n has ~ ~ been ’ ~ demonstrated for InSb, pyroelectric, and Golay cell detectors. Using techniques similar to those described in this chapter, coherent detection experiments have been previously reported in the visible and the near infrared with photoemissive device^,^.' photodiodes,2.’z and

’

M. C. Teich, Proc. l E E E 56, 37 (1968). 7aM.C. Teich, Proc. IEEE 57, 786 (1969). 7bM.C. Teich, Electron Technology (to be published). C. H. Townes. Quantum Electronics, Past and Prospects, presented at the 1968 annual meeting of the Am. Phys. SOC.,January 30, 1968. Also private communication. E. H. Putley, Proc. IEEE (Correspondence) 54, 1096 (1966). l o H. A. Gebbie, N. W. B. Stone, E. H. Putley, and N. Shaw, Nature 214, 165 (1967). A. E. Siegman, S. E. Harris, and B. J. McMurtry, in “Quantum Electronics 111” (P. Grivet and N. Bloembergen, eds.), p. 1651. Columbia Univ. Press, New York, 1964; B. J. McMurtry and A. E. Siegman, A p p l . Opt. 1, 51 (1962). l 2 G. Lucovsky, M. E. Lasser, and R. B. Emmons. Proc. IEEE 51, 166 (1963); G. Lucovsky, R. 8. Emmons, B. Harned, and J. K . Powers, in “Quantum Electronics 111” (P. Grivet and N. Bloembergen. eds.), p. 1731. Columbia Univ. Press, New York, 1964.

9.

COHERENT DETECTION IN THE INFRARED

LOG,,

363

(FREQUENCY)

FIG.1. Minimum detectable number of photons versus frequency from radio waves to X rays. The peak at log,, I’ = 13.45 corresponds to optimum heterodyne detection at the C 0 2 laser wavelength. (After Townes.’)

photoconductors.5~1 3 , 1 4 The use of an InAs diode has permitted heterodyne measurements to be extended to 3.5 p.15 For frequencies 2-10’6.Hz the large energy per photon makes it relatively easy to detect individual photons, so that the heterodyne technique is not particularly useful. The configuration for a generalized heterodyne receiver in the optical or infrared is shown in Fig. 2. Its operation is made possible by the “nonlinear” response of the photodetector to the incident total radiation electric field. Two electromagnetic waves of different frequencies (wl and 02) mix at the photodevice and produce an electrical signal with the difference frequency (wl - w2). When one of these beams is made to be strong (if it is locally produced, it is then called the local oscillator or LO), the sensitivity for the process is considerably increased over the straight detection (video) case because of the high conversion gain between power at the input and at the difference frequencies.2 In addition to this high conversion gain, the l3

l4

M. DiDomenico, Jr.. R. H. Pantell, 0. Svelto, and J. N. Weaver, Appl. Phys. Letters 1. 77 (1962): R. H. Pantell, M. DiDomenico, Jr., 0. Svelto, and J. N. Weaver, in “Quantum Electronics 111’’ (P. Grivet and N. Bloembergen, eds.), Columbia Univ. Press, New York, 1964: G. Lucovsky, R. F. Schwartz, and R. B. Emmons, Proc. IEEE (Correspondence) 51. 613 (1963). P. D. Coleman, R. C. Eden, and J. N. Weaver, I E E E Trans. Electron Dec. 11,488 (1964). F. E. Goodwin and M. E. Pedinoff, Appl. Phys. Letters 8, 60 ( I 966).

364

M. C . TEICH

BEAM SPLITTER

IRIS

7 *Wl+

PHOTO -

w2

cos(w, ' W 2 ) t

8

w2

I'

LOCAL

OSC I LL ATOR BEAM (L.0.)

w I

I

AMPLIFIER

p5b-l OSCILLOSCOPE

FIG. 2. The generalized infrared or optical heterodyne receiver. (After Teich.7)

heterodyne detector exhibits both strong directivity and frequency selectivity. It is the frequency selectivity of the coherent detection process which permits the noise bandwidth to be reduced to a very small value. The heterodyne detector is linear only insofar as the detector output power is proportional to the input signal radiation power. At optical and infrared frequencies the heterodyne detector acts as both an antenna and a receiver,16 and has an integrated effective aperture limited by approximately A*. Careful alignment between the LO and signal beams is necessary in order to maintain a constant phase over the surface of the photodetector. The use of coherent detection in a communications system is therefore limited by the atmospheric distortion of the wavefront, which imposes a restriction on the maximum achievable signal-to-noise ratio.' Heterodyne detection is consequently most useful for detecting weak signals which arc coherent with a locally produced source. It should be mentioned that the coherent detection technique is capable of furnishing information about the frequency spectrum of a signal beam.6 In the case where both the signal and the LO derive from the same source (such as in the experiments dcscribed in this chapter), the hetcrodyne signal can provide information about the velocity of a target through the Doppler shift. This is also possible if the LO and signal beams arise from different, but frequency locked, Heterodyne detection is also useful for heterodyne spectroscopy'.' and in the study of physical processes occurl6 "

'*

A. E. Siegman. Proc. IEEE 54. 1350 (1966). D. L.Fried, IEEE .I. Quuntum Electron. 3, 213 (1967); Proc. I E E E 55, 57 (1967). H. 2. Cumrnins, N. Knable, and Y. Yeh. Phys. Reu. l,etters 12, 150 (1964).

9.

COHERENT DETECTION IN THE INFRARED

365

ring in materials. Use of the technique has already been made in the design of a laser Doppler velocimeter, which measures localized flow velocities in gases and liquids.' 9 9 2 0 The measurements reported here have been performed at 1 0 . 6 ~in the middle infrared region. It is the availability of the high radiation power from the COz laser together with the 8-14 p atmospheric window2' which make sensitive detection at 10.6 y important for systems use. Furthermore, it is at these longer wavelengths that the higher sensitivity available from coherent detection is particularly valuable, since the user may discriminate against various noise sources including the blackbody radiation from objects at room temperature, which is appreciable at 10.6 p. In the experiments reported below a minimum detectable radiation power which is within a factor of five of the theoretical quantum limit hv Afhas been observed. Because the setup employed in these experiments detects the scattered radiation from a diffusely reflecting moving surface, it is, in effect, a miniature prototype C 0 2 laser radar. Thus, experiments on the power-spectraldensity and the envelope probability distribution of the homodyne"" signal are also discussed. Use of the technique in a full-scale CO, laser radar, which has been recently set up and operated by Bostick,22is mentioned. We begin with a discussion of the quantum theory of heterodyne detection and compare this with the classical theory. We then proceed to experimental results.

II. Quantum Theory of Infrared Coherent Detection We present here a quantum theory of coherent detection which differs from both the classical and the semiclassical treatments. The theory, which has been applied over the entire electromagnetic spectrum:' reduces to the classical result in the limit of low radiation frequencies (hv < kT) and, for a certain class of fields, to the semiclassical result for high radiation frequencies (hv $- kT). The primary distinction from the classical theory is that double-frequency and sum-frequency components do not appear in the heterodyne signal, to good approximation, when hv $- kT, which is the region of interest for the work described here. The theory is valid for fields of an arbitrary statistical nature. l9 'O

Y. Yeh and H. Z. Cummins, Appl. Phys. Letters 4, 176 (1964). J. W. Foreman, Jr., E. W. George, J. L. Jetton, R. D. Lewis, J. R. Thornton, and H. J. Watson,

IEEE J . Quantum Electron. 2, 260 (1966); R. D. Lewis, J. W. Foreman, Jr., H. J . Watson, and J. R. Thornton, Phys. Fluids 11, 433 (1968). J. C. Stephenson, W. A. Haseltine, and C. B. Moore, Appl. Phys. Letters 11, 164 (1967). *'"The terms homodyne and heterodyne are used interchangeably throughout this chapter. H. A. Bostick, IEEE J . Quantum Electron. 3, 232 (1967). 2 3 M. C. Teich, Appl. Phys. Letters 14, 201 (1969); J. Phys. Chem. Solids (to be published).

'' ''

366

M. C . TEICH

1. OPTICAL AND INFRAREDFREQUENCIES

A generalized schcmatic of the ordinary heterodyne receiver has been given in Fig. 2. Two plane parallcl electromagnetic waves of frequencies o1and w 2 impinge normally on an ideal quantum-mechanical photodetector in its ground state. The detector has an energy level structure such that there is no excited state within an energy kT of the lowest level. This is a suitable assumption for the middle infrared or optical detector. It has been shown by G l a ~ b e that r ~ ~the~ average ~ ~ count rate for such a detector at the space-time point xo = rorto may be expressed as the first-order correlation function Glt)(xo, so),where with p the density operator for thefield,z5*26 and E - and E f the negative- and positive-frequency portions of the electric field operator, respectively. The subscripts p, v label Cartesian components. Only projections of the field along a single (possibly complex) unit vector are considered, so that the correlation function above may be written as a scalar quantity rather than as a tensor. Coherent detection experiments are frequently performed using a given beam and a time-delayed form of the same beam2’ (so-called homodyne detection) so that it is more convenient to discuss field correlations relative t o the radiation source rather than to the That is, the output of a detector illuminated by a single beam is proportional t o G(’)(X’,x’), where x‘ = r, t‘. When illuminated by a phase-retarded form of the same beam the output ofthe detector at lime t’ may be written as G(”(x”,x”) where x” = r, t” and t” > t’. Thus phase retardation is equivalcnt to time displaccment at the detector, allowing for the coherence time to be considered as a parameter. For the heterodyne experiment we may simply write the total electric field operator as a superposition of the operators for the constituent waves.” Therefore the positive-frequency component of the field present at the photodetector, E + ( r ,t ) , may be written E+(r,t ) = All?@,

t,)

+ I,E+(r, t2).

(2) The complcx coefficients A, and 1, contain the relative strengths of the two waves, and are taken to be independent of the properties of the field. The R . J. Glauber, Phys. REU.130, 2529 (1963). R. J. Glauber, in “Quantum Optics and Electronics” (C. deWitt, A. Blandin. and C. CohenTannoudji, eds.), p. 65. Gordon and Breach, New York, 1965. ’’ K.J . Glauber, Phys. Ref).131,2766 (1963). ” S. Jacobs and P. Rabinowitz, in “Quantum Electronics 111” (P. Grivet and N. Bloembergen, eds.), p. 481. Columbia Univ. Press, New York, 1964. M. C. Teich and G. J. Wolga, Phys. Reo. Lefters 16, 625 (1966). 24 25

‘’

9.

COHERENT DETECTION IN THE INFRARED

367

count rate R may therefore be expressed as R = tr{pE-(r, t)E+(r,t ) ) = tr(p[A,*E-(x,)

+ Lz*E-(xz)l

where, as above, the space-time point x t = r, t , is relative to the radiation source. Using the correlation function identityz4 [G"'(x],

xZ)]*

=

G"'(x~, XI),

(4)

this rate may be written in terms of the first-order time-dependent correlation functions @')(ti, t j ) as

R

=

(A1(ZG'l'(t,, t t )

+ (Az\2G'1'(tz,t z ) + 2 Re(Al*3,zG'1'(tl,t z ) ).

(5)

The first two terms on the right represent the intensities which would be contributed by each beam independently of the other; the last term represents the interference. We have assumed that the angular alignment condition required for optimum photomixing is maintained,29so that the angle between the beams is restricted to a value smaller than A/a, where 3, is the radiation wavelength and a is the detector aperture. For this case the correlation function may be taken to vary slowly over the detector, and its spatial dependence suppressed, as above. We could, alternatively, retain the spatial dependence, in which case the condition for first-order coherence discussed in the next paragraph will automatically require the alignment condition to be fulfilled in order to obtain optimum phot0mixing.2~ If the radiation incident on the detector possesses precise first-order coherence, two interesting consequences follow. The first relates to constraints on the correlation functions,30and will provide us with the magnitude of the heterodyne signal. The second concerns the density operator for the radiation field,31and will allow a physical interpretation for the beating process. The condition for maximum fringe contrast, or first-order coherence, has been shown by Titulaer and Glauber3' to be equivalent to the factorization of the correlation function into two complex quantities €(tl) and

W z ): G"'(t1,

t z ) = &*(t,)&(t,).

(6)

With Eq. (3,under conditions of first-order coherence of the total incident radiation field,23we therefore obtain

R

=

IAIIZG(l)(tl,t t )

+ (&1zG'1)(t2,t z ) + 2 Re(ill*d*(tl)i/z&'(t2)}.

'' A. E. Siegman, Appl. Opt. 5, 1588 (1966). 30 31

U. M. Titulaer and R. J. Glauber, Phys. Rev. 140, 3676 (1965). U. M. Titulaer and R. J. Glauber, Phys. Rev. 145, 1041 (1966).

(7)

368

M. C. TEICH

We may also write Eq. (5) in the equivalent form

R

= 1A112G(1)(tl,t l )

+ 11212G(1)(t2,

+ 211111121 IG(”(t1

Y

t2)

t2)l C O S l M l Y t 2 )

+ @S

(8)

9

where q5(tl, t,) is a time-varying function derived from G(’)(tl, t,). The phase angle 8 depends on the geometry of the experiment. While the first-order coherence condition has been used in obtaining Eq. (7), this is not so for the result in Eq. (8). Using the correlation function equality30 for first-order coherent fields, lG(l)(xl, x ~ ) I = [G‘”(x,, X ~ ) G ‘ ’ ) ( Xx~,,) ] ~ ’ ~ ,

(9)

we obtain yet another expression for R,

R

= ( A 1 ( 2 G ( 1 ) (ttil),

+ (A2(2G(1)(t2,t z )

+ ~ [ I A I I ~ G ‘ ” ( ~~1I ) l ~ 2 1 2 G ( 1 ) (t2)]1’2 ~23 7

cos{4(ti, t 2 ) > ,

(10)

which is equivalent to Eq. (7) except for the (unimportant) suppression of 8. These results are valid for general fields (nonstationary as well as stationary) with arbitrary statistical properties (since only first-order correlation functions appear). We now direct our attention to constituent beams which are stationary. Individual first-order coherence for these fields implies monochromaticity, and the functions &*(tl) and &t2) for well-collimated, fully-polarized beams (of frequency w1 and w2, respectively) may be expressed as25 &*(t,)= [G(’)(tl, t,)]”’ exp(iw,t,)

(11)

&(t2) = [G(’)(t2,t,)]1/2 exp( - icu,t,).

(12)

and

Here again the times t l and t , are relative to the source. Using these fields, the last term in Eq. (7) may be written

2 Re{Al*&*(tl)A2&(t2)) = 2 Re{Al*A2[G(1)(tl, tl)G(’)(t2, t2)I1I2 x exp(iwltl)exp( - i u 2 t 2 ) } .

(1 3)

Inserting the product exp( - i w 2 t l )exp(iw2tl) = 1 , we obtain 2 Re(ll*b*(tl)A2&(t2)}= 2 Re{Al*A2[G(”(tl,tl)G“)(tz, t2)]1/2 x exP[i(wi - u 2 ) t i I exP[iw2(ti

- t 2 ) I ) . (14)

9.

COHERENT DETECTION IN THE INFRARED

369

For stationary constituent fields Eq. (7) thus becomes

R = lAIIZG(')(tl,t l ) + ]A2\2G(1)(tz, t2)

+ 2[G(')(t,, tl)G(')(tz, tz)]'/'

Re{Al*A2exp[i(o, - w2)tl] exp(io,T)), (15 )

where the quantity w2z = wz(tl - t z ) may be thought of as a phase difference between the beams. Since we do not have advance information about the phase of a particular beam in any experiment, however, in using the theory we should properly choose states which are averaged over phase. Although the interference term in Eq. (15) will vanish through the ensemble average in this case, the interference would be present in any individual experiment. We assume that we can select an ensemble by considering only experiments with the same phase difference. This permissible procedure is entirely analogous to that used for spatial interferen~e.'~For convenience we shall choose the phase difference w2z in such a manner as to precisely cancel the phase factors arising from A t * and ,Iz. The counting rate for a restricted ensemble such as that discussed above, and for a field possessing first-order coherence with stationary constituent beams, may therefore finally be written as R

=

IAIIZG(')(tl,t i )

+ ~A2~zG(')(tz, t2)

+ 2[1A1(2G")(tl,t1)lAz(2G(1)(t2,tz)]1'2

COS(w1 - w2)t.

(16)

The phase difference has been conveniently chosen as described above, and t , has been written as t in the interference term. We note that G(')(tl, t l ) and G(')(tz, tz)are count rates which are constant in time and do not possess any fluctuating components. In terms of the classical intensities I, and I z for the individual beams this is equivalent to R

=

I1

+ + 2(11 Iz)l/z COS(w1 - wz)t. 12

(17)

This expression differs from the usual classical result3-' in that it does not contain sum- and double-frequency components of w , and w z . This will be made more explicit later. Although the correct result may be obtained semiclassically by using the analytic the range of validity of Eq. (17) (high frequencies such that hv S kT) appears naturally in the quantum treatment. Furthermore, the quantum theory may be used to obtain an expression valid throughout the electromagnetic ~pectrum,'~ as indicated earlier. 32

L. Mandel and E. Wolf, Rev. Mod. Phys. 37,231 (1965).

370

M. C. TEICH

I t is observed from Eq. (10) that for nonstationary beams with a firstorder coherent field the interference term exists but is not sinusoidal. The result in Eq. (5) is valid even when there is not maximum fringe contrast (first-order coherence). In that case, however, the equality in Eq. (9) no longer holds, and must be replaced by the inequality3'

From this it is evident that the photomixing term will be reduced below its maximum value when there is a departure from precise first-order coherence of the total incident radiation field. Thus, optimum sinusoidal photomixing is the result of temporal and spatial first-order coherence of the total incident radiation field, and stationarity of the constituent beams.23

a. Density Operator The restriction which first-order coherence places on the density operator for the field has been discussed by Titulaer and G l a ~ b e r . ~They ' have generalized the definition of a mode to include nonmonochromatic solutions to the wave equation, and have thereby derived a density operator for the most general type of field possessing first-order coherence. This operator may be obtained by replacing the creation operator akt in the single-mode density operator by a more general creation operator h f . This latter quantity creates a photon in a particular superposition of modes which may be considered as specifying a particular type of photon wave packet. Therefore a field which has first-order coherence may be regarded as consisting of photons of only a single (in general nonmonochromatic) variety. It has also been shown that if a field possesses such a density operator, it is first-order coherent. Since any field expressible in Glauber's P-representation may be separated into a coherent and an incoherent portion, furthermore, only the coherent portion will contain photons of the variety that give rise to a heterodyne signal. The heterodyne detection process may then be considered as the annihilation of a single photon of this variety. Thus even in the presence of a single one of these photons a heterodyne signal may still be observed. As in the case of spatial i n t e r f ~ r e n c e ,therefore, ~~ D i r d c ' ~well-known ~~ comment, "Each photon interferes only with itself. Interference between two different photons never occurs," applies to the heterodyne experiment. This is not surprising, since we are considering a type of interference experiment which is a one-quantum process. For multiple photon processes, such as two33 34

R. L. Pfleegor and L. Mandel, Phys. Rev. 159, 1084 (1967); J . Opt. Snc. Am. 58, 946 (1968). P. A. M. Dirac, "Quantum Mechanics," 4th ed., Chap. I, p. 9. Oxford Univ. Press, London, 1958.

9.

COHERENT DETECTION IN THE INFRARED

371

quantum d e t e ~ t i o n ~ * , or ~ ~the - ~ Hanbury-Brown-Twiss ’~ effect, this is not necessarily true.25 b. Uncertainty Principle The uncertainty principle also shows that it is not useful to consider the photons of the constituent beams separately. In fact, in a heterodyne experiment we are unable to determine from which beam a photon is absorbed in a given time interval. Consider a description in which there are two alternate ways in which the system can evolve from its initial state to the final state : by absorption of a photon from beam 1 or by absorption of a photon from beam 2. In order to ascertain which beam gave rise to the ejection of a particular photoelectron, its energy would have to be measured to within a value A E given by AE < hlw, - w21. From the uncertainty principle

AE AT 2 h ,

(19)

the time AT required for such a measurement would be AT 2 h/AE

=

lo1-

(20)

The required measurement time is greater than the period of the beat frequency, and such a measurement would therefore wash out the time interference. Thus one cannot ascribe a detected photon to one or the other of the constituent beams. A related argument has been applied by Pfleegor and Mande133to independent beam spatial interference a t the single-photon level. c. Ciussicul Theory

In the classical theory the total electric field vector E , is given by E,

El cos(o1t)

+ E2 COS(o,f),

(21) where E l and E , are the amplitudes of the individual incident waves. Assuming that E , and E 2 have the same polarization, the count rate R, from the classical detector is proportional to the intensity of the radiation or to the square of the total electric field :

R , = E,,

=

= E l 2 cos2(w,t)

+ E , E , COS[(W,

-

+ Ez2 C O S ~ ( C J ~ ~ ) + E,E2 COS[(O, + w&].

(uZ)~]

(22)

The usual argument invoked at this point is that the detector cannot follow the instantaneous “intensity” at the sum- and double-frequency components if its resolution time is larger than the period of the radiation. Since the M. C. Teich and G. J. Wolga, Phys. Rev. 171,809 (1968). 35aM.C. Teich and P. Diament, J . Appl. Phys. 40, 625 (1969). 35bP. Diament and M. C . Teich, J . Opt. SOC. Am. 59,661 (1969). 35

372

M. C . TEICH

electron-photon correlation time36 is - 2 x 10-14sec in a metal, this providesa cutoff for the optical region. In any case, the post-detector circuitry generally has very limited frequency response, so that only averages of the first, second, and fourth terms in the above expression are observed. Thus such terms are usually ignored in the optical'-5 and in the ir~frared,~ and no contradiction with experiment is observed. However, it is clear from the quantum analysis that these rapidly varying terms never appear for the usual absorption detector when hv $- kT, and therefore would not be observed even with detectors of arbitrarily small resolving time.

2. SIGNAL-TO-NOISE RATIO A parameter which is of interest in evaluating the usefulness of a receiving technique is the signal-to-noise ratio. In this section we discuss the operation of an infrared (optical) heterodyne receiver and calculate the expected signal-to-noise ratio at the output of the detector. Considering either the quantum theory or the classical theory with the usual assumptions, the response r of the detector to the two incident waves is given by

+

r = p(&Ei2 +E2*

+ E l & cos[(wl - m2)tI) = rdc +

rlpI

(23)

where a proportionality factor fl containing the quantum efficiency is now included (previously fi was arbitrarily taken equal to 2). It is assumed that the detector has a sufficiently high frequency response to follow the signal at the difference frequency (al- 4. If we confine measurement of the signal to a band pass about the difference or heterodyne frequency (also called the intermediate frequency or IF), then it follows that r]F = PEIB2 cos[(w, - c u z ) t ] . (24)

+

However, since rdc = $(El2 EZ2),the detector response may be written in terms of its dc component :

For a very strong LO beam, which is the usual experimental condition, E 2 $- El,and it follows that rIF = 2(E1/E2)rdc Cos(wIFt). (26) The mean-square photodetector response for a sinusoidal signal is then given by ($F) = 2(Pl/P2)rk (27) 7

where P, and P2 are the radiation powers in the signal beam and LO beam, respectively. 36

P.S. Pershan and N. Bloembergen, Appl. Phys. Letters 2, 117 (1963).

9.

COHERENT DETECTION IN THE INFRARED

373

a. Photoemitter and Ideal Reverse-Biased Photodiode

If we now consider the noise response rn in the detector as arising from shot n o i ~ e , ~which ’ , ~ ~ is the case for the photoemitter and the ideal reversebiased photodiode, then the mean-square noise response is given by the well-known shot-noise formula (r”2> = 2 e r d C A .

7

(28)

“(“)

where Af is the bandwidth of the receiver. Hence the signal-to-noise ratio (S/N),,,,, may be written (S/N),,,,, = __ cr:,> = (rn2> e Af p2 However, since rdc arises from the comparatively large LO, it is related to the LO beam power P2 by the quantum efficiency q : rdc

= (qe/hv)P2.

(30)

Thus, for a sinusoidal signal, the signal-to-noise ratio become^^^,^' (S/N),,,,,

= qP,/hv Af

(photoemitter and reverse-biased photodiode). (31a)

From this relation it is seen that the value of the signal-beam radiation power necessary to achieve a (S/N),,,,, = 1 is given by

p y = hv Af/q

(photoemitter and reverse-biased photodiode). (31b)

This quantity is defined as the minimum detectable power, and is denoted by PFin.It has been assumed that experimental conditions are such that the “excess noise”39-40a above shot noise may be neglected. This is usually, but not always, true for single-mode laser sources operating well above threshold, where intensity fluctuations are quieted. If the two radiation beams impinging on the detector are not parallel to within a certain angular tolerance,16.“ and do not illuminate the same area, or the radiation is not normally incident upon the p h o t ~ d e t e c t o r , ~ ~ then (SIN) and PFinwill differ from expressions in Eqs. (31a) and (31b). The radiation beam incident on the detector must also possess first-order coherence for this result to hold.23In the experiments reported in this work the conditions required for the relations given in Eqs. (31a) and (31b) have B. M. Oliver, Proc. I.R.E. (Correspondence) 49, 1960 (1961). H. A. Haus, C. H. Townes, and B. M. Oliver, Proc. I.R.E. (Correspondence) 50, 1544 (1962). C. Freed and H. A. Haus, Phys. Rev. 141, 287 (1966). 40 J. A. Armstrong and A. W. Smith, in “Progress in Optics” (E. Wolf, ed.), p. 213. NorthHolland Pub., Amsterdam, 1967. 40sJ. J. Mezrich, Circuit Model for Amplitude Noise in Lasers. M.S. thesis, Massachusetts Institute of Technology, Cambridge, Massachussetts, January 1969 (unpublished). 4 1 V. J. Corcoran, J . Appl. Phys. 36, 1819 (1965). 4 2 A. J. Bahr, Proc. ZEEE(Correspondence) 53, 513 (1965). 37

38

’’

374

M . C. TEICH

been satisfied. For a sufficiently large LO power the theory derived in thc form given above has been experimentally verified both for the case of photoemitters5 and for back-biased photodiodes. 1 2 , * In particular, Hanlon and have recently verified Eqs. (31a) and (31b) in a bandwidth of 1 Hz using an InAs diode detector. h. Phntorondurtor and Photouoltaic Diode

For the case of a photoconductor the noise behavior differs from simple shot noise, and the results derived above arc not directly applicable. Photoconductor noise is a complicated phenomen0n,4~and depends to a great extent on the nature of the p h o t o c o n d ~ c t o r In . ~ ~the ~ limit of large LO powers, however, extrinsic Ge :Cu is expected to display simple generationrccombination (g-r) noise.45 Since the behavior for simple g-r noise is the same as that for shot noise except for a factor of t ~ o , ' -47~ it. may ~ ~ be shown that the signal-to-noise ratio for Ge:Cu has a valuc just one-half as large as that for a photoemitter or a nonleaky reverse-biased photodiode of the same quantum efficiency. The same result has also been obtained as a special case (in the absence of trapping) of a relation derived by DiDomenico and Anderson4* for CdSe. In the photovoltaic cell, on the other hand, the same processes occur as in the reversed-biased photodiode. However, instead of generating a current, a voltage results from the dipole-layer charge, since the cell is effectively open circuited. Thc detcctivity and the real noise equivalent power (RNEP) for both the reverse-biased p-n junction and the photovoltaic detector have recently been discussed by van Vliet,44 who has shown that the RNEP for the photovoltaic cell is higher than that for the reverse-biased photodiode by a factor of $. It follows that the (electronic) noise power, which is proportional to the square of the RNEP, is a factor of two greater for the photovoltaic configuration. Therefore the signal-to-noise ratio for the photovoltaic device, as for the photoconductor, is just one-half that for the photoemitter or the reverse-biased photodiode. It should be pointed out, however, that the advantage gained in signal-to-noise ratio for reverseJ. Hanlon and S.F. Jacobs, JEEE J. Quantum Electrun. 3, 242 (1967). K. M. van Vliet, A p p f . O p f .6, 1145 (1967). 44aVan Vliet44 has separated photoconductors into four classes, each of which behaves differently : intrinsic, minority trapping model, two-center model, and extrinsic. " H. Levinstein, Appl. Opt. 4, 639 ( I 965). 46 R. C. Jones, Proc. I.R.E. 47, 1841 (1959). '' A. van der Ziel, "Fluctuation Phenomena in Semi-Conductors." pp. 22. 65. Butterworths, London and Academic Press, New York, 1959. 48 M.DiDotnenico, Jr. and L. K.Anderson, Signal-to-Noise Performance of CdSe Bulk Photoconductive Detectors. Bell Telephone Lab., Murray Hill, New Jersey (unpublished memorandum). 43 44

9.

COHERENT DETECTION IN THE INFRARED

375

biased photodiode operation can only be realized for detectors having a high reverse-bias dynamic resistance, as will be seen later. The signal-to-noise ratio and minimum detectable power for the extrinsic photoconductor and for the photovoltaic junction are therefore given by (SIN),O,,,

=

vP,/2hv Af

1

(photoconductor and photovoltaic diode).

(324

PFin= ( 2 / q ) hAf. ~ (32b) These devices are a factor of two less sensitive than a photoemitter or ideal reverse-biased photojunction of the same quantum efficiency [compare Eqs.(3la)and(31b)],andafactor of2/ylesssensitivethan the perfect quantum counter. (For the photoconductor, although both the signal and the noise depend on the photoconductor gain G , the ratio may be shown to be independent of this parameter. * 3, The operation of photoconductive Ge:Cu as a heterodyne detector near the theoretical limit given by Eqs. (32a) and (32b) was demonstrated by Teich et ( ~ 1 . ~ ' Similar experiments performed on Ge:Hg by Buczek and Picusso have also been found to agree closely with the predictions of Eqs. (32a) and (32b). In later sections we discuss in detail the experimental results of heterodyne measurements on photoconductive Ge :Cu and on photovoltaic Pb, -,Sn,Se. In both of these cases the experimental agreement with the theory outlined in this section is quite good. It should be kept in mind, nonetheless, that the expressions given here have been derived explicitly for a sinusoidal heterodyne signal. Ill. Measurement of the Signal-to-Noise Ratio 3. EXPERIMENTAL ARRANGEMENT

A block diagram of the experimental arrangement used for the heterodyne measurement^',^^ in photoconductive Ge:Cu is shown in Fig. 3. The radiation from a C02-N,-He laser, with an output power of approximately 10 W at 10.6p, was incident on a modified Michelson interferometer. One mirror of the conventional interferometer was replaced by an off-center rotating aluminum wheel which had a roughened edge obtained by sandblasting. The diffusely scattered radiation from the wheel provided a Dopplershifted signal which was recombined at the beamsplitter with the unshifted 49

M. C. Teich, R. .1. Keyes, and R. H. Kingston, Appl. Phys. Letters 9, 357 ( I 966). C. J. Buczek and G. S. Picus, Appl. Phys. Letters 11, 125 (1967); G. S. Picus and C . J. Buczek, Far Infrared Laser Receiver Investigation. Hughes Res. Lab., Malibu, California, Interim Tech. Rept. No. 4, Contract AF33(615)-3487, 1967 (see also Repts. 1-3).

376

M. C . TEICH

I

I

IRIS

WIRE GRID POLA~IZER

COLD BAFFLE

ATTENUATOR

ROTATING WHEEL

BEAM

'

SPLITTER

I

,-,

/-L.O.

BEAM

Ge:Cu DETECTOR AT 4'K

2 LOAD

RESISTOR

MIRROR

FIG. 3. Experimental arrangement for heterodyne measurements with a Ge :Cudetector. The electric field vector lies perpendicular to the plane of the paper. (After Teich.')

LO radiation reflected from the mirror of the other interferometer leg. Both the mirror and the beamsplitter were cocked at a slight angle to the usual 90" and 45" (respectively) in order to prevent this reflected radiation from feeding back into the laser. Heterodyne detection measurements with scattered radiation at 0.6328 j L have been made previously by Gould et aL5' and by others.52A. E. Siegman has calculated the maximum radiation power to be returned by a random ~ c a t t e r e r . ' ~ ' ~ ~ The experimental apparatus, with the exception of the rotating wheel and the chopper, was mounted on a granite slab supported by compressed fiberglass blocks. To further reduce the effect of acoustic vibrations the 1.25-m-long Brewster window sealed laser tube was set on shock mounts and enclosed in a wooden shield paneled with acoustic tile. The laser was operated well above threshold and was very carefully tuned to operate on a single line and mode, so that no excess noise (above shot noise) was expected from the beam. This was accomplished by blocking the signal beam and then adjusting one laser mirror for a TEMoo mode and the absence of any observable beat signal. The interferometer mirror was then adjusted to give the largest signal-to-noise ratio when the signal beam was permitted to pass. Back and forth adjustments were made until a mirror position was found for which all of the above conditions were coincident. An uncoated Irtran I1 flat (of thickness 0.64 cm) served as a beamsplitter, and front surface 51

'*

G. Gould, S. F. Jacobs, J. T.LaTourette, M. Newstein, and P. Rabinowitz, Appl. Opt. 3, 648 (1964).

R. D. Kroeger, Proc. I E E E (Correspondence)53, 211 (1965); G. A. Massey, Appl. Opt. 4, 781 (1965).

53

A. E. Siegman, IEEE Trans. Antennas Propagation IS,192 (1967).

9.

I

w OSCILLOSCOPE

I

I F

C02 LASER

CHOPPER

-ni-

377

COHERENT DETECTION IN THE INFRARED

VOLTMETER

I I

ATTENUATOR

BEAM SPLITTER /

MATCHING TRANSFORMER

MIRROR&t

Pbx Sn,’-x Se DETECTOR AT 77°K

FIG. 4. Experimental arrangement for measurements with a Pb, -,Sn,Se detector. The arrangement is similar to that shown in Fig. 3, with the exception of the detector output circuitry. (After Teich.’)

mirrors were of standard aluminum-coated glass. These mirrors were highly reflective in order to prevent thermal distortion and consequent deformation of the wavefront of the reflected radiation. An Irtran I1 lens of focal length 2.54 cm was inserted in the signal beam to focus the radiation to a single point on the sandblasted rim of the rotating wheel. The purpose of the lens was twofold: It served to collect sufficient scattered radiation to permit an incoherent (nonheterodyne) measurement of the scattered signal power at the detector for calibration purposes, and it also ensured spatial coherence of the scattered radiation over the receiver aperture. This is analogous to the technique used to obtain spatially coherent thermal radiation, where the source is focused onto a pinhole aperture stop. This ensures that all points on the wavefront emanating from the pinhole arise from the same source point and are therefore correlated. The coherence properties may be deduced from the van Cittert-Zernike t h e ~ r e r n1., 5~4 Irises were used to maintain the angular alignment of the wavefronts of the two beams to within Lja, the required angular tolerance for optimum photomixing (a is the detector aperture).I6 It should be noted that this angular alignment restriction is 20 times less stringent than in the visible region of the spectrum. A Perkin-Elmer wire-grid polarizer ensured that the

’‘ M. Born and E. Wolf, “Principlesof Optics,” p. 505. Pergamon Press, Oxford, 1959.

378

M. C . TEICH

FIG. 5. Photograph of the heterodyne apparatus. (After Tcich.’)

recombined beams, which impinged normally on the photodetector, had a common linear polarization. Thc output from the detector was fed through a controlled-bandwidth, low-noise amplifier to a thermocouple-type rms voltmeter. Alternately, the signal was fed sirnultaneously to an oscilloscope and to a spectrum analyzer. The setup used for the heterodyne measurements with photovoltaic Pb, -,Sn,<Se is shown in Fig. 4. It is essentially identical to the arrangemenl for Ge :Cu, with the notable exception of the detector output circuitry. For the high-impedance photoconductor (dark resistance 600 kilohms) a 1-kilohm load resistor is used to convert the photocurrent to a voltage suitable for amplification. For the low-impedance photovoltaic device ( - 1.5 ohms), on the other hand, the voltage is both increased and transformed in impedance by thc use of a matching transformer. A photograph of the actual apparatus used in these measurements is shown in Fig. 5.

-

4. EXPERIMENTS WITH

PHOTOCONDUCTIVE

GE :C U

n. Detector Fabrication and Characteristics

The copper-doped germanium detectors used in the heterodyne experiments were made by indiffusion of Cu into high-rcsistivity n-typc gcrmanium host material for a period of 16 hr at 760°C. The samples, which were

9.

COHERENT DETECTION IN THE INFRARED

379

2 mm x 2.2 mm x 3 mm in size were then quenched in air. The resulting copper atom concentration was 6.8 x 10’5cm-3, and the compensation by the original donors was such as to produce a free-hole lifetime of about 2 x lO-’sec at 4°K. With a bias voltage of 13.5 V on the detector its (incoherent) low-power responsivity was 0.2 A/W by calibration with a blackbody source of known temperature. The detector was operated near liquid helium temperature. b . Heterodyne Operation at kHz Frequencies Figure 6(a) shows a multiple-sweep display of the heterodyne signal obtained at the detector output with a signal beam radiation power of 1 x 10- * W. The loss of definition of the waveform in the third cycle reflects the finite bandwidth of the heterodyne signal. Figure 6(b) shows a single trace of this signal for a longer time scale. The modulation bandwidth is caused by statistical fluctuations of the heterodyne signal arising from the moving diffuse surface of the wheel.

FIG.6 . (a) A multiple-sweep display of the heterodyne signal from a Ge:Cu detector. The loss of definition of the waveform in the third cycle reflects the finite bandwidth of the heterodyne signal. (b) A single-sweep of the signal shown in (a), but with a longer time scale. The modulation of the signal envelope arises from the random nature of the scattering surface. (After Teich.’)

380

M. C . TEICH

Ge:Cu DETECTOR -c0 "'-HETERODYNE FREQUENCY: 70kHz

a a do4K

W

B

- 30 mU

g ro3-

h

Y

w

z

- i o cn

0 -0 -4

0

FIG.7. The data points, obtained from a typical run, represent the observed signal-to-noise ratio of the heterodyne signal in Ge:Cu, (S/N),,,,,, for a given signal-beam radiation power (P,).The theoretical curve, given by the expression (S/N)pawer = qP$ZhvAJ is in good agreement with the data. The minimum detectable power Prin(defined as that signal beam power for which the heterodyne S/N is unity) corresponds, in a I-Hz bandwidth, to 7 x 10-20W. (After Tei~h.~)

The results of a typical experimental measurement of the heterodyne signal-to-noise ratio for the detector are shown in Fig. 7. The filled circles represent the observed signal-to-noise power ratio data points, (S/N),,,,,, as a function of the signal beam radiation power (P,or PI).Only noise arising from the presence of the single-mode, single-frequency LO beam (which was the dominant contribution to the noise) is considered. Various values of P, were obtained by inserting calibrated CaF, attenuators in the signal beam, while the unattenuated power was measured by chopping the signal beam in the absence of the LO. As indicated earlier, the presence of the lens facilitated this measurement. A plot of the theoretically expected result for a sinusoidal signal [Eq. (32a)], (S/N),ower = vPs/2hv M

9

(33)

is also shown in Fig. 7. Using an estimated quantum efficiency q = 4,it is in good agreement with the experimental data. Had noise from sources other than the LO been taken into account in computing the S I N , the

9.

COHERENT DETECTION IN THE INFRARED

381

experimental values would still be within a factor of two of the theoretical curve. Measurements were made with an LO power of 1.5 mW. With a heterodyne signal centered at about 70 kHz and an amplifier bandwidth of 270 kHz the experimentally observed minimum detectable power Prin(defined as that signal beam power for which the heterodyne SIN is unity) was 2 x 10- l4 W. In a l - H z bandwidth this corresponds to a W, which is to be compared with minimum detectable power of 7 x the expected value (2/q)hvAf

NN

7.6 x

W.

(34)

The experimental measurement is therefore within 6 dB of the theoretically perfect quantum counter, and is in substantial agreement with the expected result for the Ge:Cu detector used in the experiments. c. Noise Modulation

Because the roughness of the wheel (- 10 p) is comparable to the radiation wavelength I., the bandwidth of the noise modulation B should be given by49

B

-

vld,

(35)

where v is the velocity at which the illuminated spot traverses the surface and d is the diameter of the focused spot on the wheel (- 50 p). This follows from the fact that every d l v seconds a completely new spot on the wheel is illuminated, giving rise to scattered radiation which is uncorrelated with that of the previous time interval. The coherence time z1 is therefore

-

dlv,

(36)

since the frequency bandwidth is given by the inverse coherence time. With

v

re

(3 7)

FA/D,

(38)

=

and

d

NN

the noise-modulation bandwidth is given approximately by B

-

r8DjFA.

(39)

Here v is the tangential velocity of the wheel (157 cm/sec), d is its angular velocity ( l o x sec- I), and r its radius (5.05 cm); F represents the focal length of the lens (2.54cm), while D is the diameter of the radiation beam at the output of the laser (- 5 mm). Using these values, a calculated noise modulation bandwidth B -30

kHz

(40)

382

M . C. TElCH

I

50

I

70

I 90

f (kHz)

FIG.8. A typical power-spectral-density trace of the heterodyne signal from Ge:Cu. The trace sweep speed was 4 sec-’. The center rrequency of 70 kHz corresponds to the period of 14psec observed in Fig. 6jb). (After Teich.’)

is obtained which is comparable with the value observed on the powerspectral-density trace shown in Fig. 8. A Panoramic model SB-15a ultrasonic spectrum analyzer operated with a trace sweep speed of 254 sec- was used for the observations. A smooth, bell-shaped curve would have been obtained by integrating and then recording the power-spectral-density curve. The center frequency of 70 kHz corresponds to the period of 14 psec observed in Fig. 6(b).Both traces were obtained directly across the (1 kilohm) photoconductor load resistor. A more detailed treatment of the powerspectral-density will be given later.

d . Possible Power Dependence of Photoconductor Gain A discrepancy between the observed values of signal and noise (individually, rather than the ratio) when compared with the values calculated on the basis of the measured responsivity has not been re~olved.~’Experiments have shown, however, that the photoconductor gain depends neither on the chopping frequency of the incident radiation nor on the heterodyne frequency, a possible cause for the disagreement. Other experiments, which were performed by placing attenuators in various positions in the optical path, indicate that amplification of frequency-shifted (scattered) radiation” by the laser is not responsible for the effect. Measurements of the small-signal

’’ W. M. Doyle, W. D. Gerber. and M. B. White, I E E E J . Quantum Electran. 3,479 (1966).

9.

COHERENT DETECTION IN THE INFRARED

383

photoconductor gain as a function of the LO power were inconclusive, and it remains possible that this effect has some bearing on the problem. It appears that this discrepancy does not occur for the lead-tin selenide photodiode detectors. e. Results for Other Materials at 10.6p

The results discussed in this section are similar to those given for Ge : Cu by Teich et aE.7.49Buczek and Picusso in their experiments with Ge:Hg used two independent C 0 2 lasers oscillating at slightly different frequencies. The minimum detectable power which they obtained (referred to a 1-Hz bandwidth) was P:'"(Ge:Hg)

=

1.73 x

W,

(41)

which is in good agreement with the results obtained for Ge:Cu using a completely different experimental configuration. More recently, Mockerssa has also achieved operation near the theoretical limit in photoconductive Cd,Hg, -,Te, while Leiba55band Abrams and Glasss5chave observed the effect in pyroelectric triglycine sulphate (TGS) and in Sr -,Ba,Nb,O, (SB N), respectively. 5 . EXPERIMENTS WITH

PHOTOVOLTAIC P B 1 - ,SN,SE

a . Delector Fabricafion The Pbl -,Sn,Se diodes used as heterodyne detectors were fabricated from Bridgman-grown crystals by Melngailis and by Calawa et a1.56--58 The band gap of these diffused p-M junction devices varies with composition (x), so that the wavelength for peak responsivity may be adjusted by varying x. The devices which were used achieved their maximum responsivity (- 1 V/W, 77°K) at the C0,-laser wavelength, and had the composition Pb0.936Sn0.064Se (see Fig. 9 for a plot of the responsivity versus wavelength for a typical diode). The nature and inversion properties of the conduction and valence bands for these alloys have been discussed in detail both for the and for single-crystal thin films.s9 The inversion behavior of 5'aH. M o d *, Appl. Opt. 8, 677 (1969). 55bE. Leiba, Compt. Rend. 268B, 31 (1969). 55cR, L. Abrams and A. Glass, Appl. Phys. Lerlers 15. 251 (1969). " I. Melngailis, unpublished work (1967). " A. R. Calawa, I . Melngailis, T. C. Harman, and J. 0. Dimmock, Photovoltaic Response of Pb,-,Sn,Se Diodes, presented at the Solid State Device Res. C o d , Univ. ofcalif. at Santa Barbara, June 19-21, 1967. '* J . F. Butler, A. R. Calawa, I. Melngailis, T. C. Harman, and J. 0.Dimmock, Bull. Am. Phys. SOC.12, 384 (1967). 5 9 A. J. Strauss, Phys. Rev. 157,608 (1967).

384

M. C . TEICH

1

10.6 )r I

m w a

‘ 0.01 1

10

I I5

(v) RESPONSlVlTY OF A Pb0,9J6 Sno,0s4Se DIODE AT 77’K WAVELENGTH

FIG.9. Responsivity of a typical Pb, ,,,Sn,,,,,Se Melngaili~.’~)

diode versus wavelength at 77’K. (After

the bands in Pbl-,Sn,Se is similar to that observed for Pbl-,Sn,Te.60 The detectivity of the devices D* was

D* > 3

x lo9 cmsec-’’2 W - ’

and the carrier concentration was

- lo” ~ r n - ~ .

(42)

b. Device Characteristics

The diodes had a 1-mm diameter active area and were operated at 77°K in the photovoltaic mode. The thin n-type layer (- 10 p ) was exposed to the LO and signal beam radiation. The I-V characteristic of diode #37, both in the absence and in the presence of the LO, is shown in Fig. 10. It is seen from these curves that the zero-current impedance, as well as the reverse impedance, of the detector is x1.5sZ. This value, which is very low, is essentially independent of the presence of the LO. Using a calibrated thermopile and the I-V characteristic of Fig. 10, the quantum efficiency and responsivity for the device were directly determined to be 8.5% and 0.9 V/W, respectively. The eficiency could be further improved by depositing an 6o

J. 0.Dirnmock, I. Melngailis, and A. J. Strauss, Phys. Rev. Letters 16, 1193 (1966).

9.

COHERENT DETECTION IN THE INFRARED

385

200

100

mA

a -100

-200

-200 -100

0

100 200

mV

mA

mV

FIG.10. (a) Current-voltage (I-V) characteristic of the Pb,,,,,Sn,,,,,Se diode used in the heterodyne experiments. The upper trace is the dark characteristic, while the lower trace is the characteristic with the (18 mW) LO applied. (b) Same characteristic on expanded 1 and V scales. (After Teich.’)

antireflection coating on the diodes. The numerical values for the quantum efficiency and the responsivity are consistent with those obtained by Melngailis using a different method at much lower radiation powers. Improvements in the device characteristics subsequent to the measurements described here are mentioned in the Conclusion. c . Discussion of Experiment

The arrangement used in the heterodyne experiments (see Fig. 4) was described in detail earlier. A transformer at the output of the detector transformed its impedance to a level appropriate for matching to the lownoise amplifier. The experimental procedure was identical to that described for measurements on Ge :Cu, i.e., various values of the signal beam radiation power P, were obtained by inserting calibrated CaF, attenuators in the signal beam. The unattenuated power was determined from the known responsivity of the diode by chopping the signal beam in the absence of the LO, and then using phase-sensitive detection. In all cases the direct response

386

M . C . TEICH

of the detector was ascertained to depend linearly on the LO radiation power. In calculating the signal-to-noise ratio, only noise arising from the presence of thc LO was considered. The noise figure of the amplifier was such that with modest LO powers of 15 mW the noise associated with the LO was typically -25% of the total noise. I t appears that higher LO powers could have been used without any difficulty; however, a rearrangcmcnt of the apparatus would have been required to obtain LO powers in excess of thc value used. Experiments wcre performed in two different regions of heterodyne frequency and bandwidth : an IF of 110 kHz with a bandwidth of 65 kHz, and an IF of 2.05 MHz with a bandwidth of 10.0 MHz. They are described below.

-

d. Heterodvne Operation at kHz Frequencies A Princeton Applied Research Model AM-2 input transformer (frequcncy range 5-150 kHz, turns ratio 1 : 100) coupled thc detector output to the high-input-impedance, low-noise amplifier (PAR Model CR4-A). Measurements were madc with an LO power of 9 mW.

Pbll Snl-,Se

DETECTOR 30

50

10

-m 2

n

W

30

$ z

\

!O 10

~

,$4

,$3

16i2

10io

1c9 toa

0

i f 7

Ps ( W a t t s )

FIG. 1 1 . The solid line is the observed signal-to-noise ratio for the heterodyne signal in

Pbl_,Sn,Se as a function of the signal-beam radiation power. The heterodyne frequency is 110 kHz and the detection bandwidth is 65 kHz.The theoretical curve. (S/N),,,,,, = qP,/2Ai,A,J, lies within the limit of experimental accuracy. (After T e i ~ h . ~ )

9.

387

COHERENT DETECTION IN THE INFRARED

The results of a typical experiment are shown in Fig. 11. The solid line is the observed signal-to-noise power ratio (S/N),,,,, of the heterodyne signal as a function of the signal beam radiation power P,. With a heterodyne signal centered at 110 kHz and a transformer-amplifier bandwidth of 65 kHz the experimentally observed minimum detectable power PFin is 1.6 x 10- l4 W. The dashed line in Fig. 11 represents the theoretical result. Using the relation (S/N),,,,, = qPs/2hvAf and a quantum efficiency q = 0.085, it lies within the limits of experimental accuracy. The observed minimum detectable power corresponds, in a 1-Hz bandwidth, to 2.5 x 10- l 9 W. Since the experiments were performed using a scattering surface, however, it must be kept in mind that the observation bandwidth for the heterodyne signal must be greater than the noise modulation bandwidth (- 50 kHz for an IF of 100 kHz) for an accurate measurement of the signal-tonoise ratio. e. Heterodyne Detection at M H z Frequencies

The behavior of the Pb, -,Sn,Se heterodyne detectors at MHz frequencies was investigated by rotating the scattering wheel faster. This was accomplished by replacing the 300-rpm synchronous motor driving the scattering wheel with a 3600-rpm motor. A small matching transformer (turns ratio 1

I

Pbx S n i - x S e

DETECTOR

to” -

- 50

2 . ,a-

- 40

9

+

a w

-

k

c

THEORETICAL

9

$ to3 z

m

-30

a w

102 -

-20

-

-10

W

z

g

3 P g z

\

10’

cn

0 U

fw

loo--

-0

I

’

lO’C

! I ,0’3

I

10’2

I

II

,61’

- -10

Af = 1 0 M H z I ,OiO

I

,09

I 10-8

I

,67

I I lo-6

P, ( W a t t s ) FIG. 12. Signal-to-noise ratio as a function of signal-beam radiation power for 2.05 MHz heterodyne signal from Pbl -,Sn,Se. The agreement of theory and experiment, as in Fig. 1 1 , is good. (After Teich.’)

388

M . C. TEICH

11 :55, 30 gauge wire, on a Ferroxcube Corporation 7F160 cup core) at the output of the detector provided an impedance of approximately 50 ohms at the input of a wide-bandwidth, low-noise, integrated-circuit amplifier. The effective bandwidth of the transformer-amplifier combination was 10.0MHz. The LO power was determined from Fig. 10 (and the known responsivity of the detector) to be 18 mW. The signal-to-noise ratio for the heterodyne signal at 2.05 MHz is shown in Fig. 12. This plot is similar to that of Fig. 11, except for the IF and the bandwidth. The minimum detectable power for this experiment is 7.6 x W, which is larger than that of Fig. 11 because of the increased bandwidth. The dashed line, representing the theoretical result, predicts a value

P y x 4.8

x

w,

(43)

which is within the experimental bracket. The observed minimum detectable power, extrapolated to a 1-Hz bandwidth, is 7.6 x lO-”W, which may be compared with the expected value

(2/q)hvAf x 4.8 x 10- l 9 W.

(44)

FIG. 13. (a) A multiple-sweep display of the heterodyne signal in Pb,-,Sn,Se. The loss of definition of the waveform in the fifth cycle reflects the finite bandwidth of the signal. (b)A single sweep of the heterodyne signal shown in (a), but with a longer time scale. This figure is similar to Fig. 6 for Ge:Cu; note the very different time scales, however. (After Teich.’)

9.

COHERENT DETECTION IN THE INFRARED

389

f. Noise Modulation Figure 13(a)shows a multiple sweep display at the detector output which is similar to that shown for Ge:Cu in Fig. 6. The loss of definition of the waveform in the fifth cycle reflects the finite bandwidth of the heterodyne signal. Figure 13(b)shows a single trace of this signal for a longer time scale. Since the noise modulation bandwidth B and the heterodyne frequency are both proportional to the angular velocity of the scattering wheel 6, their ratio is independent of the IF and depends only on geometrical factors. Therefore Figs. 6 and 13 appear very much alike in spite of their very different time scales. This will be discussed quantitatively and in detail in Part IV. g. Results for Pb, -,Sn,Te

Heterodyne detection has also been observed in Pb, -,Sn,Te diodes operated in the photovoltaic m ~ d e . ~The ~ particular * ~ ~ ~alloy - ~composition ~ used had x = 0.17 (Pbo.83Sno.17Te),which has its peak response at 10.6 p when operated at 77°K. The detector output voltage was observed to be proas is portional to the square root of the signal beam power (cc &), expected for heterodyne operation. The responsivity of these preliminary diodes was too low, however, to observe the noise associated with the LO. This, of course, is necessary for optimum heterodyne detection. Recent advances in the operation of these diodes (see Chapter 4 by Melngailis and Harman) make them appear very suitable for heterodyne detection, however. IV. Detection from a Moving Diffuse Reflector Most of the measurements discussed previously have been concerned with a mean detection rate or a time-averaged value of the signal-to-noise ratio. They are therefore related specifically to the first-order coherence properties of the incident radiation. Information other than average count rates, such as the spectral distribution of the mixing signal and the probability density of its envelope, has also been obtained e~perimentally.~" Quantities such as these may be shown to depend on correlation functionsz4 of the radiation for example, have field higher than first-order, however. Freed and related the power-spectral-density of the photocurrent for a direct (nonheterodyne) detector to the second factorial moment of the photocounting distribution, and thus to a second-order correlation function of the radiation 60aM.C. Teich, unpublished. I. Melngailis and A. R. Calawa, Appl. Phys. Letters 9, 304 (1966). 6 2 I. Melngailis, A. R. Calawa, J. F. Butler, T. C. Harman, and J. 0. Dimmock, Photovoltaic Effect in Pb,Sn, -,Te Diodes, presented at the Intern. Electron Devices Meeting, Washington, D.C., October 26-28, 1966. 61

390

M. C . TEICH

I

LASER

W I R E GRID POLARIZER

OSCILLOSCOPE

t

I

MIRROR

&

Pb, Sn,-,Sa OET ECTOR AT 77'K

SPECTRUM

FIG.14. ExperimenVal arrangement for power-spectral-density and statistical measurements with a lead-tin selenide photovoltaic detector and a sandblasted aluminum scattering wheel. (Aftcr Teich.")

field. The spectral-density for the photomixing signal has been considered by Forrester6'" who obtained an expression for this quantity in terms of the spectral-densities of the light beams, for the case of Gaussian radiation. Mandel"' has considered the mixing of two independent laser modes and has arrived at an expression similar to that given by Forrester. The spectrum for the heterodyne signal is not strongly dependent on the higher-order coherence properties of the individual sources, however. In this section, the fluctuation properties of the homodyne signal arising from the scattering wheel experiments are discussed. This is generally the configuration of an infrared laser radar, as mentioned previously. In particular, we investigate the power-spectral-density of the heterodyne signal and the probability density of its envelope when the radiation oscillator is fully coherent, i.e., a single-mode stabilized laser operated well above threshold. The parameters we study provide direct information about a target, such as its velocity and its statistical nature. They are also useful in the optimum processing or transmission to a distant point of the heterodyne signal. As a simple example, the signal amplifier should be designed for minimum noise figure, and its bandwidth chosen sufficiently large to pass the heterodyne signal. Such design will, in general, depend upon both the h2aA.T. Forrester, J Opt. Sor. Am. 51, 253 (1961) h2bL Mandel, Phys. Rev. 138,8 7 5 3 (1965).

9.

COHERENT DETECTION IN THE INFRARED

391

fluctuation and spectral properties of the input signal. Information about the nature of the scattering medium may also be obtained from careful examination of the details of the homodyne signal. This is the basis of the use of the technique for heterodyne spectroscopy. For example, the homodyne return from a moving puff of steam is considerably broader in frequency than the return from a diffusely reflecting moving metallic target, as will be seen later. This results, of course, from the large velocity spread of the constituent water molecules. Further information may be obtained, in a similar way, by studying the probability density of the homodyne signal or its envelope. These quantities are much more strongly dependent on the higher-order correlation functions of the radiation field than is the photomixing spectrum. In fact, the electric field probability distribution of an unknown radiation source may be determined by the heterodyne mixing of this source with a stable oscillator, as will be shown. We first proceed to describe the details of the experimental arrangement to measure these parameters, and then present our results for the power-spectraldensity and probability distribution of the envelope of the homodyne signal.

6. EXPERIMENTAL ARRANGEMENT The experimental arrangement for these measurements is illustrated in Fig. 14. It is quite similar to the arrangement shown in Fig. 4, with the noted absence of certain components required only for measurements of the signal-to-noise ratio. All experiments described in this section were performed with the photovoltaic lead-tin selenide diode. The output of the detector was fed into a Tektronix type 585A oscilloscope for the probability density measurements, and into a Panoramic type SPA-3a spectrum analyzer for the power-spectral-density measurements. In distinction to experiments designed to measure signal-to-noise ratios, the heterodyne signal was displayed without amplification. In these experiments, the LO power was maintained at a level of approximately 18 mW, while the signal beam radiation power was sufficient (2l o p 7W) to provide a very high signal-to-noise ratio. The heterodyne signal was centered at about 2.0 MHz and had a mean voltage level of about 0.03 V. 7. POWER-SPECTRAL-DENSITY OF THE HETERODYNE SIGNAL The time trace of a typical heterodyne signal and its envelope, obtained from an oscilloscope photograph, is represented in Fig. 15. It has the appearance of a narrowband random process, i.e.,

B/v, < 1,

(45)

where B is the heterodyne signal frequency bandwidth and vD is the heterodyne or Doppler frequency (which is used interchangeably with ~ , ~ / 2 7 1The ).

392

M . C. TEICH

k 5 . 0 psec 5

FIG.15. Time trace of a typical heterodyne signal and its envelope. (After Teich.'")

quantities B and B/v, are easily calculated for 3 cases : (a) focused radiation on the rotating wheel, (b) unfocused radiation on the rotating wheel, and (c) a typical radar experiment. For a radiation spot of diameter d on the wheel, a completely new area of the wheel is illuminated every d/vl seconds, giving scattered radiation which, as before, we assume to be uncorrelated with that of the previous time interval, It should be pointed out that only the uncorrelated case is considered here, which is equivalent to taking an infinite variance for the surface roughness distribution. This model could be modified (to include a time-dependent mean and a finite variance) in order to allow for a determination of the target's mean path, or surface shape, which might be possible in some applications. Nevertheless, for the uncorrelated case, the heterodyne signal frequency bandwidth may be written as

B x: v,/d.

(46)

This is a more accurate result than that given previously in Eq. (35). The quantity ul represents the wheel velocity perpendicular to the beam axis, and is equal to v cos # where u is the tangential velocity of the wheel and 4 is the central angle shown in Fig. 14. Thus, forfocused radiation, the heterodyne signal bandwidth Bfocis given by Bfoc % (rdD/FA) cos #,

(47)

which is similar to Eq. (39) but more precise. For any reasonable value of 4,

9.

COHERENT DETECTION IN THE INFRARED

393

the contribution to the bandwidth arising from the finite spot size on the scattering wheel may be neglected in this case. The Doppler frequency vD, as is well known, is given by the relationship vD = 2~11/R= (2u/R)sin 4,

(48)

where u l l is the wheel velocity component parallel to the radiation beam axis. The ratio of bandwidth to heterodyne frequency Bfoc/vDmay then be written B,,,/vD

x (D/2F)cot 4.

(49)

This ratio depends only on geometrical factors, as has been pointed out previously. For moderate values of 4, this quantity will be less than or of the order of unity in most cases, although it may be seen that the narrowband nature of the signal will be destroyed for sufficiently small values of 4. For the case of unfocused radiation and the rotating wheel, there are two individual contributions to the finite bandwidth : the u,/d component as in the last case, and the contribution arising from the spread in Doppler frequencies over the finite spot size on the wheel. We denote this latter quantity by A v D . From Eq. (48),it is easily seen that AvD

= ( 2 A$/R) ~ cos 4

(50)

for the usual case of A 4 4 1 and thus, AVD/VD

X

Cot 4 A4.

(51)

But, since A 4 is given by the relation

Aq5 x d/(rcos (p),

(52)

where d again represents the (unfocused) spot size on the wheel, we obtain AvD/vD

x (d/r) csc 4.

(53)

The u,/d contribution is easily seen to be = (1/2d) cot 4 ,

(54)

VD

so that the total fractional frequency spread Bunfoc/vD x [(d/r)’ csc’

-

4

B u n f o c / ~ D may

+ (1/2d)’cot2

be written as

(55)

For most situations, this quantity will be smaller than unity for moderate values of 4 (e.g., for d/r 0.1, and R -4 d, Bunfoc/vD< 1 provided only 4 > 5”), so that the signal will usually possess a narrowband character in this case as well. Generally for the unfocused case, I 4 d 4 r, so that the Doppler-frequency spread will be the dominant term.

394

M . C. TEICH

We now consider the return from an infrared rudur beam tracking a moving solid target. If it is assumed that the beam sized is of the order of the target size, then the frequency broadening arising from the target’s diffuse nature will be negligible. But in analogy with the previous case treated, there will be a contribution arising from the spin or rotation of the target about an axis perpendicular to the beam direction, which gives rise to a Doppler-frequency spread. In this case, then, the center frequency of the mixing signal is given by VD =

2ull/l

(56)

= Vr

(57)

where now “11

is the radial velocity of the target as a whole. Then, an order-of-magnitude estimate of the bandwidth may be given by Bradar

-

2 ( 2 ~ r o J A )x 4r0) JJ-,

(58)

where r is the “radius” of the target, urot is its rotational velocity, and w I is the component of angular velocity perpendicular to the beam direction. Therefore, the bandwidth to Doppler frequency ratio may be written as Bradar/VD

2rco L/ur,

(59)

which indicates a narrowband signal when 2 r o , < v,. Thus, for the radar configuration discussed, the center frequency of the heterodyne signal determines the radial velocity of the target (0,) while the bandwidth of the signal may provide information about the spin or rate of rotation of the target. Coupled with the time dependence of the amplitude of the return (reflecting the infrared radar cross section), specific information may also be obtained, in principle, about the surface characteristics and shape of the target. For a beam size which is smaller than the target, on the other hand, one can scan the target to determine its velocity profile and thus its rate of rotation (e.g., the moon). The contributions would be similar to those observed for unfocused radiation falling on the scattering wheel, with the additional consideration that a center-of-mass translational radial velocity will increase the center heterodyne frequency vD. Therefore, in analogy with a microwave radar, a good deal more may be learned about a target than just the magnitude of a single one of its velocity components. The validity of Eqs. (47)and (49)above has been demonstrated experimentally with the rotating scattering wheel. For a 5.05-cm radius wheel rotating at 3600 rpm (4 = 12071sec- ’), with F = 2.54 cm, D x 5 mm, and 4 x 30”, we calculate the values Bloc = 0.3 & 0.1 MHz

(60)

9.

COHERENT DETECTION IN THE INFRARED

395

FREQUENCY ( M H z )

FIG.16. Experimentally measured power-spect ral-density of the heterodyne signal as a function of frequency. Also shown is the full-width at half-maximum (FWHM) of the curve. (After Teich l a )

and

Bft,,..\'D

=

0.17

0.05

from Eqs. (47) and (49), respectively. The experimentally measured (relative) power-spectral-density under these conditions is shown in Fig. 16. In this figure, the power-spectral-density scale is linear and the frequency resolution is approximately 0.05 MHz. The measured values of Bfoc= 0.3 MHz (FWHM) and Bfoc/vD= 0.15 are in good agreement with the predicted values above. The narrowband nature of the signal for these parameter values is most clearly displayed on a multiple-sweep display such as is shown in Fig. 13a. The loss of definition in the fifth cycle reflects the ratio Bfoc/vD. As the angle 4 is decreased (see Fig. 14), maintaining focusing of the beam on the wheel rim and the same experimental configuration, the number of cycles before loss of definition decreases, reflecting the increasing value of Bfc,c/vD(acot 4). For sufficiently small values of 6,the narrowband nature of the signal disappears, as expected, and the multiple-sweep display loses all resemblance to the kind of picture seen in Fig. 13a. On the other hand, adecrrase in the ratio B/v, has been observed by simply removing the focusing lens from the experimental arrangement leaving 4 unaltered. This operation had the effect of adding cycles to a representation such as that shown in Fig. 13a. This effect is understood on the basis of Eqs. (49) and (55), keeping in mind that for the unfocused case

dlr

+ A/2d,

(62) and that d is limited to about 2 mm by the iris aperture for these experiments. The heterodyne signal amplitude may decrease in this case, however, if the

396

M. C. TEICH

detector resolves the illuminated spot on the wheel. This has been discussed previously. Analogously, for optimum detection in a real radar experiment, the receiver aperture must be sufficiently small so as not to resolve the return signal,’ 1 * 5 2 in order to maintain spatial coherence. We have discussed the power-spectral-density of the homodyne signal in terms of the size, granularity, and configuration of the scattering target. It has not been necessary to refer specifically to the coherence properties of the scattered radiation. Such is not the case, however, if we investigate the statistical nature of the heterodyne signal or its envelope. For these parameters, it is necessary to have direct information about the statistical nature of the scattered radiation signal, or about its higher-order correlation functions. This is discussed in the next section. 8. PROBABILITY DENSITY OF

THE

SIGNAL ENVELOPE

A knowledge of the statistical behavior of the heterodyne signal is useful for the optimum processing and transmission of the signal, as well as for providing information concerning the nature of the scattering medium. Because of the narrowband nature of the homodyne signal in many cases of interest, it is useful (and practically speaking, simpler) to investigate the form of the envelope probability density function. We may then compare the theoretically expected results with those obtained from experiments with a known scatterer, and thus verify the validity of our theoretical model and method of calculation. It has been shown earlier that double- and sum-frequency heterodyne terms do not appear in the properly formulated quantum theory of infrared heterodyne detection. For radiation fields which possess a positive-definite weight function in Glauber’s P-repre~entation,~~ which is the case for all fields considered here, the heterodyne detector response may be written in terms of a semiclassical representation as cc

+ 41.

-5f”ELO COS(OJL,~)E~ COS(O~~

(63) Here, as before, rIFrepresents the photodetector response at the intermediate frequency, EL, and E , represent the magnitude of the electric field for the local oscillator (LO) and the scattered (S) beams, respectively, o the angular frequency of the particular radiation beam, and 6 is a phase angle. The operator 9 stands for the “low frequency part of.” Now, if the LO arises from a well-stabilized single-mode laser above threshold, as assumed earlier, then ELo and wLo are strictly constant. The addition of a constant phase has been omitted for simplicity. The random scattering from the rotating wheel (see Fig. 14) has the effect of converting the “coherent” incident LO radiation to narrowband Gaussian2’ radiation. This conversion of radiation statistics is similar to that obtained by inserting TIF

9.

COHERENT DETECTION IN THE INFRARED

397

a rotating ground-glass screen in the transmission path of a laser beam and is a consequence of the central-limit theorem. Such experiments have been performed by Martienssen and Spiller62cto convert deliberately a coherent laser mode to narrowband chaotic radiation in order to observe a positive Hanbury-Brown-Twiss correlation. Thus, the scattered radiation differs from the LO radiation in two respects: its frequency is altered (Doppler shifted), and its statistical properties are changed. As a consequence, the scattered beam radiation field may be represented as a narrowband Gaussian random process (centered in the infrared) and may be written in standard form62das E,(t)cos[w,t + 6(t)].From this, we rewrite rlF as

Since we obtain finally

But this expression for the homodyne signal voltage is itself, as well, in the form of a narrowband Gaussian random process. Now, however, it is centered at the Doppler frequency. Nonetheless, although both constituent beams (LO and S) are stationary, optimum sinusoidal photomixing is not obtained because the additional requirement of first-order coherence for the total incident field is satisfied only for time intervals well under a coherence time. (The detection has, nevertheless, been shown earlier to be optimum.) It is therefore seen that for an experimental arrangement such as described here, the heterodyning process effectively translates the fluctuation properties of the scattered field down to the Doppler frequency. Stated differently, the heterodyne voltage accurately reflects the scattered beam electric field distribution in a beating experiment performed with an amplitude-stabilized LO without fluctuation. Indeed, another example of this is the mixing of two strong amplitude-stabilized fields. Hinkley et ~ 1 . ~have ’ ~ mixed the radiation from a single-mode COz laser with that of a single-mode Pbl -,Sn,Te semiconductor laser operated well above threshold and obtained a sinusoidal beat signal with almost no fluctuation. The envelope of the heterodyne signal in this case has essentially a delta-function voltage probability distribution, reflecting the absence of amplitude fluctuations, and therefore, the coherent 62cW.Martienssen and E. Spiller, Am. J . Phys. 32,919 (1964). 62dW.B. Davenport, Jr. and W. L. Root, “An Introduction to the Theory of Random Signals and Noise,” p. 160. McGraw-Hill, New York, 1958. 62eE.D. Hinkley, T. C. Harman, and C. Freed, Appl. Phys. Letters 13, 49 (1968).

398

M. C. 'IEICH

nature of the signal beam. However, on reducing the diode laser power and using very careful measurement techniques,62' they have been able to measure the linewidth and Lorentzian shape of the heterodyne signal power-spectraldensity and thereby directly observe the quantum phase fluctuations in a Pb,,,sSn,,,2Te diode laser above threshold, thus verifying the form of the Schawlow-Townes formula. We note that while amplitude fluctuations (such as from the scattering wheel) will result in spectral broadening, pure phase or frequency modulation will not be observable in studies of the envelope but will, of course, be evident in the power spectrum. Thus, measurements of the signal statistics and its spectral-density provide complementary information. Hence, information about a scatterer may be obtained if the behavior of the radiation beam incident on the scatterer is known, or the fluctuations of an unknown radiation source may be studied by mixing with a stable LO. We now direct our attention to the probability density function for the homodyne signal envelope in the case of scattered radiation from the metallic wheel. As is well known, for a narrowband Gaussian random process (NBGRP),62dthis should be Rayleigh distributed. A typical trace (sample function) of the homodyne signal and its envelope has been shown in Fig. 15. The probability density of interest was experimentally obtained by sampling the envelope at 1.0psec time intervals. Some 15 oscilloscope photographs similar to the one represented in Fig. 15 were analyzed in this fashion, providing 754 data points. The envelope voltage was always taken to the nearest 0.01 V. These data are presented in the histogram of Fig. 17 where, on the relative envelope voltage scale, 1 V actually represents 0.01 V. Also plotted in the same figure is the Rayleigh density function P ( V ) = (Vb)exp(- V 2 / 2 a ) ,

(67)

which, as may be seen by inspection, fits the experimental data very well. This expected fit was confirmed by performing a chi-squared test."g A value of x 2 = 8.28 with 7 degrees of freedom was obtained, giving a probability P = 0.3 that the deviations from the Rayleigh density function would be expected to be greater than those here observed on repeating the series of measurements. This result provides strong evidence that the signal envelope may indeed be fitted by a Rayleigh distribution. The single parameter M in the distribution p ( V ) above was chosen by setting the observed average envelope voltage ( VUbJ equal to the average calculated from the Rayleigh distribution ( VRay).Performing the average,

<

I

a)

VRay)

=

V p ( v ) dv,

0

62fE. D. Hinkley and C. Freed. P l i j : ~ .Re!,.Lrttrr.v 23, 277 (1969). ''2aR. I). Evans, "The Atomic Nucleus," p. 774. McGraw-Hill. New York, 1955

9.

399

COHERENT DETECTION IN THE INFRARED

10.20

I51

->

v)

z 2

a

t>

- 0.15 v)

K

z

g 10'

W

0

m

*

0

t

LL

0 -0.10

a

w m

; a m

I

0

a

= I

n

2

5'

- 0.05

VOLTAGE (relative scale)

FIG.17. The heterodyne signal envelope probability density versus voltage. The experimental result (histogram) and the theoretical prediction (Rayleigh density function) are both shown. (After Teich.'")

and setting (Gay)

= (V b s )

>

(69)

we obtain =

(2/n)

<

Vbbs)'.

(70)

Thus, taking (Vobs) = 3.73 relative voltage units from our data (its actual value for the series of experiments performed was 0.0373 V, as may be seen approximately from Fig. 15), we obtain a value CI

=

8.9

(71)

in units of V2. The particular distribution plotted in Fig. 17 may therefore be written as p( V ) = 0.1 12V exp( - 0.0562V').

(72)

400

M. C. TEICH

The most-probable voltage V, is found from the relation = 0,

(73)

which, for the Rayleigh distribution, gives the prescription

v, = &.

(74)

For the experiments described here, Vp = 2.98 and p(VJ = 0.203. These results are consistent with those obtained by Gould et who studied the heterodyne signal obtained by scattering visible radiation from different portions of a piece of white bond paper. Finally, it should be mentioned that Goodman has made a detailed comparison of the statistical performance of an optical energy-detection radar with a heterodyne radar for pulsed applications.62h,6 2i

V. An Infrared Laqer Radar 9. DOPPLER RADARCONFIGURATION

Improved angular resolution and pointing for a radar system may be obtained in the infrared with the use of a laser. Recently a prototype 10.6 p infrared laser radar has been constructed and operated by Bostick using a Ge :Cu heterodyne d e t e ~ t o r .The ~ ~ experimcntal '~~ arrangement is shown in Fig. 18. The COz laser beam was incident on a modified Michelson interferometer, the conventional leg serving as the LO beam. The other mirror was removed and the (signal) beam was pointed at a target by a plane mirror attached to an inverted radar-type pointing mount on the roof of the laboratory. The laser beam was brought onto the mirror along the fixed axis of the mount in order to preserve an azimuth-elevation system. The system has been operated in the following modes : (1) a position servo loop for fixed directions, (2) manual tracking of moving objects, and (3) an auto-track control loop. The large Dewar containing the Ge:Cu detector, as well as the laser and the modified Mersenne beam expander, may be seen clearly in the photograph of the setup shown in Fig. 19. 10. RADARRESULTS

The return signal from a target is Doppler frequency shifted by an amount 2u,/l, where u, is the radial velocity of the target. At 1 0 . 6 ~this is equivalent to about 85 kHz/mph, so that radial velocities of moving objects 6ZhJ.W. Goodman, Proc. IEEE 53, 1688 (1965). 62'J. W. Goodman, IEEE Trans. Aero. Elect. Syst. 2, 526 (1966).

'.' H. A. Bostick, MIT Lincoln Laboratory, private communication.

9.

COHERENT DETECTION IN THE INFRARED

401

FIG.18. Drawing of the Doppler-type CO, laser radar system. (After B o s t i ~ k . ~ ~ )

such as automobiles and low-flying airplanes may be observed at moderate heterodyne frequencies (below 20 MHz). The large oscilloscope screen (see Fig. 19)is the output of a spectrum analyzer which displays the radar return as a function of frequency. The tracking of a truck at a range of 1.5 miles is shown in Fig. 20. The vertical axis represents the strength of the heterodyne signal, while the horizontal axis represents the heterodyne frequency. The large spike at the

402

M. C.

TEICH

FIG.19. Photograph of the radar setup. (After B o s t i ~ k . ~ ~ )

FIG.20. Radar signal observed from a truck moving with a radial velocity of 32 mph. The range of the truck was 1.5 miles. (After B o s t i ~ k . ~ ’ )

9.

COHERENT DETECTION IN THE INFRARED

403

FIG.21. Radar return from steam. The broad bandwidth of the heterodyne signal reflects the large velocity spread of the constituent water molecules. (After B o s t i ~ k . ~ ~ )

left of the figure represents the zero-frequency beat, while the radar reflection from the truck is seen at 2.7 MHz. The radial velocity of the truck was therefore about 32 mph.63aA radar return from steam is shown in Fig. 21. In this case the zero-frequency spike is at the center of the figure, and the upper and lower sidebands of the signal are seen. The average speed of the scattering water molecules is about 2.3 mph, but the broad width of the return reflects the large velocity spread of the constituent molecules. For the solid target, the signal appears to be quite narrowband as discussed earlier.

VI. Photoconductors and Photodiodes in the Infrared :A Comparison Optimum heterodyne detection has been achieved in the infrared using both photoconductive and photovoltaic detectors. The question of the advantages of each naturally arises. 1 1. SIGNAL-TO-NOISE RATIO The signal-to-noise ratio for heterodyne detection was given earlier, where it was shown that for equal quantum efficiency the nonleaky reverse-biased photodiode has a (S/N),,,,, which is superior to that of the photoconductor 63"Sincethe speed limit in the area was 25 mph, this fellow should have been ticketed!

404

M. C . TEICH

and the photovoltaic device by a factor of two. Therefore, from the point of view of SIN it is preferable to operate a (sufficiently high reverse-impedance) diode in a back-biased, rather than in a photovoltaic or photoconductive, configuration. This statement is also valid for direct detection, where the detectivity D* for reverse-biased operation is augmented by $ over photovoltaic and photoconductive operation.44 On the other hand, a leaky photodiode characteristic may give rise to adverse effects when operated back-biased, as discussed by Pruett and P e t r i t ~ . ~ ~ 12. FREQUENCY RESPONSE Aside from the possible improvement in signal-to-noise ratio, another advantage in operating a photodiode in the reverse-biased configuration may be increased frequency response. DiDomenico and S ~ e l t oand ~~ Lucovsky et a1.I2 have shown that the frequency response for a heterodyne photodiode is either transit-time or RC limited. Reverse-biasing increases the diode depletion layer, reducing the capacity of the device and therefore increasing its frequency response. (Reducing the carrier density will also decrease the diode capacity.) However, the Pbl -,Sn,Se photodiodes which were employed had RC time constants 1.5 nsec (with R z 1.5 ohms and C z 1100 pF), which was considerably less than the 20-nsec response time. (The response time was measured by connecting the diode directly to a properly terminated 50 ohm line and illuminating it with a 1-nsec risetime GaAs injection-laser pulse.) It is believed that these diodes are presently limited by effective carrier lifetime. This time could be reduced by decreasing the junction depth and therefore the carrier storage time. Photovoltaic operation may be preferred in certain cases. For example, with diodes having a low reverse impedance a reverse voltage could cause .undue heating. In photovoltaic operation the circuitry is and with low revcrsc-resistance devices (less than 50 ohms) the use of a broadband transformer might be adequate for impedance transformation and a satisfactory amplifier noise figure for frequencies up to 1 G H z . ~ ~ For the photoconductor with ohmic contacts the basic frequency response is similar to that of the photodiode; it is lifetime- or RC-limited.'3,65*67 Using fast pulse techniques in 2-mm3 samples of uncompensated and Sb-compensated Ge :Cu (C z 10 pF), Bridges et aL6* have recently observed a frequency response of 1 nsec, which is quite close to the RC limit for the

-

-

-

64 65

66 67

G . R. Pruett and R; L. Petritz, Proc. I.R.E. 47, 1524 (1959). M. DiDomenico, Jr. and 0. Svelto, Proc. I E E E 52. 136 (1964). C. L. Ruthroff, Pror. I.R.E. 47, 1337 (1959). 0. Svelto, P. D. Coleman, M. DiDomenico, Jr., and R. H. Pantell. J . Appl. Phys. 34. 3182 ( I 963). T. J. Bridges, T. Y . Chang, and P. K. Cheo, Appl. Phys. Letrers 12, 297 (1968).

9.

COHERENT DETECTION IN THE INFRARED

405

50-ohm system which they used. Similar measurements have been made by Buczek and Picus5' in the several-hundred-MHz region. It should be mentioned that by proper compensation Ge :Cu detectors with lifetimes as short as 10-'2sec have been made.69 However, it must be kept in mind that when high frequency response is obtained by matching into a 50-ohm system the responsivity of the high-impedance photoconductor is considerably reduced.

13. DEVICE~ S P O N S I V I T Y For optimum heterodyne detection it is necessary that the LO be sufficiently strong so as to provide the dominant source of noise (to overcome the amplifier noise). A high responsivity is therefore desirable so that the LO radiation power may be kept moderate. Because the photoconductor responsivity is proportional to the photoconductor gain G, which is given by r/T, with r the free-carrier lifetime and T the transit time across the device,47 it is higher for thin photoconductors. Therefore, a compromise between responsivity and RC frequency response must be made. A discussion of the tradeoffs necessary for optimum photoconductor heterodyne operation at high frequencies (+ 2 GHz) has been given by Arams et al." and is also discussed by them in Chapter 10 of this volume. Thin Ge:Cu detectors have been fabricated for this purpose. On the other hand, photodiodes having high reverse-impedances should have high responsivity, and, since the gain is unity, should in general require less LO than the photoconductor. 14. TEMPERATURE OF OPERATION Finally, perhaps the most striking characteristic of the Pbl -,Sn,Se (as well as the Pbl -,Sn,Te and Cd,Hg, -,Te) photodiode detectors is their ability to operate well at liquid nitrogen temperatures (77°K). By contrast, Ge :Cu requires near liquid helium temperatures (4"K), while Ge :Hg requires liquid hydrogen temperatures (18°K). The diodes are therefore more convenient to operate and more suitable for field use than are the photoconductors. Nevertheless, the quantum efficiency of the photodiode reported in this work is below that of the photoconductor by a factor of about four, and the minimum detectable power is therefore correspondingly higher. In recent work, however, Melngailis' has described Pb, -,Sn,Te diodes with external quantum efficiences of almost SO%, which is the reflection-limited maximum. The minimum detectable power 69 'O 71

R. J. Keyes, MIT Lincoln Laboratory, private communication. F. Arams, E. Sard, B. Peyton, and F. Pace, I E E E J . Quantum Electron. 3, 241 (1967). 1. Melngailis, Laser Action and Photodetection in Lead-Tin Chalcogenides, presented at the Intern. Colloq. IV-Vl Compounds, Paris, July 15-1 8, 1968.

406

M. C . TEICH

for both the Pbl-,Sn,Te and the Ge:Cu detectors should thus be comparable. Both photoconductors and photodiodes are seen to be useful for infrared heterodyne dctcction, the choice of a particular dcvicc depending on the deaircd application. VII. Conclusion Heterodyne techniques, which have been used extensively in the radio wavc and microwave rcgions, and more rcccntly in the optical (visible) portion of the clectromagnctic spectrum, are equally as valuable in the infrarcd. The availability of the high power COz laser, coupled with the 8-14 p atmospheric window, is expected to make the infrarcd heterodyne recciver important for communications applications. It is more sensitive than the optical heterodyne receiver because of thc smaller photon energy (thc minimum dctectable powcr is proportional to the photon energy). An infrared heterodyne radar system has been operated. A truck was tracked and its radial velocity determined at a range of 1.5 miles. in recent work, returns from helicopters and airplanes have also been obtained. The technique might also prove useful for infrared heterodyne spectroscopy experiments. The quantum theory of heterodyne detection in the optical and infrared has been discussed and compared with thc classical theory. An important result which obtains from the quantum treatment is the absence of sum- and double-frequency components (2wl, 20,, and w 1 + 02) from the heterodyne signal. This is in distinction to the classical result. A condition for optimum photomixing is that the total radiation field incident on the detector possess first-order coherence. It has been shown that heterodyne detection may be interpreted as a process in which a single nonmonochromatic photon is annihilated. The theory applies for fields of arbitrary statistical properties. In accordance with the theory, theoretically optimum infrared coherent detection has been achieved a t kHz heterodyne frequencies using liquidhelium cooled, copper-doped germanium detectors. Detailed considerations pertaining to the dctector properties for coherent and incoherent applications have been given by Kcyes and Quist in Chapter 8. Lead-tin chalcogenidc photovoltaic detectors at liquid nitrogen temperatures have also been operated optimally at kHz and MHz heterodyne frequencies. The incoherent detection aspects of these devices are discussed by Melngailis and Harman in Chapter 4. They are presently effective to wavelengths considerably beyond 10 p, and have external quantum efficiencies approaching 50%. The responsivity of a Pbo.936Sn,.o,,Se diode has reached 3.5 V/W at 77°K. These detectors have been operated at dry-ice temperatures (195°K) with a response which is down by only a factor of 20 from its value at 77°K.

9.

COHERENT DETECTION IN THE INFRARED

407

Furthermore, diodes such as Cd,Hg, -xTe72(which peak a t 10.6 p with have now been fabricated with reverseimpedances in excess of 50ohms, so that impedance matching is less of a problem. With the availability of these higher impedances at the amplifier input an added advantage is that the noise figure of the amplifier is improved, thus requiring less LO to overcome amplifier noise. In addition, if the diode reverse-impedance reaches a level where it is much greater than the load resistance, an additional factor of two can be gained in the signal-to-noise ratio with reverse-biased operation. The “higher-order’’ properties of the infrared heterodyne signal are useful either in the processing of a known signal, or in obtaining information about an unknown target or signal which cannot be obtained from measurements of average signal values. Expressions for the ratio of heterodyne signal bandwidth to Doppler frequency have been obtained for both focused and unfocused radiation incident on a diffuse wheel, as well as for a typical infrared radar configuration. Agreement with experiments using a focused radiation beam was good. Knowledge of the center frequency, bandwidth, and time-dependence of an infrared radar signal provides information about the radial velocity, spin, surface properties, and shape of the target. Information is also contained in the statistics of the heterodyne signal. The envelope probability distribution for radiation scattered from a rotating diffuse wheel was found to be Rayleigh distributed. In short, infrared heterodyne detection is now a well-understood process and appears to have a good deal of potential in the fields of communication, radar, and infrared physics. Its application and use in more complex configurations than those presented here is therefore certain to follow. A three-frequency mixing scheme, for example, has recently been proposed as advantageous in the acquisition and tracking of radar (or communications) signals when the target (or transmitter) velocity is either unknown or changing rapidly.73

x

= 0.195) and Pb,_,Sn,Te71

ACKNOWLEDGMENTS I wish to thank I. Melngailis for supplying the Pb,-,Sn,Se and Pb,_,Sn,Te detectors used in the experiments reported in this chapter, and to acknowledge many valuable discussions with him, with R. J. Keyes, and with R. H. Kingston. I am grateful to C. H. Townes for the use of his unpublished figure (Fig. 1). and to H. A. Bostick for permission to use Figs. 18-21, which are also unpublished.

’* 73

C. V k i e and A. Ayas. A p p l . Phys. Letters 10, 241 (1967). M. C. Teich, Appl. Phys. Letters 15, 420 (1969).

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CHAPTER 10

Infrared Heterodyne Detection with Gigahertz IF Response F. R . Arams E . W . Sard B. J . Peyton F. P.Pace I. INTRODUCTION . .

. . .

.

. .

.

. .

.

. .

. . . 1. Mixer Output Resistance . . . . . . . . . . . 2. Frequency Response Measurement . . . . . . . . . IV. IF PREAMPLIFIER.. . . . . . . . . . . . . . . v . PREDICTION OF PERFORMANCE FROM MIXERI-v CHARACTERISTIC , . VI. RESULTS ON HETERODYNE DETECTION IN Ge:Cu . . . . . . . 3. Mixer Element . . . . . . . . . . . . . . . 4. Packaged Receiver . . . . . . . . . . . . . . 5 . System Measurements to 1 GHz . . . . . . . . . . 6. System Measurements ai an I F of 10 kHz . . . . . . . . 7 . Conclusions . . . . . . . . . . . . . . . .

409 4 10 415 415 415 419 420 42 1 42 1 422 423 424 425

VII. EFFECTSOF BIASVOLTAGE AND OPERATING TEMPERATURE ON MIXER . . . . , . . . . . . , . . . . . . RESPONSE APPENDIX A . . . . . . . . . . . . . . . . . APPENDIXB , . . . . . . . . . . . . . . . . APPENDIXC , . . . . . . . . . . . . . . . .

426 429 43 1 432

11. DESIGNFORMULASFORPHOTOCONDUCTWEMIXERS . . . . 111. MIXERRESPONSE MEASUREMENTS USINGGe:Cu , . . . .

. . . . .

I. Introduction Substantially increased receiver sensitivities are obtainable using heterodyne detection compared to envelope detection in such applications as infrared communications and radar. Moreover, heterodyne detection preserves phase and frequency, which are of importance in some applications. Heterodyne detection becomes increasingly attractive at longer infrared wavelengths, since the receiver sensitivity limit is set by quantum noise, which is directly proportional to frequency.Ig2These considerations also apply to other coherent receivers such as laser amplifier^.^^^ A. E. Siegman, S. E. Harris, and B. J. McMurtry, in “Optical Masers” (J. Fox, ed.), pp. 511-526. Wiley, New York, 1963. S. Jacobs and P. Rabinowitz, in “Quantum Mechanics 111” (P. Grivet and N. Bloembergen, eds.), pp. 481487. Columbia Univ. Press, New York, 1964. B. M. Oliver, Proc. IEEE 53,436 (1965). F. Arams and M. Wang, Proc. IEEE 53, 329 (1965).

409

410

F. R . ARAMS, E. W. SARD, B. J. PEYTON, AND P. P. PACE

This chapter discusses analyses and experiments on heterodyne detection in photoconductors in the 10.6-p region where the high-power carbon dioxide (CO,) laser has become a ~ a i l a b l eA . ~prime objective was to obtain an I F difference-frequency bandwidth extending to the gigahertz region in combination with nearly theoretical sensitivity. Such IF response is of practical interest to system designers in view of the large Doppler frequency shifts encountered with fast moving targets. For example, the two-way Doppler shift for a relative velocity of 10,000mph is 840 MHz. The large bandwidth is also of interest for communications and for detecting short pulses. Analyses on heterodyne mixing6*' have been extended to obtain engineering equations useful in optimum infrared receiver design. Expressions for noise equivalent power (NEP) and mixer conversion gain (G) are given in terms of such parameters as IF amplifier noise factor, mixer resistance, bias voltage, and mixer material properties. A quantum noise factor (QF) is defined as a useful figure of merit in measuring receiver sensitivity normalized to the ideal quantum noise limit. U H F and microwave measurements up to 4 G H z are presented on the generation-recombination (g-r) noise spectrum of a compensated germanium :copper (Ge :Cu) mixer using a mixer geometry and circuit arrangement intended to yield maximum mixer conversion gain and IF bandwidth. Finally, an alternative analysis is presented in which mixer conversion gain, and hence NEP, can be calculated directly from the mixer currentvoltage ( I - V ) characteristic in a manner analogous to microwave mixers. 11. Design Formulas for Photoconductive Mixers

Various formulas can be found in the literature for calculating the performance of an infrared bulk photoconductive mixer.'l7 However, modifications and additions are required to obtain explicit design equations useful in designing for optimum receiver performance, considering such parameters as local-oscillator power, bias power, IF amplifier noise temperature, mixer resistance, and mixer material parameters. In the approach presented here infrared mixer performance is expressed in terms of two principal factors :(1) sources of noise attributable to the mixer element itself and to the IF amplifier following the mixer, and (2) conversion gain, which numerically describes the limitation in the frequency-conversion process in converting the available infrared signal power to the intermediate frequency. C . K. N. Patel, Phys. Rev. 136, A1187 (1964). M. DiDomenico, Jr., and 0.Svelto, Proc. I E E E 52, 136 (1964). 0. Svelto, P. D.Coleman, M. DiDornenico, lr., and R. H.Pantcll, J . Appl. Phys. 34, 3182 ( I 963).

10. INFRARED

HETERODYNE DETECTION

411

FIG.1. Conversion gain of bulk photoconductive mixer versus IF for various material time constants.

This approach has found general acceptance in the design of microwave mixers8 The derivation for infrared mixers is given in detail in Appendix A. For simplicity it is assumed that the photoconductor operates in the linear region of its I-I/ characteristic, and that photocurrent is directly proportional to bias voltage. The conversion gain is given by

G =@ 1 (I) 2hv, T, 1 + ~ 0 ’ 7 ~ ’ where q is the infrared absorption (quantum) efficiency, q is the electronic charge, V is the mixer bias voltage, 7 is the lifetime of principal carriers, h is Planck’s constant, v, is the signal frequency, T, is the transit time of carriers, and o is the angular IF difference frequency. Substituting numerical values in Eq. (l), Fig. 1 shows the variation of conversion gain with the intermediate frequency for three values of z. Two ordinates are shown, depending on what value is taken for transit time. Note that a variation in G with I F frequency does not necessarily indicate that

* H.

C. Torrey and C. A. Whitmer, Crystal rectifiers, MIT Radiation Lab. Series, Vol. 15, McGraw-Hill, New York (1947).

412

F. R. ARAMS, E. W. SARD, B. J. PEYTON, AND F. P. PACE

receiver sensitivity will vary in the same manner, since the conversion gain may be sufficient to override IF amplifier noise. Instead it indicates that it may be desirable to insert a gain-equalizing network in the I F at a place at which receiver sensitivity has already been established. Receiver sensitivity is given (Appendix A) by NEP

=

2hv,B

-

v

+

k(T,

+ T;,)B G

where NEP is the noise equivalent power in watts for S j N = 1, B is the IF bandwidth, T, is the physical temperature ofthe mixer, and TiFis the effective input noise temperature of the IF amplifier (also see Appendix B). The first term of Eq. (2) represents quantum noise attributable to the mixer element itself. The factor of two arises due to g-r noise in photoc ~ n d u c t o r s . The ~ ~ ' ~term involving T, represents Johnson noise due to the mixer element proper. For cooled infrared mixers we can usually take T, 4 TiF. Note that the mixer material parameters (such as z and p) are .implicit in G. At radio and microwave frequencies it is customary to normalize receiver noise to kT,B in order to define a noise factor.' In an analogous manner in coherent infrared and optical systems, which are fundamentally limited by quantum noise, it appears appropriate to normalize the NEP to the quantum noise hvB. Quantum noise factor (QF) is thus a figure of merit to describe quantitatively how closely a given receiver approaches the theoretical minimum. For photoconductive heterodyne receivers it is given by

'

Note that for an ideal coherent receiver QF has a lower limit of unity (0 dB) and is independent of B. Figure 2 is a graph of the calculated QF (and hence NEP) as a function of I F for three values of T for an IF noise factor of 3 dB. This graph was obtained using the conversion gain values of Fig. 1. The 0-dB reference level corresponds to an NEP = 1.87 x W/Hz at 10.6p. Using the parameters shown in Fig. 2, we obtain QF = 5.5dB, which corresponds to NEP = 6.7 x 10-20W/Hz-a value reasonably close to the theoretical minimum. This quantum noise factor consists of 3 dB (factor of two) due to the g-r noise, and 2.5dB due to a calculated quantum efficiency of lo l1

K. M. van Vliet, Proc.IEEE46,1004(1958). L. K. Anderson and B. McMurtry, Appl. Opt. 5, 1573 (1966). IRE Subcommittee 7.9, Proc. I.R.E. 51, 436 (19631.

413

10. INFRARED HETERODYNE DETECTION 18

r =

16

SEC

14

12

m

10

z 1,8

10-9 SEC T i 10-10SEC

0

6 4

2

0 10 MHz

I GHz

I00 MHz I F FREQUENCY

FIG. 2. Quantum noise factor (NEPIhvB) of bulk photoconductive mixer versus frequency (QF = OdB corresponds to NEP = 1.87 x W/Hz).

0.56 for Ge :Cu. In Fig. 2 a match is assumed between mixer and IF amplifier. The design tradeoffs in receiver sensitivity are summarized in Fig. 3, which shows quantum noise factor at an I F of 1 GHz as a function of z with TF and T, as parameters. The QF at any I F less than 1 GHz will be lower than the values shown in Fig. 3. As Fig. 3 indicates, QF = 7 dB is

24 22 20

-

16

5

14

0

LL 0

0.56

V = 10 VOLTS

18 m

7=

TRANSIT TIM, T, IN SEC 1.25 X 1.25 x IF PREAMP IF PREAMP NOISE FACTOFi NOISE FACTOR F = 768 IF (II6O0K)

= 3 d0 (290°K)

= 1.3 dB (100*K)

12 10

= 0.2 d 0 (15'K)

8

= 10.4 d 0 (29OOOK) = 7dB ( 116OUK)

= 3dB ( 290' K)

6

4 I(

'0

10-8 CARRIER LIFETIME T IN SECONDS

FIG. 3. Quantum noise factor fNEP/hvBB)at 1000 MHz as a function of IF noise factor and detector time constants.

414

F. R. ARAMS, E. W. SARD, D. J. POYTON, AND F. P. PACE

calculated, compared to the theoretical minimum of 5.5 dB, using T = l o p 9 sec, T, = 1.25 x 10p’sec, and FlF = 7 dB. The conversion gain for these values is near - 3 dB at 1 GHz and i- 1 I dB a t 100 MHz (Fig. 1). As in the microwave case, an increase in IF noise factor does not necessarily increase QF by the same number of decibels. For example, an increase in IF noise factor from 7 to 10 dB would increase the QF at 1 GHz by about 2 dB under the conditions given. An important parameter in achieving high-frequency response is the mixer I F output resistance7 given by

Ro = LZhvLo/4Pl?PLo.r (4) where R, is the IF output resistance, L is the photomixer interelectrode spacing, p is the mobility of principal carriers, and PLois the local-oscillator power. The lower limit on R , is approached in Eq. (4)when the number of carriers generated by the local oscillator, given by An = ?jd‘Los/hv,o. approaches the total available number of impurities n in the mixer element. To avoid saturation effects, we design so that An + n. A low photomixer capacitance is also required to obtain a circuit R C product consistent with the desired IF response. For the mixers discussed here the I F input resistance R,, 6 R,. Thus in order to obtain an IF network frequency response fiF = 1/27cR,,CO to, say, 2 GHz, we require that the photomixer capacitance be 1.4 pF or less for R,, = 50 ohms. Finally, conversion gain can be simply calculated by substituting Eq. (4) into Eq. (1). We then obtain 7

where Pbias= V Z / R o . Examination of the above expressions for conversion gain and noise equivalent power indicates the following criteria for quantum-noise-limited large-] F-bandwidth infrared mixer design : high mixer quantum efficiency ; carrier lifetimes in subnanosecond region ; low mixer resistance, achieved by appropriate mixer geometry and sufficient laser local-oscillator power ; (4)short mixer carrier transit time; (5) low mixer capacitance; (6) linear mixer operation, including absence of carrier depletion due to excess local-oscillator power ; and (7) low-noise IF amplifier.

10.

INFRARED HETERODYNE DETECTION

415

Only a few infrared detector materials are candidates for meeting the above criteria. Photoconductive Ge operating at 4.2"K in which Sb compensation is used to significantly decrease the carrier lifetimeI2-I4 is a prime candidate for wideband IF applications. Both Ge :Cu and Ge : Hg, which are useful from approximately 5 to 28 p and from 4 to 13 p, respectively, have been investigated. Other materials that are receiving increasing attention for infrared heterodyne detection include impurity-doped silicon, such as Si :A1,15 HgxCdl -xTe, PbxSnl -xTe, and Pb,Snl -,Se. Initial work on these materials has so far been at lower modulation frequencies. 111. Mixer Response Measurements Using Ge: Cu

1. MIXEROUTPUTRESISTANCE As indicated in Part 11, two key parameters for a sensitive photoconductive mixer having a high I F response are short carrier lifetime and low IF output resistance. As Eq. (4) shows, a reduction in lifetime normally increases R , . However, in photomixers a low resistance and short lifetime can be achieved simultaneously provided that sufficient local oscillator power is applied, which is available at 10.6 ,LA from the COz laser. Figure 4 shows a scope photograph of the effect of local oscillator power on the I-V characteristic of a compensated Ge:Cu element at 4.2"K. The mixer resistance is 500 kilohms without laser power applied (lowest trace) and is reduced to 1000 ohms or less with laser power. The three upper curves in Fig. 4 are for full laser power, and attenuations of 3.2 and 6.4 db, respectively, obtained with teflon attenuators. The curves show that mixer current is essentially proportional to laser LO power in the linear region, as desired, and carrier depletion has not been reached.

2. FREQUENCY RESPONSE MEASUREMENT A quantum-noise-limited heterodyne receiver will be sensitivity limited due to g-r noise originating in the infrared mixer (Eq. 2). Quantitative data on the g-r noise as a function of I F will thus yield information on receiver IF response and mixer parameters and permit the calculation of conversion gain and NEP. An advantage of the g-r noise spectrum measurement is that it can be carried out using only the local oscillator laser source. U H F and microwave measurements have been made on the g-r noise spectrum of compensated Ge :Cu mixer elements. The experiments were l2

"

l4 lS

T. Vogl, J. Hansen, and M. Garbuny, J . Opt. Soc. Am. 51, 70 (1961). G. S. Picus, J . Phys. Chern.Solids 23,1753 (1962). J. T. Yardley and C. B. Moore, A p p l . Phys. Letters 7 , 311 (1965). R. A. Soref, Electron. Letters 2,410 (1966); see also J . Appl. Phys. 38, 5201 (1967).

416

F. R. ARAMS, E. W. SARD, B. J. PEYTON, AND F. P. PACE

10 V / D I V POSITIVE VOLTAGE FIG.4. Plot of I-V characteristics of compensated Ge:Cu mixer. Upper three traces: with 0, 3.2, and 6.4 dB laser power attenuation: lowest trace: with no laser power applied.

carried out directly at 10.6 p using a mixer geometry and circuit arrangement intended to yield maximum mixer conversion gain and IF bandwidth. The mixer was mounted in a low-capacitance coaxial structure connected inside a liquid-helium Dewar directly to 50-0hmcoaxial cable. A minimum interelectrode spacing served to minimize transit time T,, thereby maximizing photogain (T/TJ,and resulted in a lower mixer resistance R , for a given available laser LO power. Figure 5 is a block diagram of the experimental setup for measuring the g-r noise spectrum. Carbon dioxide (CO,) laser power was focused by a spherical mirror onto the mixer, thereby reducing the photomixer resistance from 500 kilohms t o approximately lo00 ohms (Fig. 4). An iris within the laser cavity serves to eliminate off-axis modes. A monitor tee was used to couple the dc bias to the mixer element. A ferrite circulator minimized mismatch of the IF amplifier. The effect on receiver sensitivity of operating the IF amplifier from a nonoptimum source (mixer) resistance is discussed in Appendix B. A substitution technique was used to measure mixer g-r noise as follows : Laser power is focused onto the mixer. The receiver output (which is a

417

10. INFRARED HETERODYNE DETECTION

E7F GENERATOR

SOURCE

IQ

ATTENUATOR

50-OHM COAXIAL LINE

___.

10-dB DIRECTIONAL COUPLER

PREAMPLIFIER (50-OHM INPUT )

RECEIVER METER

CIRCULATOR

DEWAR

LOCAL OSCILLATOR

INFRAREE MIXER NaCl W I N D W SPHERICAL MIRROR

co;

IRIS

LASER

FIG.5. Block diagram of experimental setup for mixer frequency response measurement

measure of the g-r noise) is measured as a function of dc bias power. An RF calibrating signal (either from a standard noise source or a signal generator) is then introduced through the directional coupler (Fig. 5) with the bias power removed (in which case there will be no g-r noise) until the receiver measures the same output as previously obtained for a particular value of bias power. The use of the coupler ensures that the R F amplifier and receiver see the same source impedance for both the measurement and calibration modes. The frequency response measurements used octave-bandwidth, low-noise (F,F= 3-5.4db), solid-state RF amplifiers with 18-db gain covering the frequency range from 200 MHz to 2 GHz. They were followed by a crystal mixer, 30-MHz precision test receiver with 2-MHz bandwidth, and outp.ut meter. The measurement setup averages g-r noise at two frequencies 60MHz apart, centered at the U H F local oscillator freq~ency.'~" The measurement frequency is varied by tuning the U H F local oscillator. The measured g-r noise current as a function of bias power is shown in Fig. 6 with IF as a parameter. As can be seen, the results at 220, 400, 475, and 600 MHz form a cluster of points. The g-r noise power level for a given bias power drops steadily as the frequency is increased from 600MHz to 1.95GHz. ""This technique was later refined by inserting an image-reject filter.

418

F. K. ARAMS, E. W. SARD, B. J. PEYTON, A N D F. P. PACE

The measurements in Fig. 6 reasonably approximate the expected proportionality of g-r noise power16 to bias power as given by

-

iK

where is the mean-square g-r noise current and Pbia5 is the dc bias power. In addition, measurements were made at 4 G H z (Fig. 6), for which a 4-GHz parametric amplifier having a noise temperature of 200°K and a gain of 22 dB was used as the I F preamplifier. This was necessary because the g-r noise level was lower than the receiver (IF) noise level. Figure 7 shows effective g - r noise power referenced to the 50-ohm IF preamplifier input as a function of IF for two values of dc bias power. The roll off occurs, as expected, at about 6dB/octave [Eqs. (5) and (611. The 3-dB roll-off point (which is the roll-over frequency) is approximately 750 MHz. In practice, the high-frequency sensitivity limitation will be set by the relative values of g-r noise and I F preamplifier noise at higher frequencies. These will depend on the particular design, considering such l6

L J Neuringer and W Bernard. J . Phy.,. Chem. S d i d \ 22, 385 (1961).

10. INFRARED

HETERODYNE DETECTION

419

FREQUENCY IN MHz

FIG.7. Measured g-r noise power as a function of IF for compensated Ge:Cu mixer. (The quantity dBm is dB referred to 1 mW.)

parameters as local-oscillator and bias power, narrowband versus broadband IF amplifier operation, mixer resistance, etc. However, it was concluded from such data as shown in Fig. 7 that operation to beyond 1 GHz is feasible using compensated Ge :Cu mixers.

IV. IF Preamplifier The photoconductive mixer must be carefully integrated with a low-noise, wideband preamplifier to fully realize the full heterodyne receiver frequency capability and sensitivity. Figures 8 and 9 show the measured noise factor and gain, respectively, as a function of frequency of a wideband IF preamplifier operating from a 50-ohm source resistance. The measured noise factor varied from 3.75 to 6.6 dB over the 20-1200 MHz frequency band and the net gain was 35 dB. The IF amplifier was subsequently matched for operation from a nonoptimum 1000-ohm source resistance, which is the infrared mixer resistance under operating conditions. With a 1000-ohm source resistance the average amplifier gain remained near 35 dB and the IF noise factor varied from 7 to 10 dB over the 201200 MHz band. Gain and noise factor measurements indicated that the IF amplifier performance is reasonably insensitive to changes in source resistance. Therefore small variations in LO power which change the mixer resistance will not drastically change the gain or noise performance of the

420

F. R. ARAMS, E. W. SAKD, B. J. PEYTON, A N D F. P. PACE

FREQUENCY I N M H z

FIG. 8. Measured noise factor versus frequency of IF amplifier operating from a 50-ohm source impedance.

IF amplifier, and hence the overall system. The IF amplifier uses a transformer-coupled input which permits the introduction of dc mixer bias through the amplifier. V. Prediction of Performance from Mixer I-V Characteristic

In microwave mixers it has been found expedient to calculate conversion gain directly from the mixer I-V curve.' An analogous approach has been worked out for the infrared photomixer as a means of gaining insight into optimum mixer design and operation. The approach is quite useful, since the conversion gain can be calculated directly from the mixer I-V characteristic (Fig. 4)without having to know the numerical values for semiconductor parameters such as lifetime, mobility, and transit time. The absorbed local oscillator power must be known. The derivation is given in detail in Appendix C. The result for the available conversion gain is

where (dI/dP)v is the rate of change of current with power for constant voltage, and (dZ/dV), is the rate of change ofcurrent with voltage for constant local oscillator power. This expression can be used to compute the G, NEP, and QF of the 10.6-pphotomixer for a variety of conditions.

10. INFRARED HETERODYNE DETECTION

I0

421

1000

I00

2000

FREQUENCY I N MHz

FIG.9. Measured net gain versus frequency of IF amplifier operating from a 50-ohm source impedance.

The available mixer gain was determined by the following methods : (1) using the mixer material parameters in conjunction with Eq. (1); (2) using the I-V characteristic of the mixer element and Eq. (7); (3) measuring the available IR input power to the mixer and the available I F power out of the mixer at 10 kHz; and (4) measuring the degradation in system NEP due to amplifier noise following the mixer at an I F of 10 kHz [Eq. (2)]. The resultant values of available gain were determined at two sets of operating conditions and exhibited excellent agreement, ranging from 9.4 to 9.8 dB.

VI. Results on Heterodyne Detection in Ge: Cu 3. MIXERELEMENT The principal performance criteria for the infrared mixer were calculated from measured data as follows. The lifetime t was obtained from the measured roll-over frequency. The measured g-r noise power yielded t/T, [see Eq. (A3)], and hence T . Using these values and a calculated value for y, the conversion gain and NEP were calculated. The results for compensated Ge :Cu at 4.2"K for particular operating conditions are as follows : Mixer dc resistance IF roll-over frequency Lifetime Calculated quantum efficiency Photogain (z/T,) Transit time Available conversion gain (calculated) NEP (calculated for F,F = 3 dB) Quantum noise factor (calculated)

1200 ohms 750 MHz 2 x lO-''sec 0.56 -0.13 -1.5 x 10-gsec + 5 dB (= power ratio of 3.2) 7.9 x 10-20W/Hz 6.2 dB

422

F. R. ARAMS, E. W. SARD, B. J. PEYTON, AND F. P. PACE

FIG.10. Packaged 10.6-11 heterodyne receiver.

For these measurements bias and laser local-oscillator powers from 15 to 100mW CW were employed. The calculated value for NEP given is in reasonable agreement with the value reported.”

4. PACKAGED RECEIVER System sensitivity measurements were made on the packaged 10.6-p heterodyne receiver system shown in Fig. lo.’* The system uses a Ge:Cu infrared mixer element cooled to 4.2”K,as discussed in the previous chapters. A system noise equivalent power (Pmin) of 7.5 x 10-20W/Hz was measured in a homodyne setup at an IF of 10 kHz. z I0

Poc * 133

n

‘L

I

01’

L -

mW

n

1

W

-

10

20

1

40

1

60 80 100 200 IF FREQUENCY IN MHz

I

I

400

I 600 800 1000

FIG.1 I . Receiver sensitivity versus IF frequency for a 10.6-11heterodyne receiver M. Teich, R. Keyes, and R. Kingston, Appl. Phys. Letters 9, 357 (1966). F. Arams, B. Peyton, F. Pace, R. Lange, and A. DiNardo. Packaged Infrared 10.6-Micron Heterodyne 1-GHz Bandwidth Receiver, International Electron Devices Meeting, Washington, D.C., October 23-25, 1968.

10.

INFRARED HETERODYNE DETECTION

423

5. SYSTEM MEASUREMENTS TO 1 GHz Noise equivalent power and available mixer gain have been inferred from system noise measurements to 1 GHz. Figure 11 shows the indirectly measured values of system sensitivity expressed as noise ratio referred to Pminas a function of IF frequency for a mixer resistance of 800 ohms and an applied dc bias power of 135mW. From Fig. 11 values are calculated for system NEP of less than 1.3 x lO-”W/Hz from 15 to 800 MHz and 32

28

24

20

16

12

8

pMIN

4

1

1

I

0 0

100 200 DC BIAS POWER IN mW

FIG.12. Measured NEP versus dc bias power at an IF of 10 kHz.

300

424

F. R . ARAMS, E. W. SARD, B. J. PEYTON, A N D F. P. PACE

20 m U

z

15

c7

10

z4 w _I m 4

4

2

5

q

0 0

too

200

300

DC BIAS POWER IN mW

FIG. 13. Available mixer gain versus dc bias at an IF; of 10 kHz.

of less than 2.3 x W/Hz up to 1 GHz. The degradation in system sensitivity near 900 MHz is caused by I F amplifier noise. Values in Fig. 11 are for the measured receiver noise. This is to be distinguished from detector noise, which is obtained by subtracting secondstage (IF amplifier) noise contributions. 6 . SYSTEM MEASUREMENTS AT AN IF

OF

10 kHz

Figure 12 shows the measured NEP at an I F of 10 kHz as a function of dc bias power for a mixer impedance of 1500 ohms, a load resistance of 10,000ohms, and a second-stage input impedance of 10,000 ohms. The NEP is below 10- W/Hz for bias power above 50 mW and decreases toward Pmi,as the bias power is further increased. The available mixer gain was calculated from measured data at 10 kHz and is shown in Fig. 13. As predicted from expressions developed previously, the available mixer gain varies linearly with dc bias power. Under the measurement conditions described the available mixer gain was 10 dB at an applied dc bias of 130 mW. The measured NEP as a function of mixer impedance is shown in Fig. 14 for a dc bias power of 76 mW. As the mixer resistance increases in value toward the input impedance of the second stage the noise factor of the second stage decreases, resulting in improved system sensitivity [Eq. (2)l. The measured value of NEP can be considered in good agreement with the expected value of Pmin= 2hvB/r] = 6.7 x W/Hz for a quantum efficiency of 0.56. This measured value of NEP corresponds to a quantum noise factor (NEPIhvB) of 6 dB at 10 kHz.

10. INFRARED

HETERODYNE DETECTION

425

FIG.14. Measured NEP versus mixer impedance at an IF of 10 kHz.

7. CONCLUSIONS Analyses and experiments have been carried out on heterodyne detection at 1 0 . 6 with ~ the objective of obtaining IF bandwidth capability into the microwave region. UHF and microwave measurements on the quantumnoise-limited generation-recombination (g-r) noise spectrum of compensated Ge :Cu photoconductive mixer elements were measured under operational conditions at 10.6 p using a mixer geometry and circuit arrangement intended to yield maximum mixer conversion gain and IF bandwidth. Engineering design equations are given for noise equivalent power NEP and mixer conversion gain G in terms of such parameters as IF noise factor, carrier transit time, carrier lifetime, mixer resistance, local-oscillator and dc-bias power, etc. An expression for quantum noise factor QF is defined. Graphs are also presented showing the effect on NEP, G, and QF of various parameters, and the tradeoffs possible to achieve high-frequency IF capability. An alternative analysis is presented in which mixer conversion gain is calculated directly from the mixer I-V characteristic in a manner analogous to microwave mixers. The effect of operating the IF preamplifier from a nonoptimum mixer (source) impedance was discussed.

426

F. R . ARAMS, E. W. SARD, B. J. PEYTON, AND F. P. PACE

A packaged 10.6-p heterodyne receiver was developed based on the above analyses and experiments showed a noise equivalent power near 10- l 9 W/Hz and an instantaneous frequency response from 10 MHz to 1.2 GHz. Later design refinements resulted in operation to 1.5 GHz with improved sensitivity above 750 MHz.

V11. Effects of Bias Voltage and Operating Temperature on Mixer Response This part presents additional experimental data obtained by Buczek and P ~ C U S on ’ ~ *the~ ~variation of detector parameters with bias field and temperature. Figure 15 shows the dependence of detector response time on dc electric field for two materials : low-compensation Ge :Cu, and partially-compensated Ge:Hg. The latter had a Hg concentration of 5.4 x loi5cm-3 and a compensating Sb concentration of 1.9 x 1014cm-3. The response time was obtained by measuring frequency response and using the relationship z = (2nfc)-‘, where fc is the 3-dB roll-over frequency; frequency was varied by beating together two 3.39-p He-Ne lasers tunable by means of piezoelectric mirror mounts. Additionally, at 10.6 p electrooptical and acoustic modulation techniques were used. At low bias fields, where the lifetime is the shortest, the heterodyne measurement technique was marginal, so that lifetime was deduced from Hall effect measurements of carrier concentration in the presence of a steady flux of 10.6-p radiation, using the expression for hole concentration p = Gz, where G is the hole generation rate due to incident infrared radiation. Figure 15 shows the decrease in frequency response and increase in response time as detector bias field is increased. Two distinct regions are discernible. For electric fields below 10 V/cm carrier lifetime remains dependence. constant, while at higher fields it approaches an The variation of mobility and carrier concentration with temperature for the same Ge:Hg(Sb) sample is shown in Fig. 16. Since the intensity of the exciting 10.6-plaser radiation was held constant, the variation in carrier concentration reflects the temperature dependence of the lifetime z. The lifetime is seen to vary as T’’2.An explanation of Figs. 15 and 16 in terms of the recombination cross section for hot holes is discussed by Yariv et d 2 ’ The variations of carrier concentration, mobility, and resistivity as functions of electric field are shown in Fig. 17 for compensated Ge :Cu at 6°K. The l9

’‘

C. Buczek and G. S. Picus, Appl. Phys. Letters 11, 125 (1967). C. Buczek and G . S. Picus, unpublished work (1968). A. Yariv, C. Buczek, and G . Picus, Proc. I X Intern. Cone Phys. Semicond., Moscow, 1968, Vol. 1, p. 500. Publishing House “Nauka”, Leningrad, 1968.

-

T=2I0K

FIG. 15. Response time as a function of bias field for uncompensated Ge: Cu and partiallycompensated Ge: Hg (after Buczek and PicusZo).

E

< 3

V/CM

/

II--

#

t I

4

10

I

I

I

I I I I I I

1

I

I I

I

10

I I l l 2

10

TEMPERATURE IN DEGREES KELVIN FIG. 16. Temperature variation of the mobility and the concentration of the photoexcited carriers in partially-compensated mercury-doped germanium (after Buczek and PicusZo).

428

F. R. ARAMS, E. W. SARD, B. J. PEYTON, AND F. P. PACE

6

10

t

1

10 9 L $ 3

I

10 ELECTRIC FIELD, V CM-'

100

FIG. 17. Electric field dependence of carrier concentration, mobility, and resistivity for compensated copper-doped germanium at 6°K (after Buczek and Picus*').

figure illustrates how the variations in mobility and carrier concentration compensate so that changes in resistivity with electric field are relatively small. This compensation effect explains why the detector I-V characteristic appears ohmic for fields up to 100 V/cm, although changes in carrier concentration and mobility begin to occur at fields as low as 5 V/cm.

ACKNO w LEDGMENT The support of Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Maryland is gratefully acknowledged.

10.

INFRARED HETERODYNE DETECTION

429

Appendix A Derivation of Design Equations The IF photocurrent generator is given6 by

where q is the quantum efficiency = (1 - R)(1 - e-uD)/(I - RepuD), R is the reflection coefficient = [(I - n)/(l + n)]’,

n is the index of refraction of the photoconductor, the photoconductor absorption coefficient, F, A is the peak photon flux at IF6, A is the area of detector = LU: z is the lifetime of principal carriers, T, is the transit time of principal carriers = L’/pV, w is the IF angular frequency, L is the interelectrode spacing, p is the mobility of principal carriers, and V is the bias voltage. a is

The overall mean-square noise current generator consists of three component noise generators: - in2 = ii-? + ic2 + i,?F, (A21

-

where ii+ is the generation-recombination noise,6 given by

where i, is the dc photocurrent = yqF,A(z/T,), with FoA the average photon flux, and B is the IF bandwidth. The second term on the right side of (A2) is given by

-

ic’ = (thermal noise of R,,) = 4kT,B/Ro,

(‘44)

where k is Boltzmann’s constant and T, is the physical temperature of mixer. A similar expression applies to the last term, namely, -

itF = (IF amplifier noise)

=

4k7;;B/R0,

(A51

where TiF is the effective input noise temperature” of the IF amplifier = (F& - l)To,with To the reference temperature = 290°K.

430

F. R. ARAMS, E. W . SARD, 13. J . PEYTON, AND F. P. PACE

The available conversion gain, or the ratio of the available IF output power to the available infrared signal power, is

IZ(o)l2RO/8Ps. (A61 The factor of eight in the denominator of Eq. (A6) is consistent with the use of peak photon flux rather than rms flux in defining l(w).Substitution of Eqs. (Al) and (4) into Eq. (A6) then gives = &F,available/Ps

=

where use has been made of the relation for modulation index, namely,

where F,A

=

photon flux at signal frequency

=

P,/hv,

(A9)

and FLoA = photon flux at local oscillator frequency z FoA

=

P,,,/hvLo.

(A10)

The conversion gain is independent of the local oscillator power except insofar as the local oscillator power possibly affects the lifetime T and transit time T, (through an effect on mobility p ) . The IF output signal-to-noise power ratio is given by

Substitution of Eqs. (Alk--(AG)and (A8HA10) into Eq. (A1 1) then gives

Thus the NEP, or the value of signal power to give an IF SIN ratio equal to unity, is

where k / q = 1/40Toin volts per degree Kelvin, when T, = 290°K. In terms of the conversion gain [Eq. (A7)], Eq. (A13) can be written

10. INFRARED HETERODYNE DETECTION

431

Appendix B Effective IF Noise Temperature under Mismatched Conditions For an isolator-preamplifier cascade operating from a nonoptimum mixer (source) resistance a correction must be made to the I F noise temperature. The effective noise temperature is given” by

T;F = Tl

+ (TZ/Gl),

(B1)

where T, is the noise temperature of the isolator, G1 is the available gain ( < 1) of the isolator, and T, = qF.We may also write where F , is the noise factor of the isolator and To is the physical temperature of the isolator x 290°K. The noise factor F , equals the ratio of the available signal-to-noise power ratio at the input to the available signal-to-noise power ratio at the output of the isolator : S./N, F,=--’--- NO So/No G,kToB’

where N , is the input noise = kToB, with k the Boltzmann’s constant; GI = So/& = 1 - (T(’, with r the voltage reflection coefficient; and B is the IF bandwidth. F,-1=

N o - GkToB - TI GkToB T’

where N o - GkToB is the internal noise in the isolator that appears as its output = JT/’kToB.Therefore

Under matched conditions (r = 0), TI = 0, G, = 1, and from Eq. (Bl) T;F = T F . Finally, combining Eqs. (Bl) and (B5)

22

H. T. Friis, Proc. I.R.E. 32, 419 (1944).

432

F. R. A R M S , E. W. SARD, B. J. PEYTON, AND F. P. PACE

The expression for the effective IF noise temperature includes the effect of the mismatched isolator. To determine the overall system sensitivity, Eq. (2), the second-stage contribution should be divided by the available gain of the photomixer. As can be seen from Eq. (B7), the receiver noise temperature TiF can be improved by cooling the terminated arm of the isolator.

Appendix C Analysis of Mixer Performance from Mixer I-V Characteristics From the I-V characteristics (Fig. 4) the total current I in the photomixer can be written as a function of the incident radiation P and the voltage V developed across it : (C1) z = f(P, V ). For an incremental change in incident radiation (AP) or voltage (AV) the concomitant change in current (AI) is expressed as :

AZ

=

(aZ/aP)V AP

+ (aZ/aV),

AV,

(C2)

where (al/aP), is the rate of change of current with power for constant voltage, and (al/aV),is the rate of change of current with voltage for constant power. An increm’ental voltage appears across the load resistor R L with sign conventions defined by A V = - R L AZ. Eliminating A V from Eq. (C2) gives

The bracketed term in Eq. (C3) pertains to the dynamic impedance of the photomixer and the load resistor. It can be shown that for maximum power transfer to the load (matched conditions) al/aV = l / R L , and for matched conditions Eq. (C3) therefore becomes AI = $ai/aP), AP.

(C4)

Since the case of interest here has sinusoidal variations in IF current due to the beat frequency between the local oscillator and the signal, Eq. (C4) is rewritten to display the peak-to-peak values of the IF current and the optical envelope power : (AI)p-p = &dl/aP)V(AP&-, .

(C5)

Consider now the incident illumination, which consists of collinear localoscillator and signal beams, whose amplitudes are given respectively by $E,sin(w,t) and $E,sin(w,t 4), where E , 9 E , , w, - w o = wIF, and 4 is an arbitrary phase angle.

+

10. INFRARED HETERODYNE DETECTION

433

The photomixer responds only to the envelope of the sum of these two beams. Neglecting second-order terms in E,, the envelope amplitude is given by $[E0 + E, cos(o,,t + 4)] ; the instantaneous power in the mixer is

where R , is the impedance of the mixer seen by the incoming radiation. From this expression we compute that the peak-to-peak variation in the absorbed power is

The signal power and local oscillator power in the load when taken independently are P,

=

Es2/R0

PLo = Eo2/Ro

(C8)

Combining Eqs. (C7)and (C8) gives (AP),-,

=

4(P,PLo)"2.

(C9)

Since the IF signal is sinusoidal, the peak-to-peak current can be expressed as

(g6F/RL)'/2,

(Az)P--P=

(C10)

where PtF is the IF power across the load. We now define the available conversion gain as the ratio of IF power under matched conditions to the signal power : G

=

PI,/P,.

(C11)

Finally, combining Eqs. (C5), ( C 9 t C l l ) gives

This expression can now be used to compute the conversion gain, noise equivalent power, and quantum noise factor of the photomixers for a variety of conditions. The equivalence of Eqs. ((212) and (C5)at low IF (07 < 1) can be shown by the following argument. Assume the mixer is initially biased at the point

434

F. R . A R M S , E. W. SARD, B. J. PEYTON, A N D F. P. PACE

I,, V, with local oscillator power P,. Increasing the LO power will increase the current proportionately at a fixed voltage while increasing the voltage will raise the current proportionately at a fixed LO power. Therefore

For a dc bias power of I,V,, substituting Eqs. (C13) and (C14) into Eq. (C12) gives

If there is a significant mixer dark conductance gD, it can be shown that Eq. (C15) is modified by the factor (1 + gD/g,)-', where go is the additional conductance due to local oscillator and Pbiss is the total dc power in both g D and go.

CHAPTER 1 1

Microwave-Biased Photoconductive Detector H . S . Sommers. Jr .

I . INTRODUCTION. . . . . . . . . . . . . . . . 436 1 . Utility . . . . . . . . . . . . . . . . . 436 436 2 . Advantage over dc Bias . . . . . . . . . . . . 431 OF OHMIC CONTACTS . . . . . . . . . . . I1 . LIMITATIONS 3. Sweepout of Minority Carrier . . . . . . . . . . . 437 4 . Injection of Majority Carrier . . . . . . . . . . . 431 . . . . . . . . . 438 111. RESPONSEOF DETECTOR-THEORETICAL 5 . Phenomenological Limit on Gain-Bandwidth Product . . . . 438 6 . Analysis of Microwave Equivalent Circuit . . . . . . . 439 DETAILS. . . . . . . . . . . . . . . 440 IV . DESIGN 7 . Reentrant Cavity . . . . . . . . . . . . . . 440 8 . Variable Coupling . . . . . . . . . . . . . . 442 9 . Sample Mounting . . . . . . . . . . . . . . 444 10. Optics . . . . . . . . . . . . . . . . . 445 FACTORS FOR BROADBAND DETECTORS . . . . . 446 V . PERFORMANCE 1 1 . Frequency Response: GB . . . . . . . . . . . . 446 446 12. Sensitivity: Information Rerriewl Eficiency /l. . . . . . V I . RESPONSE OF VARIOUS I R PHOTOCONDUCTORS-EXPERIMENTAL . . 448 13. Silicon . . . . . . . . . . . . . . . . . 448 14. Germanium . . . . . . . . . . . . . . . . 450 15 . Indium Arsenide . . . . . . . . . . . . . . 453 16. Indium Antimonide . . . . . . . . . . . . . . 453 11. Mercury Cadmium Telluride . . . . . . . . . . . 456 . . . . . . . . 451 18 . Mercury-Doped Germanium at 10.6 p OF SENSITIVITY WITH REPRESENTATIVE BROADBAND VII . COMPARISON DETECTORS . . . . . . . . . . . . . . . . . 458 458 19. Retrieval Eficiency fl . . . . . . . . . . . . . 20. Scope Pictures . . . . . . . . . . . . . . . 459 FOR FURTHER RESEARCH. . . . . . . . . . . 462 V I I I . AREAS 21 . Reduction of Microwave Noise . . . . . . . . . . 462 22. Increase in Gain-Bandwidth . . . . . . . . . . . 464 23. Increase in Optical Field of View . . . . . . . . . . 464

435

436

H. S. SOMMERS, JR.

I. Introduction 1. UTILITY

The photoconductive detector with microwave bias’.’ gives a highperformance front end for optical receivers.2 Its advantage over other detectors is a high SIN at low light levels for information bandwidths approaching a gigahertz. At very large bandwidths or very high subcarrier frequencies it cannot compete with the photodiode, but in the UHF or below its performance rivals or exceeds even the silicon avalanche diode. The full potential is reached when the volume of the phototransducer can be very small, which means with intrinsic photoconductors and a diffractionlimited optical system. However, it can also work well as a miniature detector with large field of view, its high sensitivity permitting use of a smaller lens with shorter focal length than that required with other solidstate detectors. In principle, it can also perform well with extrinsic photoconductors in spite of the increased size needed to give reasonable optical absorption, but this application has not been studied in detail. 2. ADVANTAGE OVER DC BIAS By definition, photoconductivity is the increase of conductivity of a material due to the absorption of electromagnetic radiation. In an appropriate circuit this change in conductivity controls the delivery of signal power to an output circuit. The circuit incorporating the photoconductor and a power supply comprises the photoconductive detector. The choice of circuit varies with the detection problem. For low cost, dc or low-frequency ac circuits are preferred. In fact, they would probably always be best except for one drawback, their requirement of ohmic contacts between the circuit and the photocond~ctor.~ In contrast, capacitive contacts can be used with a high-frequency bias supply. For large devices, where the spacing of the contacts is great, the effect of the contacts is usually negligible, but with small phototransducers the nature of the contact becomes important. As for most solid-state devices, it is the small device which gives the high gain-bandwidth product and the best SIN at high frequencies. Hence it is in broadband receivers for systems such as optical communication or radar that the microwave-biased photoconductive

’ B. Kovits, ed., Design Digest, Space Aeronautics, April, 1959; F. A. Brand, H. Jacobs, S. Weitz, and J. W. Strozyk, Proc. I E E E (Abstr. Tech. Papers) 51, 535 (1963); D. V. Eddolls and T. F. Knibb, Electron. Letters 4, 337 (1968); J. C. Bass, D. V. Eddolls, and T. F. Knibb, Electron. Letters 4, 429 (1968); D. V. Eddolls and H. C. Wright, Brit. J . Appl. Phys. ( J . Phys. D . ) Ser.2 1, 1449 (1968). H. S. Sommers, Jr. and E. K. Gatchell, Proc. IEEE 54, 1553 (1966). A. Rose, “Concepts in Photoconductivity and Allied Problems.” Wiley (Interscience), New York, 1963.

11. MICROWAVE-BIASED PHOTOCONDUCTIVE DETECTOR

437

detector offers the most promise, and in particular in the IR, where photomultipliers are not available.

II. Limitations of Ohmic Contacts 3,

SWEEPOUT OF MINORITY CARRIER

The most serious effect of ohmic contacts on the photoconductive element is the limitation on the gain by the sweepout of minority carriers. Adapting the phenomenological approach of R ~ s eto~ take . ~ explicit account of both members of the photoinduced pair, the photoconductive gain G of a material with ohmic contacts is

where zpc is the photoconductive (majority-carrier) lifetime and z its transit time across the crystal, zz is the minority carrier lifetime, and b is the mobility ratio of majority to minority carrier Increasing the electric field enhances the gain by reducing the transit time at fixed lifetime up to the field at which minority carriers are swept out. Above this, sweepout reduces the photoconductive lifetime to the pair lifetime, which is the minority-carrier sweepout time.5 In terms of zz, the lifetime of the minority carrier at low field (the free-pair lifetime), we have the limiting conditions 7

G6 1

> zJb,

(2)

+ bzpc/z,.

(3)

The photoconductive gain saturates at the field which just sweeps out the minority carriers, but the gain-bandwidth product (GB = G/271zp,) continues to grow. Here ( 0 4 ) is the information bandwidth. In this extreme of carrier sweepout the photoconductor resembles a diode with ohmic contacts, which give it a small current gain equal to the ratio of the sum of the freecarrier mobilities to the pair drift m ~ b i l i t y . ~ 4. INJECTION OF MAJORITY CARRIER

Even if the minority-carrier lifetime is so short that no sweepout occurs (as in extrinsic photoconductors), the performance at high fields will be degraded by space-charge injection from the ohmic contacts.374The increase in density of majority carriers that sets in when the transit time drops to the dielectric relaxation time ,,z, will change the photoconductive lifetime in a A. Rose, RCA Rev. 12, 362 (1951). H. S. Sommers, Jr. and W. B. Teutsch, Proc. IEEE 52, 144 (1964).

438

H. S. SOWERS. JR.

way determined by the nature of the recombination process, but the gainbandwidth product is still specified. At high fields it has the limiting form

(4) where the asterisk indicates that the relaxation time is to be evaluated at the operating point.6v6aHowever, this increase of GB through the drop in the relaxation time is accompanied by a reduction of the device impedance. If the principal source of noise is the following amplifier, the usual case in broadband IR receivers, the drop in impedance at fixed current gain will reduce the SIN. G B = b/2nzzl,

111. Response of Detector -Theoretical

5. PHENOMENOLOGICAL LIMITON GAIN-BANDWIDTH PRODUCT

Before analyzing the response of the actual microwave circuit it is instructive to discuss the upper limit to the response from a phenomenological approach.' The internal gain of the photoconductor is limited to the number of reversals of the bias field in a photoconductive lifetime, since each carrier can cross the sample once per reversal,6b

G G 2fo(zpc+ 72).

(5)

The microwave bias frequency is fo. A limited additional current gain is produced by the output transformer coupling the photoconductor to the following amplifier. If Qo is the loaded Q of the circuit, the overall current gain can be G G 4fhpcQ0

(6)

and GB

2fOQoln =L f o Q o .

(7)

Comparison with Eq. (4) clarifies the advantage of microwave bias for broadband systems. In a dc circuit large gain-bandwidth requires high conductivity and low device impedance" ; with microwave bias the supply frequency sets the limit irrespective of the resistivity of the phototransducer.

' R. W. Redington, Phys. Rev. 115, 894 (1959). 6"In this chapter the trapping of majority carriers is neglected. Such trapping does not affect the low-frequency gain, but it increases the device response time and lowers GB,3.4 "At very high field, the carriers will traverse the photoconductor early in the microwave cycle, and the current will become capacitive. The detector now behaves like a photocapacitance rather than a photoresistance, but the current gain is still given by Eq. (5). The effect of the very high field is to change the phase and the harmonic content or the detector output. (See Eddolls and Wright.') "See also R. L. Williams, J . Appl. Phys. 40, 184 (1969)for compensated extrinsic case.

1 1. MICROWAVE-BIASED PHOTOCONDUCTIVE DETECTOR

I-#

REFLECTION CAVITY

439

CIRCULATOR

5

LIGHT INPUT (A.M.)

FIG 1 Photoconductive demodulator. Go

=

l,/ayF (After Sommers and Gatchell.’)

It is also apparent why very high bias frequency is desirable, for at fixed cavity bandwidth the limit on G B is proportional to the square of the driving frequency. Implicit in Eq. (7) is the assumption that the microwave field penetrates the photoconductor without being screened by the free carriers, which also requires high frequency, fo

’1 / 2 T d .

(8)

As a reference, the lower limit for 10-GHz bias is 20 ohm cm material. 6. ANALYSIS OF MICROWAVE EQUIVALENT CIRCUIT

The block diagram of the microwave circuit which has been most fully studied is shown in Fig. 1. The input signal F, an amplitude-modulated optical carrier, is focused on a small piece of photoconductor mounted in the gap of a reentrant cavity. The photoconductor is biased by a klystron connected to the reflection cavity through a circulator. Power reflected from the cavity passes through the circulator to a TWT and to a second detector. To operate, the coupling to the cavity is adjusted so that essentially all the bias power is absorbed in the cavity (critical coupling), only enough power being reflected to bring the second detector to the region of linear response. This requires about 1 mW of power at the second detector for a conventional video crystal diode terminated in 50 ohms. The response of the photoconductor to the light makes the impedance of the cavity follow the envelope of the optical signal, which modulates the reflection coefficient of the cavity and converts the input signal into sidebands of the microwave power returned to the TWT. These weak sidebands beat with the unmodulated microwave power, giving a homodyne action to the second detector. The video output reproduces the envelope of the optical input.

440

H. S. SOMMERS, JR.

The photoconductive gain of the circuit is defined as the gain from the optical input to the first source of circuit noise, the TWT in Fig. 1. It is the ratio of the signal current delivered to the TWT to the rate of production of photoexcited charge in the phototransducers. From first-order perturbation theory the gain can be derived as a function of frequency and circuit parameters.2-6a

where 6 is the depolarizing factor for the photoconductor in the cavity; v and t are the drift velocity and lifetime, respectively, of each photocarrier; m is the angular frequency of the signal; [E2/W11/2is a geometrical parameter, equivalent to a cavity-filling factor in paramagnetic resonance work, with E the electric field in the gap without the sample when energy W is stored in the cavity; R is the input impedance of the TWT; and Af is the bandpass of the cavity. The first bracket shows the dependence on the photoconductor. Although both carriers contribute in principle, one usually dominates. With sufficient bias field the only material parameter affecting G B is the saturated drift velocity of this carrier. The second bracket, [B2/W]'i2,is the figure of merit of the cavity used as an optical detector. It is a geometrical parameter independent of the photoconductor and the bias field. The challenge to the microwave engineer is to increase G B by increasing the cavity parameter at fixed cavity bandwidth. From its dimension, (volume)- 1/2,it is apparent that improvement comes from reducing the volume under the center post of the cavity, which must be done without increasing the capacitance of the cavity or shadowing the photoconductor. The last bracket is dictated by the application. The input impedance of the amplifier is about 50 ohms for large bandwidths, while the cavity bandpass must exceed twice the desired information bandwidth. When the microwave sidebands fall outside the bandpass of the cavity the gain plummets.

IV. Design Details 7. REENTRANT CAVITY

The cavity serves two purposes : it enhances the electric field in the region of the sample, which gives a large figure of merit, and it matches the high impedance of the sample to the low impedance of the microwave line, giving a current gain from the coupling.

11. MICROWAVE-BIASED PHOTOCONDUCTIVE DETECTOR

441

0.

A.TRANSVERSE O P T I C A L PORT

insef f pasf

-3

6. AXIAL OPTICAL PORT

FIG.2. Two geometries for reentrant optical detector cavity. (After Sommers and Gatchell.’)

Figure 2 is a cross section of two versions of the same reentrant cavity which differ in the way that the light is admitted. In version A, the horizontal light beam enters through the sidewall of the cavity. This is a good geometry for the microwave circuit, since the current is conducted from the post through the sample to the copper cap of the cavity. It also permits a long absorption length for the photoconductor without increasing the gap height, which is an attractive feature for an extrinsic material with small optical absorption coefficient. With this geometry it is difficult to take advantage of the high absorption coefficient of intrinsic samples, which permit reduction of the sample thickness to a micron or less. Such a thin sample mounted across the gap would require a backing plate, increasing the stored energy W at fixed field. Version B, in which the light enters through a port on the axis of the cavity, permits a film of the photoconductor to be mounted flat against the end post. In principle, this should lead to very high performance, but it introduces the age-old problem of passing the light through a port which is transparent at optical frequencies and reflecting at microwave. Theoretically, the port could be closed with a wafer of a degenerate semiconductor

442

H. S. SOMMERS, JR.

with resistivity about lo-’ ohm cm, which would have a skin depth at 10GHz of 1 p and an optical absorption length much greater than this. The practical goal of mounting the film onto this semiconductor and making good contact between post and film and between semiconductor and end cap has not yet been reached. This design offers the hope of confining most of the stored energy to the phototransducer. In either cavity the resonant frequency is mainly determined by the length of the post. Reduction of the gap lowers the frequency (Fig. 3). When the gap is less than 5 0 p the effect is very large, showing that the capacitance under the post is now storing an important fraction of the electrostatic energy. Figure 3 shows various characteristics of the cavity as a function of the position of a probe 0.012cm in diameter inserted through the end cap. The curves are the resonant frequency (shown with measured points) and the derived parameters [Ez/W]’’z [Eq. (9)], and the ratio of electric field to root of exciting power. All are plotted against the magnitude of the gap between probe and post. Note that the calculated upper limit for the cavity parameter, assuming the entire capacitance to be the 0.005-cm gap under the post [see Section 22, Eq. (1211 is 6 x lo9 V/cm J”’, while the measured parameter is 1 x lo9. This indicates that the gap itself is still only a small part of the total capacitance of the cavity. 8. VARIABLE COUPLING

Two convenient types of variable coupler are a tapered waveguide beyond cutoff with a movable dielectric insert (Fig. 4), and a loop coupling in OSM coax. Either one needs a micrometer drive to give sufficient sensitivity and the mechanical stability necessary to prevent microphonics. The adjustable element must be located at the cavity to avoid storage of energy between coupler and cavity. It is difficult t o get sufficient coupling with the tapered waveguide, even when the hole through the end of the cavity is so large that the cavity almost loses reality. This coupler only works well when it couples through a hole in the end of the cavity, and then only for cavities with Qo of 200 or more. At lower Q partial success can be achieved by inserting a screw as a resonant antenna, but this is not a good solution, because of difficulties of deciphering resonances due to the cavity from those of the antenna and because of a reduction of bandwidth. The insert screw does not work with the lower cavity of Fig. 2, in which the microwave port is in the sidewall of the cavity. The loop coupling has sufficient adjustment to couple to any cavity. It also has the advantage of being an untuned element, making it easier to locate the cavity resonance. Two mechanical motions are required, one to control the depth of insertion and the other the rotation of the loop about the axis of the coax. This latter is less critical and serves as the fine control.

443

11. MICROWAVE-BIASED PHOTOCONDUCTIVE DETECTOR m

n

0 0 *

lo?

N

(LEFT SCALE)

N

n? -

a w

I (3

z 10.;

a!

0

~

K a n

0

z W

3 W O

PARAMETERS

a

LL

0

5 I0.C

0

a

(RIGHT SCALE)

z

1-

8 W a

I

9.8

1

I

I50

100

2

GAP IN L./

FIG.3. Performance of reentrant cavity at different gap spacings.

The loop can be inserted through a hole in either the end or the sidewall of the cavity. The position of the hole is not critical, since the coupler has such a wide adjustment range, but the fit should be snug to avoid hysteresis in adjustment and microphonics. For convenience, a rotating joint is incorporated in the coaxial line.6d

T-

0.

TAPERED GUIDE 0.063

-4

2.50

1! 'i, 2.188

TEFLON INSERT FIG.4. Variable coupling in tapered +in. x 1 in. waveguide. All dimensions in inches.

hdA suitable rotating joint in OSM coax is made by Sage Laboratories, Natick, Massachusetts.

444

H. S. SOMMERS, JR.

9. SAMPLE MOUNTING

The simplest way of mounting is to cement the edge of a thin platelet of the photoconductor to a raised nub on the removable end cap and assemble the cap to the cavity with appropriate shims so that the sample touches the post. Assembly is simplified by coating the end of the post with a small ball of indium to give compliance. This geometry requires the light to enter through the side port. Although samples as small as 50 x 50 x 2 0 p can be readily mounted in this fashion, there are several drawbacks. The most serious is the difficulty of dissipating the microwave power, often milliwatts or more. The sample does have a good depolarizing factor, which may be nearly unity because the parallel component of E is continuous across a surface, but the cavity parameter is low because the sample occupies such a small part of the gap. Cavity assembly is apt to be tedious; it is much simpler if the sample is mounted on a small piston inserted through the bottom of the cavity [Fig. 2(B)]. A micrometer drive can then be used to press the piston until contact is made to the center post. Friction holds the piston in place. For smaller samples it is convenient to cement the photoconductor to a small block of insulator. Sapphire is good because of its high thermal conductivity. Metallizing the top and bottom of the sapphire helps the heat flow as well as improving the microwave circuit, since it avoids an air gap

InSb

POLE PIECE 6 A P PH IR E

InSb ON SAPPHIRE IN p WAVE C A V I T Y FIG.5. Sample mounted in gap of reentrant cavity.

1 1.

MICROWAVE-BIASED PHOTOCONDUCTIVE DETECTOR

445

between pole face and dielectric. Again the depolarizing factor can be near unity, but the high dielectric constant of the sapphire increases the energy storage. Figure 5 is a photograph of a piece of InSb on sapphire assembled in a transverse cavity. The InSb has an exposed face 25 x 25 p and is 10 p thick. The cross section of sapphire is as small as could be cut with a string saw, about 53 x 5 0 p ; it extends across the pole face, which is about 200 p. 10. OPTICS The hole in a wall of the cavity (Fig. 2) permits f/4optics. The limit on the optical aperture is set by microwave leakage, a very large aperture being possible if the hole is sealed with a conducting transparent material. For the cavity with illumination through the end cap a conical light pipe would be appropriate. The photoconductor would be bonded to the small end of the pipe with a suitable transparent conducting material. Both the bonding material and the photoconductor must have higher index of refraction than the light pipe so as to avoid total internal reflection at the inner end. Approximate analysis of a conical light pipe reveals the following optical properties, but no experimental study has been reported : (1) Conical pipe : included angle of cone, 25, ; diameter of tip, d ;diameter of base, d sin B,/sin 24 ; critical angle of material of cone, 8,. (2) Optical performance : effective numerical aperture for source on cone axis, sin 8,; included angle of field for half intensity, 45,. A simple comparison can be made with the infinite conical pipe and with a perfect lens by thinking of each as a receiving antenna focusing the light onto the transducer of diameter d. For a source on the axis, the infinite cone reaches the thermodynamic limit of collection efficiency for a system with numerical aperture sin 8,. As the source moves off the axis, the gain remains constant to the field angle *5,, where the source passes outside of the cone and the gain drops discontinuously to zero. The truncated cone has only onequarter as high a forward gain, which stays constant to the same field angle k5,,but then the gain drops gradually and reaches zero at +35,; the field for half gain is +24. Finally, the perfect lens with field of view f 2 # and numerical aperture sin 8, also has forward gain one-quarter the infinite cone, but maintains constant gain to k25, where it drops abruptly to zero. Hence the truncated cone is similar to the perfect lens, the difference being that the gain of the cone drops more gradually, beginning sooner but mqintaining finite response somewhat longer. As mentioned earlier, these conclusions for the truncated light pipe are only approximate, being best for small cone angles, and the pattern complexity will increase at large cone angles.

446

H . S. SOMMERS, JR.

V. Performance Factors for Broadband Detectors 11 . FREQUENCY RESPONSE:G B

The performance of a detector at large bandwidth is indicated by the gain-bandwidth product GB. Equation (9) for the trap-free photoconductive detector with microwave bias describes a constant GB for bandwidths exceeding the roll off of Go determined by the photoconductive lifetime. In this region a tradeoff between Go and B is obtainable with a simple postdetection high-pass filter. Implicit in Eq. (9) is the assumption that B is less than the device cutoff, which is roughly half the bandpass of the microwave cavity (i.e., B < Af/2). For bandwidths less than G B the gain of the detector exceeds unity; if the pumping source does not contribute excess noise, the photoconductor should be more sensitive than a diode detector with unity gain5 Because of the high performance of microwave cavities, the cutoff frequency can be very high and the device can be useful at bandwidths well into the microwave range; with a 10-GHz pump, however, the cavity cutoff will restrict the upper limit to the low UHF. With the materials actually available for IR detectors two deviations from Eq. (9) can be expected. Some crystals, of which silicon is a good example,’ do not show a single photoconductive lifetime with a roll off of (l/w), but instead show a slow droop in gain at high frequencies. The GB product does not have a region of constant value and seems to increase slowly with bandwidth. The second departure occurs for samples that are so conductive as to screen the microwave field. The screening reduces the depolarizing factor 6 below the value determined by the dielectric constant of the lattice. This lowers GB, since it reduces G by a factor which is independent of modulation frequency. 12.

SENSITIVITY : INFORMATION

RETRIEVAL EFFICIENCY p

The sensitivity of a broadband optical receiver, which is best measured by SIN, is easily expressed in terms of the information retrieval efficiency j which is a dimensionless parameter defined in terms of the gain of the detector and noise in the receiver.2 Physically, the ratio of p of the receiver to the quantum efficiency a of the phototransducer is just the ratio of the height of a pulse due to absorption of a single photon to the rms amplitude of the zero-signal noise. The parameter p is so chosen that when the ratio @/a) exceeds unity the receiver can count single photons. This is also a sufficient condition, although not precisely necessary, that the receiver be

’ .I.R.

Haynes and .I. A. Hornbeck, “Photoconductivity Conference” (R. G. Breckenridge, B. R. Russell, and E. E. Hahn, eds.), p. 321. Wiley, New York, 1956.

1 1.

MICROWAVE-BIASED PHOTOCONDUCTIVE DETECTOR

447

limited by noise-in-signal rather than amplifier or dark noise for all values of SIN greater than 1. Except for photomultipliers, (P/a) 4 1 because of degradation of the signal by transducer or amplifier noise. Quantitatively, the ratio of signal power to noise power for a receiver with small retrieval efficiency is SIN = (rnpF/4B)'

for

p < p,.

(10)

The critical value p, depends on the nature of the transducer, the nature and the size of the noise sources, the bandwidth, and the modulation depth of the ~ i g n a l . ~For " the photoconductor this critical value is p, A c(, the quantum efficiency ; for the junction diode or the photomultiplier it is p, G 2a. In Eq. (10) F is the average photon flux of the optical carrier, m is the modulation depth, and B is the information bandwidth. The quantity mF/4B is a reduced signal strength in photons/bit, which is a measure of signal level at any bandwidth. If the receiver has a large retrieval efficiency, SIN is linear in the signal intensity for all inputs giving greater than unity SIN, and the analogous form is SIN = m&F/4B,

for

p > /Is.

The linear dependence holds whenever SIN is limited by shot noise from the signal. The most sensitive detector will be the one with p > ps 2 1 ; such a receiver will retrieve all the information available from the incoming signal. The classic example of shot-noise-limited performance is the photomultiplier, which follows Eq. (11) provided that the modulation frequency of the signal is appropriate for the tube. Except for this, the shot-noise limit is not reached at low signal level, and Eq. (10) describes the performance of all other detectors (i.e., photoconductors, optical diodes, bolometers, etc.). The parameter p has a characteristic variation with information bandwidth which can be readily predicted from the definition. At narrow band'"The value /3 = /{<,deduced by equating Eqs. (5)and (8) of Sommers and Catchell' at unity SIN, assures that the receiver is shot-noise-limited for all useful signal levels. It is given by

fi,

= a(m/r)l/(n-

11(8~~/j,)"-Z/Z(n-1)

The new symbols are a number (r) which is unity for a detector giving full generationrecombination noise (photoconductor), and half if it has only generation noise (diode, photomultiplier): a number (n)which describes the variation of the shot-noise output at the device terminals with internal gain (noise power varies as (3"); and (in),the equivalent noise current of the amplifier (the average current which would give shot noise equal to the amplifier input noise). The fundamental charge is q. When the zero-signal noise from the transducer is important, as it always is for sufficiently small bandwidth, p cannot reach the critical value to give shot-noise-limited performance at low signal level.

448

H. S. SOMMERS, JR.

widths where G is constant, p always increases with B because the transient response to a short pulse grows faster with B than does the noise voltage. The parameter p always falls at large bandwidths because of the drop in G . For intermediate bandwidths it has a flat maximum. The receiver is at its peak in this region, although the performance may still be far from ideal.

VI. Response of Various IR Photoconductors-Experimental Quantitative measurements have been made on a number of high-purity semiconductors using a GaAs laser for signal generator. Assuming that the photoconductive lifetime is independent of the wavelength, these measurements can be used to predict the performance for all wavelengths shorter than the fundamental gap. The conditions of the measurements are summarized below’ : Optical wavelength Microwave frequency Microwave power Cavity bandwidth Materials Sample preparation Size Illumination

8500 A nominal 9.5 GHz nominal 50 pW to lOOmW 25-300 MHz Commercially-available high-resistivity singlecrystal ingots Lapped, etched, and cemented to sapphire block 25 x 25 x 10 p nominal Through sidewall of cavity, f / 4 optics

13. SILICON a.

Single Crystal (5000 ohm cm p-type at 300°K)

Silicon has an atypical frequency response which does not show a single lifetime. Above 1 kHz the gain drops slowly with modulation frequency, with the first sharp break at several MHz (Fig. 6). The performance was the same at 300 and 80°K. The value of GB of 3 x lo9 Hz was reached with 6mW of microwave power, insufficient to drive the carriers to saturated drift velocity, but all the sample could dissipate. The information retrieval efficiency p is also shown in Fig. 6. In this measurement there was an excess noise with a l/w spectrum, originating in the klystron, which rose to 10 dB at 200 kHz, and accounts for the rapid drop in /3 for narrow bandwidths. This performance is not as good as germanium. b. Epitaxial Film (150 ohm cm p-type, p = 200 cmz V - ’ sec-

’ at 300°K)

The epitaxial layer (15 p thick), grown by vapor-phase transport, had low mobility and high free-carrier concentration. The gain saturated at about

449

11. MICROWAVE-BIASED PHOTOCONDUCTIVE DETECTOR

10 m W bias power due to sample heating, well below saturated drift velocity. This material behaves more nearly like a typical insulating photoconductor, with a single photoconductive lifetime which increases on cooling. Figure 7 shows the gain versus frequency and fl versus bandwidth I

.\

I

I

I

I

I

I

10-2

P

t a 10-3 LL

0 W

10-4

102

I

I

102

I

I

1

I 1

I

J

lo4 106 FREQUENCY OR BANDWIDTH IN Hz

FIG.7. Silicon film; performance at 300 and 195°K.(After Sommers and Gatchell.’)

450

H. S . SOMMERS, J K .

at 300 and at 195°K. This modest drop in temperature increased the lifetime from 10-4sec to at least isec. The reduced temperature improves the sensitivity at very narrow bandwidths, as shown by the extension of the plateau for j to 200Hz. Because the low-frequency noise at such narrow bandwidths originates in the klystron rather than the following amplifier, the sensitivity at small bandwidth is maintained at very small bias power (400pW in Fig. 7). Of course, GB drops with reduction in power. At 80°K very long time constants developed, and the crystal needed minutes or perhaps hours to reach equilibrium. 14. GERMANIUM

High-purity germanium provides a classic example of the change in photoconductive gain on substitution of RF for dc bias. With a mobility ratio of approximately one and an identical lifetime for both carriers its gain with dc bias is restricted to two, and germanium is considered to be of no consequence as a photoconductor. With microwave bias, however, the performance of germanium is outstanding. Its sensitivity approaches the goal of a photon counter. The saturation of drift velocity at high electric fields is shown in Fig. 8, a graph of photocurrent gain against bias power at various temperatures

I 102 MICROWAVE B I A S POWER IN

104

pL .w

FIG.8. Germanium, n-type; saturation of gain with electric field. (After Sornrners and Gatchell.2)

451

1 1. MICROWAVE-BIASED PHOTOCONDUCTIVE DETECTOR

for an n-type sample. The crystal showed sufficient carrier freeze out to keep its resistivity above 10 ohm cm even at the highest mobility, and so freecarrier screening was never significant. The shift with temperature for the bias power to give velocity saturation is consistent with the change in the low-field mobility, indicating a temperature-independent saturated drift velocity of lo7 cmisec, which agrees well with the accepted value.* According to Eq. (9), a photoconductor with a single lifetime should have a frequency roll off at the rate l/w. Figure 9 shows that germanium nearly obeys this expectation, as well as illustrating the change in lifetime with temperature and the constancy of GB. The room-temperature curve is the gain for a sample of 40 ohm cm n-type germanium, mobility of 1800 cm2 V-' sec-', with sufficient bias power (5 mW) to almost saturate the drift velocity. The gain is constant to 3 MHz, indicating a room-temperature lifetime of 50 nsec. At 195°K (not shown) this has changed to p-type, nearly intrinsic. The response is slower and the roll off is flatter, suggesting a complicated recombination pattern which may involve both localized I oe

los

f U (3

I-

z

w

a a 10 L3 0

0 I-

0

I

a

2

10

I'0

10' FREQUENCY IN Hz

10"

I oa

FIG. 9. Germanium; gain at various temperatures. (After Sommers and Gatchell..

E. J. Ryder, Phys. Rev. 90, 766 (1953); J. B. Gum, Progr. Semicond. 2,213 (1957).

452

H. S. SOMMERS, JR.

centers and surface recombination. It is more typical of silicon than of germanium. This sample is still p-type at 8WK, with a hole mobility larger by an order of magnitude, p = 4.4 x lo4 cm2 V - sec- For this curve the power of $mW drives the carriers well into saturation. There is a long region where the gain drops at (l/w),indicating a single well-defined photoconductive lifetime which has grown to at least 5 msec. The behavior at 145°K of the n-type sample of Fig. 8 is also included. It shows a sharp break at 600 Hz, or 0.3 msec, but does not drop at (l/m). This roll off seems to be intermediate between the behavior at 195" and that at 80°K. For these very pure crystals the sign of the majority carrier seems to be of little consequence. The good quantitative agreement, with no adjustable parameters, between these curves and Eq. (9) indicates that majority-carrier trapping is unimportant. This is in sharp contrast to experience with insulating photoconductors such as CdS, whose frequency response drops much sooner than the photoconductive lifetime defined by Eq. (3). The sensitivity of germanium is very high, with a retrieval efficiency rivaling good photomultipliers at their optimum wavelengths for bandwidths up to 10 MHz. Plots of B against bandwidth are shown for various temperatures in Fig. 10. In general, the plateau for p lies in the range of constant GB, from the reciprocal of the photoconductive lifetime to the cutoff imposed by the bandpass of the cavity. Depending on the noise spectrum, the plateau may be flat or have a small positive or negative slope. At 300°K the l/w noise extended to at least 10 MHz, and so the plateau should be flat2 The value of 3% for B is very good for IR detectors. At lower temperatures the driving power for carrier saturation is less, giving reduced l/onoise and increased p. At 195°K p also reached several percent, and 10% at 145 and at 80°K. The drop in p a t larger bandwidths corresponds to the region of white noise, where the l/w noise is below the noise of the TWT. Q

10-1

k e w

I 10" 0 W

e

3

p

10-8 102

104 BANDWIDTH IN H z

108

FIG.10.Germanium;retrievalefficiencyatvarioustemperatures.(AfterSommersand Gatchell.z)

1 1.

MICROWAVE-BIASED PHOTOCONDUCTIVE DETECTOR

453

15. INDIUM ARSENIDE(0.01 ohm cm n-type, p = 3.2 x lo4 cm2 V - ' sec-' at 80°K) Because of its high conductivity, free-carrier screening reduced the performance of InAs, although its long lifetime still makes it attractive for work at small bandwidth. The sample began to heat with 450 pW of bias power. While germanium with comparable mobility reached velocity saturation at this power, the InAs was far from saturation, because of the reduction of the internal field by screening. This accounts for the low G B shown in Fig. 11, only lo8 Hz, and the low value of about 2 x for /?.A sample with better heat sink was able to dissipate 60 mW of power and reached a G B of 4 x lo8 Hz, but the lifetime was reduced to 100 nsec by the high field. 16. INDIUM ANTIMONIDE

a. P-Type (15 ohm cm, p

=

6 x lo3 cm2 V - ' sec-' at 80°K)

P-type indium antimonide is an unusual semiconductor in having both a low mobility ratio ( b G 1) and a high lifetime ratio for the two carrier^.^^'^ Like InAs, the majority carrier lifetime drops at high electric fields. Figure 12 shows the gain against frequency at low and at high fields (0.5 and 2.3mW bias power). The shoulder on the low-power curve at higher frequencies is the contribution of the very high mobility, short lifetime electrons; the final drop is the cavity cutoff, for the electron lifetime is less than 1 nsec. The entire curve is in reasonable agreement with Eq. (9),

z 2 I-

gz e

104

3 V

0

I

a

lo2 1.0

102

104

106

FREQUENCY OR BANDWIDTH IN Hz

FIG.11. Indium arsenide; performance at 80'K

lo

S. W. Kurnick, A. J. Strauss, and R. N. Zitter, Phys. Rev. 94, 1791 (1954). R. A. Laff and H. Y. Fan, Phys. Reo. 121, 53 (1961).

454

H. S . SOMMERS, JR.

z

u

a

s 10'

I .o

FREQUENCY Hz

FIG.12. Indium antimonide, p-type; gain at low and high fields. (After Sommers and Gatchell.2)

using published values of hole and electron mobility and lifetime" and a calculated depolarizing factor 0.3.I Here is another striking example of the advantage of rf bias for intrinsic photoconductivity, this time with a material of very short minority carrier lifetime. From Eq. (3), the maximum gain under dc bias has two contributions, unity from the minority carrier and the ratio (majority carrier lifetime to minority carrier sweepout) for the majority carrier. In contrast, Fig. 12 has in addition to the majority carrier gain of lo4 a minority gain of about 10'. The maximum value that the minority carrier gain can have is the product of the transfoi-mer gain, which in a sense is an artifact since it is only due to matching the photoconductor impedance to the microwave output circuit, and the minority carrier transit gain, whose limit is the number of field reversals in its lifetime. For this sample, the upper limit to the minority carrier gain is 200, taking as the transformer gain the root of the sample resistance to the waveguide impedance (1.5 x 104/50)'/2 or 17, and the number of reversals as (2 x lO'"/sec) (6 x 10- l o sec) or 12. The only number not directly measured is the electron lifetime, taken from Laff and Fan." Incidentally, the quick calculation shows that the electron gain has essentially reached the theoretical limit for p-type InSb of this quality at this microwave frequency.

'*R. M. Hozorth and D. M. Chapin, J . Appl. Phys. 13, 320 (1942)

11. MICROWAVE-BIASED PHOTOCONDUCTIVE DETECTOR

455

The curves of photoconductive gain at several modulation frequencies against microwave bias power (Fig. 13) have some interesting features. At 3 MHz, where the electrons make the major contribution, the carrier drift velocity is independent of field from 1 to 20 mW bias power. (At 20 mW the sample breaks down by pair generation. The hole lifetime changes irreversibly and does not recover until the cryostat is heated.) The estimated field intensity (top scale) gives a saturation curve in reasonable agreement with published data for n-type material.I2 The distortion of the electron distribution becomes noticeable above 50 V/cm, with breakdown at about 800. At 1 kHz the conduction is by the holes. Their velocity distribution is independent of field throughout this region because of their low mobility. The abrupt drop in response at 600 pW bias is due to a drop in the lifetime of the excess holes, a drop associated with the heating of the electrons. The hole lifetime drops at least an order of magnitude, for the response at powers above 4 mW is due to electrons. The curve at 300 kHz shows about equal contributions from each carrier at low field, with the hole contribution disappearing by 3 mW. The change in the hole lifetime due to saturation of the electron velocity suggests that the hot electrons change the charge distribution in the recombination centers. This implies that more than one type of center is ESTIMATED FIELD IN V/cm

lo3 5

za (3

5 102 W

a: 5 0 0 I0 I

5

n

10' 5 5

Id

5

5

5

lo2 lo3 pWAVE BIAS POWER I N p W

10'

FIG.13. Indium antimonide, p-type; saturation ofgain with electric field. (After Sommers and Gatchell.')

'* M. Glicksman and W. A. Hicinbothem, Jr., Phys. Reu. 129, 1572 (1963).

456

H. S. SOMMERS, JR.

involved in the photoconductivity of InSb, which is consistent with present ideas. O The retrieval efficiency at 2 mW of power continued to rise with bandwidth to the cutoff of the cavity (Fig. 14). It appears that the photoconductivity of the electrons in high resistivity p-type InSb should make a very sensitive detector for bandwidths in the 100-MHz range. 6. N-Type (T = 80°K)

The response of n-type InSb seems to vary considerably with the sample, even for high-purity crystals with electron mobilities of at least 5 x lo5cm2 V- sec- I . A crystal with resistivity of 0.4 ohm cm showed a velocity saturation curve beginning at 80 pW of bias power and flat from 0.5 to 5 mW. Its lifetime was less than 5 nsec. A 1 ohm crn crystal had a lifetime of 1 pec, which dropped with field for power above 10pW, where velocity saturation first appeared. It may be that both holes and electrons contributed at low modulation frequency. The gain-bandwidth product was lo9 Hz, and the retrieval efficiency 0 had a flat plateau at 1% from lo6 to lo' Hz bandwidth.

17. MERCURY CADMIUM TELLURIDE"^ (Minneapolis-Honeywell sample, p-type at 80°K) The carrier drift velocity seemed to saturate at 30mW of bias power, suggesting a mobility of about lo3 cm2 V-' sec-'. Figure 15 shows the gain

a k U

w I LL

O

W

16~

a 3 E LL

Id*

I.o

to2

104 BANDWIDTH Hz

lo6

lo8

FIG.14. Indium antimonide, p-type ;retrieval efficiency at low and high fields.(After Sommers and Gatchell.') I2"Thisunpublished work was jointly supported by the U.S. Army Electronics Command, Fort Monmouth, New Jersey under Contract DAAB07-67-C-0252, and by the RCA Laboratories, Princeton, New Jersey.

1 1. MICROWAVE-BIASED PHOTOCONDUCTIVE DETECTOR BANDWIDTH IN

. I00

z

4'K

457

Hr

1

*

4

U

W

10 -

104

-

10 6 FREQUENCY

IN Hz

FIG.15. Mercury-cadmium telluride ;response at low temperatures.

against frequency and the retrieval efficiency against bandwidth at 77°K. At helium temperature the response was about the same, but at 145°K it was much inferior.

18. MERCURY-DOPED GERMANIUM'~~ AT 10.6 ,u (Texas Instruments Sample, T = 4°K) The sample contained 1.1 x 10l6Hg atoms/cm3 and had an absorption coefficient of4/cm and a mobility of lo4cm2/v sec. It was cut to a square bar of cm2 cross section and 4 x lo-' cm long, givinga single-pass absorption of 0.16. The pole pieces of the cavity were shaped to chisel ends lo-' x 4 x lo-* cm and the sample cemented between them. With a cavity Q of 50 (bandpass of 200 MHz), 30 mW of power saturated the gain. The sample lifetime was measured to be 7 nsec, photoconductive gain to be 25, and the gain-bandwidth product lo9 Hz. The retrieval efficiency rose as the rootofthebandwidthtoamaximumof2 x 10-3atthebandwidthof25 MHz [NEP = 2.5 x W(Hz)-'/', and D* = 4 x 1010cm(Hz)'/2W-']. A direct comparison of dc and rf bias for broadband applications was made by putting electrodes onto a sample of the same material, inserting it in the same cryostat, and connecting it through six inches of coaxial cable (35 pF capacitance) to the same video amplifier. A comparison of the two at an information bandwidth of 80MHz is shown in the following tabulation.lZb lZbWewish to thank T. E. Walsh and C. Sun for permission to include some of their results at 10.6 p prior to publication. (To be published in IEEE J. Quantum Elec. and Proc. IEEE.)

458

H . S. SOMMERS, JR. ~-

(W

NEP (10.6 11, 1.5 MHz, 1Hz) (W/Hz1I2)

D* (10.6 p, 1.5 MHz, 1 Hz) (crnH~"~/W)

2 x 107 7 x 108

9 x 10-" 2.5 x

1.1 x 108 4 x 109

Gain bandwidth

DC bias RF bias

Even with an extrinsic photoconductor in which carrier sweepout is not a problem, the microwave bias gives much better performance for a broadband system.6cOfcourse at small information bandwidth where the amplifier input impedance can be very high, the dc biased material would reach the BLIP limit for a room-temperature background.

VII. Comparison of Sensitivity with Representative Broadband Detectors 19. RETRIEVAL EFFICIENCY p Figure 16, a plot of retrieval efficiency fl against bandwidth B, indicates the sensitivity of various detectors for 8400-A light. The solid curves are for various photoconductors with microwave bias. These do not reach the critical value of B,, and so their SIN for weak signals is quadratic in the input signal and is described by Eq. (10). The broken lines give 4, for the best commercially available devices and for two experimental avalanche diodes. The long dashes indicate the bandwidths where the photomuhiplier reaches the critical value p,. In this region S/N is linear in the input and is given by Eq. (11). At lower bandwidths dark-current noise keeps p below p,, and SIN is again quadratic in signal, Eq. (10) (short dashes). A selected 7102 photomultiplier with S-1 cathode cooled to 195°K is shot-noise-limited for B > 50kHz; its critical value is 8, lo-'. The Philco L-4501, a small-area silicon diode, reaches its peak value /3 G 10by about 40 kHz when working into a low-noise preamplifier with lo6 ohm input resistance. An experimental silicon avalanche diode13 driving an amplifier with 30-MHz bandwidth would reach the shot noise limit above lo8 Hz; the excess noise due to the avalanche process holds p, to about 1.5 x lo-' at B = 30MHz.'" A germanium avalanche diode cooled to -25°C has a rather similar perf~rmance,'~ but the excess noise is somewhat worse. The photoconductors are a germanium single crystal at 145"K, a silicon film cooled to 195"K,and single-crystal indium arsenide and indium antimonide in liquid air. All drive a TWT amplifier with 10 dB noise figure.

'

W. N. Shaunfield, Semiconductor-Components Div., Texas Instr. Inc., Dallas, Texas. Private communication (to be published).

11. MICROWAVE-BIASED PHOTOCONDUCTIVE DETECTOR

I

10'

I o4

lo6

459

Io8

VIDEO BANDWIDTH Hz

FIG.16. Retrieval efficiency of various IR detectors for 8400-Alight.'3a

For bandwidths less than 10' Hz the photoconductors with microwave bias are very high performance IR detectors. 20. SCOPEPICTURES

The high sensitivity that microwave-biased detectors achieve in the appropriate bandwidth region is illustrated by some scope photographs. Figure 17 compares the response to 8400-A light of a selected 7102 photomultiplier (its quantum efficiency is maximum at this wavelength) with an InSb photoconductor in liquid nitrogen. The pulse length in the photograph is about 40nsec and the pulse height about 2 x loT7W. The photoconductor shows no noise at this signal height, while the photomultiplier shows only shot noise (noise-in-signal). Although the photomultiplier has a high internal gain which is essentially noise-free, giving p > fis = 2a, its low quantum efficiency of 0.4% degrades the incoming signal much more 13"Figure 16 indicates that both the lnSb photoconductor and the 7102 photomultiplier have a figure of merit of about 1 which means that they will reach unity SjN at equal light levels. However, because the photoconductor obeys Eq. (10) while the photomultiplier follows Eq. ( I I), the photoconductor outperforms the 7102 at all useful signal levels ( S / N > 1). At very low levels the photomultiplier will have the better S I N , but here reception is so noisy that the improved performance is of little practical importance.

:<,

460

H. S. SOMMERS, JR.

In Sb

2 0 nsec/div FIG.17. Comparison of p-type indium antimonide photoconductor and 7102 photomultiplier for 8400-A light. Pulse height: 10’ photons.

than does the amplifier noise of the photoconductive detector with microwave bias. 13a Figure 18 compares the same photomultiplier, now cooled to 195°K to eliminate dark noise, with a germanium photoconductor at 145°K. Here the pulse length is 0.5psec and the input signal is much smaller. With a pulse height of 2 x W the photoconductor with microwave bias (middle trace) shows a good signal, while the photomultiplier trace (bottom) does not break the baseline. It shows the presence of a pulse, but its height cannot be estimated. It requires 50 times the signal intensity to give performance equivalent to the germanium (top trace). A final example is a Philco L4501 silicon photodiode driving a load of 6 in. of 50-ohm cable connecting it to a high impedance amplifier, compared with the same germanium photoconductor in Fig. 19. With a pulse length of 1 psec and 50 times the power, the diode barely registers a signal, while the photoconductor shows no noise. (The overshoot originates in the postdetection filters which shape the bandpass of the receiver to pass this pulse.) Figure 20 is a comparison of two actual communication receivers in breadboard form. The input signal is a tv test pattern broadcast as a vestigial sideband FM modulation on a 5-MHz subcarrier impressed on the beam of a 1.15-p laser. The front end of one of the receivers is a detector custommade from the best available components, a Philco L-4530 InAs photo-

1 1.

MICROWAVE-BIASED PHOTOCONDUCTIVE DETECTOR 7102 AT 195'K 3.7 x lo4 PHOTONS/PULSE

Ge AT 1 4 5 O K 7.7 x 10 PHOTONS/PULSE

7102 AT 195'K 1.1 x 10' PHOTONS/PULSE

FIG.18. Comparison of n-type germanium and 7102 photomultiplier for 8400-A light.

461

462

H. S. SOMMERS, JR. Ge

Si P / N J U N C T I O N

c

FIG. 19. Comparison of p-type germanium photoconductor and silicon photodiode for 8400-Alight. Pulse height: 6 x lo4 photons.

diode mounted directly to the input of a low-noise preamplifier with 3 dB noise figure and 1000 ohm input impedance. The other receiver was a microwave-biased photoconductive detector. The picture on the right comes from the diode illuminated with lO-'W of signal; the left-hand picture is from the p-type germanium photoconductor (operated at room temperature) with 2% as much input signal. Cooled to 145"K, the germanium would have required only & of this light level.

VIII. Areas for Further Research OF MICROWAVE NOISE 2 1. REDUCTION

Because the photoconductor in the microwave cavity has only capacitance contacts, the only noise associated with the phototransducer should be generation-recombination noise associated with traffic between the free

11. MICROWAVE-BIASED PHOTOCONDUCTIVE DETECTOR

Ge 1.8 x lo-' W A T T S

I n A s DIODE 1.3 x

463

WATTS

FIG.20. Comparison of p-type germanium and indium arsenide photodiode for 1.15 p light.

band and the doping level. This noise will be unimportant if the number of free carriers is sufficiently smalL5 In studies of the microwave-biased photoconductor' no noise associated with the material has been noticed. On the other hand, the retrieval efficiency has been severely limited by some noise other than that of the following amplifier. The photoconductive gain required to give p = 1 for an amplifier with 10 dB noise, a 50 ohm input impedance, and bandwidth B is about 108/B1'2.5With the G B approaching 10" Hz that these devices display, unity retrieval efficiency should be attained for B < 104Hz. The failure to observe fi > 0.1 implies an excess noise of around 20 dB at lo4 Hz. It has an approximately l/ospectrum. This excess noise is associated with the klystron, but not in a fundamental way. It seems to be due to failure to hold the klystron frequency close enough to the resonant frequency of the cavity, which gives a conversion of FM noise of the klystron to AM noise by the discriminator action of the cavity. Only when this source of noise is removed will the performance be limited

464

H. S. SOMMERS, JR

by the more fundamental sources of noise : amplifier noise, generationrecombination noise, and, ultimately, noise-in-signal.

22.

INCREASE IN

GAIN-BANDWIDTH

The two available parameters determining the gain-bandwidth product [Eq. (9)] are the maximum drift velocity of the carriers and the cavity performance parameter. With the exception of InSb, carrier drift velocities saturate at about lo7 cm/sec, and so it is doubtful if any new material will give much improvement. Material work will reduce the free-carrier concentration toward the limit assumed in the analysis, but the screening by free carriers is harder to avoid as the development extends farther into the IR. There is much improvement possible in the cavity parameter before fundamental limits are reached. The ideal cavity would concentrate all the electric field in the photoconductor, which would then resemble a planeparallel capacitor filled with dielectric and having no fringing field. Now the sample should be treated as integral with the cavity, and the cavity parameter would be (Ez/W)"2= [E2/$CV2]'/2= (87t x 1012/EAd)1/2,

(12)

where E is the relative dielectric constant of the photoconductor, A and d are its area across the post and its thickness, respectively, and I/ is the voltage drop across the gap for the internal field E. With diffraction-limited optics and an intrinsic photoconductor with high optical absorption coefficient the transducer size might be reduced to a cube of 5 p on edge, which would give a cavity parameter of 10" V/cm J'l2. Since this is two orders of magnitude higher than the measured parameter of the empty cavity, there is still much leeway for imaginative engineering.

23.

INCREASE IN OPTICAL

FIELD OF VIEW

So far the emphasis has been on improved sensitivity. An important practical consideration is the field of view of the detector; the larger the field, the easier the detector is to use. For a simple lens the included angle of view is the ratio of detector width to focal length. A large detector area is required to give a large field of view with a large-diameter lens. From experience with other detectors fl (which is proportional to the reciprocal of the noise-equivalent-power) should vary as the reciprocal of the detector width. l4 Achieving this is another problem in cavity design, requiring scaling the post dimensions and gap to encompass a larger-area photoconductor. The cavity parameter will also drop, hopefully by no l4

R. Clark Jones, Proc. Z.R.E. 47, 1495 (1959).

11. MICROWAVE-BIASED PHOTOCONDUCTIVE DETEClVR

465

more than the reciprocal width of the photoconductor. Lower microwave frequency and a larger cavity may be preferred. This change would be consonant, since the larger device will have a reduced GB and so a smaller bandwidth.

This Page Intentionally Left Blank

CHAPTER 12

Imaging and Display Robert Sehr Rainer Zuleeg

I . INTRODUCTION . . . . . . . . . . . . . . I . General . . . . . . . . . . . . . . . 2 . History . . . . . . . . . . . . . . . I1 . BEAM-SCANNED I MAGI NG DEVICES . . . . . . . . . 3 . The Vidicon. . . . . . . . . . . . . . 4 . The Plumbicon . . . . . . . . . . . . . 5. The Sicon . . . . . . . . . . . . . . 6 . Infrared Sensitive Vidicon . . . . . . . . . . 7 . Laser Scanned M O S Device . . . . . . . . . 111. ELECTRONICALLY SCANNED PHOTODETECTOR ARRAYS. . . 8 . Photosensitive Structures and Their Applicability to Imaging 9 . Monolithic Structures . . . . . . . . . . . 10. Thin-Film Polycrystalline Imaging Arrays . . . . . 1v. IMAGE READOUT METHODS FOR PHOTODETECTOR ARRAYS. . 1 1 . Photocurrent Mode . . . . . . . . . . . I2 . Photon Fiux Integrution Mode . . . . . . . . 13. Excitation Storage Mode . . . . . . . . . . 14. Random Access . . . . . . . . . . . . . V . IMAGING CHARACTERISTICS OF PHOTODETECTOR ARRAYS . . VI . ARRAY AND SCANNING CIRCUIT INTEGRATION . . . . . VII . DISPLAY DEVICES. . . . . . . . . . . . . 13. Ferroelectric-Controlled Electroluminescent Display . . 16. Scanned Electroluminescent Diode Array . . . . . VIII . PARALLEL READOUT IMAGECONVERTERS . . . . . . . 17 . Nonregenerative Image Converters . . . . . . 18. Pseudoregenerative Image Converter . . . . . .

. . . . . . . . . . . . . .

.

.

. . . . . . . .

. . . . . . . .

467 467 468 470 470 474 474 477 480 483 483 487 493 497 497 499 504 504 505 508 508 509 514 520 521 524

I . Introduction 1 . GENERAL Electrooptical imaging and the instantaneous transmission of images from inaccessible or distant places emerged as a technological challenge from the discovery of the photoelectric effect of selenium. Today. almost 100 years later. a complete “first generation” solution to this problem has been provided in the form of television.

467

468

ROBERT SEHR AND RAINER ZULEEG

Providing increased accessibility and range for visual perception is only a part of the overall goal of broadening human sensory perception. Imaging as an intelligence gathering process is not confined to the visible portion of the spectrum. It is of interest from the ultraviolet (UV) to the microwave part of the electromagnetic spectrum. The principal factors determining the spectral region of interest for imaging are : (1) the spectral emission, reflection, and absorption characteristics of the target scene, and (2) the wavelength of the scene illuminating source (sun, incandescent light, laser, etc), and the spectral absorption characteristics of the transmission medium. It is within this frame of reference that terrestrial temperatures between 250 and 2500°K and the wavelength of high energy density lasers combine with the transmission characteristics of the earth’s atmosphere to render the spectral region between 0.5 and 30 p a region of high information content for passive and active’ imaging under various terrestrial conditions. Consequently, the extension of optical imaging beyond the visible into selected bands of the infrared spectrum between 1 and 40p is a major objective of modern solid-state device technology. This chapter deals with the principles of solid-state imaging techniques and discusses practical devices and their characteristics. Emphasis is placed on electronically scanned planar devices fabricated from monocrystalline materials. Parts 111-VI cover this subject in detail. Beam scanned devices in which photoconductivity is the image converting mechanism are briefly treated in Part 11. Image conversion and visible display techniques by scanned electroluminescent panels are treated in Parts VII and VJII. 2. HISTORY With the discovery of the photoconductive property of selenium in I873 by Willoughby Smith’ a basis was given for the rather old and fascinating idea of “instantaneous transport of optical images.” Only two years later R. Carey proposed the first image sensor in the form of a mosaic consisting of a large number of minute selenium cells, thus imitating the human eye. However, the first actual device was built thirty years later by Rignoux and Fournier2a in 1906. They constructed a photodetector array consisting of 64 individual selenium cells, each connected by two wires to a corresponding shutter. A simple image such as a numeral projected on the

’ In active imaging the scene i s illuminated by a light source from the imaging position, and the image is formed with the reflected radiation. No special light source is used in passive imaging W. Smith, Nature (February, 1873). ”P. Rignoux and G. Fournier, Reu. Gen. Elec. 1,23 (1906).

12.

IMAGING AND DISPLAY

469

matrixzb was converted by the elements into electrical currents which operated the shutters. Illuminated from behind, the array of shutters reproduced the pattern. The idea of dissecting the picture into small elements, converting the illumination of each element into electric current, and transmitting each through a separate wire (channel) simultaneously, leads to an impractically complicated transmission system for high element density arrays. Therefore parallel (or simultaneous) readout of the image was soon replaced by serial (or sequential) readout. Already in 1884 Nipkow3 .proposed to sample (scan) the image, point after point, in a time-sequential manner by means of a rotating disk with holes precisely located on a one-turn spiral. However, this scheme has the disadvantage of severely reducing the illumination level of the image. To reproduce time-varying images sharply for the human eye, all image elements have to be sampled in less than 1/20 sec, a time interval within which the eye cannot distinguish optical changes. Thus for a 300-line frame, i.e., a 90,000-element image, the rotating Nipkow disk exposes each picture element only 1/1,800,000 sec. This difficulty was overcome with the invention of the iconoscope by Zworykin4 around 1930. The image sensing target of this device is exposed to the picture all the time, and the photoelectric image conversion mechanism is continuously active rather than only during readout time. In other words, the photon flux, constituting the incident image, is integrated during the exposure time just as in the human eye. In the iconoscope the image is converted into a stored charge pattern by means of a photoemissive instead of a photoconductive layer. The stored charge pattern is sampled and erased by an electron beam. Several other image tubes utilizing photoemissive targets, such as the image orthicon and image dissector tube, have improved on the characteristics of the original icono~cope,~ especially with respect to sensitivity, by orders of magnitude. Photoconductivity as the principally utilized effect for imaging returned with the introduction of the vidicon6 in 1950. Its major advantage was greater simplicity, ruggedness, and longer life. However, it had severe shortcomings with respect to sensitivity and speed of response. These were eliminated in later versions introduced under the names of Plumbicon and Sicon (see Part 11). ZbTheterms array and matrix will be used interchangeably throughout this chapter. P. Nipkow, German Patent No. 30105, January, 1884. V. K. Zworykin, Proc. I.R.E. 22, 16(1934). Consult D. G. Fink, “Television Engineering.” McGraw-Hill, New York, 1960, for a description of various television cameras and their operating principles. P. K. Weimer, S. V. Fourge, and R. R. Goodrich, Electronics 23, 70 (1950).

470

ROBERT SEHR A N D RAINER ZULEEG

Parallel to the development of improved image tubes in the 1960's allsolid-state imaging devices began to emerge from the laboratories as a direct result of advances in silicon technology. Sophisticated microelectronic processing techniques allowed not only the fabrication of planar detector arrays of relatively high density, but also of large scale integrated switching arrays required for scanning. As with most other solid-state devices, their advantages in relation to tube devices are smaller volume, weight, and power consumption, and greater reliability under certain extreme operating conditions such as high acceleration rates. But beyond being merely a replacement for tube devices, solid-state imaging arrays are gaining importance for their two major features : ( 1 ) devices are planar, and therefore highly flexible in system applications; and (2) the spectral response can be extended to the intermediate infrared spectrum, where critical imaging requirements have so far gone unsatisfied.

11. Beam-Scanned Imaging Devices

3. THEVIDICON Beam-scanned imaging devices of the vidicon type are historically and logically the forerunners of the planar, all-solid-state, electronically scanned devices which will be treated in detail in Parts 111-VII. The scanning electron beam can be considered as a multipath switch, connecting and disconnecting serially the image elements of the target film so that the image information can be transmitted sequentially through the transmission channel. The vidicon may be divided into three sections, as shown in Fig. 1 : the electron gun section, the scanning section, and the target section. The electron gun produces, by means of a thermionic cathode and associated electrodes, a focused beam of electrons which strikes the photoconductive layer of the target. The scanning action of the beam is achieved by periodic deflections, either magnetically or electrostatically. The target consists of a high resistivity photoconductor layer applied over a transparent electrode onto the flat glass faceplate. The high resistivity photoconductor layer and the transparent electrode (signal plate) form a capacitor which is connected to the target voltage, + V,, viu the load resistor R,. The photoconductive target layer is a continuous semiconductor film which is not divided into separate image elements, as is the case with the photocathode in the iconoscope. Nevertheless, because of its high lateral resistance, the film behaves as if it consists of separate image points of the size of the electron beam cross section.

471

12. IMAGING AND DISPLAY Target section,

gun section-

Scanning section ,Glass

face plate

Photoconductive layer

Electron beam

Video signal, v, out

FIG. 1. Schematic drawing of a vidicon imaging tube, showing the major elements of the device

The equivalent circuit of an image element of the target plate is a capacitor Ci in parallel with a photocurrent generator Gi, as shown in Fig. 2. In operation the capacitors Ci are periodically connected to the target voltage V, by the electron beam, and a charge Qi = V,Ci is thus stored. Signal electrode

/

/

Image element

I

I_

-I

0 VS

FIG.2. Equivalent circuit for the vidicon.

472

ROBERT SEHR AND RAINER ZULEEG

During the frame time T,-the time elapsing before the beam returns to the same picture element-C, partially discharges, owing to the photocurrent IK(Li)which has been generated by the illumination Li. When the electron beam returns to the same element it must replenish an amount of charge AQi = AVCi, which depends on the illumination level Li. A charging current i s , proportional to AV, flows each time the beam completes the circuit containing an element. This current causes a corresponding voltage difference across the load resistor R,, and consequently the signal voltage V, is a sequential, electrical replica of the various illumination levels of the optical image. The vidicon operates in the charge storage mode. That is to say, the optical image is converted into a stored charge pattern which is periodically scanned and erased by the electron beam. Erasing the charge pattern creates the video signal. Because the photoelectrical conversion mechanism is operative all the time, i.e., during scan time to as well as sample (or discharge) time t , (Fig. 3), this mode of operation is sometimes also referred to as photon flux integration mode. Charge storage mode operation in a vidicon places a basic requirement on the semiconductor film-namely, that the relaxation time of the photoelectrons be much greater-than the frame period tF, which is usually greater than 1/25 sec. If this condition were not fulfilled, the image points would diffuse laterally, and contrast would be “washed out.” As a consequence of this requirement, a simple criterion for a photoconductor applicable to vidicon targets may be given. It states that the dark resistivity should be higher than 10l2ohm cm. Resistivities of this magnitude and slow chargecarrier relaxation are usually found in semiconductors with deep lying trapping states, which cause the dark conductivity to be small through charge compensation and reduction of mobility. Electron beam

EB

1

o n t

3

I

I to------I

I ’

TF

ic= Sample time

1

= ;t

Scan time

rF=Frame period

Time, T

T;=

Somple frequency

FIG.3. Definition of time intervals in the scan cycle.

12.

IMAGING AND DISPLAY

473

The semiconductor compound first used in vidicon targets was antimony trisulfide7 Sb,S3, which kept its unique position for more than ten years. It is applied in polycrystalline form by evaporation onto the target plate. Depending on evaporating conditions, its dark resistivity ranges from 10' to l O I 3 ohm cm, and the onset of nonlinear, space charge limited dark current (I,, K V 2 )lies between 5 and 15 V. The space charge current limits the target voltage and thus the sensitivity of the device. However, the most undesirable feature of Sb,S3 is its slow photoresponse at low illumination levels, which limits its use for video pickup. Much work has been directed toward finding more sensitive, fast response materials or configurations for vidicon targets. These are discussed in the following subsections. Vidicon with CdSe Target

Although vacuum deposited CdSe films had been considered quite early for vidicon application, their high dark conductivity prevented actual use. Shimizu and Kiuchi* found that selenium vacancies in the film were a major cause for the space charge limited dark current. By treating the film in selenium vapor they obtained acceptable dark resistivity at the usual target field strength of about lo5 V/cm. With a CdSe target thus prepared they measured a sensitivity of more than ten times that of a Sb2S3target In contrast to Sb2S3, which is a p-type photoconductor, CdSe is n-type. It is therefore necessary to explain the detection process differently for the two materials8 When the p-type Sb2S3 is illuminated electron-hole pairs are created. The holes, as majority carriers, travel under the influence of the electrostatic field, E = Q/Cd (d is the thickness of the film), to the back side of the film and render the surface potential more positive. This potential increment is neutralized by the scanning electron beam so that the potential decreases to its initial value. In the CdSe film under illumination photoexited holes are captured by existing recombination centers, thereby neutralizing a corresponding amount of space charge of trapped electrons. This is accompanied by the rise of the surface potential at the surface exposed to the electron beam, which allows more electrons to flow into the layer during the sample time. The electron flow through the layer during the sample time (see Fig. 3) will cease when the free electrons and the trapped holes combine. The associated current gain is given by

G

=

Z,/T,,

(1)

where z, is the lifetime of the electrons in the semiconductor and T, the transit time through the film.

' S. V. Fourge, R. R. Goodrich, and A. D. Cope, R C A Rev. 12, 335 (1951). K. Shimizu and Y. Kiuchi, Japan J . Appl. Phys. 6, 1089 (1967).

474

ROBERT SEHR AND RAINER ZULEEG

4. THEPLUMBICON A new type of vidicon having high sensitivity, speed, and resolution was introduced under the name Plumbicon' in 1964. The higher performance of this device is due to the p-i-n layer structure of the target film. The high, built-in electric field exerted across the intrinsic layer by the p and n contacts assures that almost all charge carriers generated in the i layer contribute to the photocurrent across the junction within their lifetime. According to Eq. (l), this results in a high current gain and consequently high photoelectric sensitivity. Photoresponse, being proportional to the carrier transit time, also improves, since the latter increases with the field strength, which is high across the intrinsic i layer. The Plumbicon target consists of a PbO layer on a SnOz layer, which form a unit consisting of three sublayers, each of different conduction type. The inner sublayer is almost pure PbO, which is an intrinsic semiconductor, while the surface layer exposed to the scanning electron beam is doped p-type. The intimate contact with the SnO, on the other side gives rise to a thin n-type layer in the PbO. The p and n layers are kept very thin, so that the intrinsic layer takes up most of the overall thickness of the PbO layer and most of the absorbed photons are stopped there. In other words, in operation, when the electron beam scans the p-type surface the photoconducting layer of the Plumbicon target constitutes a reverse-biased p i - n diode. The dark current is the low reverse current through this diode. The high sensitivity is a consequence of high photon absorption in the intrinsic layer and high carrier collecting efficiency through the built-in field. One particularly desirable feature of an imaging device is image fidelity, i.e., the proportionality of the output signal, here photocurrent I,, with luminous flux L. In general, an equation of the form

I , = CLY (2) holds true, where C is a constant and 0 < y d 1. Figure 4 shows the measured relationship between I,, and L for a Plumbicon. The top line refers to unfiltered illumination ( W ) ,while the lower three curves are obtained with red (R),green (G), and blue ( B ) filters. Plotted in log-log presentation this relationship appears as a straight line. This means y has a single value, close to unity, for the Plumbicon over its entire dynamic range. In contrast, the value of y is a function of L for the conventional vidicon. 5 . THESICON

In the original vidicon the photosensitive target is a semi-insulating photoconductor with relatively low sensitivity and slow response. In the Plumbicon

' E. F. DeHaan, A. Van Der Drift, and P. M. Schampers, Philips Tech. Reo. 25, 133 (1964).

12.

475

IMAGING AND DISPLAY

10

5

t 5 2 0 01

2

5

+L

10-3

2

5

10-2

2

lirn)

FIG.4. The measured variation of photocurrent in a Plumbicon as a function of luminous flux L. Here W , R, G, and B refer to unfiltered illumination and illumination through red, green, and blue filters, respectively.

the performance characteristics are upgraded through the use of a large area, graded p i - n junction, but high resistivity is still associated with each layer. Carrying the idea of a junction structure as the photosensitive target a step further, a new device with superior performance was demonstrated in the form of the Sicon." Here the target consists of an array of electrically isolated, reverse-biased diodes each representing one image element. This device has several important features. 1. The dark current and the photocurrent can be made independent of the target (reverse-bias) voltage to result in a response characteristic with y = 1. 2. The time constant associated with the charge storage in an array of reverse-biased diodes can be made very much larger than the relaxation time of the photocarriers in the bulk, provided the material lends itself to p - n junction fabrication. 3. Electron beam bombardment and intense light spots do not affect target performance. 4. Higher speed and sensitivity of response can be achieved.

The long charge storage time constant that can be obtained with isolated diode arrays is particularly important, since it implies that such a device can be made with a long wave photoresponse without cooling the target below 300°K. Whereas in a bulk photoconductor vidicon target the charge lo

M. H. Crowell, T. M. Buck, E. F. Labuda, J. V. Dalton, and E. J. Walsh, Bell System Tech. J . 46,491 (1967); Proc. Intern. Solid Stare Circuits Conj 1967, p. 128 (1967).

476

ROBERT SEHR AND RAINER ZULEEG

decay time T,, is given by6 Tb

= EEop

(3)

7

and for the open-circuited diode it is given by" where IR is the reverse leakage current, E and e0 are the dielectric constant and the permittivity of free space, respectively, p,, is the electron mobility, p is the resistivity, and I/ is the applied voltage. It is immediately apparent that high resistivity is required for vidicon operation with bulk photoconductors, while the isolated junction vidicon target calls for low resistivity. Since it is almost always possible to obtain low resistivity from intrinsic (high resistivity) material by doping, a large number of semiconductors may be adaptable for junction structures in vidicon targets. Furthermore, intrinsic semiconductors with band gaps less than 1.5eV, whose resistivities are less than 10"ohmcm at room temperature due to thermal activation, may qualify, and thus provide vidicon targets with infrared response. It must, however, be borne in mind that the resistivity p in Eq. (4)cannot be reduced indiscriminately. The breakdown efectric field strength F , sets a lower limit to p and thereby an upper limit to t d .With the lower limit for td fixed by the charge storage time, Asec, required for a frame period, Wendland" has given a criterion for the resistivity of a material to be applicable to diode array vidicon targets :

Any semiconductor in which a junction can be formed and which satisfies the inequality of Eq. (5) can be used for a charge storage vidicon target. For germanium the criterion of Eq. (5) is not quite met, but for silicon it is. The actual target structure used by Crowell et d . ' O is shown in Fig. 5. The target consists of a 540 x 540 diode array with center-to-center spacing of 20 p which is about half the diameter of the electron beam. The p-type islands are formed by boron diffusion through 8 p holes in the S i 0 2 film. Ohmic contact to the array is obtained by a gold ring evaporated onto the N region at the perimeter of the wafer. In order to make the target self-supporting and at the same time provide the optimum thickness for sensitivity, which is governed by the carrier collection efficiency, the completely processed diode array is etched on the illuminated side to thickness of less than 1.5 mil in the center area, leaving a rim about 4 mil thick for structural support. An antireflection coating on the etched surface reduces light losses. +

"

P.H. Wendland, IEEE Trans. Electron Dev. 14, 285 (1967).

12. IMAGING AND DISPLAY

477

"-region

-

substrate

1

I

I

mage

FIG.5. Schematic view of Sicon target. (After Crowell et al.")

In operation the scanning electron beam periodically charges the p-type islands down to cathode potential, while the potential of the n-type wafer is held to a constant voltage between 5 and 10 V. The SiO, film, also charged to cathode potential by the beam, remains there and isolates the substrate wafer from the beam. The incident light associated with the image is absorbed in the silicon, creating electron-hole pairs. The minority carriers (holes) then diffuse to the depletion region of the diodes, discharge the diodes by an amount proportional to the light intensity. The recharging of the diodes by the scanning beam creates the video signal. Based on a simplified model in which the p regions of the array are replaced by one large area p-layer with no lateral conductivity, the collection efficiency q, i.e., the ratio of collected holes to photon-generated holes, was calculated." Assuming a minority-carrier lifetime of approximately 10 psec, a surface recombination velocity of about lo4 cm/sec, and a wafer thickness of around 10-3cm, gives 4 x SO% for uniform illumination with visible light. 6. INFRARED SENSITIVE VIDICON

Image readout from a vidicon requires that the stored charge pattern decay with time constant T larger than the frame period zF (see Fig. 3), which is usually taken as b s e c . From Eq. (3) it is easily verified that bulk photoconductive targets require a resistivity of 10" ohm cm or more to meet this condition. Since resistivities of this magnitude are not obtainable from semiconductors with band gaps of less than 1.5 eV at room temperature,

478

ROBERT SEHR AND RAINER ZULEEG

it follows that wavelength response beyond A (p) = 1.24/Eg(eV) x 0.8 ,u is not possible without cooling the photoconductive target. It should be noted that this statement applies also to materials which contain impurity levels separated by 1.5eV or less from the band edge, since at 300°K a large enough fraction of these levels will be thermally ionized to produce sufficient free carriers to diffuse the stored image. Another effect of thermally freed charge carriers on a semiconductor imaging target must be considered too-namely, their limitation on the dynamic range of the device. Consider the case where the stored charge pattern is due to ionization of donor levels in the energy gap. If because of the target temperature a large fraction of these levels has been emptied, a photon flux corresponding to a low light level will produce a saturated response, and higher light levels cannot be sensed. To avoid saturation, the following relation must be satisfied" :

n,

+

< Nd,

(6)

where n, is the number of electrons per cubic centimeter in the conduction band due to target temperature, n, is the number of electrons per cubic centimeter excited by the radiation to be detected, and Nd the number of donors per cubic centimeter. It can easily be shown from semiconductor statistics (see, e.g., Blakemore' 3, that this relation leads to the condition Nd

> N c exp[(Ed - EF)/kT1.

(7)

Since N, , the degeneracy concentration of the conduction band, will always be larger than the donor concentration N , , condition (7) states that for a target temperature T the Fermi level E , must lie appreciably below the donor level Ed. If-as in most semiconductors-the electron mass is larger than the hole mass, the Fermi level moves upward with temperature, and will thereby reduce the dynamic range of the device. For intrinsic semiconductors as targets Gebel" gives a minimum gap energy of 0.05 eV for 300°K operation ; however, this certainly cannot be obtained in practice, because it represents the limit toward degeneracy. In the use of bulk photoconductivity for charge-storage vidicon operation condition (6) is automatically taken care of, but it may become a limiting condition for isolated junction array targets. A vidicon with spectral response between 1.0 and 2.5 p has been developed by Redington and Van Heerden14 using a gold-doped silicon target cooled close to liquid nitrogen temperature. Other silicon dopants, such as Ga, R. K. H. Gebel, Adoan. Electron. Electron Phys. 16,461 (1962).

'' J. S. Blakemore, "Semiconductor Statistics," p. 122 ff. Pergamon Press, Oxford, 1962.

l4

R. W. Redington and P. J. van Heerden, J . Opt. Soc. Am. 49,997 (1959).

12.

IMAGING AND DISPLAY

479

Bi, and In, were also investigated, with little success. Unsatisfactory results were also obtained with Cu-, Au-, Ag-, and Te-doped germanium. The authors point out that at liquid nitrogen the response should extend to 5 p. For 20°K they predict a response t o about 35 p. Because of the limited doping concentration allowed by condition (6), semiconductors have a necessarily low absorption coefficient in the extrinsic regime. Increasing the absorption by using very thick targets provides no remedy, since both resolution and target capacitance are inversely related to thickness. Resolution suffers because of the sideways diffusion of carriers (image washout), while target capacitance limits the voltage excursions of the video signal. An infrared vidicon requires cooling not only of the target and its surrounding structure, but the target must also be shielded from the infrared radiation emanating from the thermionic cathode which emits the scanning electron beam. The apparatus of Redington and van Heerden is shown in Fig. 6. The electron beam is deflected by two sets of hemispherical deflection electrodes and follows a circular or elliptical path through them. The arrangement and shape of these electrodes permit the electron beam to strike the target perpendicularly. Photocurrent resulting from radiation

Electron gun 1 FIG.6. Demountable infrared vidicon tube. (After Redington and van Heerden. 14)

480

ROBERT SEHR A N D RAINER ZULEEG

8

1.6

12

2.0

2.4

Wovelength ( p )

FIG.7. Ahsolute sensitivity, in electrons per photon, of a gold-doped silicon target versus wavelength. The rise of the curve toward shorter wavelength is due to increased light absorption, while the subsequent drop at longer wavelength i s due to decreased collection efficiency of photoelectrons. (After Redington and van Heerden.I4)

from the cathode could not be detected with a copper-doped germanium detector in place of the target. The target was a 1.5-cm-diam, 1.0-mm-thick Si :Au wafer clamped in position with indium pads for good thermal and mechanical contact. The absolute spectral response of a Si:Au target is shown in Fig. 7. The peak at the short wavelength end demonstrates the effect of volume excitation, while the decrease of response toward the long wavelength end shows that carriers generated near the surface are not contributing to photoconductivity during their lifetime.

7. LASER-SCANNED MOS DEVICE An interesting and novel approach to infrared imaging has been reported by Phelan and D i r n m 0 ~ k . In I ~ their experiment an InSb structure consisting of a semitransparent metal film-oxide layer-n-type InSb sandwich cooled to 77°K uses a scanning laser beam instead of an electron beam for readout. The infrared image focused onto the wafer was confined to radiation between 4 and 5 p and had an incident power density of 100 pW/cm2. The other side of the wafer, with the transparent metal film surface, was continuously scanned in two directions with a 0.63-11 helium-neon laser. With a vertical scan frequency of 1 kHz and a 10 kHz frequency in the horizontal direction, a continuous oscilloscope display was obtained. The 1-mW laser Is

R. J. Phelan and J. 0. Dimmock, A p p l . Phys. Letters 11, 359 (1967)

12.

IMAGING AND DISPLAY

/-

He-Ne Laser

481

SphericalJ focusing mirror

_f

Laser scanned imaging system

FIG.8. Experimental setup for infrared imaging by means of a laser-scanned metal-oxidesemiconductor device. (After Phelan and Dimmock.L5)

beam was focused to a spot about 0.3 mm in diameter. The experimental arrangement is shown in Fig. 8. The deflection of the laser beam was accomplished by two rotating mirrors which were synchronized with the sweep frequencies of the oscilloscope. The detection of an infrared image in the vicinity of 5 p relies on the nonlinear photovoltaic response of the depletion region in the InSb near the oxide interface. For an ideal diode the open-circuit photovoltage is proportional to the logarithm of photocurrent. The incident laser beam saturates a spot on the detector which is electrically isolated from neighboring areas by the high resistivity of the depletion region. With no image on the detector each spot yields the same signal to the external load because the spot voltage is driven to depletion region saturation. Since each spot represents a capacitor coupled to the semitransparent metal electrode, just as in the vidicon, there will be no output signal as the laser passes from one spot to the next, and one spot signal decreases as the next increases. If an

482

ROBERT SEHR AND RAINER ZULEEG

FIG.9. An oscilloscope image obtained with the experimental imaging arrangement of Fig. 8. (After Phelan and D i m m o ~ k . ' ~ )

image element of the detector, defined by the laser spot size, has an infrared signal incident on it, this element will contribute less response voltage as the laser scans across it because there is less voltage change from driving the element to saturation. It is this voltage imbalanze which drives a current through the external load and thus provides the video signal. It is interesting t o note that while the vidicon target is operated as a photocurrent generator with high internal resistance (Section g), the laser-scanned MOS target operates essentially in the (almost) open-circuit photovoltaic mode. A photograph of an oscilloscope display is shown in Fig. 9. The height of the letters of the image was 3 m m on the detector, whose active area measured 2 cm in diameter. The device was not externally biased, but rather relied on the field effect bias originating from the trapped charges in the oxide and at the oxidesemiconductor interface. Actually, the scanning laser beam enhances the amount of trapped charge and fixes it at a steady-state value. The MOS detector described above can also be used for infrared image storage by operating it under different conditions. Image storage for over 1 hr has been observed. The interested reader will find further details on this operating mode in the original paper.I5

12.

IMAGING AND DISPLAY

483

111. Electronically Scanned Photodetector Arrays

8. PHOTOSENSITIVE STRUCTURES AND THEIR APPLICABILITY TO IMAGING In electronically scanned imaging devices an array of switches replaces the sequentially sampling beam of beam scanned devices. By proper sequencing of the switching array any element of the detector matrix can be connected to a readout line in any desired sequence. Of course, for arbitrary, or truly random access, of any detector element or subarray, important for certain applications, not only the sequencing of the switching array, but the latter itself becomes rather complex (see Section 14). Another difference with respect to the vidicon is the geometrical definition of the image element in the imaging target. While in beam scanned devices the image is defined by the sampling-beam diameter, in electronically sampled detector matrices the image element is defined by individual and separate photodetector elements. These elements may be photoconductors, photodiodes, or transistors. However, the application of a particular detector element to imaging depends on its operating characteristics and the methods used to fabricate it. The latter may impose restrictions on the array fabrication, the former on the scanning circuitry. The simplest configuration of a photoconductor element is a bar cut out of single-crystal material, or a thin film of vapor deposited material on a suitable substrate, which in either case is provided with two ohmic contacts. Figures 10a and lob, respectively, give the basic geometries. The bar-type structure has been extensively used for extrinsic infrared detectors of Ge doped with Hg, Cu, Cd, and some

OHMIC metal contact

I

Substrate

\

(b)

FIG.10. Structures of semiconductor photoconductors. (a) Bar-type photoconductor element (Ge or Si): (b) thin-film photoconductor element (PbSe or CdSe): and (c) planar (diffused) photoconductor element.

484

ROBERT SEHR AND RAINER ZULEEG

other impurities. The thin-film type is primarily useful with vapor deposited photoconductors such as CdS, CdSe, and/or deposited PbSe using a wet process. A planar version of a photoconductor element is shown in cross section in Fig. 10. It consists of a vapor diffused n-type layer with defined geometry and doping level. The element is isolated from the substrate by the formed p n junction. Ohmic contacts are provided on the top surface by an N + diffusion, which is then contacted by evaporated aluminum. Thermally grown SiOz serves as a diffusion mask and as passivation. The structures of Figs. 10a and 1Oc have been employed by SorefI6 to evaluate the extrinsic photoconductivity properties of silicon. His experimental results on extrinsic photoconductors of Si :B, Si :Al, Si :Ga, Si :P, Si :As, and Si :S.b indicate that these materials are equivalent to the doped germanium photoconductors, such as Ge :Cu and Ge :Hg. Spectral response to near- and intermediate infrared (0.6-30 p ) radiation is obtainable, and a theoretical spectral response of background-limited doped silicon photoconductors is presented in Fig. 11. It is expected that the doped silicon photoconductors will yield the same infrared sensitivity, speed of response, and maximum operating temperature for peak sensitivity as doped germanium photoconductors now in use. Practical advantages over doped germanium photoconductors are cost, reproducibility, and ease of fabrication of complex arrays. These advantages are a result of the highly advanced fabrication technology of silicon planar devices as applied to device integration for microcircuits. Photoconductor elements lend themselves especially well to the fabrication of imaging matrices with spectral response in the visible and infrared part of the spectrum, i.e., for imaging in spectral bands where semiconductors have to be used which do not permit p-n-junction formation. They are best applied in polycrystalline form and exhibit peak detection capability at the temperatures below 100°K which are required for infrared imaging. Photodiodes and transistors are impaired at these low temperatures in their functioning as detectors, since they rely on fully ionized impurities and sufficient lifetime of minority carriers for proper operation. Photodiodes and transistors for imaging matrices are fabricated by planar technology. The cross section of these devices is shown in Fig. 12. The diode can either be used as a photocurrent electric cell, or a photovoltaic cell. The photocurrent cell is essentially a reverse-biased junction, and the induced photocurrent I , , is additive to the reverse or “dark” leakage current l o . In this configuration the photodiode is a current generator with high internal resistance. When the diode is operated in the photovoltaic mode it is essentially open-circuited, and the incident light develops a photovoltage ‘I’

R. A. Soref, J . Appl. Phys. 38, 5201 (1967).

12.

485

IMAGING AND DISPLAY

1 300°K background

',

/

/

-si

/

P

B

----I

--

SI Sb

I

I

I

I

I

4

6

10

20

40

Wavelength

(pi)

FIG. 11. Theoretical spectral response for six species of background-limited doped-silicon photoconductors. (After Soref.16)

across the terminals. The equivalent circuit is then a voltage generator with an emf in series with a comparatively low resistance. The open-circuit voltage V,, varies linearly with light intensity at low light levels, but vaiies logarithmically at high light levels. The logarithmic response at high light intensities is a characteristic which is utilized in lightmeters. Since the Emitter

(0)

Collector

(b)

FIG.12. Planar silicon structures. (a) Photodiode: and (b) n-p-n phototransistor.

406

ROBERT SEHR AND RAINER ZULEEG

photovoltaic effect results in moderately small signal voltages, the photocurrent mode is preferred in most electronic applications, where the photocurrent is measured across a reasonably large load resistance. This circuit arrangement produces a voltage output in ranges which are practical for electronic applications with large signal-to-noise ratios. An important parameter of a photodiode or detector is its quantum efficiency q. If the photon flux rate in photons/sec/cm’ at a wavelength /z is incident on a device, then the quantum efficiency is defined by

where I , is the diode photocurrent, A the diode area, and y the electron charge. Quantum efficiencies in silicon diodes range in the visible spectrum typically from 50 to 90%. A phototransistor in the n-p-n configuration is shown in Fig. 12b, where the actual photodiode is the collector-base junction. In the phototransistor the collector junction current I , is equivalent to the photocurrent of a single photodiode, but is amplified by the common emitter short-circuit current gain p of the bipolar transistor. Thus the collector current I , can be represented by I , = (1

+ fi)lD.

(9)

The phototransistor operates normally in a grounded emitter configuration with a floating base. Base current is introduced by the photocurrent emanating from the collector diode. Defining the quantum efficiency of a phototransistor by uT = I , / ~ ( D A , where , A , is the collector area, it follows from Eqs. (8) and (9) that VT

=

(1 + f i ) q D ?

(10)

which is the efficiency of the normal photodiode multiplied by the (1 + fi) factor. The sensitivity of the phototransistor is therefore considerably enhanced over that of the photodiode. The foregoing comparison shows that the phototransistor provides the highest sensitivity for imaging matrices, but requires more elaborate fabrication techniques. As a result, uniformity of response is expected to be not as good as in imaging matrices of photoconductors or diodes. There are two different approaches to the fabrication of imaging matrices : The monolithic array of phototransistors, diodes, or conductors, which is confined to monocrystalline material, and the thin-film array, for which a large number of semiconductor materials qualify.

487

12. IMAGING AND DISPLAY 9. MONOLITHIC STRUCTURES a . Undoped Silicon Arrays

The rapid advancement of silicon planar technology in recent years has made it possible to fabricate large numbers of active devices on one wafer (large-scale integration-LSI). A major reason for bringing this development about is the fact that silicon most easily grows an oxide film on its surface under controlled conditions, which provides a natural passivation barrier, or, in conjunction with the photolithographic process, a diffusion mask for the repeated diffusion processes necessary in device array fabrication. A perspective cross section through a phototransistor array, indicating the basic design as well as the necessary processing steps in the fabrication of the device, is shown in Fig. 13a. The equivalent electrical circuit is given in Fig. 13b. A photodiode array would look similar except for one missing n diffusion, namely, that for the n-type emitters. Starting material for the array is a p-type silicon substrate of about 0.5 ohm cm resistivity onto which an n layer 1&15 p thick and a resistivity of 0.54.7 ohm cm is grown epita~ially.'~ A diffusion of p-type walls all Collector columns _3

Emitter rows

SIOZ insulation not shown (0)

I

l

l

I

Y"

(b)

FIG. 13. Phototransistor matrix. (a) Perspective view of design : and (b) equivalent-circuit representation.

'' M. A. Schuster and W. F. List, Trans. Met. SOC.A I M E 236,375 (1966).

488

ROBERT SEHR AND RAINER ZULEEG

FIG.14. A 64 x 64 phototransistor matrix with p -njunction isolation of collector columns. ( a ) Matrix mounted and bonded to circuit board. 64 x 64 elements contained within f x f i n . squared; and (b) enlarged portion of matrix. Devices spaced on 5-mil centers (McDonnell Douglas Corporation).

the way through to the substrate follows t o separate the n layer into strips. Then the individual transistor bases are formed by p-diffusion. The final diffusion step is n-type to produce the transistor emitters within the area of the bases. Evaporated aluminum strips connect all emitters in a row, while all collectors in a column are internally connected by the epitaxiallygrown n strips. Contact to these is made a t the column end through diffused n+ bonding pads. At the crossover points of the A1 strips with the p-type isolation walls a SiOz film serves as isolation between the two. A photograph of an actual 64 x 64 element array, mounted on a circuit board, is shown in Fig. 14. Center-to-center spacing of the individual elements is 5 mil. Contacts to the odd and even rows and columns of this experimental device are made by thermocompression bonding of 1-mil-diam gold wires. It is quite obvious that the step and repeat operations, which are initiated by high precision photomasking, require accuracies of less than 0.1 mil

12.

IMAGING AND DISPLAY

489

FIG15. Imaging system performance. Photographs from monitors of 100 x 128 (upper) and 200 x 256 (lower) element matrices (courtesy of Westinghouse Electric Corporation). (After Anders et al.")

la

R. A. Anders, D. E. Callahan, W. F. List, D. H. McCann, and M. E. Wing, Western Electronic Show and Convention, 1967, Paper 13/1.

490

ROBERT SEHR AND RAINER ZULEEG

otherwise, geometrical definition of the image element suffers, as consequently, does uniformity of response. Another possible source of nonuniform response from the various elements of the array is material or diffusion inhomogeneity. Therefore epitaxial growth and diffusion must be carried out under well-controlled conditions. Phototransistor matrices from 10 x 10 to 200 x 256 elements have been from various laboratories. The imaging quality of these devices is illustrated in Figs. 15 and 16, which are photographs of television displays with video input from the detector arrays. The upper and lower “portraits” in Fig. 15 were taken with 100 x 128 and 200 x 256 element arrays, respectively. The light lines are due to an emitter short” in the corresponding rows. Figure 16 shows images of letters and symbols imaged by a 10 x 10matrix from a positive or negative black and white transparency. A gray scale pattern made from a neutral density filter with areas of 100, 80,64, and 51% transmittance is also shown to demonstrate gray level discrimination. Besides the array of isolated phototransistors shown in Fig. 13, other device configurations have been used. In particular, Dyck and Weckler” describe various monolithic designs combining p n diodes with MOS transistors and n-p-n phototransistors with MOS transistors. The latter combination has the advantage of not requiring isolation between the devices, thereby eliminating crossover interconnections and crosstalk arising from it. This will be discussed more fully in Section 12. b. Doped Silicon Arrays for Intermediate IR Imaging

It was pointed out in Section 6 that thermally generated charge carriers will limit the photoresponse and dynamic range of an imaging device [see Eq. (7)]. If the free-electron concentration n,, e.g., places the Fermi level at the temperature T within 2kT of the conduction band edge, degeneracy sets in, and a light signal incident on the device certainly will not be detected. To reduce the free-carrier concentration and thus permit photogeneration of carriers, the temperature must be lowered. By doing this, however, the minority-carrier lifetime decreases rapidly, thus prohibiting the use of junction photodetectors based upon bipolar current flow at temperatures below 100°K for most semiconductors and in particular for silicon devices. On the other hand, to obtain photoresponse over a reasonable dynamic range for radiation with wavelength longer than 5 p, temperatures below l9

’’

P. J. W. Nobel, IEEE Trans. Electron Deu. 15,202 (1968). R. H. Dyck and G. P. Weckler, l E E E Truns. Electron Deu. 15, 196 (1968). A. F. Behle, P. Y. Chao, H. Speer, and S. H. Watanabe, Proc. Microelectron. Symp. 1968, p. C2, St. Louis, Missouri (1968).

12. IMAGING AND DISPLAY

Gray scale

491

on lOxl0

loo% 6 4%

8 0O/O

5 1 o/o Transmittance

Symbol "PLUS"

on

FIG.16. Image display of 10 x 10 phototransistor matrix (McDonnell Douglas Corporation).

about 100°K are imperative. This limits semiconductor-imaging devices applicable for the near and intermediate wavelength IR spectrum to the photoconductor element only. SorefZ2has described such an array sensitive between 2 and 30 p fabricated from boron-doped silicon. Other semiconductors such as Ge :Au, Ge :Cu, Hg,Cd, -,Te, Pb,Sn, -,Te, and Pb,Sn, -,Se also show photoresponse in this spectral region, but either do not match the ease of processing which silicon does (as already mentioned at the beginning of Section 9a) or are not yet well enough known with respect to their chemical and metallurgical properties. A perspective view of part of the array is shown in Fig. 17. The design of this array elegantly solves the ever-present problem of crosstalk between

** R. A. Soref, I E E E Trans. Electron Dew 15,209 (1968).

492

ROBERT SEHR AND RAINER ZULEEG

FIG.17. Monolithic photoconductor imaging array: (a) Perspective view of part of the array: [b) equivalent circuit for array; (c) cross section through an element: and (d) equivalent circuit for individual element. (After Soref.”)

individual array elements by placing a p n junction in series with each photoconductor element. The asymmetrical current-voltage characteristic of the diode substantially reduces the current in the nonaddressed elements. The addressed element has such a polarity during readout as to forward-bias the series diode, giving optimum detector output. With a quantum efficiency of 7% at 10.6 p and a response time of about 0.2 psec the detectivity per element was calculated to be D* = 1 x lo8 cm Hz”’W-’. The measurements were made at a temperature of 25°K. These experimental results are very encouraging and indicate the possibility of obtaining high-resolution imaging matrices for the infrared region. A direct readout of the individual picture element is possible by electronically scanning the X-Y matrix. Application of the charge storage mode (see Section 13) can be utilized to improve the sensitivity. The MOST switching element combined with the photoconductor may offer new integration aspects, since it is capable of operating at cryogenic temp e r a t u r e ~ .To ~ avoid interconnect problems among the matrix, the scanning circuitry, and the amplifier circuits, it will be advantageous to integrate the whole system and operate it in the cold environment. 23

R. A. Soref, Intern. Electron Dev. Conf., Paper 5.7. Washington, D.C., October 1967.

12. IMAGING

AND DISPLAY

493

c . Imaging Arrays with Narrow-Gap Semiconductors

With the rapid advancement of semiconductor technology narrow-gap compound semiconductors of the III-V, II-VI, and IV-VI families are obtained in more exacting stoichiometry and are processed with better controlled techniques. The formation of p-n junctions by diffusion or by vapor and liquid phase epitaxy may result in the fabrication of diode arrays.z3a Indium antimonide, with an energy gap of 0.18 eV and a photoresponse threshold of 6.8 p is a promising material. Ten-element linear modules have been fabricatedz4 which can be mounted on alumina substrates to form arrays of 100 elements or more. This technique of fabricating an array has limitations of about 100 ,u per element with a separation gap of 25 p. The detectivity of such an InSb detector element was measured as a function of wavelength at 77°K with 27t sr of 300°K background. A typical peak detectivity of 4.5 x 10" cm Hzl/' W-' at 5 p was obtained,24 which is very close to the theoretical background-limited detectivity of about 6.5 x 10" cm HZ"' W - ' for this element. Presently under investigation and development are ternary compounds of lead-tin-telluride, lead-tin-selenide, and mercury-cadmium-telluride detectors. Further development of these materials is required in the photomechanical work process to facilitate photodetector array fabrication for immediate infrared imaging. The relevant research necessary to produce such a solid-state intermediate infrared imaging system will probably be oriented toward achieving the overall materials-to-scanning context and will be aimed at the optimum use of the existing photolithographic and photomechanical integration capabilities. 10. THIN-FILM POLYCRYSTALLINE IMAGING ARRAYS

The monolithic imaging array fabrication described so far is a byproduct of large scale integration techniques developed especially for silicon. As such, it is at the present to a large degree restricted to this material, or at least to a semiconductor whose chemistry and metallurgy is well understood. With other materials solid-state imaging devices can be fabricated by evaporation of polycrystalline films. The major advantage offered by this approach is the high element density and large area coverage that can be obtained with high uniformity. Its principal drawback lies in the nature of the polycrystalline material itself, in that it does not yield basic parameters such as mobility, lifetime, etc., as good as in monocrystalline material, and Z3"Ionimplantation appears less suitable for planar junction formation in infrared detectors, because resulting surface damage increases the surface recombination rate of photongenerated charge carriers. 24 F. D. Morten and R. E. J. King, lnfrared Phys. 8, 9 (1968).

494

ROBERT SEHR AND RAINER ZULEEG

Element being

scanned

Column of

tronsistors

FIG. 18. Equivalent circuit for the completely integrated 180 x 180 element array, showing method for attaching scan generators and coupling out the video signal. Storage of excited carriers in the photoconductor provides light integration. (After Weimer P I d.”)

thereby yields devices of lower u priori performance. Another problem is time stability of the device characteristics, but this can be overcome through proper passivation methods. Weimer2’ has pioneered the thin-film transistor (TFT), and was also first in fabricating a TFT integrated circuit26 containing lo5 elements. In combining thin-film photoconductors as shown in Fig. 10b with TFT’s he has subsequently devised a self-scanned imaging matrix having 32,400 imaging elements2’ Integrated with the matrix on the same glass substrate are two 180-stage shift-register scan generators and associated video coupling transistors. Figure 18 gives the equivalent circuit for the completely integrated 180 x 180 element array and indicates the method of connecting scan generators and video output. The imaging array can be operated in the charge storage mode as well as in a mode particular to this device, termed “excitation storage mode,” which will be discussed in Section 13. The diode switches, necessary for 25

26

P. K. Weimer, Proc. 1.R.E. 50, 1462 (1962). P. K . Weimer, Proc. I E E E 52, 1479 (1964). P. K.Weimer, G. Sadasiv, J. E. Meyer, Jr., L. Meray-Horvath, and W. S. Pike, Pmc. IEEE

*’

55, 1591 (1967).

12.

IMAGING AND DISPLAY

495

FIG. 19. Photograph of a completely integrated image sensor comprising the photosensitive array, the horizontal and vertical scan generator, and the video coupling circuit (courtesy of RCA). (After Weimer et a!.")

excitation storage, are incorporated into the matrix by a proper sequence of the deposited layers. The photoconductive elements consist of CdS or CdS-CdSe mixture to which an ohmic contact is formed by overlying indium or aluminum on one end and a rectifying contact on the other end by a tellurium layer. For readout the tellurium contact is biased positively, and thus presents a low resistance path for the excitation stored signal from the phot oconductor. Figure 19 shows the actual and completely integrated imaging sensor. The center-to-center spacing between elements in the array is 2 mils. The picture quality produced by this imaging sensor can be assessed from Fig. 20, which is a photograph of a television monitor with video input from a 125 x 140 element thin-film array. The advantages of large, thin-film, integrated scanning circuits combined with the image-sensing matrix on a common substrate are obvious when cost and complexity of the imaging system are considered and compared with monolithic silicon integrated circuits. Laboratory thin-film integrated circuit techniques have mastered the complexity required for combining the scanning circuit and the image sensor on one common substrate, which

496

ROBERT SEHR AND RAINER ZULEEG

FIG.20. Picture transmitted by scanning 125 x 140 elements on an image sensor. The vertical scan is at standard tv rates, and the display is on a tv monitor (courtesy of RCA). (After Weimer e f 0 1 . ~ ' )

cannot be equaled with large scale integration of bipolar transistors. Silicon MOST integrated circuits will probably rival the thin-film approach eventually, and it is conceivable that technology improvements will yield monolithic-silicon photosensor arrays which are complemented by scanning circuitry and video processing circuits on the same substrate. So far the thin-film technique has not advanced beyond the laboratory stage, and the devices and circuits are plagued by drift and deterioration of electrical characteristics with time. Continued research and development may eventually overcome the device stability problems, and thin-film passive and active elements may then become practical for complex integrated circuits for all solid-state vidicons of photosensitive element density between lo5 and lo6. An alternative to the all thin-film approach of image sensor arrays combined with the associated circuitry is conceivable which avoids the instability problems of the TFT's and takes advantage of the polycrystalline thin-film photosensor array, This design employs a silicon single crystal substrate which contains the peripheral MOST scanning circuitry and video coupling circuitry flanking the four sides of a deposited polycrystalline photosensor mosaic. The designer would have the freedom of selecting the deposited photosensitive material for a specific imaging response in a desired spectral region.

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497

IV. Image Readout Methods for Photodetector Arrays There are two principally different methods for transforming the twodimensional set of photoelectric information bits into a time sequential set of signal bits for one-channel transmission t o the display device or some other electronic data processor. These are: (1) the photocurrent mode, and (2) the charge storage mode (or photon flux integration). However, depending on the particulars of the imaging array, such as the characteristics of the individual array element (sensitivity, internal impedance, etc.) and the manner of their integration (isolated in one direction or none), there are variations of (1) and (2). Thus a recently developed technique in connection with the thin-film array27 may be added: (3) the excitation storage mode. Corresponding to these readout modes there are variations of the switching circuits which accomplish these functions. 1 I . PHOTOCURRENT MODE

In this conceptually simplest mode an element of the array is connected with one terminal to a battery and the other to ground via a switch and a limiting resistor. Image readout is achieved by sequentially switching each element from ground to the input terminal of a high-gain current amplifier. The photocurrent from each element, flowing only during the sample time, provides the video signal. The simplest mechanization of this scheme is shown for a linear array in Fig. 21. All floating-base phototransistors are tied to ground through a 3-V collector supply. The single-pole, double-throw switches keep all elements grounded through a 300-ohm resistor, except the one element whose current is read out through the amplifier. The amplifier yields an output voltage V,,, proportional to R I , , where I, = (1 + @Zp, which is proportional to the light intensity according to Eq. (9). The switching function has been implemented by MOS as well as bipolar transistors. Photocurrent readout has also been applied to planar using p n junction isolation techniques such as shown in Fig. 13. Here all collectors of the n-p-n phototransistors are common to a column, which are the X outputs, and all emitters are common to a row, the Y outputs. Thus the crossed common collector columns and emitter rows provide access to any individual element. with respect to response Matrices of various geometries were inve~tjgated'~ characteristics and speed of the photocurrent mode. The result shows that this readout mode can be very ambiguous when the phototransistors are integrated into high element density matrices. Nevertheless they yield a true photocurrent readout when all the elements are grounded except the one being sampled. In this case crosstalk is minimized. However, switching

498

ROBERT SEHR AND RAINER ZULEEG I

I I

I

I

I

I I

I

I I

I

+' -It+-

_3"+

Collector supply

I I I I

i I

Linear array of N-P-N pholo tronsistors

I I

Current amplifier

Swiiches (commutator)

FIG.21. Current-mode readout of linear

p

pi

phototramistor array.

from one column to the next introduces large transient responses which limit the scan rate. At moderate light intensities this transient requires up to 5 psec before it subsides to the steady-state photocurrent. Figure 22 shows a sample response of one element taken on a 64 x 64 matrix. The initial voltage spike is due to the load condition of the measuring circuit, and simply consists of an RC time constant when the device is in the "dark." This time limitation on the load, with R , = 10 kilohms and V, = + 3 V, is presented in the decaying dashed curve. During illumination with 50 ft-cd, the device response rises as shown by the dashed curve, leveling off at the steady-state value. Since sampling can only be done after the decay time, where static and dynamic response have a one-to-one correspondence, the current mode readout has a basic speed limitation. Consequently, at a fixed frame rate the total number of elements which can be sampled in one complete frame is limited.

Fici. 22. Sampling response of phototransistor in a matrix. Horizontal: 5 pecldiv: vertical: 2.5 jiA/div: illumination: SO ft-cd.

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12. PHOTON FLUX INTEGRATION MODE

The readout mode corresponding t o the charge storage mode in the vidicon is termed photon flux integration. It was first described by Weckler” and offers the advantages of increased photosensitivity and scanning speed. In this mode of operation the sensitivity of the solid-state transistor array is superior to the vidicon. As in the vidicon charge storage mode, so in the photon flux integration mode, each element is active throughout the frame time. The p-n junction diode storage mode operation is described by aid of Fig. 23. When the diode is charged to Yothrough a perfect switch the voltage decay V ( t ) under open-circuit conditions is related only to material and junction properties and is independent of junction area. For V (t )k 0 it can be shown2’ that

The variable second term on the right-hand side of Eq. (11) is related to the generation-recombinat ion current by Igpr = (Aqni/2T,)W,

(12)

and the capacitance C of the assumed linear graded junction by

c=A(~uE~E,~/~~)~/~T/-~’~,

(13)

and the depletion layer or space-charge width

(0)

t, =Sampling time To = Scan time t o = Reciprocal of sample frequency

(b)

FIG.23. Storage-mode operation of a p-n junction. (a) Ideal circuit: and (b) sampling and storage sequence. (After Weckler.”) 28

G . P. Weckler, I E E E J . Solid-State Circuits 2, 65 (1967).

500

ROBERT SEHR AND RAINER ZULEEG

In the above equations W is equal to the space-charge width, A is the junction area, q is the electron charge, n, is the intrinsic carrier concentration, u is the linear doping gradient, and zo is the effective lifetime in the space-charge region. Planar silicon technology yields pn junctions which hold the charging voltage with less than 10% loss for several seconds in the dark. With reasonable values of zo from 5 to 10psec usually less than 1% decay of voltage is encountered for millisecond lengths of time. If the diode is illuminated, the photocurrent I , = 1,AH (15) (with I , the photosensitivity of the diode, A the photosensitive area, and

N the illumination level) adds to the diode dark current Ig+. As a consequence of the increased current, a more rapid discharge of the junction capacitance occurs. For sufficiently short integration times or high illumination levels the generation-recombination “dark” leakage current I,, may be neglected, and the voltage as a function of time and illumination level isz8 V ( t )= [v

y - 310H(12/yuEZE02)1’3t]3/2

.

(16)

Theoretical relations like Eq. (16)and correlation with experimental measurements are presented in Fig. 24 for V, = IOV, u = 3 x loz9m-4, and I, = 0.048 A/m2/ft-cd.

H in ft-cd L

I

I

3

FIG.24. Measured and calculated voltage decay characteristic or an open-circuited, reversebiased p - n junction for several values of incident illumination. (After Weckler.28)

12.

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IMAGING AND DISPLAY

Compared to the photocurrent mode, where each array element is exposed (and thus active) to the light only during the sample time t,, the photon flux integration mode provides an effective gain Geff given by2* Geff =

1 + (hk)?

(17)

where to is the scan time. Since t,/t, is a large number, this gain can be very high. At the same time, variations of the scan time by electronic adjustments in the scan circuit allow one to vary the sensitivity. The limit in sensitivity and gain is imposed by the finite charge time necessary for charging the pn junction capacity of a diode. Sampling times of 0.1-0.2 p e c per element are practical for photodiode or phototransistor arrays operated in the photon flux integration mode. Minimum and maximum illumination levels have been reported for representative devicesz8: Hmin z 0.02 ft-cd, and H,,, x 6.6 x lo5 ft-cd. This may be compared with Hminx 0.1 ft-cd for the current mode set by the dark current, and H,,, x lo3 ft-cd set by the saturation level of the photocurrent. Thus the dynamic range of the photon flux integration mode is about three orders of magnitude larger. Several practical storage mode structures have been developed28 and described. The combination of the p-n junction photodiode and the switch can be realized in an integrated structure with a p-channel MOST (metaloxide-semiconductor-transistor). Since the photodiode and the source diode are in parallel, it is possible to combine both diodes without affecting the operation of the structure. This is shown pictorially in Fig. 25. The combined structure then allows integration to closely spaced arrays of photodetectors. A linear array of photodiodes and MOST switches and its layout is shown in Fig. 26. Recharge readout

Sampling voltage

I

+

N

I

I

T iRL I

o

i

Charging1 voltaae

1

(a)

(b)

FIG. 25. Practical circuit for storage mode operation of a p-n junction photodetector. (a) separated photodiode and MOST switch: and (b) combined photodiode and MOST switch. (After Weckler.28)

502

ROBERT SEHR AND RAINER ZULEEC

Common ground

Common drain

Photc diode

Control gates

1

z

(a)

(b)

FIG 26. Linear integrated photodetector array for photon flux integration mode operation. (a) Integration topology of linear photodetector array: and (b) circuit representation of linear integrated circuit. (After Weckler.28)

Elements of an imaging matrix operating in the PFI mode must possess the three functional elements of: (1) a charge storage element, (2) a current generator and output proportional to the incident illumination level, and (3) a nearly ideal switch. It is therefore possible to use a p-n junction as the switching element. A normal phototransistor can be utilized and operated in the charge storage mode. In this configuration the collector junction acts as the photodiode and the charge storage element by virtue of the collector-to-base capacitance Cc.. The small area, low leakage emitter diode performs the function of a switch. Figure 27 shows a practical structure using a p-n junction as the switch. A schematic representation of a linear array of phototransistors is also shown in Fig. 27. Finally, the linear array can be expanded to form two-dimensional arrays, which are currently under development.20*28 An array of lo4 phototransistors and lo4 MOST’S, with a schematic representation as shown in Fig. 28, uses the additional MOST’s as logic gates for coincident sampling of the phototransistor. When row-column coincidence occurs the MOST is to perform an “AND” function. The array does not require isolation of the individual devices, and therefore eases integration into arrays. The technique of combining storage mode with the MOST logic eliminates the need for sampling a number of output

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503

FIG. 27. Phototransistor operation in the PFI mode. (a) Practical structure using a p-n junction as a switch: and (b) schematic representation of a linear array of phototransistors. (After Weckler.28)

channels, as would be required by simple paralleling of linear arrays. The logic electronics confines the signal current to only one dimension of the sampling systems, thus preventing crosstalk. Only one common signal terminal for all elements of the array is necessary for video signal processing. From the preceding discussion and a comparison with the currentmode operated array as described by Strull et u E . ~ it~ becomes apparent that the two-dimensional phototransistor array with MOST coincidence logic operating in the PFI mode offers the greatest advantage with respect to simplicity of electronics, solid-state fabrication, and sensitivity. 29

M. A. Schuster and G. Strull, I E E E Trans. Electron Den 13,907 (1966).

504

ROBERT SEHR AND RAINER ZULEEF Column

Column

I N

I N+I

Row M t l

,

c

FIG. 28. A schematic representation of the two-dimensional phototransistor array with MOST logic gates for coincidence sampling. (After Dyck and Weckler.zo)

1 3. EXCITATION STORAGE MODE

This sampling mode is a special case of the photon-flux integration which was developed in connection with the thin-film imaging array.” Its primary, but limited, applicability lies with arrays of photoconductive elements where photon flux integration would be possible only by adding shunting capacitors across the photoresistive elements. In the excitation storage mode the effect of the light is stored as excited carriers whose lifetime should approximate the scanning period. Although the effective duty cycle of current flow through each element is only N - ’ times that of an element with full charge storage, this loss in signal can be compensated by using a photoconductor with an internal gain of N electrons per photon. The effective quantum yield of the sensor thus approaches N ( I / N ) = 1, the value equal to the maximum quantum yield expected with photon flux integration. 14. RANDOM ACCESS

Certain applications of imaging devices require variable scan rate or random access to an element or matrix portion. The photon-flux-integration mode is not suitable for such applications, because variation of scan time changes the sensitivity and dynamic range (see Section 12). However, the

12.

IMAGING AND DISPLAY

505

photocurrent mode is applicable because the current readout produces a signal proportional to the incident light at the time of interrogation. It is possible then to use variable scan rates or incomplete scans, or to provide random access to the individual matrix elements. This mode is thus more suited for pattern recognition and guidance schemes, where it is not desired to continually scan the entire matrix but rather to concentrate processing on selected areas of the array for certain periods. But the scan rate and sensitivity limit its usefulness (see Section I 1). In high-element-density matrices of more than about 50 x 50 elements the described switching transient limits the frame rate for standard television practice, which provides 63.5-psec time for scanning one line in the U S . television system. V. Imaging Characteristics of Photodetector Arrays

The important parameters describing a photodetector array for imaging are : (1) absolute sensitivity, (2) spectral sensitivity, (3) uniformity of response, (4) resolution, and (5) speed of response. In contrast to individual detector elements, for which such parameters as sensitivity and speed of response are primarily determined by material constants, for detector arrays these values are primarily determined by element structure, element integration, and readout mode. Some of these relations have already been mentioned in the preceding sections. Absolute sensitivity of the imaging array is determined primarily by the device structure (photoconductor, diode, transistor) and by the sampling mode. The combination of phototransistor sampled in the photon flux integration mode provides the highest sensitivity available for electronicallyft-cd. The value of about lo-’ ft-cd scanned imaging devices, about for a similar array sampled in the photocurrent mode is to some extent dependent on phototransistor design and processing because both will influence the limit-setting dark current. Spectral sensitivity in the case of photoconductor arrays is, of course, the same as that of an individual element, and as such is primarily determined by material constants. Ionization energy of the charge carriers, their lifetime, and device geometry are of principal importance. For the diode and transistor, device geometry plays a dominant role. In particular, junction depth and impurity profile variations between devices of the same structure will result in different spectral responses. This effect can be utilized to shift the peak response of pn-junction device arrays. A representative spectral response of a silicon n-p-n transistor within the array is shown in Fig. 29 together with the spectral response (dashed curve) of a silicon junction photodiode. Surface effects caused by planar device fabrication contribute further to the distortion of the “normal” absorption curve. This is especially

506

ROBERT SEHR A N D RAINER ZULEEG

Incident radiation wovelength ( F ) FIG. 29. Spectral sensitivity of a silicon phototransistor in mosaic (continuous curve), and single photodiode (dashed curve). (After Anders et d.")

true for the SiOz passivation film on the silicon surface. Antireflection properties of a quarter-wavelength thick SO, film can produce peak responses at a particular wavelength. Uniforntity qf'response is a very critical performance parameter. It depends on the material homogeneity and processing uniformity. For the sake of a graduated gray scale the response uniformity should be high. A reproduction of a gray scale by a 10 x 10 matrix was shown in Fig. 16. With present silicon planar technology a high degree of uniformity is obtained. A typical response distribution curve of the elements of one matrix is shown in Fig. 30. Minimum and maximum detectable signal levels are approximately 10 nW and 1 mW, respectively. The sensitivity is betwen 10' and lo3 pA/mW. Resolution is determined by the element density of the array. There seems little doubt that silicon will remain indefinitely the dominant material for microelectronics and the fabrication of solid-state imaging systems. The construction of both thin-film and monolithic systems has demonstrated a resolution in excess of 100 lines. Although arrays with resolution inferior

12.

507

IMAGING AND DISPLAY

I00 VCE a,

p

e

= 3 volts

95% 80 250 f t

C .VI

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60

20% of median

E

a,

c

0 a,

m 40 t

c

I A

a,

e

n“

Median

I

20

I

I

0

YL-2 1

40

I

+I 60

3%

I 70

80

90

Photo current (FA)

FIG. 30. Response distribution of elements within a matrix at different light intensities (McDonnell Douglas Corporation).

to broadcast television standards are now practical, one would require an array with approximately 512 x 672 elements to satisfy the tv standards. It is conceivable that both thin-film techniques and planar silicon techniques will eventually reach this goal. A considerable amount of research must be devoted t o the development of matrices with higher element density and sufficient uniformity. Speed ofresponse is related to the particular device and the method of readout. Although the response time of a single phototransistor with an active base area of 4 x 4 mils square is in the range of0.5-1.0 psecs, this speed cannot be realized when the device is incorporated in the multielement matrix (see Section 11). In the photocurrent mode the response time is limited to about 3-5 psec. This time imposes a limitation on the scanning rates of large arrays using this mode of readout. Since, e.g., the time for each television line is approximately 63.4psec, only about 20 elements in one line could be sampled to produce a “low” resolution image. In a high resolution image of 512 x 672 elements only 0.12 psec is allotted for the readout time of the individual element. Sampling times of 0.1-0.2 psec per element are practical for photodiode and phototransistor arrays when operated in the photon flux integration mode (see Section 12). This readout mode therefore leads to all solid-state “high” resolution imaging when a monolithic sensing array with X Y readout is provided with external commutation circuits.

508

ROBERT SEHR A N D RAINER ZULEEG

VI. Array and Scanning Circuit Integration The switching speeds necessary to operate large arrays impose severe demands on the response characteristics of the array and on the scanning circuitry. A short readout time is available when the matrix is scanned in the 5-10 MHz frequency range, which would be required, e.g., in application to standard US. television. The mostly capacitative impedances of the interconnects between elements and between matrix and scanning circuitry then become important. To minimize this impedance and thereby allow high scan rates, the detector matrix and the scanning circuitry must be in close proximity so as to allow short interconnects. Several methods have been conceived to achieve this integration. The ideal solution, of course, is the LSI (large scale integration) of the scanning circuitry with the photodetector array on one common substrate. Practical methods so far exercised in the laboratory include separate fabrication of array and scanning circuits and providing connections by thermocompression bonding of hundreds of small gold wires. This can be done on suitable substrates, such as ceramics, with plated and etched large interconnect patterns and joining of the substrates by standard multiterminal miniature connectors. Figure 14 is an example of this method. Another modification, and considerable improvement, would be the bonding of the array and the various scanning and video processing circuitry on one common ceramic substrate and interconnecting the terminals of the closely spaced chips with metal interconnects. Thermocompression bonding seems feasible, but may not be reliable and economical. Other methods for providing these large numbers of small metal interconnects will be sought. If, e.g., the voids between the circuit chips can be filled with some kind of glass or epoxy material which will give a smooth transition between the circuits, then metal interconnects can be deposited either by conventional evaporation through a mask or by evaporation with a laser beam.

VII. Display Devices

A planar, solid-state, optical display panel for viewing by the human eye has been a long-established aim of electrooptical device research. Spurred by the benefits which would result from “flat television receivers,” this goal is receiving continued high attention. Work towards electroluminescent display panels with ac-activated polycrystalline ZnS goes back to the early 1 9 5 0 ’ ~ . ~However, ’ electroluminescent (EL) cells alone do not produce a satisfactory image display for two reasons : First, the electrooptical conversion efficiency of dielectric30

H. K. Henisch, “Electroluminescencc,” pp. 296 ff, 307 ff. Pergarnon Press, Oxford, 1962.

12. IMAGING AND DISPLAY

509

embedded luminescent powders is low, and second, the electroluminescent decay time is very short.Thus a brightness-voltage characteristic results which is insufficient for a high brightness, high contrast display, while the short luminescent lifetime prevents a complete image from persisting for a full frame-time. A further problem, closely related to the inefficiency of dielectricembedded EL powders, lies in the short energizing time for each cell. If there were 100 x 100 cells in the array, each element would have the ac voltage applied for only of a frame time, i.e., for only a small fraction of a cycle. The brightness developed in such a short fraction of a frame time would be minimal. These considerations have led to the development of ferroelectric controlled electroluminescent displays, which are discussed in the following section. With the improvement of crystal growth methods, particularly epitaxial techniques, a new approach to fast switching displays has been taken in the form of diode arrays fabricated from mixed-crystal III-V compounds. Gallium arsenide phosphide, Ga(As - ,PJ and gallium aluminum arsenide, (Ga, -xAl,)As, are currently being investigated. Display panels with epitaxially grown (GaA1)Asdiodes are the subject of Section 16b. 15 . FERROELECTRIC-CONTROLLED ELECTROLUMINESCENT DISPLAY The short electroluminescent decay time and the relatively low brightness of electroluminescent cells require the cell to be energized throughout a frame time. This cannot be done by direct scanning, and so a control device that is capable of rapid switching and of storing video information is associated with each panel cell. A circuit including a ferroelectric capacitor fulfills these basic requirements, and the first EL-ferroelectric panels were described by Sack3’ and by Rajchman and B r i g g ~More . ~ ~ recently Lechner and c o - ~ o r k e r shave ~ ~ developed improved ferroelectrically controlled EL cells and have built large display arrays. The basic ferroelectric control circuit is shown in Fig. 31. Assuming for the moment an ideal ferroelectric (i.e., a ferroelectric having a square hysteresis loop and a threshold electrical field), the circuit operates as follows: If the ferroelectrics F E , and F E 2 are initially poled oppositely, E. A. Sack, Research 12, 54 (1959). J. A. Rajchman and G. R. Briggs, U.S. Patent 3,041,490, June 1962. 3 3 B. J. Lechner, Ferroelectric Electroluminescent Displays, in “Agard Conference Proceedings No. 23-Displays for Command and Control Centers” (I. J. Gableman, ed.), Chap. 25, pp. 35 1-372. Technivision Services (Division of Englehard Hanovia International, Ltd.), Slough, England, 1969; B. J. Lechner, A. G. Samusenko, G. W. Taylor, and J. Tults, Ferroelectric controlled electroluminescent displays, Pror. Nat. Aerospace Electron. Conf., Dayton, Ohio, May 1966.

3’

32

510

ROBERT SEHR AND RAINER ZULEEG

Poled oppositely

Poled ollke

blocked stote

unblocked stote

(0)

(b)

lntermedmte state (C i

FIG.31. Basic ferroelectric control circuit. (After L e ~ h n e r . ' ~ )

they remain in this saturated opposing polarization for either polarity of the field produced by the ac generator A . Hence the ferroelectrics do not switch and no current flows in the circuit (Fig. 31a). If F E I and F E 2 are initially poled alike, they switch in unison when driven by the ac generator, and current flows through the EL cell (Fig. 31b). Switching only over the partial hysteresis loop as illustrated in Fig. 31c produces an intermediate gray level (halftone). Since the initial polarization of FE, determines the switching state of the circuit, the circuit can be set to any intermediate state by applying a voltage between the terminals x and y. Because there is a threshold voltage V, for switching, it is possible to select (or address) a ferroelectric control circuit by coinciding additive voltage swings (coincidence selection). For example, to switch the circuit from the blocked state to the unblocked state a voltage + V is applied to x and - V to y . With V,/2 < V < V, switching will occur only if + V at x and - V at y coincide. Intermediate states are obtained by modulating either the amplitude or the duration of one of the two selection signals. The basic ferroelectric circuit has been designed33 into a display matrix as shown in Fig. 32. The ferroelectric FE3 between point x and the column lines serves as an isolation element. It prevents short-circuiting of the ferroelectric F E , to ground through the internal impedance of the column and row generators Riand C; (i = 1,2,. . .).

12.

IMAGING AND DISPLAY

511

FIG.32. Display matrix concept using the basic ferroelectric circuit. (After L e ~ h n e r . ~ ~ )

The less than ideal characteristics of practical ferroelectrics limit the performance of the basic circuit of Figs. 31 and 32 in two ways. First, because ferroelectrics do not have a true threshold, the half-select signals, which address other circuits in the array, gradually unblock a blocked (i.e., a dark) image element. Thus a gradual lighting of supposedly dark elements occurs. However, with the best ferroelectric ~ e r a r n i c s ~presently ~.~ used this effect poses no serious problem. A greater problem is the imperfect squareness of the ferroelectric loop. The latter allows some current to flow in the blocked circuit. The EL cell is thus not completely dark and the contrast is spoiled. With niobium-doped Pb(ZrSnTi)03ferroelectricceramics this effect limits the contrast to about 2 : 1 at brightness levels of 3-4 ft-lm. which circumvents this Lechner has devised a new control shortcoming. The circuit, shown in Fig. 33, consists of two basic circuits 34

35

36

G. W. Taylor, J. Appl. Phys. 38,4697 (1967). C. Wentworth and G. W. Taylor, Am. Ceram. SOC. Bull. 46,1186 (1967). B. J. Lechner, Digest of Technical Papers, 1965 Intern. Solid-state Circuits Conf., Philadelphia, Pennsylvania, 1965; B. J. Lechner, U.S.Patent 3,197,744, July 1965; B. J. Lechner and G. W. Taylor, U.S. Patent 3,393,345, July 1968; B. J. Lechner, U.S. Patent 3,478,224, November 1969.

512

ROBERT SEHR AND RAINER ZULEEG

A

-

A

- Row generator (provides negative pulse)

Center tapped sine wave generator

C - Column generator (provides positive pulse) V B -Back biasfor diode D

FIG.33. Control circuit with center tapped a c generator in

a

bridge arrangement. ( A f t e r

Le~hner.~~)

with center-tapped ac generator in a bridge arrangement and the EL cell connected between the points of balance. The upper ferroelectric pair F E , and F E 2 is always unblocked, whereas the lower pair F E , and FE4 is switched between the blocked and unblocked states. When unblocked, all four ferroelectrics switch in unison, the bridge is balanced, and the EL cell is dark. Instead of relying on the squareness of the hysteresis loop, the current through the EL cell now depends only on the balance of the bridge. When F E , and F E , are blocked the bridge is unbalanced and current flows through the EL cell, causing it to light. The current and hence the brightness depends on the degree to which FE3 and F E , are blocked. Figure 34 shows how the improved circuit is incorporated into a matrix. It differs from the matrix in Fig. 32 in that no reset pulses are required and the ferroelectrics are switched to the blocked state to turn the EL cell on. Display Address Technique Typical switching times of ceramic ferroelectrics are t , = 10psec. This establishes a minimum time for addressing an element or a row of elements. Consider a matrix with i7 rows and m columns which is to be addressed an element at a time. The frame time TFis given by TF = nmt,.

(18)

Allowing guard bands for timing errors, t , is assumed to be 20psec. For a

12.

A1; A2 R1; R 2

C1; Cg; C3

513

IMAGING AND DISPLAY

- Sine wave generators for row 1 and row 2

-

- Row pulse generators for row 1 and row 2 - Column pulse generators for columns 1, 2 and 3

FIG. 34. Incorporation of control circuit of Fig. 33 into a matrix. (After L e ~ h n e r . ~ ~ )

smear-free image TF z 30 msec, so that

nm = TF/ts = 1500 elements.

(19)

Obviously, the resolution for a 1500-element array cannot be high. However, for line-at-a-time addressing TF= nf,, and in this case the array may consist of 1500 rows each consisting of m elements. Thus in this addressing mode large display matrices are possible. In this case a serial-to-parallel conversion must be performed when the video information arrives sequentially in real time as from a vidicon camera. Figure 35 shows a block diagram of a line-addressed 1200-element display with serial video input. The horizontal scanner causes the video signal for one line to be sequentially sampled by the sampling gates. These samples are stored and the information is transferred to the display en mame when the column drivers are simultaneously activated in coincidence with the appropriate row driver. This process is then repeated for successive lines. A 1200-element display matrix33 driven by a vidicon camera is shown in operation in Fig. 36. This display consists of 30 rows of 40 elements, each 0.2 in. sq. The ferroelectric circuits were constructed on 4 in. x $in. x 0.003 in. ceramic strips3’ with 20 circuits on each strip. The device has a

514

ROBERT SEHR AND RAINER ZULEEG

___------__--

Excitation

I

I

I

I

I

I I

L, Vertical scanner Information transfer signal

1 generators

vioeu

Horizontal scanner

-A

FIG. 35. Block diagram of a line addressed 1200-element display with serial video input. (After L e ~ h n e r . ~ ~ )

frame rate of 30/sec and a line addressing time of 40 psec. The 40 elements of each row are sampled ar 20.6-psec intervals. The total horizontal line timeis thus40 x 20.6 psec + 40 psec + 62 psec(f0rguardbands) = 926 psec. This corresponds to a line frequency of 1080 Hz. Scanning signals for the matrix are obtained from clock-driven vertical and horizontal scanners which operate synchronously with the deflection of the electron beam in the vidicon. The maximum “on” brightness which is achieved with a column pulse amplitude of 45 V varies between 11 and 20 ft lm. The average value, plotted in Fig. 37, is 16ftlm, and the upper and lower decile points are 19 and 13 ft lm. For column pulses of 15 V or less all cells have essentially zero brightness. At intermediate halftone settings the variation in brightness is greater. This is by design so as to favor higher brightness at the expense of gradual transfer characteristics.

ELECTROLUMINESCENT DIODE ARRAY 16. SCANNED In contrast to dielectric-embedded powder EL cells, which can only be activated with alternating current and require power densities of several

12.

515

IMAGING AND DISPLAY

FIG.36. The 1200-element model display system in operation. (After L e ~ h n e r . ~ ~ )

hundred watts per centimeter squared, electroluminescence in single-crystal devices can be excited with low voltage, direct current, and with power densities of less than 100 W/cm2. Furthermore, the switching speed, i.e.,

L

M

I_

60

Column pulse amplitude i V )

FIG.37. Averagc value of brightness as function of column pulse amplitude. (After L e ~ h n e r . ~ ~ )

516

ROBERT SEHR AND RAINER ZULEEG

“turn-on time constants,” for electroluminescence in monocrystals is at least an order of magnitude faster than the 1 psec or more for EL panels. In spite of these well-known advantages, monocrystalline display devices are only now on the threshold of reality. The reason for this slow progress is associated with the technological problems of materials preparation. Solid-state displays designed for the human eye as detector require semiconductors with band gaps larger than 1.8 eV. Band gaps of this magnitude are generally associated with melting points in excess of 1400°C and high equilibrium vapor pressures. This is so because the band gap is the result of the bonding forces in the crystal, and these, in turn, determine the temperature at which the crystal melts. The practical problems encountered in the growth of single crystals compound rapidly as the melting point increases, particularly when good single crystals with high purity and controlled doping are required. Silicon carbide and the 11-VI compounds with energy gaps of more than 2 eV and melting points of 1400°C and higher are good examples, in that they have yet to be grown in large, homogeneous, single crystals. An additional difficulty is the formation of a p n junction in these materials. Conventional techniques such as diffusion are not applicable and new methods such as ion implantation have yet to prove successful. Without the ability to make the material into simple p-n junctions, the full benefit of a single-crystal device cannot be realized, since the forward-bias junction is the most efficient radiative structure. A further complication arises from the differentiation between direct and indirect optical transitions associated with the band structure of a particular semiconductor. Wide-band-gap materials with band structure allowing direct optical transitions, and thereby higher electrooptical conversion efficiency, are the exception rather than the rule. When all these considerations are combined they point out the rather narrow restrictions involved, and consequently the small number of semiconductor materials that qualify for use in electrooptical displays, while the majority are presently burdened with problems relating to the band structure or to the materials technology. a. Gallium Phosphide Diodes

Among the more common 111-V compound semiconductors, there are three which on account of their large energy gap would qualify for electroluminescent display applications. These are AIP, AIAs, and Gap. However, all three have indirect optical transition^,^' and the first two have melting

’’ C . Hilsum and A.

C. Rose-lnnes, “Semiconducting Ill-V Compounds,” pp. 33 and 65. Pergamon Press, New York and London, 1961.

12.

517

IMAGING AND DISPLAY

5 1

/ \ Diode P26 298

')c

2 t

-

2

1 Infrared

Red Zn-0 pair band

Greed

c

z

LT

I 12 L " " 14 " " " 16 ' 18 20 22 Photon energy in electron volts

2

FIG. 38. Emission spectrum from a forward-biased Zn-diffused diode at room temperature. (After Gershen~on.~')

points above 1600°C. The third, Gap, with an energy gap of 2.25eV, has been investigated longest and its preparation and device fabrication is best understood. But AIAs, having a gap energy of 2.20 eV, has received much attention lately as a constituent in epitaxially-grown (Gal -,Al,)As (see Section 16b). Pure G a P as well as GaAs-GaP alloy electroluminescent diodes and small arrays of individual diodes are now commercially a~ailable.~'They are primarily used for alphanumerical display." The material is grown epitaxially, either from the vapor phase or by growth from the liquid phase on a GaAs substrate which is subsequently dissolved. Although GaP is an indirect gap semiconductor, its electroluminescent efficiency is high. This is because the emitted light is not due to band-to-band radiative recombination, but originates from two other radiative recombination mechanisms. Figure 38 shows a typical room temperature forward-biased emission spectrum from a diode prepared by zinc diffusion into an n-type crystal containing tellurium and oxygen. Two emission bands appear in the visible, separated spectrally and pa ti ally.^' A weak green band is generated close to the junction boundary, while a much stronger red band originates on the p-side of the junction. The red band has been shown to be due to donoracceptor pair recombination involving shallow zinc acceptors and deep oxygen donor,41while the origin of the green band at room temperature is not quite clear. It may be due to shallow pair recombination or to nitrogen Monsanto Company, St. Louis, Missouri and Hewlett-Packard Company, Palo Alto, California. 39 D. K. Hillman and G. E. Smith, I E E E Spectrum 5,62 (1968). M. Gershenzon, Bell Sysfem Tech. J . 45, 1599 (1966). 4 1 M. Gershenzon, R. A. Logan, and D. F. Nelson, Phys. Rev. 149, 580 (1966). 38

518

ROBERT SEHR AND RAINER ZULEEG

traps which arise from isoelectronic substitution of nitrogen for phosphorus atoms, but band-to-band recombination is ruled out because the observed efficiency is orders of magnitude higher than the indirect gap would allow. Quantum efficiencies for the red and green emission depend upon the junction preparati~n.~’ The external efficiency for red eIectroluminescence was reported to be as high as 1.5 on an alloyed junction made over six years ago. Diodes with efficiencies up to 7 % are being produced today. The green emission is about 100 times less efficient than the red. However, as far as the human eye is concerned, it is the integral of the product of the emission curve and the visual acuity curve that counts. Thus the G a P green emission corresponds to about 650fm/W. For the red band this value is only 20 I m p in spite of the higher efficiency.

x4’

6. Integrated Gallium-Aluminum Arsenide Diode Arrays One of the big problems in the fabrication of diode array displays is the growth of homogeneous large area crystals with uniform junction characteristics. A major advancement in this area has been the solution regrowth first described by Nelson43 for GaAs and later applied to (Gal -,AI,)As for the fabrication of highly efficient electroluminescent diodes.44 Much better uniformity of the Ga-AI ratio can be achieved in this system (variations amount to less than 2% along the growth axis) than in the Ga(As,_,P,) system. The reason is probably the better match in size of the mutually substituting Ga-A1 atoms. The high uniformity of the crystals, the high flatness of the junction, and the virtual elimination of competing deeplying levels45 result in (Ga,-,Al,)As, 0 < x < 0.35, light-emitting diodes with external quantum efficiency of up to 1.2% at current densities of about 50 A/cm’ at 300°K. The switching time for light emission was measured to be 60 n ~ e c . ~ ~ ~ The promising feature of this technique is that junctions with very uniform characteristics can be grown over large substrates. This permits the fabrication of diode arrays in sifu, provided it is possible to have the epitaxial growth occurring only in designated areas or by somehow integrating diode platelets after the growth cycle. The second method is currently being developed46 for the fabrication of visible display panels. The following goals must be aimed at in the design of such panels. 42

H. G. Grimmeiss and H. Koelmans. Phys. Lerters 8, 233 (1964).

‘’ H.Nelson, RCA K e n 24, 603 (1963).

H. Rupprecht, in “Gallium Arsenide”

(Proc. Intrm. Sympositttn, Reading, 1966). p. 57. Inst. Phys. and Phys. SOC., London, 1967. 4s S . M. K u and J . F. Black, J. Appl. Phys. 37,3733 (1966). 45aH.Rupprecht, T. M. Woodall, and G. D. Pettit, Appl. Phys. Letters 11, 81 (1967). 46 H. B. Wetzell, Private communication, March 1968. 44

12.

519

IMAGING AND DISPLAY

Diced GaAeAs

Y-Inputs 1

FIG.39. Perspective view of (Ga, -,AI,)As light emitting diode array. (After W e t ~ e 1 1 . ~ ~ )

(1) The size and diode density of the array should not be limited by the integration technique. (2) Address should be by means of a cross-grid wiring matrix. (3) Heat sinking should be adequate to allow the diodes to be driven to their saturation levels for maximum light output. (4) The fabrication method should lend itself to batch processes. One approach which comes close to meeting these conditions is depicted in Fig. 39. The fabrication of the array starts with metalizations of the grown diode platelets to provide ohmic contact to both the n and p surfaces. The platelets are then cut into regular squares or rectangles as large as the original substrate materials will permit. Next the platelets are bonded to the broad conductive metal strips of an insulating substrate of high thermal conductivity such as boron nitride. The mounted platelets are then diced without cutting through the conducting strips by using masking and etching techniques to form small diode islands. After backfilling the grooves and thus providing a smooth surface a second set of conducting strips is applied to the top of the diode array, perpendicular to the bottom strips in order to form a cross-grid pattern for X-Y scanning of the array. The final operation consists of etching into the diode islands to expose the emitting junctions. The diameter of the etched holes should be as large as possible for several reasons : (1) the remaining p-n layer surrounding the holes will be small, resulting in high current density for low driving currents ;

520

ROBERT SEHR AND RAINER ZULEEG

TABLE I COMPARISON OF DISPLAY CHARACTERISTICS' ~

Electrical optical characteristics

EL panel

Incandescent lamp

Brightness (ft Im) Life (hr) Voltage (V) Current ImA) Speed Color

8 400 ll5ac 1 1 psec White

500 10,Ooo 4.5 72 1 msec White

_ _ _ _ ~

Gas discharge

GaP diode

90

200

2000

40,000 2 dc 20 100 nsec Green-red

160 ac 0.2 85psec Neon-red

GaAlAs diode

1000 >40,000 2 dc 15 60 nsec Red

~

"After W et ~ e1 1 . ~ ~

(2) more junction area is exposed for maximum light output ; and (3) less nonradiating surface remains, rendering the display more continuous. By filling the cavities with a glass or epoxy of high index of refraction the external quantum efficiency can be further increased. With present microelectronic techniques it appears possible to fabricate diode arrays with up to 100diodes/in. Proper heat sinking provided, (GaA1)As diodes have exhibited brightness levels of 150 ft lm. Depending on ambient light conditions, six to eight points on the gray scale have been estimated using Hardy's criteria.47 In Table I the principal parameters of various display devices are summarized. As can be seen from the values given, the diode display appears the most promising approach with the proviso that a large scale integration technique can be perfected.

VIII. Parallel Readout Image Converters The three principal domains of imaging are (1) the viewing of inaccessible or distant scenes, (2) the direct viewing of scenes at very low light levels (image intensifier), and (3) the direct viewing of scenes at spectral illuminations different from the visible, particularly in the infrared (image converter). In this classification the scanned devices discussed in Sections 2 and 3 are most applicable either for distant imaging or for nonvisible imaging, while very low light level viewing, below ft-c, is presently the exclusjve domain of photoemissive tube devices. The following discussion pertains 47

A. C. Hardy, Rept. E 1385, Instrumentation Lab., M.I.T., Cambridge, Massachusetts, July 1963.

12.

IMAGING AND DISPLAY

521

only to converters with response times that permit the imaging of a moving picture.

17. NONREGENERATIVE IMAGECONVERTERS For the direct viewing of nonvisible images planar image converters have been developed which contain a radiation-sensitive layer and an electrooptical display layer sandwiched together with the necessary electrodes. The display layer is generally a polycrystalline electroluminescent (EL) material, while the radiation sensitive layer may be a photoconductor (PC) sensitive to x-rays, ultraviolet, visible light, and infrared, or it*may be an infrared sensitive element such as a thermistor array. Although not very efficient with respect to energy conversion, these polycrystalline devices have the outstanding feature that they can be made in large panels (up to 20 x 20 in.) and thus provide pictures on a one-to-one scale. The basic structure of a solid-state image converter is shown in Fig. 40a. The EL-PC layers are usually applied to a glass substrate, which provides the mechanical support. The optical isolation layer between the radiationsensitive input layer and the EL output layer prevents undesirable optical feedback between the two. The equivalent electrical circuit of the converter Transparent electrode Electroluminescent layer Optcol isolation layer Radiation sensitive layer Transparent electrode Glass substrate

(a 1

Resolution element

*

RPC

REL

(bl

FIG.40. Solid-state image converter. (a) Basic structure: and (b) equivalent circuit.

522

ROBERT SEHR AND RAINER ZULEEG

panel is shown in Fig. 40b. Each image spot or resolution element is a series combination of photoconductor impedance Z,, and electroluminescent impedance Z E L , each of which has a resistive component RPc and RE,, respectively, and a capacitive one, Xpc and XEL,respectively. The operation of the device rests upon the radiation controlled variations of impedance Zpc in the photoconductor layer, which causes a corresponding increase or decrease of voltage drop across the electroluminescent layer, intensifying or reducing its light emission proportionally. This voltage divider action of the PC-EL pair provides a nonregenerative amplification function which depends on the relative impedance of the PC and EL layers. It is quite obvious that RE, represents a parasitic path across the electroluminescent EL layer, and should therefore be much larger than XEL:

The fact that this condition is poorly met in most electroluminescent materials is the reason for their low energy conversion efficiency. With a loss tan 6 x 0.01 the electrooptical conversion efficiency is of the order of 1%.48

For the PC input layer it is a basic requirement that the opticallycontrolled impedance range embrace the impedance of the EL layer. But since the radiation-induced impedance changes are resistive only, because the radiation has no effect on X,, this requirement can be stated in the form RLi < X,, < R g ) ,

(21)

where L stands for illuminated and D for dark. A primary performance characteristic of an image converter is the ratio of photons emitted by the EL layer to photons incident on the PC layer. A measure of the photon output is the brightness BE,,which is related49 to the applied voltage V,, by

BE, = uf” exp( - kV;2/2),

(22)

where f is the excitation frequency and n a constant (0.5 Q n < l), and u and k are constants relating to the maximum brightness. Keeping in mind conditions (20),the applied voltage V,, can simply be expressed in terms of the PC-EL impedances and the excitation voltage V, (see Fig. 40) by

48

49

G. F. .I.Garlick, Aduan. Elecfron. Electroll Phys. 16, 607 (1962). G . Diemer and J. G. Van Santen, Philips Res. Rept. 15, 368 (1Y60).

12.

523

IMAGING AND DISPLAY

10

1 +

a 3 c

3

1

0.1

001 Io

I0-'0

-~

10-8

I6 '

10-6

Photoconductivity FIG.41. Effect of photoconductor capacitance on EL output. (After Stewart.5o)

For V,, > 10 V Eq. (22) can then be expanded in the form BE, = @{I

-

k[i(

1

+% XE,

RPC RPC f X P C

)I1"}.

(24)

From Eq. (24) it can easily be shown5' that high efficiency and high contrast ratio require50a that X,, 9 XEL.If this condition is not fulfilled, the shunting impedance X,, limits the voltage swing across the EL layer and thereby reduces the light output. Figure 41 shows how the minimum brightness of the EL output layer depends on the capacitive and resistive component of the P C input layer. No matter how efficient the resistive component is, the contrast ratio of the EL layer is limited by the PC capacitance. In order to realize extremely small PC capacitance, Stewart5' has used a special electrode structure, shown in Fig. 42. The radiation enters the photoconductor layer through the windows in the common electrode. The type of construction affords good optical absorption efficiency, since none of the radiation is lost to absorption or reflection from a transparent electrode. Moreover, radiation entering at an oblique angle and passing twice through the photoconductor is reflected back into the bulk of the PC layer. This has the effect of broadening the spectral response by extending the shortwavelength cutoff. The spectral response with a CdSe photoconductor is shown in Fig. 43. The 20 x 20 element array is fabricated on a 0.007-0.009-in.-thick glass substrate. The apertures in the common electrode are 0.04in. in diameter 5 0 R. D. Stewart, I E E E Trans. Electron Deu. 15, 220 (1968). ""The expression equivalent to Eq. (24), as given by Stewart," erroneously contains a factor ek and neglects a factor k in front of the inner bracket.

524

ROBERT SEHR AND RAWER ZULEEG Top view of PC electrodes (not to scale)

la) Side view of PC-EL converter (not to scale)

Common electrode Continuous photoconductor CdSe Opaque dielectric Individual electrodes Electroluminescent layer TransDarent electrode EL light output

(b)

FIG.42. Structure of photoconductor-electroluminescent converter. (After S t e ~ a r t . ~ ' )

on 0.05-in. centers. The diameter of the individual electrodes on the opposite side of the 0.002-in.-thick photoconductor is 0.02 in. The calculated capacitance Cpc of this structure is 1.25 x 10-I4F, and the ratio of the capacitance of the 40-mil-diam EL element C,, to Cpc is 2900. This is almost two orders of magnitude larger than a parallel-plane structure of the same dimensions would yield. The overall operating efficiency of the image intensifier is essentially that of the EL material alone: 7-12 I m p . The entire 20 x 20 array dissipates 15 mW/in.2 at 200 V. 18. PSEUDOREGENERATIVE IMAGECONVERTER

The most important operating parameters of an image converter are sensitivity, response time, and transfer function. While sensitivity and response time are predominantly determined by the photoconductor

12.

525

IMAGING AND DISPLAY

10

\A I0,OOO

12. 00

FIG.43. Spectral response of a CdSe photoconductor. (After Stewart.”)

material and the applied voltage, the transfer function in the general form

which relates the light output of the device, in lumens per unit area, to the light input, is a complex function of both materials, the PC and EL layers, as well as the device structure, the operating voltage V, and frequency w. The exponent y in Eq. (25) is generally taken to describe the transfer function Lo,, with the understanding that it refers to the center portion of the transfer curve. Since gamma determines the slope of the curve (in a double-log plot), it can be interpreted as the gain of the device. Two examples of transfer curves were shown in Figs. 4 and 41. For a given PC-EL combination and device structure there usually exists an optimum operating voltage and frequency which establishes the y, or gain, of the converter. A three-terminal converter developed by Kohashi et al.” differs remarkably in this respect. Not only can the gain vary over a wide range, but it can also be inverted, i.e., y can vary within a range of positive and negative values. When operating the converter with a negative y the original, positive image incident on the PC layer is emitted as a negative image from the EL layer. Areas that were originally dark are emitted light, and vice versa.

’’ T. Kohashi, T. Nakamura, H. Maeda, and K. Miyadi, Aduan. Electron. Electron Phys. 22B, 683 (1966).

526

ROBERT SEHR AND RAINER ZULEEG

lo2

I

Light input (arbitrary units)

FIG. 44. Different transfer functions obtainable with thc image-converter panel. (After Kohashi et d s ' )

The change of imaging mode is accomplished by applying two ac driving potentials with the same frequency and varying the phase and amplitude relation between the two. The different transfer functions obtainable with the converter are shown in Fig. 44. Curves A , B, and C correspond to positive image transfer of standard, low, and high y and contrast ratio, respectively, curves E and F to negative image transfer of large and small y and contrast ratio, respectively. Curve C represents an intermediate image transfer function between positive and negative, i.e., a V-shaped characteristic which is obtained for a certain phase and amplitude relation between the two driving potentials. A cross section through the three-terminal converter together with a schematic representation of operating conditions is shown in Fig. 45. This converter is composed of three principal layers.

(1) A photoconductive layer about 80 p thick of CdSe powder is bonded with epoxy resin. Incorporated with the layer is a parallel fine grid electrode of 10-p-diam tungsten wire and 0.6 x 0.6 mm grid dimension. (2) An electroluminescent layer of ZnS powder about 50 p thick is bonded with epoxy resin onto a transparent electrode of SnO, on a glass plate. (3) There is a transparent dielectric layer between the photoconductor layer and the second transparent SnO, electrode. Between the photoconductor and the electroluminescent layers is an optical antifeedback layer consisting of an opaque layer and a reflective BaTiO, layer.

12.

527

IMAGING AND DISPLAY

Glass plate Transparent electrode Transparent dielectric layer Fine grid electrode PC layer (CdSe) Opaque layer BaTiO3 reflecting layer Electroluminescent layer (ZnS) Transparent electrode 1,

FIG. 45. Cross section of three-terminal converter together with a schematic presentation of operating conditions. (After Kohashi et ~ 2 1 . ~ ' )

The converter is operated by applying two ac potentials V, and V, of the same frequency but of differing phase, as illustrated in Fig. 45. Here II is the lateral photocurrent due to the voltage V, and the light input intensity Li, and I , is the capacitive current associated with V,. The current that flows through the electroluminescent layer is the vector sum l 3 of the currents I , and I,. Light output Lo from the EL layer is nonlinear and increases rapidly with the amplitude of current 1 3 . The current I , is an incremental function of V,, while I , is an incremental function of V, and the incident light level Li . Therefore by adjusting the amplitude and phase relationships of the potentials V, and V,, the amplitude of Z3,and thereby the electroluminescent light output L o , becomes an incremental, decremental, or V-shaped function of Li. Since the variation of gain and output image polarity is reminiscent of an amplifier with a regenerative feedback loop of variable gain, the term pseudoregenerative converter is used. A photograph of test pictures for a positive, a V-shaped, and a negative image emitted from a 20 x 20cm EL layer is shown in Fig. 46. As can be seen, white areas in the positive image (a) are black in the negative image (c) and gray in the V-shaped image (c). The measured image resolution was greater than 800 lines with static input images. For a moving picture the resolution increases. The response time (risetime) of the converter is of the order of lOmsec, but is strongly dependent on illumination level. Nevertheless the device is

528

ROBERT SEHR AND RAWER ZULEEG

FIG.46. Output images of image converter panel in various modes of operation. Output images for: (a) positive, (b) V-shaped, and (c) negative characteristics. (After Kohashi et nLsl).

capable of reproducing flicker-free moving images. This quality, combined with the negative image transfer function, makes it ideally suited as a motion picture film editing device. ACKNOWLEDGMENT Thanks are due to 9. J . Lechner for his helpful comments on the section concerned with display devices.

Author Index Numbers in parentheses are footnote numbers and are inserted to enable the reader to locate thosecross referenceswhere theauthor’snamedoes not appear at the point of reference in the text. A Abraham, A., 30,33,41(27) Abrams. R . L., 285,383 Abnkosov, N.Kh., 187,188,190(19) Albers, W., 114,I40 Allgaier, R. S., 129 Almasi, G. S., 186,252 Alper, T., 187,188,190(20) Anders, R. A., 489,490(18),506 Anderson, L. K., 374,412 Anderson, R.L., 85 Andrews, J. C., 273,278(17) AntonEik, E., 30 Arams, F., 346,349(31), 353(31), 405,409,422 Armstrong, J. A., 373 Arnold, R. T., 260 Ashley, K. L.,89 Astheimer, R. W., 273,285,303,313 Attard, A. E., 33(32), 34(32), 35, 36(32),

43(32), 47(32), 49(32), 54 Avery, D. G., 16,17,46,63(4) Ayache, J. C., 203,204(52), 217,218 Ayas, A,, 407 Ayas, J., 199,204(36), 242,245(36), 246(36),

250

B Bahr, A. J., 373 Bailly, F., 186,203(12), 236,237(83), 238,252 Baird, J. R., 89 Bardeen, J., 167 Bardsley, W., 127 Barrie, R.,19, 20(17) Bartlett, B. E., 46,68,234 Baruch, P.,95 Bass, J. C., 436 Bates, R.L., 302 Beattie, A. R.,215

529

Bebb, H. B., 343 Beerman, H. P., 260,279(10), 285 Behle, A. F., 490,497(21) Bell, E. E., 336 Bennett, H.E., 29,31 Bernard, W.. 418 Betts, D. B., 303 Black, J. F., 518 Blair, J., 182, 183, 187, 190(3), 234,241(3),

243 Blakemore, J. S . , 31,215,217(71), 478 Blatt, F. J., 167 Bloembergen, N., 372 Blue, M.D., 199,202,203,214 Blunt, R. F., 17,63 Boltaks, B. I., 138,139(31) Born, M., 377 Bostick, H. A., 346,365,400,401,402,403 Boulton, J. S., 127 Bozorth, R. M., 454 Brand, F. A., 436 Bratt, P., 5 , 12(2) Braunstein, R.,89,90 Brebrick, R. F., 129,137,138,140,186 Bridges, T.J., 404 Briggs, G. R., 509 Brown, R. N., 200 Bube, R. H., 226 Buck, T.M., 475,476(10), 477(10) Buckley, R. E., 273 Buczek, C. J., 346,375,383,405,426,427,428 Bullis, W.M., 26,27(19), 28(19) Burdick, G. A., 260 Burgess, R. E., 223,355 Burstein, E.,336

Butler,J.F.,112,113,114(8),116(9),117,123, 126,127,138,159,383,389 Bylander, E. G., 112

530

AUTHOR INDEX C

Cadoff, 1. B., 288.293,297,298 Cady, W. G., 259 Calawa,A.R., 112,113, 114, 115(16),116(16), 118(16), 119(16), 120, 121, 140, 141, 143, 151(12), 157, 383, 389 Callahan, D. E., 489,490(18), 506(18) Cardona, M., 192, 193(28), 195, 198, 199, 200(39), 201(28),254(28) Carlson, R. O., 187, 190(16) Chang, T. Y.. 404 Chantry, G . ,275 Chao, P. Y., 490, 497(21) Chapin, D. M., 454 Chapman, R. A., 343 Chasrnar, R. P., 187, 287, 294(15), 297(17), 301(25), 308(34), 309(35) Cheo, P. K.,404 Cholet, P., 16 Choo, S . C., 39, 48(35), 54(35) Chynoweth, A. G., 260 Coates, D. G . , 154, 165(39) Cohen-Solal, G . , 186. 203, 204(53), 236, 237, 238,252 Coleman, P. D., 363. 374(14), 404,410,414(7) Conklin, J . B., Jr., 112 Cooper, J., 260, 272(7), 273(7), 278(7) Cope, A. D., 473 Corcoran, V. J . , 373 Corrigan, F. R., 298 Crowell, M. H., 475. 476, 477 Cruceanu, E., 187 Cuff,K. F., 159, 169 Cummins. H. Z., 364, 365 Cunnell, F. A., 18 Cunningham, R. W., 26,27,28

DeVore, H. B., 40 Dexter, R. N., 202, 210 Diament, P., 371 Dickey, D. H., 189, 190(24), 195, 199, 201(31, 32), 204(31. 32), 210(31) DiDomenico, M.. Jr., 346. 363, 374, 375(13), 404, 410, 414(7), 429(6) Diemer, G . , 522 Dimmock. J. O., 112, 113(1), 114, 151(12), l57( 13), 383,384, 389,480,481,482 Di Nardo, A,, 422 Dirac, P. A. M., 370 Doyle, W. M.. 382 Dresselhaus, M. S., 199, 201(31, 32), 204(31, 32), 210(31) Duley, W. W., 281 Durham, E. W., 187 Dyck, R. H., 490, 502(20), 504 Dziuba, E. Z . , 189, 190(25),202, 234

E Eddolls, D. V., 436, 438 Eden, R. C., 363, 374(14) Egli, P. H.. 288, 298 Ehrenreich, H., 30, 31(24) Eisenman, W. L., 302 Ellen, P. C., 234 Ellett, M. R., 159, 169(42) Ernmons, R. B., 346,362,363,374(12),375(13), 404(12, 13) Engler. W., 5, 12(2) Esaki, L., 112, 1 l3(5) Evans, R. D., 398

F D Dacus, E. N., 289 Dalton, J. V., 475, 476(10), 477(10) Davenport, W. B., Jr., 397, 398(62d) Davies, T. J., 63, 64(57) Davisson, J . W., 336 Deans, J., 234 Decque, J., 204, 250(54) DeHaan, E. F.,474 DeNobel, D., 184 Desse, M . , 95 DeVaux, L. H., 16. 17, 63(4)

Fan, H. Y., 28, 29, 35, 36, 39, 40, 47, 49(33), 453, 454, 456(10) Fedorova, N. N., 95 Fink, D. G., 469 Finn, M., 114, 115(16), 116(16), 118(16), 119(16), 120(16), 121(16), 140(16), 141(16), l43( 16) Flood, W. F., Jr., 29, 32(22) Folberth, 0. G., 95, 104 Foreman, J. W., Jr., 365 Forrester, A. T., 346, 361, 364(1), 372(1), 390 Foss, N. A,, 240

531

AUTHOR INDEX

Fourge, S. V., 469,473, 476(6) Fournier, G., 468 Fourny, J., 204, 250(54) Frederikse. H. P. R., 17, 63 Freed, C., 353, 373, 389, 397, 398 Fried, D. L., 364 Friis, H. T., 431

G Galavanov, V. V., 39 Galazka, R. R., 188, 190(20a), 202, 204. 212, 243(59) Galginaitis, S., 187, 190(15) Garbuny, M., 415 Garfunkel, J. H., 203 Garlick, G. F. J., 522 Gatchell, E. K . 102, 436, 440(2), 446(2), 447, 448(2), 452(2), 463(2) Gavrishchak, 1. V., 204, 210 Gebbie, H. A., 285, 362 Gebel, R. K . H., 478 Ceiling, L., 308 George, E. W., 365 Gerber, W.D., 382 Gershenzon, M . , 517. 518(40) Gibson, A. F., 30 Giriat, W., 201 Glass, A . M., 285, 383 Glauber, R. J., 366, 367, 368(25, 30), 369(25), 370, 371(25), 389(24), 396 Glicksman, M., 455 Gobeli, G. W., 28, 29 Goldberg, A . E., 16 Goldsmid, H. J., 292 Goodman, J. W., 400 Goodrich, R. R., 469, 473, 476(6) Goodwin, D. W., 16, 17, 46, 47, 49(49), 50 Goodwin, F. E., 363, 374(15) Goryunova, N . A., 95 Could, G., 376, 377(51), 396(51), 400 Granger, R., 199, 204(34), 241(34), 242, 250, 25 1 Gray, P. E., 292, 293 Grimmeiss, H. G., 518 Groves, S. H., 195, 197,200 Grube, R. H., 325,326(5) Griin, K. 114 Gubner, E., 140

Gudmundsen, R. A., 361, 364(1), 372(1) Gulyaeva, A. S., 38, 39 Gunn, J . B., 451

H Haas, C., 114, 140 Hadni, A , , 260,279(11), 285, 298 Hall, L. H., 167 Halsted, R. E., 189, 190(26) Hanlon, J., 374 Hansen, J.. 415 Hardy, A. C., 520 Harman, T. C., 63,113, 114,1I5,116(9,16). 117, 118(16), 119(16), 120(16), 121(16), 123, 126, 127, 135, 140(16), 141(16}, 143(16), 151(12), 157(13), 159(27), 164(18), 165,183,190,195, 199, 201, 204, 210, 212, 234, 254. 353, 383, 389,397 Harned, B.. 346, 362, 374(12), 404(12) Harp, E. E., 26, 27(19), 28(19) Harris, L., 289, 298 Harris, S. E., 346,361,362,363(2), 372(2), 409 Haseltine, W. A., 365 Haus, H. A,, 373. 389 Havens, R. J., 301 Hawkins, T.D. F., 30, 31(25) Haynes, J. R., 446 Heasell, E. L., 39, 48(35), 54(35) Henisch, H. K . , 508 Henninger, Y . , 260, 279(11) Henoc, J., 186 Henry, P. S. H., 130, 138(26), 139(26) Herman, F., 112 Herschel, W., 287 Hicinbothem, W. A,, Jr., 455 Hill, D. E., 89 Hillman, D. K., 517 Hilsum, C., 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 516 Hinkley, E. D., 353, 397, 398 Hobden, M. V., 89 Hollis, J. E. L.,39, 48, 54 Holter, M. R., 294 Honig, J. M., 135, 159(27), 195 Hornbeck, J. A., 446 Howarth, D. J., 19, 20(17) Hrostowski, H. J., 29, 32 Hulme, K. F., 18, 20, 21, 63, 64 Hurle, D. T. J., 127

532

AUTHOR INDEX

I Iglitsyn, M. I., 38(37), 39 Ioffe, A. F., 298 Ivanov-Ornskii, V. I., 189, 190(25), 197, 203, 204(4Y)

Ivleva, V. S., 38(37), 39

J

Jackson, J. K., 302 Jacobs, H., 436 Jacobs, S. F., 346, 361, 362(5), 363(5), 364(3), 366, 369(3, 3, 372(3, 5), 374, 376, 377(51), 396(51), 400(51), 409 Jarnieson, J. A., 325, 326 Jaumot, F. E., 292, 294(12) Jensen, J. D., 154 Jetton, J. L., 365 Johnson, K. M., 335 Johnson, L. E., 112 Johnson, P. 0..361, 364(1), 372(1) Jones, F. E., 287, 294(15), 297(17), 301(25), 308(34), 309(35) Jones, R. C., 4, 267,301,325, 314,464 Jones, R. H.. 19, 20(17)

K Kallen, D., I14 Kamadjief, P., 203, 204(53) Kane, E. 0.. 18,253 Kaye, S., 85 Kelemen, F., 187 Kent, M. J., 30 Kesamanly, F. P., 197 Keyes, R. J., 346, 348(29), 375, 381(49), 383(49), 405,422

Kimmitt, M . F., 30, 261, 273(15). 278 King, R. E. J., 46, 68, 493 Kingston, R. H., 346, 348(29), 375, 381(49), 383(49), 422

Kiuchi, Y.,473 Kleinman, D. A., 87, 88 Kleiner, W. H., 195 Knable, N., 364 Knibb, T. F., 436 Koelmans, H., 518 Koga, M., 260, 279( 13)

Kohashi, T., 525, 526, 527, 528 Kolesar, D. F., 188, 189, 190(21) Kolm, H., 353 Kolomiets, B. T., 197, 203, 204(47, 49) Koster, W., 95 Kot, M. V., 203,204 Kraus, H., 240 Krebs, H., 114 Kremenchugskii, L. S., 260, 279(12) Kroeger, R. D., 376, 396(52) Kruse, P. W., 5, 17, 39, 40, 43, 53, 65, 68, 69, 70, 203, 204, 205(58), 210, 218, 221(74), 225(74), 232(74), 234, 246, 252, 301

Ku, S. M., 518 Kudman, l., 89 Kuglin, C. D., 159, 169(42) Kurnick, S. W., 16, 17, 30, 31(26), 39, 63(4), 453

L Labuda, E. F., 475,476(10), 477(10) Ladd, L. S., 187, 190(18) Laff, R. A,, 35, 36, 39,40,47,49(33), 453,454, 456(10)

Landsberg, P. T., 215 Lang, S. B., 260 Lange, R.,422 Lasser, M . E., 16,346,361,362,369(4), 372(4), 374( I2), 404( 12) LaTourette, J. T., 376, 377(51), 396(51), 400(51)

Lawson, J. L. 331 Lawson, W. D., 17, 63(4), 154, 165(39), 203, 204

Lebloch, H., 249, 250(94), 252(94) Lechner, B.J.. 509,510,511,512,513,514,515 Leiba, E., 285, 383 Lennard, J. K., 77, 78, 79. 80, 82 Levinstein, H., 5, 6, 12(2). 374 Lewis, R. D., 365 Lewis, W. B., 325 Liang, S. C., 63 Limperis, T..329 Lipson, H., 336 List, W. F., 487,489,490(18), 497(17), 506(18) Logan, R. A., 517 Long, D., 19, 28(16), 41, 170, 177, 181, 182, 190(1), 191, 192(1), 193(1), 194, 195, 196, 197(1), 198,199,200(37), 201(1),208,209(64), 210(64), 214, 222, 226, 233(1), 330, 356

533

AUTHOR INDEX

Lopez, A., 85 Lorenz, M. R., 189, 190(26) Lorimor, 0. G., 189, 190(23) Lucke, W. H., 292 Lucovsky, G., 346, 362, 363, 374(12), 375(13), 404 Ludeke, R., 240 Ludlow, J. H., 260, 261,273(15), 276, 278(15)

M McCann, D. H., 489,490(18), 506(18) McDermott, P. S., 235 McFee, R. H., 325, 326(5) McGlauchlin, L. D., 5, 39, 40(39), 43(44), 53(52), 65(58), 68(61), 69(6J, 62), 70(61), 218, 221(74), 225(74), 232(74), 301 McMurtry, B. J., 346, 361, 362, 363(2), 372(2), 409,412 McQuistan, R. B., 5,39,40(39), 43(44), 53(52), 65(58). 68(61), 69(61, 62), 70(61), 218, 221(74), 225(74), 232(74), 301 MacRae, A. U., 5, 12 McSkimin, H. G., 188, 190(22) Madelung, O., 18 Maeda, H., 525, 526(51), 527(51), 528(51) Mali, M., 204 Mal’kova, A. A,, 197, 203, 204(47, 49) Mal’nev, A. F., 260, 279(12) Mandel, L., 346, 361, 364(6), 369, 370, 371, 390 Marfaing, Y.,186, 203, 204(52, 53), 217, 218, 236, 237(83), 238, 249, 250(94), 252 Markov, Yu.,199 Maronchuk, Yu. Y., 203, 204(46) Martienssen, W., 397 Martinuzzi, S., 204, 250(54) Massey, G. A., 376 Matreev, 0. V., 116 Mavroides, J. G., 188, 189, I90(21, 24), 195, 199, 201(31, 32), 204(31, 32), 210(31) Medved, D. B., 85, 100, lOl(25) Mekhtiev, A. Sh., 197 Melloni, M., 287 Melngailis, I., 112, 113, 114, 115, 151(12), 157(13), 159, 164(18), 165, 199, 204, 236, 238(87), 241(35), 383, 384, 389,405 Meray-Horvath, L., 494, 495(27), 496(27), 497(27), 504(27) Merrian, J. D., 302

Meyer, J. E., Jr., 494,495(27), 496(27), 497(27), 504(27) Mezrich, J. J., 373 Miller, E., 288, 293, 297, 298 Mitchell, G. R., 16 Mitchell, W. H., 260, 276(14) Miyadi, K., 525, 526(51), 527(51), 528(51) Mocker, H., 383 Moore, C. B., 365,415 Morten, F. D., 493 Moss, T. S., 17, 18, 30, 31(25), 40, 46,63(4) Mshenskii, V. A., 203,204(46) Mullin, J. B., 63, 64 N Nakamura, T., 525, 526(51), 527(51), 528(51) Nasledov, D. N., 37, 39, 54 Neda, A,, 187 Nelson, D. A., 187 Nelson, D. F., 517 Nelson, H., 89, 90(8), 518 Neuringer, L. J., 418 Newnham, R., 182, 183, 187, 190(3), 234, 241(3), 243 Newstein, M., 376, 377(51), 396(51), 400(51) Nicolosi, S. J., 16, 17, 63(4) Niculescu, D., 187, 202 Niculescu, N., 202 Nielsen, S., 203, 204(44) Nikolic, P. M., 112 Nipkow, P., 469 Nobel, P. J. W., 490 Norr, M. K., 123, 153(23) Novikova, S. I., 187, 188, 190(19) Novoselova, A. V., 116 Nudelman, S., 294

0 Ober, H., 114 Oliver, B. M., 373, 409 Oswald, F., 103

P Pace, F., 346, 349(31), 353(31), 405,422 Pankove, J. I., 89,90(8) Pantell, R. H., 346, 363, 375(13), 404, 410, 414(7)

534

AUTHOR INDEX

Parker, S. G., 240 Patel, C. K . N., 410 Paul, W., 195, 197, 240 Pauling. L., 96 Pedinoff, M. E., 363, 374(15) Pehek, J., 5, 12(2) Peretti, E. A,, 95 Pershan, P.S., 372 Petersen, P. E., 215 Petritz, R. L., 145, 227, 404 Pettit. G. D., 518 Peyton, B., 346, 349(31), 353(31), 405,422 Pihnn, W. G., 87 Pfleegor, R. L., 370, 371 Phelan, R. J., 480, 481, 482 Philipp. H. R., 30, 31(24) Picus, C;.S., 346, 375, 383,405,415,426, 427, 428 Pidgeon, C. R., 200 Pike, W. S., 494, 495(27), 496(27), 497(27), 504(27) Plass, G. N., 325, 326(5), 328 Powell, J. M., 30. 31(26) Powers, J . K., 346, 362, 374(12), 404(12) Prdtt, G. W., Jr., 112 Prince, M. B., 87 Prior, A. C., 116, 154, 165(39) Pruett, G . R., 145. 227, 404 Psoda. M., 188, 190(20a) Putley. E. H., 19, 20(17). 203, 204(44), 260, 261, 273( 15). 276( 14). 278( 1 9 , 285, 362

Q Quarrington, J. E., 19, 28, 30

R Rabinowitz, P., 346, 361, 362(5), 363(5). 366. 369(5), 372(5), 374(5), 376,377(51), 396(51), 400(51), 409 Rajchman, J . A,, 509 Ray, B., 182, 183,234, 243(2) Read, W. T., 35,41,48 Rediker, R. H., 151 Redington, R. W., 438, 478, 479, 480 Reese, W. E., 89 Rennie, A. E., 16, 17(2), 46 Richards, R. G., 325, 326(5) Rignoux, P.,468

Rittner, E. S., 41, 166. 167(43) Roberts, V., 19, 28, 30. Rodot, H., 186, 204 Rodot, M., 204,236,237(83), 238,249,250(94), 252(94) Roess, L. C., 289 Rolik, C i . P., 100, lOl(25) Root, W. L., 397. 398(62d) Rose, A., 335, 436, 437, 438(3, 4) Rose-Innes, A. C., 18, 19, 20, 21, 22, 23, 24, 25, 516 Ross, I. M.. 17 Ross, M., 346 Rupprecht, H., 518 Ruthroff, C. L., 404 Ryder. E. J., 451 S Sack. E. A,. 509 Sadasiv, G.. 494. 495(27). 496(27), 497(27), 504(27) Sdker, E. W., 18 Samoilov, V. V., 260, 279(12) Samusenko, A. G., 509, 510(33), 513(33) Sard, E., 346, 349(31), 353(31), 405 Saunders, G. A,, 187, 188, 190(20) Saur, W. D., 200, 203 Sawyer, D. E., 151 Scanlon, W.W., 137 Schampers, P. M., 474 Schlickman, J. J., 253 Schmit, J. L., 183, 184, 185, 186,200,201(39b), 204, 205(58), 206, 207(63), 249, 253(39b) Schmitz, W. D., 46 Schneider, W. E., 302 Schodder. G. R., 114 Schoolar. R. B., 154 Schuster, M. A., 487, 497(17), 503 Schwartz, R. F., 363, 375(13), 404(13) Schwarz, F., 285 Scott, M. W., 200,201(39a), 203(39a). 214(39a), 253(39a) Sella, C., 236,238(85) Segall, B., 189, 190(26) Seidel, T.. 89 Seraphin, B. O., 29, 31 Shaunfield, W. N., 458 Shaw, N ., 260,276( 14), 285,362 Shih, C., 95 Shimazu, M., 273, 278(19)

535

AUTHOR INDEX

Shimizu, K., 473 Shneider, A. D., 203, 204, 210 Shockley, W., 35, 41, 48, 147, 167, 214 Siegman, A. E., 346, 347, 361, 362, 363(2), 364, 367,372(2), 373( 16), 376. 377(16), 409 Simashkevich, A. V., 203, 204(46) Skillman, S., 1 I2 Skripkin, V. A., 197 Slack, G. A., 187, 190(15) Smetannikovd, Yu. S., 37, 39, 54 Smith, A. C., 186,252 Smith, A. W., 373 Smith, B. A., 95 Smith, G. E., 517 Smith, J. P.. 240 Smith, R. A., 287, 294, 297, 301, 308. 309 Smith, S. D., 30, 31(25) Smith, W., 468 Smollett, M., 177, 217(la) Sniadower, L., 188. 189, 190 (20a, 25) Sommers, H. S., Jr., 102, 436, 437, 438(5), 440(2), 446(2,5), 447,448(2), 452(2), 463( 2,5) Soref, R. A,, 415,484,485, 491,492 Sosnowski, L., 202, 204,212 Speer, H., 490, 497(21) Speerschneider, C. J., 183, 184, 185, 186, 240 Spencer, P. M., 183 Spenke, E., 150 Spiller, E., 397 Spitzer, C. R., 273 Spitzer, W. G., 189, 190(23) Stafsudd, O., 304 Stair, R., 302 Stanford, A . L., Jr., 260, 279(8) Steckel, F., 260 Stelzer, E. L., 200, 201(39h), 236, 238, 239, 240(82), 253(39b) Stephenson, J. C., 365 Stevens, N., 304 Stewart, R. D., 523, 524, 525 Stierwalt, D., 106 Stiles, P. J., 112, 113(5) Stocker, H. J., 63 Stone, N . W. B., 285, 362 Strauss, A. J., 16, 17,33(32), 34(32), 35,36(32), 43(32), 47(32), 49(32), 54,63(4), 112, I13(1), 114, 120, 151(14), 186, 195, 199, 201, 204, 210(31), 212,241(35), 254,383,384,453 Strozyk, J. W., 436 Strull, G., 503

Stuckes, A. D., 187 Sturge, M. D., 89 Suda, K., 260, 279(13) Suits, G. H., 46, 294 Sun, C., 457 Suzaki, Y., 273, 278(19) Svelto, O., 346, 363, 375(13), 404,410,414(7), 429(6)

T Ta, Yeou., 260 Takami, K., 260, 273, 278(19), 279(13) Takatsuji, M., 273, 278(19) Tauc, J., 30, 33, 41 Taylor, G. W., 509, 510(33), 511, 513(33, 35) Teich, M. C., 346, 348, 362, 364, 365, 366, 367(23), 369(23), 370(23), 371,372(7),373(23), 375, 376, 377, 378, 379, 380, 381(49), 382, 383, 385, 386, 387, 388, 389, 390, 392, 395, 399,406,422 Terhune, R. W., 46 Teutsch, W. B., 437, 438(5), 446(5), 463(5) Thoma, B., 95 Thomas, D. G., 188, 190(22) Thomas, R., 260,279(11) Thomson, S. P., 288 Thornton, J. R., 365 Titulaer, U. M., 367, 368(30), 370 Torrey, H. C., 41 I , 420(8) Townes, C. H., 362, 363, 373 Tufte, 0. N., 212, 236, 238, 239. 240 Tults, J., 509, 510(33), 513(33) Turner, W. J., 89, 336 Tyler, W. W., 337, 338(13), 339 Tyrziu, V. G., 203, 204(46)

U Uhlenhech, G. E., 331 V

Van Der Drift, A., 474 van der Ziel, A,, 147, 374, 405(47) van Heerden. P. J.. 478,479,480 van Roosbroeck, W.. 87, 167,214 Van Santen, J. G., 522 Van Vliet, K. M., 5, 41, 50, 221, 223, 224(75), 230(75), 374, 404(44), 412

536

AUTHOR INDEX

Vergnat, P., 260,279( 1 1) Verie, C., 199,204,206,207(38), 212,241(34), 242, 245(36), 246(36), 249, 250, 251, 252, 407 Vieland, L., 89 Vink, H. J., 140 Vogl, T., 415 Volkov, A. S., 39

W Wagner, J. W., 115 Walsh, E. J., 475, 476(10), 477(10) Walsh, T. E., 457 Wang, M., 409 Washwell, E. R., 169 Wasscher, J. D., 114 Watanabe, S. H., 490,497(21) Waters, W. R., 302 Watson, H. J., 365 Weaver, J. N.. 346, 363, 374( 14), 375(13), 404( 13)

Weckler, G. P., 490, 499, 500, 501, 502, 503, 504

Weimer, P. K., 469, 476(6), 494, 495, 496, 497(27), 504(27)

Weiner, S., 303, 313 Weiss, H., 18, 93, 95 Weitz, S.. 436 Welker, H ., 15, 18, 93 Wendland, P. H., 476 Wentworth, C., 51 , 513(35) Wertheim, G. K., 5, 54 Wetzell, H. B., 518, 519, 520 Wheatley, G. H., 29, 32(22) White, D. J., 280 White, M. B., 382 Whitmer, C. A,, 411, 420(8) Whitsett, C. R., 187 Wiley, J. D., 202, 210

f

Willardson, R. K., 115 Williams, D. B., 66, 67, 69, 77, 80, 81, 82, 83 Williams, L. R., 159, 169(42) Williams, R. L., 226, 438, 458 Wing, M. E., 489, 490(18), S06(18) Wolf, E., 369, 377 Wolf, M., 87 Wolfe, W. L., 294 Wolga, G. J., 366, 371 Wood, A. D., 273, 278(17) Woodall, T. M., 518 Woodbury, H. H., 337. 338(13), 339 Woolley, J. C.. 95, 182, 183, 234, 243(2) Wright, G. B., 195, 199, 201(31), 204(31), 210(31)

Wright, H. C., 436, 438 Wurst, E. C., Jr., 16 Wyncke, B., 260, 27% 11)

Y Yardley, J. T., 415 Yariv, A,, 426 Yates. H., 328 Yeh, Y., 364, 365 Young, A. S., 203,204(44) Youtz, P., 114, 115(16), 116(16), 118(16), 119(16), 120(16), 121(16), 140(16), 141(16), 143( 16)

Z Zakrzewski, T., 204 Zemel, 3. N., 154 Zhmurko, I. S., 203 Zissis, G. J., 294 Zitter, R. N., 17, 31, 33, 34, 35, 36, 39, 40, 41, 43,47,49(32), 54, 57,63(4), 453

Zlomanov, V. P., 116 Zworykin, V. K., 469

Subject Index B

A Absorption coefficient AlSb, 93 direct gap semiconductors, 86 GaAs, 90-93 GaSb, 93 Ge, 93 Hg,-,Cd,Te, 202-204 InSb, 27-29, 93 InAs, 93 InP, 93 Pb,-,Sn,Te, 335 Si, 93 Activation energies, see Impurity activation energies Aluminum antimonide (AISb), absorption coefficient, 93 Ambipolar diffusion length, 40 magnetic field, 58 Analytic signal, 369, see also Coherent detection Annealing PbSn chalcogenides, 118, 128-137, 142-144 two-zone, 136, 137, 143, 144 Antimony oxide (Sb,O,), 473 photoresponse, 473 resistivity, 473 Arrays, 336 Atmospheric window, 365 Auger effect Hg,-,Cd,Te, 2 14-2 17 InSb, 30, 47 theory, 215, 216

Background-limited infrared photoconductor, 12, 41, 53, 225, 227, 322, 326, 342, see also BLIP Band inversion, 112 Band structure CdTe, 194 HgTe, 195-199 InSb, 191 nonparabolic bands, 192-194 Pb,-,Sn,Se, 112-114 Pb,-,Sn,Te, 112-1 14 Beamed-scanned imaging devices IR vidicon, 477-480 Au-doped Si, 478-480 quantum efficiency, 480 laser-scanned MOS device, 4 8 0 4 8 2 Plumbicon, 474, 475 Sicon, 474-477 collection efficiency, 477 Vidicon, 470-473 CdSe target, 473 charge storage mode, 472 Sb,S, target, 473 Bias, see also Detector bias power effect on g-r noise, 418, 419 on mixer gain, 414, 422-425 voltage effect on carrier concentration, 426428 on frequency response, 422-425 on mixer gain, 411, 422-425 on mobility, 426-428 on resistivity, 426-428

537

538

SUBJECT INDEX

Black body emittance. 323, 324 Black body temperature, 7 standardization, 4 BLIP, 12, 41, 53, 225, 227, 322, 326, 342, see also Background-limited infrared photoconductor Bridgman technique Pb,.,Sn,Se, 119-128 Pb,,Sn,Te, 119-128 Broad band systems, see also MBPD microwave bias, 438, 439 performance factors, 446-448 frequency response, 446 quantum efficiency, 446 retrieval efficiency, 446-448 sensitivity, 446-448 signal-to-noise ratio, 447 Burstein-Moss effect, 233 C

Cadmium selenide (CdSe), 473, 526 conductivity, 473 spectral response, 525 Cadmium telluride (CdTe), 178, 183 band structure, 194-196 dielectric constant, 190 effective masses, 195, 196 elastic constants, 188-1 90 energy gap, 178, 194, 195 melting temperature, 184, 185 thermal conductivity, 187 thermal expansion coefficient, 187 Calcium difluoride (CaF,) attenuators, 380, 385 Carrier injection, see Injection Carrier lifetime, 437 Hg ,$d,Te, 2 13-2 18 InSb, 31-39 Cavity figure of merit, 440 parameter, 440, 442, 464 reentrant, 439-443 resonant frequency, 442 Cellular growth, 126 Characterization, infrared detectors, 3-12 C0,-N,-He Laser, heterodyne measurements, 375-377 Coherence first order, 367, 370, 373, 389

higher order, 389, 390 spatial, 367, 377 Coherence time, 381,397 Coherent radiation detection, 345-359, 361ff, see also Heterodyne detection, Homodyne detection, Photomixing analytic signal, 369 atmospheric distortion, 364 classical theory, 371, 372 conversion gain, 363 counting rate, 369 directivity, 364 frequency selectivity, 364 linearity, 364 optimum sinusoidal mixing, 397 photoconductors, 363 photodiodes, 362 photoemissive devices, 362 quantum theory, 365-371 return from steam, 403 semiclassical theory, 365-372, 396 signal-to-noise ratio, 372, 380-389 submillimeter region, 362 three-frequency configuration, 407 tracking of truck, 401, 402 Compensation, doped Ge, 426-428, see also Germanium (doped) Constitutional supercooling, 126-128 Contacts capacitive, 436 Hg,_,Cd,Te, 246 ohmic, limitations, 437 ohmic, minority carrier sweepout, 437 Conversion gain, see also Heterodyne detection, Mixing current-voltage characteristic, 420, 432-434 design criteria, 414, 429,430 effect of dark conductance, 434 methods of measurement, 421 variation with IF frequency, 411, 422425 with mixer parameters, 41 I , 424 Correlation function coherent detection, 366 second order, 389 Crystal evaluation, Hg,_,Cd,Te crystal perfection, 244 density, 242, 243

539

SUBJECT INDEX electron-beam microprobe, 243, 244 stoichiometry, 244 Crystal growth, see Preparation techniques

D D*, 4, 6, 7, see also Detectivity, normalized, L): InSb arrays, 493 pyroelectric detector, 270 radiation thermopiles, 301, 3 11 Si monolithic arrays, 492 thermal detectors, 8, 301 D 9, 43, 328, 332-336, see also D*, Spectral detectivity diode detector, 146-148, 159 Ge:Hg, 333 InSb detectors, 72, 75, 76 intrinsic versus impurity PC, 335 PbSn chakogenides, 138-162, 169-171 Pb,_,Sn,Te, 333 PC mode, 224-226 Hgl-,Cd,Te, 226, 227 PV mode, 231, 232 Hg,_,Cd,Te, 232, 233 Density operator, radiation field, 367, 370, 371 Depolarizing factor, 440, 444-446 Detectivity, 4, see also D* background noise-limited, 225, 23 1, 232 detectas PbSn chalcogenide, 154-1 58 photoconductive, 224-226 photovoltaic, 145-148, 23 I, 232 g-r noise-limited, 225, 226 hSb, 40 Johnson noise-limited, 224, 225 normalized, 4, see also D* particular wavelength, 6, see also D* A pyroelectric detector, 270 p-n junction, reverse biased, 374 shot noise-limited, 232 spectral, definition, 224 Detector bias, see also Bias microwave, photoconductive detector, 436 Detector design, 39, 40

c,

Detector theory photoconductive mode, 219-227 photovoltaic mode, 227-233 Diffuse reflector heterodyning, 389-400 focused case, 392 radar case, 394 target motion, 394 unfocused case, 393 narrow band random process, 394 power spectral density, 389-392 Diffusion Hg,_,Cd,Te, 186, 187 P b ,_,Sn,Se, 137- 143 Diode detectors, see also Photovoltaic detectors detectivity, 146-148 efficiency, 148, 149 l/f noise, 146 fabrication, 151-153 injection current, 145 I-V characteristic, 160 Johnson noise, 146, 147 quantum efficiency, 145, 155 saturation current density, 147 shot noise, 147 voltage responsivity, 146 Direct gap semiconductors, 18, see also Energy gap absorption coefficient, 86 NBSFD, 92 Display, 467ff, see also Imaging Display devices, 508-520, see also EL (electroluminescent) displays Doppler shift, 364, see also Heterodyne detection heterodyne measurements, 375 Doppler velocimeter, 365, see also Heterodyne detection

E Effective mass CdTe, 196 Hg,_,Cd,Te, 201 HgTe, 196, 197 Pb,-,Sn,Te, 159 ZnTe, 196 EL (electroluminescent) displays, 508520

540

SUBJECT INDEX

EL (electroluminescent) displays (cont.) comparison of characteristics, 520 EL panel, 520 Ga,_,Al& diode, 520 GaP diode, 520 gas discharge, 520 incandescent lamp, 520 ferroelectric control, 509-512 switching times, 512 scanned diode arrays, 514-520 Ga,-,AI,As, 5 18, 520 GaAs,_,P,, 517, 520 Gap, 516-518 Elastic constants CdTe, 189, 190 HgTe, 188-190 Electrical conductivity, see specific materials Electroluminescence, Hg,-,Cd,Te, 204 Electron-beam microprobe, 238, 240, 243-244 Electronically scanned photodetector arrays, see also Photodetector arrays doped detectors Ge, 483 Si, 484 film detectors, 484 InSb elements, 493 D*, 493 LSI, 508 monolithic structures D*,492 quantum efficiency, 492 response time, 492 Si doped, 490 undoped, 487 planar technology photodiodes, 484,485 transistors, 484, 485 quantum efficiency, 486 phototransistors, 486 Si diodes, 486 structures, 483-492 thin film arrays, 493-496 Electrooptical imaging, see Imaging Energy conversion devices, 87 Energy gap CdTe, 195, 196 common semiconductors, 176, 177

Kg ,-,Cd,Te, 198-200 HgTe, 195-197

InSb, 176, 191 Pb,_,Sn,Se, 112-1 14 Pb,.,Sn,Te, 112-1 14 wavelength units, 176 Environmental radiation, see Radiation, environmental Extinction coefficient, InSb, 29-3 1 Extrinsic detectors, 9

F l/f Noise, 5, see also Noise diode detector, 146 PbSn chalcogenide detectors, 170 Fabrication diodes, lead-tin chalcogenide, 151-154 heterodyne detector, 35 1-353 heat sinking, 352 Hg,-,Cd,Te contacts, 246 element preparation, 245 encapsulation, 246-248 surface treatment, 246 windows, 248 InSb, 62-70 MBPD, 444,445 PC detector, 62-70 PEM detector, 62-70 pyroelectric detector, 273-276 Field of view, 326, 327, 464 Frequency response broad band detectors design criteria, 41 1, 413, 414 improved (via compensated materials), 415, 421, 426 measurement technique, 41 5-419, 42 1 microwave, 415-419, 421, 422 roll-over frequency, 421 variation with bias voltage, 426-428 InSb detectors, 73-75 photoconductors versus photodiodes, 404

G g-r Noise, 5 , 40-42, 328-331, see also Generation recombination noise, Noise background flux, 328, 399

541

SUBJECT INDEX

cavity wall photon flux, 328-330, 334 Ge:Cu, 374 heterodyne local oscillator, 347-349, 374 InSb, 50 mixer, 412-419 PbSn chalcogenide detectors, 170 P C mode, 221-224 signal flux, 328, 329 thermal, 330, 344, 355-358 impurity photoconductor, 330, 357 intrinsic photoconductor, 330, 357, 3 58 Gain, photoconductive, 440 frequency dependence, 440 saturation, 437 Gain-bandwidth product, 436438,464 improving cavity parameter, 464 limit, 438 Ga,AI,_,As, 518 GaAs,P,-,, 251 Gallium antimonide (GaSb), absorption coefficient, 93 Gallium arsenide (GaAs) absorption coefficient, 90-93 NBSFD, 87,94 Gallium phosphide (Gap), 516 Gaussian random process, 396-398 Generation recombination noise, 5, 40, 41, see also Noise, g-r Noise InSb, 50 Germanium absorption, 93 detectors, 9 doped compensated (for high-frequency response), 415,426-428 (3-doped, 336340, 342-345 compensated, 415, 418,419 frequency response, 35 heterodyne detection, 348-353, 374-382,415-419,422-425 noise modulation, 38 1 photoconductor gain, 382, 383 detectors D * , 11 D: (Hg-doped), 333 Hg-doped, 178, 334, 336, 426 MBPD, 457, 458

heterodyne detection, 375, 383, 415 solubility of Cu, 339 MBPD, 450452,459, 461-463 Golay cells, 8 Graded-gap structures, 252

H Hall coefficient, see specific materials Hanbury-Brown-Twiss effect, 371,397 Havens limit thermal detector, 301, 302 Heat sinking heterodyne detector, 352 Heterodyne detection, 321-359, 409ff, see also Coherent radiation detection, Homodyne detection, Photomixing basic equations, 346-350 circuit, 347 conversion gain, 363 detector characteristics, 378-389 Cu:Ge, 379-383 detector fabrication Ge:Cu, 378,379 Pb,_,Sn,Se, 383-3 87 Pb,-,Sn,Te, 389 Doppler shift, 364 Ge:Cu, 346,421425 GHz response, 354,415-419,422-425 Golay cells, 362 Hg,-,Cd,Te junctions, 354, 355 high-frequency detection, 354, 415419, 422-425 InAs diode, 363, 374 InSb diodes, 354, 362 LO power, 352,353 mixer, see Mixing NEP, 412 noise, 347-349 Pb,-,Sn,Te junctions, 354 photoconductors compared to photodiodes, 403-406 device responsivity, 405 frequency response, 404 signal-to-noise ratio, 403, 404 temperature of operation, 405 photovoltaic detectors, 171 power detection limit photoconductor, 348 photoemitter (reverse p-n junction), 348 pyroelectric detector, 362

542

SUBJECT INDEX

Heterodyne detection ( f o n t . ) quantum noise limited, 421, 423 receiver analyses, 429-43 4 10.6 micron, 421-426 sensitivity, 412 shot noise, 373 signal-to-noise ratio, 348 thin-film Pb,_,Sn,Te, 355 Heterodyne detection (diffuse reflector), see Diffuse reflector Heterodyne receiver (sensor) configuration, 363, 364 detector fabrication, 351-353 measured characteristics, 422-426 noise, 424 Heterodyne signal amplitude fluctuations, 398 envelope, 396-400 probability density, 396-400 “higher-order” properties, 407 noise, 347-349 power-spectral-density, 382, 391-396 line width, 398 Lorentzian shape, 398 Heterodyne spectroscopy, 364, 391 Homodyne detection, see also Heterodyne detection hornodyne action, 439

I Iconoscope. 469 IF amplifier effective noise temperature, mismatched conditions, 43 1 noise, 412, 419-421, 429 signal-to-noise ratio, 430 wide-band, 419-421 applications, 415 IF signal GHz bandwidth, 409ff heterodyne receiver, 347-349 Image converters, 520-528 nonregenerative, 52 1-524 pseudoregenerative, 524-528 Image intensifiers, see Image converters Imaging, 467ff, see also Display, Imaging devices history, 468-470

parameters, 505-507 absolute sensitivity, 505 resolution, 506, 507 response speed of, 507 uniformity of, 506, 507 spectral sensitivity, 505, 506 readout methods, see Photodetector arrays, Readout methods solid state, 468, 470 spectral region, 468 Imaging devices, see also Imaging beam scanned, 470-482, see also Beam scanned imaging devices electronically scanned, 483-496, see also Electronically scanned photodetector arrays Impact ionization, InSb. 30 Impurity activation energies, InSb, 21 Incoherent radiation detection, low level, 322-345 Indium antimonide (InSb) absorption coefficient, 27-30, 32, 93 band structure, 191 carrier lifetime, 18, 31-39, 43, 47, 48, 54 carrier mobilities, 18, 20, 23-25, 28 conductivity, 22 effective mass ratio, 28 energygap, 15, 16, 18, 19, 176, 191, 493 extinction coefficient, 29-3 I g-r noise, 40-42, 50, 51, 55-57 Ge doping, 20, 2 1, 26-28, 29 Hall coefficient, 20, 22, 26, 27 impurity activation energies, 20, 21 internal photoeffect, 33 intrinsic carrier concentration, 19, 20, 44 intrinsic detectors, 11 magnetoresistance, 26, 59, 60 MBPD, 453-456, 459, 460 NBSFD, 94 nonparabolic bands, 18, 192, 193 quantum efficiency, 30, 33 recombination, 3 1-39,41-43, 48-50, 58,59 refractive index, 29-3 1 resistivity, 21, 22, 25, 44 spectral response, 10

543

SUBJECT INDEX Indium antimonide (InSb) detectors, 10, see also Indium antimonide detectivity, 10, 18, 72, 73, 75, 76, 493 performance data, 70-83 statistical distribution, 77-83 photoconductive, 15-83 photoelectromagnetic, 15-83 responsivity, 18, 45 Indium arsenide (InAs) absorption coefficient, 93, 94 detectors, 10 heterodyne detection, 363, 374 MBPD, 453, 459-462 NBSFD, 94 Indium arsenide phosphide (In,As,-,P), NBSFD, 87 Indium phosphide (InP), absorption coefficient, 93 Information retrieval efficiency, see Retrieval efficiency Injection, majority carrier, 437 Interference, photon, 370 Internal photoeffect, InSb, 30 Intrinsic carrier concentration, see afso specific materials Hg,_,Cd,Te, 253-255 Intrinsic detectors, 10 spectral response, 10 Intrinsic photoexcitation, InSb, 30 Irradiance, 42 1

Johnson noise, 5, 40, 331, 334, see also Noise, thermal diode detector, 146, 147 mixer, 4 12,429 PC mode, 222 PV mode, 231 pyroelectric detector, 268, 284, 285

K k p theory, 192-198, 203, 204, 253-255 Kelvin relation, 288, 292 KMER, see Kodak Metal Etch Resist Kodak Metal Etch Resist, 67 Kodak Photoresist, 67 KPR, see Kodak Photoresist

L Laser emission Hg,-,Cd,Te, 204 Pb,_,Sn,Te, 397 quantum phase fluctuations, 398 Laser radar, 365 Lead oxide (PbO), 474 Lead selenide (PbSe), detectors, 9 D : , 10 Lead sulfide ( P b S ) , detectors, 9 D : , 10 Lead telluride (PbTe), detectors, 9 Lead-tin chalcogenide detectors, 111-174, see also Pb,_,Sn,Se, Pb,Jn,Te Lead-tin selenide (Pb,_,Sn,Se) annealing, 118, 128-137 band structure, 112 carrier concentration, 115, 116, 122, 135-137 carrier mobility, 115, 116, 122 detectivity, 158-162 detectors, temperature of operation, 405 diode, I-V characteristic, 385 energy gap, 113, 177 heterodyne detection, 375, 378, 383388, 415 noise modulation, 389 ohmic contacts, 152 phase diagram, 121 response speed, 161-163 responsivity, 154-158, 384, 406 Lead-tin telluride (Pb,_,Sn,Te) absorption coefficient, 335 annealing, 118, 128-137 band structure, 112 carrier concentration, 115, 116, 122, 131-134, 161, 163, 171 carrier mobility, 115, 116, 122, 171 detectivity, 158-162, 333 detectors, 10 temperature of operation, 405 diode, I-V characteristic, 160 effective mass, 159 energy gap, 113, 161, 177,201 heterodyne detector, 355, 384, 389, 415 ohmic contacts, 152 phase diagram, 121, 126 properties, 334

544

SUBJECT INDEX

Lead tin telluride (Pbl-,Sn,Te) (cont.) response speed, 161, 162 responsivity, 157, 158, 165 Lead zirconium tin titanium oxide (Pb(ZrSnTi)O,), 51 1 Lifetime bulk, 167 hole, Ge:Cu, 344 PC, 166 radiative recombination, 167 reduction, 337 Li,SO,*H,O, pyroelectric detectors, 260, 284 LO (local oscillator), 347-349, see also Heterodyne detection effect, mixer resistance, 414-416, 422425 lasers, 364 noise, 386 power, 352, 386, 421, 422 photoconductor gain, 382, 383 LSI (large scale integration), photodetector arrays, 508

M Magnetoreflectivity, Hg,-,Cd,Te, 204 MBPC, 435ff, see Microwave-biased photoconductor detector Mercury cadmium telluride (Hg,_,Cd,Te) absorption coefficient, 202-204 alloy-composition determination, 240, 242-244 Auger recombination, 216, 217 Brillouin zone, 181, 182 carrier lifetime, 213-21 8 conduction band structure, 192 conductivity, 204-212 crystal evaluation, 242-244 crystal growth, 234-241, 251, 252 crystal perfection, 244 crystal preparation, 233-242 crystal structure, 180-182 cyclotron resonance, 201, 204 density, 182, 183, 242, 243 detectivity, 226, 227, 23 1-233 detector characteristics PC, 249, 250 PV, 250, 251 detector fabrication, 244-248

detectors, temperature of operation, 405 dielectric constant, 190 diffusion, 186, 187, 235-242 effective mass electrons, 193, 201, 202, 204, 217 holes, 180, 193, 21 1, 217 elastic constants, 188-190 electrical contacts, 245, 246 electrical properties, 204-212 electrolurninescence, 204 energy band structure, 189-202 gap versus temperature, 200, 201, 249, 250 general discussion, 177-180 graded-gap devices, 245, 252 Hall coefficient, 186, 204-212, 241 Hall mobility, 204, 209-213 heterodyne detection, 383, 415 impurities, 186, 212, 213, 252 interdiffusion, 186 intrinsic carrier concentration, 206208, 253-255 laser, 204 lattice constant, 182, 183 lattice properties, 180-1 89 lifetime, excess carrier, 213-218, 222, 252 magnetoreflectivity, 204 MBPD, 456,457 mobility electrons, 206-210 holes, 211-213 noise, generation-recombination, 222 optical absorption, 198, 200, 202, 203, 214 optical phonon energies, 190 p-n junctions, 204, 227ff, 241, 242, 250, 251 PC, 203 response time, 226 PEM effects, 204 phase diagram, 183-186, 241 photoconductive mode, 219-227 photoconductivity, intrinsic, 200, 203, 204,217, 249, 250 photoelectromagnetic effect, 204, 217 photoluminescence, 204 photovoltaic detectors, 179, 250, 251 photovoltaic effects, 198, 204, 241, 250, 251

545

SUBJECT INDEX

photovoltaic mode, 227-233 physical parameters, 187-190 purification, 233, 234, 252 radiation recombination, 214, 21 5 recombination, 213-218 stoichiometric defects, 213 thermal conductivity, 187, 190 thermal expansion, 187, 188, 190 Mercury cadmium telluride (Hg,-,Cd,Te) detectors, 10, 175-225, see also Mercury cadimum telluride Mercury sulfide (HgS), impurities, 212 Mercury telluride (HgTe), 178, 183 band structure, 195-199 dielectric constant, 190 effective masses, 196-198 elastic constants, 188-190 energy gap versus temperature, 200 impurities, 212, 213 magnetooptical effects, 200 “negative” energy gap, 178, 195-198 optical absorption, 202,203 thermal conductivity, 187 thermal expansion coefficient, 187, 188 Mercury zinc telluride (Hg,-,Zn,Te), 199 crystal growth, 233 energy band parameters vs composition, 202 lattice constant vs composition, 182 thermal conductivity, 187 Microwave-biased photoconductor detector, 435ff versus dc bias, 436 extrinsic PC, 436 intrinsic PC, 436 measured response Ge, 450-452 Ge(Hg-doped), 457, 458 Hg,,Cd,Te, 456, 457 InAs, 453 InSb, 453-456 Si epitaxial film, 448, 449 single crystal, 448, 449 microwave equivalent circuit, 439, 440 noise reduction, 4 6 2 4 6 4 optics, 445 angle of field, 445 conical light pipe, 445 numerical aperature, 445

performance factors frequency response, 446 retrieval efficiency, 446-448 sensitivity, 446-448 signal-to-noise ratio, 447 reentrant cavity, 439, see also Cavity reflection cavity, 439 sample mounting, 444 shot noise limit, 447 variable coupling, 442, 443 Minimum detectable power, 7, 332-336 heterodyne detection, 373 photoconductor (extrinsic), 375 photovoltaic diode, 375 Minority carrier sweepout, 437 Mixer resistance dark, 415, 416 effect on mixer gain, 425 photoexcited, 414, 415 variation with bias voltage, 428 with carrier lifetime, 414 with carrier mobility, 414 with temperature, 421 Mixing, 410, see also Mixer resistance, Photomixing bias power, 41 7-4 19 bias voltage, 41 I, 426, 427 conversion gain, 410, 41 1, 414, 420, 421, 430, 433 dark conductance, 434 frequency response, 415-417 heterodyne detectors, basic equations, 346-3 50 I-V characteristics, 420 performance analysis, 432-434 NEP, 421 mixer, 421 noise, 410, 412-419 output resistance, 414, 415 performance, 410,420-422, 432-434 photoconductive, design equations, 410-415 response measurement, 415-419 wide-band applications, detector materials, 415 Multiphoton processes, 370

N Narrowband detectors, 349 NBSFD, 85

546

SUBJECT INDEX

Narrowband self-filtering detectors, 85108, see also NBSFD binary 111-Vmaterials, 94 fabrication, 89, 98, 102-105 field-of-view, 99, 105, 106 GaAs materials, 98-102 InAs,P,, materials, 102-106 performance data, GaAs devices, 106108 quantum efficiency, 101, 102, 106 reverse bias tuning, 100, 101 signal-to-noise data, 102, 106 spectral response, 99, 100, 105 ternary 111-Vmaterials, 94-97 tuning techniques compositional, 93 junction depth, 94 reverse biasing, 94 temperature, 93 NBSFD, 85-108, see also Narrowband self-filtering detectors NEP, 3, 4, see also Noise equivalent power Nipkow disc, 469 Noise amplifier, 268, 412, 429, see also IF amplifier background, 225, 227, 231, 232, 323325 “excess,” heterodyne detection, 373 l/f, 5, 40, 146, 222, 328 g-r, 5, 40, 41, 42, 50, 221-224, 328330, 412, 415419,429 heterodyne receivers, 347-349, 424 InSb detectors, 40, 41, 56 Johnson, 5, 40, 146, 147, 221, 222, 331, 412, 429, see also Noise, thermal MBPD, 462-464, see also Signal-tonoise ratio PC mode, 221-224 photon, 5, 53, 325, 326, 328 photon induced, 41 PV mode, 230, 231 pyroelectric detector, 266-271 quantum, heterodyne receiver, 409, 410,412-414 radiation, 267

shot, 147, 230,231, 374 photodiode (reverse biased), 373 photoemitter, 373 spatial inhomogeneities, 325 filtering techniques, 325 temperature, 5, 267 thermal, 40, 42, 50, 429 InSb photoconductors, 46 preamplifier, 347-349 Noise equivalent power, 3, 4, 326-328, see also NEP, RNEP diode detector, 146 Ge:Cu, 342, 343 heterodyne receiver, 412, 423-425 10.6 micron design tradeoffs, 412,414,429-430 effect of IF amplifier, 412,424, 426 variation with mixer parameters, 412, 423-425 pyroelectric detector, 268-272 Noise modulation bandwidth, 381, 382, 389 Noise spectra, InSb detectors, 73-77 0

Optical absorption coefficient, see Absorption coefficient InSb, 27,29, 30 Optical communication receivers, 460463 Optical transmission, ZnSb, 32 P p-n Junction detector, 86-92, see also

Photovoltaic detector reverse-biased detectivity, 374 RNEP, 374 P-representation, 370, 396 PC detectors, see also Photoconductive detectors basic circuitry, 219 g-r noise, 42, 222-224 InSb, 15-17,41-57 preparation, 62-70 minimum detectable power, 375 mixers, 410-419 signal-to-noise ratio, 375 thermal noise, 42

SUBJECT INDEX

Peltier coefficient, 290, 291 PEM detectors, 15-17, 176, 252, see also Photoelectromagnetic detectors InSb, 15-17,57-76 preparation, 62-70 Performance data, see also specific materials InSb-PC detectors, 70-83 InSb-PEM detectors, 70-83 pyroelectric detector, 276-282 thermal detectors bulk materials thermopiles, 305-307 evaporated thermopile arrays, 3 12317 thin film devices, 307-3 11 Phase diagram Pb,-,Sn,Se system, 121 Pb,,Sn,Te system, 121, 126 Pb-Te system, 114, 115 Photoconductive current, short-circuit mode, 41 Photoconductive detectors, 15-17, 176 see also PC detectors g-r noise, 42, 374 heterodyne detection, 374, 375 InSb, 15-17,41-57 preparation, 62-70 PbSn chalcogenides, 163-171 carrier lifetime, 166-168 detectivity, 169-171 responsivity, 164-166, 169-171 microwave bias, 436, see also MBPD thermal noise, 42 Photoconductive response time, 41 Photoconductivity, 8, 176, 436 Hg,-,Cd,Te, 203, 217 Photocurren t collection efficiency, 477 decay time Sicon, 476 Vidicon, 476 diode, 486, 500 Plumbicon, 474 Sicon, 475 transistor, 486, 500 wavelength response, 478 Photodectector array, 483, see also Electronically scanned photodetector arrays

547

characteristics absolute sensitivity, 505 integration, 508 resolution, 506 response speed of, 507 uniformity of,506 spectral sensitivity, 505 monolithic structures, 487 silicon doped, 490 undoped, 487 narrow-gap semiconductors, 493 photosensitive structures, 483 photoconductor element, 483 photodiode, 485 phototransistor, 485, 490 thin-film structures, 493 Photodiode current, 486, 500 versus MBPD, 436 quantum efficiency, 486 reverse biased, heterodyne detection, 373 structure, 485 Photoelectromagnetic effect, see also PEM detectors Hg,_,Cd,Te, 204, 217 InSb, 15-17, 57-76 Photoemitter, heterodyne detection, 373 Photomixing, 377, see also Heterodyne detection, Mixing optimum, 377, 406 sinusoidal, optimum, 370 three-frequency, 407 Photon counting condition for, 446 versus heterodyne detection, 362 Photon detectors, 8 detectivities, 12 time constants, 12 Photon noise, 5, 325, 326, 328, see also Noise Phototransistor, 485, 487, 497 current gain, 486 response time, 498, 501 Photovoltaic detectors, see also Diode detector, p-n Junction detector basic configuration, 228 carrier lifetime, 172-174

548

SUBJECT INDEX

Photovoltaic detectors (cont.) detectivity, 145-148 efficiency, 148, 149, 171, 172 fabrication, 151-153 Hg,_,Cd,Te, 204 InSb, 16, I7 junction capacitance, 150 minimum detectable power, 375 NBSFD, 85-108 quantum efficiency, 87-92 response speed, 149-151 reverse biased detectivity, 374 RNEP, 374 saturation current, 149, 171, 172 signal-to-noise ratio, 375 spectral response, 86-90 structure, 144, 145 surface recombination velocity, 149 Piezoelectric phenomena, 259 Planck distribution, 322, 323 Plumbicon, 469 Polarization, spontaneous electric, 259 Power-spectraf-density, heterodyne signal, 382 Preparation techniques annealing, 118, 128-137, 142-144 cellular growth, I26 constitutional supercooling, 126-128 diffusion, 137-142 Hg,_,Cd,Te, 233-242 annealing, 240, 241 junction formation, 241, 242 melt growth, 234 purification of elements, 233, 234 vapor phase growth, 235-240 InSb, 63, 64 Pb,-,Sn,Se, 114-144 Pb,-,Sn,Te, 1 14-144 PV mode, see Photovoltaic detectors Pyroelectric detector, 259-285 detectivity, 270, 280, 281 electrical circuit, 263-266 electrode geometry, 283, 284 excess temperature, 262, 263 fabrication, 273-276 noise amplifier, 268, 269 Johnson, 268 radiation, 267

noise equivalent power, 268-272, 274 performance, 276-282 high-frequency, 278, 279 NEP, 276-280,284 response, 282 TGS performance, 265, 284, 285 thermal circuit, 261-263 thermal wave, 262, 263 propagation constant, 263 total energy mode, 273 voltage responsivity, 264-266 Pyroelectric materials, properties, 260, 266 Pyroelectric phenomena, 259 pyroelectric coefficient, 259, 260

Q Quantum efficiency diode detector, 145 internal photoeffect, InSb, 30, 33 mixer, 41 1, 421, 424 Pb,,Sn,Se, 155 Pb,_,Sn,Te diodes, 405 photovoltaic detector, 87-92 Si diodes, 486 Si monolithic arrays, 492 Quantum noise factor, 410,412-414 sensitivity limit, 422-424

R Radar energy detection, 400 heterodyne Doppler, 400 pulsed, 400 laser, 365, 4 W 0 3 configuration, 400 results, 400403 Radiation, environmental, 322 Radiation thermopiles, 287-3 18, see also Thermopiles arrays, 3 12-3 17 D* criterion, 301 design criteria, 299 detectivity, evaporated thermopiles, 311 device figure of merit, 299-301 Havens-limit thermal detector, 301, 302 M , criterion, 301, 302, 311

549

SUBJECT INDEX noise equivalent power, 3 11 properties profile, 302 responsivity, 296, 297 bulk thermopiles, 307 evaporated thermopiles, 309-3 11 time constant bulk thermopiles, 307 evaporated thermopiles, 3 11 Radiative recombination Hg,_,Cd,Te, 214-217 theory, 214 Rayleigh density function, 398-400 Readout methods, photodetector arrays charge storage mode (photon flux integration), 497, 499-504 effective gain, 501 illumination level, 501 excitation storage mode, 504 pattern recognition, 505 photocurrent mode, 497, 498 random access, 504, 505 Receiver (10.6 micron heterodyne) conversion gain, 411, 413, 421-425 design criteria, 414, 429-430 Ge (Cu doped), 415, 422-425 gigahertz frequency response, 413,414, 419, 422-424 NEP, 412, 422-425 summary of characteristics, 421-425 Receiver sensitivity, heterodyne detection, 412, 413, 422 Recombination, see also Carrier lifetime Hg,_,Cd,Te, 213-218 InSb, 35, 39, 43, 48, 54 Refractive index, InSb, 29-3 1 Response, see also Responsivity, spectral Hg,_,Cd,Te detectors PC, 249, 250 PV, 250, 251 pyroelectric detector, 265, 282 thermal detectors, 302-304 Response speed, 5, see also Response time PbSn chalcogenide detector, 161-163 radiation thermopiles, 3 11 Response time, 7, 8, see also Response speed compensated Ge:Hg, 426, 427 PC,41, 47,54, 59 Hg,-,Cd,Te, 226

PEM, 47, 59 uncompensated Ge:Cu, 426, 427 Responsivity spectral, 43, see also Voltage responsivity Ge:Cu, 342 InSb detectors, 72-77 PC, 45-57 PEM, 60,61 lead-tin chalcogenide detectors, 154-158, 165, 169-171 measurement, 341 Pb,_,Sn,Se diode, 384, 406 P C mode, 220, 221 photoconductors vs photodiodes, 405 PV mode, 228-230 voltage, 264, see also Pyroelectnc detectors radiation thermopiles, 3 11 Retrieval efficiency, 446-448 bandwidth variation, 447, 448 critical value junction diode, 447 photoconductor, 447 photomultiplier, 447 RNEP, see also Noise equivalent power, Real noise equivalent power p-n junction, reverse-biased, 374 photovoltaic detector, 374 Roll-over frequency, see Frequency response Rough-target heterodyning, see Diffuse reflector

S Scanning circuits, 494, 508 integration, 508 thin-film, 494 Scattered radiation heterodyning, see Diffuse reflector Scattering wheel, 375 Screening, free carrier, 439 Seebeck coefficient, 290 Sensitivity, see Noise equivalent power, Responsivity Sensitizing techniques, 9 Shockley-Read recombination, 39, 41 Hgl..,Cd,Te, 217, 218, 222, 223 InSb, 48, 50, 54

550

SUBJECT INDEX

Sicon, 469 Signal-to-noise ratio coherent detection, 372 heterodyne detector, 348 Ge:Cu, 380, 381 Pb,,Sn,Se, 386-388 IF output, 430 MBPD, 436 measurement, 375-378 photoconductor extrinsic, 375 versus photodiodes, 403, 404 photodiode (reverse biased), 373 photoemitter, 373 photovoltaic diode, 375 quantum theory, 372 shot noise limit, 447 Silicon absorption coefficient, 93 Al-doped, heterodyne detection, 415, 484 Au-doped, 478 detectors, 9 D:, 10, 492 MBPD, 448-450 p-n junction, 484, 485 quantum efficiency, 480, 486, 492 spectral response, 480, 485 Solid solutions, 111-Vcompounds, 96, 97 Solubility, see also Solid solutions substitutional alloys, 95-97 Spectral cutoff, 8 Spectral detectivity, see also D: InSb, 46, 51, 53, 56 PC detectors, 46, 51, 53, 56 PEM, 61,62 Spectral response, 6-8, 42 InSb, 40, 73 p-n junction devices, 86 Spectral responsivity, see Responsivity, spectral Speed of response, 5, see also Response speed Stationarity, 368 Stefan-Eoltzmann law, 322 Strontium-barium niobate heterodyne detection, 383 special materials, 383 pyroelectric detectors, 285

T Target motion, see Diffuse reflector Temperature, operating, photoconductors versus photodiodes, 405, 406 Temperature noise, 5 , see also Noise TGS, see also Triglycine sulfate, Pyroelectric detector heterodyne detection, 383 properties, 260 transmission, 275 Thallium sulfide (TI.$,), detectors, 9 Thermal conductivity CdTe, 187 Hg,-zCd,Te, 187 HgTe, 187 Thermal detectors, 7, 8, 260 bolometer, 8 D*, 8 Golay, 8 pyroelectric, 8 time constant, 8 Thermal expansion CdTe, 187 HgTe, 187, 188 Thermal wave, 262, see also Pyroelectric detector Thermoelectric materials, 297, 298 figure of merit, 297 Wiedemann-Franz ratio, 297, 300 Thermopiles, see also Radiation thermopiles design criteria, 299 history, 287-289 materials criteria, 297, 298 figure of merit, 297 radiation detectors, 287-3 18 responsivity, 296, 297 theoretical background, 289-297 heat balance, 292-296 Peltier coefficient, 290, 291 Seebeck coefficient, 290 Thomson coefficient, 29 I , 292 Thin-film transistor, 494 Thomson coefficient, 291, 292 Time constant, see Frequency response Time sequential information retrieval, see Readout methods, Photodetector arrays Tin oxide (SnO,), 478, 526

551

SUBJECT INDEX

Total energy detector, 272, 273 Transmission, see Optical transmission Triglycine sulfate, 260, 274, 275, see also TGS Tuning techniques, NBSFD compositional, 93 junction depth, 94 reverse biasing, 94 temperature, 93

U Uncertainty principle, 37 1

Vidicon, 470, 471 Voltage responsivity, 146 diode detector, 146

W Wavelength units, energy gap, 176 Wide-band detectors, 349, see also Broad band systems Wiedemann-Franz law, 297 Wien displacement Iaw, 322 Windows, IR transmission, 248

V van Cittert-Zernike theorem, 377 Vapor growth technique 116-1 19 Pb,-,Sn,Se, Pb,-,Sn,Te, 116-1 19

Z

Zinc sulfide (ZnS), 508, 524 Zinc telluride (ZnTe) band structure, 194-195

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