Advances in Electronics and Electron Physics, Volume 47

ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS

VOLUME 47

CONTRIBUTORS TO THISVOLUME

J. N. Churchill T. W. Collins Anthony J. Davies Gilbert J. Declerck J. Franks F. E. Holmstrom A. Moschwitzer Paul A. Muls P. A. Ramsdale Roger J. Van Overstraeten

Advances in

Electronics and Electron Physics EDITEDBY L. MARTON Smithsonian Institution, Washington, D.C. Associate Editor

CLAIRE MARTON EDITORIAL BOARD T. E. Allibone E. R. Piore H. B. G. Casimir M. Ponte W. G. Dow A. Rose L. P. Smith A. 0.C. Nier F. K. Willenbrock

VOLUME 47

1978

ACADEMIC PRESS

New York San Francisco London

A Subsidiary of Harcourt Brace Jovanovich, Publishers

COPYRIGHT @ 1978, BY ACADEMIC PRES~ INC. , ALL RIGHTS RESERVED. N O PART O F T H I S PUBLICATION MAY B E REPRODUCED OR TRANSMITTED I N ANY F O R M OR BY ANY MEANS, ELECTRONIC OR MECHANICAL, INCLUDING PHOTOCOPY, RtCORDING, OR ANY INFORMATION STORAGE AND RETRIEVAL SYSTEM, W I T H O U T PERMISSION I N WRITING FROM T H E PUBLISHER.

A C A D E M l C PRESS, I N C .

111 Fifth A v e n u e , N e w Y o r k , Ne w York I0003

Uriitcrl K i r r p l m i Eriitiori prrblislied l)>> ACADEMIC PRESS, INC. (LONDON) LTD. 24/28 O v a l R o a d , L o n d o n NW1 7DX

LIBRARY 0 1 CONCiRL55 ISBN 0-12-014647-

CATALOG C A R D

N L M U L R :49-7504

9

P R l N l LD IN I HL U N I l f D b I A T t 5 0 1 AMLRICA

CONTENTS CONTRIBUTORS TO VOLUME 47 . . . . . . . . . . FORE WORD . . . . . . . . . . . . . . . .

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vii ix

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1 2 13 30 45 47 48

Ion Beam Technology Applied to Electron Microscopy J . FRANKS 1. Introduction . . . . . . . . . . . . . . . . I1. Production of Ion Beams . . . . . . . . . . 111. The Sputtering Process . . . . . . . . . . . IV . Ion Thinning for Transmission Electron Microscopy . V . Ion Erosion for Scanning Electron Microscopy . . Vl . Conclusion . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . .

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Microprocessors and Their Use in Physics ANTHONY J . DAVIES

1. Introduction . . . . . . . . . . . . . . . . . . . . .

. . . I11 . The Architecture of Microprocessors . IV . Memory and Peripheral Devices . . . V . Software . . . . . . . . . . . 11. The Technology of LSI Circuits

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VI . Linking the Experiment to the Microprocessor . VII . Typical Applications . . . . . . . . . . VIII . Current and Future Trends . . . . . . . Appendix I . . . . . . . . . . . . . Appendix I1 . . . . . . . . . . . . . References . . . . . . . . . . . . . Bibliography . . . . . . . . . . . .

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51 54 61 75 83 88 100 109 111 117 118 118

Wire Antennas P. A . RAMSDALE I . Introduction . . . . . I1 . Analysis . . . . . . 111. Unloaded Antennas . . IV . Passive Loaded Antennas V . Active Antennas . . . VI . Antenna Selection . . VII . Concluding Remarks . References . . . . .

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123 124 152 163 172 187 192 192

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I. I1. I11. IV . V.

CONTENTS

Characterization of the MOSFET Operating in Weak Inversion PAULA . MULS.GILBERT J . DECLERCK. AND ROGERJ . VAN OVERSTRAETEN Introduction . . . . . . . . . . . . . . . . . . . . . Accurate Model for the Drain Current in a MOSFET . . . . . . Determination of the Surface State Density from Drain Current vs Drain Voltage Measurements in Weak Inversion . . . . . . . . Influence of Potential Fluctuations on the Mobility in Weak Inversion General Conclusion . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . .

Modeling of the Transient Response of an MIS Capacitor T . W. COLLINS.J . N . CHURCHILL. F. E . HOLMSTROM. A N D A . MOSCHWITZER I . Introduction . . . . . . . . . . . . . . . . . . . . I1. Dynamic Equations . . . . . . . . . . . . . . . . I11. Simplest-Case Example . . . . . . . . . . . . . . . IV. Computer Simulation: Flatband to Inversion Transient for MIS Structure . . . . . . . . . . . . . . . . . . . . . V . Results . . . . . . . . . . . . . . . . . . . . . VI . Examples . . . . . . . . . . . . . . . . . . . . . VII . Conclusion . . . . . . . . . . . . . . . . . . . . List of Symbols . . . . . . . . . . . . . . . . . . . Reverences . . . . . . . . . . . . . . . . . . . . AUTHORINDEX. . . . . . . . . . . . . . . . . . . . . SUBJECT INDEX. . . . . . . . . . . . . . . . . . . . .

197 201 224 24 1 262 265

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261 270 214

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279 282 317 325 326 328

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331 338

CONTRIBUTORS TO VOLUME 47 Numbers in parentheses indicate the pages on which the authors’ contributions begin.

J. N. CHURCHILL,* General Products Division, International Business Machines Corporation, San Jose, California (267) T. W. COLLINS,General Products Division, International Business Machines Corporation, San Jose, California (267)

ANTHONYJ. DAVIES, Department of Physics, University College of Swansea, Swansea, United Kingdom (51)

GILBERT J. DECLERCK, Laboratory ESAT (Elektronica, Systemen, Automatisatie en Technologie), Departement Elektrotechniek, Katholieke Universiteit Leuven, Leuven, Belgium (197) J. FRANKS, Ion Tech Ltd., Teddington, Middlesex, England (1)

F. E. HOLSTROM,t General Products Division, International Business Machines Corporation, San Jose, California (267) A. MOSCHWITZER,$ General Products Division, International Business Machines Corporation, San Jose, California (267) PAUL A. MULS,Laboratory ESAT (Elektronica, Systemen, Automatisatie en Technologie), Departement Elektrotechniek, Katholieke Universiteit Leuven, Leuven, Belgium (197)

P. A. RAMSDALE, Department of Electrical and Electronic Engineering, Royal Military College of Science, Shrivenham, Swindon, United Kingdom (123) ROGERJ. VAN OVERSTRAETEN, Laboratory ESAT (Elektronica, Systemen, Automatisatie en Technologie), Departement Elektrotechniek, Katholieke Universiteit Leuven, Leuven, Belgium (197)

* Present address: Dept. of Electrical Engineering, University of California, Davis, California 95616. t Present address: Dept. of Physics, San Jose State University, San Jose, California 95192. $ Present address: Technische Universitat Dresden, Dresden, G.D.R. vii

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FOREWORD “Ion Beam Technology Applied to Electron Microscopy” by J. Franks deals with the very interesting technique of thinning specimens by ion bombardment in order to make them suitable for electron microscope observation. After a review of the suitable ion sources, the sputtering process is investigated. The article ends with a discussion of applications in both transmission microscopy and surface scanning microscopy. A. J. Davies examines the state of the art of microprocessors and their use in physics. The extremely rapid growth of this field, and the quasiexperimental reduction in size and cost, may make any review almost obsolete before it is written down. Nevertheless, the basic concepts d o not change overnight and that is why this review should be useful to the reader in choosing and using a microprocessor in his own particular application in physics. In our 19th volume (1964) we presented a review entitled “Endfire Antennae.” P. A. Ramsdale has written, under the title “Wire Antennas,” what might be considered a sequel to the earlier review. Although he comes to the conclusion that “the time when all forms of wire antenna can be said to be well understood and when useful new variants stop appearing looks to be well into the future,” the review contains a very useful survey of how improved gain, greater bandwidth, and reduced size can be traded off against one another. Metal-oxide-semiconductor field-effect transistors are the subject of a review by P. A. Muls, G. J. Declerck, and R. J. Van Overstraeten. They emphasize the importance of the effect of weak-inversion current on circuit characteristics and on the investigation of the physical properties of the interfaces involved. By using suitable models, theoretical characteristics can be derived and compared with actual performance data. Our 34th volume (1973) included a review of metal-insulator-semiconductor varactors. The present volume ends with a review of “Modeling of the Transient Response of an MIS Capacitor,” by T. W. Collins, J. N. Churchill, F. E. Holmstrom, and A. Moschwitzer. For such modeling, the rate equations for hole, electron, and trap occupancy are coupled with Poisson’s equation and lead to a computer simulation of the switching transient. We expect to publish in forthcoming volumes the following reviews: M. P. Shaw and H. Grubin L. E. Cram

The Gunn-Hilson Effect Solar Physics ix

X

FOREWORD

Digital Filter High Power Millimeter Radiation from Intense Relativistic Electron Beams Auger Electron Spectroscopy Sonar Electron Attachment and Detachment Electron-Beam-Controlled Lasers Amorphous Semiconductors Electron Beams in Microfabrication. I and I1 Design Automation of Digital Systems. I and I1 Magnetic Liquid Fluid Dynamics Fundamental Analysis of Electron-Atom Collision Processes Electronic Clocks and Watches Review of Hydromagnetic Shocks and Waves Beam Waveguides and Guided Propagation Recent Developments in Electron Beam Deflection Systems Seeing with Sound The Edelweiss System A Computational Critique of an Algorithm for the Enhancement of Bright Field Electron Microscopy Large Molecules in Space Recent Advances and Basic Studies of Photoemitters Application of the Glauber and Eikonal Approximations to Atomic Collisions Josephson Effect Electronics Signal Processing with CCDs and SAWS Flicker Noise Present State of High Voltage Electron Microscopy Noise Fluctuations in Semiconductor Laser and LED Light Sources X-Ray Laser Research Ellipsometric Studies of Surfaces Medical Diagnosis by Nuclear Magnetism Energy Losses in Electron Microscopy The Impact of Integrated Electronics in Medicine Design Theory in Quadrupole Mass Spectrometry Ionic Photodetachment and Photodissociation Electron Interference Phenomena Electron Storage Rings Radiation Damage in Semiconductors Solid State Imaging Devices Particle Beam Fusion Resonant Multiphoton Processes Magnetic Reconnection Experiments Cyclotron Resonance Devices

S. A. White T. C. Marshall and S. P. Schlesinger P. Holloway F. N. Spiess R. S. Berry Charles Cason H. Scher and G. Pfister P. R. Thornton W. G. Magnuson and Robert J. Smith R. E. Rosensweig H. Kleinpoppen A. Gnadinger A. Jaumotte & Hirsch L. Ronchi E. F. Ritz, Jr. A. F. Brown J. Arsac T. A. Welton M. & G. Winnewisser H. Timan F. T. Chan, W. Williamson, G. Foster, aod M. Lieber M. Nisenoff W. W. Brodersen and R. M. White A. van der Ziel B. Jouffrey H. Melchior Ch. Cason and M. Scully A. V. Rzhanov G. J. Bene B. Jouffrey J. D. Meindl D. Dawson T. M. Miller M. C. Li D. Trines N. D. Wilsey E. H. Snow A. J. Toepfer P. P. Lambropoulos P. J. Baum R. S. Symons and H. R. Jorg

xi

FOREWORD The Biological Effects of Microwaves Advances in Infrared Light Sources Heavy Doping Effects in Silicon Spectroscopy of Electrons from High Energy Atomic Collisions Solid Surfaces Analysis Surface Analysis Using Charged Particle Beams Low Energy Atomic Beam Spectroscopy Sputtering Reliability Photovoltaic Effect Electron Irradiation Effect in MOS Systems Light Valve Technology High Power Lasers Impurities in Tokamaks Visualization of Single Heavy Atoms with the Electron Microscope Spin Polarized Low Energy Electron Scattering Defect Centers in 111-V Semiconductors Atomic Frequency Standards Fiber Optic Communications Electron Scattering and Nuclear Structure

H. Frohlich Ch. Timmermann R. Van Overstraeten D. Berenyi M. H. Higatsbergar F. P. Viehbock and F. Riidenauer E. M. Horl and E. Semerad G. H. Wehner H. Wilde R. H. Bube J. N. Churchill, F. E. Hofmstrom and T. W. Collins J. Grinberg V. N. Smiley K. Bol J. S. Wall D. T. Pierce and R. J. Celotta J. Schneider and V. Kaufmann C. Audoin G. Siege1 G. A. Peterson

Supplementary Volumes:

Image Transmission Systems High-Voltage and High-Power Applications of Thyristors Applied Corpuscular Opticw coustic Imaging with Electronic Circuits Microwave Field Effect Transistors

W. K. Pratt

G. Karady A. Septier H. F. Harmuth J. Frey

The advice and guidance of many friends and colleagues were again instrumental in putting together our present volume. Our thanks extend also to the devoted staff of Academic Press. By now they are in the front rank of the friends to whom we are indebted. L. MARTON C. MARTON

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ADVANCES IN ELECTRONICS A N D ELECTRON PHYSICS, VOL. 41

Ion Beam Technology Applied to Electron Microscopy J. FRANKS Ion Tech Ltd. Teddington, Middlesex, England

I. Introduction.. ..................... ............. 11. Production of Ion Beams ........ 111. The Sputtering Process.. .................................................................. 13 A. Sputtering Yield ................................. B. Surface Topography ............................. C. Ion Bombardment Induced Damage ................................................. 24 D. Some Ion Etching Rates and Sputtering Yield Data ................................ 26 IV. Ion Thinning for Transmission Electron Microscopy ................ 30 A. Ion Erosion Equipment Characteristics .......................................... B. The Evolution of Ion Thinning Equipment.. .................................... C. Ion Thinning Procedures and Results ................................................ 38 V. Ion Erosion for Scanning Electron Microscopy ............... A. Ion Erosion Equipment ..................................... B. Results.. ...................................................... VI. Conclusion ................................................................................. ' 47 References .................................................................................. 48

I. INTRODUCTION The high resolution attainable with transmission electron microscopy (TEM), which can provide direct magnification up to 500,000 times, makes this an outstanding technique for examining the microstructure of materials. The thickness of the specimens must be restricted to 100-200 nm, however, in order to avoid undue absorption of the incident electrons. It has therefore been necessary to develop methods for preparing thin specimens of materials that have widely varying mechanical and chemical properties. A detailed review of preparation techniques is given by Goodhew (1972). Soft materials, such as biological specimens, may be prepared by microtoming, although difficulty is sometimes encountered when hard particles are present. For some metals, semiconductors, and other inorganic materials, chemical etching and electrolytic techniques are suitable. In one widely used method, the material is placed in a jet etching tank and the etching process observed through a lens with a light source behind the specimen. When the 1 Copyright @ 1978 by Academic Press, Inc. All rights of reproduction in any form reserved. ISBN 0-12-014647-9

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J . FRANKS

specimen perforates, the etching process is immediately arrested by flushing the specimen with an inhibiting wash. The areas round the perforation are usually sufficiently thin to allow micrographs to be taken. The etch process generally takes 5-10 min. Difficulties arise when materials are not homogeneous; preferential etching may occur, second phases may be leached out, and in semiconductors p-type material may etch at a different rate from n-type material. Even when a material can be controllably etched, the etchant may form a contaminating layer on the surface. For materials for which suitable etchants do not exist, such as some glasses, ceramics, and geological specimens, various preparation techniques have been tried. The specimen may be crushed and fine slivers selected, or thin sections may be produced by very careful mechanical polishing (Barber, 1970). These operations require a considerable skill and can generally not be applied to brittle granular materials or materials with voids. Castaing and Laborie (1953) developed a new preparation technique to avoid the difficulties they encountered when attempting to thin aluminum alloys containing 4% copper by electrolytic polishing. With the electrolytic technique an oxide layer formed and some redeposition of copper occurred, A1,Cu precipitates etched slower than the matrix and gave rise to a relief structure, and as soon as a hole appeared, the edges dissolved rapidly leaving few thin areas. Instead of electrolytic polishing, they used a two-stage process involving mechanical polishing followed by etching of both faces of the specimen in succession with a parallel beam of 3000 eV ions. The resulting specimen was clear without any oxide film or deposits, the A1,Cu precipitates thinned evenly with the matrix, the edge of the hole was not attacked at an enhanced rate and the rate of erosion (about 0.05 pm/min) could be controlled. Later writers found that ion erosion was specially suited to “difficult ” materials such as ceramics, glasses, and geological specimens (Bach, 1970a; Barber, 1970). Ion thinning equipment is now widely used in association with the transmission electron microscope in the study of nonbiological materials. In scanning electron microscopy (SEM) surface features may be obscured as a result of mechanical treatment or chemical contamination. Recent work (Franks, 1977a,b) has shown that surface features can also be rendered clearly visible after ion treatment of the specimen. 11. PRODUCTION OF ION BEAMS A variety of mechanisms exist by which sufficient energy may be imparted to a gaseous atom or molecule to cause ionization. The gas may be ionized thermally, by a high voltage discharge, by a radio frequency field or

ION BEAM TECHNOLOGY A N D ELECTRON MICROSCOPY

3

by electron impact where electrons are derived from a heated filament, or by secondary emission from a cold cathode. These methods of producing ions have given rise to ion sources of various types (Carter and Colligon, 1968). The mechanism selected depends on the purpose for which the sources are to be used. At one end of the scale the requirement may be for beams of low intensity with small energy spreads and at the other end, for sources capable of producing very high intensity beams. For specimen preparation for electron microscopy, the ion source is used as a machining tool, energy spread considerations are of secondary importance. Cold cathode ion sources of various designs have been used since the work ofcastaing (1955a,b, 1956),Castaing and Laborie (1953), and Castaing and Lenoir (1954) in most specimen preparation equipments, because a useful output can be obtained from these sources that can be compact and, when well designed, need relatively little maintenance (there is no filament to bum out). Castaing’s source (1955a, 1956) could even be conveniently mounted inside an electron microscope to monitor the thinning process. D

FIG.1. Hollow anode ion source showing anode A, insulating tbbe B, cathode C, gas inlet D, and outer case for attachment to bombardment chamber (after Tighe and Hockey, 1969).

The sources favored by Castaing and many later authors (Paulus and Reverchon, 1964; Gentry, 1964; Abrahams et al., 1968; Barber, 1970; Holland et d , 1971; Heuer et d., 1971) were developments of a construction originated by Induni (1947), who used it as cold cathode electron source for an electron microscope. A construction of a positive ion source (Tighe and Hockey, 1969), is shown in Fig. 1. Gas flowed across the end of the insulating tube into the anodeecathode region. A simplified diagram of this hollow anode source is

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Anode

A

-

Insulator - Cathode C -

FIG.2. Schematic diagram of hollow anode ion source. Distance between anode and cathode d , diameter of each anode aperture d , , diameter of each cathode aperture d , , P , gas pressure in discharge region, P , gas pressure in ion collection region.

shown in Fig. 2. The distance between anode and cathode was about 1.5 mm. According to Paulus and Reverchon (1961) the volume AC bounded by the anode and cathode forms the accelerating region, the distance between anode and cathode being smaller than the mean free path of the ions, thus the ions are all accelerated by almost the same potential drop, and energy losses due to collisions are practically negligible. The anode was perforated in order to allow electrons from the cathode C to ionize the gas in the hollow anode region. The gas was introduced through a regulating valve to control the pressure within the ionizing chamber to the value required to maintain the intensity of the discharge, depending on the cathode aperture and pumping speed. For a pumping speed of 300 liter/sec, the total open area of cathode must not exceed 4 to 5 mm2 divided into 25 apertures. Each cathode aperture (diameter d,) was concentric with a larger anode aperture (diameter da). The efficiency of the source, defined by the ratio lu/lt, where I , is the ion current emitted by the source and I , is the total discharge current, was a maximum when d,/d, was about 4, independent of voltage and ion current or whether there were one or more sets of apertures. This construction with an anode to cathode aperture ratio of 4, has been

ION BEAM TECHNOLOGY A N D ELECTRON MICROSCOPY

5

found most efficient by authors subsequent to Paulus and Reverchon (Gentry, 1964; Abrahams et al., 1968; Barber, 1970; Holland et al., 1971; Heuer et al., 1971) and is also used in commercial equipment produced in France, the UK and the USA (details of manufacturers are given by Heuer et al., 1971). It is interesting to note, however, that Azam (1964) and later Ward (1971) dispensed with the anode perforations. Instead their anode consisted of an open-ended cylinder as shown in Fig. 3 inside a closely spaced cathode cylinder, the distance between the walls of the cylinder being such that at the operating pressure ( 1 O - I Torr) the discharge potential was on the left-hand branch of the Paschen curve, above the applied anode potential. The cathode end plate contained a grid that could be plane, concave (asshown in the diagram) for producing a focused beam, or convex for a diverging beam. The gas pressure was chosen such that the discharge area covered the area of the grid but no more.

r --

--

-Gas

Inlet

-High

Voltage

lnsula tor

Anode

C a t hode

\. ;.I C:j FIG.3. Hollow anode source configuration (after Ward, 1971).

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J. FRANKS

Holland et al. (1971) studied the operation of the Paulus and Reverchon source (1961) in some detail. Referring again to Fig. 2, the source was operated with an argon flow rate of 0.1 Torr liter sec- the pressure P , in the discharge region was about 0.4 Torr and the pressure P , in the collection region was about 0.2 mTorr. Figure 4 is a plot of the current flowing in the main discharge as a function of the voltage applied to the electrodes. The ion current at 6 kV, with the discharge current less than 1 mA was about 100 pA, giving an average current density of 300 pA cm-’. To find the effect of the volume enclosed by the anode cylinder on the ion source operation, a plug was inserted into the anode cylinder, the gas being introduced across the end of the insulators. The anode was therefore in effect solid with short blind holes in the end facing the cathode. The solid plug had no measurable effect on the performance of the source, as shown in Fig. 4. Also, the output currentdischarge current ratio remained the same over the pressure and voltage ranges tested.

’,

-

I

0 . 2 2 mtorr

0.7 -

Normal electrode arrangement

plug

0 With blanking

0.5 -

inside anode

U E

0.3 -

0.1 I I

I 2

4

6

8

kV

FIG.4. Current-voltage plots for glow discharge ion source (Holland et al., 1971)

Some measurements were made on the effect of varying the diameters of the anode and cathode apertures from the optimum ratio 4:l (anode:cathode) with the anode and cathode holes the same size (0.02 in. diameter). The ion output current was negligible, the working chamber pressure increased from 0.2 to 0.5 mTorr and slight increases in either voltage or pressure caused uncontrollable increases in discharge current. With both anode and cathode hole sizes increased to 0.04 in. diameter, ion output currents of

ION BEAM TECHNOLOGY A N D ELECTRON MICROSCOPY

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50 PA were obtained, but the working chamber pressure was increased by an order of magnitude (2 mTorr) and the discharge could only run stably for less than a minute. The instability was characterized by a rapid transient increase of discharge current and a cone-shaped discharge extending into the vacuum chamber from one of the cathode holes. These sources operated under the abnormal glow discharge conditions in which the cathode fall potential is current dependent. Thomson and Thomson (1933) obtained the following relationships for abnormal glow discharge conditions :

+ BP,j-'" v = Ff'ZP,' + E

P,d, = A

where V is the applied voltage, j the current density, d , the cathode dark space, and A , B, E , and F are constants. For a discharge to take place, d , < d , the separation of the electrodes. For simplicity, consider d , = d. For a uniform field between two parallel plates at a separation of d mm, Eqs. (1) and (2) give the corresponding conditions of pressure and density. For a dark space d , = d = 1.5 mm and I/ = 6 kV, then for argon gas and an aluminum cathode, Thomson and Thomson gave A = 5.4, B = 0.34, F = 2.940, and E = 240. The solution of Eqs. (1) and (2) gives P, = 0.37 Torr and j = 5.44 x lo2 mA cm-2. For a total discharge current of 1 mA, the corresponding active cathode area is therefore only 1.84 x cm2. Holland considered therefore that for this ion source of several square centimeters in area, the discharge must be localized to account for the relatively low total current measured. Localization must occur in the regions where the ion beam is extracted. The normal distance of 1.5 mm between the anode and cathode plates was taken, to estimate the discharge operating conditions. The discharge path is greatest in the region of the perforations and will be roughly equal to x as shown in Fig. 2. The discharge will be confined to areas where the mean free path is sufficient for it to be sustained, i.e., to the region of the perforations, and this is also a region of intense field concentration. The pressure of argon in the anode space was measured to be 0.42 Torr, and the mean free path for electron collision at this pressure at 20°C is 1.1 mm. Holland concluded that the volume contained in the cylinder is not necessary to sustain the discharge. The relative dimensions of the holes in the anode and cathode are important, however. As the cathode aperture becomes larger, and therefore x decreases, it becomes increasingly difficult for a discharge to be maintained. Following the work of Holland et al. (1971), a simplified source was

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J. FRANKS

constructed by Crockett (1973) with the same electrode configuration as the previous types but from which the hollow anode construction had been omitted (Fig. 5). The anode hole diameter was 4 mm, the cathode hole 1 mm, and the electrode spacing 1.4 mm. Ion currents of up to 0.7 mA for argon and 2 mA for hydrogen were obtained with an applied potential of 8 kV. An analysis of the energy distribution of the ions with a parallel plate

,

Insulating space

-

Pressure 10" torr I

i

Gas inlet pipe

Earthy Cathode

FIG. 5. Glow discharge ion source without hollow anode space (Crockett, 1973).

analyzer yielded two peaks (Fig. 6), the high energy peak occurring at the plasma potential V, close to the anode potential, and the second peak at about 1/3 of the energy. In Crockett's proposed mechanism, the electrons necessary to maintain the discharge are liberated from the cathode bombarded by ions and neutral atoms. Most of the electrons are released near the cathode hole through which many of the ions pass, because the ions are focused towards the cathode hole and collide with the sides of the hole at a glancing angle for which the secondary emission coefficient is high. The cathodic electrons accelerate along the field lines with a high probability of reaching the anode before suffering a gas collision. The mean free path of these electrons is estimated to exceed the gap separation of 1.4 mm from consideration of their energy and the interelectrode gas pressure. An anode hole significantly larger than the cathode allows the high energy cathodic ions to strike the bore of the anode hole so that secondaries are emitted into a very low field. These anodic secondary electrons may

ION BEAM TECHNOLOGY A N D ELECTRON MICROSCOPY

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Voltage V/Vc

FIG.6. Glow discharge source-ion energy distribution. V, is the plasma potential close to the anode potential (after Crockett, 1973).

suffer one or more ionizing collisions before returning to the anode. A smaller anode hole will restrict the number of fast electrons entering this low field region; electrons liberated from the front of the anode are unlikely to travel a significant distance due to the high electric field. This mechanism for the production of ions in a low field anode region resembles earlier considerations of processes in hollow anode sources, but it is now shown that the larger cavity does not contribute. The gas ions from the anode region will initially accelerate along the field lines toward the cathode. However, the collision cross section of ions in the gas is significantly greater than that of electrons. For Ar' in argon the collision cross section in the energy range 0-10 kV is of the order of cm2 and taking the mean pressure in the gap as 0.3 Torr, then the mean free path is about 0.2 mm. An ion is therefore likely to suffer a collision while traveling to the cathode. According to Davis and Vanderslice (1963) symmetrical charge exchange collisions are most probable in an abnormal glow discharge, a collision will therefore result in the formation of an energetic neutral and a slow-moving ion. The ion will accelerate and leave the source with an energy determined by the potential at its last point of collision. This accounts for the continuum of energies between the two peaks of Fig. 6. The high energy peak is due to ions that reach the anode without a collision, the low energy peak represents ions formed closer to the cathode hole. Near the cathode there is a rapid drop in gas pressure, ions are therefore less likely to suffer a collision in this region, hence very low energy ions are unlikely to be formed and there will be a preponderance of ions of intermediate energy.

10

J . FRANKS

Crockett accounted for the drop in output of the source during operation, as a result of the edge of the cathode sputtering away. Many of the ions (and neutrals) will then hit the surface more normally, resulting in decreased electron yield, while the enlarging hole also results in a lowering of the interelectrode gas pressure. The discharge current may be restored by increasing the gas pressure until the pumping system can no longer maintain the differential pressure between chamber and source. To operate an ion source near the chamber pressure of 10-4-10-3 Torr, in order to avoid differential pressure problems, electron paths must be lengthened to the extent that the same number of ionizing collisions occur for a given energizing voltage as at the higher pressure, which accords with Paschen's law (Thomson and Thomson, 1933). An ion-thinning equipment operating at Torr is described by Hietel and Meyerhoff (1961), in which a magnetic field is used to produce long electron paths. In their structure, the specimen formed part of the cathode. McIlraith (1966) showed that charged particles of one sign can be confined to a limited volume solely by means of an electrostatic field. In particular, electrons can be induced to describe long oscillatory paths without the aid of a magnet. The potential field must contain a single saddle point with three planes of symmetry and the lines of force of the corresponding force field must at a distance be asymptotic to lines passing through the saddle point. An example of a field meeting these requirements is shown in Fig. 7. The poles A and A' could be a pair of equally charged rods, a pair of equally charged spheres, or a charged ring. The field has a saddle point at 0. In the Y

I

D/

FIG.7. Force field resulting from a pair of equal poles A and A' (McIlraith, 1966).

ION BEAM TECHNOLOGY A N D ELECTRON MICROSCOPY

11

vicinity of the origin the lines of force are strongly curved; elsewhere they are essentially straight and radiate from 0. D is the locus of points for which the electric field component Ex is zero. Outside D, Ex is directed away from the Y axis, while inside D it is directed toward the Y axis. The shape of D depends on the geometry of the electrode system. D always passes through the poles, for a pair of parallel rods, D is a circle. If a negatively charged particle is released from rest at the point P, the particle initially follows a line of force but owing to its momentum, it fails to follow the sharp bend at A and so its trajectory crosses the X axis. Mcllraith showed that depending on the distance of P from 0, the particle may describe one of a family of stationary trajectories or follow trajectories that are stable but not stationary, i.e., each trajectory lies within a fixed envelope that does not contain the poles (Mcllraith, 1972). An ion source with an electrode configuration to produce a saddle-field point is described by Franks and Ghander (1974) for the case of a spherical cathode and an annular anode. A schematic diagram of the source and associated circuitry is shown in Fig. 8. The source contained a refractory metal anode and two hemispherical aluminum cathodes of radius 11 mm. The ion exit aperture in the cathode was 1.5 mm diameter. An approximation to an annular anode was achieved with a plate anode with a central aperture, shielded on either side by plates

Anode

1

I

'I'

Gar

FIG.8. Schematic diagram of spherical saddle-field ion source and associated circuitry (Franks and Ghander, 1974).

J. FRANKS

12

at cathode potential, the anode protruding beyond the shields into the central region. Because of the symmetry of the source, two ion beams emerged in diametrically opposite directions. One of the beams could be used as monitor, this beam was collected in a cup mounted on the source and the current ( I s z ) measured. With argon, an ion current of about 100 pA was obtained at 6 kV at a chamber pressure of 2 x lop4 Torr. The energy profile is shown in Fig. 9. As the pressure in the source is low, the mean free path of the ions will be greater than the dimensions of the source and therefore the probability of creating slow ions by the charge exchange mechanism previously discussed will be small. When the cathode aperture was increased to 6 mm, the central intense beam remained confined to its original diameter at the cathode; the angle of divergence was about 4.5", obtained from etch patterns. Further low energy peaks also appeared that were dependent on orientation. For sputtering purposes the characteristics of the source were maintained when the cathode aperture was enlarged. 4.0

3.5

3.0 6

-: a

-4

P = 2 x 10 Torr VT= 6 kV IT=4 mA

2.5

C

2.0

a

U

gc

1.5

1.0 L

0 5

0

u 2 3 4 E n e r g y keV

FIG.9. Argon ion energy distribution in beam from 1.5 mm cathode aperture in spherical saddle-field source (Franks and Ghander, 1974).

ION BEAM TECHNOLOGY A N D ELECTRON MICROSCOPY

13

111. THESPUTTERING PROCESS A . Sputtering Yield

Sputtering is the removal of material from a target as a result of the interaction of incident ions or neutrals of sufficient energy with the target. Depending on energy, other effects may occur during sputtering, such as structural damage to the target, ion implantation, backscattering of ions and neutral atoms, and emission of charged particles and electromagnetic radiation (Holland, 1972). The sputtering process occurs through the transfer of momentum from incident ions to atoms at the surface of the target. At low energies, collisions between ions and target atoms can be treated as elastic collisions between rigid spheres. From the conservation of energy and momentum, the amount of energy transferred from an ion of mass M , and energy E to an atom of mass M , in a head-on collision is given by T

= 4M, M,/(M:

+ M;)E

S

= O M ,M , / ( M :

+ M$)E

(3) Maximum energy transfer occurs when M , = M 2 . Removal of atoms will occur when the energy transferred exceeds the usual matrix binding energy of 5-10 eV. The hard sphere model applies for energies up to about 1 keV, at higher energies an increasing fraction of the incident energy is transferred to atoms in layers remote from the surface and is not reflected back to the surface to excite surface atoms and break surface bonds. The surface layer within which collisions can result in sputtering is usually about 10 nm thick. The number of such collisions, which an ion can make, i.e., the sputtering yield S will depend on its collision cross section 0 so that (4) Spencer and Schmidt (1971) quote the following expression for yield originally derived by Almen and Bruce (1961):

where no is the number of atoms per unit volume of the target material and EB is the heat of sublimation of the material expressed in electron volts per atom. G is a function of the mass numbers M , and M , and atomic numbers Z , and Z , of the impinging ion and target atoms. For higher energies a random cascade theory developed by Sigmund (1969) has proved to be the most promising concept for the theoretical description of the sputtering process. For an angle of incidence 8 from normal and an incident ion energy E , Sigmund obtained the yield

s(e,E ) = + ~ c - ~ ~ s , ( E ) c ; ~ u ; ~

(6)

14

J. FRANKS

where CL is a function of the mass ratio M , JM, , S , ( E ) is the stopping cross section. U o is the surface binding energy for the target material and Co is a constant. Because of the complexity of the sputtering process, these expressions can only provide a guide to the variation of yield to be expected with such parameters as the mass and energy of the incident ion and nature of the target. The effect of increasing energy of argon and krypton ions on the yield from a polycrystalline copper target is shown in Fig. 10.

Ion energy (eV)

FIG. 10. Yield in atoms removed per incident A r t and Kr' ion on polycrystalline copper as a function of incident ion energy (after Melliar-Smith, 1976).

Deviation from a linear law occurs at low voltage and a decreasing fraction of the momentum is transferred to surface atoms as the more energetic ions increasingly penetrate further into the matrix. Figure 10 indicates that the penetration at any voltage is less for the heavier ion. According to Trillat (1964) for energies below 5 keV or for a depth of penetration less than 1 to 2 nm, the impact of ions produces a simple surface effect due to the transmission of momentum from an incident ion to a surface atom without perturbation of the neighboring atoms. Above 5 keV deeper layers are affected and secondary collisions can occur. However, Laegreid and Wehner (1961) found that even at low energy, the yield increases more slowly than linearly with voltage. These authors measured the yield for 28 elements under neon and argon bombardment. A representative family of curves is shown in Fig. 11.

ION BEAM TECHNOLOGY AND ELECTRON MICROSCOPY

15

1.6

0

100

200

300

400

500

600

I o n energy (eV)

FIG. 11. Yield as a function of incident energy of argon ions, indicating deviation from proportionality even at low energy (after Spencer and Schmidt, 1971).

Tsong and Barber (1973) compared yield theories of Thompson (1968), Sigmund (1969), and Brandt and Laubert (1967) with some experimental results. For a variety of materials including polycrystalline copper, fused silica and germanium and silicon at room temperature under argon ion bombardment, the sputtering yield increases with ion energy above a threshold, between 1 and 10 keV the increase is slower and finally a maximum is reached. The yield stays approximately constant between 10 and 100 keV. All three theories predict the virtual independence of yield from ion energy in this range. At still higher energies the yield decreases, as previously discussed. In the range 3-12 keV, Paulus and Rever hon (1964) obtained a dependence of yield as the logarithm of the inciden!t ion energy for a ferrite. This is the energy range of particular interest for ion-thinning processes. Figure 10 shows the yield for polycrystallic copper; for single crystals the yield may depend on crystallographic orientation. In the (1 11) direction, a higher yield is obtained than for the polycrystalline (average) case, while in the (110) direction the yield is lower (Wehner and Anderson, 1970). When the ion beam direction coincides with a low density of projected lattice points, the ions penetrate more deeply and the sputtering yield decreases. According to Eq. ( 5 ) the sputtering yield is a function of the heat of sublimation EB. Figure 12 shows the sputtering yield with argon ions of 400 eV as a function of target atomic number for a range of elements (Laegreid and Wehner, 1961). The variation with atomic number of the maximum yield obtainable (i.e., at a voltage corresponding to the peak in a yield curve

16

J. FRANKS

2-6 2.4 2.2 2.0

2

1.8

0 1.6

0,

1.4

;;

1.2

-Y TI

Cr

1.0

.- 0 8 > 0.6

Re

Zr

04

Th

Ti

02

.C

0

1

I

I

I

I

1 0

20

30

40

50

Atomic

number

I

I

I

I

60

70

80

90

-

FIG. 12. Sputtering yields with argon ions of 400 eV as a function of target atomic number for a range of elements (Laegreid and Wehner, 1961).

50 30

rt

Zn

Cd

10

8

6

Re

Th

4 2

0

0

1 0

20

30

40 Atomic

50 number

60

I 70

80

90

FIG. 13. Maximum sputtering yield S,,, for bombardment with argon ions plotted as a function of atomic number showing a periodicity related to the filling of the d electron shells (Kanaya et al., 1974).

ION BEAM TECHNOLOGY A N D ELECTRON MICROSCOPY

17

similar to Fig. 10) is shown in Fig. 13 (Kanaya et al., 1974).The variation of sputtering yield with element may be compared with the corresponding variation of inverse heat of sublimation. shown in Fig. 14 (Spencer and Schmidt, 1971). H

1.5

n E

-2;

v

c 0

E

CS I0

09 08

Na

0.7 0.6

0.5

Ba

n a a 0.4 c 0

0.3 0 V

Si

c

b La

Ta

;0.2 = lc 0) >

015

0.1

I

I

10

X)

I

I

I

I

IJW, I t 80 90 100

3 0 4 0 5 0 6 0 70 A t o m i c number

FIG. 14. Inverse of the heat of sublimation of elements as a function of atomic number (Spencer and Schmidt, 1971).

Published data on the heat of sublimation of elements can therefore act as a guide to sputtering yields. The important effect of lattice environment on sputter rate may be illustrated by the observations that the yield of copper from the alloy Cu,Au is larger than the yield for pure copper and that the total sputtering yield of Cu,Au is larger than either elemental yield (Coburn, 1976). The variation of yield from silver, copper, and tantalum as a function of the atomic number of the incident ions at 45 keV also exhibits marked periodicity according to Almen and Bruce (1961) as shown in Fig. 15. The maximum sputtering rate is reached for each row in the Periodic Table as the electron shells are filled. N o such periodicity however, is displayed by any of the yield determining quantities in present theories. More recent results of Andersen and Bay (1972, 1973) quoted by Oechsner (1975) on the sputtering of silicon, silver, and copper substrates, again with a variety of bombarding ions at 45 keV, d o not exhibit these fluctuations.

18

J. FRANKS

B e C ONeMgSi S A C a T l C r F e N i Z n C a S e K r S r Z r M o Li B N N a A L P C l K ScVMnCoCuGaAsBrRbY Nb 0

1 0

20

30 Ion

PdCdSnTeXeBaCeNdSmGdDy A g h Sb I C s L a P r Eu

40

atomic

50

60

YbHf W Ta

70

PtHgPb Au TL Bi

80

number

FIG. 15. Sputtering yield of silver, copper, and tantalum as a function of bombarding ion atomic number (Spencer and Schmidt, 1971).

Experimental results for the light element Si accord well with Sigmund’s theory (1969) as shown in Fig. 16, but there is an increasing deviation with the increasing mass M 2 from copper to silver. Anderson and Bay bombarded the targets with small doses of ions. Oechsner attributed the discrepancies between their results and those of Almen and Bruce to implantation of bombarding ions, causing a reduction in yield. Such effects have been demonstrated, e.g., for the sputtering of copper with 45 keV V ions, where a continuous reduction of yield with increasing bombarding dose has been observed by Andersen and Bay (1972) and at doses above l O I 7 ions/cm2 by Almen and Bruce. From a practical point of view, the results of Almen and Bruce in Fig. 15 are useful for selecting ions that allow high yields to be maintained. The advantages of using inert gas ions are clear. In the presence of an active gas such as oxygen, however, the yield does not depend only on a physical process such as momentum transfer but also on chemical processes. The addition of oxygen may reduce the sputtering yield of metals such as titanium, and aluminum, which readily oxidize but enhance the yield from organic materials such as photoresists (Melliar-Smith, 1976). +

ION BEAM TECHNOLOGY A N D ELECTRON MICROSCOPY

19

30

2

2.0

;.

0.7

w .z

1.0

s 0

m

03

V

02

w

0

E,

-

Theory,Sigmund, 1969 Anderson and Bay, 1973 4 5 keV Ions

05

o Si-normalizad to SAr-5, 0 Cunormalized to S

0.1

+

2 0.07

Ag-normalized to 5

0.05 1 0

20

30 4 0 5 0 6 0 70 Ion atomic number

80

90

FIG. 16. Normalized sputtering yield of silicon, copper, and silver from low dose measurements with normally incident 45 keV argon ions compared with theoretical results (Oechsner, 1975).

So far, the yields have been considered from ion beams incident normally on a substrate. Release of target material will be enhanced if the ion incidence angle is raised, because more energy will be transferred to the surface layer within which cascade collisions can result in sputtering. The depth ( d ) of this layer is usually about 10 nm and according to Holland (1972) the yield S will tend to be proportional to d/cos 8, where 8 is the ion incidence angle. However, as ions are reflected at high incidence by surface electric fields, S reaches a maximum before 8 = 90"at glancing incidence. Spencer and Schmidt (1971) consider that as the angle of incidence is increased, the transfer of momentum in a direction to remove an atom from the surface becomes more favorable. They quote the theoretical work of Macdonald (1970) who obtained a (cos O)-'.' dependence of yield on angle. Sputtering yield varies with angle of ion incidence typically as shown in Fig. 17. The yield increases slowly near normal incidence, then increases rapidly beyond about 30" to reach a maximum dependent on the incident ion, its energy, and on the matrix atoms. Thompson (1968) and Brandt and Laubert (1967) obtained a sec 8 dependence but Tsong and Barber (1973) commented that this function does not fit experimental values well except when M , 4 M , . Sigmund (1969) obtained a (cos 6)variation that generally accords more closely with experimental results. For practical purposes the etch rate rather than the sputtering yield is often of importance. The difference in angular dependence is illustrated by Figs. 18a, b (Melliar-Smith, 1976).This difference is due to the cosine dependence of the ion flux. The etch rate for a beam at an incident angle 0 is related to the yield S(O) at that angle by the expression R = (n/no)s(e)cos o

(7)

20

J. FRANKS

0

1 0 20 3 0 4 0 5 0

6 0 70 8 0

A n g l o of incidence

0

(8)

FIG.17. Variation of sputtering yield S with incident angle of A r + ions at 5.6 keV on Schott lead glass SF59 and silica glass (Tsong and Barber, 1973).

where n is the number of ions per second per unit area normal to the direction of the beam and no is the number of atoms per unit volume of the target material. Evidently the yield for gold (for which MI -4 M , ) varies as sec 8 up to the maximum, while for the lighter materials the yield varies more rapidly with angle.

I

I

I

I

.

I

I

I

/

. l

c

0

I

I20

-

too

-

20

-

I

I

I

I

L

2.0

P .=GI c

-

: 1.0

"

a a In

15

1

I

I

I

1

I

I

30

45

60

75

I5

30

45

Angle of incidence

(e",

(b) I

60

Angle of incidence

75

(e",

FIG. 18. Effect of angle of incidence on (a) sputtering yield, and (b) ion etching rate for gold, aluminum, and photoresist (Melliar-Smith, 1976).

ION BEAM TECHNOLOGY A N D ELECTRON MICROSCOPY

21

B. Surface Topography

The variation of etching rate with angle has important consequences as regard the surface topography resulting after ion erosion. Any deviations from flatness in the initial surface will result in corresponding variations in the angle of incidence of the ion beam over rhe surface and hence in variations in erosion rate. Barber et al. (1973) have applied Frank’s kinematic theory of orientation-dependent dissolution of crystals, on the consideration that both the rate for sputtering and for chemical etching of a surface element depend on the orientation of that element. From a knowledge of the etch rate dependence on angle for a material [proportional to S(0) cos 61, the theory provides a method of constructing equi-erosion ” profiles for any initial surface shape. The construction involves the use of a polar diagram of “erosion slowness,” where the erosion slowness at an angle 6 is defined as the reciprocal of the etch rate at 6 compared with the etch rate at normal incidence, i.e., S ( 6 ) cos 6/S(O). An example of a slowness erosion curve for silica is shown in Fig. 19 together with three profiles representing stages in the transformation from a sphere after three periods of sputtering. “

30

20 \

‘7 ? ‘p ?O 3 0

Erosion slowness curve I o n beam

FIG. 19. Erosion slowness curve for silica and derived profiles at three intervals during the sputtering of a silica sphere (after Barber et a / . , 1973).

22

J. FRANKS

In a review of theories of sputter-induced surface morphology, Carter et al. (1977) discussed a kinematic wave equation for amorphous solids, which describes how a point of given orientation on a surface moves in space and time as the surface is sputtered. The generalized approach is compatible with the slowness erosion theory of Barber et al. Carter et al. also discussed perturbation effects due to variations in the particular flux and local yield variations. Sigmund (1973) showed that under oblique incidence the most pronounced sputtering effect may not coincide with the point of impact. As a consequence surface irregularities on a microscopic scale may give rise to local yield variations, which can cause the formation of nuclei of macroscopic irregularities. To account for the sputtering features on crystalline surfaces, Carter et al. consider that the same type of S - 8 variation relevant to amorphous solids can be applied, but with local perturbations due to channeling effects and imperfections such as precipitates, dislocations, and grain boundaries. In preparing specimens for electron microscopy, especially for transmission, it is generally desirable to produce samples that are as smooth and flat and parallel as possible. If a specimen contains phases that sputter at widely different rates, it is difficult to approach this ideal. But from the foregoing considerations of the effect of ion angle of incidence on etch rate, it follows that unwanted surface irregularities may appear even on homogeneous materials without surface impurities. Barber et al. (1973) have constructed profiles showing the development of a convex surface irregularity into an extending " hummock " for the case of a rotating silica glass surface undergoing bombardment at 60" to the surface normal. This construction accords with Tsong and Barber's (1972) earlier observations that hummocks grow on a rotating fused silica surface under ion bombardment. The greatest number of hummocks occur at angles of ion incidence corresponding to maximum sputtering yield (75" for fused silica under Ar+ bombardment), at angles near normal incidence there are virtually none. Also, if the specimen is stationary, no hummocks occur, whatever the angle of incidence, but near 75" the surface has a " sandblasted " appearance. Tighe and Hockey (1969) observed pits and sometimes hillocks on ionthinned single crystal specimens of alumina which could not be associated uniquely with dislocations or impurity precipitates. These features were similar to the randomly occurring irregularities that form on surfaces during thermal etching rather than to dislocation etch pits resulting from chemical etching. Other authors, however, generally relate sputtering features to defects or impurities. Bach (1970a) found that contaminants on the surface o r inhomogeneities in the surface of glass and ceramics caused the formation of pyramids and other structures. Also, if the ion density was low (1 pA/cm2), charging effects

ION BEAM TECHNOLOGY AND ELECTRON MICROSCOPY

23

could cause dunelike formations. Navez et al. (1964), in a study of glass surfaces, observed striations parallel to the beam for grazing angles above 75", parallel ridges perpendicular to the beam for angles between 60" and 20", and globular structures near normal incidence. The occurrence of surface features parallel to the ion beam near grazing incidence, perpendicular to the beam at higher angles and the formation of disordered structures, cones and pyramids near normal incidence, appears to be common for a wide variety of metals and insulators, e.g., Magnuson et al. (1961), Wegmann (1964), Hauffe (1971), Wilson and Kidd (1971), Teodorescu and Vasiliu (1972), and Witcomb (1974). Witcomb demonstrated the association of a slow sputtering precipitate with formation of cones in stainless steel. Berg and Kominiak (1976) induced cone arrays on copper by coating the surface with a layer of carbon or oxide both of which sputter more slowly than copper. The low yield species tends to protect the underlying bulk material. The effective sputter yield of small amounts of impurity on a matrix material in some cases may be lower than the bulk sputtering rate of that impurity (Coburn, 1976). Witcomb (1975) applied Frank's kinematic theory of crystal dissolution (Barber et al., 1973), to the conical ion bombardment structures and found good agreement between theory and experiment. It is evident that the dependence of sputtering yield on angle plays an important part in determining surface structure. Other processes, which occur during sputtering and which may contribute to observed effects, include redeposition of sputtered materials on to closely adjacent planes, ion reflection at grazing incidence, dechanneling at dislocation lines, surface binding energy modifications arising from variations in crystallographic orientation or elastic stress, and diffusion processes (Vasiliu et al., 1975). Hauffe (1971) found that uniformity of sputtering over a surface can be achieved by rotating the specimen, oscillating the ion beam direction or by simultaneous bombardment from many different directions. Barber et al. (1973) show a set of photographs of special interest to our main theme as these illustrate surface structures on indium phosphide after ion bombardment under typical ion-thinning conditions. The experimental arrangement is shown in Fig. 20. The specimen was bombarded with Ar' ions in the energy range 4-10 keV, the angle of incidence was 60".The masking effect of the specimen holder caused the specimen to become dished at the center, where it was exposed to ions from all azimuthal direction, while the extreme periphery of the dish was only subject to unidirectional attack. The observed structures were explained by dividing the dished specimen into three areas centered on the axis of rotation; for the central regions the formation of hummocks would be expected according to Frank's kinematic theory and these are shown in Fig. 21a. At the other extreme in region 1, sharply peaked

24

J. FRANKS

Masks

Specimen

I U A x i s ot rota tion

FIG.20. Experimental arrangement for ion bombardment of a flat specimen. The broken lines indicate a section through the specimen at the onset of erosion, while the solid lines represent a section through the specimen after an extended period of bombardment. Undercutting of the mask has been deliberately exaggerated (Barber et al., 1973).

cones were found (Fig. 21b). As discussed previously, these were caused almost certainly by surface impurities. Once the eroded area was subject to the variation in azimuthal angle, the impurities were undercut and the cones disappeared. In region 2, on account of the slope, rotational symmetry was lost and ion trajectories between I and I' in Fig. 20 made the main contribution to erosion. A typical slope in region 2 was about 10" to the mean surface. With this angle and assuming a sinusoidal starting surface, a slowness surface construction resulted in a stepped topography (Fig. 2 lc). C. lon Bombardment Induced Damage

Castaing and Jouffrey (1964) observed defects introduced in single crystal gold layers by ion bombardment. The process of formation of defects was followed by mounting an ion source in an electron microscope and observing a specimen subjected to successive bombardments of brief duration, each bombardment corresponding to a charge of 0.1 ions per surface atom. The ion source was operated at 4 kV with air as the ionized gas. Stacking faults suddenly appeared presumably when the density of point defects reached a certain limit. Drum (1965) attributed specks appearing in sapphire after ion bombardment to the clustering of point defects at room temperature, he gave the range of 2 keV argon ions in sapphire as about 5 nm. According to Trillat (1964) the range of argon ions in aluminium is 1.1 nm for an energy of 2 keV and 2.0 nm for 5 keV. At higher energies, deeper layers of the matrix are affected and secondary collisions occur that

ION BEAM TECHNOLOGY A N D ELECTRON MICROSCOPY

25

FIG.21. (a) Flat-top hummocks formed at the center of a dish in I n P by ion bombardment. (b) Cones produced by unidirectional ion attack near the periphery of the dished region. (c) Hummocks giving way to ridges or steps as the distance away from the axis of rotation increases (Barber et a/., 1973).

can perturb the lattice and introduce faults and cause oriented recrystallization. Heuer et al. (1971) in a study of ceramic materials observed that although ion thinning introduced point defects in specimens, this had not proved to be a major limitation of the process, as few foils exhibited visible radiation damage, although a mottled background was occasionally seen. The authors attributed the absence of appreciable visible damage after ion thinning to the low energy of the ions and their oblique angle of incidence (up to 30" from glancing incidence). For 10 keV argon ions at normal incidence, penetration is less than 10 nm in most ceramic materials; for

26

I. FRANKS

grazing incidence, penetration is 1/4 to 1/3 of this distance so that many of the defects formed can be eliminated by migration to the surface. Barber (1972a) also observed a decrease in depth of damage from maximum at normal incidence (0")to about 1/3 to 1/4 of maximum at 70". Ion channeling will occur at certain angles but this is less important when samples are being rotated continuously. Small defect clusters caused by ion damage can coalesce to form dislocation networks if there is sufficient defect mobility. The degree of damage has been found to depend on target temperature, hence the ion current should be limited. In some materials (semiconductors and minerals) ion bombardment can cause loss of crystallinity. The extent of phase change is minimized by the use of low energy ions (below 5 keV) and bombardment at glancing incidence. Ions of sufficient energy may also become implanted (Barber, 1972c)that may lead to the nucleation and appearance of gas bubbles under the action of an electron beam. Again this effect can be largely avoided by using argon ions below 5 keV or heavier ions (Melliar-Smith, 1976). In general, damage caused by ion sputtering manifests itself as defect clusters and dislocation loops in metals and as an amorphous layer in other materials. In a study of the effect of sputtering on carbonate single crystals (mainly calcite), Adetunji and Barber (1978) measured the sputtering yield and depth of the amorphous layer as a function of angle of incidence of the beam and crystallographic direction. They found an inverse relationship between yield and the disturbed layer, and also an effect of temperature on these quantities. This latter effect was attributed to the chemical nature of the material that can readily decompose with loss of carbon dioxide.

D . Some Ion Etching Rates and Sputtering Yield Data

Ion etching rates and sputtering yields have been measured for a variety of materials. Ion etching rates are given in Table I for argon ions at normal incidence, with the current density normalized to 1 mA/cmZ. In Tables I1 and 111 some sputtering yields are listed again for argon ions normal to the surface of the specimen. The sputtering yield Y is derived from the measured etch rate using the relation (Bach, 1970b) Y = VDLe/AtM

(8)

where V is the sputtered volume in cm3, D is the density of the material in gm ~ m - L~ is, Loschmidt's number, M is the molecular weight in gm, A is the ion current in amperes, t is the duration of bombardment in second, and e is the charge of an electron ( e = 1.602 x A sec).

ION BEAM TECHNOLOGY AND ELECTRON MICROSCOPY

27

TABLE I INCIDENCE, ION CLRRENT DENSITY NORION ETCH RATESFOR ARGON IONSAT NORMAL MALIZED TO 1 mA/cmZ Etch rate (nm/min) at Material

0.5kV

1 kV

5 kV

8.3

Alumina (1702)

16 Aluminum

30 41 68

90 51

195

45

Copper (bulk) Chromium Gd-Ga garnet Gallium arsenide

20-40

(100)

28 102 65 295

Gold

105 155

Iron Lithium niobate (Y cut) Molybdenum (bulk)

38 23

Resist materials: COP electron resist KPR KTFR

44 33 86 120 39 45 84 98

Polymethyl methacrylate Riston 14 Shipley A 2 1350

130

40 27 30 35

Manganese Niobium Permalloy

215 235 32 35 62

25 20 40 60 70.5

Silicon (100) (100)

21.5 45 40

60 40 70

130 128

Reference" Gloersen (1975) Spencer and Schmidt (1971) Gloersen (1975) Somekh (1976) Garvin (1973) Spencer and Schmidt (1971) Gloersen (1975) Melliar-Smith (1976) Gloersen (1975) Somekh (1976) Gloersen (1975) Spencer and Schmidt (1971) Somekh (1976) Garvin (1973) Spencer and Schmidt (1971) Gloersen (1975) Spencer and Schmidt (1971) Garvin (1973) Gloersen (1975) Melliar-Smith (1976) Melliar-Smith (1976) Melliar-Smith (1976) Spencer and Schmidt (1971) Somekh (1976) Gloersen (1975) Somekh (1976) Garvin (1973) Melliar-Smith (1976) Spencer and Schmidt (1971) Melliar-Smith (1976) Spencer and Schmidt (1971) Gloersen (1975) Gloersen (1975) Somekh (1976) Melliar-Smith (1976) Spencer and Schmidt (1971) Gloersen (1975) Garvin (1973) Spencer and Schmidt (1971) Garvin (1973) (continued)

28

J. FRANKS

TABLE I (continued) Etch rate (nm/min) at ~

Material

0.5 kV

Silica (evaporated film) (quartz 001) (quartz Y cut)

28 33 30

65 47 200 350

Silver Soda lime glass Stainless steel (304) Tantalum

5 kV

1 kV

130

20 25 15 33 20 18

Titanium Tungsten Vanadium Zirconium

22 32

Reference Gloersen (1975) Gloersen (1975) Garvin (1973) Spencer and Schmidt (1971) Melliar-Smith (1976) Spencer and Schmidt (1971) Gloersen (1975) Gloersen (1975) Gloersen (1975) Somekh (1976) Somekh (1976) Gloersen (1975) Melliar-Smith (1976) Melliar-Smith (1976)

TABLE I1 SPUTTERING YIELDSFOR 5 keV ARGON IONS AT NORMAL INCIDENCE' Material z-AIZO, CaCO, CaF, Ge LiF MgO NaCl PbS SiO, TiO, ZnS

(001) (1011) (111) (111) (100) polycrystalline (100)

(100) (100) (1011) (001) (110)

Bach (1970b).

Sputtering yield

0.90 1.15 0.8 1 2.47 1.72 2.76 0.82 2.40 2.58 1.05 0.90 2.60

ION BEAM TECHNOLOGY AND ELECTRON MICROSCOPY

TABLE 111 SPUTTERING YIELDSFOR ARGONIONS

AT

NORMAL

INCIDENCE

600 eV" Be A1 Si Ti V Cr Fe

co Ni cu Ge Zr Nb Mo Ru Rh Pd Ag Cd Sn Hf Ta W Re 0s

Ir Pt Au Pb Th U

0.80 1.24 0.53 0.58 0.70 1.30 1.26 1.36 1.52 2.30 1.22 0.75 0.65 0.93 1.30 1.46 2.39 3.40

1 keVb

45 keV'

1.1 1.94 1.F 1.13 1.o 1.34

2.3

1.86-2.16 2.90-3.64 1.55 1.06 0.98 1.14-1.24

3.5 6.8

3.06 3.84.7 11.2

1.5

5.3 10.8 4.3

0.83 0.62 0.62 0.91

0.91 1.10

1.6 2.3

0.95 1.17 1.56 2.43 (500)

2.0 3.08-4.02 4.2

0.66 0.97

Laegreid and Wehner (1961) Oechsner (1975). ' Tsong and Barber (1973).

5.3 10.2 10.5

29

30

J. FRANKS

IV. IONTHINNING FOR TRANSMISSION ELECTRON MICROSCOPY A . Ion Erosion Equipment Characteristics

Spencer and Schmidt (1971) specified the following desirable characteristics for ion erosion equipment: Singly ionized ions must enter the specimen chamber at low pressure as a well-collimated beam; the ionized gases can be inert or reactive; the kinetic energy of the ions can be varied; the ion flux can be varied independently; the angle of incidence of the ion beam with respect to the sample surface can be varied; the sample is not in a plasma environment (this extends the range of applicability to low melting point materials and to organics). Ideally one ion at any instant would remove one atom from the surface without disturbing the neighboring atoms. For a beam composed entirely of singly ionized argon ions uniformly spaced in time, a current of 100 pA would represent one ion approximately every sec. Since the interaction time for elastic collisions is of the order of 10-14-10-15sec, each ion interaction with the surface may be considered independently. With larger currents many ions could impinge on the sample within the interaction time but still be so widely spaced that the concept of each single unit acting independently is still appropriate. They concluded that at low ion energies when the sputtering yield is about one atom per ion, the possibility for damage-free surface preparation is high compared with other techniques. Efforts over the past quarter of a century have been directed towards realizing these ideal conditions.

B. The Evolution of Ion Thinning Equipment The technique of preparing specimens for transmission electron microscopy by ion thinning was introduced by Castaing and Laborie in 1953. They used an Induni-type ion source for thinning specimens of an aluminum copper (4 %) alloy that had been difficult to polish electrolytically. The specimen was first thinned by mechanical polishing and then each face was exposed alternately to the ion beam. In contrast to the results obtained with chemical etching, the specimen remained clean without an oxide layer, the etch rates of precipitates and matrix were similar and fairly large thin areas were obtained. This method of thinning from bulk material also presented a truer picture of the bulk structure than that obtained with evaporated thin films of the same alloy. In particular many more precipitates were observed in material thinned after heat treatment because the probability of precipitate nucleation in the evaporated film is small (Castaing, 1955a, b, 1956; Castaing and Laborie, 1954). However, on ion bombarding either side of the specimen alternately, a light contamination could become visible on the side

ION BEAM TECHNOLOGY A N D ELECTRON MICROSCOPY

31

that was last turned away from the beam. Castaing (1955b) introduced a system in which both sides of the specimen were ion eroded simultaneously (Fig. 22). The ion sources were disposed coaxially on either side of the specimen and normal to it and produced seven ion beams to provide extensive thinned areas. The specimen could be illuminated from one side and viewed through a microscope from the other to monitor the thinning process. Gentry (1964) used a similar equipment to thin cobalt and aluminum-zinc (40 %) alloy. Compared with electrolytic etching he found the ion-thinned cobalt samples marginally inferior, but found that for the alloy, the precipitates were etched away with the electrolytic technique but were preserved in the ion-thinned specimens.

FIG.22. Schematic diagram of equipment for simultaneous erosion of specimen from both sides (Castaing, 1955b).

Instead of thinning the specimen in a field-free environment, Hietel and Meyerhoff (1961) made the specimen part of the common (stationary) cathode of a double ion source (Fig. 23). To reduce the chamber pressure sufficiently and avoid undue scatter of the beam, the sources were operated in the Penning mode with the aid of an electromagnet (argon pressure Torr, accelerating voltage 1.5 kV). The quality of silicon single crystals, thinned in this equipment, was very dependent on previous mechanical preparation. Uniform removal was achieved when the silicon surface was previously polished until no structure was visible under microscopic examination. Otherwise the surface became covered with hemispherical hillocks. A number of authors have described ion-thinning configurations based on single ion sources. Drum (1965) thinned sapphire and silicon carbide

32

J. FRANKS

&a-

d

FIG. 23. Schematic diagram of thinning system with Penning ion sources. K central cathode with specimen, A anodes, H auxiliary cathodes, E electromagnet, F telescope, and L lamp (Hietel and Meyerhoff, 1961).

crystals placed below a cathode aperture of a discharge tube and resting on a magnet. The specimens were normal to the beam. With an applied voltage of 2 kV at a pressure of 0.03 Torr of argon the current density was 1 mA/cm2. The thinning process required two to three days to produce holes surrounded by adequately thin regions in crystals originally about 125 pm thick. Halfway through the process, the ion beam was applied to the reverse side of the disk, so that all grinding damage was removed. Point defects (due to the beam), stacking faults, and dislocation networks were observed. Hirthe et al. (1967) thinned rutile by placing the specimens on a cathode within a discharge tube. With 3 kV at a pressure of 0.05 Torr and a discharge current of 1 mA, the etch rate was about 15 pm/hr. Transparent areas were about 20 pm x 1 mm. Networks of dislocation were observed, but there appeared no evidence of ion damage. Bach (1970a) used a Penning source in a more sophisticated system, in which the specimen holder could be rotated with a motor drive about an axis normal to the plane of the holder and the angle of incidence of the ion beam on the specimen could be varied. The specimens could also be ion eroded on the reverse side through an aperture in the holder. Glass and glass-ceramic specimens were thinned with a 5.6-kV argon beam with a current density of 100 pA/mm2 at incidence angles between 85 and 88". Operation close to grazing incidence ensured that the transmissive areas were as large as possible, even when the specimens were inhomogeneous. Grooves formed on specimens thinned in a stationary holder but were eliminated when the holder was rotated.

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However, most of the later thinning systems have evolved from Castaing's (1955b) two-source system, because simultaneous erosion from both sides avoids redeposition of sputtered material, removes damaged layers caused by previous mechanical treatment and, of course, doubles the thinning rate. From a study of porous ferrites, Paulus and Reverchon (1964) concluded that thinning at 75" would minimize pitting of the surface and increase the sputtering yield. Accordingly a rotary holder driven by a motor was mounted such that both faces of the specimen could be exposed to ion beams at angles almost to grazing incidence (up to 85") as shown in Fig. 24.

I

U

I crn

FIG.24. Ion-thinning equipment with rotary stage near grazing incidence to the ion beam (Paulus and Reverchon, 1964).

This arrangement formed the basis of commercial equipment manufactured first in France and then in the UK and US, with further refinements being introduced. The sources are of the type shown in Fig. 1, Originally, quartz insulators were used but Abrahams et al. (1968) favored Teflon, because the quartz tended to chip during assembly causing instabilities in the beam. They also simplified the means of aligning the multiple hole cathode. Other improvements included a telescope that tilted with the beam (previously the specimen had to be rotated to horizontal for viewing), and an

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J. FRANKS

offset motor to avoid having to interpose the light source between motor and specimen (Fig. 25). Ion currents could be monitored with two measurement shutters that swivelled into place in front of the sources. Tantalum holders replaced stainless steel because tantalum has a higher resistance to sputtering. The authors favored an ion beam current of 100 pA at 6 kV and stated that departures from these values (such as to 60 pA at 5 kV or 200 pA at 7 kV) resulted in rough surfaces. They claimed good results for most materials from filter paper to ceramics; the thinning rates generally were 4 pmh- '/gun. Telescope

shutter

Telescope pro1ec 1Ion shutter urnrny

Ion gun Light source

Motor

Ion current

(a)

FIG.25. Schematic illustrations of (a) earlier ion-thinning machine, and (b) improved version (Abrahams et al., 1968).

Tighe and Hockey (1969) also replaced glass insulators in the sources by Teflon, and since this material expands during operation, the outer metal holder was grooved to ensure even gas flow. Both sources were operated from the same power supply and the beam current varied by adjusting the gas flow. The authors considered ion thinning particularly suited to ceramics because the times necessary for thinning were comparable to those needed for some chemical methods, radiation damage from argon ions was less severe in ceramics than in metals and the existing dislocation substructures were not changed by the thinning method.

ION BEAM TECHNOLOGY A N D ELECTRON MICROSCOPY

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Prior to ion erosion, disks 3 mm in diameter were cut from mechanically polished sections. The disk thickness was limited only by the fragility of the sample and the depth of polishing damage and typically was 40-60 pm. Samples that were particularly fragile or fragmented because of internal strain were prepared by cementing a supporting ring to the thin section or to the disk specimen. Most of the materials were thinned using an operating voltage of 4-6 kV and a beam current of 100 pA/cm2 in each source. Some typical thinning rates were A1203, F e 2 0 3 , and Zr,03 1 pm/hr, SiO, , Cu,O 4 pm/hr, and MgO 0.5 pm/hr. Barber (1970) again found ion thinning especially useful for ceramics, glasses, and minerals. His equipment contained two sources of the hollow anode type producing seven beams. Each anode was connected through a large ballast resistor to a stabilized 10 kV, 10 mA DC supply. The vacuum chamber was pumped at a rate of 300 liter/sec to maintain a working Torr. The sources were operated at 6 kV vacuum of between 10-3 and with an argon ion current of 70 pA measured on retractable probes. The samples were sandwiched in a thin stainless steel holder rotated at 6 rpm. The inclination of the exposed surfaces with respect to the beams could be preset to angles between 0 and 30". Although eroded from both sides, the specimen was partially surrounded by a liquid-nitrogen-cooled shield further to minimize redeposition. The cathodes had a life of 160 hr before the sources became unstable. Typical erosion rates for ceramics such as dense alumina were 1 to 2 pm/hr, with a glancing angle of 20" and an ion current density of 200 pA/cm-'. Where possible, samples were prethinned to 25-30 pm although porous or friable materials were generally thicker. Temperature measurements made by embedding a fine copperconstantan thermocouple in a glass sample blank indicated that under the stated bombardment conditions, the sample attained a constant temperature of about 130°C after 15 min. Heuer et al. (1971) further improved the Paulus design. A fast pumping system was used to maintain a dynamic vacuum of about l o p 5Torr in the chamber with a leak rate of liter/sec through the sources. The power supply was provided with a large resistor in series with the input to prevent prolonged arcing, a persistent problem with high energy plasmas, by limiting the current t o the sources. A separate power supply operated the two sources, minimizing their interaction. Cathodes with seven holes and a single hole were compared. The singlehole design was found to be the more satisfactory for thinning small disks (2-3 mm diameter), fairly uniform thinning was achieved over an area of about 1 mm'. The single hole structure had the additional advantages of

36

J. FRANKS

inexpensive fabrication and freedom from alignment problems with the anode. Difficulties were still experienced with the Teflon insulators, electrically with arcing and mechanically with creep causing dimensional instability. Insulators of polycrystalhne alumina were found to be the best replacement. Stainless steel, aluminum, and tantalum were tried as cathodes. Tantalum had the highest resistance to sputtering but was the most costly, and stainless steel was chosen as the best compromise. For single-hole operation, 1.5-mm thick cathodes were used with a 1-mm diameter hole. The cathode had to be replaced when the hole expanded to about 2.5 mm, which typically occurred after 100-150 hr operation. The specimens were clamped between plates in a specimen holder, mounted on the shaft of a small synchronous motor, which rotated the specimen in its own plane at about 15 rpm. A small high-intensity lamp, mounted beneath the hollow shaft of the motor, illuminated the bottom face of the specimen. The specimen was viewed with a wide angle stereo zoom microscope ( 8 0 x ) through a window in the top of the chamber. The rotation/illumination system could be tilted during operation from outside the chamber to angles between 60" and 90" glancing to the ion beams. The microscope could be used to view the specimen at any angle, but for critical observation the specimen was rotated perpendicular to the microscope. Sources were operated between 5 and 7 kV with a 50 pA beam current for single-hole sources and 100 pA for multiple-hole cathodes. The equipment was used to thin a range of ceramics, semiconductors, and terrestrial and lunar rock specimens. The authors considered ion thinning to be a " universal " tool for preparing microscope foils of nonmetallic inorganic solids. Some problems remained, the most serious being the appearance of undesirable surface topography and the occurrence of appreciable radiation damage. However, these effects generally were considered not to interfere seriously with electron microscopic examination. Following the work of Holland et al. (1971) and Crockett (1973), which showed that the hollow anode sources used in the thinning equipment so far described are of an unnecessarily complex construction, the simpler sources are now used in some commercial equipment. Instead of using the plane cathode sources discussed so far, Ward (1971) incorporated hollow anode sources of the Azam type (1964) in his equipment. The ion beam emerges through a cathode grid curved into a section of sphere. With the grid protruding into the source (see Fig. 3) the beam is focused, with the opposite curvature a diverging beam is obtained. For ion thinning the focused configuration was used in two sources mounted vertically. The anodes, cathodes, and grids were made of tantalum, vertical mounting of the sources was favored to avoid the need for frequent cleaning as sputtered tantalum occasionally flaked off. With the sources operating at

ION BEAM TECHNOLOGY A N D ELECTRON MICROSCOPY

37

4-6 kV, 1 mA the cathode life was 100-150 hr. With a conical tantalum spiral instead of a grid, the lifetime was extended to 300 hr. The rotary thinning stage was driven by a motor external to the vacuum system and could be set at any angle between 0 and 90" to the beam. A low power microscope was set at 45" to the beam axis, for examination the specimen stage was therefore inclined to 45". The equipment, intended for use with radioactive materials in a glove box, was tested with molybdenum, T h o , , and MgO specimens. Useful thin areas were obtained and some radiation damage was observed. Another type of cold cathode source was incorporated in the ionthinning equipment described by Franks and Ghander (1974). The operation of this saddle-field source differs from that of the hollow anode type in that with a dc potential applied, the electrons describe long oscillating paths about the saddle-field instead of a single traverse of a few millimeter between cathode and anode. The saddle-field source can therefore operate near the chamber pressure of Torr without differential pumping and in this way resembles the Penning source. The absence of a magnet, however, makes these sources very compact. Instead of tilting the specimen stage, the sources were mounted on an arm that was tilted so that the angle of incidence of the beams with the specimen could be varied from glancing to normal incidence, the stage and specimen remaining horizontal and therefore always in the focal place of a binocular microscope mounted above the specimen chamber. The rotary stage consisted of a flat stainless steel toothed wheel with tantalum plates between which the specimen was held. The toothed wheel was driven via a meshing gear wheel and motor. In an earlier design (Franks and Ghander, 1974) the motor and lamp illuminating the specimen were mounted inside the vacuum system, in later versions these components were mounted externally (Franks, 1977a, b). An impression of the internal arrangement is shown in Fig. 26. The power supply was of the current-controlled type with a transistor feedback circuit providing a dynamic impedance of about 5 MR, instead of using a ballast resistor. The two sources, operated at about 5 kV, 1.5 mA and providing argon ion beams of about 100 PA, were energized from a single power supply. The output was adjusted by varying the gas flow and was continuously monitored by measuring the intensity of the beams emitted from the back of the sources (the sources are symmetrical about the anode); there was therefore no need to interpose monitoring plates between source and specimen. The ion beam emerged through a single aperture 1.5 mm diameter in the aluminum cathode. The beams were formed by the internal electrode system (Section 11), and therefore the intensity was maintained as the cathode enlarged. The cathodes needed only to be replaced after long intervals of operation (e.g., 500 hr).

38

J. FRANKS

High voltoge supply

Angular adjustment Needle valve

Needle valve

-

FIG.26. Internal arrangement of ion-thinning equipment with saddle-field ion sources (Franks, 1977a.b).

A large variety of materials have been thinned with this equipment: metals, semiconductors, and insulators including composites. The importance of thinning near-glancing incidence for some " difficult " materials was illustrated by results with a three-phase copper aluminum alloy (Franks, 1977b). After rapid thinning at an angle of about 60",the specimen was thinned at 80" for some 10 hr with the aim of producing useful thin areas, but only a few narrow transparent regions were obtained skirting the fairly numerous well-distributed penetration " pinholes." The picture improved considerably, however, after a further 10 hr thinning at 85" (Fig. 27). The number and area of the penetrated regions hardly increased but the improvement in the extent and uniformity of the transparent areas was very marked. C . Ion Thinning Procedures and Results

Ion thinning is now such a well-established technique for preparing specimens for transmission electron microscopy that in many recent papers bare mention is made of this process when it is used, and no details of the

ION BEAM TECHNOLOGY A N D ELECTRON MICROSCOPY

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FIG. 27. (a) Three-phase copper-aluminum alloy thinned at 80". (b) Specimen (a) after further thinning at 85".

40

J. FRANKS

operating conditions are given. It would therefore be difficult and not very instructive to provide a comprehensive list of all materials that have so far been thinned by ion etching, but results from selected papers can illustrate the scope and possible limitations of the technique, and procedures recommended by various authors. 1. Metals Ion thinning was introduced as a technique superior to chemical etching for alloys such as aluminum-copper and brass by Castaing and Laborie (1953). In most of the work, two multibeam ion sources were used, with a stationary specimen near normal incidence. A similar system was used by Gentry (1964) to thin aluminum alloys with 40% zinc and cobalt. For comparison thin specimens of these materials were also prepared by electrolytic etching. The results with cobalt favored electrolytic etching (Gentry remarked on the speckled appearance of ion-etched specimens), but in the case of the alloy, the precipitates were preferentially dissolved during electrolysis. Duker and Schlette (1964) thinned aluminum and copper foils with xenon as the discharge gas, with a discharge voltage of 15 kV and a current of 60 PA. The specimens were held stationary and were exposed to the beam at angles between 75" and 88". The thinning rate for rolled aluminum foil was 20-30 nm/min, being greater parallel to the rolling direction [crystallite orientation (1 lo)] than in the perpendicular direction [orientation (1 1 l)], indicating that faster sputtering occurs in the direction of more densely occupied atomic rows. Dislocation loops formed, extending to a depth of at least 30 nm. Ion bombardment also produced a dislocation network in copper. The sputtering rate for copper was 75 nm/mh. Molybdenum foils were thinned (Ward, 1971) from both sides, inclined at 60" to the beams. A discharge potential of 6-8 kV was initially applied to ensure rapid thinning and then decreased to 2.5-3.5 kV to reduce radiation damage. Transmission electron micrographs revealed grain boundaries but also speckling due to damage. Thoria and magnesia were also thinned and Ward noted that the damage was partly a function of etching angle and applied voltage, being smallest at low values of both these parameters. However, the effect persists in metals, whereas in ceramic materials the degree of damage is so small as seldom to be noticeable. Molybdenum-ruthenium alloys (Flewitt and Tate, 1972) were prepared for ion thinning from 0.5 mm slices that were spark-machined from the ingots and then mechanically ground to 0.2 mm. The thinned specimens were suitable for obtaining the structure of the phases and for a study of defects.

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Domain structures in single-crystal gadolinium (McKendrick et al., 1977; Chapman et al., 1977) were examined by TEM on specimens that had first been chemically polished and finally eroded by argon ions. Ion etching was also advantageous when thin foils needed to be prepared from fine wires (Thompson and Flewitt, 1970). If the sections are to be thinned electrolytically, a coating metal or alloy must be found that is electrochemically compatible with the wire. Alternatively, micromanipulative techniques have been devised to obtain both longitudinal and transverse sections directly but such techniques suffer the disadvantages of handling and lack of reproducibility. With ion etching, the wire diameter needs to be increased with another material but the only requirement is for a similar ion-thinning rate rather than for electrochemical compatibility. Bundles of copper-clad niobium-25 % zirconium alloy wires were copperplated and sectioned. The sections were mechanically ground to 0.2 mm and then thinned with argon ions from either side. The sources were operated at 4.5 kV producing 40 pA beams. Initially an angle of 70" was used to achieve rapid thinning (0.5 pm/hr). In the final stages the angle was increased to about 85" and erosion continued for 12 hr to minimize the depth of the disturbed layer and the differential thinning rate between the wire and matrix. Transmission electronmicrographs showed the fibrous structure of the cold-drawn wire in a longitudinal section and the cell boundaries in a transverse section. 2. Semiconductors

Semiconductors have been thinned to electron transparency by chemical and by ion-erosion techniques. The techniques were compared in a TEM study of silicon and gallium arsenide by Pettit and Booker (1971) and Lidbury et al. (1971). The chemical technique had the advantages of speed, cheapness, and simplicity and damage was unlikely to be introduced into the specimens. However, preferential etching could occur, for example, at crystallographic defects. In polar semiconductors, a chemical that produced a good polish on one face might heavily etch the opposite face. In specimens containing an exposed p-n junction, a step might be introduced at the junction because of a difference in etch rates between p- and n-type material. Also, no universal polishing solution existed for all materials. Ion thinning was a slower process but could be applied generally to semiconductors, independently of their chemical composition. No difference in erosion rates had been observed between p- and n-type material, and no differences appeared in the surface structure of opposite faces of ion-etched polar semiconductors. The authors ion-etched specimens from both sides with argon as the

42

J. FRANKS

discharge gas, a discharge voltage of 6 kV and an angle of incidence of 70-75”. Transmission electron micrographs obtained with chemical etching and ion etching were compared. Both methods gave good results, for revealing crystallographic defects in silicon, while the ion beam method was slightly better for defects in gallium arsenide. The slightly poorer definition of dislocations obtained with the chemically etched gallium arsenide specimens may have been due to residual chemical stain on the surface. An examination was made of the interfaces between epitaxial layers on substrates of silicon on silicon and gallium arsenide on gallium arsenide by viewing the layers “edge-on.” The specimens were prepared by dividing a slice into two and sticking the parts together with the epitaxial layers facing each other, cutting a cross-section specimen and polishing mechanically to 25 pm and finally thinning to electron transparency. The chemical jet thinning method did not prove suitable for these specimens because the acid polishing solution tended to penetrate between the two layers causing preferential etching. Satisfactory specimens were obtained with the ion-etching technique. To examine the interface between silicon grown epitaxially on sapphire (Linington, 1971), specimens were first mechanically ground and thinned from the substrate side until the interface between the silicon and sapphire was reached. The layer was then ion thinned from both sides, the rate on either side being adjusted to produce a hole with edges at a given distance from the interface. The dislocation density was observed to increase as the interface was approached. 3. Nonmetallic Inorganic Materials

Ion thinning has found its widest application in the preparation of ceramics, glasses, and minerals as other techniques for many of these materials have proved very difficult and unreliable (Barber, 1970). Radiation damage is generally less severe than in some metals (Ward, 1971) and can often be distinguished from the original microstructure (Heuer et al., 1971). The early work by Paulus and Reverchon (1964) showed that it was possible to prepare good transparent specimens of porous ferrites by thinning the material on a rotating stage near grazing incidence. A few examples are reported of material thinned under stationary conditions from one side: Drum (1965) thinned sapphire and silicon carbide with 2 keV argon ions at normal incidence. In sapphire the range of the ions was 3 nm and small clusters of defects were observed as specks. On heating to 800°C the specks transformed to dislocation loops forming networks of dislocations. Annealing at 900°C removed many of the visible defects but small bubbles 4 nm in diameter appeared.

ION BEAM TECHNOLOGY A N D ELECTRON MICROSCOPY

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The silicon carbide did not exhibit specks after thinning but on annealing for one hour at loOo"C, small dots appeared that the author attributed to the agglomeration of defects produced during thinning. Hirthe et al. (1967) thinned rutile, again stationary and at normal incidence at 2 kV and 1 mA. No evidence of damage was reported. Bach (1970a) thinned glass and ceramic specimens close to glancing incidence (85-88") from one side only, but split the specimen holder to allow ion erosion from the reverse side. The specimens were mounted on a stage that could be rotated. The materials were prepared by grinding to less than 0.1 mm and then polishing with diamond abrasive against a spherical surface (10-20 mm) radius almost until penetration. Grooves formed in specimens that were not rotated during the thinning process; generally, microcrystallites and segregations were observed in the various materials. Bach also prepared a transverse section of a TiOz surface coating in which the surfaces were protected by pressing them together during cutting and polishing, and were then separated for etching. In most of the later work, however, systems of the type described by Paulus and Reverchon were used, in which both surfaces of a rotating specimen are eroded simultaneously by ion beams incident at glancing angles. Tighe and Hockey (1969) prepared satisfactory specimens by this method from many ceramic materials, regardless of composition, porosity, and total strain ,resulting from deformation. Grain boundaries and pores were not etched preferentially. The deformation structure of indents on an alumina sample were also obtained, the material being eroded from one side only. In a further paper, Tighe (1970) listed a range of materials that had successfully been thinned by ion bombardment : alumina, magnesia, zirconia (all with various additives), metal-ceramic composites, and rock specimens. The thickness of the disks prepared by mechanical processes before ion bombardment varied from 150 pm for porous periclase brick to 45 pm for alumina and quartzite. The ion thinning rate was g 2 pm/hr depending on the operating conditions and on the material. Grain boundaries, pores, impurity precipitates, and dislocations were observed directly. The same thinning technique was used in a detailed examination by Hockey (1971) of lattice defects introduced as a result of plastic deformation of alumina by indentation and abrasion. Barber (1970) also gave examples of thin foils of glasses and minerals, prepared by ion thinning. He noted that impurity-doped alumina shows fine scale surface features on thinning, whereas no such effects were observed on pure alumina (Barber, 1972b).Possibly the sputtering process revealed small local variations in impurity concentration (Barber, 1972~). To deal with particulate matter consisting of grains up to about 1 mm

44

J. FRANKS

diameter, Barber (1971) embedded the particles in a low viscosity epoxy, tightly packed with alumina to ensure that the etching rate of the mounting matched that of the specimen. Heuer et al. (1971) found that any radiation damage introduced by ion thinning in materials such as alumina, magnesia, zirconia, and various minerals, could be distinguished from the original defect structure. The specimens were thinned at glancing incidence on a rotating stage. A similar technique was used in a study of twinning in europia (Bisbyand Moore, 1975). The effect of ion thinning was studied in detail on a glass-ceramic of composition Li20 . A120, . 4sio2 + 4.9wt% TiOz (Clinton, 1972). The fi-quartz and fi-spodumene phases that form in this material are particularly susceptible to ion beam damage, it therefore provides a sensitive means for observing the effects of different ion erosion conditions on beam damage. The material was ground to about 30 pm with carborundum and finally lapped to 15 pm with diamond-impregnated copper lap, after which it was ion thinned. With an applied potential of 6 kV, an ion beam current of 40 pA from each source, and an angle of incidence of 70", the etching rate was 1 pm/hr/source. Thinning was uneven and damage occurred to a depth of 0.05 pm. When the specimen angle was increased to 75" and the specimen thinned under the same current and voltage conditions as previously, there was an improvement in the uniformity of the surface but the thinning rate was reduced to 0.5 pm/hr/source. The uniformity of ion thinning was further improved by increasing the angle of incidence to 80°, with the disadvantage of an erosion rate of only 0.3 pm/hr/source. An improved thinning rate without serious loss of uniformity was achieved by first thinning at 70" for 7 hr until the specimen was penetrated, and then thinning for a further 3 hr at SO". This procedure also had the effect of reducing the damaged layer from 0.05 pm with 70" bombardment to 0.025 pm after the further bombardment at 80". Ion thinning may also be used with advantage on specimens with physical structures that can cause difficulties with other techniques, for example, when the materials are of a porous or fibrous nature. Porous structures, such as alumina catalyst supports (Faulkner et al., 1972) have been prepared for examination by TEM by crushing the material, which allows the microstructure to be examined, but larger voids or macropores are often destroyed. The reentrant nature of the surface limits the usefulness of replication techniques. Thin sections may be produced by an ultramicrotome but the cutting process tends to modify the structure of the hard, brittle, and extremely fragile material. It also produces a great deal of debris so that care must be

ION BEAM TECHNOLOGY AND ELECTRON MICROSCOPY

45

taken when interpreting the results. In specimens prepared by ion thinning, the structure appeared to be preserved. A thin disk (3 mm diameter) was mounted on a rotating stage and held at an angle of 70-75" to two opposing energetic (5-8 kV) beams of argon ions at a beam current of 4-50 pA each. The erosion rate was about 1 pm/hr. The fine porous structure was the same for crushed and ion-thinned specimens, so that it appeared that ion erosion does not change the fine structure. The author also concluded that the large pore sizes remained unaltered during ion thinning because no structure developed on ion-thinned single crystals of dense alumina. V. ION EROSION FOR SCANNING ELECTRON MICROSCOPY The SEM has played an important part in studies of the effects of ion etching on surface morphology (Section 111,B). However, under carefully controlled conditions, ion erosion may be used to reveal surface features obscured by deposits of mechanical and chemical origm without introducing confusing artifacts (Franks, 1977a,b). Trillat (1964) recommended the use of light sputtering by low energy ions (1-5 keV) to clean surfaces, sputtering removes slightly adherent surface impurities such as oxide and oil films. Ion etching is also used under conditions when differences in etch rate are accentuated in metallographic examination to reveal grains and subgrains and inclusions (Ward, 1971), and in studies of other materials and composite structures (Dhariwal and Fitch, 1977; Dhariwal et al., 1978). The TEMs accommodate specimens up to about 3 mm diameter, but in SEM, specimens may be typically 1 cm in diameter, and accordingly ion equipment for the SEM must provide for erosion over this larger area. Radio frequency sources have been used (Baltz, 1971; Stuart et al., 1969), as well as dc instruments of various designs, with the common feature that the specimen to be etched is supported on a cathode at about 10 cm from the anode (Ward, 1971). Ward commented that most of these dc instruments suffer in various degrees from two major faults: the inability to handle irregular shaped specimens and an unstable discharge. He advocated the use of ion sources in which the discharge is created and from which ions emerge through an aperture or apertures in the cathode. A . Ion Erosion Equipment

Cold cathode sources of various designs have been constructed for larger area erosion. A hollow anode source with 25 apertures arranged in concentric circles with an outer radius of 4.5 mm produced uniform sputtering over an area of 4 mm radius (Paulus and Reverchon, 1961). The specimen was mounted on a rotating stage driven by an electric motor inside the vacuum

46

I. FRANKS

chamber. Stage and motor could be tilted through an axis in the plane of the specimen to permit bombardment at angles of incidence from 0" to 90".A fixed water cooling coil was mounted below the rotating stage, the thermal path to the specimen being completed through an annular bath of mercury. Ward (1971) used the Azam-type source both for thinning and for etching metallographic specimens. His metallographic stage was constructed of tantalum because of its low sputtering properties and was water cooled. The stage remained stationary. Franks (1977a) used a large area version of the saddle-field ion source with a plane of symmetry normal to the anode plane instead of the axis of symmetry of the fine beam source (Section 11). The anode and cathode apertures are slots instead of circular holes, and electrons oscillate about a saddle line. The ion beam produced covers an area of about 1 x 1 an at a distance of 5 cm from the source. Specimens for SEM were prepared in the equipment shown in Fig. 24, in which the wide beam source replaced the upper line beam source. The specimen was placed on the horizontal rotating stage and the source continuously rocked over the specimen from near glancing to normal incidence about the central horizontal axis of the arm. As the driving motors for the stage and arm were not synchronized, the angle of incidence of the ion beam on any part of the specimen varied in a random way with the effect of avoiding as far as possible the formation of artifacts by the beam. B. Results

An example of the use of rf etching was given by Baltz (1971) in an investigation of structural and magnetic properties of Ni-Fe films deposited on Be-Cu wire. Ion etching revealed the shapes of Ni-Fe grains and structure of the upper layer obtained after various heat treatments; the shapes could be correlated to magnetic properties. Ward (1971) used a cold cathode Azam-type source to etch a variety of metals including uranium, molybdenum, nickel, and some alloys and nonmetals such as uranium oxide, thoria, and alumina, and some composites. Grain structures and inclusions were revealed in SEMs. Ward noted that in the case of resin-bonded graphite fuel elements, the structure of the graphite and resin binder were well delineated after krypton etching, whereas no combination of voltage and current produced a satisfactory etch with argon. Fitch and Rushton (1972) used a saddle-field source to argon ion etch nickel, molybdenum, copper, and acrilonitrile butadiene styrene plastic specimens. Attempts have recently been made to elucidate structures of biological material by rf and ion-beam etching. The attractiveness of ion etching is that

ION BEAM TECHNOLOGY A N D ELECTRON MICROSCOPY

47

in principle it can remove superficial layers in a controlled way and reveal structures (Lewis et al., 1968). However, it appears that biological materials are prone to the formation of artifacts such as cones. Some authors considered the interpretation of ion-etching pattern produced in soft tissue to be so problematical as to discourage the use of this technique (Boyde and Wood, 1969), nor was it possible to relate etching patterns to characteristic subsurface structures (Hodges et al., 1972). Fulker and Holland (1971) compared effects of rf etching and ion-beam etching on biological tissues and concluded that the difficulties involved in interpretation placed serious limitations on the usefulness of ion etching these materials. In a subsequent paper (Fulker et al., 1973) however, ion etching was found effective in revealing structures close to the lumenal surface of epithelial tissue from cow urinary bladder. The cones produced by directional etching could rarely be interpreted in terms of cell structure, but cone formation could be reduced by rotation of the specimen. Systematic differences in the appearance of rf and ion-etched normal cells compared with infected blood cells and sickle cells, and normal cells compared with malignant cells were described in a series of papers (Lewis et al., 1968; Stuart et al., 1969; Ambrose et al., 1970). In later work (Frisch et al., 1975a,b),the confusing effect of cones and other structures were avoided by etching for short periods of time and also by etching specimens cooled by liquid nitrogen. Spector (1975) etched avian red cells in the specimen chamber of a SEM with an argon ion beam. He found that nuclear structure, intercellular vacuoles, and other features in the cells were revealed with little difficulty in interpretation. It appears that as yet there is no agreement about the interpretation of results obtained with ion-etched biological materials, and further work is needed on the effects of etching time, etching gas, ion energy, type of ion, specimen temperature, and other relevant variables before conclusions can be drawn regarding the usefulness or otherwise of this technique for biological investigations. VI. CONCLUSION

Ion erosion has proved an increasingly valuable tool to electron microscopists, especially those engaged in examining classes of materials such as ceramics, composites, impurity-doped semiconductors, and alloys. These materials are difficult to etch chemically or can contain constituents that etch at widely differing rates. Where chemical or electrolytic etching are possible, however, the liquid techniques are still favored because the equipment is generally less costly, the etching rate is faster and of course there is

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no radiation damage, although specimens may suffer chemical contamination. Because of the relatively slow ion-etching rates, materials are commonly prethinned by mechanical or chemical means or a combination. Some specimens may be prethinned to say 25 pm quite readily, in other cases a considerable amount of skill and patience may be required (e.g., Clinton, 1972). In other cases still, specimens cannot be prethinned to less than a few hundred micrometers because the material may be friable and crumble or inclusions may be lost from the matrix. Future developments may therefore be directed to more speedy ionetching techniques to avoid tedious prepreparation. On the other hand, it is desirable that the final stage of thinning proceed slowly to allow close control over the extent of the thinned area and to eliminate as far as possible any radiation or other damage introduced during the earlier rapid stages. Sources to be developed for this final stage must preferably be capable of producing low energy ions (down to a few 100 eV) with a current density as high as possible without damaging the material by excessive heating. For some insulating materials, a neutralized beam may be desirable. The beam must be well collimated so that it may be effectively directed on to the rotating specimen close to glancing incidence. Argon is commonly used as the ionized gas, but where rapid erosion combined with minimal damage are important, a heavier (and more expensive) inert gas may be preferable.

REFERENCES Abraham, M. J., Buiocchi, C. J., and Coutts, M. D. (1968). Reo. Sci. Instrum.39, 1944. Adetunji, J., and Barber, D. J. (1978). J . Mater. Sci. 13, 627. Almen, O., and Bruce, G . (1961). Nucl. Instrum. Methods 11, 257 and 279. Ambrose, E. J., Batzdorf, U., Osborn, J. S., and Stuart, P. R. (1970). Nature (London)227,397. Andersen, H. H., and Bay, H. (1972). Radiat. Efl. 13, 67. Andersen, H. H., and Bay, H. (1973). Radiat. Efl. 19, 139. Azam, M. N. (1964). I n “Ionic Bombardment,” p. 207. Gordon & Breach, New York. Bach, H. (1970a). J . Non-Cryst. Solids 3, 1. Bach, H. (1970b). Nucl. Instrum. Methods 84, 4. Baltz, A. (1971). Electron Microscy, Proc. l n t . Congr., 7th, 1970 p. 621. Barber, D. J. (1970). J . Mater. Sci. 5, 1. Barber, D. J. (1971). Am. Mineral. 56, 2152. Barber, D. J. (1972a). Proc. Eur. Reg. Conf. Electron Microsc., Sth, 1972 p. 293. Barber, D. J. (1972b). Proc. Eur. Reg. Conf.Electron Microsc., Sth, 1972 p. 302. Barber, D. J. (1972~).Colloq. Ger. SOC. Electron Microsc., 5th 1972 p. 585. Barber, D. J., Frank, F. C., Moss, M., Steeds, J. W., and Tsong, I. S. T. (1973). J . Mater. Sci. 8, 1030. Berg, R. S., and Kominiak, G. J. (1976). J . Vac. Sci. Technol. 13, 403. Bilsby, C. F., and Moore, D. A. (1975). Cermurgia Int. 1, 72.

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Boyde, A., and Wood, C. (1969). J. Microsc. (Oxford) 90, 221. Brandt, W., and Laubert, R. (1967). Nucl. Instrum. Methods 47, 201. Carter, G., and Colligon, J. S. (1968). “ Ion Bombardment of Solids.” Heinemann, London. Carter, G., Colligon, J. S., and Nobes, M. J. (1977). Radiat. Eff.31, 65. C a s t i n g R. (1955a). Rev. Metall. (Paris), Part 2 52,669. C a s t i n g R. (1955b). Colloq. Microsc. Electron. C.N.R.S. Toulouse p. 117. Casting, R. (1956). Proc. Int. Con5 Electron Microsc., 3rd, 1954 p. 379. Casting, R., and Jouffrey, B. (1964). In “Ionic Bombardment,” p. 83. Gordon & Breach, New York. Casting, R., and Laborie, P. (1953). C . Hebd. Seances Acad. Sci. 237, 1330. Casting, R., and Laborie, P. (1954). C . Hebd. Seances Acad. Sci 238, 1885. Castaing, R., and Lenoir, G. (1954). C . Hebd. Seances Acad. Sci. 239,972. Chapman, J. N., McKendrick, W. H., Ferrier, R. P., and Hukin, D. A. (1977). Int. Con$ Rare Earth Actinides, 1977, p. 228. Clinton, D. J. (1972). Micron 3, 358. Coburn, J. W. (1976). J. Vac. Sci. Technol. 13, 1037. Crockett, C. G. (1973). Vacuum 23, 11. Davis, W. D., and Vanderslice, T. A. (1963). Phys. Rev. 131, 219. Dhariwal, R. S., and Fitch, R. K. (1977). J . Mater. Sci. 12, 1225. Dhariwal, R. S., Ball, P. C., Marsland, E. A,, and Fitch, R. K. (1978).Proc. Int. ConJ Low Energy Ion Beams, 1977, p. 151. Drum, C. M. (1965). Phys. Status Solidi. 9, 635. Diiker, H., and Schlette, W. (1964).In “Ionic Bombardment,” p. 119. Gordon & Breach, New York. Faulkner, D., Sagert, N. H., Sexton, E. E., and Styles, R. C. (1972). J. Catal. 25, 446. Fitch, R. K., and Rushton, G. J. (1972). J. Vac. Sci. Technol. 9, 379. Flewitt, P. E. J., and Tate, A. J. (1972). J . Less-Common Metals 27, 339. Franks, J. (1977a). Microscope 25, 227. Franks, J. (1977b). Proc. Conf Electron Microsc. A.G., 1977, p. 57. Franks, J., and Ghander, A. M. (1974). Vacuum 24,489. Frisch, B., Lewis, S. M., Stuart, P. R.,and Osborn, J. S. (1975a). Scanning Electron Microsc. 1975. Part 1, 165. Frisch, B., Lewis, S. M., Stuart, P. R.,and Osburn, J. S. (1975b). Micron 6, 101. Fulker, M. J., and Holland, L. (1971). Micron 2, 117. Fulker, M. J., Holland, L., and Hurley, R. E. (1973). Scanning Electron Microsc. 1973, Part 3, 379. Garvin, H. L. (1973). Solid State Technol. 16, 31. Gentry, B. (1964). In “Ionic Bombardment,” p. 142. Gordon & Breach, New York. Gloersen, P. G. (1975). J . Vac. Sci. Technol. 12, 23. Goodhew, P. J. (1972). In “Practical Methods in Electron Microscopy” (A. M. Glauert, ed.), Vol. 1, Part 1. North-Holland Publ., Amsterdam. Hauffe, W. (1971). Phys. Status Solidi a 4, 111. Heuer, A. H., Firestone, R. F.; Snow, J. D., Green, H. W., and Howe, R. G. (1971). Rev. Sci. Instrum. 42, 1177. Hietel, B., and Meyerhoff, K. (1961). Z. Phys. 165, 47. Hirthe, W. M., Melville, A. T., and Wackman, P. H. (1967). Rev. Sci. Instrum. 38, 223. Hockey, B. J. (1971). J . Am. Ceram. SOC. 54, 223. Hodges, G. M., Muir, M. D., Sella, C., and Carteaud, A. J. P. (1972). J . Microsc. (Oxford) 95, 445.

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86B-88B,1335. Magnuson, C. D., Merkel, B. B., and Harkins, P. W. (1961). J . Appl. Phys. 32, 369. Melliar-Smith, C. M. (1976). J . Vac. Sci. Technol. 13, 1008. Navez, M., Sella, C., and Chaperot, D. (1964). In “Ionic Bombardment,” p. 339. Gordon & Breach, New York. Oechsner, H. (1975). Appl. Phys. 8, 185. Paulus, M., and Reverchon, F. (1961). J . Phys. Radium [8] 22, Suppl. 6, 103A. Paulus, M., and Reverchon, F. (1964). In “Ionic Bombardment,” p. 324. Gordon & Breach, New York. Pettit, H. R., and Booker, G. R. (1971). Proc. 25th Anniu. Meet. Electron Microsc. A.G. p. 290. Sigmund, P. (1969). Phys. Reu. 184, 383. Sigmund, P. (1973). J . Mater. Sci. 8, 1545. Somekh, S. (1976). J . Vac. Sci. Technol. 13. 1003. Spector, M. (1975). Micron 5, 263. Spencer, E. G., and Schmidt, P. H. (1971). J. Vac. Sci. Technol. 8, S52. Stuart, P. R., Osborn, J. S., and Lewis, S. M. (1969). Proc. Scanning Electron Microsc. Symp., 2nd, 1969 p. 241. Teodorescu, I. A,, and Vasiliu, F. (1972). Radiat. 15, 101. Thompson, M. W. (1968). Philos. Mag. [8] 18, 377. Thompson, S. J., and Flewitt, P. E. J. (1970). Metallography 3, 477. Thomson, J. J., and Thomson, C. P. (1933). “Conduction of Electricity through Gases.” Cambridge Univ. Press, London and New York. Tighe, N. J. (1970). In “ Ultra Fine Grain Ceramics,” p. 109. Syracuse University Press, Syracuse, New York. Tighe, N. J., and Hockey, B. J. (1969). Symp. Electron, Ion Laser Beam Technol., loth, 1969 p. 375. Trillat, J. J. (1964). In “Ionic Bombardment,” p. 13. Gordon & Breach, New York. Tsong, I. S. T., and Barber, D. J. (1972). J . Mater. Sci. 7 , 687. Tsong, 1. S. T., and Barber, D. J. (1973). J . Mater. Sci. 8, 123. Vasiliu. F., Teodorescu, I. A., and Glodeanu, F. (1975). J. Mater. Sci. 10, 399. Ward, J. W. (1971). Microstructures 2, 11. Wegmann, L. (1964). Schweiz. Arch. Angew. Wiss. Tech. 30, 143. Wehner, G . K., and Anderson, G. S. (1970). I n “Handbook of Thin Film Technology” (L. I. Maissel and K. Clang, eds.), pp. 3-16. McGraw-Hill, New York. Wilson, I. H., and Kidd, M. W. (1971). J . Mater. Sci. 6, 1362. Witcomb, M. J. (1974). J . Mater. Sci. 9, 551. Witcomb, M. J. (1975). J . Mater. Sci. 10, 669.

eff

ADVANCES I N ELECTRONICS A N D ELECTRON PHYSICS. V O L 47

Microprocessors and Their Use in Physics ANTHONY J . DAVIES Department of Physics University College of Swansea Swansea. United Kingdom

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11. The Technology of LSI Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A . Bipolar Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Unipolar (MOS) Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C . Comparison of Technologies., . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I11. The Architecture of Microprocessors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A . The Microprocessor as a Logic Element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Choice of Word Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C . Single and Multichip Implementations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D . The Instruction Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E . The Processor-Memory Switch . . . . . . . . . . . . . . . . . . .............................. I V . Memory and Peripheral Devices ............................... A . Main Direct-Access Memory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Bulk Storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Input and Output Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V . Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A . Assemblers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. High-Level Languages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V I . Linking the Experiment to the Microprocessor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A . Measuring Instruments and Analog-to-Digital Converters ....................... B. Interfacing and Transmission Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V11. Typical Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A . Setting Up the System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B . Particular Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII . Current and Future Trends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51 54 54 56

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92 100 100 103 109 111 117 118 118

I . INTRODUCTION

The development of the high-speed digital computer has had a profound effect on modern science and on physics. in particular . A whole new realm of problems. which were previously incapable of analysis. can now be 51

Copynght 0 1978 hy Academic Press . Inc All rights of reproduction in any iorm reserved ISBN 0-12-014647-9

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examined and very few physicists will not have had occasion to use a computer at some period during their career. Most early work was done on large-scale central systems that had to cater for the varied needs of many different workers. These systems were consequently expensive and not suitable for on-line use by the experimentalist who often needed to have complete control over the machine in order to make measurements in real time. The introduction of the minicomputer in the early 1960s thus led to a great increase in the use of computers in experimental physics. These machines were expensive when first introduced but such has been the rapid advance in technology that modern minicomputers are an order of magnitude more powerful and yet cost less than 25% of the price. The Digital Equipment Company’s PDP8, for example, has dropped from about $15,000 in 1965 to about $2,000 today, while the proportionate cost of the central processing unit compared with the total system cost has dropped from over 75% to about 10%. When minicomputers first appeared, integrated circuit technology had just begun to develop but large failure rates and packaging problems limited the number of components (e.g., transistors and diodes) per device to about a dozen so that their cost was relatively high. Nowadays very large scale integrated (VLSI) circuits are in volume production with densities in excess of 50,000 components per square centimeter. These advances, together with associated improvements in circuit design, have made it possible to fabricate a complete central processing unit on a small number of silicon chips, thus leading to the development of the “ microprocessor,” which is having as revolutionary an effect on experimental physics and instrumentation as the powerful central machine had on theoretical physics and data processing. Indeed, it is now possible to buy a complete computer, consisting of a microprocessor, memory, timing, and inputloutput circuits, on a single chip. Figure 1 shows the Intel Corporation 8748, which measures 5.6 x 6.6 mm and contains some 20,000 transistors. With microprocessor chips costing as little as a few pounds, distributed processing using microprocessors can take over many tasks that were formerly carried out on large systems with a great reduction in cost. In dedicated control problems hardwired logic has almost universally been superseded by microprocessors that provide cost savings, increased flexibility, and greater ease of design. This article is concerned with the part that microprocessors have to play in physics and how their architecture and the technology used in their manufacture can influence their suitability for a given application. Since the microprocessor cannot be considered in isolation from the rest of the system, the performance of the associated peripherals and memory have to be considered before a complete system can be configured as well as such factors as

FIG. 1. Intel 8748 single-chip microcomputer that combines a microprocessor, program and data memory, timing, and input/output interfaces on a single silicon chip.

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the availability of suitable software and the different means of linking the constituent parts of the system together, It is hoped that, as well as being a basic introduction to microprocessors and microcomputers, the information presented will enable the reader to decide the best means of choosing and implementing a microprocessor in his own particular application in experimental physics or instrumentation. 11. THETECHNOLOGY OF LSI CIRCUITS

Integrated circuit technology was made possible in the early 1960s by the development of thin-film technology and the ability to produce planar silicon crystal wafers. These wafers were formed by slicing from a cylindrical ingot of crystalline silicon, and then thin film technology enabled one to define active or insulating regions of the wafer by photolithography thus creating components such as transistors, diodes, capacitors, or resistors. Two basic component types, “unipolar” and “bipolar,” may be fabricated where these designations refer to the type of charge carrier present in the device. In bipolar devices there are two charge carriers of opposite polarity, whereas in a unipolar device only one charge carrier is present. A . Bipolar Devices The most common and important bipolar integrated circuit device is the transistor and, just as with discrete components, there are two types: npn transistors where the charge carriers are electrons, and p n p transistors where the charge carriers are holes. Since electrons have a much greater mobility than holes, we would expect rzpn transistors to have a much faster frequency response and they are the most commonly used in integrated circuits. The main structural features of an npn transistor are shown in Fig. 2. By extending the aluminum base structure to make contact also with the n-type collector region, it is possible to create a Schottky, or surface barrier, diode from the single base electrode (Fig. 3). The aluminum base and lightly doped n region form a rectifying contact while the heavily doped n + region makes an ohmic contact with the collector. This device is known as a Schottky transistor and the Schottky diode clamped between the base and C

E

s102

p Substrate

B

B4 E

FIG.2. Cross section of an npn bipolar transistor and its schematic representation.

MICROPROCESSORS AND THEIR USE IN PHYSICS

55

E

P Subsirale

E

FIG.3. npn transistor with Schottky diode clamp between base and collector together with schematic of equivalent circuit and the symbol for a Schottky transistor.

collector reduces propagation delay times by preventing the transistor from saturating. It also makes it possible to consider diode-transistor logic (DTL) competitively with transistor-transistor logic (TTL) or emitter-coupled logic (ECL). Bipolar transistors are relatively high-speed devices, and even the smallest sized have the ability to switch relatively large currents rapidly so that it is possible to drive the capacitors associated with interconnections between discrete circuit packages. Thus high-speed systems can be built up from several separate IC packages with different functions. This is one reason for the widespread use and popularity of logic families such as TTL that depend on the bipolar transistor. Much has been heard recently of integrated injection logic (I'L) which is a bipolar technology based on direct-coupled transistor logic (DCTL). The basic circuit element is a multielectrode npn transistor coupled with a p n p transistor (Fig. 4). An epitaxial layer of n-type material is grown on an n + silicon substrate. After masking, two p-type diffusions are made into the epitaxial layer followed by selective n + type diffusions, which then define both lateral and

"P"P+ n-type

n+

material

Substrate

E

c

FIG.4. Basic 12L structure with its equivalent circuit

56

ANTHONY J. DAVIES

vertical transistors. The collector of the pnp transistor functions as the base of the npn and the base of the pnp is common with the emitter of the npn. The resulting 12L circuit has important improvements in speed, power dissipation, and density compared with other technologies.

B. Unipolar ( M O S ) Devices 1. The MOSFET

The most important type of unipolar device is the planar metalinsulator-semiconductor structure (usually known as MOS) typified by the field effect transistor (MOSFET). This is formed on a p - or n-type silicon substrate and in Fig. 5, a p-channel device is shown where the highly doped source and drain regions have been formed by diffusion into an n-type substrate. The whole structure is then covered with a thin oxide film and metallic contacts made with the source and drain by cutting through this film. The gate electrode, however, is placed on top of the oxide layer and covers the whole of the channel region. Source

Gate(-)

Drain

Indu'ced P channel n substrate

FIG.5. Cross section of a p-channel MOSFET.

The FET operates by means of the field effect, which is produced in the channel between the source and the drain by the voltage on the gate. As the magnitude of the (negative) gate voltage is increased, the induced positive charge in the semiconductor increases leading to increased conductivity and current flow due to p-type carriers from source to drain. This is an example of an enhancement mode device where there is no current flow between the source and drain unless a voltage is applied to the gate. In a depletion mode device, current flows without any gate voltage and current cut-off occurs at a higher voltage called the threshold voltage. Figure 6 shows an n-channel depletion mode MOSFET. Negative gate voltages once again induce positive charges in the channel resulting in a depletion of the majority carriers (electrons) and a reduction in conductivity. It is possible to make an external connection to the substrate, thus producing a tetrode device but it is more usual to connect the substrate to the source internally making it into a triode. The circuit symbols for the

57

MICROPROCESSORS A N D THEIR USE IN PHYSICS Source

Gale

Difrused

Drain

Source

Gate(-)

Drain

n channel p substrate

(b)

(a)

FIG.6. Cross section of an n-channel depletion-type MOSFET (a) without and (b) with gate voltage applied.

different p-channel MOSFETS tend to vary but commonly used ones are shown in Fig. 7. For n-channel devices, the direction of the arrows is reversed. Another important MOS transistor configuration, often used as a storage element, is the floating-gate avalanche-injection (FAMOS) device shown in Fig. 8, which is essentially a p-channel MOSFET in which no connection is made to the silicon gate. Triode

Tet rode

4& Source

Gate

Depletion mode type

Substrate

I

Drain

G{

Enhancement mode type

{Sub

D

0

FIG.7. Commonly used circuit symbols for p-channel MOSFETS. The lower right symbol is often used for both depletion and enhancement devices and the substrate is understood to be connected to the source.

58

ANTHONY J. DAVIES

% Drain

Floating gate

Substrate

n substrate Source

FIG.8. Cross section of p-channel FAMOS MOSFET.

Operation of this device depends upon the avalanche injection of electrons from the source or drain to the floating gate by the application of junction voltages in excess of about - 30 V. The number of electrons transferred is a function of the amplitude and duration of the applied voltage and, once this is removed, the electrons are trapped by the surrounding oxide that has a very low conductivity. Chapple (1976) gives charge decay characteristics which indicate that at 125°C about 90% of the induced charge will be retained for as long as ten years. The presence or absence of charge can be sensed by measuring the conductance between source and drain. The device may, however, be discharged by illumination with ultraviolet light that causes a photocurrent to flow from the floating gate to the substrate. 2. Complementary MOS ( C M O S )

It is possible to reduce power dissipation to very low levels (- 50 nW) by using complementary p-channel and n-channel MOS devices on a single chip. Figure 9 shows a typical structure implemented by means of p-diffusion in an n-type substrate. The basic CMOS inverter circuit is shown in Fig. 10 where the p-channel and n-channel transistors are connected in series by connecting their drains and gates. When V," = V,, (logic I), the upper transistor will be nonconductive while the lower transistor is conductive pulling V,,, to earth (logic 0).Conversely, if V,, = 0 the lower transistor will be nonconductive and the upper transistor will conduct causing V , , to appear at the output. S,

D.

G,

G,

S.

P we11 n Substrate

n-channel MOSFET

p-channel MOSFET

FIG.9. Basic complementary MOS (CMOS) structure.

MICROPROCESSORS AND THEIR USE IN PHYSICS

59

$

V0"I

GZ

3 s , -

FIG. 10. Complementary MOS inverter.

Note that in both states at least one transistor is in the OFF state and the quiescent power dissipation, which is the product of the OFF leakage current and VDD, will be very low. As has been pointed out by Verhofstadt (1976), however, the dynamic power dissipation may be very much greater than this and, for a single gate operating above 1 MHz in a small scale integrated circuit, the power requirements of the different technologies are not very different. In LSI circuits, however, the internal gate drive requirements are very much less and CMOS technology has a considerable advantage. The other advantages of CMOS are its higher speed, its need for only one power supply, its wide operating range, and immunity from the effects of noise. Its basic disadvantage is its relatively lower circuit density.

3. Silicon-on-Sapphire ( S O S ) It is not strictly necessary to use silicon as the substrate in an IC device. The active region of silicon may be placed on a substrate of any material that has similar physical properties. One alternative substrate that has been employed is sapphire (another is spinel) and the resulting technology, called silicon-on-sapphire, has been mainly used in the implementation of CMOS circuits. An important feature of SOS technology is the elimination of parasitic capacitances between the electrodes and the substrate. The operating speed is thus increased and power consumption reduced. 4. V-Groove MOS ( V M O S )

One of the most interesting advances in MOS technology has been the development of the V-groove MOS process (Rodgers and Meindl, 1974). VMOS substantially reduces channel lengths and increases packing density by incorporating both drain and gate on a notch that accesses a source in the

60

ANTHONY J. DAVIES

substrate (Fig. 11). The vertical arrangement of the elements decreases parasitic losses and power dissipation and the compact size leads to very high operating speeds that are comparable with bipolar devices. Drain

Soirce

FIG. 11. Structure of V-groove MOS gate.

C. Comparisoii o j Technologies

Compared with the corresponding bipolar devices, early MOS transistors were slow and had a very limited drive capability. Thus, for simple circuits where the fabrication costs were small compared with the packing, testing, and handling costs, MOS transistors offered no advantage and a much lower performance. Enhancement mode MOS devices did, however, have the advantage of being self isolating (i.e., nonconducting with no gate voltage), whereas the bipolar transistor needed some means of separating the individual transistors. This allowed MOS devices to be very closely packed and when microprocessors were first developed, the only technology capable of fabricating the complex complete processing unit was MOS. Although these early microprocessors were of low speed, they were perfectly adequate for many logic systems and thus they found widespread acceptance. Since then MOS technology has improved rapidly and some manufacturers (such as Intel) are of the opinion that it can be further developed to meet nearly all forseeable needs. When comparing different LSI technologies, the three most important parameters, besides cost, are the propagation delay, the power dissipation, and area associated with each gate. Table I summarizes these for the most commonly used technologies. We see that for the highest speeds there is nothing to touch ECL, and LSI circuits using this technology are already having a profound effect on the architecture of large computer systems. Due to its high density and relatively good performance NMOS (nchannel MOS) is likely to be the main technology for those medium speed

MICROPROCESSORS AND THEIR USE IN PHYSICS

61

TABLE I TYPICAL PARAMETERS ASSOCIATED WITH LsI TECHNOLOGIES'

Technology

Static power dissipation/gate (mw)

Propagation delay/gate (nsec)

Area/gate (mil')

PMOS NMOS CMOS TTL ECL I'L

2-3 0.2-0.5 < 0.001 1-3 5-15 < 0.2

> 100 40-100 15-50 3--10 0.5-2 >5

8-12 6-8 10-30 20-60 20-50 4-6

' Verhofstadt (1976)

applications requiring the minimum number of individual LSI chips. TTL (in particular Schottky-TTL) is the natural choice for high-speed moderately complex circuits. CMOS will find applications in industry, aerospace, and military applications where its good noise immunity, low power requirements, and relatively high speed can be exploited. 12L is still relatively new and as yet has not found widespread acceptance. It has, however, the capability of operating at a very low voltage (- 1 V) and thus it has a better speed x power factor than any other technology or circuit form. It is also compatible with linear devices so that digital and analog circuitry can be combined in the same integrated structure. 111. THEARCHITECTURE OF MICROPROCESSORS A . The Microprocessor as a Logic Element

There are very many different approaches to the design of a microprocessor, but a very instructive one from the point of view of the physicist is to regard it as an extension of a general purpose gate. Following the development used by Brown (1977), a general purpose gate will, in general, have two inputs, at least one output, and a means of selecting the kind of operation that is to be performed on the inputs (such as addition, subtraction, or one of the logical operations NAND, NOR, etc.) (see Fig. 12). In order to avoid having to assert the inputs and output the whole time, it is customary to store them in latches and if these have a tristate output (i.e., as well as outputting " high " and " low " signals they can switch off and

62

A N T H O N Y J. DAVIES

A outputs

inputs

C

B

seieci or cointrol FIG. 12. General purpose gate with two inputs and one output.

data bi

address

FIG. 13. General purpose gate with tri-state input/output. latches, data bus, and timing circuitry (Brown, 1977).

MICROPROCESSORS AND THEIR USE IN PHYSICS

63

present a high impedance), then a common set of wires called a “data bus” can be used to transmit signals to and from the device (Fig. 13). In Fig. 13 the timing circuitry is used to latch data sequentially into the latches A, B, S , and C and to control the output of C. The sequence of operations is controlled by a counter the output of which is called an address and defines where data are coming from and going to. At each timing count a word of data is fetched and put into A, B, or C, or read out from C. Since it is often desirable not to have to go through the complete cycle of operations, the counter can be preset (or loaded) with a number in the same way as A, B, or S. As Brown points out, Fig. 13 shows a slightly simplified microprocessor with two data inputs, a function select, and a tristate output. The general purpose gate is referred to as an “ arithmetic and logic unit ” (ALU) and the various latches as registers. If the register is used to deposit the result of an arithmetic or logical operation, then it is called an accumulator. In order to define the data input and various functions selected in the gate, this microprocessor would normally be connected to a memory that is simply a matrix of data storage elements. Each element has an address that can be selected by the microprocessor either via a separate address bus or by time multiplexing with the data along a common bus. Data may then be read from or written to this memory element via the data bus depending on the function selected. The memory may be used to store both data and instructions so that we thus have a processor, or general purpose gate, that can take data and instructions from memory and put resulting data back into memory. Clearly we must also have some means of communication with the outside world, and thus most microprocessors reserve certain memory addresses (known as “image memory”) for external input and output devices. Address decoders detect the address and enable the appropriate device via a tristate buffer or latch. Our complete microprocessor system would then be as in Fig. 14 and, depending on what instructions are in memory, the system can accept data from two sources, perform some operations (which may be simple or complex), and output to one destination. Whereas this system may not be as fast, for example, as the corresponding hardwired logic equivalent, it has tremendous flexibility and the number of outputs and inputs can easily be extended. Likewise the sequence of operations can be changed by altering the contents of memory. Thus in designing any system that can tolerate the operating speed of a microprocessor, in essence the design process is simply reduced to asking (a) how many inputs and outputs does the system have, and (b) what operations must be performed on the inputs to produce the outputs?

ANTHONY J. DAVIES

64

microprocessor

hTH-1 demder

tristate buffer

r

I L

I

data in

dauout

6

6

FIG.14. Typical microprocessor system (Brown, 1977).

B. Choice of’ Word Length Microcomputers are usually classified according to their word length, that is, the number of bits that can be handled by their central processing units, and this determines the range of numbers that can be represented, the number of binary variables that can be processed in parallel, and the number of different states that can be represented. Table I1 shows these variables for the most commonly used word lengths. Since the word length of the memory is the same as that of the processor, if large numbers are to be stored more than one word of memory must be used per number. In addition, whereas 16 bit machines can directly address 64 k (1 k = 1024) words of memory, an 8 bit machine can only directly address 256 words. Numerical calculations are normally carried out to the base ten and thus decimal numbers will require four bits for their representation (usually in binary coded decimal). Thus most pocket and desk calculators, electronic scales, cash sales terminals, etc., employ four bit microprocessors, the most common and successful to date being the Intel 4004/4040 and the Rockwell PPS-4.

65

MICROPROCESSORS AND THEIR USE IN PHYSICS

TABLE I1

THEEFFECTOF Word length Number range

LENGTH

4

8

16

0 - 15

0 -+ 255

0 -+ 65, 535

n

0-

- 2”-’ Number of binary variables Number of states

CHOICE OF WORD

+ (2” - 1 ) or + 2“-’ - 1

-+

n

2”

-8

+

4 16

+7

- 128 -+ 8 256

+ 127

-32, 768 + 32, 767 16 65, 536

In transferring alphanumeric information, it is necessary to go to a longer word length and 8 bits has now become the accepted standard with information most commonly being represented by the ASCII character set (Appendix 11). Other character sets can be employed for special purposes. Thus, in communications and similar work, 8 bit machines such as the Intel 8080 and Motorola 6800 are most suitable and the majority of microprocessors manufactured today have this word length. The current trend, however, is towards large word length machines and 16 bits may well become the standard in the future. These microprocessors can perform all the functions traditionally associated with a minicomputer and machines such as the DEC LSI-11 and Data General Micro-NOVA are more powerful than many minicomputers. Although 16-bit processors, the instruction set will almost invariably allow 8 bits (1 byte) to be manipulated so that data can be stored and transmitted economically.

C . Single and Multichip Implementations In the practical implementation of a microprocessor, the architecture and technology used in the manufacture will depend on the application. One obvious trend where speed is not an essential requirement is toward the complete “computer on a chip.” Here a single chip will contain the processor, memory and interface for connecting peripheral devices. In order to get the high packing density needed, PMOS or NMOS technology is normally used although the recently released Fairchild 9440 uses Isoplanar IzL technology. Table (a) in Appendix I lists the more common single-chip microcomputers currently available. Building a processor from several chips with a smaller number of components can have several advantages such as lower failure rate during manufacture, fewer pins per device, and the ability to employ bipolar technologies such as Schottky TTL.

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A N T H O N Y J. DAVIES

Several manufacturers have developed multichip processors using bitslice” architecture where normally there is one common control chip and several identical two or four bit slices,” each on a separate chip, for the arithmetic and logic units and registers. If the slices are connected in parallel it is possible to make up a machine having any desired word length. One of the most important developments in the last few years has been that of microprogrammed machines, where the control unit has all the features of a classical computer including some local read-only memory (ROM). Using a stored microprogram, this inner computer” translates an instruction in the user’s program into a series of its own microinstructions that are then executed. The microprogram thus defines the instruction set of the machine and can simulate the behavior of other computers or can be optimized for a given usage. It is easy to add instructions late in the development of the processor and, in some designs, the basic instruction set can be added to by the user. This is similar to writing a subroutine but very much faster. Figure 15 illustrates the two levels of program, the microcode being within the CPU while the conventional program is stored in memory. “

“

“

-

I

I

Control

--

I I

Microprogram

ROM

in

I I

I I

I

I

I I I I I

I I I

-

I

I

I

I

-

I

I

Arithmetic and logic u n i t

I

I

A

I

I

I I

I t

I I I I

I

Registers

I

I

11

L - - - - - - - - - - - - _ - - - - - - - - - - - - - - - - J

Data buslt

I

1‘ Address bus

MICROPROCESSORS AND THEIR USE IN PHYSICS

67

When assessing the speed of a microprogrammed machine, one must be careful not to confuse the cycle time of the microprogrammed control unit with the time to perform an instruction in the main programme. For example, if the minimum cycle time is 175 nsec, then account must be taken of the time to access the microcode plus the clock width and this gives a typical microinstruction cycle time within the CPU of about 400 nsec. Since a typical main program operation (say register to register add) will involve about 3 microinstructions, the total time involved is about 1.2 psec (rather different from 175 nsec). It is interesting to note that when first suggested by Wilkes (1969), the microprogrammed CPU was called a “microprocessor” although this term has, of course, now changed to mean a miniaturized processor produced by large-scale integration technology. The combination of microprogramming and bit-slice architecture can give rise to a very powerful and flexible machine suitable for a wide range of applications. Table (b) in Appendix I summarizes the technology and architecture used in the most commonly occurring microprocessors.

D. The Instruction Set In addition to execution speed, the performance of a microprocessor is specified by the number of instructions in the instruction set and by the efficiency of its programming, i.e., the number of instructions needed to specify a given task. The instruction set will be closely related to the architecture of the machine and the ultimate application of the system must be closely borne in mind in deciding which particular microprocessor to employ. One of the most powerful instruction sets is that used by DEC in its PDP-11 family when over 400 instructions are available. Since it has become semistandard, a number of microprocessors have their instruction sets based on that of the PDP-11. These include the General Instrument Corporation CP-1600 and the Motorola 6800 (as far as is possible with an 8-bit machine). Most machines have three classes of instructions relating to memory reference, operator or accumulator control, and input/output. One of the most important features of the PDP-11 set is that, since peripherals are considered as image memory, all instructions used to manipulate data in memory can be used equally well for data in peripheral devices. For example, data in an external device register can be tested or modified directly by the CPU without bringing it into memory or disturbing the general registers. Another important factor to consider in an instruction set is the number and type of addressing modes available. In general, the central processor will require the following information for each instruction :

68

ANTHONY J. DAVIES

(i) (ii) (iii) (iv) (v)

the address of the next instruction, the code specifying the operation, the address of the first source operand, the address of the second source operand, and the destination address.

Hardware is usually used to reduce the amount of information required, otherwise the instruction would be unduly long and excessive storage would be required for a program. Thus (i) is provided by a separate special register called the " program counter " PC. Since most instructions are obeyed in sequence, it is only necessary to increment the PC to provide the next instruction address. Branch or jump instructions may be used to load the P C with the relevant address if the next instruction is out of sequence. Further, items (iv) and (v) may be removed by using a fixed accumulator A as the source of one of the operands and also for the destination operand. The disadvantage of the resulting l-address instruction is that a larger number of operations are required to make up for the lack of generality. For example on the PDP-11, the single instruction ADD x , Y adds the contents of location X to location Y and stores the result in location Y. For machines that use a single accumulator for these arithmetic operations, the following three instructions would have to be performed : LDA X : load contents of memory location X into accumulator ADD Y : add contents of memory location Y to accumulator store result at location Y STA Y : This not only makes programming more tedious but leads to increased storage and execution times for a given task. Most machines use a mixture of instruction formats, the most common being l-address and 2-address instructions. Each of the address fields in an instruction contains information about the location of the operand but is not necessarily the actual address. The different ways of specifying the operand addresses are known as addressing modes and, when taken together with the range of operations available in a particular microprocessor, will to a great extent determine its power and range of applications. The most commonly used addressing modes are as follows: (i) Immediate. Here the address field contains the operand itself and this mode is normally used for loading constants or initial values of variables into registers or memory locations. The magnitude of the numbers represented is limited by the length of the field. (ii) Direct. In this case the address field contains the actual address of the operand. The maximum directly addressable memory depends on the field length and is 256 for 8 bits and 64 k for 16 bits.

MICROPROCESSORS AND THEIR USE IN PHYSICS

69

(iii) Indirect. The field contains the address of a memory location (or the name of a register) the contents of which is the address of the operand. Often a designer wishes to keep the total length of the instruction short so that the address field is limited and cannot directly address the whole of the memory space. The limited address field is then used to specify a register or a memory location that is long enough to be capable of addressing the whole of memory (in 8 bit machines two successive words may be concatenated to store the address). This mode is also useful when programs have to be relocated in memory. If direct addressing were used, then all instructions referring to a given operand would have to be altered. With indirect addressing, a table would be constructed that suitably modifies the operand address specified in the memory location (or register) defined by the address field. The program itself would not have to be altered. Very often one wants to operate successively on sequential elements of a table of operands. In order to simplify this procedure many machines provide facilities for automatically stepping through such a table via one of the machine registers. The address of the first operand in the table is placed in the register and operated on by an instruction using the indirect addressing mode. The address in the register is then automatically incremented (or decremented) so that it contains the address pointing to the next operand in the table. This form of indirect addressing is known as the auto increment (decrement) mode. (iv) Indexed. In this mode the address field contains a number that is summed with the contents of a specified register (sometimes a special “index” or “modifier” register) to form the address of the operand. This mode is particularly effective when the same sequence of instructions have to be applied to different sets of operands (say data values). The index register is set to point to the first set of operands and after the completion of the calculation is reset to point to the second set so that during the subsequent calculations addresses corresponding to the second set of data will be generated. (v) Relative. Here, instead of an absolute address, the address field specifies the displacement from a base address, which is normally that contained in the program counter register. This mode is useful for writing code that is independent of the actual position it is stored in memory since the location referenced is always defined relative to the PC. When instructions are relocated in memory, the operands are moved by the same amount. Some machines allow mixed addressing modes so that, for example, the two source operands may be addressed using different modes. It should also be noted that different manufacturers use slightly different nomenclature and that the individual machine manuals should be consulted for precise details of addressing modes in a particular case.

70

A N T H O N Y J. DAVIES

The number and type of operators specified in the operator field will depend on the architecture and application the designer had in mind. Binary operators will require two source operands while unary operators will require only one; both have to specify a destination operand. The most commonly met operators are as follows: Binary operators : Arithmetic

Boolean

add, subtract multiply, divide

exclusive OR

A N D , OR

Control compare

Unary operators : shift, increment, decrement, negate, complement, test, clear move.

E . The Processor-Memory Switch 1. Size and Complexity of’ the Switch

As pointed out by Aspinall (1977) the system shown in Fig. 14 may be considered as having three components-the microprocessor, memory (and image memory defining various input and output peripherals), and a switch linking the processor, memory, and peripherals. For a full discussion of the processor-memory switch, the reader is referred to the chapter on Comparison of Devices: The Processor-Memory Switch,” in Aspinall and Dagless (1977) but we here summarize the main features that need to be considered when selecting a microprocessor. The size and complexity of the switch is determined predominantly by packaging problems associated with the number of pins it is economical to produce on an integrated circuit package. If separate routes are used for addressing and transferring data to and from memory, then a large number of pins will be required. The address must be sent from processor to memory to select the memory location (or register) required, but since a data transfer can only be in one direction, the data bus can be a bidirectional route that halves the number of pins. When the number of pins is critical, then a single bidirectional route can be used for addressing and data transfer as in Fig. 16. In order to transfer data to or from memory, the address must first be set on the buffer, followed by a processor cycle to transfer the data. The total number of processor cycles needed to effect a transfer will depend upon the word length of the processor and the total memory size. For example, an 8-bit processor having 64 kbytes of addressable memory will need two cycles to generate the 16-bit address and one further cycle to transfer the data. A 16-bit processor would only require two cycles. “

MICROPROCESSORS AND THEIR USE IN PHYSICS

PROCESSOR

I

ADDRESS REGISTER

SWITCH

MEMORY

71

(F’

I \

/

\

\

/

DATA

I

FIG.16. Processor-memory switch : single bidirectional route (Aspinall and Dagless, 1977).

In addition to conventional memory, the total addressable memory may contain image memory through which the processor may communicate with external peripheral devices. Transfer of data from the processor requires a simple MOVE instruction that passes the data from a register within the processor to the distant destination register (defined by a unique specified memory address) within the device. Normally the device will also contain separate status and command registers that enable the processor to determine the current state of the device and to control its operation (Fig. 17). Since the total addressable memory is usually very large (typically 64 kbyte), it is possible to allocate several hundred (or even thousand) locations to image memory, which is ample to deal with all situations likely to be met in practice.

2. Direct Memory Access ( D M A ) An important factor in a microprocessor is the time to access data and instructions in memory. Most processors will have allowed for a reasonable access time within their internal timing but when using image memory (or indeed slow speed conventional memory), it is highly desirable for the processor to have a pause facility that enables it to wait for the access to take place. The Intel 8080, for example, will enter a WAIT state until the memory

72

ANTHONY J. DAVIES

DATA FROM DEVICE STATUS SIGNALS FROM DEVICE COMMAND TO DEVICE

WRITE TO MEMORY

FIG. 17. Image memory of input device (Aspinall and Dagless, 1977).

responds indicating that the data are available. If the processor does not contain the pause facility, then intermediate buffer registers must be used. When particularly high-speed transfer is desired between memory and peripheral devices, the switch may allow the peripheral to have direct access to the memory when required without processor control. A DMA controller is therefore provided that is able to transfer data directly to or from memory along the bus highway (Fig. 18). At the beginning of the DMA transfer the amount of data to be transmitted is specified together with the start and finish addresses. The DMA controller then requests control of the bus in order to carry out the transfer. Although on large systems the DMA controller may interleave with the processor by cycle stealing,” on most microprocessors the processor is idle while the transfer occurs. “

I

1

A

FIG.18. Typical bus highway system with DMA controller for a processor with a bidirectional data bus.

MICROPROCESSORS AND THEIR USE IN PHYSICS

13

3. Interrupts In many cases external devices require the processor to respond within a certain critical time and thus a signal line is provided that enables the peripheral to “interrupt the processor. The latter suspends the program presently being executed, stores the contents of all its central registers in a reserved part of memory (so that the program can be resumed when required) and begins a new program to service the interrupt. There are three types of interrupt. The simple interrupt merely tells the processor that a single external device requires servicing. When more than one device is present, the processor must identify the device by examining their status registers in turn to see which has an interrupt bit set. Alternatively, on some processors (such as the Intel 8080) the processor acknowledges the interrupt and the device identifies itself on the data bus during the instruction fetch part of the interrupt cycle. During the interrupt routine it is normally desirable to disable the interrupt signal line to the processor so that all other interrupting devices are ignored. The uector interrupt specifies which of the several external devices requires attention by means of a unique vector address that specifies the service routine appropriate to that device and, finally, a priority interrupt not only specifies which device is interrupting but also defines its priority relative to other devices so that multilevel interrupts are possible. In addition to maskable interrupts many processors include a nonmaskable interrupt for dealing with very urgent events such as power failure. In general each device will require a different interrupt service routine. It may happen that a low priority device may require a long interrupt routine that can be much longer than the critical response time of a higher priority device. In order to avoid loss of data, it is necessary that the low priority routine should enable the interrupt signal very early so that higher priority devices may in turn interrupt it as if it were a normal program. The situation may arise where the main program and several interrupt routines are suspended by an active routine servicing a high priority device. The housekeeping routines needed to keep track of the status of each routine when interrupted can add significantly to the time required to service each interrupt although certain hardware features can be incorporated into the design to minimise these overheads. For example, some manufacturers have improved performance in interrupt handling by having two or more banks of identical registers in parallel. When an interrupt occurs control is transferred to one of the other banks, thus eliminating the need to save data in memory. In theory the various interrupt routines can be treated as independent of each other so that the interrupt mechanism is transparent to the user. It can ”

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ANTHONY J. DAVIES

be very difficult, however, to ensure that the routines d o not corrupt each other and that all devices are serviced within their critical response times. 4. Polling As mentioned above a general peripheral interface will consist of a data register, a command regster, and a status register. Flag bits in the status register indicate when the device is ready to receive or send data. Instead of using the interrupt facility, therefore, these flag bits may be interrogated by the main program to see whether a device requires servicing or is ready to send or receive data. A considerable amount of time may be lost in waiting for the required flags to be set, however, and thus when a number of peripherals have to be serviced, it is possible to interrogate or “poll” their status registers at intervals, making sure that the maximum time that can elapse between successive polling of a given device is short enough to ensure that no data are lost. A typical timing diagram is shown in Fig. 19.

’

-t,4 I

I

El

Device 2

I

1

i-j

‘tz-

-T-

FIG. 19. Timing diagram for a polling system

Suppose devices 1 and 2 are input or output devices having service routines B and C that require maximum times t , and t Z , respectively, to transfer the data. If the main program is divided into segments that take a maximum time t o to execute, then T = to + t l + t , must be less than the critical response time of the devices. Due to the fact that in general the external devices will operate asynchronously with a long period between successive operations, very often the sections B and C will d o nothing, except to test to see whether the device requires servicing, before proceeding to the next stage in the cycle. If sections A, B, and C share common registers in the processor, then it will be necessary to incorporate housekeeping routines that preserve and restore the contents and this can introduce considerable overheads. In many microprocessor applications involving manipulation of data with little computation, a polling scheme is perfectly adequate and allowance can be made for the response times of the various devices.

MICROPROCESSORS AND THEIR USE IN PHYSICS

15

Both polling and interrupts are needed because the processor is called upon to perform more than one simultaneous task. With the ever-decreasing cost of microprocessors, however, many of these tasks would be performed by dedicated processors so that the processing would become distributed, i.e., associated with a particular piece of hardware. This is the type of computer system that will increasingly be found in the future. IV. MEMORY AND PERIPHERAL DEVICES A. Main Direct-Access Memory 1. Read and Write Random Access Memory ( R A M )

The amount of fast direct-access memory required by a system can vary enormously. When using a minicomputer it is not uncommon to find systems with 64 kbytes or more of memory, while in a dedicated control system as little as 1 kbyte may be required. The traditional form of fast memory is the ferrite core. This has the very important advantage that it is nonvolatile, that is, information written on it is preserved when power to the machine is switched off. This can be very important if there is only a slow device for inputting information (such as the paper tape reader on a teletype), when a great deal of time and effort can be wasted reading in programs and data. Although, due to its reliability and nonvolatility, core still has a foothold in the minicomputer market, large machines are now served almost universally by faster and smaller semiconductor devices consuming less power than core. Similarly in the microprocessor field semiconductor memory is almost certain to dominate. The first main type of semiconductor memory is “read and write” random access memory (RAM) that can be used as a direct replacement for core but which, in general, is volatile so that its contents must be refreshed every 2 msec or so. Thus, unless one has back-up battery power supplies, any programs or information must be reloaded every time the computer is switched on. With the decreasing power needed by new devices (in particular those using CMOS technology), battery supplies can be used to preserve memory contents for periods up to several weeks. Refreshed (or “dynamic”) RAM memory is rapidly being superseded by “static” RAM which, although volatile, does not need to be refreshed, resulting in more reliable operation since the refresh circuitry is no longer needed. In bipolar and static RAM semiconductor memories, the basic memory

ANTHONY J. DAVIES

76

-

2

-

-

cell uses a transistor bistable to specify the logic state. Figure 20 shows a single MOS static RAM cell that consists of a bistable cross-coupled FLIPFLOP circuit plus the gating network. The number of devices is considerably less in dynamic MOS memories where the parasitic gate-to-substrate capacitance is used to store information and this leads to a greater density of storage cells on a chip (Fig. 21). Refresh circuitry is needed to compensate for the charge leaking from the storage capacitor. The basic memory cells are arranged in an addressable matrix, and any individual cell can be accessed by applying suitable column and row addresses-the access time for each cell being approximately the same. The Read select

I

W r i t e select

Write

data

-

-L

Re’ad data

FIG.21. Basic dynamic MOS RAM memory cell

77

MICROPROCESSORS AND THEIR USE IN PHYSICS

memory cells may be latched or unlatched. In latched memories the output data are valid as long as the latch signal is true and are thus independent of the state of the processor. For very high speeds such as is required when storing data in a buffer or cache memory, bipolar random access memories are usually used. With better isolation techniques TTL and ECL memories can operate at 10 nsec or less for 1 kbit. For access times of the order of 50 nsec static TTL or Schottky TTL can be used and the latter has the important advantage of simple interfacing with standard TTL devices. Power dissipation is typically about 0.5 mW/bit. Texas Instruments has made 12L bipolar devices with 75 nsec access time for 4 kbit and power dissipation of 120 pW/bit (in addition, only a single 5-V power supply is needed). Present day fast MOS memories usually require more complex interface and clock circuits than bipolar and this may degrade actual memory-system performance by a considerable amount ( > 50%). Current developments in MOS are toward more standardized packaging and limiting power requirements to a single 5 V supply. Nevertheless, low access-time devices are now available, typically 70-80 nsec for static NMOS RAM and CMOS on sapphire. The rapid development in lithographic techniques has led to a decrease in cell dimensions and Intel produce devices with channel lengths of 4 pm, gate-oxide thickness less than 100 nm, arsenic-doped junctions below 1 pm, and access times of about 45 nsec. American Microsystems using VMOS technology have built a 1024-bit static RAM requiring a single 5 V supply and having 45 nsec access time likely to be reduced to about 30 nsec. 2. Read-only Memory ( R O M ) The second type of random-access semiconductor memory is readonly” memory or ROM, which is used to store information permanently. ROM is nonvolatile but cannot be altered during the operation of the computer. When produced in large volumes they can be programmed by the manufacturer using a mask during fabrication when the cost can be as low as 0.05 cents/bit. The individual memory cell positions are defined by row and column selection lines, and to encode a 1-bit, a transistor is implemented at that particular cell location; the absence of a transistor encodes a 0 bit. In many applications and in development work, only a small number of ROMs may be required and the high initial costs and delays involved with mask-programmable ROMs are undesirable. This led to the development of field programmable devices such as the fusible link bipolar PROM. This is essentially a memory matrix in which each cell consists of a transistor or “

78

ANTHONY J. DAVIES

diode together with a fuse or “fusible link” in series with one of the electrodes. Application of an appropriately high voltage to a cell that is to represent a 1 bit causes the link to break while those cells with unblown links represent 0 bits. Although fast (access times 50 nsec), the disadvantage of the fusible link PROM is that its programming is permanent so that their use can be uneconomical in development work where a program may be discarded after only a few runs. 4 s a consequence, erasable EPROMs were developed based on the FAMOS process described previously in Section II.B.l. Data may be written electrically and is represented by the presence or absence of stored charge in the floating-gate electrode. Reprogramming is achieved by erasing the device by exposure to ultraviolet light and rewriting the complete memory array. Selective reprogramming of specific memory locations is not possible. Access speeds are comparable with other MOS devices, 450 nsec being typical. An alternative to the EPROM is the electrically erasable and reprogrammable ROM (or EAROM), which is erased by applying a high voltage (230 V) to the device’s reprogramming pins. EAROMs either use a modification of the FAMOS cell or trap charge in an oxide-nitride interface beneath the metal gate electrode of a transistor. These devices are rather slow, however, with read times of 2 4 psec and erase times 100 msec for the nitride devices. Newer devices such as those produced by General Instrument’s Microelectronics (GIM) division may, however, be selectively erased and rewritten and also offer improved access times 5 1 psec. N

-

B. Bulk Storage Many devices are available for the bulk storage of programs and data. Most of these were developed for use in minicomputer systems and hence are expensive compared with the cost of a microprocessor. Indeed most manufacturers earn over ten times the value of the microprocessor from the sale of supporting component parts. Where it is necessary to access information in a random manner, the magnetic disk cartridge is the standard backing store on most minicomputers. Typically these disks have a capacity of 2.5 Mbytes, an average access time of 70 msec and transfer rates of 180 kbytes/sec. They are ideal for storing operating systems and programs that need to be rapidly switched in and out of the main store. Each disk cartridge costs $100, however, and a typical single drive with controller is about $lO,OOO. In most applications associated with microprocessors the fast transfer rate of the cartridge disk is not essential and thus the “floppy disk” is an ideal alternative. This is a flexible disk of 7.74 in. diameter made of Mylar

MICROPROCESSORS AND THEIR USE IN PHYSICS

79

coated with oxide and normally designed for recording data on one side only. The floppy disk was originally developed by IBM and the IBM recording standard has been adopted as standard by many manufacturers. IBMformatted disks are divided into 77 tracks each consisting of 26 sectors. The individual sectors contain 128 bytes that include a blank field, an address field, a data field of 80 bytes, and a check-bit field. Thus, each diskette has about 243 kbytes capacity with an access time 290 msec and a transfer rate 30 kbytes/sec. In order to increase the diskette capacity to nearer the theoretical maximum of 400 kbytes, many users prefer to use their own formats but this is, of course, at the expense of compatibility. Hardware sectoring is also used by some manufacturers and here a hole in the disk is used to indicate the start of a sector by a photoelectric pulse as the hole passes between a light source and a detector. Most disks have 32 sector holes allowing 32, 16, 8, 4, 2, or 1 sectors for each track. Recent months have seen the introduction of double density floppy disks and also two-sided recording where both sides of the disk are coated and each side is in contact with its own read/write head. Typically a dual drive floppy disk system costs about $3000 and each diskette about $5. The demands of the low end of the market has also led to the introduction of small drives or “minifloppys,” which use small size diskettes having a total capacity of about 110 kbytes (90 kbytes when formatted) on 35 tracks. Access time is about twice that of the conventional floppy drive but a one-off drive costs less than $400 and a complete minifloppy and controller subsystem can be obtained for about $600 in kit form. Where data may be accessed in a serial manner and fast access time is not critical, magnetic tape cassettes or cartridges may be used. Cassettes are relatively slow (- 560 bytes/sec writing and reading rate) and have a smaller capacity than the 3M-type cartridge. The latter has 4 tracks per tape and a transfer rate of 5 kbytes/sec, the total capacity being 2 Mbytes compared with 92 kbytes for a cassette. Once again the low end of the market and, in particular, the hobbyist has created a demand for low cost tape storage and several manufacturers have produced interfaces that enable information to be stored on an ordinary domestic audio tape recorder. These, however, d o not have the reliability and flexibility of digitally controlled recorders. In the next few years new forms of bulk storage are likely to become available using charge-coupled devices (CCD) or magnetic bubble memories. Slower than most RAMS, these fill the gap between MOS and magnetic disk and tape. The cost per bit (0.2 cents) is two orders of magnitude greater than mass magnetic storage but increased density should lead to a projected cost of 0.05 cents/bit for bubble devices by 1979. When small amounts of storage capacity are required, CCDs and bubble

-

-

80

ANTHONY J. DAVIES

chips are much more competitive (for example the minifloppy disks now cost around 0.06 cents/bit), so that they will start to penetrate the market in the very near future.

C . Input and Output Devices Despite its slow operating speed and unreliability, the most common device for inputting and outputting information is still the faithful teletype. It is still the only device that has a keyboard, can read and punch paper tape, can print results in permanent form, and costs less than $1500. They are now rapidly being superseded by cathode ray display terminals that are capable of much higher operating speeds (up to 960 characters/sec as opposed to 10 characters/sec), but which have the disadvantage of not producing a permanent copy of any information output to them. A fast paper tape reader is a useful input device on any system although the recent trend has been away from paper tape and towards an entirely floppy disk-based configuration. With disk-operating software, a typical editing and assembling session taking, say, up to three hours on a 10 character/sec teletype using paper tape software, can be completed in 5 min. With a cassette or cartridge based system it might take 20 mins to half an hour. In designing a system, too often little attention is given to the way in which results are presented. Almost invariably the scientist,’and in particular the physicist, will want to express these sooner or later in graphical or pictorial form. Instead of leaving a teletype to clatter away for hours producing results that are then laboriously plotted by hand, it is far better to consider incorporating a graphical display terminal such as the Tektronix 4012 (based on a storage cathode ray oscilloscope) or a mechanical plotter. In its simplest form the plotter could be an X-Y recorder with pen up/down control driven by a suitable interface incorporating digital/analog converters and pen control logic lines. Much more versatility and accuracy is given by a digital plotter such as the Tektronix 4662 or the Hewlett Packard 9862A. The Tektronix plotter, for example, can plot up to 10 vectors per second, and has hardware character generation, automatic scaling and rotation, these facilities being provided by a built in microprocessor. The graphical presentation of results also has obvious advantages in the teaching field (Fig. 22). In some cases it is desirable to be able to vary the displayed picture dynamically. For example, if one has stored a complete waveform, then it might be desirable to scan through this using a refreshed (as opposed to a storage) CRT, which can show any desired part of the trace. In the past refreshed graphic displays have been very expensive, but

MICROPROCESSORS AND THEIR USE IN PHYSICS

81

FIG.22. Simulation of the build-up of a diffraction pattern produced by photons passing through a narrow slit. The output was generated on a Tektronix 4012 storage display terminal (Brissenden and Davies, 1975).

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A N T H O N Y J. DAVIES

commercially produced vector generators such as the Sigma Electronics QVEC (Wadbrook, 1975) have brought low cost graphics within the reach of a much wider circle of users. The QVEC can display upward of 2000 vectors at flicker free rates (normally 50 or 60 Hz) and also has a hardware character generator that takes an average of 7 p e c to produce an alphanumeric character. Figure 23, for example, shows a typical display obtained from a multichannel signal averaging system that is used to measure the evoked response in patients. This involves monitoring the electrical activity of the brain in response to various stimuli and the photograph shows a typical visual evoked response; 128 responses are averaged and displayed as a series of 256 vectors. Five channels are shown simultaneously and, as the averaging process takes place, the display shows the random noise reducing and the signal becoming clearer. Various low cost do-it-yourself vector generators based on microprocessors have also been described (for example, Hilford, 1976), but it is easy to underestimate the development time needed to produce a practical implementation of these designs.

FIG.23. Five channel, signal averaged display of the electrical activity of the brain in response to a visual signal.

MICROPROCESSORS A N D THEIR USE I N PHYSICS

83

V. SOFTWARE A . Assemblers

When using large-scale computing systems, the scientist is almost certain to write his programs in some high-level language such as FORTRAN, ALGOL, BASIC, or m/1, which is then translated into machine language by a compiler or interpreter. The machine language consists of a sequence of binary words or instructions defining the task that is to be performed by the machine. When microprocessors first appeared, the programmer had to write his programs directly in this form and this was a time-consuming process prone to considerable errors even though the task was simplified somewhat by the ability to input information in octal (radix 8) or hexadecimal (radix 16) format rather than directly in binary (see Table 111). TABLE 111 COMPARISON OF BINARY, OCTAL, HEXADECIMAL, AND DECIMAL NUMBERS Binary

Octal

Hexadecimal

Decimal

oo00

0

ooO1 0010 001 1 0100 0101 0110 0111 loo0 1001 1010 1011

1 2

0 1 2 3 4

0 1 2 3 4

5 6 7 8

5 6 7 8

3 4 5 6 7

10 11 12 13

9 A B

10 11

9

1100

14

C

12

1101 1110 1111

15 16 17

D E F

14

loo00

20

10

13 15 16

From the table we see that octal numbers correspond to groups of three binary bits and hexadecimal to groups of four. Thus, although octal has traditionally been more popular, hexadecimal is being increasingly used due to the preponderance of 4, 8, and 16 bit machines. Programming has now been made considerably simpler by assembly languages that are available for all microprocessors. These languages allow

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A N T H O N Y J. DAVIES

symbolic (mnemonic) representation of bit patterns representing data, addresses, and instructions. For example, the mnemonics LD, ST, and MOV could be used for the instructions load, store, and move. In the DEC PAL language MOV A B means “move the contents of location A to location B.” The assembly language must be translated into the equivalent binary machine code by an assembler that also checks for certain types of programming error. The assembler is itself a program that either can be run on the microprocessor itself or, more commonly, on a suitable minicomputer or large-scale machine. This is because the process of translation requires a high-speed input/output device and reasonable amounts of main and backing store (such as floppy disks) to keep the intermediate code during the several passes of the assembler. When the assembly is carried out on a larger machine, a simulator ” program is also normally provided so that program execution can be conveniently checked and debugged. Real-time performance of the program could, of course, only be verified by transferring the object machine code to the microprocessor system. In their enthusiasm to get started early workers found themselves with a minimal microprocessor system plus a teletype. In this type of system the assembler program alone can take 30 min to load on the teletype paper tape reader. The source program is input twice and an assembler listing produced. If any errors are found the source tape has to be corrected (which may involve loading an editor program) and the process repeated. Finally when no errors are present on assembly, a third pass of the source tape produces the binary object tape that must be loaded, tested, and debugged. If any errors are found, then the whole procedure starts once again. No wonder that earlier enthusiasm often died a quick death and there was a strong demand for powerful and flexible development systems. Some of the problems have been overcome recently by providing resident software, such as assemblers, editors, and loaders, on read only memory when they are instantly available and input/output is reduced to solely inputting the source tape. Most installations, however, prefer to have at least one powerful development system (involving considerable capital investment), the software for a given application being developed on this and then transferred to the minimal microprocessor system necessary for the given application. Assemblers produced for running on a large-scale or minicomputer system are known as cross assemblers and are normally writ ten^ in a high-level language such as FORTRAN in order to make them easily transportable from one machine to another. Assembly language statements typically have four fields “

LABEL FIELD

OPERATION FIELD

OPERAND FIELD

COMMENT FIELD

MICROPROCESSORS A N D THEIR USE IN PHYSICS

85

and are either symbolic machine instructions, directions to the assembler program, or comment statements that are simply listed but not translated. All assemblers allow a label to be attached to an instruction so that symbolic names may be given to data and program segments that may be then referenced by name from elsewhere in the program. The operation or op-code field specifies the operation to be performed or is an assembler directive (assemblers allow the programmer to insert assembly directives or pseudo-operations in the program code that control the operation of the assembler but do not generate any code). The operand field specifies the addresses of the operands to be used in the operation while the comment field has no effect on the translation but is used for documentation purposes in the program listing. Some assemblers accept free format with the various fields being separated by delimiters, while others (particularly card-based ones) use a fixed format with the various fields having to occupy particular columns. Generally column-independent fields are more flexible and give the programmer complete control over the format of his source program. In assessing the power and efficiency of an assembly language Watson (1976) suggests that the following features are highly desirable: (a) The listing of the source and object programs and system messages should be clear and easy to understand. The Motorola 6800 assembler, for example, automatically aligns the fields in the source program listing. It is also desirable to be able to control the position of the listing on the printer page and to include a heading at the top of each page. (b) The programmer should be able to define and manipulate meaningful symbols. The mnemonic symbols representing data, addresses, or instructions are usually restricted to six or eight characters and must begin with an alphanumeric or special character. Despite these restrictions the options available are usually sufficient for the programmer to define recognizable easily remembered symbols. ( c ) Constants should be able to be specified in a form convenient to the programmer (for example decimal, hexadecimal, octal, binary, or ASCII) and the way of specifying the base should be clear and easily remembered. The assembler should perform all the conversions to and from binary. On the Intel 8080 and Motorola 6800 the following nomenclature is used:

Hexadecimal Octal Decimal Binary ASCII

Constant 121, 128 121, 1012 letter Y

Intel 8080 12H 12Q or 124) 12 or 12D lOlB ‘y’

Motorola 6800 $12 @ 12 12 %lo1 ‘Y

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A N T H O N Y J. DAVIES

Here we see that the Intel indicators are very straight forward while the Motorola hex, octal, and binary indicators are arbitrary and can lead to confusion. (d) Good error diagnostics should be provided. Any assembler should flag any source program statements that are syntactically incorrect but should not abort at the first error. They should continue the program translation as far as possible and give explicit clear error messages. Together with good error diagnosis this can considerably reduce program debugging time. Current assemblers vary greatly in their diagnostic ability but, as a general rule, cross assemblers provide more extensive and explicit debugging aids. (e) A MACRO facility should be available. Very often programs will include sequences of instructions that have to be executed at several different points. These sequences can be executed by a subroutine call where the program jumps to the given sequence and returns to the calling point after execution. The code need only be written out once but there is an overhead in execution time for each subroutine call. This overhead can be avoided at the expense of memory storage requirements by writing out the sequence each time it is required but this process can be very tedious. If a MACRO processing facility is provided, however, the programmer defines a MACRO by associating a name with the sequence of instructions that are only written out once. Subsequently, whenever this name appears in the operator field the assembler substitutes the instruction sequence for the statement. Very often the constants or variables in the instruction sequence may have different values at different points in the program and in this case a parametrized MACRO facility is extremely useful. Here the MACRO definition consists of a template with formal dummy parameters. In addition to the name, each MACRO call then includes the actual parameters that are substituted for the dummy parameters by the assembler. Example of a MACRO Processor MACRO definition MACRO

SWAP

x, z MOV Y, x MOV z, Y

MOV

template

X, y, Z

Source program _

- -

L1:

__

_

SWAP _ _

- -~_

_

-~_

_ . .

A, B, c

L1:

- _ - -

MOV

L2: -

SWAP _

~~

D, E , F -

_

A, C B, A

MOV

MOV

~~

.

Output text

-~ -

L2: MOV MOV

c, B _~

-

D. F E, D F, D

MOV

.~~ _

MICROPROCESSORS A N D THEIR USE IN PHYSICS

87

The MACRO facility can be a great advantage since program development time is greatly reduced and standard functions can be defined in a library available to all users. Very few assemblers have a MACRO facility at present. Notable exceptions are the Intel 8080, DEC LSI-11, and Fairchild’s F8 cross assembler. (f) The assembler should be able to output relocatable object programs that can be loaded into any suitable part of memory using a relocating loader that suitably modifies the object program addresses. (g) A linking editor should be available so that symbols may be defined in one program and referenced in another independently assembled program. The various commercial assemblers provide these facilities in various degrees and when choosing a microprocessor, the user must check whether the available features meet his requirements. Likely to become increasingly popular are incremental assemblers that translate each instruction as it is typed in, any syntactic errors usually being detected immediately.

B. High-hue1 Languages Since assembly code is a mnemonic form of the machine language, the programmer has to know details of the hardware of the processor and peripheral equipment. This means that he is able to make use of the special features of the machine and, provided he has the experience, can produce an efficient program both as regards execution time and storage requirements. Unfortunately the time to produce an error-free program increases rapidly with increasing program length especially if the programmer is inexperienced. Where program efficiency is not an important criterion, it may well be worth considering the use of a high-level language, the most popular of which are BASIC, FORTRAN, PASCAL, or a derivative of P L / l . Now a high-level language may be regarded as defining a particular type of (abstract) processor just as the machine language of a microprocessor defines its hardware and vice versa. Hence, if we have a program written in a high-level language we have the choice of translating it to machine code using a “compiler” or the hardware has to be modified to enable it to ‘‘ understand the language. This latter process is brought about by writing an “interpreter,” which is a program stored in the hardware designed to enable the system to accept the language as its machine language. The disadvantage of this approach is that the interpreting program is permanently resident in memory and that the performance of the processor is inevitably reduced. An interpreter would have, of course, to be based on the actual system ”

88

ANTHONY J. DAVIES

whereas a compiler could be a cross compiler run on a large-scale development system. Programs written in BASIC are normally interpreted, whereas FORTRAN and p L / l are compiled into machine code. The University of Strathclyde have developed a high-level language (STAB), which is compiled into an abstract machine code (STAB-12) and is then interpreted on the actual processor. Since almost invariably the microprocessor is concerned with operation in real time, the high-level languages already mentioned may not be suitable due to their lack of efficiency-they produce compiled machine language programs that occupy more store and take much longer to perform a given task than the corresponding program written directly in machine code. This can be overcome to a large extent by modifying the language to allow machine code segments to be embedded in the high-level language so that those parts of the program that are critical as regard speed or are hardwaredependent can be dealt with efficiently (this is possible, for example in STAB, BCPL, and ~ ~ 3 6 0 ) . In addition, high-level languages such as CORAL 66, R T L / ~ ,and PL/M have been specially designed for such applications and are becoming increasingly popular. GEC Semiconductors, for example, have released a resident CORAL 66 compiler, R C C S O , for Intel’s 8080, which has all the standard features of the officially defined CORAL 66 together with many features specially appropriate to microcomputer work. Other manufacturers are shortly expected to announce resident compilers for FORTRAN and subsets of pL/1. The ultimate aim of all program development methods is normally the preparation and fabrication of suitably programmed ROM. Whether this is done using a cross assembler (or cross compiler) on an in-house or bureau computer or on the host microprocessor will depend on the relative costs involved and on the proficiency and experience of the programmer. The present trend is toward using high-level languages on in-house microcomputer development systems based on the relevant microprocessor. The software can be developed and tested on this system, written into ROM and then transferred to the actual system. Despite recent advances, microprocessor hardware is far ahead of the software and this is likely to be the situation for several years to come. VI. LINKING THE EXPERIMENT TO THE MICROPROCESSOR A . Measuring Instruments and Analog-to-Digital Converters

Most experiments in Physics will have some instruments producing results directly in digital form and, in addition, a number of transducers outputting analog voltages that have to be converted into a suitable digital representation using the appropriate analog-to-digital (A/D) converter. The

MICROPROCESSORS AND THEIR USE IN PHYSICS

89

problem then arises as to what is the most efficient and cost-effectivemeans of linking the various instruments and converters to the microprocessor(s) which, besides collecting and analyzing data, may also have the capability of outputting digital and analog information to control some part of the experiment. Many of the instruments that the physicist will meet (for example frequency synthesizers, counters, digital voltmeters, etc.) will themselves contain microprocessors, the latter having almost universally replaced hardwired logic. Their considerable processing power is also often made use of in, for example,.digital processing oscilloscopes. One of the first in the field, the Model 1722A from Hewlett Packard (Fig. 24) provides LED readout of time intervals or frequency and can also measure peak or instantaneous voltages. Other oscilloscopes can calculate rise times, integrate, differentiate, and even have built in programs for power spectrum analysis.

FIG.24. Hewlett Packard 1722A oscilloscope with built-in microprocessor that gives LED readout of time intervals and peak or instantaneous voltages. Period of displayed waveform is calculated and displayed on LED readout in window at right, as in HP pocket calculators: 0.878 -6, i.e., 0.878 x sec or 0.878 psec.

90

ANTHONY J. DAVIES

In most of these instruments the user need not be aware that a microprocessor is involved and can treat it as a black box, only being concerned with such features as noise immunity, power requirements, frequency response, and so on. The choice of A/D converter is determined by the accuracy and speed required to adequately represent the analog output of the particular transducer being used. There are basically two types of A/D converter: (a) integrating converters that are accurate but slow (1-50 msec typical conversion time), and (b) successive approximation converters that are less accurate but have conversion times typically in the range 1-50 psec (see Table IV). TABLE IV

PERFORMANCE OF AID CONVERTERS Range of conversion times Type of converter

8 bits

10 bits

12 bits

Integrating Successive approximation

0.3-20 msec 0.8-30 psec

1-30 msec 1-40 psec

540 rnsec 2-50 psec

16 bits

-- 250 400

msec psec

An integrating converter gives a time average of the input voltage over a fixed time interval and so does not require a sample and hold circuit. The most widely used version employs a dual slope technique using the circuit shown in Fig. 25. Initially the input is grounded so that any offset errors are cancelled out by storing the appropriate error signal on the feedback capacitor. Next, the input voltage is integrated over a fixed number of clock pulses and subsequently the input of the converter is switched to a reference voltage of opposite polarity to the signal. The integrator output thus decreases, and the number of clock pulses counted between the connection of the reference voltage and the time when the integrator output reaches zero gives a digital

-

SWITCH ANALOG INPUT

I NT EG RAT0 R

0

COMPARATOR

b -0

CONTROL LOGIC AND CLOCK

FIG.25. Integrating analog-to-digital converter (Fullagar et al., 1976).

MICROPROCESSORS A N D THEIR USE IN PHYSICS

91

measure of the input voltage. The accuracy is immune to long-term changes in the capacitor and comparator and is only limited by the short-term equality of the clock pulses, which can easily be held to one part in lo6. The fastest integrating A/D converters have conversion times of the order of 0.3 msec, and thus if a faster frequency response is required, successive approximation converters must be employed (Fig. 26). Here the output from a digital-to-analog (D/A) converter is compared with the signal input, starting with the most and proceeding to the least significant bit one at a time. The current bit is set at logic 1 and if the D/A output is less than the input voltage, is left at logic 1, whereas it is set to 0 if the converse is true. ANALOG INPUT VRFF

I

DIGITAL OUTPUT

FIG.26. Successive-approximationanalog-to-digital converter (Fullagar et al., 1976).

There are many sources of error in successive approximation converters the major contributions being from the D/A converter, the comparator, and the voltage reference. Despite this, any well-designed converter should have an accuracy of +tLSB over the full operating temperature range, and response times of the order of a few microseconds are easily attained. When connecting the transducer to the A/D converter, great care should be taken to avoid ground loops and very long cable runs. Wherever possible differential outputs and inputs using screened twisted pair cables should be employed so that common-mode rejection means that a high-accuracy signal will be presented to the sample and hold circuit of the A/D converter. An added refinement is to actively drive the screen at the common-mode voltage of the signal.

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ANTHONY J. DAVIES

B. Interfacing and Transmission Problems 1. Interfacing AID Converters The interface between an A/D converter or measuring instrument and the microprocessor is primarily determined by the distance the data has to be transmitted. For data collection over several hundred yards, serial transmission over twisted pairs to the EIA-RS-232 standard (see Section VI.B.3) is the best choice. Whenever possible, however, especially in the case of high-sampling rates, the converter or instrument should be as near as possible to the microprocessor and use a parallel interface. Many of the more popular microcomputer systems have A/D converters and interface on a single board that plugs directly into the microprocessor bus. Figure 27 shows the Analog Devices RTI-1200 subsystem, which is compatible with the Intel SBC-80/10 and which has 16 differential inputs, a 12 bit A/D converter, and two 12 bit digital/analog outputs.

FIG.27. Analog Devices RTI-1200 subsystem with 16 differential analog inputs, 12 bit A/D converter and two 12 bit digtal/analog outputs.

If a ready-built board suitable for the application is not available, then most microprocessor families provide general purpose programmable interfaces for medium-speed applications and DMA interfaces for very highspeed applications. Let us consider for our present purposes a typical programmable parallel interface (the DEC DR11C) connected to an A/D converter and thence to a number of analog inputs via a multiplexor (Fig. 28).

READY7

INTR A

AOMUX

AOUUX

IOROUTBUFI

05

INTR 0

INTERRUPT CONTROL LOGIC

INTR EN8 A

r l N T R EN0

AODBR (ORINBUFI

I

OATA

00

J

09 00 REGISTER B I T ASSIGNUENT UAP

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7

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I I I

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N L U U L

1

G I

I

N

X

5 ;41

e

R

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I I I

1

I I

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FIG.28. Analog acquisition system with programmable parallel interface (the Digital Equipment Company DRllC).

L

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ANTHONY J. DAVIES

With this interface the loading of the ADMUX register with the appropriate multiplexor line number switches the multiplexor to the appropriate input and also starts the A/D conversion by a pulse on the START CONVERSION line. When conversion is complete, bit 7 of the ADCSR register is set and this bit may be used as a flag which is continuously tested by putting the microprocessor into a WAIT loop. This procedure is simple and satisfactory for successive approximation converters where the instruction times are comparable with the conversion times but can be very inefficient when, for example, slow integrating A/D converters are employed. In these cases it is better to use an interrupt driven interface. In the DR1 lC, for example, bit 6 of the ADCSR register enables interrupts and, when bit 7 of the same register is set following completion of the conversion, a vectored interrupt takes place that is directed at the appropriate service routine. This routine may then initiate the next A/D conversion before proceeding to manipulate the input data and perhaps returning to a main program performing lengthy calculations while awaiting the next interrupt. In general, it is simplest to use successive-approximation converters with a flagged interface when many channels of analog data must be sampled but each channel requires little manipulation of the input data. On the other hand, when only one or two channels involving slow-sampling rates are present and a large number of computations must be carried out for each channel, integrating converters plus an interrupt-driven interface would be more suitable. Typically the execution times involved in servicing the interface and transferring data to a buffer area of store are of the order of 20 psec and it is this time, not the actual conversion times, that determines the input data rate and the latter is typically limited to about 50 kHz. If this rate is too slow, then it is possible to use a DMA interface to enable the converter to feed output directly into memory. Typical data rates attainable will depend upon the microprocessor but will range from 1 to about 3 Mwords/sec. It is important to remember that at this rate the direct access memory will quickly become full so that if a lot of data is to be transferred, the A/D converter will have to be double buffered with the converter filling one buffer while the data in the second is being transferred, for example, to disk. Even with double buffering, however, the maximum rate can be strictly limited. A typical disk drive can store about 6000 readings in one revolution of the disk and this is the optimum buffer size to avoid head movement. The revolution time is about 17 msec so that if the buffer is filled quicker than this, the system will not keep up. To record the very highest speed events converters are available that have conversion rates of up to 250 MHz and these must have their own dedicated high-speed ECL memories. The length of the events will, of course,

MICROPROCESSORS AND THEIR USE IN PHYSICS

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have to be very short due to the finite size of the associated buffer memory. Once data are in this memory, it can be transferred to the main microprocessor memory at a much slower rate.

2. Standard Instrument Interfaces When linking instruments to each other and to external processors, it is desirable, as far as possible, to use an internationally recognized standard. One such standard CAMAC (Abbott, 1975) is very suitable for use in large centers but the initial costs involved in using this system may be too great in small laboratories, particularly in limited applications. A much cheaper alternative and one which is now becoming internationally accepted is the IEEE 488-1975 standard digital interface for programmable instrumentation (this is identical with the new ANSI Standard MC1.l). Most instruments will, in the future, have interfaces conforming with this standard. The Hewlett Packard Interface Bus, which is an implementation of the above standard, has 16 lines (8 data and 8 control) and can accept a maximum of 15 devices with a total path length of about 20 m (Fig. 29). At any one time one device is bus controller and the remaining units may be (a) able to talk (one unit only), (b) able to listen (14 units maximum), or (c) passive. Devices may be divided into four categories: (i) those able to talk, listen, and control; (ii) those able to talk and listen; (iii) those able to listen only; (iv) those able to talk. The eight data lines carry data in bit parallel, byte serial form from the talker to one or more listeners. Three of the control lines effect the transfer of each byte using a handshaking technique, while the remaining five lines ensure an orderly flow in the system. One of these lines is the attention line and during any transmission any other device besides the talker can request attention. The controller then has to handle the request, decide priorities and, perhaps, for example, transfer control to another device. Over short distances the maximum data rate is 1 Mbyte/sec, which falls to about 250-500 kbytes/sec over the full transmission distance. Normally the controller will be a microprocessor, calculator, or minicomputer, and most of the units are dedicated talkers or listeners, so that data collection is then very simple and the IEEE 488-1975 interface is very suitable for measuring instruments. Using a calculator such as the Hewlett Packard 9825A as controller is both cheap and convenient since the associated peripherals (such as floppy disks or magnetic tape cartridges) can be used for program and data storage.

ANTHONY J. DAVIES

96

TALK, LISTEN, AND CONTROL

-DATA -NOT -NOT

-REMOTE

VALID READY FOR DATA DATA ACCEPTED INTERFACE CLEAR ATENTION SERVICE REQUEST ENABLE END-OR-IDENTIFY

FIG.29. Typical system using the Hewlett Packard Interface Bus, which is an implementa tion of the IEEE 488-1975 standard digital interface for programmable instrumentation.

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MICROPROCESSORS AND THEIR USE IN PHYSICS

3. Asynchronous and Synchronous Serial Transmission When linking instruments or peripherals over large distances (greater than about 10 meters), it is usually most convenient to transmit data in serial form over a twisted pair cable rather than in parallel over a multiwire bus. The most commonly used serial link is the EIA-RS-232 standard, which is asynchronous and requires framing information for each character transmitted. The asynchronous format consists of 8 bits of data preceded by a “start” bit and terminated by 1, I$, or 2 stop bits (Fig. 30a). The start bit is logic zero (SPACE) and is defined as a positive voltage between 6 and 12 V whereas the stop bit is logic one (MARK) and is negative voltage between -6 and - 12 V. For current loop connections current flow normally indicates MARK and an absence of current SPACE. START bit

’

START bit

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I - - - - A

STOP l ! Lb i It D a ’ t a l L ’

STOP i l Kb i t ’

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-

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4

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(b)

FIG.30. (a) Asynchronous and (b) synchronous transmission formats.

The leading edge of the start bit is used for synchronization purposes, the receiver then sampling the data in the middle of each bit, thus allowing for small differences in frequency between the transmitter and receiver. At least one stop bit must be present in order that the receiver may synchronize with the next start bit. For high volume and high speed, synchronous transmission is usually preferable. Here instead of adding bits to each character, characters are grouped into “records” with framing (“ SYN”) characters added to each record that can also be used for synchronization purposes. Note that 10n bits are used in transmitting n characters in the asynchronous mode against 8n + 16 in the synchronous mode, which corresponds to 10,000 and 8016 bits, respectively, for transmitting a 1000-character record. For short messages, however, asynchronous transmission is more efficient, 10 as opposed to 24 bits being used to transmit a single character. Both types of interface may be readily implemented using special LSI support circuits such as the UART (universal asynchronous receiver/transmitter), USRT (for synchronous transmission), or USART

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ANTHONY J. DAVIES

(both kinds of data transmission). The UART, for example, is essentially a parallel to series converter when transmitting and a serial to parallel converter when receiving (Fig. 31). Since external clocks are used for timing purposes, any data speed can be accommodated although it will often be convenient to use a standard baud rate (75, 110, 150, 300, 600, 1200, 2400, 4800, and even 9600 bits/sec).

r

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hT R A N S M I7

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clock

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control bus

FIG.31. Serial asynchronous data transfer using UART chips.

The serial link has a number of drawbacks including the need for a fixed baud rate and the need to provide filler characters during any mechanical movements of a peripheral. Nicoud (1976) has suggested a simple means by which the versatility of a serial link can be greatly increased. In his so-called “SIMSER” (SIMple SERial) standard, in addition to the data the synchronizing clock is also transferred between the units (Fig. 32). Notice that the receiver supplies the clock to the transmitter so that if the receiver cannot take in any more data, it can assert the FULL line and stop the transmission thus providing a limited handshaking facility. Most UARTs and microprocessor interfaces are suitable for building a SIMSER interface, and it can be used to provide the maximum data transfer rate making it particularly suitable for linking microprocessors to displays or other microprocessors.

4. Other Interfaces A number of alternative interface standards have been proposed (for example, Nicoud, 1976) but none of these has, as yet, been generally adopted although the MUBUS standardized microprocessor bus (Nicoud, 1975) has

MICROPROCESSORS A N D THEIR USE IN PHYSICS

1/2 UART or6251

TxCP

R x CP i l 6 x i

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R x ROY I F U L L J

---- - - _ _ _ _ _

99

--- ------- -

1

I

R x RDY

FIG.32. SIMple SERial (SIMSER) standard (Nicoud, 1976).

met with some acceptance in industry and universities in Europe (Vuille, 1975; Conte et al., 1976). A very interesting simple interface that does not make use of interrupts or DMA has been proposed by Fisher (1975) and is applicable to those processors whose activities may be suspended during data transfers (e.g.,the Intel 8080 or the Intersil IM6100). Figure 33 shows how a simple external flip-flop can be used with the Intel 8080. Suppose the latter wishes to output some data, then the OUT line first of all clears the flip-flop, which in turn halts the processor and leaves the data available on the data bus. An external device may then read this data and return a DONE signal to raise the READY line and restart the microprocessor that will respond within one cycle time ( - 500 nsec). Allowing for the program execution time, the maximum data rate is 62 kbytes/sec. When inputting data the processor will respond within 500 nsec after the READ signal is raised giving an overall response of about 1 psec.

I n t e l 8080 microprocessor READY

~~~

~

FIG.33. Simple input/output interface making use of a microprocessor READY line.

ANTHONY J. DAVIES

100

Fisher describes the application of this interface to a floppy disk controller that requires only about 20 ICs compared with 40-80 ICs in an interrupt driven structure and 80-100 ICs if DMA is used. VII. TYPICAL APPLICATIONS A. Setting U p the System

Microprocessors have suddenly become very fashionable and it is very tempting for the physicist to think that they are the answer to all his problems in data collection and analysis in experimental physics. Consider, however, a typical traditional data acquisition system shown in Fig. 34. Analogue signals from experiment

ttt

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Analogueldig ital converter

ROM

- 'lit processing-

Disc or magnetlc tape store

Paper tape readerlpunc h CRT display

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t t

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FIG.34. Typical system for on-line collection and analysis of experimental data.

Looking at this system, one realizes that a lot of equipment is involved and if a minicomputer is used, the total cost is likely to be of the order of $25,000,the cost of the CPU and say 32 kbytes of memory being about one fifth of the total. Thus replacing the minicomputer by a microprocessor does not bring a great saving in overall cost. All too often one hears the story of a research worker buying a microprocessor and teletype and then wondering exactly how to use it. He ends up with all the equipment in the diagram at practically the same cost and with a great deal of effort. In deciding whether or not to buy a microprocessor, one must be careful to decide whether or not an existing minicomputer system would do the job more conveniently and cheaply. Due to the large capital involved, in the past the tendency has been to

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link a number of remote experiments to one powerful machine where use may be made of the powerful processing and peripheral devices that are available. With the decreasing cost and increasing power of microprocessors and associated peripherals, in many instances it is now more attractive to distribute the processing power as much as possible among the various experiments only linking to a central machine when, for example, large amounts of computing power, specialized software, or access to a large data base, are required. This decentralization has been considerably facilitated by the development of the low cost peripherals (floppy disks, digital magnetic cassette drives, etc.) mentioned previously. Having satisfied himself that a microprocessor is suitable for his particular application, how does a worker go about choosing a suitable machine? It is perhaps true to say that with the very powerful processors now available, practically any of these will be more than adequate for most applications. The choice then boils down to a matter of convenience. Is there a development system already available for a particular processor and what expertise is there available in the laboratory? Is the software adequate and is there a facility available for programming suitable read-only memory? From experience these points are all too often overlooked. The research worker purchases a cheap microprocessor kit and then spends months of fruitless effort trying to incorporate it into his system. In the author’s opinion, for the experimental physicist, it is essential to have a large-scale development system available with at least floppy disks, fast input/output and preferably the same type of processor that is intended to be used in the experiment. On the software side a good assembler plus editing and debugging facilities are required, possibly together with a microprocessor-orientated high-level language. It is particularly helpful if the prototype microprocessor system can be developed and debugged with the aid of an “in circuit emulation” (ICE) development system such as the Intellec MDS (Kline et al., 1976). This system contains two processors, one a supervisor and the other, the ICE processor, interfaces directly to the prototype system as a direct replacement for the appropriate microprocessor package. In this way the development system debug aids, and software are available in the prototype system and the hardware in the latter can be debugged in its final working environment. Also if a production unit is found to be faulty, the ICE processor can be connected and error diagnostics run on the Intellec MDS. Some in circuit emulation systems are now being developed that can be used in conjunction with a range of processors, thus eliminating the need for a different development system for each type of microprocessor being used. By using different plug-in emulation boards, the Tektronix 8000 Series, for

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ANTHONY J. DAVIES

example, can work with the Intel 8080, the Motorola 6800, Zilog Z80, Texas Instruments 9900, and the Intel 8085 and further additions are expected shortly. This system also has an optional PROM programmer and real time Logic Analyzer Probe (Fig. 35).

FIG.35. Tektronix 8OOO series in-circuit emulation system with PROM programmer and Logic Analyzer Probe.

When building up a prototype microprocessor system, it is possible to buy either individual components or ready-made boards suitable for a particular function (processor, memory, input/output, etc.). Since an appreciable part of the cost of a system is in the printed circuit boards, it is very tempting to take the former course and to attempt to build one’s own system from scratch. Very few laboratories, however, will have the necessary design and fabrication facilities to make this a feasible proposition. A much better alternative is to buy a kit where the components and circuit board are provided ready to assemble at a cost that is usually well below the price of the individual components. These kits come in various shapes and sizes and some include ROM chips with programs to control peripherals and provide editing and debugging facilities. One of the first and most popular kits was

MICROPROCESSORS AND THEIR USE IN PHYSICS

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the MITS Altair 8800 based on the Intel 8080 processor, one of its chief attractions being that BASIC could be used for programming. Despite the enhanced cost most workers will, however, prefer to purchase standard ready-made computer module boards that plug directly into a bus highway. Provided that one has chosen a popular machine, this also enables one to make use of standard interface and applications boards (such as the A/D data acquisition system already mentioned) available from a number of manufacturers.

B. Particular Applications From time to time there will inevitably arise occasions where the choice of microprocessor and peripherals can be critical. This can be due, for example, to a noisy environment, a requirement for high-speed operation or a need for extremely low power consumption, and it is instructive to see how the technology and architecture of the microprocessor can influence the final choice. 1. Fast Switching Contexts

In some applications there is a need for the processor to be able to switch very rapidly between a number of tasks. For example, there may be a number of data inputs that have to be sampled rapidly and that have different service routines. Most microprocessors find this a difficult task to cope with due to the large overheads involved in saving and restoring the contents of the central registers. The Texas Instruments TMS 9900, however, is ideally suited for this purpose. The TMS 9900 is a single chip, 16 bit, NMOS microprocessor that has 69 instructions with five addressing modes and allows operations to be performed on 16 bit words, 8 bit bytes, or any group of bits up to a maximum of 16. The 16 registers in the TMS 9900 are, however, not situated on the CPU chip but are in a block of external memory known as the workspace. A 16 bit register on the chip is used to point to the first of the 16 consecutive memory locations that define the workspace. As Gebler (1976) points out this architecture has one obvious disadvantage: It is obviously slower operating on operands fetched from memory rather than from on-chip registers. On the other hand, this architecture allows very fast switching. In a conventional microprocessor, when an interrupt is received or subroutine called, a sequence of instructions is initiated that stores the current contents of the important registers so that these can be used by the subroutine or interrupt service routine. Furthermore, these values must be restored on returning to the main program.

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On the TMS 9900 on the other hand, the transfer of register contents to memory is not necessary since it is already in memory. All that is needed is to address a new workspace and to save the contents of the P C and status register. This means that the switching time is about 12.6 psec compared with 22 psec for the 6800, 52.5 psec for the 8080, and 106 psec for PACE. Thus, in applications requiring rapid context switching, the TMS 9900 would be an ideal machine and an on-chip multiplier/divider greatly speeds up arithmetic computations. If the number of input channels is limited, then an alternative approach is to use one of the microprocessors that have multiple banks of central registers when each bank may be dedicated to servicing a particular input, and again switching time is very rapid. 2. Low Power Situations When the basic requirement is low-power consumption the obvious technology to use is CMOS. Very few CMOS microprocessors have been made up to the present time and the most popular of these is the 12 bit Intersil IM6100. Incidentally, a 12 bit word is an ideal size for many applications in physics as it gives a resolution of 1 part in 4096 as opposed to 1 part in 256 for the 8 bit machine. The latter often have to use two words for data storage when the accuracy of 1 part in 65,536 is often far greater than is needed. The IM6100 has a single 12 bit bus highway on which addresses, instructions, and data are time multiplexed. It has one maskable interrupt, one nonmaskable interrupt, plus a DMA request line. An important point is that, since all the constituent parts of the system are static, a DMA transfer can be of any length since there is no dynamic memory to be refreshed. As on the Intel 8080 a WAIT signal can extend the C P U cycle to accommodate slow main or image memory. This feature is also very useful in multiprocessor applications. The architecture and instruction set are compatible with the PDP8/E so that a large amount of ready-made software is available. The major feature is, however, its low-power consumption and when running at 5 V with an add execution time of 5 p e c , the CPU draws a maximum 12.5 mW of power. This compares with at least 500 mW for a corresponding NMOS processor. In addition, since the whole system is static, when fast processing is not required the system clock can be slowed down to conserve power even more, the current drain being proportional to the operating frequency. Figure 36 shows a typical application described by Watson (1977). This is an unmanned meteorological station operating off a very limited power

MICROPROCESSORS AND THEIR USE IN PHYSICS

105

---------IM6102 Timer

lM6312 R.O.M.

4kx 12 Maas storage R.A.M. (up to 32k x 12) Field 0

4kx 11 R.A.M.

Field 7

FIG.36. Single microprocessor meteorological station using CMOS technology (Watson, 1977).

source. Various transducers input analog voltages corresponding to temperature, humidity, wind speed, and direction, which are multiplexed into an A/D converter, digitized, and then read by the CPU under the control of the IM6101 parallel interface element. The latter is not a port in the conventional sense but acts as an input/output controller providing access to the bus highway. It can also specify a vector address to which program control is transferred upon receiving an interrupt. The data are stored in RAM together with timing information obtained from the IM6102 real time clock. This system can be accessed by radio or telephone over a serial link constructed from IM6403 CMOS UART's when the data may be transmitted and the system clock resynchronized. The system may be left to run continuously for long periods relying on battery, solar, or wind power.

3. Multiprocessor Systems The decreasing cost of microprocessors has led to the possibility of using more than one central processing unit in a system. This may be simply to increase system throughput, to provide added reliability in critical applications, or to make greater use of system resources. For example, in a system where data are collected from various transducers spread throughout the laboratory, it is sensible to distribute the processing capability so that each

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ANTHONY J. DAVIES

remote activity may be tested and monitored on the spot. Faulty sections may then be isolated and repaired without bringing the whole system to a halt. The various microprocessors in a system may be interconnected in several different ways and, for a fuller discussion of this subject, the reader is referred to Anderson and Jensen (1975) or Aspinall (1977). In the laboratory it is usually best to use a fairly simple system where one processor acts as master with a number of slave processors connected in a hierarchical manner. The slave processors operate under the overall control of the master processor that treats them as peripheral devices and polls each in turn to see whether it requires control of the connecting bus highway in order to make a transfer to or from the master processor. Alternatively the slave devices may issue a bus request signal that is acknowledged by a signal, granting bus control, that is daisy-chained through the slave processors so that simultaneous bus requests are resolved on a priority basis, the nearest slave having highest priority. Gebler (1977) describes a typical hierarchical system where the master processor is an Intel 8080, with its own memory and peripherals, which is connected by a multiprocessor interface to the bus highway of a number of National Semiconductor SC/MP slave processors. The latter are used to control the input and output from various low-speed peripherals such as teletypes, integrating A/D converters, etc. In this particular application the Intel 8080 is used to control the input/output operation of high-speed peripherals such as floppy disks and may itself function as a slave for a remote large scale computer. In order to simplify the software and reduce the burden on each slave, one of these is used as a controller, supervising communications between the microprocessors and also with the operator’s console (usually a teletype). Theoretically in a multiprocessor system it is possible to connect every microprocessor to every other. For a system of n processors, however, each processor would have to have n - 1 input and output ports, and hardware and software constraints restrict n to a fairly small number (normally 2 or 3). With the present state of the art, it is much more feasible to consider a fairly restricted structure such as a ring system. A typical ring system, again a meteorological station (Fig. 37), is described by Watson (1977). Here every input and output card contains its own dedicated IM6100 microprocessor which, besides providing more processing power, enables the software for each section to be entirely independent. The input processors read and process data and then pass the information to common memory via the data bus. The output processor can then read the data from the common memory when they are required. In order to provide

MICROPROCESSORS A N D THEIR USE IN PHYSICS Analogue input

Analogue input

Analogue input

output card

POUT

I

output card

PIN-

T

Analogue input

I/

I

POUT

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107

I

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output card

PIN-

t

POUT

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.

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Digital output

output

FIG.37. CMOS multimicroprocessor meteorological station. Each input and output card contains a dedicated IM 6100 cpu.

concurrent access to common memory, a ring priority system is employed each processor having control over the data bus in turn. If a processor requires access to this bus when it is already being used, then the WAIT feature on the processor is asserted so that the processor’s activity is suspended until the bus becomes available. In low-power situations this approach would be impossible with NMOS processors due to the power consumption of each additional processor. With CMOS, however, each processor only requires a small amount of additional power that makes the system viable. As mentioned previously, multiprocessor systems are also often used in applications reqiliring high-system integrity such as satellites. In order to provide increased reliability, one common procedure is to use triplemodular redundancy (Wakerly, 1976), where each processor is triplicated and errors are eliminated by placing majority ‘‘voters” at the outputs, errors produced by a faulty processor being masked by a simple majority vote. Since the voters themselves may fail, they can also be triplicated giving the typical connection scheme shown in Fig. 38 where there are no critical single-point failures and the system will continue in operation in spite of any single failure of a processor or voter. In a microprocessor system, however. besides permanent failure, a transient failure may cause a particular processor to get out of synchronization so that provision must be made for resynchronization. Wakerly (1976) considers two examples of small microcomputer systems and shows that the

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A N T H O N Y J. DAVIES

-

Non-redundant system

U

Triple-modular redundancy s y s t e m

Microprocessor

0

Voter

FIG.38. Triple-modular redundancy connection scheme.

time to system failure may be increased by a factor of three or more when triple-modular redundancy is employed. 4. Control

Minicomputers and microcomputers have been used for a number of years in control systems where their computing power enable complex functions to be realized. One typical application is in a digital servo system (Fig. 39). Here, each synchro consists of a rotor winding and a stator winding, the rotor windings in each case being supplied with a reference signal (usually about 400 Hz). The outputs from the stator windings enter synchroto-digital converters that produce digital information concerning the angular position of the rotor of each synchro. Taking the angular position of synchro 1 as a reference, the microprocessor can then use this information to control the motor that is mechanically linked to the rotor of synchro 2. Velocity and acceleration feedback may, for example, be required to ensure Synchro 1

Synchro 2

Ref

Ref

FIG.39. Typical digital servo system.

Motor

MICROPROCESSORS AND THEIR USE IN PHYSICS

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adequate tracking, and an arbitrary angular offset or scaling may also be included. Microprocessors have a considerable advantage over minicomputers in this kind of application. Their small physical size enables them to be installed close to the controlled device and their cheapness means that each system can have its own dedicated processor. The particular microprocessor employed will depend upon the response and accuracy required. In high-precision applications 14 bits accuracy is quite common and a 16 bit machine is the obvious choice. Wenham (1977), for example, has described a microprocessor-based servo system used to control a very high precision air bearing rotary table. In order to provide the necessary computing speed the Plessey Miproc- 16 microprocessor was used, this having 16 bit word length, a 350-nsec instruction time, and being especially suited to control applications. The rotary table was fitted with a moire fringe system for determining its angular position to an accuracy of k0.2 sec of arc and the drive system consisted of a directly coupled dc torque motor. The motion of the rotary table could be synchronized with another movement, which could be either linear or rotary, using the firmware multiply and divide provided in the Miproc standard instruction set. Due to the high precision required in this application, 32 bit accuracy was necessary, which meant that double precision arithmetic had to be employed. AND FUTURE TRENDS VIII. CURRENT

Technological improvements in LSI circuits are expected to continue unabated for many years to come and by the end of the decade it will be possible to manufacture chips with some hundreds of thousands of components. This increase in density will be matched by increases in performance and even during the next few months important announcements are expected of powerful new machines. Intel are introducing a whole new range of processors and Zilog are expected to release a 16 bit processor, the 28000, having the power of a PDPll-70 CPU and yet only costing of the order of an LSI-11. MOS memory is also advancing rapidly and although the 16 kbit dynamic RAM has only just arrived, 65 kbit and larger RAMS are under development. In addition, Texas Instruments and various Japanese firms plan to produce chips with up to 1024 kbits, when photolithography must be replaced by exposure to a scanning electron beam in order to get the required resolution. Access time will decrease to 120-150 nsec for dynamic and 40-60 nsec for static 4 kbit RAMS in the near future. Improvements are not only being made to processors and to memory but

110

A N T H O N Y J. DAVIES

also to interfaces. One of the most important advantages of microcomputer systems is that input/output chips have and are being developed that are software controlled. Thus, instead of having a different type of interface card for each device, a single interface can be used for a whole range of different devices. This produces great savings in cost and ease of maintenance. Specialist chips are also being developed for particular purposes, such as floppy disk controllers and CRT display drivers. Intel will shortly announce a single chip CRT driver that provides raster and cursor timing, light pen detection, and can display from 1 to 80 charactersfrow with 1 to 64 rowsfscreen. For reasons of convenience the next decade will tend to be dominated by single board microcomputers with flexible programmable inputfoutput. The trend toward more powerful and complete computers on a single chip will not effect this since one still has to place the chip on a printed circuit card with input/output and power connections. In the early 1970s the rather slow development of the use of microprocessors was mainly due to the nonavailability of suitable software. This situation is now beginning to change and current thinking is towards the implementation of high-level languages that are specially orientated toward real-time applications. During the next few years there will still be a tendency for the research worker to regard the microcomputer as a replacement for the minicomputer. With the development of the power of the microprocessor this distinction will soon disappear; all one will be concerned with is the overall performance of the system. General purpose systems aimed at performing a large number of different tasks will still tend to be relatively expensive whereas the cost of a microprocessor will decrease to such an extent that it will soon be treated as just another circuit element. We must learn to regard it in very much the same way as we now look at transistors, diodes, and simple firstgeneration integrated circuits.

APPENDIXI Popular Microcomputers and Microprocessors These tables should not be taken as definitive and the reader should refer to the manufacturers’ literature for full specifications of a particular machine. Nearly all machines have cross and resident assemblers available. TABLE (a)

POPULAR SINGLE-CHIP MICROCOMPUTERS Manufacturer

Device

Architecture

Technology NMOS

64 x 8 GP Registers 2kx8ROM

Single chip version of F 8 2 psec typical instruction time

Isoplanar 12L

RAM ROM

Emulates the NOVA instruction set

NMOS

512 x 12 ROM

31 instructions with 1 psec typical execution time

Fairchild Semiconductor

3870

8 bit parallel

Fairchild Semiconductor

9440

16 bit parallel

General Instrument

PIC 1650

8 bit parallel

On-chip memory

Comments

(continued)

TABLE (a) (continued) Manufacturer

Device

Architecture

Technology

On-chip memory

Intel Corp.

8048/8748

8 bit parallel

NMOS

64 x 8 RAM 2 k x 8 ROM/ EPROM

Over 90 instructions. Cycle time, 2.5 psec.

MOS Technology

6600

8 bit parallel

NMOS

192 x 8 RAM 2kx8ROM

57 instructions with 2.5 psec typical execution time

MOSTEK

3870

8 bit parallel

NMOS

64 x 8 scratch pad 2kx8ROM

Software compatible with F8 2 psec typical execution time

Rockwell International

PPS-4jl

4 bit parallel

PMOS

128 x 4 RAM 2kx8ROM

50 instructions; 12.5 psec cycle time

Texas Instruments

1000/1200 and 1100/1300

4 bit parallel

PMOS NMOS & CMOS versions

64 x 4 RAM 1 k x 8 ROM for lo00 (for 1100 x 2)

43 instructions, 24 psec cycle time

Texas Instruments

TMS 9940

NMOS

256 x 8 RAM 2 k x 8 ROM/ EPROM

Software compatible with T M S 9900 family

Western Digital

CR 1x72

PMOS

32 x 4 RAM 512 x 10 ROM

37 instructions, 6.25 psec cycle time

-

'4

16 bit

4 bit parallel

+

Comments

TABLE (b)

POPULAR MICROPROCESSORS

Manufacturer

Device

Advanced Memory Systems

IM2650

Advanced Micro Devices

AM2901

Data General

mN601

Architecture 8 bit parallel

Technology NMOS

(R

=

Languages Resident; C = Cross)

FORTRAN IV

16 bit parallel

Schottky TTL NMOS

User defined and (R/C)

FORTRAN I V BASIC

-

75

(C)

PLUS

4 bit slice

and

No. of operating Instructions

184

(c)

Comments Equivalent to Signetia 2650 Microprogrammable Compatible with NOVA range software

Electronic Arrays

9002

8 bit parallel

NMOS

FORTRAN

Electronic Product Associates

Micro-68

8 bit parallel

NMOS

FORTRAN I V

Fairchild Semiconductor

F8

8 bit parallel

NMOS

Fairchild Semiconductor

MACROLOGIC

4 bit slice

CMOS or Schottky TTL

Ferranti

F100-L

16 bit parallel

Bipolar CDI (collector diffusion isolation)

General Instruments

CP1600

16 bit parallel

NMOS

87

Instructions similar to PDP-11

General Instruments

Series 8OOO

8 bit parallel

PMOS

48

Predecessor of F8

Instruction set based on Intel 4040

w

BASIC

and

14

(C) 16

User defined

CORAL

66(C)

Unusual instruction set with 2 psec typical execution time Microprogrammable

153

(continued)

TABLE (b) (contmirrd) Manufacturer

-

Device

Architecture

Technology

Intel C o r p

2 hit slice

Schottky TIT

Intel Corp

4 bit parallel

PMOS

Intel Carp

X bit parallel

NMOS

Languages ( R = Resident: C = Cross)

No. OF operating Instructions

LJser defined

PL!M

(R/C)

RASlC

Microprogrammable

59

Most popular 4-bit microprocessor

76

Most popular 8-bit microprocessor

66 and

CORAL

Comments

(c)

+

K hit parallel

Intel Corn

NMOS

PL/M

BASIC

lntersil

1 M6100

12 hit parallel

CMOS

Software compatible with 8080A. Only needs 5 V power supply

(R/C) 66 and

CORAL

(c)

ALGOL. K X ’ A L ,

60

HASIC, hORTKAP.

and

Monolith~c Memories

6700

4 bit slice

Schottky TTL

M O S Technolog)

MCS 6500

X hit parallel

NMOS

niHw

User defined

FORTRAY IlASIt’

Motorola

4

Motorola

4 hit slice

hit

slicc

(R/C)

(R/C)

Low voltage, low power. Executes PVPXII: instruction set Microprogrammable

55

(H)

Schottky TTL

l l s x dcfined

Microprogrammahlc

ECL

User defincd

Microprogrammable

Motorola

M6800

8 bit parallel

NMOS

M P L / ~( C )

National Semiconductor

SC/ M P

X bit parallel

PMOS, NMOS

FORTRAN IV

National Semiconductor

PACE

National Scmiconductor

IMP-16

PIessey

Miproc-16

BASIC

16 bit parallel

PMOS

16 bit parallel

FORTRAN

(c) (c)

FORTRAN

Schottky TTL

PL-MIPROC

FORTH

8 bit parallel

CMOS

Rockwell

PPS-4. -4/2

4 hit parallel

Rockwell

PPS-8, -812

Scientific Micro Systems Signetics

46

Single supply 14 volt PMOS, 5V N M O S

45

Similar to Data General NOVA1200

43

Similar to Data General NOVA1200

(R)

PMOS + TTL

C D P 1802D

Instruction set similar to PDP-II

(R)

SM/PL

16 (4 x 4 bit slice)

(c)

72

SMjPL

(c)

(R)

83 o r 170 91

Noise immunity IS 30",, of supply voltage ( 3 15 V)

PMOS

50

Single- 17 V supply

8 bit parallel

PMOS

99

Sophisticated architecture

Microcontroller

8 bit parallel

Schottky TTL

2650

8 bit parallel

NMOS

Limited instruction set designed for fast control applications (R), FORTRAN and CORAL 66 (C)

PLUS

75 f

BASIC, PASCAL,

Texas Instruments

Suitable for fast control applications

SBP0400 A

4 hit slice

IZL

User defined

Static device with single 5 V supply Microprogrammable; can operate with low voltage supplies

(continued)

TABLE (b) (continued)

Manufacturer

Device

Texas Instruments

S481

Texas Instruments

TMS-9900

Architecture 4 bit slice

16 bit parallel

Technology

Languages (R = Resident; C = Cross)

Schottky TTL

NMOS

llser defined

).OUTRAN, B A S K

COBOL, PASCAL, CORAL

Texas Inqtruments

SBP-9900

Western Digital

MCP-1600

8 bit pipelined (16 bit cpu)

NMOS

Z1log

Z80A

X bit parallel

NMOS

--

16 bit parallel

12L

No. of operating Instructions

Comments Microprogrammable; version available t o emulate TMS9900

69

TMS9980 is 8 bit data bus version

69

12L version of TMS9900. Single low voltage supply

and

66 (R)

As for TMS-9900

Digital equipment; company bases its LSI-11 on this chip set. Also available in version similar t o Data General Eclipse

msic (R), PL/Z (R/C), ALGOL. FORTRAN, and conm (C)

158

Software compatible with Intel 8080 but not pin compatible. Two banks of GP registers.

117

MICROPROCESSORS AND THEIR USE IN PHYSICS

APPENDIXI1 7-BIT ASCII CODE Octal Code

000 00 1 002 003 004 005 006 007 010 01 1 0 12 013 014 015 016 017 020 02 1 022 023 024 025 026 027 030 03 1 032 033 034 035 036 037

Char

NUL SOH STX ETX EOT ENQ ACK BEL BS HT LF VT FF CR

so

SI DLE DCl DC2 DC3 DC4 NAK SYN ETB CAN EM SUB ESC FS GS

RS

us

Octal Code 040 04 1 042 043 044 045 046 047 050 051 052 053 054 055 056 057 060 06 1 062 063 064 065 066 067 070 071 072 073 074 075 076 077

Char

SP ! #

s

% &

(

1*

+ ~

I 0 1

2 3 4 5

6 7 8 9

< -

> ?

Octal Code 100 101 102 103 104 105 106 107 110 111 112 113 114 115 116 117 120 121 122 123 124 125 126 127 130 131 132 133 134 135 136 137

Char (a

A B C D E F G H I J K L M N 0

P

Q R S T U V W

X Y Z [

\

I

A

-

Octal Code 140 141 142 143 144 145 146 147 150 151 152 153 154 155 156 157 160 161 162 163 164 165 166 167 170 171 172 173 174 175 176 177

Char \

a b C

d e f g h 1

j

k 1 m n 0

P q r S

t U V

W X

Y z

i I } 5

DEL

118

ANTHONY J. DAVIES

ACKNOWLEDGMENTS I wish to thank Professor D. Aspinall. Dr. E. Dagless, and Dr. J. Mason, Department of Electrical and Electronic Engineering, University College of Swansea, for the help and information they have made available and also Dr. R. Dowsing, Department of Computer Science, University College of Swansea, for his advice on the section on software. I am also indebted to the various firms and research workers who provided diagrams for reproduction.

REFERENCES Abbott, D. L. (1975). ESONE C A M A C Bull. 12, p. 2. Anderson, G. A.. and Jensen, E. D. (1975). A C M Comput. Surr. 7 . No. 4. Aspinall. D. (1977). Proc. C E R N Sch. Compuf., 1976 p. 117. Aspinall, D.. and Dagless, E. L. (1977). Introduction t o Microprocessors.” Academic Press, New York. Brissenden, T. H. F., and Davies. A. J. (1975). Much. Teach. 72. 49. Brown. D. (1977). Syst. Int. 4, No. 10, 30. Chapple. K. (1976). Microprocessors 1, No. 1, 9. Conte, G., Del Corso, D., and Giordana, M. (1976). Euromicro Newts/. 2, No. 2. 7. Fisher, E. (1975). Electron. Des. 23, No. 5, 52. Fullagar, D., Bradshaw. P., Evans, L., and O’Neill, B. (1976). Electronics 49, No. 25. 81. Gebler. P. (1976). New Electron. 9, No. 3, 14. Gebler. P. (1977). Electron. Eng. 49, No. 587. 51. Hilford. M. H. (1976). Microprocessors 1. No. 1, 49. Kline, B.. Maerz. M., and Rosenfeld, P. (1976). Proc. l E E E 64, 937. Nicoud, J. D. (1975). Euromicro Newsl. 1, No. 3, 3. Nicoud, J. D. (1976). Proc. IEEE 64. 896. Rodgers, T. J., and Meindl, J. D. (1974). IEEE J . Solid-Sfate Circuits sc-9, 239. Verhofstadt, P. W. J. (1976). Proc. I E E E 64, 842. Vuille. J. P. (1975). Euromicro Newsl. 1. No. 3, 8. Wadbrook, D. G . (1975). Syst. Int. 3, No. 9, 30. Wakerly. J. F. (1976). Proc. I E E E 64, 889. Watson, D. (1977). New Electron. 10, No. 16, 66. Watson. 1. M. (1976). Proc. IEEE 64. 910. Wenham. R. E. (1977). N e w Electron. 10. No. 16, 100. Wilkes, M. V. (1969). A C M Comput. Surr. 1, No. 3. ‘I

BIBLIOGRAPHY The study of microprocessors and their applications is such a fast growing and rapidly changing subject that a bibliography becomes out-of-date extremely quickly. The following, however, gives a reasonable survey of the field. More detailed information can be obtained by referring to manufacturers literature and the user’s manuals for the individual machines.

MICROPROCESSORS (GENERAL A N D COLLECTIONS OF ARTICLES) Altman, L. (ed.) (1976). “Microprocessors,” Electronics Magazine Book Series. McGraw-Hill, New York. Anderson, G. A,, and Jensen. E. D. (1975). A C M Comput. Sum. 7, No. 4.

MICROPROCESSORS AND THEIR USE IN PHYSICS

119

Aspinall, D., and Dagless, E. L. (1977). “Introduction to Microprocessors.” Academic Press, New York. Cain. G . (ed.) (1975). “Microcomputers: Fundamentals and Applications, 1974.” MINICONSULT, London. Compcon. IEEE Computer Society International Conferences held twice yearly. Digest of papers. Gilder, J. H. (1975). All about microcomputers. Comput. Decisions 7, No. 12, 44. Gordon, D., Wright, D. W., and Davies, A. C. (1976). “An Introduction to Microprocessors.” City University, London. Healey, M. (1976). ‘’ Minicomputers and Microprocessors.” Hodder & Stoughton, London. IEEE (1976a). Special issue on microprocessor technology and applications. Proc. IEEE 64, No. 6. IEEE (1976b). “Symposium on Trends and Applications in Micro and Mini Systems.” Gaithersberg. McGlynn, D. R. (1976).*‘ Microprocessors, Technology, Architecture, and Applications.” Wiley (Interscience), New York. Martin, D. P. (1974). “ Microcomputer Design.” Martin Research Ltd., Chicago, Illinois. Ogdin, C. A. (1976). “EDN pC Design Course,” EDN Nov. Cahners Publ. Co., Inc., Boston, Mass. Osbourne, A. (1976). “An Introduction to Microcomputers,” 2 vols. Osbourne & Associates, Berkeley, California. Proceedings (1974a). “Conference on Computer Systems and Technology.” IEE, London. Proceedings (1974b). “Symposium on Electronics” (1974) [Comptes rendus, J. d’Electronique, 1974, Lausanne]. Proceedings (1974~).1st National Microprocessor Conference. Microprocessors: Economics, Technology. Applications.” Arthur D. Little. Inc., Cambridge, Massachusetts. Scientific American (1977). Sci. 4m. 237, No. 3. Soucek, B. (1976). “ Microprocessors and Microcomputers.’’ Wiley, New York. “

SURVEYS OF MICROPROCESSORS Anonymous (1975). “Microprocessor Field Survey and Data Book.” A. H. Systems Inc., Chatsworth, California. Bews, M. (1974). Microprocessors survey. N e w Electron. 7, No. 22, 40. Cushrnan, R. H., ed. “Annual Microprocessor Directory,” Published annually in November edition of EDN. Cahners Publ. Co. Inc., Boston, Mass. Datapro Research Corp. (1976). ‘‘ Microprocessor and Microcomputer Specifications.” Datapro Res. Corp., New Jersey. IEEE (1975). IEEE Spectrum 12, No. 6. Infotech (1977). “Microprocessors, Infotech State of the Art Report.” Infotech, Maidenhead. Theis, D. J. (1974). Microprocessor and microcomputer survey. Datamation 20, No. 12, 90. Torrerra, E. A. (1974). Focus on microprocessors. Electron. Des. 22, No. 18, 52.

TECHNOLOGY A N D SYSTEM DESIGN Altman, L. (1976). Advances in designs and new processes yield surprising performance. Electronics 49, No. 7, 73. Barber, M. J. (1974). “State of the art in LSI.” Bell Telephone Labs., Murray Hill, New Jersey. Blakeslee, T. R. (1975).“ Digital Design with standard MSI and LSI.” Wiley (Interscience), New York.

120

ANTHONY J. DAVIES

Bower, R. W. (1976) “CCD Large Scale Memory,” Proc. Wescon. Western Periodicals, North Hollywood, California. Buie, J. L. (1976). “VLSI Bipolar Technology,” Proc. Wescon. Western Periodicals, North Hollywood, California. Grove, A. S. (1967). “Physics and Technology of Semiconductor Devices.” Wiley, New York. Hnatek, E. R. (1976). Semiconductor memories: A review. Microprocessors 1, No. 2, 85. Hodges, D. A. (1976). Trends in computer hardware technology. Cornput. Des. 15, No. 2, 77. Iasis (1975) “ Microcomputer Design,’’ 6 vols. Warr, Foote & Rose, Los Altos, California. Richman, P. (1973). “ MOS Field Effect Transistors and Integrated Circuits.” Wiley (Interscience), New York. Verhofstadt, P. W. J. (1976). Evaluation of technology options for LSI. Proc. l E E E 64,No. 6, 842. Withington, F. G. (1975). Beyond 1984: A technology forecast. Datamation 21, No. 1, 54.

PARALLEL PROCESSING AND NETWORKS Abramson, N., and Kuo, F. F., eds. (1973). Computer-Communications Networks.” PrenticeHall, Englewood Cliffs, New Jersey. Anderson, G . A., and Jensen, E. D. (1975). ACM Comput. Surt.. 7, No. 4. Aspinall, D., Dagless, E. L., and Dowsing, R. D. (1977). Design methods for digital systems including parallelism. IEE-ECS 1, No. 2. Enslow, P. H., ed. (1974). “Microprocessors and Parallel Processing.” Wiley, New York. Raphael, H. A. (1975). Join micros into intelligent networks. Electron. Des. 23, No. 5, 52. Russo, P. M. (1976). An interface for multi-microprocessor computer systems. Proc. COMPC O N , 1976. Siewiorek, D. P. (1976). Process coordination in multi-microprocessor systems. Euromicro Workshop, Nice, 1976 p. 4. Weissberger, A. J. (1974). Distributed function microprocessor architecture. Comput. Des. 13, No. 11, 77. “

SOFTWARE Barron, 1. M.. ed. (1976). The value of high-level languages. Microcomput. Anal. 1, No. 5, 2. Bass, C., and Brown, D. (1976). A perspective on microcomputer software. Proc. I E E E 64. No. 6, 851. Brown, P. J. (1975). ” Macroprocessors and Techniques for Portable Software.” Wiley. New York. Gibbons, J. (1975). When to use high-level languages in microcomputer-based systems. Electronics 48, No. 16, 107. Husson, S. S. (1970). “Microprogramming: Principles and Practices,” Prentice-Hall, Englewood Cliffs, New Jersey. Martinez, R. (1975). Look at trends in microprocessor-microcomputer software systems. Comput. Des. 14, No. 6, 51. Nauful, E. S. (1976). Software support for microprocessors poses new design choices. Comput. Des. 15, No. 10, 93. Opdenduk, T. (1976).Software considerations for microprocessors. Computer 9, No. 1.36. Pokoski, J. L., and Holt, 0. (1975). Developing software for microcomputer applications. Comput. Des. 14, No. 3, 88. Watson, 1. M. (1976). Comparison of commercially available software tools for microprocessor programming. Proc. I E E E 64,No. 6, 910.

MICROPROCESSORS AND THEIR USE IN PHYSICS

121

APPLICATIONS Burke, G. R. (1976). Microprocessors in control systems. Microprocessors 1, No. 1, 38. Cain, J. T., ed. (1977). Special edition on microprocessors and education. Computer 10, No. 1. Jenkins, R. W., and Evans, W. A. (1977). A microprocessor controlled frequency synthesised signal source. Proc. Con& Programmable Instrum., 1977, IEE, London. Lee, S. C., ed. (1977). Special edition on microprocessor applications. Computer 10, No. 9. McDonnell, D. (1974). Microcomputers for digital servo systems. New Electron. 8, No. 20. Nichols, A. J. (1976). An overview of microprocessor applications. Proc. IEEE 64, No. 6,951. Pfeiffer, E. A. (1975). “ Potential Applications of Microprocessors in Medical Instrumentation,” Session 24/4. Wescon. Western Periodicals Co., North Hollywood, California. Soucek, B., and Carlson, A. D. (1976). “Computers in Neurobiology and Behaviour.” Wiley, New York. Thornley, A. (1976a). Designing a microcomputer-based control system. Control Instrum. 8, No. 2, 22. Thornley, A. (1976a). Matching the program to a microcomputer-based control system. Control Instrum. 8, No. 3, 38. Weissberger, A. J. (1975). Application ideas for microprocessors. Instrum. Control Syst. 48, No. 10. 19.

BIBLIOGRAPHIES Mayne, K. D., and Pache, J. E., eds. (1975). “Microprocessor Applications Bibliography.” IEE, London. Ward, A. R. (1974). LSI microprocessors and microcomputers. A bibliography. Computer 7 , No. 7, 35. Ward, A. R. (1976). LSI microprocessors and microcomputers. A bibliography continued. Computer 9, No. 1, 42. Wright, D., Gordon, Ms. D., and Spencer, R. D. (1977). “Microprocessors. Infotech State of the Art Report.” Infotech, Maidenhead.

PERIODICALS WHICH REGULARLY INCLUDE ARTICLESON MICROPROCESSORS Computer (IEEE Computer Society). Computer Decisions (Hayden Publ. Co. Inc). Computer Design (Computer Design Publishing Corp.). Control and Instrumentation (Morgan-Grampian). Digital Design (Benwill Publishing Corp). Dr. Dobbs Journal of Computer Calisthenics and Orthodentia. EDN Magazine (Cahners Publ. Co. Inc.). Electronic Design (Hayden Publishing Co. Inc.). Electronic Engineering (Morgan-Grampian). Electronics (Electronics International, McGraw-Hill). Euromicro Newsletter (North Holland). Microprocessors (IPC and Technology Press Ltd.). New Electronics (Northwood). Proceedings IEEE (IEEE, New York). Radio and Electronic Engineer (I.E.R.E., London). Solid State Technology (Cowan Publ. Corp.). Systems International (Gershire Ltd.).

This Page Intentionally Left Blank

ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS. VOL. 41

Wire Antennas P. A RAMSDALE Department of Electrical and Electronic Engineering Royal Military College of Science Shrivenham. Swindon. United Kingdom

I. Introduction ............................................................................... I1. Analysis .................................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Current Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B . Integral Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................ C . Methods of Solution .................................................................. D . Numerical Methods .................................................................. E. Interconnected Wires ................................................................. F. Wire Grid Modeling .................................................................. G . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I11 . Unloaded Antennas ....................................................................... A . General Trends ....................................................................... B . Resonant Length Antennas .......................................................... C . Electrically Short Wires .............................................................. D . Electrically Long Antennas .......................................................... IV . Passive Loaded Antennas ................................................................ A . In-Line Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................. B. Coated Wire Antennas ............................................................... V . Active Antennas ........................................................................... A . Introduction ........................................................................... B. Integrated Antennas .................................................................. C . Nonintegrated Antennas ............................................................. VI . Antenna Selection ......................................................................... A. Fundamental Limits .................................................................. B. Antennas in Systems .................................................................. C . Synthesis and Optimization .......................................................... D . Conclusions ........................................................................... VII . Concluding Remarks ..................................................................... References .................................................................................

123 124 124 125 132 133 146 148 152 152 152 153 159 162 163 163 171 172 172 173 178 187 187 188 189 191 192 192

I . INTRODUCTION Although wire antennas have been used since Hertz first demonstrated electromagnetic waves in 1887. it is an area in which there is still considerable activity today . Over the years many alternative forms have been 123 Copyright @ 1978 by Academic Press. Inc. All rights of reproduction in any form reserved. ISBN 0-12-014641-9

124

P. A. RAMSDALE

employed but new types continue to appear and even now it is difficult to predict their performance with great precision. In modern communication systems, the antenna is often the physically largest item, and although size reduction is desirable, this is difficult to achieve without degrading other properties. Wires are the main antenna forms from VLF up to UHF. Dipoles are also found at higher frequencies, however the subject then becomes dominated by reflector and horn types together with various printed antennas that are now increasing in importance because of their compatibility with modern microwave circuits. This review attempts to explain the present position in our knowledge of wire antennas. In Section I1 numerical analysis methods are compared to show their relative strengths and weaknesses. The following three sections describe the major properties of specific antenna types. These are unloaded forms, in which the parameters are controlled by changes to the geometry, forms containing passive loads, the effect of which is to modify the current distribution and hence radiation properties, and antennas containing active devices that are used either for altering the current distributions or for matching or amplification. In Section VI the selection of an antenna type for a given system requirement is considered, and synthesis and optimization methods are described. 11. ANALYSIS A . Current Distribution If the current distribution on the surface of an antenna is known, then it is a fairly straightforward exercise to evaluate the other important parameters, i.e., the terminal impedance of the antenna, its near and far fields, etc. Unfortunately, the current distribution is known exactly only for a limited number of antenna shapes and forms and these do not include cylindrical wires of finite length. The integral equation used for their analysis is formed by satisfying boundary conditions at the antenna surface. It is possible to set up the integral equation in several forms but all of these have some inherent difficulties in their solution. In most modern solution methods, the integrations are carried out numerically and the current distribution is found after a large matrix has been inverted. Consequently it is problems of matrix conditioning, stability, and solution convergence that are of great interest today. However, before embarking on these often lengthy computations, it is important to consider the inherent limitations and weakness of the integral

WIRE ANTENNAS

125

equations, otherwise their shortcomings may become obscured by concentrating too much on the detail of numerical techniques. As well as computing accurate solutions for antenna parameters, there is also a need to gain a physical understanding of how an antenna works. This is particularly the case for the relatively new types, such as active antennas. In such cases the use of simple current approximations is often appropriate. The most common is the sinusoidal current distribution that is suggested by treating the dipole as an opened out transmission line (Colebrooke, 1932). Various low profile antennas formed by horizontal wires and their reflections in the ground are even closer to transmission lines in their method of working, and so a sinusoidal current is an even better approximation to the true distribution in these cases.

B. Integral Equations 1. Alternative Forms of’ Integral Equation

Like all electromagnetic analyses, the problem of the currents flowing on a wire antenna requires Maxwell’s equations to be satisfied at some boundary. Suitable integral equations can be set up in several ways but for all the common techniques, the starting point is the time-varying form of Faraday’s law that relates the electric field E, and magnetic field H, in a linear, lossless, isotropic medium (p, E ) by

V x E = -jwpH

(2.1)

Integration of Eq. (2.1)readily leads to an equation relating the electric field to the vector and scalar potentials A and 4

E = - jw A

-

V4

(2.2)

A thin-walled tube is shown in Fig. 1. Although this differs slightly from the physical problem of a solid wire cylindrical antenna, it is more amenable to analysis. The total current consists of currents flowing on both the interior and exterior walls of the tube but unless the overall structure is thick, the interior current is very small and the current can be approximated by only the exterior current. The vector potential on the tube surface can be expressed in terms of this current 1, as .h

A Z ( z )= p

1

‘-h

I,(z’)G(z,z’) dz‘

(2.3)

126

P. A. RAMSDALE

k4 FIG. 1. Cylindrical antenna approximated by a thin walled tube.

where

the integration in Eq. (2.4) being taken around the circumference of the wire with R the distance from the source point P' t o the field point P thus The scalar potential depends on the electric charge density 1

*h

4 ( z ) = r. '1 - h o(z')G(z,2 ' ) d-' ~

IT

(2.6)

the charge density being the rate of change of current along the cylinder

+')

-

=-

-

1 dZ(z') ___ dz'

\to

(2.7)

If the wire cylinder is a perfect conductor, then at its surface the tangential E field is zero and this condition relates the scattered field E , produced by the current and charge, t o the incident field E' impressed on the antenna

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+ E”) = 0

(2.8)

n x (E‘

where n is a unit vector normal to the surface of the cylinder. In Harrington’s moment method (1967), Eqs. (2.2b(2.8) are used to relate the unknown antenna current to the incident field. In the usual derivation of the Pocklington (1897) form of the integral equation, the scalar potential in Eq. (2.2) is eliminated by use of the Lorentz condition

so that Eq. (2.2) becomes (2.10) Then the substitution of A from Eq. (2.3) leads to

[g+

k2

1j h

Z,(z’)G(z,

z’) dz‘

=

-jcoEEi

(2.11)

-h

which is the Pocklington integral equation. Richmond (1965) used this equation for numerical solutions of scattering antennas. Subsequently, Thiele (1966) and many others have used the same equation in studies of driven antennas. Harrington was also really solving this integral equation, although he did not show it in a single combined form. However, his method (Section 11,D,3), by considering both vector and scalar potentials, leads naturally to the use of finite difference operators, and, for the current approximations he used, these give better results than by carrying out the differentials of Pocklington’s equation in a continuous fashion. Note that for the Pocklington integral equations, El is the E field incident on the wall of the cylinder. This enables any incident field to be considered including the excitation source of a driven antenna, the effects of which may occupy any fraction of the total antenna length. An alternative form of the integral equation can be set up by equating vector potentials. The vector potential has been expressed in terms of the current distribution in Eq. (2.3) and it may also be found by solving Eq. (2.10) for a specific excitation. This is usually taken to be an idealized delta function generator of voltage V , the electric field intensity incident on the antenna being zero at all points of the surface except across this infinitesimal generator region. Thus

a2 A, __ + k Z A , = azz

-j

k2 ~

o

Vd(z)

(2.12)

128

P. A. RAMSDALE

The solution of this nonhomogeneous equation can be found in the form of a complementary function and a particular integral; hence many minor variants are possible but a common form of Hallen's (1938) equation is

fh

z ' ) dz'

Z,(z')G(z,

= -

B sin kz

+ C cos kz +

'-h

where C is usually evaluated from the condition that the current falls to zero at the ends of the wire, B is zero for antennas symmetric about z = 0, such as the antenna of Fig. 1, and q is the intrinsic impedance of the medium. Thus Hallen's equation is less general than Pocklington's as it only applies to the delta-gap driven antenna that is a poor model of most physical situations. The excitation region corresponds to two circular knife edges separated by a vanishingly small distance, thus implying that the antenna terminal susceptance is infinite. A further conceptual problem arises as Eq. (2.13) does not have an integrable solution (Wu, 1969) because the right-hand side of the equation has a discontinuous first derivative at z = 0. Popovic (1973b) considered a finite belt generator as a more suitable representation of a practical excitation. This led to a modified integral equation not having all the Hallen equation disadvantages. The impressed field is taken to act over a finite length belt region (Fig. 2a) (2.14)

The integral equation now becomes

I h I=(z')G(z,z ' ) dz'

.-h

[ B sin k z

= -

rl

+ C cos k z + I/ 1

.Z

f(s) sin k ( z - s) ds

'0

To avoid the delta function generator problems, a continuous finite function is required for f ( z ) . Popovic found such a function that contained terms enabling it to be correlated with a monopole coaxial line excitation (Fig. 2b, c)

'

.f ( 2 ) = {

1

1 + cos(nz/d) 2d 0.

IzI I d

(2.16)

d<

IZI

I h

An approximate analysis of the belt generator antenna and the coaxial line fed antenna shows that the excitation zone in both cases can be represented

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129

FIG.2. (a) Monopole antenna driven by finite size belt generator; (b) monopole antenna driven by coaxial line; (c) impressed field along monopole antenna.

by a similar form of four-terminal network. A quasistatic equivalence between the capacitances of the two networks can then be found and these shown to be approximately equal if d

= 2.18(b - a )

(2.17)

where b/a is the ratio of outer to inner coaxial line conductor radii and the monopole is merely an extension of the inner above the ground plane, as shown in Fig. 2b. An alternative approach uses a frill of magnetic current as a means of representing the electric field across the aperture of the coaxially fed monopole. The tangential electric field at points along the monopole can then be obtained for a given excitation voltage (Tsai, 1970). This gives a suitable incident field distribution for the solution of a practically driven monopole by Pocklington’s equation. Surutka and Velickovic (1976) looked at the problem of solving a practically fed dipole antenna. A two-wire line was used and integral equations derived both on the surface of the dipole conductors and on the surface of the line conductors. This gave simultaneous integral equations containing the current distributions on both the lines and the dipoles and these were solved. 2. Approximations to the Integral Equations

The exact kernel G(z, z’) shown in Eq. (2.4)introduces a singularity into the integral equation when the source and field points coincide. This presents computational difficulties but there are ways in which it can be evaluated. For example, Pearson (1975) extracted the singularity by partitioning the kernel into a complete elliptic integral and expanding. This

130

P. A. RAMSDALE

results in an expression comprising a logarithmic term and a well-behaved, easily computed residual term G R ( z ,z ’ ) so that the left-hand side of Eq. (2.13) can be rewritten as -

Ih I ( z ‘ )In 1 z nu .-,, 1

~

- z’

I dz‘ + [

h

I (z ’)G R (z ,2 ’ ) dz‘

(2.18)

‘ -h

Provided low-order expansions are used for the current, the singularity in the first integral can then be extracted analytically. However, most analyses use a simplified form of the kernel G ( z , z ’ ) in order to eliminate the singularity and to avoid the extra computation of an integration around the wire. For the simplified kernel, the assumptions are made that the wire is thin and the current is flowing entirely along the central line of the wire, although the perfectly conducting wire boundary condition is still satisfied at the wire surface. This approximation is good for thin wires (a < h and a 4 A) but breaks down for thick wires. The kernel becomes G(z, z ‘ ) =

exp( - j k R ) 4nR

(2.19)

where

R

= [ ( z - 2’)’

+ a2I1l2

(2.20)

The antenna radius a represents an equivalent average radius from the current filament to the true current surface. It will be seen in Section II,D,3 that in moment method solutions the antenna wire is divided up into subsections. For such cases, the use of the approximate kernel is only valid provided not only the whole antenna but Thus particular care must be also these subsections are thin (u 4 hsubsection). taken when striving for increased accuracy or checking the convergence of solutions, because in these cases the subsections are reduced in length. Thus the approximate kernel validity limit can be reached. An example given by Imbriale and Ingerson (1973) is shown in Fig. 3. The solution method is described in Section II,D,3,c. The computed input resistance of a half-wave dipole (h/a = 12.5) is plotted against the number of subsegments used in the calculation. Thus for this antenna, h/u per segment is about unity when 12 segments are used. The curve marked a uses the approximate kernel and does not converge because the subsections are not thin enough. Integration around the wire gives the exact kernel form for which good convergence can be seen. The final curve uses a two-term equivalent radius to give a closer approximation to the exact kernal without requiring an extra integration, but again the solution is not convergent. However, for an

131

WIRE ANTENNAS 130

I

I

I

1

I

I

120

-

-

110

-

-

m

E

c

9 U C

a +

.-

-f

term equivalent radius

100-

-

3

n

-

90

-

80-

-

I

I

I

I

I

I

antenna of h/a = 50, the two-term equivalent radius does give comparable results to the exact kernel, while use of the approximate kernel is still unsatisfactory. 3. Limitations of the Integral Equations Having set up the integral equation, the following limitations should be noted : (i) The equation is developed from that of a hollow thin tube, the current being the sum of its interior and exterior currents, and it is only valid to consider the interior current as being negligible for thin wire cases. (ii) For scattering problems, the incident wave is treated as rotationally symmetric and this requirement is violated by too thick a structure. (iii) The flat ends of the wire and flat walls of any excitation gap are not included in the equation formulation. However, Taylor and Wilton (1972) have formulated an extra E term by using a quasistatic model for an end cap closing the antenna tube, and this can be added into the integral equation. The two most common forms of the integral equation are due to Hallen and Pocklington. Hallen’s has the disadvantage that it is specific to the physically unrealizable case of a delta generator source. The equation also contains constants that require evaluation by imposing additional boundary

132

P. A. RAMSDALE

conditions on the current. However, because the singular integrand arising from the kernel C(z, 2’) in the equations, has to be differentiated in the Pocklington form, the Hallen equation does have the advantage of having a lower order integrand singularity. Even when the kernel is simplified, the matrices set up in numerical solutions of the integral equation are better conditioned when based on Hallen’s form. C. Methods of’ Solution

Until the mid-sixties, the most successful approach to the solutions of integral equations had been the application of iterative schemes for Hallen’s equation (King and Middleton, 1946; King, 1956). These methods are only appropriate for relatively short antennas (h < A) and become laborious if too many iterations are required. Variational techniques were used by Tai (1950) and Storer (1951), and these gave the antenna terminal impedance from the starting point of an approximate current distribution. The results are comparable to King-Middleton results for conventional dipoles but a reasonable starting current approximation is required and this may not be readily available for other antenna shapes. Fourier series expansions have been made to produce good results for the current distribution by Duncan and Hinchey (1960). However, Hallen’s equation was used and difficulties were experienced in evaluating its constant C. To overcome this problem and to get a fairly rapidly converging series, Duncan and Hinchey incorporated the King-Middleton modified zeroth-order solution and their success owes as much to the use of this already good result as to their use of a Fourier series. Some further comments on this work are made in Section II,D,2a. All of the above techniques are inappropriate for long wires and for thick wires. The long wire problem has been tackled (Wu, 1961) by approximating the antenna by a semiinfinite one from - h to + 00, as this converts the integral equation into one of the soluble Wiener-Hopf type. The thick antenna has been studied by Chang (1966), and King and Wu (1967). The major complication is that it is necessary to remove the effects of the interior currents that become significant for a thick tube. Although not the first to use matrix solutions, there is little doubt that Harrington’s (1967) unified treatment of matrix methods for field problems marked a major turning point in the direction of antenna analysis. Since then, numerical techniques have been used for the overwhelming majority of wire antenna problems. In particular, the advent of subdomain moment methods has led to the solution of very complicated wire structures. Their study would have been almost impossible using the classical techniques.

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D. Numerical Methods

1. Numerical Solution Techniques The basic approach to the solution of the antenna integral equation is to rewrite it as a set of linear algebraic equations in which the unknown quantities are the coefficients of a suitable expansion of the current distribution. Two steps are required: first, getting a suitable approximation to the integral and second, ensuring that the resulting equation is satisfied. This can be either at points or averaged over suitable domains. A full review of the possibilities has been made by Jones (1974). All of the various forms of integral Eqs. (2.11), (2.13), and (2.15) can be written in a general form of

[ I ( z ’ ) K ( z ,z ‘ ) dz‘ = f ( z )

(2.21)

[where K ( z , z’) is either the kernel G(z, z’) or its modified form after performing differential operations]. Some alternative numerical solution methods for this equation will now be considered. a. Collocation. It is assumed that over a domain the current distribution where I,(z‘) is a known function and a, an unknown is of the form a, Z,(z‘), constant. In general there will be a series of such terms

I(z’) =

1 a,l,(z’)

(2.22)

m= 1

where the range of m can be due to both domains and functions. Thus the integral equation becomes a,

I,(z’)K(z, z’) dz‘ = f ( z )

(2.23)

m=l

In the collocation method the equation is satisfied at a series of points z, . However, it must be realized that this does not say anything about the behavior of the antenna current between these matching points, and it is not always a reasonable assumption that the current distribution is well behaved in such regions. Further difficulties associated with such point matching have been discussed by Bates et al. (1973). b. Galerkin method. In the general Galerkin method the matching is averaged over the antenna domain. Thus instead of satisfying the integral equation at points only, it is enforced over the length of a testing function w,(z). This is equivalent to taking far more matching points and setting up

134

P. A. RAMSDALE

sufficient equations by summing these suitably. Thus applying the Galerkin method to Eq. (2.23),we get ..

n

As well as a choice of basis functions, there is a wide choice of testing functions although the extra integrations involved restrict the practical choice somewhat. However, if a delta function is used for wr(z),the method reverts back to that of collocation. In computational terms, Galerkin’s method is an expensive technique in that it introduces additional integrations, but the effect of these is to render the equation insensitive to discontinuities in the current approximation and its derivatives by averaging both sides of the equation. This effect is particularly important in getting good convergence for solutions of Pocklington’s equation.

2. Entire Domain Solutions There are various basis functions that can be used as approximations to the current distribution. These can be divided into two types: the entire domain bases that are defined and nonzero over the whole of the antenna, and the subdomain bases that are nonzero only over subsegments of the antenna. In this section entire domain bases will be considered. Although there are an infinite number of possible basis series, it is clear that if a form closely resembling the actual current distribution is chosen, then it will yield a good solution even for low orders. However such a choice may not be consistent with the function being easily integrable along the whole of the antenna. Various entire domain solutions will be considered and can be grouped into type by the particular integral equation and numerical technique adopted. a. Hallen collocation. This approach was adopted as long ago as 1952 (Storm, 1952) with a Fourier series being used for the unknown current basis function and the simplified kernel used in Hallen’s equation. For thin antennas good results were obtained with low-order solutions. Duncan and Hinchey (1960) extended this Fourier series technique to higher order and used the exact kernel in the integral equation. However they found problems associated with the constant C of Hallen’s Eq. (2.13) that had not been apparent in the lower-order work of Storm. As C is unknown, it is tempting to move it to the left-hand side of the equation a, m=l

(. Z,(z’)K(z, z ’ ) dz’ + j ~

’

rl

C cos kz

= -j-

v sin . k 1z I

2rl

(2.25)

135

WIRE ANTENNAS

After setting up sufficient equations by point matching, the coefficients a,,, and C can be found as functions of the voltage V. Unfortunately, as C is an independent unknown, it leads to a set of equations with a unique solution for every value of n. The effect, which is least noticeable for very thin antennas, is that both C and the solution for the antenna current oscillate as n varies. If the C term is left on the right-hand side of the integral equation, then the coefficients a,,, are found as a function of both C and V , i.e., the currents that would be caused by these two excitations taken separately. C can then be determined using the condition that the total current goes to zero at the end of the antenna. In Duncan and Hinchey’s work a fairly elaborate scheme was adopted so that this boundary condition was not satisfied exactly, but it enabled a given order Fourier series for the current to give the least squares best fit over the entire antenna. Although the series in terms of C and V had been slowly convergent, this rate was improved by incorporating a good low-order approximation to the current in the evaluation of C. Hence, good 25th-order results for half and full wavelength dipoles were evaluated. A slightly different trigonometric series was used by Neff et al. (1969) in solving Hallen’s equation. The method of solution was the same as Storm’s except that the series used was rn nnlz‘J I+’) = a, cos __ Cm b, sin ___ n=l n=2 2h

+ (ntt)

( n odd)

(

(n even)

)

(2.26)

It can be seen that for rn = 1, the current is approximated by a single cosine term. This is just the same as the zero-order current distribution. For a thin half-wave dipole, the classical impedance 73 + j4ln is then found by dividing the driving voltage by the current at the center. For rn = 2, a sine term is added to the expansion, and results in good agreement with higher order iteration schemes are found. Similarities with the various King-Middleton iterative results can be seen as both approaches add trigonometric terms to the zero-order approximation until a sufficiently accurate series has been derived. Popovic (1970) has used an entire domain collocation technique in a series of papers. A polynomial series is used for the current approximation so that n

Z(Z’)=

C1b,(zl”-l

(2.27)

m=

or n-

1

(2.28) m= 1

136

P. A. RAMSDALE

the latter form being chosen so that the condition of zero current at the antenna end is satisfied. In Popovic’s work, the constant C is again moved to the LHS of the integral equation and hence convergent solutions for the current distribution are not found. Thus in this form it is important to use the method for approximate solutions only. Popovic has used this technique for an investigation of antennas containing various discrete and continuous loadings, the properties of which are discussed further in Section IV,A. Extreme accuracy was not required for this study, although, for second- and third-order polynomials, the unloaded dipole results were claimed to be similar to those obtained by the Chang-King five-term iterative theory. There are further problems with Popovic’s solution. The longer the antenna the greater are the number of matching points required. With the entire domain solution if a single polynomial is used over the whole of the antenna, then its order must also rise. The delta generator excitation contained within Hallen’s equation then becomes better matched and so the computed terminal susceptance rises. Thus it is usual to split the antenna into subsections to keep the polynomial order low. (One of the matching point equations then has to be replaced by an equation satisfying current continuity at the intersection.) The driving point singularity has previously been considered in great detail (Wu and King, 1959)and, as it is of very short range, the use of more suitable functions such as Duncan and Hinchey’s Fourier series enables it to be missed out until very high-order series are used. Popovic (1973b) introduced his belt generator (described in Section II,B) to form an alternative integral equation (2.15) that overcomes the driving point singularity difficulty. Its method of solution is exactly the same as for Hallen’s equation. Despite all of these problems, Popovic’s polynomial solutions are useful because of their computational simplicity. The low-order form gwes a good fit to the expected current distribution for short antennas, although for longer wires a trigonometric type of series is a more likely solution. b. Pocklington collocation. Richmond (1965) studied scattering from a wire by solving Pocklington’s equation. Various bases were tried : Fourier, Maclaurin, Chebyshev, Hermite, and Legendre series. Of these, the Chebyshev and Legendre polynomials gave the fastest convergence. Scattering only was considered, the wire currents being found as functions of the incident field. To treat the wire as a radiator, one method is to assume that a unit current generator is acting at an infinitesimal gap in the wire (Thiele, 1966). The field is set to zero at all the matching points and an equation summing the current components to unity is included in the matrix. From the current distribution obtained, field patterns can be evaluated, but without a relationship to some driving voltage, the antenna terminal impedance remains unknown. Techniques such as the magnetic frill current (discussed in Section II,B)

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enable incident E fields, from practical driving sources, to be calculated in terms of driving voltage. Using such a method, the current distribution on the antenna can be calculated as a function of driving voltage, so that the input impedance is then known. c. Hallen-Galerkin. At first sight, any entire-domain Galerkin’s method looks as though it would be involved because of the double integrals that have to be evaluated over the whole antenna length. However it is often possible to reduce the computation by carrying out transformations to change these integrals to a form in which the kernel appears as a function of a single variable only. Starting from Hallen’s equation, Silvester and Chan (1972) formulated a Bubnov-Galerkin solution for a dipole using the same functions for both current bases and testing functions. Thus, using the simplified kernel, the double integral of Eq. (2.24) takes the form exp( - j k R ) (2.29) dz dz‘ Even for simple approximating functions the straightforward evaluation of these integrals is difficult. However by suitable transformations and using polynomial functions, Silvester and Chan produced integrals that could be carried out exactly by a Gauss-Legendre quadrature formula of appropriate order allowing these integrals to be evaluated rapidly. Good results were obtained for low-order polynomials (second and third order) so that the matrices for inversion were small. d. Pocklington-Galerkin. Silvester and Chan (1973) solved the Pocklington equation in a similar manner to that adopted in their Hallen equation solution. Lagrangian interpolation polynomials were used as basis and testing functions and the double integrals formed by the Bubnov-Galerkin procedure were then transformed to remove the pseudo-singularity and enable exact integration to be carried out by the use of Gauss-Christofel quadrature formulas. As in their Hallen equation work, Silvester and Chan found that low-order solutions gave adequate results. Popovic (1971) adopted a variational approach that can also be shown to be equivalent to Galerkin’s method. Pocklington’s equation (2.12) is multiplied throughout by Z(z) dz and integrated from end to end, a delta function generator being used as the excitation source. Dividing all of the terms of the equation by I(0)’ gives an expression for driving point impedance ZI,

138

P. A. RAMSDALE

For small changes in the current function, the first variation of this impedance is zero, and hence its derivative can be equated to zero. Popovic used a polynomial series, Eq. (2.28), as in his earlier work and determined the coefficients b, by

(2.31) The double integrals involved could be converted into single integrals, and hence their numerical evaluation was not too lengthy.

3 . Subdomain Solutions A major problem with high-order entire-domain solutions is that the evaluation of the integrals becomes lengthy, since integration over the whole antenna structure is required for all of the terms in the current basis series. The use of basis functions that exist only over subsections of the complete antenna domain means that the integrations are also only required over one subdomain. If suitable subdomain basis functions are chosen then the integrations can be performed analytically (i.e., as they extend over shorter ranges their order is lower than the corresponding entire domain functions). The name method of moments is often used to describe the reduction of the original integral equation into a matrix equation. After dividing the wire into subsections the unknown currents on each are related to the incident field by an impedance matrix. The elements of this matrix describe the electromagnetic interactions between the subdomains. Inversion of this matrix gives an admittance matrix that allows the current distribution to be found for any source field. ‘ I The accuracy of the solution depends on the way the impedance matrix is derived but for a given scheme, providing it is convergent, the solution accuracy improves as the number of segments N is increased. However as the calculation time for a general matrix increases as N 2 and its inversion time as N 3 it is desirable to keep N as small as possible. Miller et al. (1971) studied a variety of wire scatterers. They used sinusoidal interpolation bases for a subdomain solution of Pocklington’s equation. This method is described in Section II,D,3,d. From the current distribution it is a straightforward operation to calculate the effective scattering cross section of various wire structures. It was found that 6-18 current samples per wavelength are sufficient to produce scattering cross section results with absolute numerical convergence accuracies of the order of 10;: or less. Fewer segments are required for the simpler geometries such as straight dipoles and circular rings. More segments are needed for various interconnected wires such as I/ dipoles and crossed dipoles. Still more segments are necessary for

WIRE ANTENNAS

139

general shapes and the examples of a squirrel cage and a conical spiral were considered. Although other antenna parameters require a different number of samples for a given solution accuracy, the increased number required with greater structure complexity can be expected to be similar, In this section several alternative subdomain solution methods will be considered. a. Vector-scalar potential. Rather than using either the Pocklington or Hallen integral equations, Harrington (1967) returned to the more fundamental equation (2.2) that relates the electric field to the vector and scalar potentials. The antenna wire was split into straight subdomains and a constant current assumed along each (piecewise uniform basis functions, see Fig. 4a). The matrix equation was then set up by point matching at the center of each subsection. The scalar potential term poses the most difficulties as it is necessary to first find the charge. This is the rate of change of current (Eq. 2.7) but as Harrington uses discontinuous currents as bases these derivatives cannot strictly be found. A finite difference form was used for the differential in Eq. (2.7) although its use really implies a linear current

(d)

FIG.4. Subdomain basis functions: (a) Piecewise uniform; (b) piecewise sinusoidal; ( c ) piecewise linear; (d) sinusoidal interpolation.

140

P. A. RAMSDALE

variation between the segments. Thus for successive segments carrying currents I ( n ) and Z(n + l ) the charge density at the intersection is given approximately by - 1 I(" + 1) - I ( n ) (2.32) u = - j[w A1

I

where A1 is the distance between the segment centers. Because the aim is to write mutual terms between segments, the two terms of this equation are best associated with their respective segments. Hence the element n is taken as consisting of a current filament I ( n ) with charge filaments at each end, the values of which are q ( n + )= o(n+)A1 = (l/jo)I(n)

(2.33)

q ( n - ) = a(n-)AI = ( - l/jo)Z(n)

(2.34)

and The mutual impedance between any pair of segments rn and n can then be found. The vector potential at the center of segment rn due to the current segment n is found from Eq. (2.3) and the scalar potential due to a charge is given by Eq. (2.6). Thus the potentials due to the two charges associated with segment n are found at both ends of segment m.As the differential of the scalar potential is required a finite difference form is again used. The difference between the two end potentials is taken and divided by the length of element rn, Al, . Hence the two components of the electric field equation (2.2) are found in terms of the current on segment n and the mutual impedance Z,, , between the segments is simply given by

Z,, = Ei(rn)A1,/Z(t7)

(2.35)

The current distribution on the antenna can then be determined by inversion of the complete impedance matrix and multiplying by the appropriate excitation matrix. For a transmitting antenna the excitation can be taken as zero across all segments except one and the source voltage applied across this segment. Otherwise more elaborate distributions such as the magnetic frill (Section II,B,l) can be used. One further point that arises from the use of piecewise uniform functions is due to the end segments on the dipole carrying zero current. The end of the wire corresponds with the center of this segment and consequently the first segment in the impedance matrix starts half a segment from the end of the wire. b. Pocklington collocation. Although piecewise uniform basis functions were used by Harrington, in general their use to solve Pocklington's equation is not common. This arises because of the problem of differentiating the

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141

current function. Harrington’s approach used a finite difference method that implicitly involves extrapolation from adjacent segments for its derivation and to some extent smooths out the discontinuity problem. If Pocklington’s equation is used directly, then no such care is taken and consequently poorly convergent solutions are obtained. This leads to choosing alternative basis functions that d o not introduce current discontinuities. Several alternative functions are shown in Fig. 4. The piecewise sinusoidal base has been used in Pocklington’s equation, the base form being

I , sin k ( A - 1 z I(z)=

-

z, 1 )

,

z,-A
sin k A 0,

(2.36) otherwise

where A is the length of one subsegment. Note that each subsection of the antenna has contributions from three basis functions. At first sight, this base appears to offer a great advantage in that the resulting integrations can be performed analytically, and hence the computation time is reduced considerably. However Pearson and Butler (1975) and Butler and Wilton (1975) have discussed various shortcomings of solutions using this base. It is found that, in general, the convergence of the solution is poor because of the rapidly varying contributions to the scattered electric field. These arise from the discontinuous derivatives of the current basis set (N.B. : Pocklington’s equation uses the second differential of the current). Figure 5 shows curves due to Butler and Wilton for a thin halfwave scatterer in which the convergence rate of various solutions is shown by plotting the center current against 1/N. The figure shows the real and imaginary parts of the center current normalized separately to a result obtained from Galerkin’s method using 31 piecewise sinusoids as basis and testing functions. The Pocklington piecewise sinusoidal collocation (P-PS-C) can be seen to be a poorly convergent solution compared to other techniques that will be considered subsequently. A further problem arises in solutions for driven antennas by collocation techniques in that the match points cannot be spaced densely enough in the feed region to accurately sample the driving field, especially when the antenna diameter is small. Pearson and Butler (1975) used a magnetic frill for the two element array shown in Fig. 6a. The poor convergence of the solution can be seen in Fig. 6b and the reason becomes clear looking at Fig. 6c. The solid curve is a plot of the E field due to the magnetic frill source, while the dashed curves show the first and second match points connected by straight lines. It can be seen that even for N = 40 the true source is not being adequately represented because the match points are too widely spaced. c. Pocklington-Galerkin. A possible Galerkin solution to Pocklington’s

142

P. A. RAMSDALE

I

I

32 22

I 16

I N =10

I N=6

L

H-PL-C P-Tk-f

-

0.81

1 \P-T/E-C

i

I 1

1 FIG.5. Convergence of normalized current at the center of a half-wave scattcrer (a = 0.0011) versus linumber of subdomains. From Butler and Wilton (1975).

equation is to use the piecewise sinusoidal functions for both the current expansion and testing functions. Such a procedure (P-PS-G) was used by Imbriale and Ingerson (1973). Their work was on relatively thick antennas and some of their results have been shown previously in Fig. 3, where a comparison between the use of the equivalent wire radius and the exact kernel in the integral equation was made. The convergence of this solution is much better than for collocation. Although the basis sets introduce discontinuities in the current derivatives

143

WIRE ANTENNAS

I

I

I

I

I

1

LO

Driven Parasite

10 L

0

005

0 10

0.45

0.20 0.25

‘/A (bl

FIG. 6. Convergence behavior of current solutions for a pair of resonant-length monopoles. (a) Two-element array. One element driven by magnetic frill; (b) modulus of currents along antenna for different numbers of subsegments; (c) E-field along driven antenna due to magnetic frill and straight lines between first and second match points. From Pearson and Butler (1975).

the Galerkin’s method produces a weighted average of both sides of Pocklington’s equation. Hence there is a better representation of the scattered field over the entire antenna length rather than an exact match at discrete matching points and rapidly varying discontinuities between. The improvement over collocation can be seen from Fig. 5. d. Pocklington-sinusoidal interpolation. An interesting basis function was used by Yeh and Mei (1967) where the current on each segment is made up of three terms Z(Z)

=

a,

+ b, cos k(z

-

z,)

0,

+ c, sin k(z

-

z,),

A A < z < z, 2 2 otherwise (2.37)

z,

--

+

where z, is the midpoint of the nth section (Fig. 4d). The coefficients a,, 6, ,

144

P. A. RAMSDALE

and c, are obtained by enforcing the requirement that the extrapolated current from a given segment matches the midpoint current in the two adjacent segments. Although this technique does not make either the current or its derivative continuous it does reduce discontinuities somewhat and their contributions do not dominate the scattered field. In Fig. 5 this technique is referred to as Pocklington-trigonometric/extrapolated continuity-collocation (P-T/E-C) and good convergence can be seen. However the discontinuities are not zero and eventually at high enough N the solutions will start to diverge. Better convergence is found by forcing the current and its derivative to be equal at the segment boundaries (Pocklington-trigonometric/continuous current and derivative-collocation, P-T/C-C). Unfortunately this method is in general unacceptably complicated for the improvement it offers as the expansion on any one segment involves current samples on all the others. e. Pockzington-continuity requirement. It has been seen that there are problems with Pocklington solutions if the basis functions introduce discontinuities in the current or its derivative. The near field behavior for four cases can be seen in some computations by Miller and Deadrick (1975) in Fig. 7. The field should go to zero away from the antenna center and end. It can be seen that the current discontinuity of the piecewise uniform bases with point matching (P-PU-C) gives very poor results. The piecewise sinusoidal Galerkin’s approach (P-PS-G) is a smoother result and the sinusoidal interpolation (P-T/E-C) gives a further improvement. The best results were obtained from the extremely complicated method involving current and charge matching at segment junctions (P-T/C-C). However, even with this continuity of the first derivative of the current the tangential fields do not go to zero except at the segment centers. Anders (1977) has studied the minimum continuity requirements for Pocklington’s equation. He has shown that appropriate basis functions must behave continuously up to their third derivative. In all previous work the functions used did not meet this requirement. Anders suggested a biquadratic spline as a suitable function for achieving this. Although the commonly used basis functions give these poor near field results the input impedance results in Fig. 7 are more consistent except for the P-PU-C case (although with a finite difference approach this too would yield a comparable value). If far fields are calculated from any of these results consistent smooth results are found. .f Hallen. Convergent results are more readily obtained with Hallen’s equation as can be seen from Fig. 5 where a piecewise linear collocation method has been used (H-PL-C). In Pocklington’s equation the electric field was very dependent on both current and charge discontinuities, whereas in Hallen’s form the electric field only enters through integration. Thus, even

WIRE ANTENNAS 10;

I

I

I

145

I

P-PS -G

Z,,= 10‘

0

0.1

End

200+j L26R

0.2

0.3

Zl,,= 79.7 + j L5.052

0.L

0.5 Center

‘/h

0

0.1

0

End

0.1

0.2

0.3

‘/h (C

)

0.3

0L

‘/h

Zl,=81.0 +j L3.8R

10

0.2

End

0.5 Center

Z1,=81.1 + j & 5 . 5 R

0-L

0.5

0

Center

End

0.1

0.2

0.3 ‘/h

0.L

05 Center

(d)

FIG.7. Tangential fields along half of a half-wave dipole for various current basis functions. From Miller and Deadrick (1975).

with no attempt to reduce the effects of discontinuities, Hallen’s equation has this good convergence. For a more involved shape of antenna, the rate of convergence can be too slow and the more sophisticated basis functions become worthwhile. Yeh and Mei (1967) used the sinusoidal interpolation technique to get faster convergence for their solution of an equiangular spiral. However, even for a quarter-wave dipole where 20 subdivisions were used for piecewise uniform bases, the same accuracy was achieved by sinusoidal interpolation using only six subdivisions.

146

P. A. RAMSDALE

g. Modijied Pocklington equation. Wilton and Butler (1976) found a method that retained the advantages of Pocklington’s equation and incorporated the good convergent behavior of Hallen equation solutions. Their first step was to form a Galerkin’s equation from Pocklington’s equation by using piecewise sinusoids as the testing functions only. Then knowing that the difficulties with Pocklington’s equation are due to the effects of discontinuities in the basis sets when differentiated, the equation is integrated twice to form an integro-difference equation. It can be shown by substitution that Hallen’s equation (with arbitrary excitation) is a solution to this and so solutions to the integro-difference equation have the same good convergence properties as Hallen’s equation even for discontinuous basis sets. The method still retains the Pocklington equation advantages of not having arbitrary constants to be evaluated by additional boundary conditions.

E. Interconnected Wires In the last section numerical solution techniques were described but no details were given of how junctions (where three or more wires meet) are treated. Compared with the straight wire problem, some modification to the method is normally required. This particular problem has received considerable attention in recent years chiefly because far more complicated structures are now being studied and in these cases many junctions often exist. Taylor et al. (1970) studied the scattering from two crossed wires, Hallen’s equation was used and a piecewise uniform collocation method of solution adopted. This two wire problem results in dual integral equations both of which contain unknown constants and additional boundary conditions must be satisfied for their elimination. Sufficient conditions are that the currents go to zero at the wire ends and that Kirchoff’s current law is satisfied at the junction. Butler (1972) formulated the coupled Hallen-type integral equations by an alternative approach to Taylor. A piecewise sinusoidal method was used for their solution and again boundary condition equations for the junction and wire ends were also required. Pocklington’s equation contains the boundary conditions of the problem, so that if it is solved correctly no further boundary conditions need be applied. However, due to the approximate nature of the numerical solutions, it is not always safe to assume that this is achieved. The antenna may be treated as an array of overlapping dipoles (Chao and Strait, 1971), this being an alternative way of considering the use of functions such as piecewise linear and piecewise sinusoidal, because along every section of the wire two of these piecewise functions exist (see Fig. 4). This approach can be extended to the junction problem by adding extra overlapping segments. For each of these segments, the current falls to zero at

WIRE ANTENNAS

147

each end and is continuous at the center. Thus the superpositions of these current bases automatically satisfy Kirchoff’s current law at all points. A problem occurs with this method if loads have t o be included in the antenna at a junction (e.g., a transistor), because the loads have to be associated with particular expansion functions. When overlapping functions coincide with these loads, the choice of which should be associated with the load then becomes quite arbitrary. This overlapping segments method can be used with piecewise uniform expansions, but due to their discontinuous nature errors in current continuity are found unless a very fine subdivision is used at the junction. Another basis function that does not satisfy current continuity at the end of each segment is sinusoidal interpolation, which matches the midpoint current in adjacent segments. For multisegment junctions, average midpoint currents are generally used. In wire antenna problems this method works well, but for wire grid modeling (Section II,F) the segments are often of different length and, for such junctions, sinusoidal interpolation also has a large current discontinuity problem. Harrington’s (1967) solution (Section II,D,3,a) uses piecewise uniform functions and a finite difference approximation for the differential operation on the current. In this way charges are defined at the end of each wire subsection. At the antenna ends the segments carrying finite current finish half a segment from the antenna end, so that the condition of zero current at the end of the antenna is satisfied. At a junction the subsections can be so arranged that they d o not overlap but end exactly at the junction point. Sayre (1973) considered the continuity equation at this junction point and deduced that for an N wire junction, N

I j = -jwN@

(2.38)

j= 1

where @ is the average charge on each of the wire segments at the junction point. This charge was taken to be distributed between the wires proportional to their areas. In the vicinity of the junction, this charge is then used instead of the normal form in Harrington’s solution, Eq. (2.33). As was stated previously, Pocklington’s equation already contains the boundary conditions, but if the solution is likely to be poor at the junction, then forcing continuity in this manner should improve the convergence. However, Mittra and KO (1975) solved various wire junctions by Pocklington’s equation with the finite difference operator and piecewise uniform expansion functions without a separate application of junction continuity. The only limitations appeared to be that if segments of different length were used, erroneous results appeared. With wires of different radius, provided they are both small compared with subsegment lengths, the method still

148

P. A. RAMSDALE

appeared to be satisfactory. Mittra and KO made comparisons between the Hallen equation results of Taylor and Butler, and the Pocklington equation results of Chao and Strait and themselves for the currents on a pair of crossed wires. Considering that the methods used different basis functions, the agreement between the results is very good. Junctions were dealt with in the full domain solution of Silvester and Chan (1973). The current distributions were approximated by using interpolation polynomials and the solution found for the case when all the wires were disconnected (disjoint structure). The advantage of using interpolation polynomials is that, when the wires are joined together (conjoint structure), as in this new antenna, fewer current coefficients are independent. A connection matrix can be constructed relating all of the interpolation points currents for the disjoint case with those in the conjoint case. This matrix incorporates Kirchoff's current law and the currents on the conjoint antenna are then found by a simple matrix multiplication. Hassan et al. (1976) started from the same full domain technique but used a different method to deal with the wire interconnections. The elements of the impedance matrix were found as before for the cases when the field and source points were on the same wire and on distinct separate wires. However, for joined wires, a more elaborate technique was used. The advantage gained in this work was that for wires joining at angles between 0" and 30" and 150" and 180", the existing integration formulas had lost accuracy and computer round-off error had increased. This was due to tl-e near singularity that occurs when the source and field points approach the junction. Suitable transformations were found to enable this singularity to be adequately handled. At the junction Kirchoff's current law was again satisfied. F . Wire Grid Modeling

There are many practical applications where wire grids are used rather than solid surfaces. For instance, the electrical effect of a continuous surface may be required but weight or wind resistance preclude its use. A wire grid can also be used to advantage in the analysis of continuous surfaces. This is a particularly useful technique for studying the properties of wire antennas mounted on metal surfaces as the antenna that must be considered is really the combined effect of both, and it is convenient to be able to handle all parts of the problem in a similar form. Another use of the wire grid is in the analysis of extremely complicated structures. A wire grid model for a conducting body appears to have been first studied by Richmond (1966) using a Pocklington-type approach and a piecewise uniform solution. He obtained satisfactory agreement for the

149

WIRE ANTENNAS

backscatter areas of round and square flat plates and spheres. Tanner and Andreason (1967) computed patterns of an antenna mounted on an aircraft, and since then many other workers have looked at both aircraft antenna patterns and aircraft scattering cross sections by wire grid techniques. In the previous sections discussion of the alternative approaches to the solution of the wire antenna demonstrated some of the difficulties and areas of error in solving relatively simple antennas. The simplest schemes suffer from discontinuity problems and consequent poor convergence. However, the addition of too many refinements limits the number of segments that can be used with a reasonable computation time. Hence, initially for wire grid modeling, most researchers have tried to use the simpler techniques but various anomolous results have often forced the adoption of the more involved methods. Some extremely revealing results were presented by Kubina and Pavlasek (1975). Pocklington's equation was solved using piecewise uniform bases and collocation. Figure 8 shows a helicopter and the computed radiation patterns for 214 and 254 elements but unfortunately, as can be seen, the

(b)

(C )

FIG.8. (a) Wire grid model of a monopole on a helicopter (Bell 47G-4A); (b) computed E i versus & radiation pattern using 214 elements; (c) computed E: versus & radiation pattern using 254 elements. Computed: --; measured : - - -; 0 = 80";,f = 675 MHz. From Kubina and Pavlasek (1975). -

150

P. A. RAMSDALE

results diverge. Even after adding additional constraints at junctions and using piecewise sinusoidal bases, their results were still divergent. Unfortunately, these various odd anomalous results are still fairly common in this type of work. It is possible to find large circulatory currents on loops of wire grids that d o not occur in the original structure, and it is most difficult to pin down when near-field errors at intersegment discontinuities are causing the whole solution to diverge. Thus it is still difficult to place too much faith in these solutions despite the reasonable agreement shown between experimental and theoretical patterns in much of the literature, although Galerkin solutions would be expected to reduce the problems of invalid near fields. Lin and Richmond (1975) have presented scattering results for aircraft using piecewise sinusoidal bases with Galerkin’s method, and their results show a gradual improvement when elements are added to form a better representation of the structure. Figure 9 shows a 70 segment model of an MIG19 aircraft and excellent agreement between calculation and experiment for the echo area at two frequencies. However, even with this method Wang and Ryan (1977) have found numerical anomolies. An example when these came about was a folded dipole attached to an aircraft skin. The erratic results may have been due to the wire grid having an internal resonance, but the addition of internal wire segments to detune did not correct the problem. Williams and Brammer (1977) were working towards the analysis of a land vehicle antenna. Work was initially carried out on the pattern of an offset monopole on a rectangular box. Theoretical results were obtained by piecewise uniform and sinusoidal interpolation collocation and by a piecewise sinusoidal Galerkin method. The sinusoidal interpolation gave the anticipated improvement over the piecewise uniform result. However, unlike the case of wires with no junctions, in a wire grid the number of unknowns for the piecewise sinusoidal method is greater. Thus the maximum number of segments that can be handled by a given computer is reduced. Hence. in this example, although the computing limit for the two collocation methods was 444 segments, only 272 could be used for the piecewise sinusoidal Galerkin method. So that in this case, piecewise sinusoidal collocation gave the closest fit to experimental results. With the extremely large matrices being used for these problems, techniques to reduce the required computer storage and inversion running times are becoming important. Pizer (1977) has given wire grid model calculation examples in which sparse matrix techniques are used. In this work, reductions of 10 to 20 times were achieved for both storage and running times. For a body several wavelengths long, interactions between distant parts are much smaller than adjoining parts. When the distance exceeds a certain limit, the interaction is taken to be zero. Thus a sparse matrix is

WIRE ANTENNAS

=t-I

151

L

t, 4

-20

I

-30

-

L = 0.826 A

a=0.005A

-LO

f

1

1

1

20

LO

60

1

80

,

(

1

100 120 1LO 160

0. degrees

Nose

1

P

1

Tai I

FIG 9 (a) Wire g n d model of aircraft (MIG 19) using 70 segments, (b) (upper) computed echo area versus aspect angle at 3 23 GHz, (lower) computed echo area versus aspect angle at 5 43 GHz Computed , measured From Lin and Richmond (1975) ~

152

P. A. RAMSDALE

formed. Sparse matrices have been used in several other branches of electrical engineering and a comprehensive review with 604 references has been compiled by Duff (1977). G. Cordusions

There are a number of alternative numerical analysis schemes for wire antennas. Subdomain methods are the most popular, but with most basis functions there is a problem of lack of continuity between the domains. This can result in significant errors because the theoretical near field is quite different from the true case. Although full domain solutions d o not introduce the same unreality, they require integrations to be made over the whole antenna. For large problems, this makes the matrix fill time unacceptably large. Wire grid modeling has all the difficulties of analysis for a wire antenna, together with the further problem of selecting a suitable mesh of wires to approximate the solid object. Unreal circulating currents and internal resonances in part of the grid are always a possibility so that, although many excellent results have been achieved, various anomalous results limit the usefulness of much current work. Very full wire representations of bodies are nowadays attempted, but it seems probable that the sensible limit has already been reached for the bases currently in use. Future work will surely concentrate on improving the conditioning and stability of the numerical model. 111. UNLOADED ANTENNAS A . General Trends

The most frequently used wire antennas are the vertical monopole and its equivalent dipole form, together with various deployments of physically long wires. Due to their simplicity and general effectiveness, there are many situations where there is little to be gained by the use of more involved types. However, in recent years, transmitters and receivers have become increasingly more broadband and capable of changing frequency rapidly. Radios and their associated feeders are designed to exhibit constant terminal characteristics so it is desirable that antennas show the same sort of consistency in both their terminal impedance and radiation patterns. If a sufficiently broadband antenna can be achieved, then tuning and matching networks are not required. This objective can be effected to some extent by modifying the geometry of the conventional monopole and dipole forms.

WIRE ANTENNAS

153

Another trend is for the size of antennas to be reduced. A small antenna has almost as large an effective area as a resonant one, and theoretically it is possible to match it perfectly to a radio. However this requires highly reactive currents, so that in its practical realization the matching circuitry is either lossy or narrowband. In this and Sections IV and V, various types of wire antenna will be considered and it will be seen that it is easy to evolve types having either a better broadband performance or a reduced size compared to the half-wave dipole. The ideal of a small broadband antenna is not generally achievable without encountering other penalties.

B. Resonant LRngth Antennas The monopole antenna is resonant when just less than a quarterwave in length. If it is thin, then its impedance changes significantly moving away from this frequency. By using thicker wire the impedance bandwidth can be improved. Although this trend has been demonstrated on many occasions, it is difficult to make accurate comparisons because it is hard to quantify the different gap capacitances that must be allowed for at the feedpoint of these antennas. When using monopoles with broadband transmitters and receivers, it becomes necessary to tune out the reactive impedance component away from resonance in order to maximize the rf power transfer between the radio and the antenna. Modern antenna tuning units can be automatic (Hodgson, 1974) and typically are capable of matching a monopole to any frequency in the H F band (1.5-30 MHz) in a few seconds. Two servo-driven variable reactances (a series inductor and shunt capacitor) form the matching network, while two discriminators generate error signals for these servo motors when the impedance of the matching network is incorrect. Thus the servos form part of a closed-loop null seeking system commonly trying to make the circuit impedance look like 50 0.Often a third discriminator is required to introduce switched reactances to bring the impedance within the matching range of the other two. Consider as an alternative to the cylindrical wire dipole the biconical antenna shown in Fig. 10a. Its action is well understood because it is possible to treat it as a terminated transmission line (Schelkunoff, 1943). Schelkunoff defined a boundary sphere, coinciding with the ends of the cones as shown in Fig. 10a. Inside the principal mode is a TEM wave, whereas outside only higher order modes can exist. At the boundary some energy is reflected and some continues so that it is radiated into space. Thus the boundary sphere, including any end caps on the bicone, effectively acts as a load impedance at the end of a transmission line. For very small angles the

154

P. A . RAMSDALE

/ I

-

-- . .

Boundary sphere

/-

/

l \R

\

FIG. 10. (a) Biconical dipole antenna (); (b) bulb dipole antenna (-); (c) terminal impedance versus half-length for bulb dipole and for 60" flare angle biconical dipole. From Kalafus (1971). - -

WIRE ANTENNAS

155

bicone reduces to the thin wire dipole. Then as the cone angle is increased, the antenna's first resonance occurs at shorter lengths and the impedance variations are reduced. Thus the wide-angled bicone is a broadband antenna. Kalafus (1971) set about fine-tuning the design of a spherically capped bicone to get greater bandwidth. He argued that the abrupt change from cone to sphere represented an impedance discontinuity for the outgoing TEM wave. Thus by smoothing out this interface, he evolved the bulb dipole shape shown in Fig. lob. The theoretical input impedance of such dipoles is shown by the solid curves of Fig. 1Oc. The VSWR is less than 1.1 over a frequency range of 1.8 to 1. A family of antennas exist, each value of 6(0 -+ 0.5h) requiring different radii a , and u 2 . For the complete set, the theoretical impedance curve is little changed. For several reasons Kalafus did not confirm these results experimentally, but a slightly modified version achieved a VSWR of less than 1.2 over a 1.8 to 1 frequency band. For comparison the dashed curves of Fig. 1Oc show the much more frequencydependent behavior of a biconical dipole. This curve is taken from measurements by Brown and Woodward (1952) for a cone that had a flare angle of 60" and an open end. However, the difference in impedance due to adding a sphere cap is quite small. It is often convenient to simulate thick antennas of either cylindrical or conical form by groups of thin wires. This is clearly the only practical approach at H F but is also a fairly common technique for VHF cones. A corresponding increase in the girth of the antenna is required. For cylindrical antennas the equivalent radius re is re = r(nr,/r)'

(3.1)

where r is the radius of the overall structure consisting of n wires of radius r o , while for conical antennas the equivalent solid angle $ e is found from

where rl/ is the solid angle of the whole structure consisting of n cones of solid angle $o (usually approximated by cylindrical wires). Details and performance of a typical modern H F cone are shown in Fig. 11. For such antennas the lower frequency limit depends on the side length, this being about 0.2A. Designs are possible for various cone angles so that reduced overall height is possible at the expense of ground area or vice versa. It should be noted that the most satisfactory shape at H F is influenced considerably by the necessary guying radius for both the central supporting tower and the antenna wires. Thus the complete assembly is large and

156

P. A. RAMSDALE

a

3

> v) Frequency ,MHr (C)

FIG. 11. (a) Practical HF conical monopole; (b) elevation radiation pattern diagrams for three frequencies: (i) 2 MHz, (ii) 14 MHz, (iii) 30 MHz; (c) VSWR over H F band (2-30 MHz). Courtesy of Racal Antennas Ltd.

reductions in size would be useful (particularly if the antenna were to be used as an element of an array). For broad bandwidth, these conical antennas must have a large maximum diameter. If this is undesirable, then some form of end cap to reduce the impedance discontinuity at the cone ends is always an alternative. Mason (1963) designed a biconical monopole for H F by capping an open wire cone with an inverted cone. A similar shape was used by Arnold (1970) as one arm of a dipole. This was used around its second resonance, at which point the addition of a suitable value-reactive circuit element kept the overall reactance almost constant. A crossed pair of these dipoles operated A/4 above ground gave a VSWR of better than 1.5 over an octave bandwidth. Other alternative shapes have been proposed, for example, the antenna of Gross (1976). The radiating structure had 28 wires with vertical upper portions forming a boxlike structure with their lower ends taken to a central feedpoint to form a cone. The feed was thus raised above ground and the ground plane wires sloped to reach the ground directly beneath the vertical radiators. Although this antenna does not perform over exactly the same

WIRE ANTENNAS

157

range (VSWR < 2 for 9-90 MHz), it was considered by its originator to give a useful reduction in size over the conical monopole. Such a claim seems slightly optimistic, since if the conical monopole of side length 0.21 was scaled to work the same frequency range, it would probably occupy a similar area. However, it is of interest that alternative shapes such as this have good broadband properties because with the many varied siting and supporting constraints placed on H F antennas, the allowable antenna shape tends to vary somewhat. One advantage of the elevated feed point of this particular type is that it enables circuitry to be incorporated beneath the antenna without having to sink it below the ground, and an array of these antennas with individual power amplifiers is envisaged. The other common resonant antenna is the dipole, and at H F this can be supported horizontally either by using specifically erected masts or by weighted suspension ends thrown over trees or other suitable supports. Arrays are also made but for much gain they occupy a considerable area. At VHF and U H F dipoles are physically small and arrays are a convenient size. Yagi arrays (Uda, 1926; Yagi, 1928) allow considerable directional gain to be achieved and their use for reception with domestic televisions is widespread. However, Yagi arrays are basically narrow-band devices. Although log-periodic dipole arrays (DuHamel and Isbell, 1957) have less directivity, broadband working is possible. Since their inception considerable research has taken place and design parameters are available. For example, Evans (1972) formulated a general design procedure for the 2 : 1 bandwidth log-periodic antenna by investigating the performance variation with a wide range of parameters. At microwave frequencies the advent of microstrip, stripline, coplanar waveguide, and other techniques for printing lines has led to these methods replacing conventional waveguide in many applications. It is feasible to print not only balanced lines, baluns, power dividers, etc., but also antenna elements. This has led to the reinvestigation of the dipole and other VHF, and even H F antennas, at microwave frequencies using printing techniques. Wilkinson (1974) has shown that by printing dipole arms on each side of a thin substrate, a parallel transmission line in the plane of the antenna can be used as the antenna feed. This approach is shown in Fig. 12a. A 256element array of such antennas was described. The radiating surface is placed a quarter wavelength in front of a reflector to produce a beam pointing in one direction only. The aperture had an essentially constant illumination, giving - 12.5 dB sidelobes and a VSWR < 1.3 over a 5% bandwidth at X-band. The losses in the elements and feed system were about 3 dB. Printed dipoles have been constructed to integrate with a triplate feed system by Hersch (1973). The ground planes of the triplate system are extended to form the two dipole arms while the center conductor is extended to excite the two arms. Figure 12b shows two dipole antennas and a feeder

158

P. A. RAMSDALE

2741 dipole

Parallel

Dipole

Lower dipale

Center conducto

Matching network \

/

Stripline

Reflecting surfaceA

\Feed pa,n,

,Dielectric

'Radiating

element

(Cl

FIG. 12. Printed dipole antennas: (a) Dipole and parallel transmission line (Wilkinson. 1974): (b) two dipoles with triplate feed system (Hersch, 1973); ( c ) wideband folded dlpole antenna (Dubost et al.. 1976).

system consisting of a power splitter and quarter-wave matching sections. This pair of elements, used on an aircraft landing system, produce a pattern that was omnidirectional in the half of the H-plane directed away from the triplate system and had a VSWR < 1.5 over a 57;, bandwidth. A wideband printed dipole has been described by Dubost et al. (1976). The element is a folded dipole with a very wide-driven section and a comparatively narrow-folded section. It is printed on one side of the substrate, while the feed line, which contains a matching element, is printed on the other. This arrangement is shown in Fig. 12c. The dipole can be operated close to a

WIRE ANTENNAS

159

reflecting surface, with a typical spacing of 1/50.One example of the dipole had a VSWR < 2 over a 21% bandwidth. Placing a dielectric between the dipole and the reflecting surface serves to reduce the antenna size and equalize the E and H plane patterns. The bandwidth of the above example was then reduced to 17.5% by using a Teflon dielectric.

C . Electrically Short Wires There are many situations when resonant antennas are physically too large. In particular, there are occasions at H F and VLF when it is inconvenient to set up extensive supporting masts and guys. When a monopole is electrically short, its radiation resistance is low, the terminal capacitance is large, and the current required to radiate a given power is high. The major problems are that a significant fraction of the power can be lost in the ground (the addition of an extensive system of conducting wires in the ground is usually beneficial), and the use of low loss matching networks results in narrow bandwidth. In addition, the high currents and voltages required can lead to high losses and flashover in the base insulator. For a given height of monopole, the simplest way to increase the radiation resistance is to add a top loading. This will modify the current distribution on the vertical section from a triangular to an almost constant current form, thus increasing the current moment so that the radiation resistance rises about four times, although the top loading does not itself radiate usefully. Kalafus (1971) used Harrington's subsegment moment method to find the current on short monopoles both with a T-type loading and with a spherical cap top loading (Fig. 13a, b). The aim of this work was to maximize the bandwidth (or minimize the Q) of the antenna subject to it being contained in a sphere of a given volume. It was found that without the cap the optimum angle between the foot of the antenna and the edge of the top loading was between 45" and 50" (Q = 160), while with the cap, the angle was between 50" and 58" (Q = 119) (in both cases the vertical section was A/25). However, with no width constraint, additional top loading was found to be always beneficial. Various forms of top loading have been tried and two others, the umbrella and spiral, are shown in Fig. 13c, d. The umbrella type (Gangi et al., 1965) is an attractive form at VLF because it is convenient to use the umbrella wires as part of the guy ropes. A figure of merit F , can be defined as F = 114f (3.3) where 7 is the radiation efficiency and Af the 3 dB bandwidth of the antenna system. Bhojwani and Zelby (1973) made comparisons between the three types shown in Fig. 13a-d for VLF use. The spiral top loaded had the

160

P. A. RAMSDALE

* / / / / / / / / / / /

(C)

(d 1

FIG. 13. Top loaded antennas: (a) T-type loaded monopole; (b) spherical cap loaded monopole; ( c ) umbrella loaded monopole; (d) spiral loaded monopole.

smallest horizontal size and required no tuning inductor because the spiral could be made long enough to resonate the antenna. However it had the lowest figure of merit. The T-type has the highest figure of merit but requires two supporting towers, a large horizontal span and a tuning inductor. The umbrella has an intermediate figure of merit and horizontal span, requires a similar tuning inductor to the T-type but only requires a single tower. In practice a complete economic analysis of these factors is required for the selection of a top loaded VLF antenna. If the vertical section of the antenna is made still shorter, then the structure becomes more like a transmission line, consisting of the horizontal wire and its reflection in the ground (King et al., 1960).The antenna can be made resonant if the overall wire length is extended to a quarter-wave. It is a small

WIRE ANTENNAS

161

step to alter the properties further by the addition of a terminating impedance to the line, a short circuit or variable capacitor being common. Various configurations of Ls, Ts and Ms are thus possible. Such antennas are useful when a low profile is required, either for aerodynamic reasons on externally mounted missile and aerospace antennas, or for concealment purposes. Considering the L-antenna (Fig. 14a) with small height h, the antenna

IC)

FIG. 14. Low-profile antennas: (a) L-type antenna; (b) hula hoop antenna; (c) half-wave closed loop antenna.

is almost resonant and its radiation resistance can be found approximately from transmission line theory as

Rrad= 120k2h2 (3.4) for a top section length of 4 4 . In the hula hoop antenna (Boyer, 1963) (Fig. 14b), the transmission line is bent round to form a circle but this has only a small effect on the input impedance (Burton and King, 1960). However the pattern is considerably different, being almost omnidirectional in the plane of the ring. A rigorous analysis of the hula hoop has been carried out by Egashira

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P. A. RAMSDALE

and Iwashige (1975). Their results indicate that the radiation resistance is only two-thirds that given by transmission line theory Rrad= 21(2kh)2

(3.5)

and as the radiation resistance of the vertical section alone is 20(2kh)’, it suggests that the mechanism may be that of a top-loaded monopole rather than a leaky transmission line. Their analysis can also be used for the halfwave closed-loop version of the hula hoop antenna (Fig. 14c) (Boella et al., 1965). Although these antennas are narrow band, replacement of the short circuit by a tuning capacitor enables the resonant frequency to be moved, and this capacitor can be combined with the antenna tuning unit to give a useful tunable antenna system.

D. Electrically Long Antennas Vertical monopoles of about 0.55i-0.625A are sometimes used at HF as antifading antennas. The null in the pattern is in the direction from which signals via an ionospheric path are likely to be received. Thus such signals are prevented from interfering with the normal groundwave. With a straight monopole, the directivity decreases at lengths greater than A/2 because the antenna current distribution contains components in phase opposition. Landstorfer (1976) modified the shape of a monopole so that these phase differences were compensated for by different path lengths. Thus the radiation from different parts of the wire was then in phase in a direction broadside to the antenna. With this new shape the wire curves away from the terminals before continuing almost vertically. As an example, a 34’4 monopole had its directivity increased by 6 dB while an experimentally optimized 3 element Yagi had a directivity of 11.5 dB. At sufficiently high frequencies it is possible to have straight vertical wire antennas several wavelengths long. However, the multilobed pattern that they produce is not generally desirable and there are usually more suitable forms (although with suitably spaced half-wave reversing stubs or their lumped circuit equivalent, the pattern can be improved, as will be described in Section IV). Long straight-end-fed horizontal wires can be used in either unterminated (standing wave distribution) form or terminated (traveling wave distribution, Beverage et al., 1923) form. The positions of the pattern nulls for both are the same but in the traveling wave case the backward nulls are greatly reduced. However, the termination absorbs power, so that it is an inefficient antenna. Applications for the Beverage antenna include the reception of M F and H F transmissions. At these frequencies the ground is not a perfect conductor and this factor must be allowed for in evaluating the

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propagation coefficient for the current along the antenna, and hence its other properties. Studies made include those of Knight (1972) and Kikuchi (1973). It is found that at high frequencies the velocity of propagation approaches the free space value. At low frequencies it is less and depends on both the ground conductivity and the height of the wire; the velocity increasing as the wire is raised. The attenuation is also frequency dependent: at low frequencies it is proportional to the square root of the frequency and at high frequencies increases to a limiting value dependent on the relative permittivity of the ground. Long traveling wave wire antennas can be combined to form a rhombic (Foster, 1937). With a suitable choice of angles, the major lobes of the patterns of the individual wires can be aligned to make them phase in a forward direction. The rhombic antenna is still widely used in H F point-topoint services due to its simplicity, high gain, and a relatively constant terminal impedance over about an octave. Due to the attenuation along a traveling wave wire, there is a limit to the practical length (and consequently gain) of a rhombus; thus the side lengths are usually made less than 82.The chief disadvantage of the H F rhombus is the large area it must occupy. An S-band rhombic antenna has been constructed (McDonough et al., 1957), the arms then being about 7 inches. This antenna was printed but it performed in a similar fashion to the lower frequency forms. The only compensation required was to change the lengths to allow for the slower propagation velocity of the dielectric sheet on which the rhombus was formed. However at these frequencies other superior antenna forms are usually available. IV. PASSIVE LOADEDANTENNAS A . In-Line Loading

The addition of lumped circuit-type components into wire antennas is a method of adding reactance or resistance. The impedance of the antenna can be modified although the lumped elements are not themselves radiating. Some forms of loading result in a considerably modified current distribution and hence markedly change the properties of the antenna. In the limit the introduction of many closely spaced lumped loads approximates to a continuous form of loading. This can also be achieved by using different materials. For example, using carbon fiber rather than a more conventional good conductor results in a continuous resistive loaded antenna. Such an antenna is lossy but does have strength characteristics that are in many ways superior to conventional antennas. As for the unloaded antennas considered in Section 111, the usual reasons for inserting passive loads into an antenna are

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either to improve its broadband performance or to lower the resonant frequency for a fixed height. 1. Analysis There are few additional analysis complications from adding loads into the antenna but two alternative approaches are used. The first method is that of superposition and is particularly appropriate for the subdomain solutions. The current on a segment is related to the voltages dropped across all the other segments by an admittance matrix, and with subsegment solutions, the same admittance matrix can be used to determine the effect of any combination of excited regions. For a normal transmitting antenna the terminal generator only produces a voltage across a few segments. The addition of an impedance Z , to a segment carrying current Ii results in an extra voltage source r/; across this segment

v = -ziz,

(4.1)

The simplest procedure is to find this voltage from two-port network theory and by superposition add the currents due to the terminal generator and r/; (Iizuka, 1965; Harrington, 1968). With subsegment solutions care must be taken if overlapping segments are used, since the load can only be associated with full segments (see Section 11,E). An alternative approach has been used in solving Hallen’s equation for the loaded wire by full domain solutions (Lin et al., 1970; Popovic, 1973a). A modified integral equation, including the extra voltage drops as function sources, is formed. For a symmetrically loaded dipole, loads Z , at kzi introduce an additional term (j/q)2Z12Z(zi)(sink I z - zi I

+ sin k I z + zi I )

(4.2)

to the right-hand side of Hallen’s equation (2.14). Its method of solution is the same as for the original integral equations. However, the solution is specific to the particular loaded antenna, and for studying any changes in loading impedance values, a different matrix has to be inverted. 2 . Short ilntennas

For a short monopole the input impedance is capacitive. It is usually brought to resonance by the use of an inductor at the base of the antenna, but the question of whether or not this is the best position for the inductor has been considered. Bulgerin and Walters (1954) and Harrison (1963) studied monopoles containing raised inductors. The effect of using a suitable inductance value is for the current moment to be increased because the

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current distribution below the coil becomes almost constant, instead of triangular. However, the value of inductance required also increases with the height of the coil. If the Q of the coils is fixed, then an optimum efficiency height occurs. It is only below this height that the radiation increases faster than the coil losses. Some sacrifice in improved efficiency is made if the coil is split into two, with one left at the terminals. However, this may be worthwhile in practice as it allows the operational convenience of tuning adjustments at the antenna base. Hansen (1975) studied these antennas using a piecewise sinusoidal moment method to get a more accurate knowledge of the current distribution than had been used in the earlier work. He derived empirical formulas for the radiation resistance improvement factor P and ratio of required coil reactance to foot loaded reactance (for resonance) a, in terms of the load point to monopole height ratio y. The antenna efficiency q is

(4.3) where R, and X are the input resistance and reactance of the unloaded antenna. Ramsdale (1975) considered the same antennas from a receiving viewpoint, in which case the important parameter is the signal-to-noise ratio (SNR) at the terminals of the antenna. This quantity depends on the directional gain and the relative ambient and sky temperatures as well as the efficiency and an expression for SNR improvement, due to raising the inductor, has been derived. For high sky temperatures, there is no improvement but at the other extreme, the raised coil gives an improvement over the foot loaded case of (4.4)

Thus the optimum loading points for efficiency and SNR can be determined. If i t is assumed that the current is constant below the load and triangular above, then

p = (1 + y ) Z

(4.5)

while an empirical fit to Hansen’s computations for the increased reactance is a = 1/(1 - 7 ) (4.6) By substituting these expressions into both the efficiency and SNR expressions, and differentiating with respect to y , the optimum inductor position is found to be a third of the way up the monopole. Hansen’s empirical fit gives

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a slightly larger value for due to the current distribution exhibiting a peak just above the load point, and hence the exact optimum points lie somewhere between 0.3 and 0.4 of the monopole height. These results contrast with earlier analyses that were insufficiently accurate and suggested a much higher optimum loading position. Calculations also indicate that, using coils of realistic Q, it is not practical to load very short monopoles due to the low efficiency. For example, a monopole shorter than about 0.08-O.09ib loaded by a coil of Q = 100 has an efficiency of less than 50°/0, even if copper losses are negligible. If the value of the inductance in the monopole is increased further, then the radiation resistance continues to rise and the resultant positive terminal reactance can be brought to resonance by a capacitor (Lin et al., 1970) However, for this increase the current at the inductor is large and, unless extremely high Q values are used, the antenna efficiency is too poor for any practical advantage. If still larger inductance values are used, then these can reverse the phase on the antenna and produce enhanced directivity. Although Lin showed improvements in directivity of the order of4 dB, with lossless loads the terminal resistance becomes very small and the gain changes rapidly with small variations in the inductance value. For coils of practical Q, the directivity is reduced and the efficiency is extremely poor. Ramsdale (1977) considered these antennas to see if their increased directive gain could improve the SNR, but because of these very low efficiencies concluded that this loading technique is of no practical use even at the high sky temperatures found at LF. Lin et al. (1973) extended their work to an array of two loaded short dipoles. The radiated power was increased by about a further four times over the single loaded dipole by using suitable inductances to resonate the system. Again, higher inductance values led to phase reversals and high directivity but a low input resistance. No work appears to have been published on either form of this array to assess the effects of finite Q on efficiency, SNR, and directivity. An alternative method of improving the input resistance for short antennas is to use the folded monopole, the effect of which is to multiply the terminal impedance by about four times. The increased resistance makes it easier to match efficiently, although far more inductance is required to tune the structure. This impedance transformation property is due to the distributed coupling between the driven and folded sections. Vallese (1972) used inductors at the base to introduce mutual coupling between the two sections. He argued that the resonance then depended on the sign and magnitude of the coupling coefficient and postulated that for an m-folded monopole, using separate lumped mutual coupling between the driven and each of the folded sections, the input impedance could be made to exhibit a number of staggered resonant frequencies with resultant broadbanding.

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A folded dipole was also used by Lamensdorf (1975) with one or more capacitors placed between the driven and fed sections. If two capacitors, of arbitrary value, are used, then any reactive input impedance can be realized for the antenna. A folded monopole having variable capacitance diodes at its midpoint and end was constructed, by altering the dc voltage the capacitances were varied over an 8 : 1 range and this enabled the antenna to be tuned for any length from 0.1431 to 0.3181. Two short closely spaced dipoles were considered by Mikuni and Nagai (1972). The spacing between the driven element and the parasitic was small and the dipole ends were joined by impedances. The object of this antenna was to develop a small VHF indoor TV antenna capable of rejecting unwanted signals (ghosts) by its directivity. The necessary spacing between elements is usually about 4 4 , but the required phasing was achieved instead by the use of a suitable complex connecting impedance value. An antenna about 4 3 long and 1/45 wide had an experimental front-to-back ratio of 20 dB. After allowing for its reduced efficiency the antenna power gain was about 13 dB down on a half-wave dipole, but under some high noise conditions use of the directional antenna could result in an improved SNR for a TV receiving system. 3. Long Antennas

For resonant length antennas, loading tends to detune and degrade performance so that most work has been either on short or quite long wires. The usual result of loading long wires is to reduce the reflection of the outgoing current wave on the wire thus making the distribution more traveling wave in nature. This leads to a broader band antenna from both an input impedance and a variation of pattern with frequency viewpoint. Altshuler (1961) introduced a 240 i2 resistor, a quarter wavelength from the end of a long monopole. This value was arrived at experimentally as giving the minimum variation of input impedance with frequency. Further measurements showed that this antenna had a good traveling wave current distribution up to the resistor. The antenna is about 50% efficient because half the power is dissipated in the resistor. Reasonable agreement between Altshuler’s experiments and theory was shown by Popovic (1973a) using a point matched full domain solution to Hallen’s equation. In an approximate analysis, Maclean (1973) compared the SNR of an antenna of Altshuler’s type with the conventional dipole. Ramsdale (1977) calculated the same parameter using a Popovic-type solution for the currents. It is found that Altshuler’s loading and indeed others that tend to give a more traveling wave form of current are less directional than the same length unloaded dipole. The lower directivity reduces the antenna SNR as does the reduction

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in efficiency due to the lossy loading. However if the SNR of a receiving system, of which the antenna is but a part, is calculated, then the mismatch between the antenna and the rest of the receiver is also a factor. In this case the SNR of a broadband system can be improved by using the greater impedance bandwidth of the loaded antenna. Various improvements to Altshuler’s antenna have been proposed so that its desirable properties can be retained but with less loss in the loading components. Nyquist and Chen (1968) showed that for any length of antenna there is an optimum complex loading and position for setting up a traveling wave current below the load, and at some lengths the load can be wholly capacitive. However, a lossless loading for general lengths would clearly have more application. Rao et al. (1969), Popovic (1973a), and Popovic and Dragovic (1974) considered monopoles containing several lumped capacitors. For all cases considered, the antennas were quite broadband. However the most interesting results are found with equal loadings, the distance between which becomes progressively smaller towards the antenna end. Such a tapered capacitive loading results in an overall decaying traveling-wave current distribution with standing-wave behavior between adjacent loadings. Rao’s results yielded an antenna having a pattern constancy over a 5 : 1 bandwidth in which range the VSWR < 3 . With a large number of loads these antennas approach the case of continuously loaded antennas. Shen (1967)constructed an approximation to the continuous resistive loading proposed by Wu and King (1965), their suggestion having been that a traveling wave current distribution could be made to exist along the whole antenna length if the antenna had the correct internal resistance per unit length (this being a function of position along the antenna). This type of loading was described as a nonreflecting resistive loading. Shen’s antennas had excellent broadband properties but like Altshuler’s were only 50% efficient. Popovic et al. (1975b) thought that there was probably an optimum loading consisting of continuous resistance and lumped capacitors. Thus a monopole antenna was constructed from a series of resistors with gaps to introduce the lumped capacitance. The resistance increased in steps from section to section and the magnitude of the capacitance was also increased towards the antenna end. Over a 2 : 1 frequency range, the average VSWR was 1.38 and the efficiency varied between 81 and 84’6. The current distribution and patterns were essentially as expected for a decaying traveling wave. In all of the above work, although the impedance variations of the antenna are small across a widebandwidth, there is a large susceptive component in this impedance. Paunovic and Popovic (1977) have extended the work on RC-loaded monopoles by developing an antenna that retains the broadband properties but has an approximately real input admittance.

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This was achieved by the addition of a simple reactive compensating network. For such a linear network the susceptance always increases with frequency (i.e., if negative becomes smaller in magnitude). In general antenna susceptances behave in a similar fashion. However by varying the antenna loading, substantial variation in the frequency response is possible. Thus Paunovic and Popovic attempted to minimize the difference between the antenna susceptance and a simple reactive compensating network, a coil across the coaxial feed at the monopole terminals, for the frequency range of interest. The results achieved are shown in Fig. 15. The reason for there being three sets of experimental results is that although the required coil was theoretically 15 nH, its accurate realization as an element across a coaxial line had to be determined experimentally. The VSWR with respect to a real admittance can be seen to be of the order 1.1 over an almost 3 : 1 frequency range. This is better than the various traveling wave forms considered previously due to their large susceptive component. It is interesting to note that for this antenna, although the resistances increased going away from the feed, the lumped capacitors required fell in value. Thus, despite the impressive impedance characteristic, the pattern 15.0

-10.0

I

1

'

1.L

1

I

I

I

1.0 2.2 Frequency, GHz

1

I

2.6

3.0

FIG. 15. Input admittance versus frequency for RC-loaded cylindrical monopole antenna, a = 3.5 mm, h = 17.75 cm. theoretical; + + experimental, without compensation; xxxxx experimental, optimally compensated; 0 0 0 0 experimental, undercompensated; 0 0 3 ~experimental, over compensated. From Paunovic and Popovic (1977). ~

+ +

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P. A. RAMSDALE

does vary somewhat because it is not of traveling wave form. Clearly. further optimization of these long loaded antennas will take place. The relative merits of high efficiency,preserving traveling wave properties, getting a good VSWR with respect to a real admittance and avoiding too involved a compensating network are likely to vary considerably from application to application. Other work on long antennas has involved modification of the field patterns. The radiation pattern of a standing wave antenna can be greatly modified by reversing the relative phase of the current in alternate halfwavelength sections. This suggests that an antiresonant network (trap-load) that can be either a parallel inductor-capacitor circuit or a quarter-wave nonradiating line should be inserted every half-wavelength. Such antennas are known as Franklin arrays (Williams, 1950). Smith (1975) studied these antennas with one trap per arm both theoretically, using both a piecewise uniform subsegment method and a polynomial entire domain solution to Hallen’s equation, and experimentally. By using traps a quarter-wavelength from the feed of a 31/2 dipole, a three-element collinear array should be formed. Smith found that the trap forced a null in the current distribution but did not set up the correct phase shift, and the pattern had a split beam. However, at a lower frequency (about 0.8 times), the collinear array type pattern was formed. Thus, in the equivalent monopole case, the required antenna is really a 0.61 inductively loaded monopole with the load 0.22 from the feed. However the input impedance has low resistance and a high capacitance. Although the directivity of the collinear array is similar to that of the standing wave antenna of the same height, it has the advantage that the pattern has few large lobes and the maximum radiation is broadside. Shen (1968) also looked at long dipoles including the 31/2 case and synthesized the voltages needed at the center and a quarter-wave from the end in order to set up a broadside pattern. For this case the antenna would have to be fed a quarter-wave from the end and have a complex load at the center. Another use of traps is in making the dipole operate in several frequency bands. The trap is in this case adjusted to be antiresonant when the outer section is a quarter-wavelength. Thus the current in this section is suppressed. Smith showed various ways in which the upper and lower resonant frequencies of the antenna could be varied. The upper resonant frequency can be controlled by adjusting the antiresonant trap frequency and the lower by either adjusting the outer section length or varying the inductancecapacitance ratio of the trap. At MF an antifading antenna is one that suppresses radiation from angles of elevation at which ionospheric reflections would come down and interfere with the normal direct ground wave to give frequency selective

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fading. Both a capacitive top and a series inductive load have often been used to allow masts of physical height 0.35-0.52 to give similar radiation patterns to 0.55-0.6252 unloaded monopoles. Davies (1977) evolved a design that resulted in a still shorter height. This consists of four base-driven sloping wires, each containing an inductive load, located symmetrically about a central insulated support. Although the computed properties of this antenna agree with measurement. the reasons for its advantages over the loaded monopole are not yet understood. However some improvement may be attributable to the increased horizontal dimensions of the antenna.

B. Coated Wire Antennas Instead of inserting loads in series form into a wire antenna, some researchers have investigated the effects of cladding wires with dielectric material. If an antenna is used in a homogeneous dielectric, rather than in air, its effective electrical dimensions are scaled up by the square root of the relative permittivity ( E , ) ~ ” . Thus antennas are physically shorter for resonance. Some reduction can be expected if the dielectric medium is limited in extent. Richmond and Newman (1976) analyzed a wire antenna coated by a thin dielectric layer (of fairly low dielectric constant). A piecewise sinusoidal subdomain solution was used, the impedance matrix being modified to account for the dielectric layer. The layer is represented by equivalent volume polarization currents that are simply related to the antenna surface charge density. The dielectric shell introduces no extra unknowns and the impedance matrix is the same size as in the unclad case. The results of analytic work are consistent with experiments of Lamensdorf (1967) for thin sleeves of low dielectric constant. For large dielectric constants, reasonably accurate analyses are only just being published, although James and Burrows (1973) and James et al. (1974) indicated that for coated monopoles a resonator action occurs in the dielectric material. Measurements on a short monopole coated by titanium oxide ( 8 , = 18) and barium titanate ( E , = 90) were made by James and Burrows (1973), while Birchfield and Free (1974) used distilled water ( E , = 80). A 50-cm field probe used from 20-60 MHz had its impedance reduced from 115-400 R to 4-88 R by cladding with a 10-cm diameter cylinder of distilled water. James et al. (1974) reported monopole height reductions of 10 at 100 MHz using ceramic coatings, in which case the material losses were about 2 dB. It is these losses that will in general determine whether height reduction by this technique is feasible and future material improvements may be significant. Various other forms of antenna have been coated. James et al. (1974) enclosed a three-element Yagi array with dielectric material ( E , N l o ) , and both the element lengths and spacings were reduced about three times.

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Woodman (1977) considered the discone antenna. Completely enclosing this antenna results in its broadband behavior being lost. However, replacing the cone section by a series of high permittivity rods and water-filled polythene cylinders at the base perimeter retains the antenna's broadband properties. For the 250-1100 MHz band, a VSWR I 2 was achieved over most of the range and the structure was 309,; smaller than the metal version. However, losses in the dielectric lowered the radiating efficiency to 45 %. Towaij and Hamid (1973) considered a long dielectric coated dipole. The dimensions were: dipole-length/wire-diameter = 188, dielectric-sleeve ( F , = 2.3) diameter/wire-diameter = 15.8, dipole length 4.56A-5.74R. Without the sleeve the radiation pattern was multilobed and had principle lobes 30" from the wire axis; the broadside lobes were smaller. The addition of the sleeve enhanced the broadside lobes by about 14 dB. At the lower frequency, the original main lobes were unchanged but at the higher frequency they fell by about 12 dB. Towaij and Hamid (1972) studied the multilayered dielectric sleeve on an infinite length wire. With just a single dielectric layer the radiation pattern was shown to vary from end fire to broadside as the dielectric thickness increased from zero to a quarter-wave. The addition of an air gap between the wire and dielectric enabled further pattern improvements to be achieved with critical dimensions of this gap.

V. ACTIVEANTENNAS A . Introduction

The application of integrated circuits has led to communication systems being packaged more compactly, with several functions carried out within each module. If this trend continues, a much closer association than normal between the antenna and its associated transmitter or receiver is suggested. Such combinations were considered in the early 1960s. An antennaverter or antenna-converter (Copeland and Robertson, 1961) was constructed by adding a diode mixer at the tip (the feedpoint) of a two-arm conical spiral antenna. By using the outsides of two coaxial cables as the passive section of the antenna, the cables themselves could be used to carry the local oscillator and if signals. Although this type of device avoids the usual losses of the sometimes long connection between the antenna and mixer, its use in practical situations is limited. The conical spiral typically has a 10 : 1 frequency coverage and the mixer will be driven by signals over the whole of this range, with consequent intermodulation problems. Conical spiral antennas have also been used for antennafiers or antenna-amplifiers (Rippin, 1965). A varactor-tuned amplifier was built into the tip of the spiral and by varying the varactor dc voltage, the amplifier frequency was tuned from 120 to 240 MHz, about 10 dB circuit gain being obtained over this range.

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Copeland et al. (1964) used resonant half-wave dipoles as the passive sections for antennafiers. These were used as elements for an array at VHF. The amplifiers had about 20 MHz bandwidth and were noise matched to the dipole (amplifier noise figure 4 dB, circuit gain 12.5 dB). For transmission, antennamitters (antenna-transmitters) were considered. In these, the antenna wire forms part of the transmitter final-tuned circuit, thus eliminating lines between the amplifier and the antenna. The performance of these various antennaverter, antennafier, and antennamitter devices can be described by considering separately the passive radiating section and the active circuitry. The active circuits d o not affect the radiation properties because the form of the antenna current distribution is not influenced by the electronics. However, a more complete form of integration is possible in that the electronics can be moved from the conventional feed point into the radiating structure. This type of antenna was first considered by Meinke (1966b), and the properties of various monopole and loop configurations containing transistors have been studied. Such antennas have unique properties, the active components modify the current distributions, and parameters such as the radiation patterns can differ for transmission and reception. However, it is questionable whether moving the electronics away from the feed is advantageous. Work on the synthesis of loaded antennas also leads to a requirement to insert active devices into the antenna. If the loadings to produce desired antenna characteristics are calculated, then the required loads may have negative real parts (Fanson and Chen, 1973), or frequency-dependent characteristics unrealizable passively, such as a negative inductance (Poggio and Mayes, 1971). Thus some form of active load is required in these cases. Tunnel diodes enable negative resistances to be inserted into the antenna structure, but, although such antennas have been made (Meinke, 1966a), they tend to be unstable. Antennas have been defined as active (Meinke, 1970) if the energy at their outputs is not exclusively derived from the incident energy at their inputs but also from energy sources in the antenna itself. This definition holds for antennas with separable amplifiers, which in this article will be referred to as nonintegrated. For completely integrated active antennas, a suitable definition requires the additional restriction that the antenna’s performance cannot be described by an amplifier in series with the passive antenna formed by the removal of the active elements from the antenna. B. lritegrated Aiitennas

Meinke (196613) proposed forms of active antennas which consisted of a combination of a loop and a monopole antenna together with a transistor at their common junction, as shown in Fig. 16a, b. These were later described

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(C )

FIG. 16. Integrated active antennas: ( a ) Fed-emitter, collector-loop monopolc (f.e.c.1 ); (b)

fed-collector, emitter-loop monopole (f.c.e.1.);(c) amplifier loaded monopole.

as “active loop-monopole antennas” by Ramsdale and Maclean (1971), the loop being required to provide a dc current path for the third terminal of the transistor. There are six possible orientations of a single transistor within the loop-monopole structure, and, for a unique definition, two of the transistor wire connections must be specified. Thus the antenna of Fig. 16a is described as a fed-emitter, collector-loop monopole antenna (f.e.c.1.).This antenna is found to be resonant when its overall length is several times shorter than the self-resonant length of the incorporated monopole. In Meinke’s initial analysis of these antennas, the wires were represented by suitable lumped impedances and only the signal received by the top section was considered, this being amplified by the transistor. For both

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f.e.c.1. and f.c.e.1. types (Fig. 16b), a height reduction factor for resonance, compared to the passive monopole, of (1 b)”’ was predicted. By superposition, the terminal impedance of a passive antenna can be shown to be the same for both transmitting and receiving. Provided that the transistors in the active antenna are acting in their linear mode, then superposition is still applicable. Thus Ramsdale and Maclean (1971), by using a more conventional antenna analysis with the approximation of sinusoidal transmitting currents on the wires, determined the terminal impedance and thus the height reduction factor for both transmitting and receiving active loop-monopoles. The transistor was treated as a two-port, and the current distribution constants were determined from the boundary conditions this imposed. Dubost et al. (1971) used similar boundary conditions but replaced each antenna wire by an equivalent transmission line. These analyses enable one to predict the effect of varying the transistor position. All three groups of workers found similar height reductions for f.e.c.1. antennas, both theoretically and experimentally, even in Dubost’s work in which the monopole wire was made very thick compared to that used for the loop. Ramsdale and Maclean (1972) considered a monopole containing an idealized amplifier at its midpoint, as in Fig. 16c. For resonance, the height h is given by

+

tan kh/2

=

JG,/G,

(5.1)

where G , and G , are the amplifier voltage and current gains, respectively. This antenna is an approximation to the loop monopole, provided it is valid to treat the loop wire as merely a short grounding connection. For example, in the f.e.c.1. case, the transistor acts as a common collector amplifier, and the expression for the height becomes tan khJ2 rr

fi

(5.2) where is the common emitter current gain of the transistor. This form gives a better agreement with experimental results than the earlier (1 + p)’~’ height reduction factor approximation. Theoretically, the use of low frequency transistors in the f.c.e.1. antenna does not result in any height reduction property. However, at higher frequencies, experiments usually show these to be of comparable resonant length to the f.e.c.1. antenna. This is partly explained by the amplifier loaded model, as in this connection there is both current and voltage gain, and hence a possibility of height reduction, depending on their ratio. In addition, the high frequency behavior of the transistor introduces complex impedances that also modify the terminal impedance. Pelletier et al. (1972) studied an f.c.e.1. antenna in which the loop wire was returned to ground inside the fed wire. The analysis was carried out using a moment method,

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and, as the loop wire now formed the inner of a coaxial line, it was screened and for the analysis could be replaced by a suitable impedance at the transistor. Theoretical and experimental work on this antenna from 100 to 300 MHz indicated that the maximum height reduction and impedance bandwidth occurred when the transistor was at the foot of the antenna. A similar result was found by Ramsdale and Maclean (1971) for the more conventional unshielded loop. A different type of 200 MHz transistor was used, but the maximum height reduction occurred when it was located at the terminals. The corresponding 200 MHz f.e.c.1. antenna had a more constant height reduction performance with position but the maximum occurred with the transistor moved only a short distance away from the bottom of the structure. Rangole and Saini (1975) extended the amplifier loaded approach to include amplifiers across the loop. The usefulness of this treatment has been questioned (Rangole et al., 1975), chiefly because the amplifier across the loop does not model a grounded transistor. This is because the free wire is connected to the top section, which acts as a high impedance rather than as an approximation to ground. The f.e.c.1. and f.c.e.1. antennas are usually regarded as receiving antennas, because in their limiting cases, with the transistor located at the feed, they become monopoles connected to receiving common collector and common emitter amplifiers, respectively. The amplifier loaded approach suggests that a fed-emitter, base-loop antenna should have a large height reduction property and in its limit it corresponds to a transmitting common base amplifier. Maclean and Morris (1975) have experimentally confirmed its small resonant size. A 1-meter loop dipole (with small loop area) and transistors located at the midpoints of the dipole arms was resonant at 1.75 MHz, a height reduction of 86 times. Although the height reduction fell slightly, to 81 times, when lowering the transistors to the feed, the power transmitted and the impedance bandwidth were then both maximized. Thus, in all of the antennas considered so far, it can be seen that little has been gained by moving the transistor away from the conventional feed point while the elevated position does make practical considerations such as biasing more difficult. However, the existence of the loop wire (which has so far been taken to be small) introduces an additional variable into the raised transistor structure. For example, the antenna height can be reduced further by increasing the loop area (Ramsdale and Maclean, 1971). In addition, the loop wire does enable the antenna to exhibit some directivity even for fairly small loops. This is due to the transistor introducing a phase shift between the monopole and loop wires. However, before considering the patterns it must be appreciated that, unlike passive antennas, the reciprocity theorem does not apply and the transmitting and

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receiving field patterns differ. Ramsdale (1971) studied the patterns of f.e.c.1. and f.c.e.1. antennas and found some front/back directivity. Unfortunately, this was greater for transmission than reception, whereas the antennas considered perform better in the receiving case for their other parameters. Wong (1974) analyzed a receiving loop monopole by a moment method. The transistor for this experimental work was mounted below the antenna ground plane and connected into the antenna structure by the use of coaxial lines inside. Thus the two-port load included these lines as well as the active device. Although this method eases the practical construction and biasing problems, it does in general reduce the antenna bandwidth. By using the coaxial lines, Wong introduced an extra phase shift into the two-port, and he calculated the field pattern front/back ratio for various values of this phase shift. For the amplifier chosen, a cardioid pattern was set up with the line lengths optimized, and a 15 dB front/back ratio was measured at 100 MHz. However, due to mutual coupling between the monopole and the loop sections, this pattern deteriorated at higher frequencies. Wong also considered the signal-to-noise ratio (SNR) due to noise generated within the antennas. Theoretical results were obtained by adding Van der Ziel noise generators to the transistor model and Nyquist generators for the resistors. Good agreement was found with experiment but no optimization was attempted. Maclean and Ramsdale (1975) developed an expression for SNR that also included the sky noise contribution 172

SNR =

v oc

4kT, BR,

+ 4k17;BR, + 4kT,,,

BR,

(5.3)

where each of the terms in the denominator is simply the open-circuit noise voltage associated with a particular resistance. Kmb,and T, are the sky, ambient, and equivalent transistor temperatures, respectively, and R , the radiation resistance, R, the input resistance due to transistor losses, and R, the antenna wire resistance. For an idealized low frequency transistor, the SNR has been plotted (Fig. 17) against transistor position for an f.e.c.1. antenna of fixed length (resonant when the transistor is at the midpoint of the monopole). It can be seen that unless the sky noise is high, optimum SNR occurs with the transistor at the foot of the monopole, but at low H F it becomes beneficial to raise the transistor. The reason for this is that although the transistor’s noise contribution increases as it is raised, the sky noise contribution falls to a minimum with the transistor at a height equal to about 0.7 of the total. The overall SNR performance depends on which of the noise contributions is dominant. Thus although integrated antennas have unique properties, so far only a limited number of cases have been found in which it is advantageous to

r,

178

P. A. RAMSDALE

0

t

e

a

7

10

0

I

I

0.2

0.L

I

0.6

I

0.8

I 1.o

Transistor height, I/h

FIG. 17. Relative signal-to-noise ratio against transistor height for varying sky noise temperature for an f.e.c.1. antenna. From Maclean and Ramsdale (1975).

move the transistor away from the antenna terminals. For the loop-monopole form, comparisons with passive antennas are difficult as the equivalent passive loop-monopole is not a practical type, whereas comparisons with the monopole are not always helpful because some of the properties are attributable to the loop wire. A general appraisal of all the possible integrated types with many alternative wire structures and a wide choice of active devices is difficult and very general statements have not been made. However, the work so far does not lead to great optimism that the improvements these antennas offer are generally worth the extra practical difficulties introduced. However, work on antenna synthesis may result in a requirement for integrated types, because they can set up current distributions that are not passively realizable. C. Nonintegrated Antennas

All commercial antennas so far have been of the nonintegrated type. In these cases the problem hinges on the interface between the antenna wire and the amplifier to which it is attached. This has been optimized for single

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elements for power match, noise match, and intermodulation products that are generated by the nonlinearities of the active components. When these antennas are used as elements of arrays, mutual coupling effects between them can also be reduced. 1. H F Antennas

Some active antennas are designed to provide an output signal independent of frequency, such antennas being referred to as aperiodic (the term frequency independent having already been established for antennas whose properties are angular rather than length dependent). The basic wire part of the antenna can be either a small loop or a short monopole or dipole. An aperiodic loop antenna was developed as an element for an array (Callendar, 1972). The loop is electrically small for which case its current is essentially constant. The radiation resistance is small compared with the reactance of the loop, and this reactance is proportional to frequency, as is the effective length and, thus, open-circuit voltage. The short-circuit current (open-circuit voltage/reactance) is thus independent of frequency. The amplifier is designed to have a low input impedance so that the loop is effectively short circuited over its working range, and if the amplifier has a high output impedance, the complete active antenna acts as a constant current source over a wide frequency range. Due to the deliberate mismatch between the loop and its amplifier, the noise matching is far from optimal and this limits the technique to situations where the atmospheric noise is high. For low input impedance transistor amplifiers, this limit lies in the middle of the H F band. The small size and low mutual coupling of these elements, together with their broadband response make them useful elements fclr receiving arrays. Various types of arrays have been constructed, the clement spacing being similar to that using any other form of element. However, their small size reduces the mounting problems so that overall the practical array will require much less land area and can be fitted into already crowded antenna farms. The electrically short monopole or dipole also has a well-behaved response. The open-circuit voltage is approximately equal t o its half length multiplied by the field strength (as the current distribution is roughly triangular). Thus by straightforward amplifier design an output independent of frequency can be produced. The amplifier must have a high input impedance (larger than the dipole impedance) and at H F an FET can be used. As this has a better noise figure than low impedance amplifiers, the usable upper frequency is slightly higher than for the active loop antenna. The noise (atmospheric, man-made, and galactic) across the H F band

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P. A. RAMSDALE

diminishes as frequency is increased. If the noise figure for the receiver is fixed, then it is possible to calculate the required output response from the antenna in order to give a constant overall noise level for the system. This response is very close to that of the short monopole open-circuit voltage. Thus, this was used by Sosin (1976) as the passive section of an active antenna. Due to the congestion in the H F band, a large number of high-level interfering signals are usually present at the antenna. The number and levels of these at the amplifier depend on the response of the antenna wire. Intermodulation products are generated between the signals due to nonlinearities in the amplifier and, in a broadband system, many of these will lie in the band and obliterate communication at various frequencies. It is because of this that the short active antenna can have an advantage over longer antennas. Due to the variation in output parameters, especially around resonance, longer antennas deliver signals at a much higher level than is necessary at some frequencies, otherwise the signal level is inadequate elsewhere in the band. Thus signals that can result in troublesome intermodulation are at a far higher level than is the case with the more even response of the active form. Sosin describes a 1-2 m active monopole that gives a satisfactory intermodulation performance for the H F band (10 kHz-30 MHz) even in the hostile radio environment of a ship (field strengths from adjacent transmitters as high as 6 V/m). An alternative element was used at H F by Collins (1974). A loop fed by an unbalanced feed has two modes, a constant current around the loop gives a figure of eight pattern and currents flowing in opposite directions on the two sides of the loop give a circular pattern. By splitting the loop into two semicircular halves and joining them at the top by a resistance and at the bottom by the feed, the relative levels of the two modes can be adjusted and an overall cardioid pattern achieved. The practical element had typically a 12-dB front-to-back ratio and the resistance in the loop raises the input resistance to around 50 Q. Thus an amplifier incorporated at the feed point can be easily matched. These elements have been used in a log-periodic receiving array (Hanna and Collins, 1976). All the elements have a broadband 50 SZ output and similar gain vs frequency response curves. They are connected to a uniform coaxial feeder via a coaxial tail, a single-stage seriestuned circuit, and a transformer, the latter providing phase inversion for adjacent elements. The elements are spaced in conventional log-periodic fashion, and experiments on 12-element arrays resulted in a frequencyindependent beam up to 20 MHz. Clearly, the use of these small elements is an attractive alternative to conventional large HF arrays. At HF the use of inefficient elements is quite adequate for reception because the major noise contribution comes from the sky and the noise

18 1

WIRE ANTENNAS

contribution, either from resistance in the antenna element or from a mismatch into the amplifier, has a negligible effect on the overall signal-to-noise ratio of the system. For transmission, inefficient elements are usually too wasteful of power. As many communication services require both transmission and reception, a common antenna is advantageous, and so active antennas can only be used in a limited number of applications. 2. V H F I U H F Antennas At VHF sky wave noise is much lower and the overall noise is largely determined by the receiver and the interconnecting circuitry from the antenna. Systems containing a passive antenna and an active antenna are represented in Fig. 18 by a series of two-port networks. Each lossy match or

Passive Antenna

Match

Line

Receiver

(a)

I

I

I

I

TA

Tamb

‘Fussive :Antenna

Match

Temperature Gain

Tomb

I I

GL

I

I L

TR

Transistor Amp1itier

___________---

;

Line

I I

-J

Active Antenna (b)

FIG.18. Equivalent two-port network representations of (a) passive and (b) active antenna receiving systems.

line contributes to the noise not only by producing noise but also by having a gain less than one that increases the effect of the following noise sources. Consider Fig. 18a; the antenna of temperature TAis matched to a lossy line, the matching circuit and the line both being at ambient temperaThe line is assumed to present a perfect match to the receiver that ture Tamb. has an effective noise temperature TR. The total system-noise temperature T, is then given by

182

P. A. RAMSDALE

As GMand G, are both less than unity, the effect of using a long lossy line is to increase the system noise considerably. This situation is quite common because receivers are often placed in convenient locations for the operators, whereas the antenna must be sited in the open at a nonscreened location. In Fig. 18b the nonintegrated active antenna is considered. The matching circuit is modified, as it is now necessary to match to the transistor impedance rather than to a line impedance. The transistor amplifier is located at the terminals of the passive section and has a gain G, and a temperature TT. The new system noise Ts is

(5.5)

If the transistor gain is sufficiently high, then the final two terms of this expression can be neglected because the line and receiver noise contributions are suppressed by the additional amplification. The transistor noise temperature depends considerably on the impedance it sees at its input; thus the passive section of the antenna should provide not only a suitable impedance for a good power match to the amplifier G,,, but also a suitable impedance for a low noise temperature T, . If the matching circuit introduces a large loss, then the optimum system noise is governed mainly by the power matching (Meinke, 1969),but for the majority of VHF/UHF active antenna designs. the best performance is found when the impedance has been optimized for the minimum transistor noise temperature. Thus the problem for a given amplifier reduces to providing the best impedance from the antenna wire to minimize either TT or Gv1.This is a common circuitry problem and can be carried out by plotting contours of constant power match and noise match on a Smith chart. Fukui (1966) showed that the loci of constant power gain and constant noise figure appear as circles on such charts. The optimum noise source impedance Zap,for a 35803E transistor is shown, in Fig. 19, over a range of frequencies. Circles of constant noise temperature are also plotted for a frequency of 1 GHz. Similar circles could be plotted for the other frequencies shown. The graphical technique has been used for the design of a large number of active antennas by Meinke and Lindenmeir. The impedance of a passive section cannot track the optimum impedance curve because it moves around the Smith chart in a clockwise direction with increasing frequency. One method of getting a good noise performance over a broad bandwidth is to use a passive antenna section whose impedance response forms a loop

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FIG.19. Source impedance for optimum noise match for a 35803E transistor with circles of constant noise temperature at 1 GHz. From Meinke (1975).

around Zap,. An example of Meinke (1975) is shown in Fig. 20a. A folded dipole with short circuits at A and B is printed on one side of an insulating plate. This is capacitively coupled t o inductors C and D on the other side. The overall impedance response gives an impedance loop around Z,,, in a band between 1 and 2.4 GHz. Various other configurations of conductors have been used to give an impedance loop. Landstorfer (1969) describes an active TV antenna for the range 470 to 800 MHz, and Lindenmeir and Meinke (1969) describe an antenna built into the wing mirror of a car. The metal hood of the mirror forms a capacitive top loading and, together with an involved printed section, produces an impedance loop for the VHF coverage of 87.5 to 108 MHz. The same structure is also used as an electrically short passive section for the M F amplifier (150 kHz-20 MHz). Flachenecker (1969) formed a lightning-proof ground antenna for airplane communication between 100 and 156 MHz. The desirable impedance characteristic was achieved by using a double-folded monopole with top capacitance as shown in Fig. 20b. This particular structure was tested by simulated lightning discharges, and both the antenna and transistor circuitry survived. Although this is an extreme case, it is generally necessary to pay some attention to the protection of the active devices. For atmospheric discharges, structures with

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P. A. RAMSDALE

li 1

lii)

(b)

FIG.20. Two examples of passive antenna sections having a loop in their impedance response. (a) Two sides of an insulated plate with printed conductors (black). From Meinke (1975). (b) Lightning proof structure: (i) Double-folded monopole with top capacitance: (ii) impedance plotted against frequency (in MHz). From Flachenecker (1969).

a ground return not through the active device would seem to be preferable. If interfering signals are the major problem, then the bandwidth of the radiating section needs to be limited. Lindenmeir (1971) used a high Q circuit for the passive part of a rocket antenna. The impedance curve encircled the optimum noise impedance point over a 32-38 MHz frequency band, but outside this range the impedance was highly reactive and signals were suppressed.

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185

Daniel and Dubost (1976) combined the broadband properties of the thick folded dipole with a low-noise amplifier. The element is shown in Fig. 21a. The driven wire has a radius eight times that of the loop sections and the whole structure is embedded in dielectric. By the addition of parasitic elements and short circuits, the impedance curve was moved near to Zopt for the transistor used. In Fig. 21b the impedance of the structure is plotted, as are the transistor noise circles at 900MHz. The overall antenna works satisfactorily from 0.4 to 1 GHz. For these types of antennas there are two possible categories of amplifier that can be used either wide-band or narrow-band (tuned or tunable) types. With a very wide-band type, cross and intermodulation can be a problem, and good noise performance is not generally possible over all of the range. Although the tuned amplifier suffers from neither of these drawbacks, it must be retuned every time a new frequency is to be received. With the antenna often sited far from the receiver, varicap tuning is thus required. One area where a tunable amplifier is acceptable is for an active set top television antenna. The variable capacitor can be calibrated in channel numbers and the short radiating sections can be well matched for good noise performance. The resistively loaded loop element used at HF by Collins (1974) has also been used in an active TV antenna (Gibson and Wilson, 1976). The passive part of the element has a broadband essentially resistive impedance across the VHF band (54--216MHz). Although at the bottom frequency the efficiency of an 18-in.-diam antenna was only 0.7%, the source impedance it presented gave a good noise figure contribution from the following amplifier. In addition the cardioid pattern enables some directional rejection of unwanted signals. Gibson and Wilson favored this antenna rather than an active 18-in. dipole for this particular application because of its more consistent noise figure performance over the entire frequency band. Anderson and Dawoud (1973), Anderson et al. (1971), and Dawoud and Anderson (1972, 1974) have studied transistor-fed printed monopole elements in arrays at microwave frequencies. As a consequence of using high input impedance transistor amplifiers, the interelement mutual coupling is reduced. Printed monopoles of approximately quarter-wave were used at about 1 GHz. The buffering effect of the amplifier gives a much more constant impedance than the unloaded monopole, and for an array the radiation pattern level and shape is also preserved over a wider bandwidth. Thus in an array the element mutual coupling effects are suppressed compared with the corresponding passive case. This is particularly useful if the active antennas are used as elements of a superdirective array (Dawoud and Anderson, 1974). An antenna array of small dimensions with high directivity is theoretically possible although its practical realization is generally

186

P. A. RAMSDALE

Matching network

Coaxial cable

Short circuit

output

Bias

(b)

FIG.21. Active folded dipole with parasitics embedded in dielectric. (a) Construction: (b) passive section impedance versus frequency (in MHz) and circles of constant noise temperaturc for HP35823E:.f= 900 MHz, V,, = 10 V. I , = 5 mA. From Daniel and Dubost (1976).

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difficult. With passive quarter-wave monopoles as the array elements, the pattern is extremely sensitive to frequency changes. However, Dawoud and Anderson constructed an experimental active array that preserved the same superdirective pattern over a much wider bandwidth. Their four-element end-fire array had a total length of 3A/8, and a 60"beamwidth was achieved for a 5",, frequency deviation. Daniel and Terret (1975a, b) considered the mutual coupling between pairs of dipoles. They constructed the locus of the load impedances to give constant coupling, this being a circle on the Smith chart. Such curves enable microwave transistors to be selected by considering the impedance they present to the wire section. For typical 1-GHz bipolar transistors and FETs, the output impedance is in both cases high and results in a reduction in coupling for transmitting antennas. However, for the receiving case, it is the amplifier input impedance that matters, and the bipolar transistor results in even more coupling than for the matched case, whereas FETs are still useful for coupling suppression, as Anderson and Dawoud's experiments had previously indicated.

3. Conclusions Thus it can be seen that a large number of nonintegrated antennas for receiving applications have appeared in recent years. At HF aperiodic dipoles and loops give consistent broadband performance and future improvements in the noise performance of amplifiers will extend their working ranges slightly. Further amplifier development should result in improved dynamic range and better intermodulation performance for the congested H F band. Again at VHF and UHF amplifier development should improve and extend the performance. Smith chart plots for noise matching, power matching, and interelement coupling have all been used. The future design of these antennas will probably involve still further use of these methods and quite complicated radiating section shapes seem likely to be empirically evolved to optimize performance. VI. ANTENNASELECTION A . Fundamental Limits

For an antenna of a given size there are limitations on the maximum directional gain and bandwidth. Although practical antennas will fall short of any ideal, this does enable an upper bound to be placed on the performance of an antenna occupying a given volume. Chu (1948)considered three

188

P. A. KAMSDALE

cases: maximum directivity G, minimum Q (or maximum bandwidth), and maximum G/Q. His conclusions were that for an antenna having a maximum dimension 2 4 the Q increases rapidly if gains greater than 4a/A are required. For lower gains the antenna is potentially broadband and an antenna generating a field corresponding to that of an infinitesimally small dipole has potentially the broadest bandwidth. A small amount of superdirectivity is quite practical, as in the case of the Yagi array but in general if antennas are to be of supergain type, then high-order spherical waves must be generated and this requires rapid amplitude and phase variations in the antenna current. The reactive power increases relative to radiated power and so the Q increases. However in practice the large currents lead to large losses, and the Q, efficiency, and power gain all fall, thus the realization of a supergain antenna is difficult. Tucker (1967) suggested that decoupling between the radiating elements of the antenna and the network connecting them would improve the bandwidth. This is because the high Q is not inherent but arises from tuning out the large reactance. However it can be seen that this decoupling technique will result in a poor power match into the antenna, so although it may be superdirective, it cannot be regarded as a supergain antenna. This decoupling method is used in the active array described in Section V,C,2. (Dawoud and Anderson, 1974) in which each element is driven by its own transistor. This prevents loop coupling (i.e., power coupled through space between elements is not fed back in the coupling network). The array is much less frequency-dependent than one in which loop coupling is not restricted. Chu’s result for minimum Q indicated that an antenna having an infinitesimally small dipole-type field has potentially the broadest bandwidth. This property is the basis of the aperiodic active HF loop and dipole antennas described in Section V,C,1. B. Antennas in Systems

An antenna is only one part of a complete communication system. Thus the antenna’s properties should not be treated in isolation; rather, they should be matched as effectively as possible to the system requirements. If the system works to a desired specification, then the antenna can be regarded as adequate. However it is often desirable to tighten some parameter; e.g., at H F it is often attractive to reduce the size of the antenna (and thus the cost of land and supporting structures). The small active antennas considered in Section V,C,l. optimize the radiation parameters in such a way that the degradation in broadband receiving system performance compared with conventional size antennas is negligible. Passive loadings

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(Section IV) may result in less efficient antennas with less directivity, but their improved impedance bandwidth can result in a better receiving system signal-to-noise ratio for certain noise conditions (Ramsdale, 1977). Smith (1977) considered the overall efficiency of an electrically small antenna combined with a matching network. Two examples having quite different behavior were shown. A wire loop antenna was cooled to decrease its resistivity so that its efficiency improved. However, the system improvement was not as great because the antenna Q was also increased, higher currents flowed in the matching network, and its efficiency fell. On the other hand, the addition of a ferrite core to a loop antenna increased both its radiation and losses. However, the resultant lower Q led to improved matching network efficiency and, in consequence, the overall efficiency was significantly better. It is extremely difficult to compare different types of antenna because of the variety of parameters that differ. However, Sosin and Butt (1976) made some interesting comparisons among H F antennas. Plots of normalized ground area and normalized cost against bandwidth were made for various designs and types. The ground area used included that required for all the supporting masts and stays. The results indicated that increase in gain depends directly on ground area, almost independently of antenna type, while the close similarity between the two plots indicated that cost is also directly related to size. In terms of choosing between antennas there is often no marked improvement from using modern types. In particular a rhombic is no larger or more expensive than the currently more fashionable logperiodic. For broadband antennas the size is little affected at low gains but increases significantly with high gain structures.

C . Synthesis and Optimization Completely general synthesis techniques have not been evolved but for many types there are several features that can be varied to give a closer match to some desired specification. By numerical analysis techniques (Section II), antenna currents can be calculated for given excitations. Typically, a multi-impedance loading of n loads to produce desired currents at n points on the antenna or the field in n directions can be found, these being unique problems. Nonlinear constraints include using n loads to give a desired terminal impedance at n frequencies or 2n reactive loads to fix n values of one of the antenna characteristics (Fanson and Chen, 1973). The problems have multiple solutions, and so search techniques are used. However, a poor initial choice will lead to a local rather than a global optimum. In general, these problems seem to be extremely ill-conditioned, and a rapid fluctuation

190

P. A. RAMSDALE

of the desired antenna characteristic between the fixed points is common. Thus the only practical approach to antenna synthesis seems to be an optimization method. However, the possible criteria for optimizing are numerous. For example, over a given frequency range, the antenna’s terminal impedance can be made as constant as possible, or its susceptance can be made as small as possible, or the mean VSWR can be minimized. With one and two capacitive loadings of variable value and position, Popovic et al. (1975a) minimized the average reflection coefficient over a given frequency range. However, as the reflection coefficient was evaluated for the mean antenna admittance, the antenna was optimized to a somewhat arbitrary impedance that was unlikely to correspond to any realizable source across the frequency band. Optimization for a reflection coefficient into 50 Q, say, is not really feasible by this approach, since the optimizing function could be minimized by either a fairly constant reflection coefficient or a more variable result having values both vastly superior and inferior to the mean (although, by a suitable weighting factor, the excessively large values could be discouraged). Popovic et al. (1977) optimized the average reflection coefficient referred to the average antenna conductance. This makes the widely varying result much less likely and gives results with a realizable impedance (as conductance is not frequency dependent). For this work a monopole with two identical closely spaced parasitic elements was used, their height and spacing being the variables. For a frequency range of 1.2 : 1, a mean VSWR of 1.09 was achieved. Harrington (1968) represented some system parameters by various performance indices of the form

[~*1“41[~1 =

[ii*][B][IY]

in which [ A ] and [ B ] are square Hermitian matrices (i.e., A,, = A:m) derived from the antenna admittance or impedance matrices, IY is an unknown column matrix (either the antenna current or voltage), * denotes complex conjugate, and - denotes the transpose of a matrix. By matrix theory it can then be shown that the maximum value of p is the largest eigenvalue of the equation

Indices that can be expressed in this form include the gain, signal-to-noise ratio, Q and efficiency. Most work has been on arrays with excitation voltages as the variables, but it is possible to use other parameters such as impedance loadings within elements, or variable lengths or element spacings, with no change in the basic method of solution.

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Sarkar and Strait (1976) optimized gain, Q and main beam radiation efficiency S (Cheng, 1971).

S=

radiation intensity in direction of maximum radiation (sum of excitation current magnitudes)’

(6.31

A low value corresponds to superdirectivity and in consequence large power losses due to the large currents. These performance indices were optimized both with and without additional constraints on nulls in the field pattern and sidelobe levels. Also one performance index was optimized subject to a constraint on another. Once the performance index is selected, a search procedure can be used with a suitable number of variables. However there are problems in selecting suitable starting values to avoid finding local rather than global optima of the indices. Until more experience has been gained, the degree of preselection required (for good initial values) is hard to predict. A specific example, carried out by Harrington (1976), was of an array of dipoles, the central one being driven and the rest, located on a circle, having reactive loads at their terminals. A univariate search technique was used to find the local maximum of the gain. The gain was optimized for a range of directions so that the required reactances for steering the optimal main beam were found. Good results depended on the initial values, and the most often used were the reactive loads that resonate the maximum gain real currents and the reactive loads that resonate the maximum gain complex currents.

D. Conclusions There are a wide variety of antenna types, and which one should be selected is very dependent on the specific application. By considering the complete communication system, it is found that there are cases when improving the characteristics of an antenna in isolation does not yield a comparable system improvement. Conversely, small and inefficient antennas can be viable, especially in high noise receiving situations. Considerable progress has been made in numerical antenna analysis in recent years, and the inverse process of synthesis is a logical extension. Functions can be evolved to describe the main system requirements and optimization methods can be used. However, although adequate control depends on the antenna having sufficient variables, with too many variables the computation time increases, and it is also difficult to avoid local optima unless considerable expertise is used in setting initial values. Whether or not these techniques can generate significantly improved antennas will not be clear until the behavior of performance indices has been studied further.

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P. A. RAMSDALE

In the future, as more computations are carried out, knowledge of various antennas in a systems context will be built up. Comparisons of quite diverse antenna types by the same functions should put antenna selection onto a far more informed basis than at present. VII. CONCLUDING REMARKS

Several numerical schemes are currently in use for the analysis of wire antennas. Subdomain methods are the most popular, but better basis functions are required to avoid the problems that arise from lack of continuity. Future work should reduce the possibility of anomalous results and improve the conditioning and stability of the numerical models. Most wire antennas have been evolved from the basic dipole and straight wire types. Changes in the geometry and the addition of passive loadings have led to improved gain, greater bandwidth, and a reduction in size, and these factors can be traded off against one another. Active loads offer still more flexibility, but to date commercially produced forms have been nonintegrated, the electronics only being used for matching and amplification. The large number of antenna types makes selection difficult, although the problem can be quantified by setting up functions describing the requirement in a systems context. For a given antenna type, the dimensions and loadings can be synthesized using optimization techniques, but practical limits for the number of variables and their initial values are not yet known. Despite the many years already spent studying and developing wire antennas, it is a subject that is still very alive today. The time when all forms of wire antenna can be said to be well understood and when useful new variants stop appearing seems to be well into the future. ACKNOWLEDGEMENTS The author wishes to thank M. H. N. Potok, J. R. James, C . Wood, P. S. Hall, and A. Henderson for their helpful and constructive comments on this manuscript.

REFERENCES Altshuler, E. E. (1961). IEEE Trans. Antennas Propag. 9, 324. Anders, R. (1977). Dig. URSI Symp. Electromagnetic W a v e Theory p. 284. Anderson, A. P. and Dawoud, M. M. (1973). IEEE Trans. Antennas Propag. 21, 371 Anderson, A. P., Davies, W. S., Dawoud, M. M., and Galanakis, D. E. (1971). IEEE Trans. Antennas Propag. 14, 537. Arnold, P. W. (1970). IEEE Trans. Antennas Propag. 18, 696. Bates, R. H. T., James, J. R., Gallett, I. N. L., and Millar, R. F. (1973). Radio Electron. Eng. 43, 193.

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Beverage. H. H., Rice, C. W., and Kellogg, E. W. (1923). Trans. Am. I n s t . Electr. Eng. 42, 215. Bhojwani, H. R., and Zelby, L. W. (1973). I E E E Trans. Antennas Propag. 21,293. Birchfield, J . L., and Free, W. R. (1974). IEEE Trans. Antennas Propag. 22,471. Boella, M., Cugiani, C., Villa, A,, and Zich, R. (1965). Electron. Lett. 1, 183. Boyer, J. M. (1963). Electronics 11, 44. Brown, G. H., and Woodward, 0. M. (1952). R C A Rec. 13,425. Bulgerin, M . A,, and Walters, A. 8. (1954). NOLC Rep. 154, 67. Burton, R . W., and King, R. W. P. (1960). Microwave J. 3, 89. Butler, C. M. (1972). IEEE Trans. Antennas Propag. 20, 731. Butler, C. M., and Wilton, D. R. (1975). I E E E Trans. Antennas Propag. 23, 534. Callendar, M. H. (1972). I E R E ConJ Proc. 24, 149. Chang, D. C. (1966). Cruft Lab. Tech. Rep. No. 509. Harvard University, Cambridge, Massachusetts. Chao. H. H., and Strait, B. J. (1971). IEEE Trans. Antennas Propag. 19, 701. Cheng, D. K. (1971). Proc. IEEE 59, 1664. Chu, L. J. (1948). J . Appl. Phys. 19, 1163. Colebrooke, F. M. (1932). J . Inst. Elect. Eng. 71, 235. Collins, B. S. (1974). Communications 74 Conf. Proc., Brighton, England, June 1974. Paper 5.3. Copeland, J. R., and Robertson, W. J. (1961). Electronics 34, 68. Copeland, J. R., Robertson, W. J., and Verstraete, R. G. (1964). IEEE Trans. Antennas Propag. 12, 227. Daniel, J. P., and Dubost, G. (1976). Proc. Eur. Microwave Con&, 6th, 1976 p. 354. Daniel, J. P., and Terret, C. (1975a). IEEE Trans. Antennas Propag. 23, 513. Daniel, J. P., and Terret, C. (1975b). IEEE Trans. Antennas Propag. 23, 737. Davies, W. S. (1977). Proc. I E E 124, 673. Dawoud, M. M., and Anderson, A. P. (1972). I E E E Trans. Antennas P ropag. 20,497. Dawoud, M. M., and Anderson, A. P. (1974). Proc. Eur. Microwave C o n f , 4th, 1974 p. 278. Dubost, G., Daniel, J. P., and Veillard, J. (1971). Ann. Telecommun. 26, 183. Dubost, G., Nicholas, M., and Harot, H. (1976). Proc. Eur. Microwacle Cont. 6th, 1976 p. 275. Duff, I. S. (1977). Proc. IEEE 65, 500. DuHamel, R. H.,and Isbell, D. E. (1957). I R E Nat. Conv. Rec. Pt. I , p. 119. Duncan, R. H., and Hinchey, F. A. (1960). J . Res. Natl. Bur. Stand., Sect. D 64, 569. Egashira, S., and Iwashige, J. (1975). I E E E Trans. Antennas Propag. 23, 709. Evans, B. G. (1972). Radio Electron. Eng. 42, 225. Fanson, P. L., and Chen, K. M. (1973). I E E E Trans. Antennas Propag. 21, 715. Flachenecker, G. (1969). Nachrichtentech. 2. 22, 557. Foster, D. (1937). Proc. I R E 25, 1327. Fukui, H. (1966). IEEE Trans. Circuit Theory 13, 137. Gangi, A. F., Sensiper, S., and Dunn, G. R. (1965). IEEE Trans. Antennas Propag. 13, 864. Gibson, J. J., and Wilson, R. M. (1976). IEEE Trans. Consumer Electron. 22, 159. Gross, M. H. (1976). I E E Conf Publ. 139, 39. Hallen, E. (1938). Nova Acta Regiae Soc. Sci Ups. [4] 11, 1. Hanna, K . A. K., and Collins, B. S. (1976). IEE Conf Publ. 139, 35. Hansen, R. C. (1975). I E E E Trans. Commun. 23,430. Harrington, R. F. (1967). Proc. IEEE 55, 136. Harrington, R. F. (1968). “Field Computation by Moment Methods,” p. 110. Macmillan, New York. Harrington, R. F. (1976). IEEE AP-S Int. Symp., Univ. Mass. p. 62. Harrison, C. W. (1963). I E E E Trans. Antennas Propag. 11, 394. Hassan, M. A., Silvester, P., Howarth, B. A., and Nasu, N. (1976). Proc. IEE 123, 509.

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Hersch. W. (1973). AG.4RD Con/: Proc. 139, 9-1. Hertz. H. (1887). Pl7ys. Chem. [N.S.] 31, 421. Hodgson, D. (1974). Communications 74 Conf. Proc., Brighton, England, June 1974. Paper 10.3. Iizuka, K. (1965). I E E E Trans. Antennas Propag. 13, 7. Imbriale. W. A., and Ingerson, P. G. (1973). I E E E Trans. Ar~tenriusPropug. 21, 363. James. J. R., and Burrows. R. M. (1973). Electron. Lett. 9, 300. James, J. R., Schuler. A. J., and Binham, R. F. (1974). Electron. Lett. 10, 263. Jones. D. S. (1974). Proc. I E E 121, 573. Kalafus. R. M. (1971). IEEE Trans. Antennas Propag. 19. 771. Kikuchi. H. (1973). Proc. I E E 120, 637. King. R. W. P. (1956). Linear Antennas.” Harvard Univ. Press. Cambridge, Massachusetts. King, R. W. P.. and Middleton, D. (1946). Q. Appl. Math. 3. 302 King. R. W. P., and Wu. T. T. (1967). Radio Sci. 2, 1061. King, R. W. P.. Harrison, C. W., and Denton, D. H. (1960). I R E Truns. Antennus Propag. 8.88. Knight. M. A. (1972). Proc. I E E 119, 821. Kubina, S. J.. and Pavlasek, T. J. F. (1975). I E E Conf: Publ. 128. 165. Lamensdorf, D. (1967). I E E E Trans. Antennas Propag. IS. 767. Lamensdorf, D. (1975). Proc. I E E 122, 353. Landstorfer, F. M. (1969). I E E Conf Publ. 58, 141. Landstorfer, F. M. (1976). I E E E AP-S Int. Symp. Unic.. Mass. p. 169. Lin. C. J.. Nyquist, D. P.. and Chen. K. M. (1970). I E E E Trans. Antennas Propag. 18. 576. Lin. C. J., Nyquist, D. P., and Chen, K . M. (1973). I E E E Trans. Antennas Propag. 21. 852. Lin. Y. T.. and Richmond, J. H. (1975). I E E E Trans. Antennas Propag. 23, 53. Lindenmeier, H. (1971). I E E Conf Publ. 77, 186. Lindenmeier, H.. and Meinke, H. (1969). Furikschau 41, 569. McDonough, J. A., Malech, R. G.. and Kowalsky, J. (1957). I R E Natl. Con11. Rec. 5. 173 Maclean, T. S. M. (1973). Radio Electron. Eng. 43, 534. Maclean, T. S. M., and Morris, G. (1975). I E E E Trans. Antennas Propag. 23, 286. Maclean, T. S. M., and Ramsdale, P. A. (1975). Electron. Lett. 11, 62. Mason, H. P. (1963). Proc. I E E 110, 1543. Meinke, H. (1966a). Radio Electron. Eng. 31. 76. Meinke. H. (1966b). Nachrichtentech. Z. 19, 697. Meinke, H. (1969). Nachrichtentech. Z . 22, 319. Meinke. H. (1970). Nachrichtentech. Z . 23. 179. Meinke. H. (1975). Proc. Eur. Microwure Cot7f., Sth, 1975 p. 337. Mikuni. Y., and Nagai, K. (1972). Electron. Lett. 8, 472. Miller, E. K., and Deadrick. F . J. (1975). In ‘‘ Numerical and Asymptotic Techniques in Electromagnetics” (R. Mittra, ed.), p. 117. Springer-Verlag. Berlin. and New York. Miller, E. K . , Burke. G . J., and Selden, E. S. (1971). l E E E Trans. Antennas Propug. 19. 534. Mittra, R., and KO, W. L. (1975). I E E E Trans. Antennas Propug. 23, 435. Neff. N. P., Siller. C. A,. and Tillman, J. D. (1969). I E E E Trans. Antennas Propag. 17. 805. Nyquist, D. P.. and Chen. K. M. (1968). I E E E Trans. Antennas Propag. 16, 21. Paunovic, DJ. S., and Popovic, B. D. (1977). Radio Electron. Eng. 47, 225. Pearson, L. W. (1975). IEEE Truns. Antennas Propag. 23, 256. Pearson, L. W., and Butler, C. M. (1975). I E E E Trans. Antennas Propag. 23, 295. Pelletier, M., Cummins, J. A,, and Sanzgiri, S. (1972). I E E E G A P , Int. Symp., 1972 p. 77. Pizer, R. (1977). Proc. U R S I Symp. Electromagnetic W a v e Theory, 1977 p. 173. Pocklington, H. C. (1897). Cambridge Philos. Soc. 9, 324. Poggio. A. J., and Mayes, P. E. (1971). I E E E Trans. Antennas Propug. 19, 544. Popovic, B. D. (1970). Proc. I E E 117, 873.

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Popovic, B. D. (1971). Radio Electron. Eng. 41, 493. Popovic, B. D. (1973a). Radio Electron. Eng. 43, 243. Popovic, B. D. (1973b). Proc. I E E 120, 544. Popovic, B. D., and Dragovic, M. B. (1974). Proc. I E E 121, 101. Popovic, B. D., Dragovic, M. B., and Djordjevic, A. R. (1975a). Electron. Lett. 11, 99. Popovic, B. S., Dragovic, M. B., and Paunovic, DJ. S. (1975b). Electron. Lett. 11, 611. Popovic, B. D., Dragovic, M. B., and Djordjevic, A. R. (1977). Radio Electron. Eng. 47, 229. Ramsdale. P. A. (1971). I E E Conf. Publ. 77, 145. Ramsdale. P. A. (1975). Electron. Lett. 11, 590. Ramsdale. P. A. (1977). Proc. I E E 124, 840. Ramsdale, P. A., and Maclean, T. S. M. (1971). Proc. I E E 118, 1698. Ramsdale. P. A., and Maclean, T. S. M. (1972). Radio Electron. Eng. 42, 233. Rangole, P. K., and Saini, S. P. S. (1975). Radio Electron. Eng. 45, 95. Rangole, P. K., Saini, S. P. S., Ramsdale, P. A,, and Maclean, T. S. M. (1975). Radio Electron. Eng. 45, 749. Rao, B. L. J., Ferris, J. E., and Zimmerman, W. E. (1969).I E E E Trans. Antennas Propag. 17, 145. Richmond, J. H. (1965). Proc. I E E E 53, 796. Richmond, J. H. (1966). IEEE Trans. Antennas Propag. 14, 782. Richmond, J. H., and Newman, E. H. (1976). Radio Sci. 11, 13. Rippin. J. F. (1965). Electronics 38, 93. Sarkar, T. K.. and Strait, B. J. (1976). Radio Sci. 11, 959. Sayre, E. P. (1973). I E E E Trans. Antennas Propag. 21, 216. Schelkunoff, S. A. (1943). “Electromagnetic Waves,” p. 441. Van Nostrand-Reinhold, Princeton, New Jersey. Shen, L. C. (1967). I E E E Trans. Antennas Propag. 15, 606. Shen, L. C. (1968). I E E E Trans. Antennas Propag. 16, 643. Silvester, P., and Chan, K. K. (1972). Proc. I E E 119, 1095. Silvester, P., and Chan, K. K. (1973). Proc. I E E 120, 21. Smith, D. L. (1975). I E E E Trans. Antennas Propag. 23, 20. Smith, G. S. (1977). I E E E Trans. Antennas Propag. 25. 369. Sosin, B. M. (1976). Commun. & Broadcasting 3, 29. Sosin, B. M., and Butt, I. K. (1976). I E E Conf Publ. 139, 30. Storer, J. E. (1951). Doctoral Dissertation, Harvard University, Cambridge, Massachusetts. Storm, B. (1952). Wireless Eng. 29, 174. Surutka, J. V., and Velickovic, I). M. (1976). Radio Electron. Eng. 46, 121. Tai, C. T. (1950). S R I (Stanford Res. Inst.) Tech Rep. 12. Tanner, R. L., and Andreason, M. G. (1967). I E E E Spectrum 4, 53. Taylor, C. D.. and Wilton, D. R. (1972). I E E E Trans. .4ntennas Propag. 20, 772. Taylor. C. D., Lin, S. M., and McAdarns, H. V. (1970). I E E E Trans. Antennas Propag. 18, 133. Thiele, G. A. (1966). I E E E Trans. Antennas Propag. 14, 648. Towaij. S. J., and Hamid, M. A. K. (1972). Proc. I E E 119,48. Towaij, S. J., and Hamid, M. A. K. (1973). Proc. I E E 120, 968. Tsai, L. L. (1970). Dig. U R S I 1970 Spring Meet. Tucker, D. G. (1967). Radio Electron. Eng. 34, 251. Uda, S. (1926). J. Inst. Electr. Eng., T o k y o 452, 273. Vallese, L. M. (1972). I E E E Trans. Antennas Propag. 20, 92. Wang, J. J. H., and Ryan, C. E. (1977). Dig. U R S l Symp. Electromagnetic Waoe Theory p . 22. Wilkinson, W. C. (1974). I E E E AP-S Int. Symp., Atlanta, Ga. p. 270. Williams, D., and Brammer, D. (1977). Dig. U R S I Symp. Electromagnetic Waue Theory, p. 302.

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ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS, VOL. 47

Characterization of the MOSFET Operating in Weak Inversion PAUL A. MULS, GILBERT J. DECLERCK, AND ROGER J. VAN OVERSTRAETEN Laboratory E S A T (Elektronica, Systemen, Automatisatie en Technologie) Departement Elektrotechniek Katholieke Uniaersiteit Leuaen Lruvm, Belgium

I. Introduction,,.............................................................................. 11. Accurate Model for the Drain Current in a MOSFET ................................. A. Occupancy of the Surface States.. .................................................... B. Model of Pao and Sah for the Source-Drain Current in a MOSFET ............. C. Simple Analytical MOSFET Model .................................................. ............................... D. Discussion and Examples ........ E. Nonuniform Impurity Doping Pr .......................................... om Drain Current vs Drain Voltage 111. Determination of the Surface State Measurements in Weak Inversion .............................................. A. Theory.. ...................................................................... B. Energetic Position of the Measured Surface States.. ................................ C. Nonuniform Doping.. ................................................................. D. Short ID-VD Method . . . . . . . . . . .................................................... E. Influence of Surface Potential Fluctuations.. ......................... F. Experimental Results and Conclusions.. .............................. IV. Influence of Potential Fluctuations on the Mobility in Weak Inversion A. Introduction.. .......................................................................... B. Carrier-Density Fluctuation-Theory of Brews ....................................... C . Measuring Procedure .................................................................. D. Experimental Results .................................................................. E. Sensitivity of the Low-Field Mobility to Fabrication-Process Parameters ........ F. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. General Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

197 201 201 208 212 217 221

227 231 231

241 243 249 253 257 259 262 262 265

I. INTRODUCTION The increasing trend of high-packing density in MOS integrated circuits introduces a power-dissipation problem. An effective way to solve this problem is the reduction of operating voltage and the use of dynamic circuits. 191 Copynght 0 1978 by Academic Press. Inc All rights of reproduction in any form reserved ISBN 0-12-014647-9

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PAUL A . MULS ET AL.

However, very small currents flowing in a weakly inverted channel below the threshold voltage are limiting the low-voltage static and dynamic operation of MOS circuits. Therefore, this subthreshold current has to be taken into account when designing integrated circuits with low supply voltage. As a first example of the importance of the weak-inversion current on circuit characteristics, we take the common static inverter. The circuit scheme, and the Vo,,-y , transfer characteristic are shown in Fig. 1. An experimental result is compared with the calculation based on the classical model,

0 Vi n

(-)

FIG. 1. Circuit diagram and transfer characteristic of a commonly used static inkerter. experimental result: () classical model without weak-inversion current. ~

ignoring the weak-inversion range. At the shoulder of the Vo,,-V,, curve, a rounding effect takes place, caused by the weak-inversion current of the driver transistor when biased near the threshold voltage. This effect is important in low-voltage circuits, because it reduces the noise margin. New high-resolution lithographic techniques offer the possibility of making very small MOS devices with micron dimensions. However. reducing the channel length of a MOSFET also leads to undesirable changes in the device characteristics. These changes become significant when the depletion regions surrounding the source and drain. extend far underneath the gate electrode. The undesirable short-channel effects can be avoided by applying the principles of device scaling as demonstrated by Dennard et al. (1974). Starting from a conventional design, all linear dimensions are reduced by a scaling factor K . This reduction includes vertical dimensions such as gate insulator thickness, junction depth, etc., as well as the horizontal dimensions of channel length and width. The voltages applied to the device are reduced by the same factor K , while the substrate doping density is increased, again using the same factor. As a result, the depletion layer widths are also scaled down. Also the threshold voltage is decreased in direct proportion to the reduced device voltages, so that the device will function properly in a circuit with reduced voltage levels. Due to the reduced voltage and current levels, the power dissipation of each circuit is reduced by K 2 .

MOSFET OPERATING IN WEAK INVERSION

199

Since the area of a given device or circuit is also reduced by K 2 , the power density remains constant. It is also interesting to note that since the device resistance V/Z remains constant, and all capacitances are reduced, the operating speed goes up by a factor K . One area, however, in which the device characteristics fail to scale is the subthreshold or weak-inversion region of the turn-on characteristic. Figure 2 shows the drain current Z, vs gate voltage V, for the original and for the scaled-down device. At small sourcedrain voltages, this relationship is linear, and its intercept with the voltage

VGW

FIG.2. I, with K = 5.

-

V,; turn-on characteristic for a standard and for a scaled-down MOSFET

axis defines the threshold voltage V,. Below V,, ID is exponentially dependent on V, as shown in Fig. 3. The slope of the In curve remains unchanged after scaling because the characteristic in the weak-inversion region is much more dependent on silicon band gap properties than on the scaled down parameters. This slope is important to dynamic memory circuits, because it determines the gate voltage excursion required to go from the low current “off ” state to the high current ‘‘ o n ” state. The storage time or refresh time of the memory cell could possibly be limited by a source-todrain leakage current when the channel is still weakly inverted in the “off” state (Fig. 4). A thorough understanding of the weak inversion operation of

FIG.3. In([, inversion.

-

V,) characteristic for standard and for a scaled-down MOSFET in weak

200

F

PAUL A. MULS ET AL.

address l i n e

data line

FIG.4. Circuit diagram of a typical MOS memory cell.

the MOS transistor can lead to devices with a steeper slope, and consequently to smaller leakage currents (Fig. 3), and longer storage times for the memory cell. Swanson and Meindl (1972) describe a complementary MOS inverter, which already functions at a supply voltage of approximately 200 mV. This circuit is useful for low-power-consumption digital applications. The turn-on voltages of the complementary MOS transistors are adjusted by ion implantation to approximately half the supply voltage. By necessity these MOS transistors are operating near their threshold voltage, where the assumptions commonly used in deriving device characteristics are inaccurate. A good knowledge of weak inversion, also for implanted devices therefore is mandatory for the determination of the transfer characteristic of the low-voltage complementary MOS inverter. In this paper we study the potential offered by the MOSFET operating in weak inversion for acquiring knowledge about the silicon-silicon dioxide interface. By comparing current-voltage measurements with a theoretical model, we shall derive the surface state density and the mobility of the minority carriers. These quantities are important for the behavior of the transistor in weak inversion, because they determine how fast the current decreases to zero when the voltage decreases below the threshold voltage, how large the leakage current is, and how close the threshold tolerances have to be. Other parameters as doping density, oxide thickness, geometry, and flat-band voltage, have also to be determined as accurately as possible. In order to analyze the experiments, a comprehensive one-dimensional model for the channel current will be developed, which takes into account the exact occupancy statistics for the surface states. This model, generally valid in all regions of operation of the transistor, will then be simplified to an analytical form, useful for computer aided design. From this analytical model we derive a new method to determine the surface state density. This technique is based on the measurement of the drain current as a function of the drain voltage at a fixed gate voltage in weak inversion. It is very simple and fast, and suffers little from fluctuations of the surface potential due to the nonuniformity of the charge at the Si-SiO, interface. Accuracy and sensitivity are better than 1 x 10'' V - ' cm-2. The method is also valid for implanted devices. It allows to scan part of the forbidden energy gap, but is of special interest for quality control purposes, when only a representative

20 1

MOSFET OPERATING IN WEAK INVERSION

value of the surface state density on a typical transistor out of a production lot is needed. We shall also examine the mobility of the minority charge carriers in a MOSFET, as a function of the surface potential. The experimental behavior of the mobility is explained by fluctuations of the carrier density in the inversion channel, under the influence of a nonuniform charge distribution at the interface between silicon and silicon dioxide. The conclusion is that the mobility in weak inversion is strongly dependent on the nonuniformity of the interface. 11. ACCURATEMODELFOR THE DRAIN CURRENT IN

A

MOSFET

A. Occupancy of the Surface States

Surface states are allowed energy levels in the forbidden energy gap, generated by irregularities of the lattice at the surface of the semiconductor crystal. These additional energy states can be either occupied or not by an electron. The theory of recombination-generation through such energy levels is known from the work of Hall (1952) and Shockley and Read (1952). Figure 5 shows the energy band diagram of a p-type silicon substrate at flat band. The positive direction is taken upwards for the energy, and down-

E

L,

FIG.5. Energy band diagram of a p-type substrate at flat band

202

PAUL A. MULS ET AL.

wards for the potential. 4Fis the potential difference between the intrinsic bulk level and the Fermi level. In thermal equilibrium the probability of occupancy of a center in the forbidden gap is governed by the Fermi-Dirac distribution function :

where El is the effective energy level of the surface state taking the spin degeneracy into account, and El: the Fermi energy level. It is useful to define the potential 4, of the surface state with reference to the intrinsic energy level Ei, at the surface:

.

Ei, - 1' = q4t (2) The total band bending of the energy bands in Fig. 6 is given by the surface potential 4 s .With the normalized values u, = 4 , / ( k T / q ) ,uF = 4F( ( k T / q ) and [ I , = 4 , / ( k T / q )the , Fermi-Dirac distribution function becomes

FIG.6. Same energy band diagram lor

4%= 440 mV

MOSFET OPERATING I N WEAK INVERSIOK

203

This function corresponds to curve 1 in Figs. 8-10, wheref,, is shown versus the location of the energy state in the forbidden gap, for several values of the surface potential. Under the assumption that the surface state density Nss(V-' c m P 2 )does not vary strongly around the middle of the energy gap, it is possible to approximate the distribution function by

.f= 1 .f= 0

for E , I EF, (us for E , > E F , (us

+ U,2 + < U,

uF) uF)

(41

All surface states below the Fermi level are occupied by an electron, all surface states above are unoccupied. Surface states can be of the donor-type or of the acceptor-type. Occupied donor states are neutral, unoccupied donor states are positive, while occupied acceptor states are negative and unoccupied acceptor states neutral. If Q,, denotes the effective (i.e., converted to the interface) fixed oxide charge per unit area, together with the charge in the surface states at flat band, the supplementary interface charge due to a band bending over a surface potential 4s,is given by

Taking (4) into account, this becomes -

it' N,,W

.EF

d~

'€>(%)

+

1

'Ev(0)

N,,W

d~

(6)

Assuming N,,(E) to be constant in the energy range of interest, Eq. (6) becomes

or

The total charge per unit area in the oxide-semiconductor interface at a surface potential 4s consequently is Qox

-

@",4,

(8)

204

P A U L A. MULS ET AL.

In Figs. 5-7, the vertically shaded region denotes the surface states already occupied by an electron at flat band. The oblique shading denotes the supplementary occupancy of surface states resulting from band bending. When a voltage is applied between source and drain of a MOS transistor, a current flows dependent on the gate voltage, and consequently the surface

FIG. 7. Same energy band diagram for 4,

=

440 mV and 4'

=

80 mV (on scale).

of the MOS device is no longer in thermal equilibrium, and the Fermi Dirac distribution function (1) no longer holds. The function governing the occupancy of the recombination-generation centers has been calculated by Hall and by Shockley and Read:

I I is the electron density in the vicinity of the center at the surface; p is the hole density; 0, the capture cross section of the center for electrons: up the capture cross section for holes, and n i is the intrinsic carrier density. Using (2) and assuming the capture cross sections for electrons and for holes to be

MOSFET OPERATING IN WEAK INVERSION

205

almost equal, (9) becomes

In the state of thermal quasi-equilibrium, we define 4cas the potential difference between the majority or bulk Fermi level EF and the minority quasi-Fermi level E,, (see Fig. 7). denotes the normalized value of 4c.The electron and hole densities can be written as

<

n = n, exp(u - u, - <) p = n , exp(u, - u )

Using for u the value us at the surface, (10) becomes, with (ll),

We shall now illustrate the general features of this function. Expression (12) can be transformed to

I-'

fHSR

=[I+

[

+

exp(u, - us) exp( - u,) exp(u, - us t) exp( - u,)

+ +

(13) In inversion (large us) or at small drain voltages (small <), 5 can be neglected with respect to uF - u s , and fHsR can be reduced to [l

+ exp{-[(us +

+ <)]}I-'

(14) This is similar to Eq. (3) where uF + replaces u,. Expression (14) is thus a quasi-Fermi-Dirac distribution function, showing that the occupancy curve moves along with the quasi-Fermi level of the minority carriers instead of with the equilibrium Fermi level. Analogously to (4) it can be stated that all surface states below the quasi-Fermi level of the minority carriers are occupied by an electron, and that all surface states above are unoccupied, as far as N , , does not vary strongly in function of the location in the energy gap near EFn.We now have fFD

=

<

ut)

- (uF

for 1' 'Fnt ( 4 s + 4, 2 4, + 4 c ) (15) for ,' > E F n , (4\ + 4, < 4, + 4 c ) For large values of <,the term exp(u, - uF - <) in (12) is negligible and,fHSR is constant independent of <,and is given by

f=1 .f= 0

fHSR =

{ 1 + [exp(u,

- us)

+ exp( - 4 3 exp( - 4))-

(16)

206

P A U L A. MULS ET AL.

From this expression it follows that when the bands are sufficiently bent. the term exp(u, - u,) also is negligible, and fHsR is pinned down at the value of 0.5 for u, = 0. These conclusions are illustrated by Figs. 8-10. Figure 8 shows the distribution function for 4, = & , being the starting point for weak inversion. At this value of the surface potential, the Fermi level coincides with the f

f

FIG. 8. Occupancy probability of an energy state vs its location in the energj gap for with 4' as parameter: ( I ) dC= 0; (2) d C= 50 mV; ( 3 ) 4c= 100 mV: (4) 4L= 200 mV; (5) q5c = 300 mV. HSR: -: FD:

4.= 4 b . and

intrinsic level at the surface, and the surface states at midgap (dt= 0) are located on the Fermi level. The parameter 4cvaries from 0 to 0.3 V. Once bC reaches the value of 0.1 V,f& does not change anymore, while the quasiequilibrium function ,/;, continues to shift parallel to the equilibrium function, over an amount 4c. Figure 9 considers $s = $&. the middle of the weak-inversion range. Until 4c= 0.1 V,,fHsRandf,. are completely identical, and are shifted over a voltage exactly equal to 4 c ,with respect to the equilibrium situation. From 4c= 0.3 V on, ,fHsR. unlikef;., , remains unchanged with increasing 4c,and takes the value 0.5 for 4, = 0. Figure 10 finally considers the beginning of strong inversion with 4, = 24,.. HerejHSRmoves parallel over an amount 4c, until the spreading of the quasi-Fermi levels is about 0.3 V. Once 4cis about 0.4 V, f,,sK remains constant and takes the value of 0.5 at midgap. As will be demonstrated later. 4cis zero at the source, and remains very small over most of the channel length in weak inversion. Only close to the

MOSFET OPERATING IN WEAK INVERSION

207

f

Ec

EF

El

E"

FIG.9. Occupancy probability of an energy state vs its location in the energy gap for 4, as parameter: (1) + c = 0; (2) dC= 50 mV; (3) 0 , = 100 mV; (4) dc= 200 mV; ( 5 ) dc= 300 mV; (6) I $ ~= 400 mV. HSR: -; FD:

I#I?

= :I#+, and with

t

I$?

+c

FIG. 10. Occupancy probability of an energy state vs its location in the energy gap for and with 4' as parameter: (1) bc= 0 : (2) bc= 50 mV; (3) dc= 100 mV: (4) mV; ( 5 ) dc= 300 mV; ( 6 )dc = 400 mV; (7) dc = 500 mV. HSR: -; FD:

= 2&. = 200

208

PAUL A. MULS ET AL.

drain 4c increases rapidly towards the drain voltage V,. On the average 4c can be considered small in the channel, and approximation (14) holds in weak inversion. In strong inversion, varies linearly from zero at the source to V, at the drain. However,f& andf,, remain equal for a larger value of $c as inversion grows stronger. Consequently (14) is likewise valid in strong inversion for V, not too large. Also with increasing inversion, the inversion charge becomes so dominant, that the charge in the surface states can be neglected. It is evident from the foregoing that (15) can be used as a good approximation in the whole operating region of the transistor, provided that the drain voltage is limited to about 1 V. According to (5) and ( 6 ) where E , has to be replaced by E F n ,and taking (15) into account, the supplementary charge in the surface states with respect to flat band is given by

when a surface potential 4sand a spreading of the quasi-Fermi levels 4care present. The total charge per unit area in the oxide-semiconductor interface somewhere along the channel depends on the values of 43and 4c,and is given by

Q,,

-

4N,,(4, - 4 J

(18)

This result is based upon the assumption of equal capture cross sections (T, and crp. There is some evidence, however, that crn can be substantially greater than crp (Cooper and Schwartz, 1974). The effect of unequal capture cross sections on the weak-inversion drain current will be discussed in Section 1I.D. B. Model Of'Puo und Sali f o r the Source-Drain Current in u M O S F E T

Pao and Sah (1966) developed a one-dimensional model in integral form for the current in a long-channel MOS transistor (source-to-drain spacings of the order of 10 pm or more). The coordinate system is illustrated in Fig. 11. The x coordinate is normal to the interface into the bulk semiconductor. The y coordinate is along the channel from the source toward the drain. The width of the channel is W and the length L. T o find the current in a MOSFET, one has in principle to solve simultaneously the current conservation equation, Poisson's equation, and Ohm's law. Using the quasi-Fermi level analysis for the minority carriers (assumed here to be electrons) in the semiconductor, these equations become div

J =0

(19)

MOSFET OPERATING IN WEAK INVERSION source

I

209

drain

gate

Y

I substrate

FIG. 1 1 . Coordinate axis and geometry of the n-channel MOSFET used in the analysis

div(grad

4 4) = - ( p - n - N,)

(20)

%i

J = -qpn

grad

4G

(21) J is the current density per unit area, E~~ the permittivity of silicon, p the mobility of the carriers in the channel, and N , the constant acceptor doping density. In addition to solving Eqs. (19)-(21) in the semiconductor, one must solve the corresponding equations in the insulator and impose the usual boundary conditions at the semiconductor-insulator interface. The model of Pao and Sah is based upon the following three simplifying assumptions : (1) The current is assumed to be parallel to the interface, or $,(x, y) = 4,(YX and t(x2 Y ) = 4 ( Y ) . (2) The potential depends primarily upon the normal x coordinate and upon the lateral coordinates only through the parameter 4,: 4 = 4(x, 4,) and u = u(x, t). (3) The requirement of current conservation, div = 0, can be replaced by the requirement d l , / d y = 0, where I , is the source-drain current. The drain current, which is a positive quantity, is defined as

1

.a,

I, =

-

W

"0

J(x, y ) d x

Using (21), and (11) for n, and assuming a constant effective mobility p :

From assumption (1) it follows that that

5 and d 4 , l d y do not depend upon x,so

2 10

P A U L A. MULS ET A L .

with .a

1

Q,,(4,,4J = -qni

exp(u - uF - 5 ) d . ~

(251

'0

the charge per unit area in the inversion layer. Integration of Poisson's equation (20) in view of assumption (2) results in

the intrinsic Debye length and F ( u , I ) the iiorwith LO2 = 2y2n, (Arts,), malized field function'

F. (u, I ) = [exp(u, - 1 1 ) - exp(u,)

+

11

+ exp(u

-

idF - L ) -

exp( - uF - 2 )

(27)

exp(u,)]'

The first two terms originate from p, the third and fourth from n, and the last one from N 4 The electrical field normal to the surface is u, kT F ( u , ,

t)

(28)

Using Gauss's law the total charge per unit area in the semiconductor can be cdlculated as

With

N,

= 1 7 ~exp(u,)

i n (29), one gets

I kT QS,= - 2qi.,,NA- [exp( - u,) I

4

- exp( - 2 4 -

L)

+ u,]

1

-

1

+ exp(u,

-

211,

~

L)

(31)

Since the terms exp( - 11,) and exp( - 2 u F - i)are negligible, Q\, becomes

Similarly the depletion charge density can be found by omitting the term

MOSFET OPERATING IN WEAK INVERSION

211

coming from n in the expression of Qsi:

QD = -[2qt;siNA(419

-

kT/q)]'"

(33)

With the use of (26), the inversion charge density (25) can be written as

Integration of the current expression (24) from the source (kept at bulk potential for the time being) to the drain, gives

The Pao-Sah current formula is finally found by bringing (34) into (35):

To complete the analysis, the surface potential determined for any gate voltage V, from Gauss's law:

Cm(K

- 4MS -

4s) = -[Qm

-

qNss(4s -

4s(4c)has

4 c ) I - Qsi

to be

(37)

4MS is the work function difference between the metal and the semiconductor, and, as demonstrated in (18),Q,, - qN,,(4, - 4c)is the interface charge at band bending. At flat band, when 4s = 4IC = 0, and Qsi = 0, the gate voltage has to be (Qox/Cox) Using (38), Eq. (37) can be rewritten as VFB= ~

M S

As already mentioned, Q,, contains the effective fixed charge in the oxide and the charge in the surface states at flat band. The key feature of the model is the use of the exact surface potential for any gate voltage. This makes the model valid in all the operating regions, and provides a continuous transition of the current solution from the weak inversion region to the saturation and nonsaturation region, without need for additional fitting parameters. This model however does not take into account two-dimensional effects in the vicinity of the drain diode, which become important at large drain voltages and short channels. The practical elaboration of the current formula (36) requires several numerical iterations, making the model, although excellent for fundamental

2 12

P A U L A. M U L S ET AL.

research, less suited for computer-aided design. Therefore we shall now develop a simplified analytical version of the model. C. Simple Analytical M O S F E T Model The total operating range of a MOS transistor can be divided into three distinct regions. When the gate voltage increases, the transistor first goes through the weak inversion region, then enters the saturation region where part of the channel is already in strong inversion while the rest is still weakly inverted, and finally reaches the nonsaturation region, where the whole channel is strongly inverted. Each region is described by a separate equation. To keep the model general, we consider biasing of the source with respect to the bulk by introducing a source voltage V,. It is known that in this case the spreading of the quasi-Fermi levels at the source takes the value V'', or 4c= V, for y = 0, and 4c= V, for y = L. The voltages V, , V,, V,, and 4, are with respect to the bulk. Define the threshold voltage VT, as the gate voltage necessary to make the surface potential 4qoin the starting point of the channel close to the source, equal to V, + 2 4 ~ Solving ~ . Eq. (39) at y = 0 with &, = V, 2& and 4c= V, yields

+

This result is in agreement with the classical definition of turn-on voltage, except for the term in N , , , which is usually neglected. It is important to notice that this threshold voltage does not coincide with the experimental turn-on voltage found by extrapolation of the linear part of an I, - V, measurement at small V,. The surface potential in strong inversion is indeed not pinned to the value V, + 24F,but increases slowly with increasing gate voltage. The three operating regions will now be studied. 1. Weak-lncersion Region

(Van Overstraeten et al., 1975)

When V, c V,, the potential 450 at the source is smaller or equal to and the whole channel is weakly inverted. In this region, the inversion charge density Q, is several orders of magnitude smaller than the depletion charge density Q,. A good approximation for Qsi in weak inversion is therefore: V,

+ 2&,

Since QD is only a weak function of

4s,we shall expand

it in a first-order

MOSFET OPERATING IN WEAK INVERSION

Taylor series around a chosen value

4so:

Qd4J Qd4J'V

with - d Q , / d 4 , Putting

=

( 4 5

-

4so)c~(4so)

C,, the depletion capacitance per unit area.

4 s =4so + ( 4 s the relation (39) between 4sand V, becomes

Analogous to V,, we now define V;. as the gate voltage necessary to make the surface potential at the source (4c= &) equal to c$so. From (39) it then follows that

With (45), Eq. (44) becomes

C,,

=

qN,, is the surface state capacitance per unit area. We further define

and M(4so) =

cox

+ cD(4so) C O X

From (46) it follows that

Since as a first approximation 4, is a linear function of V' , we see that for C,, << Cox+ CD,i.e., for not too large values of N,, , or for small values of the applied drain voltage VD, 4, becomes fairly independent of c$=. Since

Q, = Qs, - QD

(50)

2 14

P A U L A. MULS ET AL.

the electron charge per unit area in the inversion layer can be found, using (32) for Qsi and (33) for QD. A first-order series expansion of (50) yields

with /? = (kT/q)-'. This expansion is valid when the following weakinversion condition is satisfied: kT

4 s < 4 c + 2 4 F + - ln(us - 1) 4

(52)

Using (49) and

From (35) it follows that the drain current is proportional to the integral of the inversion charge density from source to drain:

Using the approximation CD(4J = CD(4so),Eq. (55) becomes with (54):

This formula clearly shows the exponential dependence of the drain current one can advantageously on gate voltage as well as on drain voltage. For 4so, choose the value Vs + $dF,because it is right in the middle of the weakinversion range. 2. Nonsaturation Region

The MOS transistor is in nonsaturation when the whole channel is strongly inverted. Everywhere in the channel 4s - dCis larger or equal to

215

MOSFET OPERATING IN WEAK INVERSION

24F, i.e., VG > vTand VD I VDSA,. VDSAT is the saturation voltage, and will be defined later. From the work of Pao and Sah (1966) it is known that when the charge of the minority carriers exceeds the depletion charge, which is the changes proportionally to 4c over most of the case in strong inversion, c$~ channel length. In this range we shall therefore use the approximation

4 s = 4 s o - v, + 4 c

(57)

Combining (39) and (57) yields Qsi = C o x ( - VG

+ VFB+

4so -

Vs + 4 c )

+ Css(4so

- ‘s)

(58)

while from (33) and (57) it follows that QD

=

-[2q&SiNA(4so

-

V, + 4~- kT/q)I”2

(59)

Using (58) and (59), Eq. (50) yields Qn

=

-cox(&- VFB) SO - &)(COX+ Css) 4ccox + [ 2 q E S i N A ( 4 s o - V, + 4 c - kT/q)l”2

(60)

The drain current once again is given by (55):

(61) +so

has to be calculated for every value of V, from (39):

css

- -(4so - Vs) = 0

(62)

cox

This is also necessary because in strong inversion, the surface potential remains to a fair degree dependent on the gate voltage, and is certainly not pinned to the value V, + 2& as usually accepted. When the drain voltage equals &AT, the channel is pinched off at the

216

P A U L A. MULS ET AL.

drain. The inversion charge, as defined by Eq. (60), becomes zero at the drain. VDsA,can consequently be found as the value of needed to make Q , in Eq. (60) equal to zero. A straightforward calculation yields

For 4soequal to Vs + 2&, (63) agrees with the classical definition of saturation voltage, except once again for the terms in C s s . 3. Saturation Region The MOS transistor operates in the saturation range, when the channel between the pinch-off point and the drain is weakly inverted, while the rest of the channel, between source and pinch-off point, is in strong inversion. This occurs when VG > V, and at the same time V, > VDsA,. The integration formula (55) for the current, has to be split in a strong-inversion and a weak-inversion part :

. ".( 1 =

VDSAT

ID=

-

'VS

Q, d4c + \Ig Q, d4.) VDSAT

(64)

The strong-inversion term is found by substituting VDsA, for VD in Eq. (61). In this case also, 4sohas to be solved from (62). For the weak-inversion term one proceeds as follows: Q , in weak inversion is given by (51) if condition (52) is fulfilled. From the approximation (57) of the potential in strong inversion, it follows that the surface potential in the pinch-off point (4c= VDSAT) can be taken as

And since we know from formula (49) that the surface potential in weak inversion is only weakly dependent on 4c, and consequently does not change much in the weak-inversion part of the channel, Eq. (65) can be adopted in the whole saturation part of the channel. Since condition (52) is satisfied for this value of bs,Q, of (51) can be used with (65) to calculate the weak-inversion component of the drain current in (64).Addition of the weak- and strong-inversion expressions finally yields the total current in

MOSFET OPERATING IN WEAK INVERSION

2 17

saturation:

{l - exp[-P(vD

- VDSAT)I)

C , has to be evaluated at the value

4s = 4so- Vs + VDSAT.

D. Discussion and Examples Figure 12 and Table I summarize the critical definitions, and give a working scheme for the analytical model. Only Eq. (62), to find 4so(VG),has to be solved numerically. This model, unlike other simplified models, has the

FIG. 12. Voltages used in the simplified model.

big advantage of a smooth behavior over the whole operating region, because the surface potential takes its exact value at every gate voltage. The model only depends on physical parameters as V,, , N A ,to,, p, and N,, ,and does not need any fitting parameters as for instance a turn-on voltage VT or a slope factor for weak inversion. The model consequently proves to be very useful if one is interested in changing the current characteristic by a technological intervention in the fabrication process. In Fig. 13 a comparison of the different models is made. The natural logarithm of the drain current is plotted as a function of the gate voltage for a transistor with the indicated parameters. Evaluation of formulas (40)and

218

P A U L A. MULS ET AL.

TABLE 1 DEFINITIONS A N D WORKING SCHEME FOR

THE

ANALYTICALMODEL

Critical voltages

Procedure

V, = V,(ref A) - V, V, = v,(ref i) - V,

1

calculate V, with (40)

1 calculate

1 calculate

4s with Eq

(49)

8 with Eq (56)

i calculate V,,,,

with Eq (63)

- 0 F l -8 calculate calculate

1,

with Eq. (61) with Eq. (66)

(45) yields V, = 1.30 V and VT= 1.03 V for 4s,,= $$F. These voltage points are also indicated on the figure, together with the voltage for which 450= 2& + 4kT/q. The curve (-) shows the Pao-Sah model (36). One remarks the linearity of the current characteristic at small gate voltages, when the whole channel is weakly inverted. Once V, 2 V, , the channel part closest to the source comes into strong inversion, while the rest remains weakly inverted. The transistor operates in saturation. As the gate voltage increases, the dividing point (4c= VDSAT)between the strong- and weakinversion part of the channel shifts toward the drain, until at large values of V, the whole channel is strongly inverted. The transistor then no longer operates in saturation. The figure clearly shows the very good agreement between the model of Pao and Sah, and the analytical three-regions approximation ( . . .). As an illustration, it is also indicated what the model becomes when the weak-inversion charge in the channel (64)is neglected (- -). The ~

MOSFET OPERATING IN WEAK INVERSION

2 19

-/ _--.-inversion 4s0=20F*CkTlq

vl:

312 +F

0.8

1.0

1.2

FIG.13. Comparison between the different models for the In(1,) - VG characteristic of a MOS transistor in weak inversion. Critical voltages and surface potential values are also indicated. Parameters: to, = 1132 A; N , = 1.64 x 1015 ~ m - ~V,,; = 0 V; N , , = 1.8 x 1010 v-I cm-2., W / L = 1; p = 200 cm2 V - I sec-'; T = 292°K; & = 309 mV. Source and bulk are short-circuited (G= 0) and V, is 1 V. Legend: (-) Pa0 and Sah model; ( .. . ..) analytical approximation of this model; (-.-.-.-.-) classical model with invariably 40 = 24F I' (- - - - - -) classical model with variable 4w.

current is too small in the saturation region, and becomes zero for V, = V, . The classical strong-inversion model (Cobbold, 1967) with 4s,,invariably equal to 2& is indicated (-.-.-.). From (56) it appears that the slope of the ln(ZD)- V, curve in weak inversion is determined by BIN = flC,,/(C,, + C, + C,,), i.e., by the oxide thickness, by the doping density,

220

PAUL A. MULS ET AL.

and by the surface state density. The slope increases for decreasing values of t o , , N A ,and N , , . However, as we shall see later, the variable mobility in weak inversion has also an important influence on the shape of the current characteristic. Finally it has to be stated that this model is the only one taking the surface states into account. Although the approximation of generalizing the Fermi-Dirac occupancy function with respect to the quasi-Fermi level of the minority carriers is used, it is evident from Fig. 14 that the exact HSR statistics are only needed in exceptional circumstances. The figure shows on

t

FIG.14. Influence of the occupancy function for surface states o n the ln(1,) - V, characteristic in weak inversion. Parameters: t o , = loo0 A; N , = 1 x 1015 c m - " : ,'L = 0 V ; sec-'; T = 295°K; + F = 293 mV: and V , = 100 mV. WIL = 1; p = 600 cm2

an expanded scale the weak-inversion part of the In(Z,) - V, characteristic of a MOS transistor with the stated parameters. At the left, the current formula (36) of Pao and Sah is given (-) for N,, = 5 x 10" V - ' cm-', with all surface states below the quasi-Fermi level of the electrons occupied (15). The same calculation has also been made with the exact Hall-ShockleyRead statistics (9) for o,,/op = 1 (---). A noticeable discrepancy is only found in very weak inversion. At the right, one can see how the curves look like when the surface state density is raised to N,, = 5 x 10" V - cm-2 and again depicts the remaining parameters stay unchanged. The curve (-) the Pao-Sah model (36) with the Fermi-Dirac occupancy function (15),

MOSFET OPERATING IN WEAK INVERSION

22 1

while the curve (---) makes use offHs, (9) with cn/op= 1. Moreover, a calculation has been made for cn/op= 0.001 (-.-.-.). If on> o,, one again approaches the FD-approximation; on/crp= 100 has been taken as an example ( . . . .). One can conclude that only in extreme cases, namely, for large N,, values and on 4 op for n-channels and op G on for p-channels, an important disagreement occurs between the currents calculated with fFD and with fHsR, and this only for small surface potentials ($J,~< $4,). A normal clean technology yields transistors with N,, low enough to make the model realistic.

E . Nonuniform Impurity Doping Profiles The calculations in Sections B and C assume a constant impurity density NA everywhere in the semiconductor. Usually this is a good approximation. However, this is not true in some special cases. The redistribution of boron or phosphorus near the silicon surface after thermal oxidation yields an important nonhomogeneous doping profile near the surface (Margalit et al., 1972). Another example is the adjusting of the threshold voltage of MOS transistors by implantation of boron or phosphorus in the channel region, which results in a shallow Gaussian impurity profile (Verjans and Van Overstraeten, 1975). To solve the Poisson equation for an arbitrary impurity profile, we use the algorithm proposed by Gummel (1964). We shall now consider in detail the two profiles discussed above. A low-energy (40 keV) boron implantation shifts the turn-on voltage in positive direction to produce n-channel enhancement transistors. The implanted impurity profile is close to the surface and can analytically be described by a Gaussian function with exponential tail (Fig. 15a). In Fig. 16, a comparison is made between the weak-inversion current characteristic of a MOS transistor with this doping profile, and the characteristic of a transistor with identical parameters, but with a homogeneous doping density ( N A= 7.6 x 1014 ~ m - ~The ) . origin of the voltage axis has been shifted in order to make the two curves coincide in strong inversion. The shape of the two curves differs only in weak inversion. The threshold shift amounts to 1.95 V. A second case that deals with nonuniform doping relates to the redistribution of impurities at the surface, due to the thermal oxidation of silicon. Margalit et al. have calculated the redistribution of boron and phosphorus after two consecutive oxidation steps for several MOS transistor fabrication processes. They show that the boron concentration decreases in a small strip near the surface, while the phosphorus piles up at the surface. Since we shall deal mainly with pchannel transistors, we take here the phosphorus redistribution profile of Fig. 15b as an example. This exponential curve is close to

222

P A U L A. MULS ET AL. ~

~

(

~

~

'

~

1

result! n g

profile

pf- l a y e r

p-layer

x (11rn1

P I

01

I

I

02

03

I

04

I

I

I

05

0.6

07

05

06

07

*

(a)

0

0

01

02

03

0 1

-

(b)

FIG.15. (a)Impunty dopingdensity of an-channel MOSFET after a boron ion implantation (energy: 40 keV, dose: 6.3 x 10" cm-'). (b) Redistribution of phosphorous in a p-channel MOSFET after two oxidation steps.

the profile resulting from a double wet oxidation at 1OOO"C.This, however, is not a normal MOS process, but a worst case. For a wet ( 1000°C,0.8 prnbdry (120O0C, loo0 A) oxidation process, the redistribution is much less prou 1.3 at the surface. The weak-inversion curnounced and gives N J N A

MOSFET OPERATING IN WEAK INVERSION

223

I PA

00 n A

10 nA

1 nA

00 p A

10 P A

I

PA

1.1 P A

FIG. 16. (1) Weak-inversion current characteristic of a MOSFET with the implantation profile of Fig. 15a; (2) corresponding characteristic for a homogeneous doping. The voltage axes are shifted.

rent characteristic of a p-channel MOSFET with the redistribution profile of Fig. 15b has been calculated in Fig. 17, and compared with the current characteristic of a transistor with identical parameters, but with homogeneous doping density ( N , = 1 x 1015 cmP3). From the figure it can be concluded that the redistribution of the impurities at the surface causes a parallel shift of the current characteristic. The only noticeable effect is a threshold shift of 0.1 V. The shape of the curve remains unchanged. The elaborate model of Pao and Sah, adapted with the Gummelalgorithm, thus allows the calculation of the drain current for an arbitrary impurity profile.

224

PAUL A. MULS ET AL.

L

I

-0 5

I

1

I

I

I

- 1 0

I

I

I

I

I

- 1.5

I

I

I

I

I

-

-2.0

FIG. 17. (1) Weak-inversion current characteristic of a MOSFET with the redistribution profile of Fig. 15b; (2) corresponding characteristic for a homogeneous doping.

111. DETERMINATION OF THE SURFACE STATEDENSITY FROM DRAIN CURRENT vs DRAIN VOLTAGE MEASUREMENTS IN WEAKINVERSION(Van Overstraeten et al., 1975) The MOS ac conductance technique of Nicollian and Goetzberger (1967) is the most accurate and the most complete technique to study the surface state properties. It permits the determination of the surface state density N,, , of the standard deviation os of the surface potential fluctuations, and of the capture cross sections. However, the complexity of the theory limits the easy use of this method. It is also well known (Castagne and Vapaille, 1970; Declerck et al., 1973) that substantial errors in the surface state density can occur using either the

MOSFET OPERATING IN WEAK INVERSION

225

low-frequency capacitance technique (Berglund, 1966), the high-frequency capacitance technique (Terman, 1962), or the low-temperature capacitance technique (Gray and Brown, 1966).The failure of these methods is due to the nonuniformity of the surface potential, mainly caused by statistical fluctuations of interface charges. Simonne (1973) proposed a simple alternative technique for the ac conductance method, based upon a mathematical property of the expression of the MOS parallel conductance. This technique yields the same information about the density of surface states as the Nicollian and Goetzberger theory, without the need for determining the surface potential and the doping density, which does not have to be constant. This simplified method is well applicable on MOS transistors in depletion, including those with a doping profile, but still requires a tiresome conductance measurement. Capture cross sections are not obtained from this technique. In this section we shall discuss a new method to determine the number of surface states. This method is based on dc current measurements in weak inversion (Guzev et al., 1971), and is applicable on MOS transistors coming from a normal production lot. Nonhomogeneous doping is allowed, but in order to avoid two-dimensional short-channel effects, the channel length should not be smaller than about 20 pm. A. Theory

Equation (56) demonstrates that the drain current at a particular gate voltage in weak inversion is given by the following expression :

when the source voltage V, is taken zero. lDmax is the maximal drain current at gate voltage V,, and can be found by putting VD equal to infinity in Eq. (56). From (47) and (48)it follows that

Every value of V, is linked to a specific value of M / N through the surface potential ds0at the source. When an 1, - VD measurement is done at a specific gate voltage in weak inversion, it is possible to calculate numerically an ID - VD curve with the same exponential shape as (67), which fits the measured points. From the value of the fitting parameter M / N , the surface state density corresponding to the applied gate voltage can be calculated from

226

PAUL A. MULS ET AL.

The least-squares approximation of the measured points yields a good accuracy. To illustrate the accuracy of the technique we calculate some I , - V, curves with the model of Pao and Sah incorporating the exact HSR occupancy statistics for the surface states. On a MOS transistor with N,, = 5 x 109 v-1 cm-' and 4,0 = $4F,and a simulated random error of 17, on the current, the value of N , , obtained with the least-squares fit of this simulation deviates from the introduced N,, over an amount never exceeding 2 x lo9 V-' cm-'. The higher the surface state density, the better also the relative accuracy. Application of the ID - V, method on a current simulation for N,, = 5 x 10" V-' cm-' and = $4F, with a random error of 3 o o on the current, gives in the worst case an error on N,, of 4 x lo9 Vcm-', i.e., a relative error of less than 10%. Another simulation allows the determination of the potential interval within which meaningful results can be expected. Figure 18 shows the N , , values obtained from a simulated I , - V, measurement in function of the potential 4,0 at which the measurements have been done. The I , - V, curves are calculated for a surface state density of 5 x 10" V-' cm-'. The full line represents the results of simulations with the HSR statistics (12) in the current expression, the dashed line is the corresponding result with the quasi-Fermi-Dirac statistics (15). At lower potential values, a discrepancy exists. This is self-evident, because the I , - V, technique is based on the weak-inversion current expression (56) which is based on the quasi-FermiDirac statistics. From Fig. 14 we already know that the quasi-Fermi approximation fails in some cases at very low surface potentials. This is even more obvious from the fact that the I , - V, technique yields wrong results in very weak inversion. The current expression (56) also does not hold at higher values of the surface potential, because the weak inversion condition (52) is not satisfied. The I , - V, technique will consequently likewise fail in this region. In order to obtain a sufficient accuracy, the ID - V, measurements have to be done in an interval of 150 mV around = i4F. The above results can be explained and clarified from a physical point of view by going back to the diagrams of the HSR- and FD-distribution functions in Figs. 8 and 9. For 4so= $+F (Fig. 9), the occupancy function shifts over an amount 4c,provided 4cdoes not become too large. This is the basis of the I , - V, method: In a point along the channel with a value 4 c ,the interface charge changes over an amount qN,, 4cwith respect to the interface charge at the source. However when 4c exceeds a certain value, the interface charge does not change anymore, and the I , - V, technique can no longer be used. In practice this limits the drain voltage in the current measurements to values below 100 mV. For 4,0 = 4F (Fig. 8), the occupancy function hardly shifts with increasing + c . Hence the interface charge changes very little along the channel, and if one still takes for this change the value

+,,

MOSFET OPERATING IN WEAK INVERSION I 10 -1

N,

227

-2

(I0 V cm

)

6 -

@F

I

1. ' 300

400

500

600

@s [mv)

FIG. 18. Result of the application of the I , - V, method on simulated current curves with N , , = 5 x 10" V - ' cm-2 vs the corresponding surface potential at the source. (1) Current curves calculated with HSR statistics; (2) current curves calculated with quasi-Fermi statistics. ON A

nnp aiitnmatir'allv w t c tnn c m n l l 2 v n l i i e fnr

N

n s d e m n n n t r n t e d in

B. Energetic Position of the Measured Surface States

In this section we shall again use the energy band diagrams of Figs. 5-7. We assume the occupancy of the surface states governed by the quasiFermi-Dirac statistics. For bsin the neighborhood of $&, this is exact when 4cdoes not become too large (4cI 100 mV). Since all surface states below

228

P A U L A. M U L S ET AL.

the quasi-Fermi level of the minority carriers are occupied and only these, it follows that the change of the interface charge with respect to flat band at a surface potential 4sis given by

in equilibrium, and to -

4P

N&JJ d4,

(71)

J-(4?-4P-4c)

in quasi-equilibrium. The relation (39) between gate voltage and surface potential consequently is

From the above, the following can be concluded: A change in the occupancy of the surface states during the transition from flat band to inversion occurs only between the points located at 45- 4p- 4c above, and 4Fbelow midgap. Consequently, a peak of N , , , located for instance at :4F below the middle of the forbidden energy band will not be detected, since its occupancy does not change. In weak inversion 4s remains almost unchanged from source to drain. + c on the other hand varies with distance in the channel, so that the upper boundary of the energy range in which the occupancy of the surface states changes, also varies along the channel.

Using a derivation similar to the one used in Section ll,C,l, it is easy to prove that the value of N , , corresponds to the average value Nssin an energy interval AE N q$c. The larger g5c, the larger also the energy interval will be. Consequently, Nss will change with 4c.The upper boundary of the interval remains unchanged for the same gate voltage, namely, q($JS,,- &) above E , . If another gate voltage is applied, another 4sois obtained, thus another upper boundary and consequently another N s s .If, for instance, 4so= t4F, the upper energy lies at &F above E , , and the lower at about $$F - 4c above E , . Thus, as long as 4c < *4F( 2 : 150 mV), the upper boundary also remains above Ei. Each point along the channel has its own specific value of 4c and consequently its own specific N s s .Q , in this point is given by (51). With

MOSFET OPERATING IN WEAK INVERSION

229

this becomes

The drain current, making use of (35) is then given by

In this, N , , is an effective surface state density in the energy range from Ei + q($s,,- 4F)to Ei + q(4so- 4F)- qT/, . Computer simulations demonstrate that this effective surface state density agrees very well with the real density at the location Ei + q(4so- &) in the forbidden gap. This is understandable since 4c remains very small over a large part of the channel. The interval q4c in which Nss is the average surface state density, consequently remains confined to the immediate vicinity of the energy point Ei + q(bs0- 4F)over a large part of the channel. It therefore is reasonable that the measured density N,, agrees with the surface state density at the energetic position Ei + q(4,0- &). It is easy to prove that 4cis indeed a weak function of the longitudinal distance in the channel. Equation (24) gives in differential form the relation between 4c and the distance y from the source. Considering that 1, is constant in the channel, integration of (24) with expression (74) for Q, yields

which proves the logarithmic dependence of this behavior. Putting (76) into (74) gives

c$c

on y . Figure 19 illustrates

This means that Q, varies linearly with distance in the channel, from a value

at the source, to a value

230

P A U L A. MULS ET AL.

I

0

20

80

60

y

100 io/a

Of

L)-

FIG.19. Behavior of the spreading dc of the quasi-Fermi levels vs the distance y in the channel. Parameters: to, = loo0 A; N , = 1 x l o i 5 ~ r n - ~ N; , , = 5 x lo1' V - ' c m - * ; = $&; and V, = 100 mV.

at the drain. It is clear that the slope of Qnin the channel, through M/N, is dependent on N,,. We can therefore conclude the following: N,, can be determined from I , - V, measurements, because the variation of $ c from zero at the source to V, at the drain, also varies the occupancy of the surface states from source to drain. The charge density in the interface thus depends on the position in the channel. In this manner, the inversion charge in the channel and consequently the drain current, is dependent on the surface state density. Another gate voltage results in another $,,, and, consequently, in another location in the forbidden energy zone where N,, is measured. Computer calculations in Fig. 18 demonstrate that N,, only can be measured with acceptable accuracy when $$F - 50 mV 4 4 $dF 100 mV. The density of surface states in the forbidden gap can thus only be traced within a range from Ei + q(&F + 100 mV) to Ei + q(;& - 50 mV). For N 4 = 1 x 10l5 cm-3 and T = 22"C, this goes from 250 meV to 100 meV above midgap. Since $F = (kT/q)ln(N,/n,), the interval can be shifted by changing the temperature. In practice, the value of N,, is measured at the position Ei q(450 - &), i.e., at the position of the Fermi level of the majority carriers (see Figs. 5-7).

+

+

MOSFET OPERATING IN WEAK INVERSION

23 1

C. Nonuni$orm Doping When the impurity concentration varies with the depth in the semiconductor, the weak-inversion technique can still be used to determine the surface state density in weak inversion. Indeed, formula (73) nowhere assumed a constant doping level. Consequently, the surface potential along the channel is in the same manner dependent on the surface state density as in a transistor with homogeneous doping. This is also proven by computer simulations. An I D - VD curve for a transistor with the implanted doping profile of Fig. 15a, and the corresponding curve for a constant background doping level have been computed. Both curves are calculated with the parameter values tox= lo00 A, N,, = 5 x 10" V-' and &so = 494 mV. Fitting with the exponential least-squares approximation (67) yields N,,= 5.03 x 10" V-' cm P2 for the homogeneous doping, and N,,=4.93 x 10" for the Gaussian profile. It appears that the impurity distribution strongly influences the I D - V, curve, but hardly affects the shape of the (ID/IDmax) - VD curve, which is determined by the surface state density. The same phenomenon is found again for the redistribution profile of Fig. 15b. Both curves have been calculated with the parameter values to, = loo0 A, N,, = 5 x 10" V - ' cmP2,and &o = 513 mV. The curve with the homogeneous doping yields N,, = 5.13 x 10'' V - ' cm-', the curve for the case of nonuniform doping gives N,, = 5.32 x 10" V-' cm-2. The value of CD in (69) was computed numerically for the nonhomogeneous doping profiles.

D. Short I D -

VD

Method

From formula (67) of the drain current in weak inversion, and from the definition of M / N (68), the following expression for N,, can be derived:

Consequently it is sufficient to consider one value of VD. From the measured ID/IDmax one can, using Eq. (78), immediately find the surface state density. It can be proven that the best accuracy is obtained when N,, is calculated with the ID/IDmax value for which In[l - ( I D / I D m a x ) ] = - 1, i.e., ID/IDmax = 0.632. From (78) it follows that N,, is then given by

In summary, the surface state density can be found from the value of VD that has to be applied in order to obtain a drain current equal to 63.2% of the

232

PAUL A. MULS ET AL.

maximal current for the considered gate voltage. The accuracy of this procedure is better than 1 x 10" V - ' cm-'. The technique is illustrated by Fig. 20, showing the theoretical I D / ' l D m a x vs V, curve for N , , = 0, together with a set of experimental curves measured on a same device but at different surface potentials. The value of VD at the intersection of each curve with the line Z, /Z, max = 0.632 has to be inserted in (79). If further CD(4,,)is determined for every value of the surface potential qj,,, N,, finally can be calcuuated. This results in a density of about 6 x 10" V - ' cm12, which agrees very well with the value of 5.9 x 10" V - ' cm-' found independently with the ac conductance technique of Nicollian-

0

20

LO

60

80

100

120

140

V,,IrnVl__,

FIG. 20. (1) Theoretical ID/IDmarvs V, curve for N , , = 0. The other curves are measured on a transistor with to, = 2000 A, N , = 1.11 x ~ r n - and ~ , N,s = 5.9 x 10" V-' ern-', for different values of the surface potential: (2) + s o = 404 mV; (3) = 485 mV; (4) @ % o = 561 mV. +50

MOSFET OPERATING IN WEAK INVERSION

233

Goetzberger. If the surface potential is not known, C Dcan be determined by means of high-frequency capacitance measurements. This shortened I , - V, method is very handy for a quick evaluation of the surface state density. A few points of the ln(ID)- V, curve in weak inversion are measured, and from these, the value of V, corresponding approximately with the middle of the linear range, is determined. For this value of V, , 4so‘v $&, and a successful I , - V, measurement can be done. A few points in the range V, = 25-50 mV together with the measurement of IDmax are sufficient. The determination of I , max is not always easy, because in some cases no maximal current is found, due to channel shortening or twodimensional effects, especially when short-channel transistors are used. As a first approximation, the value of I , at V, N 200 mV can then be taken as IDmax. For a more precise determination of the surface state density, the more accurate least-squares approximation of the entire I , - V, curve is recommended. E. Influence of Surface Potential Fluctuations

Brews (1975) has demonstrated that for small fluctuations of the interface charge, the drain current can be written as I D = IDO( - f(O,’ )) (80) where I,, is the current carried by a uniform device with the same average carrier density, and ( 0 , ’ ) is the variance of surface potential fluctuations. According to the analytical expression found by Brews, ( 0 , ’ ) depends on the surface potential and consequently on V, . However, since in weak inversion the surface potential remains nearly constant over the whole channel length, provided the drain voltage is kept small ( <200 mV), ( 0 % )can be assumed independent of VD. The (ID/IDmax) - VD curve is thus not influenced by (0,’). The experiments will indeed demonstrate that the weak-inversion technique yields the real surface state density, and that no corrections have to be made for surface potential fluctuations.

F. Experimental Results and Conclusions

The experimental results reported in this section are obtained by means of a least-squares fit of a measured I , - V, curve. The drain voltage takes 32 different values in the series: 2,5,7,10,12,. . . , S O mV. The channel current is measured with a Keitley 616 electrometer connected between the source of the MOSFET and the ground. The bulk is at ground potential. In this way the leakage current of the reverse-biased drain diode is not measured. Using the electrometer in the feedback (fast) mode, guarantees a negligible small

TABLE I1 PROPERTIES OF THE EXPERIMENTAL DEVICES

MOSFET No. 1 TRI-8JV

P(ll1)

No. 2 TRI- IJV

P(ll1)

No. 3 MOST 250872/2

n(lO0)

No. 4 MOSIMP 270875/7

n(ll1)

No. 5 WINMOS 290775/13

n(ll1)

No. 6 MOST 181073/5

n(lO0)

Doping (~m-~)

Oxide

Substrate

0%

QA

( k T / q ) (10" cm-')

5.69

L Z 10

3.07

2.46

Profile of Fig. 15a. N,,,,, = 7.6 x 1014

5.69 x

L

3.76

2.9

A

Homogeneous N , = 1.05 x 1015

1.11 x 1 0 - ~

~ = 9 3 W = 119

0.5

Homogeneous N , = 1.67 x 1015

5.18 x

L = 216 W / L = 1.11

4.6

5.0

Homogeneous N , = 1.43 x 1015

3.77

L = 196 W / L = 9.82

2.2

2.61

1687 A

Homogeneous N , = 1.07 x 1015

5.18 x

L = 216 W / L = 1.1 1

1.6

1.93

1119 8,

Dry to, = 975

Dry = 1410 A

Dry t,, = 1128 A

Dry

Wet t O x=

N,' (10" V - ' cm-')

Homogeneous N , = 7.6 x 10i4

to, = 975

to, =

Geometry (pm)

A

Dry

t,

Active gate area (cm')

x

10

'

2

10

235

MOSFET OPERATING IN WEAK INVERSION

internal voltage drop ( < 0.1 mV), and consequently also a negligible sourcebulk leakage current. As a first example, we treat a n-channel(ll1) transistor with a homogeneous doping density. The parameters of the transistor are given in Table 11. Figure 21 shows the three-terminal gate-bulk (CGB)and gate-source-pluscapacitance versus gate voltage measurements at 1 MHz, from drain (CGSD) which values for the parasitic capacitances, for the active gate area, and for the depletion charge capacitance C, are derived (Bateman and Magowan, 1970). The figure also shows the valye of the gate voltage in depletion, at which the ac conductance is measured. The resulting (G,/o) - o curve is pictured in Fig. 22. By means of the Simonne analysis, the standard deviation of the surface potential, and the surface state density are found to be

n

-

0.L6 p F ( - L O V )

0

-10

v,rw

-9

FIG.21. Three-terminal capacitance vs gate voltage measurements on MOSFET No. 1 (see Table 11). The point at which N,,has been determined with the ac conductance analysis of Simonne is also indicated.

236

P A U L A. M U L S ET AL. -9 -2 G p l w I10 F cm

I

1 .o

0.9

1 . 1

3

4

5

I

I

l

l

1 , , , ,

6 7 8 9 1 0

FIG.22. Experimental G,/(tu

I

, . . .I

20 -

,

, ( . I I

I

30

w ) curve for

50

I

I l l . . , ,

70

100

MOSFET No. 1 at V,

,..FIkHzI

= - 3.30

V

(T, = 2.46 kT/q and N , , = 3.07 x 10"' V - ' cm-2. Figure 23 shows the ln(1,) - V, curve of the same transistor, measured at V, = 108 mV. I, - V, measurements have been done for different values of the gate voltage in weak inversion. The resulting values of N,, out of the In - V, measurements, have been plotted in function of the corresponding gate voltage, together with the N , , value found with the method of Simonne. The agreement is excellent for gate voltages in the lower part of the ln(1,) - VG curve, while the increase of N,, at larger gate voltages already has been explained theoretically in connection with Fig. 18. Besides, it is not excluded that N,, does indeed increase towards the band edge. Our second sample originates from the same lot as the transistor above. It has the same geometry and is characterized by the same parameters (Table 11). However, its threshold voltage has been shifted by a boron ion implantation (energy 40 keV, dose 6.3 x 10" cm-2 and a 30 min annealing

237

MOSFET OPERATING IN WEAK INVERSION

VD=108mV

j_ l_ _ ~ ~

- 3.0

V,CVJ

diode l e a k a g e 0 . 0 4 5 PA

-2.5

-2.0

-

-1.5

FIG.23. Experimental In(l, - V,) curve of MOSFET No. 1, with the N , , values resulting from 1, - V, measurements at different gate voltages, compared with the N,, value resulting from the method of Simonne.

at 900°C) (Verjans and Van Overstraeten, 1975), resulting in a doping profile represented in Fig. 15a. As above, three-terminal capacitance measurements have been done, which are shown for comparison in Fig. 24. Also for comparison, the ( G p / o ) - o curve measured at the indicated gate voltage is shown in Fig. 25. Simonne's analysis yields N,, = 3.76 x 10" V-' cmp2, and r ~ = , 2.9 kT/q. This indicates a light degradation of the quality of the

238

P A U L A. MULS ET AL.

20.15 p F l + L O V )

1

0.52 pF 0 1 -10

I

j

-6

I

I

-6

I

I

-L

I

I

-2

I

I

0

V-lVI 1

1

2

1

1

L

1

'

b '-

6

Frti. 24. Three-terminal capacitance vs gate voltage measurements on MOSFET No. 2 (see Table 11). The point at which N,, has been determined with the ac conductance analysis of Simonne is also indicated. Compare with the homogeneous doping case in Fig. 21.

interface with respect to the nonimplanted case. Figure 26 shows the ln(lD)- V, curve of the implanted transistor at VD = 102 mV. One notices the less steep slope, due to the enhanced impurity concentration. As for the nonimplanted transistor, I , - V, measurements have been carried out at different gate voltages in the linear part of the ln(Z,) - V, curve. The N , , values resulting from the least-squares fit of the I , - VD curves, have also been plotted versus the corresponding gate voltages. The agreement at lower current densities with the result of the ac conductance technique once again is excellent. The increase of N , , at higher gate voltages can again be explained by the increasing inversion whereby the approximations in the formulas on which the method is based fail, and by a possible increase of the

MOSFET OPERATING IN WEAK INVERSION

L.l I

3

I

5

6 7 8 9 1 0

. . ~ * ~' ~ ~ ~ . 1

20

I

,

'

'

I

50

I

239

F (kHz1 ' I " . . ' ' ' -

I00

FIG.25. Experimental (C,/w) - w curve for MOSFET No. 2 at V, = with the homogeneous case in Fig. 22.

- 1.33

V. Compare

surface state density towards the band edge, as reported in the literature (e.g., Ziegler and Klausmann, 1975). The third sample is intended as an illustration of the sensitivity and accuracy of the weak-inversion method. A p-channel (100)transistor is considered with parameters stated in Table 11. Special care has been taken in order to keep the surface state density on this wafer as low as possible. The surface potential of the transistor has been determined as a function of the gate voltage by means of the method of Berglund (1966) and Kuhn (1970). The knowledge of the relation between dsoand V, allows to plot the N,, values resulting from I , - V, measurements in weak inversion vs the respective values of the surface potential at which the current measurements have been done. The result is shown in Fig. 27. An experimental ac conductance curve on a special test capacitor near the transistor, has been fitted with a theoretical curve. Using the analysis of Nicollian and Goetzberger, a surface state density of 5 x lo9 V - ' cm-' is found. The agreement is excellent in the middle of the weak-inversion range. These experiments demonstrate, by comparison with the ac conductance technique, which takes account of surface potential fluctuations, that the weak-inversion method to measure the surface state density suffers very little from the inhomogeneities of the interface charge. Provided sufficient attention is paid to the practical realization of the measurements, the weakinversion method can reach a sensitivity and overall accuracy better than 1 x 10" V-' cm-2.

100 p i

I 0 pb

1

u

100 n b

10 n P

1 nP

100 pP

10 pP

1

PP

0.1 pP

-0.L

-0.2

0

0.2

0.6

0.L

0.8

1.0

1.2

FIG.26. Experimental ln(1,) - V, curve of MOSFET No. 2. with the N,, values resulting from I , - V , measurements at different gate voltages, compared with the N,, value resulting from the method of Simonne. Compare with the homogeneous doping case in Fig. 23.

-

0

Gplw

- -W -LOO

- Os LmV)

*

- 500

-600

FIG.27. Comparison of the Nsbvalues resulting from I , - V, measurements on MOSFET No. 3 vs the respective values of the surface potential at which the measurements have been done, with the N s , value found with the Nicollian-Goetzberger analysis on a nearby test capacitor.

MOSFET OPERATING IN WEAK INVERSION

24 1

IV. INFLUENCE OF POTENTIAL FLUCTUATIONS ON THE MOBILITY IN WEAKINVERSION A . Introduction

The carriers in the shallow inversion layer of a MOS transistor are easily influenced by nonuniformities in the vicinity of the isolator-semiconductor interface. Localized charges in the oxide and in the channel can not only cause scattering of the carriers, but they can also give rise to fluctuations of the potential in the semiconductor. These potential fluctuations in turn cause carrier-density fluctuations, which alter the current characteristics of the MOS transistor. From Hall measurements and dc conductance measurements, Fang and Fowler (1968) already found that the mobility of the carriers in the channel exhibits a maximum near the threshold voltage of the transistor. As reason for this phenomenon they assume scattering by charged surface states or ions in the oxide near the interface, whereby local cavities are induced in the inversion layer. Those early results of Fang and Fowler have also been confirmed by measurements of Murphy et al. (1969), who conclude that below a certain threshold voltage, the mobility is mainly affected by ionized impurity scattering at the Si-SiOz interface, and that the charged impurities are more effectively screened with increasing carrier density in the channel, which results in a mobility increasing with the gate voltage. Above the threshold voltage, some other mechanism, such as surface phonon scattering, must be responsible for the decrease of mobility with increasing gate voltage. Van Overstraeten et al. (1973) explained the anomalous slope of the ln(Z,) - V, characteristic of the MOSFET operating in weak inversion by surface potential fluctuations. Due to experimental inaccuracies in the determination of the surface potential, these authors found no evidence of a drop of the mobility in weak inversion for their samples. This led to a misinterpretation of the influence of the potential fluctuations on the weak-inversion current. In Section IV,D accurate experimental results will be presented and discussed, making use of Brews’ theory. Guzev et al. (1972) and Chen and Muller (1974) have also interpreted their current-voltage measurements in terms of nonuniformities in the channel, which introduce potential barriers, obstructing the free motion of the carriers. Chen and Muller measured the channel conductance onsas a function of the gate voltage at a very small drain voltage by means of a lock-in amplifier, and employed Berglund’s method to determine the mean surface potential and the corresponding inversion-layer carrier density n(cm-2).

242

PAUL A. MULS ET AL.

The conductivity mobility is finally obtained by using pn

= onslqn

The mobility obtained using this technique appears to approach a constant value when the inversion-layer density is lower than lo9 cm-2, starts to increase with the inversion-layer population when the latter is about 10" cm-2, and reaches a maximum when the density is approximately lo1 cm '. Thereafter, mobility decreases with increasing carrier density. These results agree in general with the measurements of Fang and Fowler, as well as with those of Murphy et al. Moreover the measuring range has been extended to weaker inversion cases (n = 108-109 cm-'). To develop a model for mobility in weak-inversion channels, Chen and Muller adopt the patchwork interpretation of the interface charge distribution, first introduced by Nicollian and Goetzberger. This patchwork model consists in describing the interface as an agglomeration of many characteristic areas or patches, each of which has a uniform surface potential corresponding to a uniform interface charge. The surface potential differs from one characteristic area to another, and is assumed to vary according to a Poisson distribution function. If the surface potential is normalized to k T / q , it was shown theoretically that the standard deviation for the normalized Gaussian distribution, which approximates the Poisson distributed potential is ~

4 O5 =

kT(C,,

+ Csi)

4Qox

1 2

In Eq. (82), Coxand C,,are the oxide and semiconductor capacitances per unit area, respectively, Q , is the average interface charge density (Clcm'), and c1 is the size of the characteristic areas. When the inversion layer conducts, the free carriers travel from one characteristic area to another. Chen and Muller simplify the model by considering in the whole channel only two potential levels with equal likelihood, separated by an effective barrier Ae, such that the mean and standard deviation of the actual potential distribution is maintained. This condition is fulfilled provided Ae = 20, k T l q (83) The carrier densities nu at the higher potential and n , at the lower potential can be written as functions of Ae and of the average density of free carriers over the whole channel: nav = (nu + n , ) / 2 . By equalizing the expression for the current density in the channel consisting of regions with higher or lower potential to the current density written in function of the average carrier density nav(J = qpnna,V,/L), an overall channel mobility pn is found, which depends exponentially on Ae. Since b e is a function of the surface potential via cs(83) and Csi (82), the simplified potential-fluctuation model proposed

MOSFET OPERATING IN WEAK INVERSION

243

by Chen and Muller, yields a theoretical potential-dependent MOSFET mobility, which approximates the dominant variations of the experimental mobility.

B. Carrier-Density Fluctuation-Theory of Brews The minority-carrier-density fluctuations in the MOS transistor, and their effect upon sourcedrain current, and consequently on mobility, are treated by a three-dimensional perturbation theory presented by Brews (1975). The fluctuations are considered to be generated by surface state charge and fixed charge. Brews distinguishes two mobilities. The microscopic mobility p is the mobility determined by scattering alone and is the one to be used in Maxwell’s equations under the assumption of no fluctuations. The MOSFET mobility p n or pp is the one deduced from MOSFET measurements. Fluctuations may affect the current flow through the introduction of new charge-density terms or modified boundary conditions into the Maxwell equations, an effect additional to the scattering contributions of the nonuniformities to the microscopic mobility. The MOSFET mobility will then be different from the microscopic mobility. The effect of fluctuations on the MOSFET mobility can also be understood as follows. A carrier-density fluctuation alters the electric field and the concentration gradients along the channel. The current-flow lines thus will bend along the channel. Consequently the charge carriers either can take a longer path through the low-resistivity regions or a shorter path through the high-resistivity regions. The resulting current therefore will be smaller at a given drain voltage, or the MOSFET mobility is decreased. At low carrier densities the fluctuations are expected to have a noticeable influence on the mobility. At high carrier densities, larger than about lo1’ carriers/cm’, the fluctuations have a negligible effect and the mobility can be explained in terms of phonon scattering at high temperatures, supplemented by surface roughness scattering at low temperatures. The analysis proposed by Brews is only valid when the departures from uniformity are small, and is built around the Pao-Sah theory of the MOSFET. Following the approach of an earlier paper (Brews, 1972) about surface potential fluctuations generated by interface charge inhomogeneities in MOS devices, Brews rejects the patchwork model because of edge effects and interactions of the patches, due to short-wavelength charge variations. Instead he proposes a small-fluctuation mathematical model for a random distribution of the interface charge. He does not break up the MOS device into discrete elementary devices, but solves the three-dimensional Poisson equation for the entire device. The result is a source-drain current reduced

244

PAUL A. MULS ET AL.

by the ratio of the carrier-density fluctuations to the unperturbed carrier density. The resulting current I , can be expressed as where I,, is the current carried by a uniform device with the same average carrier density, and (a:) is the variance of relative carrier-density fluctuations averaged over the depth of the inversion layer. At room temperature, Boltzmann statistics apply, so that (0:) can be interpreted equally as the variance of surface potential fluctuations. Assuming small fluctuations and a low drain voltage, an approximate formula for (a:), including a simplified treatment of the screening effect of the inversion layer, gate, and bulk semiconductor is found to be

with CSi= C, + Cinv,and Gin\ the inversion-layer capacitance. In this formula Go,is the average interface charge density per unit area, and

C;. = (ESi

+ cox)/A

(86)

is the “resolution” capacitance per unit area, where 2 is related to the average distance of the minority carriers from the interface or, more generally, from the charges responsible for the fluctuations. Formula (85) for the variance (0,”) of the relative carrier-density fluctuations averaged over the depth of the inversion layer, is identical to the expression derived in the earlier paper of Brews (1972) for the variance of surface potential of. In this earlier work however, 1, was defined as the minimum wavelength of the interface charge variations. We shall now try to draw the parallel and point out the differences between both formulas, which are of the same form and have been derived following the same mathematical procedure, but which have their own specific meaning, and consequently have to be placed in their own context. The purpose of the earlier paper was to derive a formula for the variance of the surface potential fluctuations generated by interface charge inhomogeneities. The MOS device is in thermal equilibrium and is biased in depletion, so that the minority charge carriers do not have to be taken into account. In principle, Brews wants to solve the three-dimensional Poisson equation for the entire device (oxide, interface, and semiconductor), but cannot d o it for the most general case and therefore has to linearize it. The linearization used is equivalent to treating deviations from the mean interface charge density as a small perturbation and working to first order. By passing to a Fourier transformation of the linearized Poisson equation, and by introducing Green’s functions, Brews finds a general expression for a: in

MOSFET OPERATING IN WEAK INVERSION

245

integral form. This expression can only be converted to a usable analytical form, provided a number of assumptions and simplifications are made: The oxide charge is Poisson-distributed and is totally located at the interface. Besides, because the integral in the expression of 0: diverges unless there is some upper limit on the rapidity of interface charge variations, it is physically reasonable to cut off the integration at a value l/A, which comes to assuming a minimum wavelength 2 for the interface charge variation. This means that no fluctuation with a wavelength smaller than A can be present, otherwise the mathematical model gives rise to infinite surface potential fluctuations, which loses every practical meaning. Formula (85) however, has been derived with another intention. In his publication of 1975, Brews aims at calculating the influence of the nonuniformity of the interface charge on the source-drain current. Of course, since here a MOS transistor in inversion is considered, the minority charge carriers will play a dominant role, in contrast with the above-mentioned case. Besides, the MOS transistor is no longer in thermal equilibrium. To achieve his goal, Brews uses a three-dimensional perturbation-theory treatment, which once again holds only for small fluctuations and yields first-order approximations. Following this theory, the drain current can be written as ID= I,, + AID, with AID the deviation due to fluctuations of the interface charge, of the zero-fluctuation current ID,. To find AlD, Brews solves the linearized Eqs. (19)-(21). By making use of Green’s functions, he finds that AID is determined by the minority-carrier-density fluctuations relative to the unperturbed (zero-fluctuation) carrier density (An/u0). By keeping V, small or L large in any case, and by assuming that all the interface charge resides at the interface and is Poisson-distributed, Brews further finds that Lil, = -t(a,’)Z,, , with (a,’) the variance of the relative carrier-density fluctuations, averaged over the depth of the inversion layer. This inversion layer averaging is the meaning of the angular brackets in formula (85). In principle (a:) has another meaning than af in the earlier paper, although in most cases (i.e., at small fluctuations and on condition that the Boltzmann statistics apply, this is at not too low temperatures), (a:) can be interpreted equally as the variance of surface potential fluctuations. Once again the expression for (of) is written in integral form, but by using the same mathematical approximation as in the 1972 paper, e.g., the introduction of the same integration boundary l / A for the same diverging integral, Brews succeeds in reducing it to the analytical form of Eq. (85). Introduction of I means that no fluctuations with wavelength smaller than A are considered. However, since (a:) is related to fluctuations of minority carriers, it is obvious in this case to connect A with the average distance of the minority carriers to the interface, because nonuniformities at the surface, which vary over distances less than A, cannot be distinguished by the minority carriers

246

PAUL A. MULS ET AL.

and consequently cannot have any influence on (0,')since they do not cause fluctuations. If the minimal wavelength of the interface charge variations would be larger than the average distance of the minority carriers from the surface, the integration could be cut off earlier, and the value of this minimum wavelength could be attributed to A. The average distance R of the minority carriers from the surface varies with the orientation of the silicon, the bulk doping density, and also with field and temperature. Stern (1972) has made a computation of the average distance of electrons from the interface in n-channel MOSFETs. For his numerical calculations, Brews assumes A = z,, from Stern's work. At low temperatures and/or high fields, R is considerably smaller than at high temperatures and low fields. This has to do with quantization effects at low temperatures and/or high fields, when only the lowest subband in the inversion layer is filled. We shall restrict ourselves to room temperatures and low electric fields. In this range, zavvaries between 100 and 300 A. The behavior of the average variance of relative carrier-density fluctuations (o:), calculated with Eq. (85), versus the inversion-layer carrier density/cm2 Ninv,for two values of the average distance of electrons from the interface A, is shown in Fig. 28, taken from Brews. For large carrier densities, the inversion-layer capacitance Cinvis much larger than C , . Consequently (0,") is small, but increases rapidly with decreasing Ninv.For Ninv below 10'z/cmz, Cinvis lower than C , . Due to the influence of the gate and

-N.

inv Icm-*)-

FIG.28. Average variance of relative carrier-density fluctuations (and of surface potential) vs inversion-layer carrier density/cm2 calculated with Eq. (85). N , = 1014 c r K 3 (-); N , = 10l6 (---); t o , = 1000 A; T = 300°K; QoJq = 10" cm-'. (Figure taken from Brews, 1975.)

MOSFET OPERATING IN WEAK INVERSION

247

of the majority carriers, the fluctuations increase more slowly with decreasCinvhas no influence anymore and the fluctuaing Ni,, . At low enough Ninv, tions show a maximum value, determined by the doping level and the oxide thickness, independent of the inversion layer carrier density. From Eq. (84) we learn that $(a,") must be an appreciable fraction of unity in order for the fluctuations to alter the current. If for instance we take (0,') = 0.1 as such a value, then for A = 200 A, the fluctuations become appreciable for Ninv5 2 x 10"/cm2. Since the fluctuations are also proportional to QJq, increasing Q0Jq shifts the threshold (0:) = 0.1 to higher values of Ninv.For very low values of QJq, the fluctuations are small at all values of Ninv,and the current is only slightly affected if at all by the fluctuations. For a common MOS transistor, this occurs for QJq 5 10" cm-2. Summarizing, one can say that the size of the fluctuations is controlled by three factors: the average distance of the carriers from the interface, Ninv, and the size of the originating nonuniformity as expressed by &. From this study of Brews one can derive several qualitative results. (a) Since the fluctuations increase with decreasing carrier density, fluctuations are most important at low carrier densities. An increase of the strength of the fluctuations extends the range of carrier densities in which the fluctuations are important to higher carrier densities. (b) For a given carrier density in the channel the fluctuations are stronger in a channel that does not extend deep into the semiconductor (A small) than in a deep channel (A large), stronger at lower temperatures and stronger at larger interface charge densities. (c) The effect of fluctuations upon the MOSFET current increases rapidly with decreasing carrier density. An abrupt reduction of current is observed once ( 0 , " ) becomes an appreciable fraction of unity, for instance, 0.1. Since I , is proportional to p, and since IDo has to be proportional to p, with the same proportionality factor [Eq. (35)], because I , is the current carried by the same transistor with the same average inversion charge density in the absence of fluctuations, one finds with the aid of Eq. (84) for the MOSFET dc conductance mobility p,:

with p the microscopic mobility, not influenced by fluctuations. By using an appropriate expression for p as a function of Ninvand T , found by an empirical fit to the experimental mobility measured by Fang and Fowler at fields above the mobility maximum, where carrier-density fluctuations are negligible, and by substituting expression ( 8 5 ) for (c,")into Eq. (87), the

248

P A U L A. MULS ET AL.

results of Fig. 29 taken from Brews are obtained for pnvs Ninv. The average inversion-layer carrier density Ninvhas to be determined from

in which all quantities have to be interpreted as averages. The agreement between Fig. 29 and the experimental results obtained by Chen and Muller is excellent. At low carrier densities, the MOSFET mobility is low due to the high value of the fluctuations limited only by the gate and majority-carrier screening. As the minority-carrier density increases, the inversion-layer screening increases and the carrier-density fluctuations decrease, resulting in an increasing MOSFET mobility. Finally, near the peak value of 10"

t

-!

.

600

>

N

,E

LOO

I

I =

10

10

-N.

10 11 10 10. inv (cm2)--

12 10

FIG.29. Behavior of the MOSFET mobility vs the carrier density in the inversion layer, calculated from the fluctuation-theory of Brews. Parameters: to, = 2000 A: N , = 2 x 10l6 cm-'; e,/q = 2 x 10" cm-'; and 1 = 200 8. (Figure taken from Brews, 1975.)

carrierslcm', the microscopic mobility decreases due to increased scattering at higher fields. For still higher carrier densities, the fluctuations are negligible and the mobility behavior is dominated by scattering. It can be concluded that the analysis of Brews about small fluctuations in the density of minority carriers, explains qualitatively well the experimental behavior of the inversion-layer mobility of the MOSFET operating in weak inversion. To summarize: N o peak in the mobility occurs at low interface charge densities ( z10'O/crn2).

At higher interface charge densities a step in the mobility occurs. The height increases with the interface charge density, and the step position moves to higher values of Ninv. Due to larger carrier-density fluctuations at lower temperatures and to a higher microscopic mobility due to weaker phonon scattering, the mobility step is larger at lower temperatures than at higher temperatures.

MOSFET OPERATING IN WEAK INVERSION

249

C. Measuring Procedure This section describes the most important experimental techniques necessary to analyze the weak-inversion current behavior.

1. Determination of' the Bulk Impurity Density

To determine the doping density, we make use of a three-terminal gateto-bulk capacitance vs gate voltage measurement on the MOS transistor in depletion. Source and drain are short-circuited to the ground terminal, and the measuring frequency is 1 MHz (Boonton 75A-S8 Capacitance Bridge). In this way, the influence of minority carriers and surface states is eliminated, because they cannot follow the measuring frequency, and only a series circuit of the oxide capacitance and the semiconductor depletion capacitance underneath the active gate area of the MOS transistor is measured. The measured differential capacitance is then analyzed following the approach of van Gelder and Nicollian (1971):

and x=

.+$ -

cox

j

-1

(89)

with CG the capacitance of the active gate region, and A the active gate area. Thus one gets a picture of the behavior of the doping as a function of depth up to the maximal width of the depletion layer. This is not possible with the CMIN ICMAX method, because this method only yields an average doping level over the maximal depletion width, which itself is already a function of the doping. Much care has been taken for the exact determination of the doping level, by measuring on the transistors themselves, and not on special test capacitors, and by avoiding all transistors with an abnormal or excessive impurity redistribution at the surface. As we shall see later on, this redistribution can be taken into account by using a slightly adapted flat-band voltage in the calculations. 2. Determination of the Surface Potential

To determine the surface potential of a MOS transistor as a function of the applied gate voltage, the quasistatic integration technique of Kuhn (1970) is employed. The capacitance between the gate and the bulk, shortcircuited with source and drain, forms the capacitive element of an analog

2 50

P A U L A. MULS ET AL.

differentiator that uses as operational amplifier a Keithley 615 electrometer in the " fast" mode on the 10- l o A range. It is known that the displacement current through the MOS device in response to a linear voltage ramp at the input of the differentiator is directly proportional to the differential lowfrequency capacitance of the MOS device. An x-y recorder connected with input and output of the differentiator consequently gives an image of the low-frequency capacitance on an unknown scale, vs V,. In order to keep the inversion layer and the surface states in thermal equilibrium at any time, the sweep rate has to be sufficiently low. Therefore, a triangular voltage is applied to the input of the differentiator with a slope of 25 mV/sec. This triangular bias yields a capacitance curve from inversion to accumulation during the rising slope, and the same curve from accumulation to inversion during the downward slope. The voltage range is 6 V wide, and is plotted on a scale of 200 mV/cm. By taking the average of those two capacitance curves, the influence of an eventual leakage path parallel to the MOS device is eliminated. Indeed, the presence of such a leakage resistance makes the horizontal axes of both curves to rotate over an equal angle but in opposite directions around the origin. Moreover, possible leakage paths have been avoided as good as possible by measuring in a dry nitrogen atmosphere. To fix the absolute values of the capacitance, a few points in the accumulation region are measured with a General Radio 1620 A P capacitance bridge at 1 kHz. This frequency is low enough to insure thermal equilibrium in the region in question. At the same time, three-terminal measurements (Bateman and Magowan, 1970) have been performed in order to determine the values of the parasitic header capacitance, interlead stray capacitances, and gate-source and gate-drain overlap capacitances, which have to be subtracted from the total quasistatic measuring value. By numerical integration of the corrected quasistatic C,*F- V, curve following the formula proposed by Berglund (1966), the surface potential 4s belonging to each V, is found, except for an integration constant 4sl,equal to the surface potential of the first measuring point, which is taken in strong accumulation. A first approach to this integration constant is obtained from the fitting of the experimental (CLF/Cox) - cjscurve with the corresponding theoretical curve for the ideal transistor with the right doping. Both curves have to concur in strong accumulation and in strong inversion, because in those regons C& is negligible with respect to CSi.The shift of the potential axes necessary to make both curves coincide is equal to the constant 4sl. Once the value of 4svs V, is more or less fixed, it becomes possible to determine N , , in a function of 4sby comparison of the measured CLF- 4, curve with the corresponding ideal curve without surface states. From this N , , behavior, and from the results of other methods (ac conductance, ID - VD), a representative N , , value is judiciously chosen. With this value,

MOSFET OPERATING IN WEAK INVERSION

25 1

the theoretical & - V, relation is calculated for the right doping density and for VFB= 0 V, and compared with the corresponding experimental relation. By adjusting $sl (measured curve) and VFB (theoretical curve), the two graphs are made to coincide as good as possible, especially in weak inversion. By this, 4sl and VF, are definitely lixed. It is, however, not always possible to reach a total agreement, because of the simplifying assumptions that have been made: constant surface state density in function of the surface potential, constant doping level in function of the depth in the semiconductor, and neglect of the potential fluctuations. The latter forms no objection when the surface potential is Gaussian distributed, because in this case the mean 4s(which is the measured one) is equal to the most probable 4s (which is used in the calculation of the theoretical curve). This, however, is no longer the case when the mean surface potential is determined by the Gaussian distribution of Qox over a number of elementary macrocapacitors (patchwork model). This is illustrated in Fig. 30 that depicts & calculated in -700

- 600 -500

-LOO

-300

- 200 -100

0

100

FIG.30. Deformation of the I$$ - V, relation by a Gaussian distribution of Q,, over a number of elementary macrocapacitors (patchwork model). Parameters: t , = lo00 A; N, = 1 x 10'' ~ r n - ~ V,, ; = 0 V; N , , = 5 x 10" V - ' cm-'; and T = 295°K. uq = 0 (-); uq= 6 x C (----).

252

P A U L A. MULS ET AL.

function of V, . The full line gives the curve for G , = 0, while the dashed line C cm-2. However, it should be emcorresponds with G , = 6 x phasized that this extreme value of G , corresponds in fact with a worst case. As can be seen on the figure, the exact values for +sl and V,, can still be obtained by fitting the theoretical curve ( G , = 0) to the experimental curve ( G , # 0) in weak inversion and in very strong accumulation and inversion. More unfavorable is the neglect of the doping profile. Figure 31 shows in full line the same ideal +s - V, curve as in Fig. 30. The dashed line this time - 700 - 600

-500

-LOO

-300

-

200

- I00 0

100 i . I I I . I I . I . I I I I I I I I

5

- 2.0

5

- 1.0

I

I

I

I

I

5

)

.

I

,

'

0

I

,

I

,

5

.

,

I

,

,

,

1.0

FIG.31. ( 1 ) Same ideal - V, curve as in Fig. 30; ( 2 ) corresponding curve for the phosphorus redistribution profile of Fig. 15b. The bulk doping level and the other parameters remain unchanged.

corresponds with the phosphorus redistribution profile of Fig. 15b. The bulk doping level and the other parameters remain the same. Again this is a worst case as in common transistors, the impurity concentration rearly rises that much at the surface. For this case, the proper measure to take is to make the theoretical curve (homogeneous doping) coincide with the experimental curve (profile) in strong and weak inversion. By taking the flat-band voltage a little larger in the theoretical curve than it is in reality, it becomes possible

,

5

MOSFET OPERATING IN WEAK INVERSION

253

with a homogeneous impurity concentration to obtain the same 4s - V, relationship in inversion as for an experimental transistor with doping profile.

3. Determination of the dc Conductance Mobility When oxide thickness, bulk doping density, flat-band voltage, surface state density, geometrical ratio and temperature of a MOS transistor are known, an I , - V, current characteristic is calculated in weak inversion, according to the model of Pao and Sah [Eq. (36)]. The constant mobility value is chosen such that the nonlinear portion of the calculated In(ZD)- V, curve coincides with the strong-inversion part of the corresponding experimental curve, measured at the same drain voltage. In our results, this experimental current curve, measured with a Keithley 615 electrometer in the “fast” mode, is always found in weak inversion to be situated below the theoretical curve with constant mobility. This indicates that the mobility as it appears in the formula of Pao and Sah, is smaller in weak inversion than in strong inversion. In this way it is possible for every value of the gate voltage and consequently of the surface potential, to calculate the value of the mobility from the ratio of the measured current to the corresponding theoretical current, calculated with the constant strong-inversion mobility. D. Experimental Results (see, also, Fang and Fowler, 1968; Chen and Muller, 1974)

As a first example we consider p-channel (111) transistor No. 4 of Table 11. Figure 32 shows the coincidence of the experimental 4s - V, curve (full line) with the corresponding ideal curve (dashed). A slight discrepancy is perceptible in strong inversion. As already stated, this can be attributed to potential fluctuations, to incomplete thermal equilibrium during the quasistatic C V measurement or to an increase of the surface state density near the band edge. From this figure, the flat-band voltage of the transistor can be determined : V,, = - 2.96 V. This shift corresponds to an oxide charge density No, = 5.0 x 10” cm-2. These data allow the calculation of the current characteristic in weak inversion. Figure 33 depicts the measured ln(ZD)- V, curve for VD = -101 mV and T = 22°C. The curve calculated with p = 254 cm2 V - ’ sec-’ coincides with the measured curve in strong inversion, and lies higher than the experimental one in weak inversion. In very weak inversion the experimental curve clearly deviates from the linear behavior. This steeper slope of the ln(ID)- V, curve at very small gate voltages, appeared for every MOS transistor that was measured. It may be caused by experimental errors due to diode leakage currents or

254

PAUL A. MULS ET AL.

-700

-600

-500

-LOO

- 300 -200

-100

0

100

FIG.32. Experimental 4T- V, curve of p-channel (111) MOSFET No. 4 (see Table 11), together with the best-fitting ideal curve, yielding V,, = - 2.96 V. Experiment (-); uq = 0 ( -). ~

~

~~

electrometer inaccuracies at these extremely low currents. Another possible explanation is the effect of unequal capture cross sections CJ, and C J as ~ shown in Fig. 14, and finally it could also be a real mobility effect at very weak inversion. The mobility behavior as a function of the surface potential shown in Fig. 34 agrees very closely with the theoretical prediction of Brews. The mobility reaches a peak value for z -750 mV and decreases in strong inversion due to scattering of the minority carriers. For 24F 2 4\ 2 $4ba plateau of constant mobility appears. The height of this plateau should be inversely proportional to the average interface charge density Qox, which occurs in the expression for (a:), Eq. (85). The influence of the interface charge density on the fluctuations, and consequently on the value of the mobility in weak inversion, is clearly illustrated in Fig. 35 where the pp - 4- characteristic of p-channel (111) MOSFET No. 5 is plotted. By fitting of the $ J~ V, curves, one finds VF, = -2.38 V, which corresponds with N , = 2.61 x 10" cm-2. The

255

MOSFET OPERATING IN WEAK INVERSION

100nA-

1OnA-

InA-

VGIVI I

-4.0

I

,

-4.2

I

'

-4.4

I

-4.6

I

I

-4.8

I

I

-5.0

1

1

-52

l

l

~

-5.4

FIG.33. (1) Measured In(lD)- V, curve for MOSFET No. 4 p-channel (111); ( 2 ) corresponding theoretical curve calculated with the constant mobility.

mobility curve is finally obtained from a ln(Z,) - V, measurement at V, = - 100 mV. The interface charge density is about half as large as in the preceding sample, which results in a mobility step in Fig. 35 that is also only half as large as the mobility step in Fig. 34. As a last example, we consider MOSFET No. 6, which is a p-channel (100) transistor with a wet-grown oxide. From the 4s - V, curve one finds V,, = - 1.32 V, which yields N o , = 1.93 x 10" ern-'. In Fig. 36 one finds the experimental In(1,) - V, curves for I V,l = 1 V, 100 mV, and 6 mV, and the calculated theoretical curve for I V, I = 1 V (dashed line). From each of those curves it is possible to derive a mobility behavior. The result is

256

PAUL A. MULS ET AL.

FIG. 34. Experimental mobility behavior vs surface potential for p-channel (1 11) MOSFET No. 4.N o , = 5.0 x 10" cm-'.

2 -1 -I wp(Cm V 5 1

A

5-

-

200

5-

100

-

5-

-@,IrnV)

OF

0

~

.

~ 5

.

.

. . -600

~

'

"

'

~

~

~

- 500

'

"

"

' 5

'

'

'

"

-600

"

i

'

~ 5

'

/

.

-700

.

>

,

I

5

FIG. 35. Experimental mobility behavior vs surface potential for p-channel (1 11) MOSFET No. 5. N,, = 2.61 x 10" cm-'.

257

MOSFET OPERATING IN WEAK INVERSION

-2.2

-2.6

-2.4

-2.8

-3.0

-3.2

-3.4

-3.6

FIG.36. Measured and calculated In&,) - V, curves at different drain voltages for p channel (111) MOSFET No. 6 which has a wet-grown oxide and N o , = 1.93 x 10" cm-'. Experiment (-); Pao-Sah (~ -). - -

shown in Fig. 37. The level of constant mobility is the same for the three curves; in strong inversion the mobility is slightly smaller at higher drain voltages. E. Sensitivity of the Low-Field Mobility to Fabrication-Process Parameters

The weak-inversion characteristic and the low-field mobility derived from it, provide a good monitor for process control in device fabrication. It gives not only a measure for the inhomogeneity of the interface as discussed

258

t

P A U L A. MULS ET AL. 2 pp(Crn

-I -I

'

3 1 2 OF 0

I I j I I/ A ,

,

,

,

,

,

,

,

,

,

,

,

.

,

*(: ~

,

, , ,

,

, , ,

,

-Os I m V 1 ,

,

,

,

,

, ,

-

FIG.37. Experimental mobility behavior vs surface potential for p-channel (1 11) MOFFET No. 6 which has a wet-grown oxide and N o , = 1.93 x 10" ern-'. The parameter in this figure is the value of the drain voltage at which the current measurements have been done V, = - 100 mV (---); from which the mobility has been derived. V, = - 6 mV (-); v, = - 1 v (----).

before, but it also discloses faults or irregularities in the process itself. A striking illustration of the latter is given by Fig. 38, which depicts the ln(ID)- V, characteristic of an n( 111) transistor on which a phosphorus ion implantation at 100 keV has been performed. A deficiency of the implantation machine caused an inhomogeneous distribution of the dose over the wafer. This is reflected by the weak-inversion characteristic, which does not behave linearly, but on the contrary consists of different segments, as if a number of elementary transistors with different threshold voltages and doping densities had been put in parallel to form one big transistor. As can be seen in Fig. 38, the values of N , , found with the ID - V, technique d o not agree with the value coming out of the Simonne ac conductance method, and moreover they show a peak. This also is an indication of the abnormal current behavior of the transistor. The weak-inversion characteristic thus clearly enables the detection of an important irregularity in the fabrication process. A greater control may lead to sharper turn on, lower leakage, or closer threshold tolerances, especially important for low-voltagenear-threshold complementary MOS applications.

259

MOSFET OPERATING IN WEAK INVERSION

I

lo

10 PA.

1 PA-

100nA-

1OnA.

1 nA.

100 p A _

-

/

10 P A -

I PA-

0.1 pA

/

1

/

I

5.0

L8

1.6

5.2

5.1

5.6

5.8

6.0

6.2

FIG.38. The possibilities given by the weak-inversion region for quality control of the fabrication process. The phosphorus ion implantation on this p-channel (111) transistor with = 1.70 x 1015 ~ m - area ~ , = 5.18 x cm2, L = 216 pm, and W / L= 1.11, is nonuniformly distributed due to a machine deficiency. This is reflected by the In(1,) - V, characteristic for V, = - 100 mV, and by the N,, values resulting from I, - V, measurements.

t , = 1130 A, N,,,,,

F . Discussion The preceding experimental results about the MOSFET mobility in function of the average surface potential enable a quantitative test of the fluctuation theory of Brews presented in Section IV,B. To that end, ~, we ~.~ first calculate . ~ ~~~-~ - the ~ .~~~ bebaviof . of .<& .vs-.Ni,,-with-the "

~~

~

~~~

~

~

~

~

~

260

PAUL A. MULS ET AL.

aid of Eqs. (87) and (88). We take for p the value of the maximal measured mobility. Then, from the Eqs. (85) and (86) follows the behavior of the cutoff parameter 1. Figure 39 shows (0,')and 1as a function of Ninvfor MOSFET No. 4 and for MOSFET No. 5. As expected, the transistor with the largest interface charge density N , also gives the largest value for (0,').When the minority-carrier density becomes too small to properly screen any longer, (a,') reaches a maximum and becomes independent of Ninv. The general form of the experimental (a:) - Ninvcurve agrees with the form of the theoretical curve of Fig. 28, but it strikes immediately that the experimental (0,')decreases much faster than theoretically predicted when a A value of 100 8, is assumed. From 10" carriers/cm2 on, (a:) starts to drop, and at 10" carriers/cm2, its value is already two decades smaller. This means that the fluctuations of the interface charge are very effectively

N,nV(~m-21

FIG.39. Experimental results for MOSFET No. 4 and for MOSFET N o 5

MOSFET OPERATING IN WEAK INVERSION

26 1

screened by the inversion charge carriers, which is also reflected in a A value of 10oO A. The peculiar behavior of I close to strong inversion is probably an artifact of the experimental analysis. For MOSFET No. 6, a lower 1 value (about 350 A) is found as can be seen in Fig. 40. In this figure the results from mobility measurements at three different drain voltages have been brought together, and one can clearly notice that the value and the general behavior of 1,following from formula (85), is only little influenced by the drain voltage used. Neither the size of 1,nor its behavior as a function of Ninvcan physically be explained by the theory of Brews. Values ranging from 350 A to 10oO A exclude the interpretation for I as the average distance of the inversion layer carriers from the surface. Formula (85) for (of), which is based on several

FIG.40. Experimental results for MOSFET No. 6. The parameter is again the value of the drain voltage at which the current measurements have been done from which the mobility has been derived. V, = - 6 mV (-- -); V, = - 100 mV (---); V, = - 1 V (----).

262

P A U L A. MULS ET AL.

approximations and simplifications, is clearly too crude to enable a quantitative description of the fluctuations of the carrier density. Brews already suggested some explanations. Possibly the fluctuations are too large (too large N o x )for the perturbation theory completely to hold, possibly the interface charge is not Poisson-distributed at the surface. Also, Brews (1975) mentioned that I will exceed z,, if the charge is distributed into the oxide, because I measures the mean separation of the charge from mobile carriers. The microscopic mobility influences, such as ion scattering at low carrier densities, must also play a role in a quantitative analysis, and the adaptation of the theory to surface roughness or dopant-ion induced carrier-density fluctuations is mandatory. In any way it should be better, as underlined by Brews, to avoid the use of the cutoff parameter I , and to account for the shape of the inversion layer more accurately with a more accurate evaluation of various integrals. The theory could further be improved by including the bias dependence of interface charge due to surface states, and by taking into account the influence of the application of a drain voltage on the distribution of the carrier density in the channel. Another explanation might be that the average distance of the minority carriers from the surface is smaller than the minimal wavelength of the interface charge variations on our samples. I then takes the value of this minimum wavelength.

G. Conclusion The dc conductance mobility of MOS transistors has been examined. Great care has been taken in the determination of the different parameters of the transistor, so that unambiguously the behavior of the mobility in function of the surface potential could be derived from a comparison of the experimental I , - V, curve with the corresponding theoretical curve. The decreasing mobility behavior and the constant low level in weak inversion have been explained qualitatively with the theory of Brews about the minority-carrier-density fluctuations induced by interface charge nonuniformities. V. GENERAL CONCLUSION

In this chapter, we described an investigation of the physical properties of the interface between silicon and silicon dioxide in metal-isolatorsemiconductor transistors, and of their influence on the channel current of a MOS transistor, particularly in weak inversion. The channel current consequently is several orders of magnitude smaller than in the normal operating region, and is thus easily influenced by nonuniformities in the vicinity of the interface.

MOSFET OPERATING IN WEAK INVERSION

263

In order to be able to derive the properties of the interface from the measured weak-inversion current, one has to calculate the theoretical current flowing through the corresponding ideal transistor. To that end, it is necessary to characterize the experimental transistor as accurately as possible. This is done by means of three-terminal capacitance measurements that yield the channel length and the capacitances between the different parts of the MOS transistor. It is also required to dispose of a current model that accurately takes account of all parameters. Starting from the one-dimensional current model of Pao and Sah, a computer program has been developed that is capable of calculating the drain current in a transistor with an arbitrary impurity doping profile. The influence on the current characteristics of doping density changes by ion implantation or by redistribution at the surface, has been traced. The change of the charge at the interface, by the gradual occupancy of the surface states at changing surface potential, has been taken into account by demonstrating that the Hall-Shockley-Read statistics for the occupancy of the surface states mostly reduce to the simple rule that all surface states below the quasi-Fermi level of the minority carriers are occupied by an electron, and that all states above are unoccupied. For transistors with constant impurity density, a simplified analytical version of this current model has been derived, which is well suited to be built in, in existing computer-aided design programs. Charges dispersed in the oxide and at the interface give rise to a nonuniform surface potential in the MOS device. Proper account has to be taken of these potential fluctuations, because they can lead to wrong interpretations of the experimental results for surface states, and because they have an important influence on the weak-inversion current. About the distribution of this charge, two hypotheses exist (Muls et al., 1977): The charge is Poissondistributed at the interface (random model), or else the interface can be divided into patches with a uniform charge distribution (patchwork model). Both charge distributions have their own model for the potential fluctuations and their own equivalent circuit for the MOS device, which however coincide for small-amplitude long-wavelength charge fluctuations. The patchwork model turns out to hold only for charge fluctuations with long wavelengths but arbitrary amplitudes, while the random model is only valid for small-amplitude but arbitrary-wavelength fluctuations. Interpretations with both models, of ac conductance (= surface-state loss) measurements on MOS capacitors in depletion, display little difference as to the resulting values of surface state density and standard deviation of the potential fluctuations. However, capture cross-section estimates depend strongly upon which model is used. Although the experiments point to the random model, more extensive conductance measurements at different gate bias values

264

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should have to be done in order to irrefutably establish how the interface charge is distributed. The random model is based on a cutoff parameter A. defined by Brews as the minimal wavelength of the interface charge fluctuations. A lot of uncertainty still exists, especially about this minimal wavelength, as the values of A coming out of the experiments are strongly divergent, and sometimes even unrealistic (Declerck et al., 1974). The surface state density on a MOS transistor can be measured using the ac conductance technique as elaborated by Simonne, whereby the influence of the potential fluctuations is taken into account according to the random model. The surface potential does not have to be known, nor the impurity density, which also does not have to be constant. However, a conductance curve still has to be measured. Therefore, a new method has been developed to determine the surface state density. This method is based on the measurement of the MOSFET channel current in function of the drain voltage in weak inversion, and is applicable to transistors coming from a common production series. This technique is simple and suffers little from surface potential fluctuations. Here also, the knowledge of the surface potential and of the impurity doping level is not required; nor has the doping level to be constant with depth in the semiconductor. The method is based on the fact that the occupancy of the surface states changes from source to drain, due to the application of a voltage at the drain. The charge density at the interface therefore is dependent on the position in the channel. In this way, the inversion charge in the channel and consequently also the channel current, become dependent on the surface state density. The weak-inversion interval inside which the method can be applied has clearly been defined, and it has been proved that the detected surface states are energetically localized at the height of the Fermi level of the majority carriers. It works out that an interval can be scanned, going at room temperature from 250 meV till 100 meV above the middle of the forbidden gap. The experiments demonstrate that the agreement between the surface state density measured with this weak-inversion method, and the density obtained with the ac conductance technique is excellent, and that the weak-inversion method possesses a sensitivity and an accuracy better than 1 x 10'' V-' cmP2. The nonuniformities in the oxide and at the interface not only bring about potential fluctuations, but also cause fluctuations of the minoritycarrier density in the inversion channel, whereby the weak-inversion current is changed. Experiments yield a drain current that in weak inversion is always smaller than the theoretically predicted current. From this. a carrier mobility can be derived that decreases with weakening inversion or diminishing minority-carrier density, and finally levels off at a constant low value at very weak inversion. This phenomenon can well be described qualitatively

MOSFET OPERATING IN WEAK INVERSION

265

by the fluctuation-theory of Brews, which is based on the random model for the interface charge distribution. At low carrier densities, carrier-density fluctuations have their maximum value, being limited in size only by a screening effect of the gate and of the majority carriers at the edge of the depletion layer. Hence the MOSFET mobility is low. As the minority-carrier density increases, the inversion-layer screening starts, reducing carrier-density fluctuations. Hence the MOSFET mobility increases. For carrier densities above a certain limit, fluctuations are negligible, and the observed mobility behavior is truly a scattering effect. Quantitatively the simple analytical expression derived by Brews for the variance of the fluctuations, is able to describe the experiments provided a cutoff parameter A is introduced. This parameter can be related to the average distance of minority carriers from the interface or to the wavelength of the oxide charge fluctuations.

REFERENCES Bateman, I. M., and Magowan, J. A. (1970). Electron. Lett. 6, No. 21, 669. Berglund, C. N. (1966). IEEE Trans. Electron. Devices 4 - 1 3 . 701. Brews, J. R. (1972). J. Appl. Phys. 43, 2306. Brews, J. R. (1975). J. Appl. Phys. 46, 2181 and 2193. Castagne, R., and Vapaille, A. (1970). Electron. Lett. 6, No. 22, 691. Chen, J. T. C., and Muller, R. S. (1974). J . Appl. Phys. 45, 828. Cobbold, R. S. C. (1967). “Theory and Applications of Field-Effect Transistors.” Wiley, New York. Cooper, J. A., Jr., and Schwartz, R. J. (1974). Solid-State Electron. 17, 641. Declerck, G., Van Overstraeten, R., and Broux, G. (1973). Solid-State Electron. 16, 1451. Declerck, G., Van Overstraeten. R., and Broux, G. (1974). J. Appl. Phys. 45, 2593. Dennard, R. H., Gaensslen, F. H., Yu, H. N., Rideout, V. L., Bassous, E., and Leblanc, A. R. (1974). IEEE J . Solid-State Circuits 9, No. 5, 256. Fang, F. F., and Fowler, A. B. (1968). Phys. Rev. 169, 619. Gray, P. V., and Brown, D. M. (1966). Appl. Phys. Lett. 8, 31. Gummel, H. K. (1964). IEEE Trans. Electron. Devices 4-11, 455. Guzev, A. A,, Kurishev. G. L., and Sinitsa, S. P. (1971). Sou. Phys.-Semicond. (Engl. Transl.)4, No. 8, 1245. Guzev, A. A., Kurishev, G. L., and Sinitsa, S. P. (1972). Phys. Status Solidi A 14, 41. Hall, R. N. (1952). Phys. Reu. 87, 387. Kuhn, M. (1970). Solid-State Electron. 13, 873. Margalit, S.. Neugroschel, A,, and Bar-Lev, A. (1972). IEEE Trans. Electron. Deoices ed-19,861. Muls, P. A., Declerck, G. J., and Van Overstraeten, R. J. (1977). Solid-State Electron. 20, 911. Murphy, N. St. J., Berz, F., and Flinn, I. (1969). Solid-State Electron. 12, 775. Nicollian, E. H., and Goetzberger, A. (1967). Bell Sysr. Tech. J . 46, 1055. Pao, H. C., and Sah, C. T. (1966). Solid-state Electron. 9, 927. Shockley, W., and Read, W. T., Jr. (1952). Phys. Rev. 87, 835. Simonne, J. J. (1973). Solid-State Electron. 16, 121. Stern, F. (1972). Phys. Reu. B 5 , 4891. Swanson. R. M., and Meindl, J. D. (1972). IEEE J. Solid-State Circuits 7, No. 2, 146.

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Terman, L. M. (1962). Solid-state Electron. 5. 285. van Gelder, W., and Nicollian, E. H. (1971). J . Electrochem. Soc. 118, 138. Van Overstraeten, R. J., Declerck, G., and Broux, G. L. (1973). IEEE Trans. Electrou. Devices 4-20, 1154. Van Overstraeten, R. J., Declerck, G. J., and Muls, P. A. (1975). IEEE Trans. Electron Devices 4-22, 282. Verjans, J. R., and Van Overstraeten, R. J. (1975). IEEE Trans. Electron. Devices ed-22, 862. Ziegler, K., and Klausrnann, E. (1975). Appl. Phys. Lett. 26, 400.

ADVANCES IN ELECTRONICS A N D ELECTRON PHYSICS, VOL. 41

Modeling of the Transient Response of an MIS Capacitor T. W. COLLINS, J. N. CHURCHILL,* F. E. HOLMSTROM,? AND A. MOSCHWITZERS General Products Diuision International Business Machines Corporation San Jose, California

I. Introduction.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11. Dynamic Equations.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111. Simplest-Case Example ......................................... ransient for MIS Structure. IV. Computer Simulation: A. General System Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Initial and Final Conditions . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Flatband to Inversion-No Traps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Equilibration Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. SRH Generation Recombination Centers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. Inversion to Flatband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VI. Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Example 1: Comparison of Depletion Layers in p-n Junctions and MIS Devices B. Example 2: Generation Rate for Holes and Electrons in the Depletion Region C. Example 3: Zerbst Plot ......... ....... D. Example 4: Transition between Low- and High-Frequency Behavior . . . . . . . . . . . E. Example 5 : Capacitance Relaxation Method . . . . . . . . . . . . . . . . . . . . F. Example 6: Current-Time Product Method . . .. . . . . . . . . . . . . . , . . VII. Conclusion . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . List of Symbols ........ , , ......, _ , . _ _ _ _ _ ._. _ ._ _ _. _. _. . . _. _ . _ _ _ ._. ._......... . . ..... References . . . _ _ _. ._. ._ _ _. ..... _ . .. . ... .. .. ....... . . .... ........ .. .... ....... ..... ......... .

261 270 214 219 279 28 1 282 286 291 305 313 317 317 3 19 320 322

325 326 328

I. INTRODUCTION

The transient response of MIS devices has continued to be a subject of considerable importance over a period of many years. The main reason for this is that the switching transients provide a quick and convenient way to obtain information needed for device design, device testing, and process control. * Present address: Dept. of Electrical Engineering, University of California, Davis, California 95616. t Present address: Dept. of Physics. San Jose State University. San Jose. California 95192. $ Present address: Technische Universitat Dresden. Dresden, G.D.R. 267 Copyright 0 1978 by Academic Press, Inc. All rights of reproduction in any form reserved. ISBN 012-014647-9

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One of the main objectives of switching transient measurements is to determine the bulk recombination lifetime and surface recombination velocity at the insulator-semiconductor interface. This measurement is usually performed by pulsing the MIS capacitor from accumulation to inversion. In this process the device sweeps through its nonequilibrium depletion capacitance mode and then relaxes to its final inversion capacitance mode. The utility of this technique arises from the fact that the relatively long response time of the device (milliseconds to seconds) is a magnification of the short carrier recombination times (nanoseconds to microseconds) and, therefore, a transient measurement of the time-dependent capacitance C(t) provides information pertaining to these very short time constants. A typical plot of C ( t )is shown in Fig. 1. C’COX

r

time (sec) FIG. 1. Typical pulsed MOS capacitance vs time. From accumulation to inversion

It is the movement of the depletion width W that enables the calculation of the time-dependent capacitance C(t).Assuming that the high-frequency semiconductor capacitance can be approximated by

the normalized total capacitance can be written as

The problem then is to derive a differential equation that describes the dynamics of W as a function of time. Several authors have studied this problem. Early authors ( I - 4 ) based their analyses on the theory of generation in the depletion region of a

TRANSIENT RESPONSE OF AN MIS CAPACITOR

269

reverse-biased p-n junction under steady-state conditions (5). The expression for the generation rate of carriers in the depletion region is given in Sah et al. ( 5 ) as

(31

G = nJ25

where 5 is assumed to be constant. Using (3), these authors derived a spatially averaged continuity equation for the surface inversion layer charge as a function of time only. Zerbst (1) added another form of generation, namely, surface generation. His interpretation was that one component of the charge build-up at the surface was due to the emission of carriers from the surface. This gives a final form of the charge equation as d Q , = q S n , + -Pi (Wdt z

w,)

(4)

where ni is also used for the available carrier density associated with the surface generation velocity S. In terms of capacitance, (4) becomes

and from this, a Zerbst plot (to be discussed later) is obtained. z is calculated from the slope of the curve and S is obtained from the intercept. Thus under this interpretation, both z and S can be obtained independently. [It is to be noted that (4) is not valid for t ---t 00.1 Sah and Fu (6,7) extended the early work and formulated more exact general expressions for the large signal case for both the applied step and ramp gate potentials. These expressions included the spatial dependence of carrier densities and recombination centers for the various phases of the transient response. However, their approximate closed-form solutions neglect the bulk diffusion current and assume d N , / d t = 0, N , 6 N A ,n = p = 0, and a generation rate of n,/r throughout the depletion region for the time in question. The numerical analysis presented in Sections IV and V relies on no such assumptions and extends the work of Sah and Fu to include the effects of the thin substrate. The common element in all of these various approaches to the MIS switching transient is the assumption that the net-generation rate for carriers in the depletion region is inversely proportional to the minority carrier lifetime z. This assumption, in turn, is based on the Shockley-Read-Hall (SRH) theory of carrier recombination (8,9). Actually, the SRH theory is not truly valid in the transient case since the derivation of minority carrier lifetime is based upon steady-state conditions.

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However, the SRH theory has often been used in transient analysis in spite of this fact. For this reason, we should expect to see some errors appear whenever the transient response of a semiconductor device is analyzed from the viewpoint of the minority carrier lifetime. It is important, therefore, to examine the transient response of various semiconductor devices carefully, in order to determine what degree of error is introduced when the steadystate theory of carrier lifetime is applied to nonsteady-state situations. We will explore this problem more thoroughly by considering two examples. First, consider a " simplest case" involving the special situation (10)where all the carrier concentrations are uniform and where there is only an infinitesimal deviation from steady-state conditions. This case is very useful because the solutions may be obtained in closed form. Hence, the dependence of relaxation time-constants upon the various system parameters may be easily explored. As seen, even in this extremely simple case, the approach to steady state does not occur according to a simple SRH lifetime but involves two or more time constants. In general, these time constants depend upon the steady-state concentrations of mobile carriers and other parameters as well as the concentration of recombination centers. Next, for the main example, we will consider the flatband to inversion switching transient of an actual MIS capacitor. The results of an exact one-dimensional computer simulation (11,12) of this system will be presented. These results will be compared with the results predicted by various approximations relying upon the steady-state theory of the SRH lifetime. As will be shown, there are substantial differences between transient responses for the exact model and the responses predicted by the steady-state theory. In particular, the results will show that, for donor-type recombination tenters in p-type material, the minority carrier generation rate in the depletion region during almost the entire transient is negligible and is not equal to n,/z as is commonly assumed (1-4). The dynamic equations that describe carrier motion and trapping by recombination centers will be presented in Section 11. The special-case example of uniform concentration and near-steady-state conditions will be considered in Section 111. In Section IV, we present the special interface constraints and initial conditions that describe the configuration of an MIS capacitor. The results of the actual computer simulation will be presented in Section V and the implications will be discussed in Section VI. 11. DYNAMIC EQUATIONS

We will assume that a uniform concentration N , of single-energy trapping centers exists throughout the semiconductor material and that these traps can be either charged negative, positive, or neutral, with concentra-

TRANSIENT RESPONSE OF AN MIS CAPACITOR

27 1

tions N - , N + , and N o . respectively. We will, further assume that at any given position x the values of these three concentrations can change only through the eight basic processes of electron and hole capture and/or emission defined in Fig. 2. Thus, although carriers in the conduction and/or valence bands are subject to drift and diffusion, the trapped holes and/or electrons are not. We will also allow for hole and electron generation at rates G, and G, , respectively, due, for example, to possible photogeneration, carrier injection, impact ionization, etc. Each of the transitions indicated in Fig. 2 involves electron states in either the conduction band (C), a trapping center (T), or the valence band (V). In each case, an electron initially in some state Si undergoes a transition to a final state S , . We will assume that the transition rates are proportional to both the number of electrons occupying the initial states and the number of empty states available in the category S , . We will also assume that, for process number j , as defined in Fig. 2, the proportionality constant is

kj = u,h(Tj

(6)

where 0 t h is the thermal velocity and aj is the effective cross-sectional area associated with the transition j . The resulting transition rates are listed in Fig. 2 [more detailed derivations of these transition rates may be found in Blakemore (10) and Moll (13)]. For transitions into the conduction band (i.e,, processes 3 and 4), we must use the efectioe number of empty states n, (14). Similarly, for the valence band (processes 7 and S), we use the effective number of valence band states p , (14). In the case of processes 1,2, 5, and 6, factors oj are the “capture” cross sections, whereas in processes 3, 4, 7, and 8, they are the “emission” cross sections. It is possible to obtain expressions for the emission cross sections in terms of the fundamental system constants by considering the special case where the system is in equilibrium [see Eqs. (33) and (34) in Section 1111. In general, the emission cross section depends upon nature of the traps as well as the location of the trap energy level relative to the valence and conduction band edges (15). Under transient conditions, it is not generally possible to define a Fermi level. Because of this, the dynamical behavior of holes, electrons, and traps in the semiconductor cannot be described by Fermi-Dirac statistics, but must be described by the continuity equations for holes and electrons, the net recombination rate equations for holes and electrons, and the rate equations for positive, negative, and neutral traps. The complete model must also include Poisson’s equation as well as the conservation equation for the total trap concentration. In addition, various auxiliary equations are needed. Appropriate boundary conditions must also be specified at the interfaces for each given device geometry.

Process Number 1

Condition Before Transition

c T

I

Condition After Transition

p

Process Description electron capture by positively charged trap

0

v2

s'i

electron capture by neutral trap

v3

cT

-+ 1

electron emission from negatively charged trap

v4

electron emission from neutral trap

T-

v5

c-

hole capture by negatively charged trap

TT V

6

0

c-

hole capture by neutral trap

T 0 I V

7

c-

hole emission from positively charged trap

TT V

8

c-

hole emission from neutral trap

T-r v-

FIG.2. Eight basic processes for carrier capture and emission through intermediate centers C , T , and V represent the conduction band, trap level, and valence band, respectively. The arrows indicate the direction of electron emission.

TRANSIENT RESPONSE OF AN MIS CAPACITOR

273

The dynamic equations for the model are as follows: Continuity of electrons

Continuity of holes 8P

-=

at

DpV2p - ppV ( p R ) - Up + G, '

Net recombination of electrons U , = k,nN+

+ k2nNo

-

k 3 n l N - - k,n, N o

(9)

Net recombination of holes

Up = k 5 p N -

+ k6pNo -

k7P1

N'

- k,plNo

(10)

Rate of equation for positively charged traps aN+ at

-- - - k , n N +

+ k,nl

No

+ k,pNo

- k,pl N +

(11)

Rate equation for negatively charged traps aNat

-- - k 2 n N o - k , n , N -

-

k5pN-

+ k,p1 N o

Poisson's equation

v2

I$=

p

-~ =

-q(p

-

n

+N, -N, +N+ -N-)

E

F

(13)

Conservation of traps N,

=

N+

+ N - + No

Electric field 8 = -V&

Equations (7) and (8) are the usual time-dependent continuity equations for electrons and holes, respectively, and they are coupled together through the self-consistent field ti, which is obtained from the solution of Poisson's equation, (13) by means of Eq. (15). Equations (9) and (10) are expressions for the net recombination (i.e., capture minus emission) of electrons and holes, respectively, through the recombination centers. They are coupled directly into the continuity equations through the terms U , and U p .

274

T. W.

COLLINS ET AL.

Equations (11) and (12) are the time-dependent rate equations for the positively and negatively charged recombination centers, respectively. It was not necessary to include a rate equation for N o since, due to Eq. (14), N o can be written in terms of N + and N - and, hence, is a dependent variable. Equation (14) constitutes a statement of the conservation of trapping tenters. Equations (11) and (12) are coupled together through Eq. (14). They are also coupled to the continuity equations in an implicit manner through the variables n and p. For purposes of generality, we have included the possibility that the recombination centers could be charged either positive, negative, or neutral. Usually, however, either donor- or acceptor-type traps will be assumed. In this case k,, k , , k , ,and k , hold for the donor-type states and k , ,k , , k , ,and k , hold for acceptor-type states. Equations (7k(15) form the “core” of the model. For a given device geometry, the model is made complete by also specifying the appropriate spatial and temporal boundary conditions. An example of this, using the switching transient for an MIS capacitor, will be presented in Section IV. 111. SIMPLEST-CASE EXAMPLE Before presenting the complete computer simulation of a flatband-toinversion transient for an actual MIS structure, we will find it instructive to examine a very simple special case which leads to a closed-form solution. This “simplest-case” example is not only useful in its own right, but will provide useful insight into several aspects of the complete MIS switching transient as well. Specifically, we will consider the special case of p-type material where the concentrations n, p , N’, and N o are all assumed to be uniform throughout the entire semiconductor and where the initial conditions correspond to only an infinitesimally small deviation from quiescent or steady-state conditions. For simplicity, we will consider only donor-type traps (i.e., k , = k , = k , = k , = N - = 0). A situation such as this, involving uniform concentrations everywhere might arise, for example, in a uniformly illuminated photoconductor. For the assumed case of uniform concentrations, all spatial variation in Eqs. (7)-( 15) will vanish. Furthermore, under nearly steady-state conditions, we may make the substitutions:

TRANSIENT RESPONSE OF AN MIS CAPACITOR

275

where the subscripts ss denote steady-state values, the carets denote incremental values, and where we have used Eq. (14) and its derivative to eliminate the unnecessary (i.e., dependent) variables N:s and fi0 from Eq. (19). By adding Eqs. (7), (8), and ( l l ) , we find that ((?/'at)(p

+ N + - n ) = G,

We see from Eq. (20) that if G,

=

- G,

(20)

G,, then

(21)

jj+fi+=fi

and

+ N:

+ No

(22) where No is a constant. Thus, if charge neutrality is established in the system at some initial time, then charge neutrality will be preserved for all time and N o will be equal to the concentration of negatively charged acceptor ions Pss

=4

s

NA.

When Eqs. (16)-(22) are applied, Eqs. (7), (8), and (1 1) split up into a set of steady-state equations and a set of incremental equations. By means of Eq. (21), we can show that whenever G, = G, = G, then Eq. (11) will be linearly dependent upon Eqs. (7) and (8) and Eq. (11) can be ignored. If we assume that G is constant and if we discard second-order products in the incremental variables, then Eqs. (7) and (8) yield the following results. Steady-state 0=G

+ k4n1 N ,

-

(k, nss + k,n,)N:

(231

=

- k6pssNT

+ ( k 6 p s s + k7pl)NL

(24)

Incremental

azjat = nz

(25)

where 0 is a matrix with elements Wii

=

-[ki(nss

+ N s s )+ h n i l

+ k4n1 O 2 1 = k 6 p s s + k7P1 W22 = -[k6(pss + NT

(27)

w12 =

and where

(26) (28)

-

N:)

+ k7PlI

(29)

276

T. W. COLLINS ET AL.

From Eqs. (23) and (24), we obtain

Equation (31) gives the quiescent value of positively charged recombination centers for any constant value of G. By evaluating the equation for the special case where G = 0, and where the system is in equilibrium, we can obtain some important information concerning the physical permissible values of o4 and 0 7 . Under equilibrium conditions, we have nss = no and pss = p o , where no and po are the equilibrium electron and hole densities. Furthermore, according to Fermi-Dirac statistics, N L must also satisfy the equation N:=NT-N:s=N -NT 1 exp[(E, - E,)/kT]

+

By comparing Eqs. (31) and (32) for the case G = 0, we see that the emission cross sections o4 and o7 of these donor-type traps are subject to the physical constraints ( I 5 ) : C4

E,)/kTl

(33)

06(pO/P1) exp[-(E~ - Ef)/kTl

(34)

= a,(no/n,) exp[(E,

g7 =

-

Since o4 and c7 are constants, these expressions will also be valid in the general case where there is drift and diffusion and/or the system is very far away from its quiescent state. Next, we turn our attention to the incremental concentration ii and p, whose time dependence is given by Eq. (25). If U is the unitary matrix that diagonalizes R, and if we define

then Eq. (25) reduces to the two independent equations

aw, /at = w+ aw_/at= 0-wwhere w + and w - are the two eigenvalues of R and where

(36) (37)

TRANSIENT RESPONSE OF A N MIS CAPACITOR

277

Equations (36) and (37) have solutions of the form W+ = A , exp( - t / z + )

(39)

W_ = A - exp(-t/z_) where A , and A _ are integration constants and where z * = - ( 0-+-) l If U f = U - ' , then from Eq. (35), we obtain the important result: ii = A , U:, exp(-t/z+)

8 =A ,

U:, exp(-t/z+)

+ A - U:, + A - U:,

(40) (41)

exp(-t/z-)

(42)

exp(-t/z-)

(431

Equations (42) and (43) give the instantaneous values of A and i, provided the two integration constants A + and A - are known. In principle, these constants could be determined from the initial concentrations h(0) and @(O), at a time t = 0. These equations, together with Eqs. (21) and (14),show that each one of the variables n, p , N + , and N o relaxes toward its quiescent value according to a linear superposition of not one but two exponential functions of time (16). This is in contrast to the relaxation behavior that is often erroneously assumed to proceed according to a single lifetime zSRH, which, in general, would not be equal to either - l / o - or - l/o+. It should be noted that the form of these results came about from our assumption of nearly steady-state conditions. For a larger deviation from quiescent conditions, the time dependence of charge components could not be described by means of simple time constants at all. There are several very important conclusions that can be drawn from the results shown in Eqs. (38), (42),and (43). For example, since the steady-state conditions depend upon the value of G , we see from Eqs. (26)-(29) and Eq. (38) that the pair of time constants that describe the relaxation toward steady-state will be different for the case where the external generation G is turned off than for the case where G is turned on. Although this conclusion was actually derived under small-signal conditions, we shall see that this same type of behavior is also observed for the complete flatband-toinversion switching transient. It is informative to evaluate the two time constants in terms of the system parameters. For simplicity, we will assume that k , = k, = k , = k7 = k. From Eq. (31), for p-type material, we have N $ z N , so that the matrix elements of IL given in Eqs. (26)-(29) become 0 1 1 % -k(nss NT + t I l ) % -kNT (444

+

= k ( n s s + n1) 0 2 1 = k(P,, + P I ) w22 = -k(P*s + P 1 ) 0 1 2

kn,

(Mb)

= kPss

(MC)

= -kPs*

W d)

%

278

T. W. COLLINS ET AL.

When these values are substituted into Eq. (38), then the expression for w + simplifies to

Therefore, if we assume that n , /N, 6 1, then we obtain

The dependence of these two time constants on the unitless quantity ps,/NT is shown in Fig. 3. The figure shows that, when p,, 6 NT,the system relaxes toward its quiescent state with the dominant Shockley-Read-Hall time constant 7SRH.However, when p,, $ N, , the dominant relaxation takes place at a much slower rate that is different from z ~ ~ ~ . It should be emphasized that the quiescent hole concentration p,, depends upon the value of G. Thus, whenever p,, > NT, the dominant time constant will depend upon the actual value of G. This situation would occur, for example, if the acceptor concentration were much greater than the trap concentration or if a very intense beam of light were incident upon the semiconductor sample. For the case where p,, NT , one should be able to

-

1000

100 10

1

0.1

0.01

NT / pss

FIG.3. Dependence of trapping centers.

7,

and

T-

on relative concentrations of steady-state holes and

TRANSIENT RESPONSE OF A N MIS CAPACITOR

279

observe two distinct time constants as the carrier concentrations approach their final steady-state values.

Iv.

COMPUTER SIMULATION : FLATBAND TO INVERSION TRANSIENT FOR MIS STRUCTURE

For the computer simulation, an ideal MIS structure (17) will be assumed. Although both n- or p-type structures with either donor, acceptor, or mixed types of SRH centers can be modeled, the bulk of the analysis will center around the p-type structure of Fig. 4. Semiconductor Metal I I

-- I

--

---

FIG.4. MIS system treated in the computer simulation.

A . General System Characteristics

In order to carry out the simulation, we must make certain assumptions as to the general characteristics of the system. These assumptions are as follows : (a) The substrate is p-type with a uniformly distributed acceptor density N A ,assumed to be fully ionized for all applied potentials. (b) Donor-type trapping centers, lying at the intrinsic level E , , are distributed uniformly throughout the entire semiconductor body. (c) The oxide is a perfect insulator. No current is allowed to flow through the oxide except for Maxwell's displacement current

J~ = a D / a t = E a q a t

(47)

280

T. W. COLLINS ET AL.

(d) The electron and the hole currents in the semiconductor must vanish at the oxide-semiconductor interface due to the repulsive forces associated with the high potential barrier between these materials. For the purpose of the computer simulation, this condition was modeled by specifying that the net current due to drift plus diffusion must vanish at the point x = Wox. Thus, we write

where subscripts s denote values at the specific grid points corresponding to the semiconductor surface located at x = W,, . The derivatives are calculated using standard difference formulations and Q, is the electric field at the surface. (e) At the Si/SiO, interface, the surface concentration of charges pFmust satisfy the equation

(f) The work function difference between the semiconductor and the metal gate will be ignored. (This effect would produce a linear shift in the flatband voltage but would not affect the transient physics of the device.) (g) In the real MIS structure, the substrate material is normally much thicker than the oxide and, to a first approximation, it can be assumed to be infinitely thick. Since, for practical reasons, it is almost impossible to numerically model such a thick substrate, a thin substrate was used instead. Care was taken so that the substrate thickness was large enough not to interfere with the physics of the surface and depletion region or to overshadow the general behavior of the device. The differences introduced by using a thin substrate will be pointed out in the discussion and results. The actual simulation model, then, reflects more closely a physical MIS structure consisting of a thin-film silicon MIS capacitor. The main difference lies in the value of the bulk spreading resistance. Also, the diffusion of minority carriers from the back contact will be more pronounced in this case. (h) At the bulk contact, it is assumed that 4 = 0, n = n b , and p = p b . (i) It is assumed in this specific example that the gate voltage & ( t ) will be a unit step function of time chosen so as t o drive the device from its initial flatband state to a final quiescent state in inversion. (j) A list of values used for various parameters appearing in the equations that constitute the model is given in Table I. This list of characteristics describes the general properties of the system that was simulated. Next, we must also consider the initial and final conditions.

TRANSIENT RESPONSE OF AN MIS CAPACITOR

28 1

TABLE 1

PHYSICAL PARAMETERS USEDIN SIMULATION Parameter

Symbol

Value

loi5 cm-3 900 A 1000 cm’iv-sec 400 cmz/V-sec 25.9 crnz/sec 10.7 crn2/sec 300°K 0.5-1.0 x l o i 5 cm-3 3.9 11.7 1.5-2.0 pn 1.0 x 1 0 - l ~cm2

Bulk doping (p type) Oxide thickness Electron mobility Hole mobility Electron diffusion coefficient Hole diffusion coefficient Temperature Trap doping Relative oxide permittivity Relative silicon permittivity Substrate thickness Capture cross section of traps

B. Initial and Final Conditions If we assume charge neutrality in the bulk, then whenever a flatband condition exists, the charge (source) term in Poisson’s equation can be written in the form p = q [ p b - nb

+ N,,

-

NA+ N +

-

N-]

=0

Under inversion and accumulation conditions, it is reasonable to assume that normal dopant ions whose energies lie very close to the conduction and valence bands are completely ionized at room temperatures. Only under heavy accumulation would we have to consider the occupation statistics of these shallow dopants. Therefore, in the source term, the quantity (ND- N A ) represents the net ionized doping density, and this will be assumed to be loOo/, ionized. On the other hand, the occupation of the deep centers under quiescent conditions depends upon the relative separation between the trap energy and the Fermi level. This energy separation will vary throughout the device whenever an external gate bias potential is applied. For example, traps whose energies lie close to the intrinsic level will have a much different occupation near the surface than in the bulk. For initial flatband conditions, it is assumed that the device is in steadystate thermodynamic equilibrium, and that (51) holds. Applying FermiDirac statistics for a given set of energy levels, the resulting nonlinear equation can be solved by graphical techniques (18), and occupancy of each

282

T. W. COLLINS ET AL.

donor and acceptor level, as well as the resultant Fermi level, can be obtained. Next we look at the final steady-state condition (i.e., inversion) near the surface. Using donor-type traps as a model, the steady-state conditions can be obtained from the rate equation for donor type traps by setting Eq. (11) equal to zero and using Eq. (14), giving N + z N,nl/n, and N; z N, (52) Substituting these values into Eqs. (9) and (10) and using n1 p1 = n f gives U , = Up = 0, which is consistent with the equilibrium Fermi-Dirac statistics. Therefore, for both the initial and final conditions, the surface charge neutrality and net recombination conditions have been reconciled. V. RESULTS

The results obtained by computer simulation of the MIS capacitor model described in Sections I1 and IV are shown in Figs. 5-54. [For the details of the numerical techniques, see Collins (12).] Figure 5 shows the pulse response of carriers at the surface for short

:

I

'

-14

-12

-10

-8

log t (sec)

FIG. 5. Surface electrons and holes vs time for both n-type and p-type substrates, flatband to depletion. W, = 180 A; V, = *0.5 V ; N , = 10''

TRANSIENT RESPONSE OF AN MIS CAPACITOR

283

times for both n- and p-type substrates (doxfor this run was 180 A). Notice the quick response of the majority carriers that are the decreasing functions and relatively slow linear rise of the minority carriers. The majority carriers sweep out in a time that is on the order of the dielectric relaxation time (tdr). The minority carriers on the other hand rise at almost a linear function of time as if being supplied by a constant current source. (This effective current source is considered under Example 3 in Section VI.) The slow rate of rise is controlled by the maximum current that can be supplied by the bulk, which in turn is established by the low equilibrium density of the minority carriers in the bulk and by generation centers in the depletion region. The difference in rate of rise between n, and p , is approximately a factor of 2.5, which is nearly the ratio of the electron mobility to hole mobility. The experiment was repeated for a device pulsed into accumulation. Again a similar response occurred except that the role of the carriers is reversed as seen in Fig. 6. Here, the majority carrier is increasing at a linear time rate while the minority carrier decreases at a rapid rate. Therefore, no matter what carrier is involved, the increasing one rises at a linear rate dictated by the amount of current the substrate can supply, and the decreasing one can respond as fast as the diffusion and drift characteristics will allow. Increasing the applied potential so that the device is pulsed completely

10-14

10-13

10-12

lo-ll

lo-10

time

FIG.6. Surface electrons and holes vs time for p-type substrate, flatband to accumulation. W, = 200 A, N, = lOI5 ~ m - and ~ , u = -0.5 V.

284

T. W. COLLINS ET AL.

into inversion reveals three distinct regions: the dielectric relaxation time, the depletion time, and the equilibration time. This is shown in Fig. 7 for the complete response from flatband to deep inversion. (The figure is for W,, = 900 8, and N , = 10’’ c m - j in a p-type substrate that will be used for the remainder of the plots.) Also shown in the figure is the response of the surface potential 4,.

I

Y)

P

-s c

m

-

log t (set)

N,

FIG.7. ns, p s , and 4, vs time, flatband to inversion. V = 1.5 V (no traps); W,,= 900 loL5~ m - ~ .

A;

=

For the applied potential of 1.5 V, the initial value for $, is about 1.25 V as computed from the pure dielectric properties of the oxide and semiconductor. During the initial relaxation time, the majority carriers deplete, building up the depleted space charge region. The surface potential 4, falls to a value that is equal to the value 4/28 N , W h ,where W, is the width of the depletion region. At this point, both n and p are small values and the continuity equations are virtually decoupled from Poisson’s equation. Therefore, during the depletion time, 4sremains relatively constant and is only a function of the physical constants of the device and the applied potential. As the electrons at the surface build up to a value that is comparable to the doping density N , and start to create an inversion layer, Poisson’s equation is again coupled to n, , and 4, begins to react and decrease further.

TRANSIENT RESPONSE OF A N MIS CAPACITOR

285

This occurs during the equilibration time when the device is approaching steady state. As n, approaches steady state, the holes that were '' overdepleted " increase until the product n . p = n: at steady-state equilibrium. This overreaction of the majority carriers occurs only if the device is pulsed far enough into heavy inversion. The final value of 4sis mainly determined by the steady-state value of the depletion width W, . Notice the wide disparity in response times between the different time regions. The initial response time for p , was in the order of 10-'2-10-9 sec while the response of n, was in the order of 10-3-100 sec. The response of the surface electron density n, is plotted in Fig. 8 for several values of applied voltage for long times. Again, all curves are linear functions of time during the rise time with rates that are a function of the applied potential. The equilibration times (90%)for all curves are approximately the same.

ld

/ =

1.0

v

= 0.9v

log t (see)

FIG.8. Minority carriers at surface vs time for several applied potentials. Step response

During the depletion time, the surface potential 4, should be directly proportional to the applied potential V, . To verify this, 4, was plotted as a function of V, , shown in Fig. 9. Indeed, +s is a linear function of V, during the nonequilibrium depletion time. The equivalent circuit during this time is simply the oxide capacitance in series with the nonequilibrium depletion

286

T. W. COLLINS ET AL.

l.*

t L

0;

0.4

0.8

1

1.2

I

1 .E

V G (volts)

FIG.9. Nonequilibrium surface potential & during depletion and steady state modes vs VG

'

layer capacitance, which acts as a simple voltage divider network. As the inversion layer builds up when the device approaches steady state, ds is diminished and ceases to be a linear function of V, . This is also shown in the figure. A . Flatband to Inversion-No

Traps

Figures 10-23 show the response of the important variables as a function of distance in the device with time as a parameter. The time spans a wide range, sweeping through all three time regons from to lo4 sec. Each curve represents an order-of-magnitude increase in time. The bulk traps were excluded (i.e., N , = 0) so that the time increments could be increased far in excess of the recombination times z in order to obtain solutions for long times with reasonable computer run times. Also, without the traps, the natural responses of the electrons and holes can be uniquely observed. Figure 10 displays n(x) for the different times indicated. n(x) starts at its flatband uniform distribution of no 2 n ? / N , and builds up to its deep inversion distribution at t 1 sec. As the electrons are drawn toward the surface at x = 0, the electrons farther in the material decrease in value to set up a gradient to support the diffusion component of the electron current. As time progresses, the electrons pile up at the surface because of the insulator boundary, and eventually come to their equilibrium distribution with the total electron current equal to zero. The transient response for the holes is shown in Fig. 11. Here, the transient depletion width is greater than the steady-state depletion width. In this

-

TRANSIENT RESPONSE OF A N MIS CAPACITOR

20! 16

-

0

1

lncreaslng time Each curve represents an order of magnltude of time from t = 1 0 - l ~sec to t = 10+4 sec

1

-

FIG.10. Log n ( x ) vs x with time as a parameter. Transient: flatband to inversion.

+

*OI

FIG.11. Log p ( x ) vs x with time as a parameter. Transient: flatband to inversion.

287

288

T. W. COLLINS ET AL.

case, p(x) starts out at its FB condition of p(x) ‘v N , & .As time evolves, the holes are swept away from the surface and at t = lo-’ sec, they come to a quasistationary distribution during the depletion time. At approximately t= sec, the hole current reverses and drives the holes, this time toward the surface. This occurs during the equilibration time. They finally come to their equilibrium distribution at the same time the electrons do at about t = 1 sec. This overdepleting and reversal of the holes is the mechanism that dictates the width of the depletion layer and controls the value of the transient MIS capacitance. If the applied potential is not large enough to cause the device to go into deep inversion, this overreaction of the hole density does not occur. This transient effect can also be seen if we plot the total semiconductor charge as a function of space and time. This is shown in Fig. 12. The nonequilibrium depletion region quickly builds up to a width of about 1.15 pm in about lop9sec. At this point, the total charge is almost totally depletion charge, and it remains this way throughout the depletion time. At about lo-’ sec, the inversion charge starts to become significant, and the device starts to equilibriate. As the electron inversion charge further

il

2.0

f

d

FIG. 12. Normalized semiconductor charge density Q , , ( x ) / 4 parameter. Transient: flatband t o inversion.

N , vs x with time as a

289

TRANSIENT RESPONSE OF AN MIS CAPACITOR

log t (sec)

FIG.13. Semiconductor charge vs time. Transient: flatband t o inversion. charge; Q, = electron charge; Q, = hole charge; QT = Q, + Q,.

QT

= total

increases, the depletion width moves in toward the surface to its equilibrium position at about lo+' sec. During this time, both the hole and electron current flow toward the surface, decreasing with time until equilibrium is established. In Fig. 13, the integrated charge in the semiconductor is shown as a function of time. Also shown are the integrated electron and hole charge describing the action of both during the equilibrium time. Note that as Qn builds up, Q, diminishes (W, decreases) to come in line with the equilibrium condition of the gate potential. This action of the hole charge can be better understood by monitoring the incremental change in hole density 6 p as a function of time. This has been plotted in Fig. 14 with 6 p being normalized to N , . During the dielectric relaxation time, the depletion region builds up and 6 p is negative and

-0.8

4

FIG.14. Normalized incremental change in hole density S p ( x ) / N , vs x with time as a parameter. Transient: flatband t o inversion.

290

T. W. COLLINS ET AL.

I01

100

n )

FIG. 15. Normalized incremental change in charge density bQ(.x)/q. N , vs T with time as a parameter. Transient: flatband t o inversion.

moves away from the surface, which means that the holes are being removed from the semiconductor. When the depletion region comes to its nonequilibrium static position at the start of depletion time, 6 p diminishes to zero. As equilibrium time is approached, the hole current becomes nonzero again and increases in the reverse direction. Thus, Sp increases this time in the positive direction and the hole packet moves toward the surface, first increasing and then again decreasing to zero when equilibrium is established. This change in sign and direction of 6 p does not change the sign of SQ, however, because during this time, the Sn component of SQ is the dominant term, and it does not change sign. 6Q is plotted in Fig. 15, and we can plainly see the component due to 6 p and an. It is also interesting to plot the electron-hole density product for the transient case being described here. This was done in Fig. 16, which shows the n-p product throughout the semiconductor from time zero to steady state. At time zero, n ( x ) p ( x )= nz throughout the device as expected siiice we are starting at the flatband equilibrium condition. As time progreses, the holes deplete and, hence, n-p decreases to a very small value throughout the depletion region. This low value is maintained all during depletion time. As the device approaches equilibrium, both ~ ( xand ) p ( x ) increase in value until equilibrium is established and again n ( x ) p ( x )= nt throughout the entire device (even in the depletion and inverse regions).' This must be so, since the device involves a perfect insulator. Steady state means thermodynamic equilibrium with n p = n f . This provides an excellent check of the numerical accuracy for initial and final values and for establishing a numerical definition of steady state.

TRANSIENT RESPONSE OF AN MIS CAPACITOR

29 1

1.6

1.4..

FIG.16. Normalized electron-hole product n ( x ) p(x)/n: vs x with time as a parameter. Transient: flatband to inversion.

The response during the equilibration time is complicated, involving very tight coupling between the time-dependent electron and hole densities and Poisson's equation. In other words, the transient MIS capacitance response cannot be modeled by looking just at the equilibration of the minority carriers (electrons in this case), but rather we must deal with both n and p and preferably the n p product. The potential distribution Cp(x)is plotted in Fig. 17 for both the semiconductor and the oxide. As previously discussed, at time zero, both the semiconductor and the oxide are considered dielectric and the initial surface potential Cps can be given as

where Liis the thickness of the silicon. Therefore, at t = O', 4sstarts out at the value given by Eq. (53). At this point, all the charge is on the gate and body electrodes since n and p have not had enough time to change from the initial FB condition. As the depletion charge builds up, $(x) changes from its straight line

292

T. W. COLLINS ET AL. oxide

FIG. 17. Potential distribution 4(x)vs .x with time as a parameter. Transient: flatband to inversion.

distribution in the semiconductor with 4sdecreasing in value to its depletion mode value of

where WD,N E is the nonequilibrium depletion width. Again, the potential distribution remains at these values for all of the depletion time and then further decreases to its equilibrium value at steady state. A somewhat different initial condition for the potential is used in Elschner et al. (19, 20). In this alternate approach the current is assumed to be limited by the series resistance R, after the voltage supply is turned on, otherwise the voltage step would give an infinite displacement current at t = 0. But shortly after the voltage step is applied ( z lo-'' sec, depending on the amount of series resistance R, of the semiconductor bulk), the solution for the potential distribution and all other results are the same as under the initial condition described above.

TRANSIENT RESPONSE OF AN MIS CAPACITOR

293

From the potential distribution, we can obtain the distribution for the electric field &(x), which is plotted in Fig. 18. In conjunction with the description of the $(x), at t = O', &(x) is uniform both in the oxide and in the semiconductor, consistent with the difference in dielectric constants of the two materials. As time evolves, the field distribution in the oxide acquires a negative slope as the charge builds up in the

8.ox'ide

semiconductor

FIG.18. Electric field &(I)vs x with time as a parameter. Transient: flatband to inversion.

semiconductor and the field in the oxide increases. The distribution settles down to its depletion value with a straight line slope of - ~ N , / E ,in~ the semiconductor during the depletion time. As the inversion charge builds, &(x) increases in the oxide and in the semiconductor inversion region near the surface. In the rest of the semiconductor, &(x) decreases from its depletion value while keeping the slope -qNA/Esi over a good part of the depletion region. The field in the oxide almost doubles in value during the equilibration period for this specific case. During this transient condition, nonequilibrium currents flow to supply the electrons and holes to their final distributions in the semiconductor and to supply the necessary neutralizing charge to the gate electrode. Obviously, the total current must be the displacement current flowing through the

294

T. W. COLLINS ET AL.

oxide. But this same total current in the semiconductor is partially displacement current and partially electron and hole conduction currents, the latter of which vanishes at the semiconductor-insulator interface. Maxwell’s displacement current (JD= dD/dt) is shown in Fig. 19 for the entire device, i.e., oxide and semiconductor. It has a high value for very short times and decreases rapidly to very small values within the dielectric relaxation time. Note that its distribution is maximum and uniform in the oxide and decreases and even changes sign in the semiconductor. The zero crossing begins at the interface and moves into the semiconductor as time evolves. JDis nonzero but very small for longer times and cannot be seen on this plot. (Remember, if there is a net electron or hole conduction current in the semiconductor, there must be displacement current flowing in the oxide.) SiO2

Si

.

N

-0.2 -O”!

.i

‘ ’ l

k l

FIG. 19. Displacement current J & ) inversion.

vs x with time as a parameter. Transient: flatband to

The hole conduction current plotted in Fig. 20 follows the same rapid decrease as J , . Its response is practically completed during the initial relaxation time also. This is the hole current that depletes the bulk of holes so as to build up the depleted region. (Positive hole particle current as drawn flows away from the surface.) Again, at the end of the dielectric relaxation time, J , is very small compared to its initial values and increases only slightly in the opposite direction during the equilibration time as previously discussed. The electron current density J , ( x ) is plotted in Fig. 21. (Positive electron particle current flows toward the surface.) Note that the significant values of J , are much smaller than the values of J , because of the smaller density of

TRANSIENT RESPONSE OF AN MIS CAPACITOR

0.6.-

-

f-

. E,

N

.'

295

10-l~

fro-12

a

--5

0.4

1

-a X

..

-I

0.2.-

0.4

1.2

0.8 x

(Wm)

FIG.20. Hole inversion.

0.4

* 10-l~

-c x

.

7

10-10

0.1.-

J n : 37 namp/cmz

,o.9

f 0

1o -

v

.

0.4

:

'

-to~ 1 o . sec ~ :

'

0.8

:

1.2

x (Wm)

FIG.21. Electron current density J , ( x ) vs x with time as a parameter. Transient: flatband to inversion.

296

T. W. COLLINS ET AL.

electrons in the bulk compared to the holes. As was expected in both Figs. 20 and 21, J, and J, vanish at the surface. J , seems to follow the same pattern as J,, starting at its high values and decreasing as time increases. When the depletion time is reached, J,, settles down to a uniform distribution in the bulk whose value is determined by the applied potential and bulk characteristics to be discussed in Section VI. This is the constant electron current that supplies the electron inversion charge at a linear rate. As the device reaches steady state, J,(x)decreases from its depletion time value to its steady-state value of zero. As the inversion charges build up, J , goes to zero near the surface first, and then this zero point moves farther into the bulk as time progresses. From this, we can conclude that steady state is reached at the surface first and then the steady-state point travels inward until the whole bulk is at equilibrium. If we monitor J , at the back contact and plot it as a function of time (Fig. 22), again the three distinct time regions are clearly shown.

4001

i

O -12

-8

-4

0

+4

log t (sec)

FIG.22. Bulk electron current density J , ( r ) vs time. Translent: flatband to inversion

It is instructive to decompose J , into its drift component J,, and diffusion component JnD during the depletion time. This has been done in Fig. 23 with the total electron current J , , and the depletion charge QD shown for reference. Notice that in the depletion region J,, is predominantly drift

297

TRANSIENT RESPONSE OF A N MIS CAPACITOR

I 0.4

I I

\ \

\

t =

10-5 sec

c

a 0

E

FIG.23. Minority current densities for transient depletion condition. J , , sion current; J , , = electron drift current; J , , = total electron current = J , ,

=

electron diffu-

+ J",.

current, while in the bulk, JnT is predominantly diffusion current. For thicker substrate devices, it was found that the drift component JnEdecreased to a very small value in the bulk and that the bulk electron current was almost totally diffusion current. Also, from the figure, we can see that JnEand J,,, become very large and have opposite signs near the surface. This large negative diffusion current is caused by the build-up of the inverted electrons near the surface. This back diffusion current eventually becomes equal and opposite to the drift current so that the net current becomes zero at steady state. If the inverted charge can leak off some way (say through a leaky oxide), then this back diffusion current never builds up to a point of being equal and opposite to the drift component. This causes the net total current to remain nonzero and this leakage current keeps supplying the charge that has leaked into the oxide. This is the situation of a steady-state nonequilibrium condition.

B. Equilibration Time Figures 24-3 1 show the same variables previously displayed, except now the time scale is adjusted for a closer look at just the equilibration time. In these figures, the response for t = 0.01 sec is plotted for a reference and then the rest of the curves are plotted for t = 0.1-2.0 sec with At = 0.1 sec. This spanned the time range for this specific device to reach equilibrium from its depletion mode. Since the figures are self-explanatory, no comment will be made except for some specific points.

298

T. W. COLLINS ET AL.

4r

o / * .

.

I

.

<

014

0: 8

,

.

.

1.2

-~-~_

x (pm)

FIG.24. Log n(.x) vs

Y

for equilibration time. t

=

0.01-2.0 sec.

Figure 28 shows how the Q(x) goes into equilibrium from its nonequilibrium distribution. Notice the depletion width W, shifts in a parallel fashion almost linear with time except close to steady state. Also, note that the width of the inverted region increases rapidly at first and then moves slowly for the rest of the time, indicating the width of the inverted region as fairly constant near equilibrium. Figures 30 and 31 show the movement of SQ(x) and S p ( x ) during this 16’

:-

of I 21

/

0-4

-

08 x (P)

--- -

FIG 25 Log p ( x ) vs x for equilibration time t

1 2

-

= 001-20 sec

299

TRANSIENT RESPONSE OF AN MIS CAPACITOR

.time

. c

(v-

I

X

0 81

-?

I

OR

/

/

x

I

c

04

0

FIG.26. n ( x ) . p(x)/nf vs x for equilibration time. t = 0.01-2.0 sec.

time. The packet of 6 p ( x ) can be plainly seen moving in toward the surface and diminishing in time. S Q ( x ) mirrors this action of the holes and the depletion width decreases to its steady-state value while 6n(x) causes the build-up in the inverted charge. Another interesting point can be observed in Fig. 29, where &(x) is SiO2

Si

I

~~

1.2

I E 0.8

t=2.

0.

FIG.27. $(x) vs x for equilibration time. t

= 0.01-2.0

sec.

300

T. W. COLLINS ET AL.

FIG.28. Q ( x ) / q . N , vs x for equilibration time. t

=

0.01-2.0 sec

x bm)

FIG.29. Electnc field 6(x) vs .x for equilibration time. t

= 0.01 -2.0 SKC

301

TRANSIENT RESPONSE OF A N MIS CAPACITOR

-2.01

FIG.30. GQ(x),iq . N , vs x for equilibration time. t = 0.01-2.0 sec. 0.41

c I

direction of mOtlOn of charge packet

FIG.31. 6 p ( x ) / N , vs x for equilibration time. t

= 0.01-2.0

sec.

plotted to show the change in the electric field both in the oxide and in the semiconductor versus time. Note at t = 0.01 sec, 8(x) is still a straight line distribution all the way up to the surface in the semiconductor. As Qinv builds up, W, decreases and €(x) decreases in the depletion region, keeping the same slope except near the surface. Because of Qinv,&(x) near the surface departs from the depletion layer theory and sharply bends upward when Qinv starts to become significant at t = 0.1 sec. Figure 32 shows the integrated electron and hole charge Q, and Q, during this time period. Q, increases linearly at first with an initial slope equal to the bulk electron current J , during the depletion time (see Fig. 22 for a plot of J , versus time. Note the value of J , during the depletion time is 37 nA. This compares with the initial slope of Q, which is 37.2 nC/sec). During the rest of this period, however, both Q, and Q, are nonlinear functions of time-Q, increasing and Q, decreasing in a parabolic fashion. It is also instructive to plot the rise of the n . p product as was done in Fig. 33 for n and p at the surface. Its response is complicated, being the product of both the electron and hole responses at the surface, and is similar to an S-shaped Fermi function. The 900/; point occurs at t = 0.9 sec, which could be defined as the point of equilibrium.

-

-

302

T. W. COLLINS ET AL.

2.0-

Q" QP

0

0.8

0.4

I 1.2

time k e c )

FIG.32. Q n , Q, vs time during equilibration time. The dashed line has a slope of J , = 3.72 x lo-* C/sec.

time k e c )

FIG.33. np/n: vs time at surface during equilibration period

The current at the back contact was again monitored for this time period and plotted against time in Fig. 34. Both J , and J , have two distinct time responses during this period. From t = 0.01 to 0.5 sec, J , and J , decrease at a relatively slow rate, while for t > 0.5 sec, J , and J , decrease at a very rapid rate. This latter period corresponds to the time when the n . p product (Fig. 33) is increasing toward equilibrium. More insight can be obtained if J , and J , are plotted against the excess depletion width (W - W,) as shown in Fig. 35. Both J , and J , have the same general form, which happens to resemble the Zerbst plot (I). When plotted in this fashion, J , exhibits an approximate linear portion that is remarkably similar to the results obtained when -d/dt(C,,/C)' is plotted

TRANSIENT RESPONSE OF A N MIS CAPACITOR

303

time (sec)

FIG.34. J , , lo-* A/cm2.

J,

time during equilibration period. J , , x

vs

A/cm2; J , , x

J

J -

0

0.10

0.20

0.30

(pm)

FIG.35. Bulk J , , J , vs (W, - W,) during equilibration period. J , , x lo-' A/cm2; J , , x lo-* A/cm2.

304

T. W. COLLINS ET AL.

against [C,/C - 13 as in the Zerbst plot. More will be said about this in Section VI. As a summary of the equilibrium period, a composite drawing showing the responses of several important variables during this time is shown in Fig. 36. The time that corresponds to the straight line portion of the Zerbst plot is indicated in the figure. The transient high-frequency MIS capacitance was computed during the execution from FB to inversion and its normalized values are plotted in Fig. 37. Also shown in the figure are measured data from Muller and Schiek

Straight line portion

I of Zerbst plot

t

x

10-1 sec

FIG.36. Composite curves showing the responses of several important variables during the equilibration period. W,. pn; $ ? , V; n , . x lo” p s , x lo4 ~ m - Q~3 <; , x lo-’ C’cm’; 6Q,. x lo-’ C/cmZ; J , . x 10 A/cm2: J , . x l o - * A/cm2.

’

t(sec)

FIG.37. Normalized transient (Muller); B = computed.

capacitance. Flatband to inversion. A = measured

TRANSIENT RESPONSE OF AN MIS CAPACITOR

305

(21). Although the response times are quite different, the shapes of the curves compare favorably. From this plot a Zerbst plot can be generated by plotting -d/dt(l/C(t)’) against [ C m / C ( t )- 11, as was done in Fig. 38. Note that a linear region is obtained, corresponding to the linear region indicated in Fig. 36. The implication of these curves will be discussed in Section VI. 3.0r

0 0

0.20

0.10

0.30

Cm/C-l

FIG.38. Computed Zerbst plot obtained from time-dependent capacitance during flatband to inversion transient. T,,, = 2.4 p e c ; S , = 6.1 cm/sec; T I = 0 0 ; Saclual = 0.

C. SRH Generation Recombination Centers

The foregoing results were obtained for the case where no traps were included. We will now discuss the case where traps are included. The computer data for the inclusion of traps are limited due to the long run times necessary to keep the system stable. However, several key points will be presented here that are pertinent to the subject. Donor-type SRH centers were introduced into the device with the following parameters: Trap density: Energy level: Capture cross section:

NT= 0.5 x 10” (cmP3)uniform E , = Ei = 0.6 (eV) gn = op = 1.0 x lo-’’ (cm’)

For the sake of completeness, both electron and hole processes are included; i.e., capture and emission of electrons and capture and emission of holes. For donor-type traps, Eqs. (9)-( 11) become

U , = k(n . N + - n 1 . N o )

up= k ( p . NO - p 1 . N + )

306

T. W. COLLINS ET AL.

and a N + / d t = Up - U ,

(57)

These equations are included in the integration scheme and solved simultaneously with Eqs. (7), (8), and (13). Note that, for the time-dependent case, a lifetime T cannot be defined because it would be a function of time also. The referenced T used here is the steady-state value of T given as T = (0 . V,, . N T ) - ' (15). As discussed in Section I, all previous transient and small-signal recombination theory is based on the assumption that recombination and generation take place through SRH centers at an energy level E , = Ei (15). Therefore, to test this theory, the exact recombination equations for SRH centers were used instead of analyzing the system using an effective lifetime T with the usual expressions U , = (n - no)/z and Up = ( p - p 0 ) / z . The question then becomes: Do the SRH centers at Ei give an effective lifetime T = (oxhNT)-'during the transient condition, and is there an effective generation rate of n , / z in the depletion region? Figures 39 to 44 show the results obtained when the SRH centers are included. It was possible to obtain data out to t z 10 sec, which is well past the depletion time and long enough to answer the above questions. Figure 39 compares the transient response for the surface electrons and holes for three cases: (1) no traps included, (2) traps included using the exact time-dependent rate equations, and (3) traps included using the quasisteadystate equations. The surprising results show that during the depletion time,

FIG.39. Transient response of surface electrons and holes for (a) steady-state trap equa). (b) no traps (- -), and (c) exact nonsteady-state trap equations (tions (-), -

~~

TRANSIENT RESPONSE OF AN MIS CAPACITOR

307

the response of n, is faster with the steady-state trap approximation and slower with the exact trap expressions than with the case having no traps. The faster response is consistent with generation in the depletion region but slower response of the exact model indicates recombination is dominant during this short time. However, as steady-state time is approached, the response of n, for the exact trap theory increases very rapidly and eventually meets the steadystate theory response curve as it must for these longer times. It is to be noted that as far as the observer is concerned, both the steady-state and the exact trap theories give essentially the same overall rise time for II,.The gross difference occurs during the nonequilibrium depletion time period that makes the presently prevailing interpretation of the MIS transient capacitance measurements questionable. The reason for this discrepancy can be explained by Fig. 40.

log t (sec)

FIG.40. ( + ) charged and

(0)neutral

flatband to inversion. Exact theory: -;

trap densities at the surface vs time. Transient: steady-state theory: - -. ~

~

Here, the response of the SRH centers at the surface are shown as a function of time. Again, the exact theory is compared with the results for the steady-state occupation statistics. Note that the exact response is much slower than the steady-state response, again pointing out that the steadystate theory is very inaccurate during transient conditions. The steady-state distributions of N + and N o for the inverted case are shown in Fig. 41. Note that the cross-over point occurs at x 21 0.25 pm, which is not very far into the depletion region, which is 0.8 pm wide. The corresponding electron and hole net recombinations during the

308

T. W. COLLINS ET AL.

FIG.41. Steady-state distributions of N + and N o trap densities vs x

transient response for the exact and steady-state theories are shown in Fig. 42 and 43, respectively. The exact theory (Fig. 42) shows that, up to a time well within the depletion time ( t 3 = 1.2 x sec), generation of minority carriers throughout the depletion region is not realized; in fact, recombination is the dominant process for electrons near the surface. This gives rise to the slower response shown in Fig. 39 for the exact case. The majority carriers (holes) on the other hand do attain a generation rate of ni/r throughout the depletion region and this rate decreases as time increases. In comparison, Fig. 43 displays the results of the steady-state theory, which does indeed give an equal net generation for both electrons and holes in the depletion region.

recombination 1

generation - 1

'

FIG.42. Exact nonequilibrium electron and hole generation and recombination vs several 5

=

(Vh

different '

u1' Nl)-l.

times.

V, = 1.5 V ;

t , = 0.5 p e c :

f2

= 0.2

msec;

t,

=

Y for 1.2 msec;

309

TRANSIENT RESPONSE OF AN MIS CAPACITOR

FIG. 43. Electron and hole net recombination vs x for several times using the steady-state - ~ approximation. (ni/T = 0.8 x 10" ~ r n sec-I).

Note that the maximum value for the generation rate is ni/2z and it occurs at its widest distribution only over +WD. Since U , and Up must approach zero as the device approaches steady state, the question can be raised: Does U , ever approach the value - n i / z in the depletion region before equilibrium is established? Figure 44 displays the exact solutions for several longer times showing the exact nonequilibrium distributions coming together and approaching the steady-state distribution as time evolves. At t N 20 msec, U , and Uphave approximately the same distributions with a magnitude of ni/2z over a distance of 0.3 pm

-

-

-

Recombination

0.8

-1. 5'

FIG.44. Nonequilibrium electron and hole generation and recombination vs x for several long times. t, = 5 msec; t , = 20 msec; t , = 100 msec.

3 10

T. W. COLLINS ET AL.

consistent with the steady-state theory. Figure 44 clearly shows the transition from nonequilibrium to steady-state conditions. What gives rise to the net recombination of electrons at the surface during the transient is the fact that both n and N + near the surface have similar response times and are changing in opposite directions (i.e., n, is increasing while N + is decreasing). During the transient, the product 11 . N + > n , N o for E , = E iand thus Eq. (9) gives a net recombination. The difference in the quasisteady-state theory lies in the fact that N + is at its equilibrium value during the equilibration time and since n < nss, the product n . N + < n, . N o and thus a net generation is obtained, which gives a completely opposite effect. The effect of the SRH centers on the electron and hole distributions can be obtained by comparing the distributions to the case with no traps included. This was done in Fig. 45, where it is observed that in this case the

FIG.45. Electron and hole density vs

Y

at t

=

1 msec for (a) no traps, (b) with traps

only significant change in density distribution occurs near the surface. For the time given at 1 msec, holes are being generated near the surface while the electrons are being recombined as previously discussed. Notice also the slight generation of electrons in the depletion region, while further into the bulk (.x > 0.8 pm) there is virtually no difference between the two cases for both the electron and hole distributions. More insight into the role of the recombination centers during the transient period can be obtained by monitoring the total electron current and several of its components. This was done in Figs. 46-48.

TRANSIENT RESPONSE OF AN MIS CAPACITOR

311

Figure 46 compares the total bulk electron conduction current J , versus time for the cases with and without traps. The free electron charge current dQ,/dt is also shown for the case with traps. The other component of J , is the electron current that is filling the trap centers with electrons, i.e., Jn

= (dQn/dt) - (dQN + / d t )

It can be seen that for both cases, J , is identical during the depletion time. However, it should be noted that the dQJdt component is practically zero so all of the electron current is involved with filling the empty traps with electrons. Therefore, during the depletion time, J , = -dQ:/dt. After the traps have been filled (mainly the traps near the surface where most of the energy band bending takes place), these recombination centers 400

I

h

log t (sec)

FIG.46. Bulk electron current vs time. Transient: flatband to inversion. No traps: -; with traps:

can start supplying electrons to build up the free electron charge Q,. This large surge of electron current from the generation centers brings the device into equilibrium sooner than in the case without traps. Figure 47 shows a close-up of the response of Q, and the electron current supplying it. Just as J , versus (WD - W,) was plotted in Fig. 35 for the case of no traps, Fig. 48 shows a similar plot for the case with traps included. Here are plotted three currents: J , , dQ,/dt, and J D ,which is the total device current (displacement current in the oxide). Notice all curves exhibit an approximate straight line portion as in the Zerbst plot discussed earlier. However, to

312

T. W. COLLINS ET AL.

time (msec)

FIG.47. Free electron charge and current vs time. Trap centers included

calculate an effective T according to the theory of Zerbst, the slope of the dQ,/dt curve should be used and not the total or electron current curves. Using Eq. (4) and the slope of the d Q , / d t curve in Fig. 48, we obtain T = 2 x 10- sec. However, this constant value is obtained only over a small

’

lwD-w m ) FIG.48. J , , J , . and dQ,/dt vs (W, W,) during the equilibration period. Trap centers included. J , = total displacement current; J n = total bulk electron conduction current; Q, = total free electron change in the semiconductor. ~

TRANSIENT RESPONSE OF AN MIS CAPACITOR

3 13

range of the curve while over other parts of the d Q , / d t curve, the effective T varies considerably. In conclusion, the transient response of the electrons in the presence of traps consists of two distinct sequential events: first, the filling of the empty trap centers with electrons supplied by the bulk leakage current and second, the build-up of the electron inverted charge by the electrons emitted from the generation centers in the depletion region. An estimate of the time required to fill the trap centers can be obtained from the equation

T = QN+/J, (58) where QN+ is the total fixed electron charge residing on the trap sites and J , is the bulk electron leakage current given as J , = qD, n,/L,. From Fig. 41, the distance over which the traps are completely filled is Ax N 0.2 pm. Therefore, we can estimate Q N + as qNT Ax. Also, for this given applied potential we know that J , = 37 nA/cm2. Therefore, calculating T, we have T = qNTA x l J ,

= 40

msec

(59)

which is in good agreement with the computed results. D. Inversion to Flatband

The numerical algorithms were also tested for the case where the device was pulsed from deep inversion back to flatband. The gate voltage was set at +IS V, which brought the device into deep inversion. After the device reached steady state, the gate voltage was switched to 0 V and the ensuing response was observed. Figures 49 and 50 show the potential 4 ( x ) and electric field &(x) as a function of time after the negative-going transient was applied. (Also shown for reference are the initial distributions for t = 0 - . ) Since the charge cannot change instantaneously, both 4(x) and A ( x ) react instantly to conserve the charge distribution in the semiconductor. The surface potential 4s changes to the value &(O+) = - W,, . 8,(0+),where &,(0+) is given by

2

a,(O-)+ AB,

represents the change in the electric field at the surface of the semiconductor due to the change in displacement charge on the gate electrode when the gate potential is changed. Therefore, at t = sec, 4, and 8,assume the values of &(O') and B,(O+), and the transient proceeds from these

314

T. W. COLLINS ET AL.

08

FIG. 49. Potential b(x) vs x with time as a parameter. Transient: inversion to Ratband.

FIG.50. Electric field A ( x )vs x with time as a parameter. Transient: inversion to flatband.

315

TRANSIENT RESPONSE OF AN MIS CAPACITOR

0 - 1 . . .

x (Lvnl ~

:

.

:

.

:

;

:

;

:

I

values. Notice the parallel movement of &(x) in the depletion region. The entire &(x) distribution decreases in a parallel fashion, causing the field in the bulk to cross zero and become negative. Both +(x) and &(x) change sec. rapidly with the field disappearing at t N Figures 51 and 52 illustrate the responses of n ( x ) and p ( x ) , respectively. p(x) assumes its equilibrium distribution in virtually the same time as the electric field &(x), which can be considered the dielectric relaxation time as previously mentioned for the transient from FB to inversion.

16-

FIG.52. Log p ( x ) vs x with time as a parameter. Transient: inversion to flatband.

3 16

T. W. COLLINS ET AL.

The electrons, on the other hand, respond in quite a different fashion. During the initial relaxation time, n ( x ) changes from its original inverted distribution to an almost uniform distribution throughout the device. n ( x ) near the surface is rapidly dispersed throughout the device by the large diffusion component near the surface and by the field-aided diffusion in the rest of the device where the electric field G(x) is negative (Fig. 50) aiding the diffusion of electrons away from the surface. After the field becomes zero, the almost uniform distribution of n(x) decreases by two mechanisms : diffusion into the bulk toward the back contact, and through recombination processes in the device. These mechanisms are slower than the initial field-aided dispersion of carriers and thus the response tails off with a longer time constant. Figure 53 shows the response n, p , N', and N o at the surface. Note the relatively fast response of the traps N + and N o during this transient from

8 .

6 4

23

00

0.5

1.0

1.5

2.0

2.5

time (nsecl

FIG.53. ti, a, N ' , N o vs time at the surface. Transient: inversion to flatband

inversion to FB as compared to their relatively slow response (see Fig. 40) during the transient from FB to inversion. This points out the fact that the response of the traps is strongly dependent on the initial conditions of the electrons, holes and the charged traps N + themselves. For these large signal cases, we cannot quote a fixed time constant for the response of the occupancy of the SRH centers. This would also hold for surface states. That is, for the large signal transient cases, a single energy level trap will exhibit a variety of effective time constants depending on the nature of the initial conditions of occupancy of the trap states. In a final view of this transient, Fig. 54 displays the normalized semiconductor charge density for several times during the transient. The distribution decays very rapidly and in a complicated manner.

TRANSIENT RESPONSE OF A N MIS CAPACITOR

317

FIG.54. Charge density Q , , ( x ) / q N , vs x with time as a parameter. Transient: inversion to flatband.

VI. EXAMPLES In this section, we will consider a number of special situations and compare the results of the full model presented here with the results that have previously been obtained using various simplifying techniques suggested in the literature. A . Example 1 : Comparison of Depletion Layers in p-n Junctions

and M I S Devices

MIS capacitance measurements are usually performed under smallsignal steady-state conditions. In order to analyze this measurement, the carrier generation rate from Shockley-Read-Hall (SRH) centers in the depletion region of an MIS device must be known. Sah ( 5 ) developed a theory for the generation of carriers in a depleted p-n junction. This theory was later applied to transient analysis of MIS devices (1-4). Starting with the rate equation for the concentration N + , expanding the concentrations around their steady-state values, and retaining only first-order terms, the

318

T. W. COLLINS ET AL.

linearized differential equation obtained is

+ k , n , + k6pss+ k 7 p l ) N t N 2 f i + k6Nys@

w l d t = -(kln,, -kl

(61)

For the reverse-biased p-n junction at low frequencies, the coefficients for the h and p terms are frequently assumed to be much smaller than that of the N + term (22). (Actually, since N : + N:, = N , , at least one of these two coefficients must always be rather large and, hence, this assumption may not be completely valid.) When these two terms are ignored, Eq. (61) becomes

-N+/z

(62)

+ k 4 n l + k6ps3 + k 7 p 1 ) p 1

(63)

dN+@

=

where =

(klnss

In the depleted region of the p-n junction, n,, ,pss2: 0 and z can be approximated as z

N

(k,n,

+ k7p1)-'

(64)

We now wish to obtain a numerical estimate for this lifetime. Comparison of Eqs. (31) and (32) for the case G = 0 shows that, for trap centers located at the midpoint between the valence and conduction bands, we have k4nl = k , no and k 7 p , = k 6 p 0 . If we assume that the depletion region of a p-n junction is similar to an intrinsic semiconductor, then the equilibrium concentration of holes and electrons in this region will be given by po , no N n , . Therefore, using 0, = 0 6 = lo-'' cm2 and u,,, = 10' cm/sec, we obtain the value z N lo-' sec. Although the foregoing analysis actually applied to carrier dynamics in a reverse-biased p-n junction, the results have nevertheless been applied to the case of transients in MIS devices (1-4). The calculated time constant of l o p 2sec appears to agree very well with the experimentally observed transition between low- and high-frequency behavior in small-signal, steady-state measurements of MIS capacitance (see Fig. 55). In order to apply the above explanation to the case of MIS devices, however, it was necessary to assume that the depletion region of a reverse-biased p-n junction is identical to the depletion region of an MIS capacitor. Actually, under steady-state conditions, the two depletion regions are not at all the same. The p-n junction depletion region, for example, is in a nonequilibrium condition such that n s s , p,, 2r 0 as assumed in the theory while under steady-state conditions, the MIS device is in thermal equilibrium and the condition nss . pss= n f must be satisfied throughout the semiconductor. (This can be readily verified by inspection of the simulation results shown in Figs. 16 and 26.) Thus, for MIS

TRANSIENT RESPONSE OF AN MIS CAPACITOR

0.5 -20

-10

0

10

3 19

20

Voltage, VG

FIG.55. The effect of measurement frequency on the capacitance-voltage characteristic of MOS structures.

devices, either nss or p,, (or both) must be at least as large as n i .We conclude, therefore, (1) that it is incorrect to attempt to use the p-n junction theory for the case of the MIS device, and (2) that the apparent agreement between the observed experimental results and the incorrectly applied theory of p-n junction may be entirely coincidental. A more accurate explanation for the observed transition frequency will be discussed under Example 4.

B. Example 2 : Generation Rate for Holes and Electrons in the Depletion Region In Section I, we noted that it is common to assume minority carriers are being generated in the depletion region of an MIS device at a rate ni/7 during the switching transient. However, as inspection of the simulation results in Fig. 42 will show, even though the majority carrier generation does proceed at roughly this rate, the generation rate for minority carriers is actually several orders of magnitude smaller. Thus, it is pairs of holes and neutral traps, rather than trap-electron pairs, which are being created in the depletion region. We conclude, therefore, that the supply of electrons that go to produce the inversion layer cannot be coming from minority carrier generation in the depletion region as is commonly assumed (23). The electrons must be supplied, instead, by diffusion-limited drift from the semiconductor bulk. (See Example 3 for a more complete discussion of this process.) These conclusions are, in fact, supported by the dynamic equations presented in Section 11. For the flatband-to-inversion switching process, the initial concentrations to be used in Eqs. (7) and (8) correspond to the

320

T. W. COLLINS ET AL.

flatband concentrations. Thus, in Eq. (31), we use the initial electron concentration n,,(O) z 0 to obtain

Also, as soon as the depletion region has formed, the concentrations 11 and p will both be very small. Using these initial conditions, then in Eqs. (7) and (8), we obtain the results =

-kln(0)

+ k 4 n l N’(0)

1

(671

z k , p , N + ( O )z 101’/cm3/sec

(68)

k , n , N o ( 0 )2 k , n , N , z lo5 cm3/sec

where we have assumed that no = n f / N , . Both of these approximate rates are in good agreement with the simulation results shown in Fig. 42. We see, therefore, that the model of Sections I1 and IV predicts results in very good agreement with experimental measurements also shows that the commonly assumed value of ni/TSRHfor minority carrier generation in the depletion region of MIS devices is in error by several orders of magnitude. C. Ex-ample 3 : Zerbst Plot

During the equilibration period in the simulation, the electron and hole currents J , and J , were monitored at the back contact and were plotted against the excess depletion width (W - W,), as shown in Fig. 35. Both J , and J , have the same form, which resembles the Zerbst plot shown in Fig. 38. When plotted in this fashion, J , exhibits an approximate linear portion that is precisely what is obtained in the Zerbst plot.’ Using Eq. (2), the transient high-frequency MIS capacitance was

Reviewing the derivation of the Zerbst plot will reveal that it is actually a plot of J , versus (W - W J .

TRANSIENT RESPONSE OF AN MIS CAPACITOR

32 1

computed during the excursion from flatband to inversion and its normalized values were plotted in Fig. 37 (curve B). From this figure, the Zerbst plot in Fig. 38 was generated. Note that a linear region and an intercept are obtained. According to the equation derived by Zerbst ( 1 )the bulk lifetime T can be obtained from the linear slope and the surface generation can be obtained from the intercept. Performing the calculation, the measured values from the computed curve were T , = 2.4 psec and S, = 6.1 cm/sec, when in fact no hulk traps or surface generation centers were included. The existing theory then cannot explain Fig. 38, which is similar to curves obtained from actual measured data even though, in this case, no traps were included in the simulation. In this case, the seemingly linear region is due to the slow decrease in the bulk electron current J , (Fig. 35) as the depletion width decreases due to the dynamics of the tightly coupled electron and hole densities. The nonlinear regions are due to the greater rate of decrease of J , near the beginning and the end of the equilibration period, while W changes almost linearly during most of this period except very close to steady state. Both J , and W approach 0 as t approaches infinity but, from Fig. 35, dJ,/dAW is finite and approaches a constant. It is realized that even in the absence of bulk generation-recombination centers, the thin substrate device will have an eflectiue generation of minority carriers due to the bulk diffusion current that is the dominant charging current in this case. The effective lifetime can be obtained by equating the bulk leakage current to an effective generation qDn,/L 6 q AWni/Teff (691 where, in the thin substrate case, L is the substrate thickness and AW (WD - W,). For A W = 0.4 pm and J , = 37 nA/cm2 (Fig. 32), T , = ~ 6~ psec, which is close to the value of 2.5 psec obtained from the slope of the Zerbst plot (see Fig. 38). The time that corresponds to the straight line portion of the Zerbst plot is indicated in Fig. 36. In the linear portion of the Zerbst plot, J , is decreasing in an almost linear fashion. At the point where the holes at the surface start to increase, there is a sharp break in the slope of J , that gives the definite break in the Zerbst plot. This has been previously interpreted as caused by a surface generation velocity S. Therefore, the fundamental dynamics of the electrons and holes themselves give an appearance of the existence of a surface generation velocity S. A true surface generation current would only aid in bringing the device into equilibrium in a shorter time, i.e., it would increase the effective value of J , during the depletion time. J,

N

322

T. W. COLLINS ET AL.

D. Example 4 : Transition between Low- and High-Frequency Behavior In this example we will use the concept of diffusion-limited drift of minority carriers discussed in Example 3, to estimate the transition between lowand high-frequency behavior in MIS capacitance measurements. To do this, we need to estimate the time required to drift a sufficient quantity of minority carriers across the depletion region to create an inversion layer. If the width of the inversion layer is W,,, , the diffusion-limited current density is J,, , and the concentration of carriers in the inversion layer is n i n v ,then the time required would be At

=Pin,

(70)

WnvlJDL

Using JDL= 37 nA/cm2 (see Example 3), ninv= p b , and Fig. 28), we obtain the characteristic time

wnv= 0.04 pm (see

sec (71) Thus, for frequencies below about 100 Hz, the diffusion-limited drift process is able to transport the minority carriers from the bulk to the semiconductor oxide interface in a time less than the period of one cycle of the applied incremental signal. Under these conditions, the measured capacitance will be equal to the oxide capacitance Cox.However, for frequencies very much greater than 100 Hz, there is not enough time in one cycle to allow very many minority carriers to be transported t o the interface, and, hence, the measured capacitance will be less than Cox.We conclude, therefore, that the transition between low- and high-frequency behavior ought to occur somewhere in the vicinity of 100 Hz. This conclusion is, in fact, supported by experimental measurements ( 2 4 ) as illustrated in Fig. 55. At

‘v

E . E.uample 5 : Capacitance Relaxation Method

Another method using the pulsed MIS capacitor to measure the minority carrier lifetime is described by Jund and Poirier (25). In this method, the minority carrier lifetime is determined from the relaxation time constant z, of the MIS capacitance between deep depletion (Fig. 56, curve 1) and the high-frequency capacitance (Fig. 56, curve 2) after pulsing it from flatband (or accumulation) to inversion. The time dependence of the MIS capacitance is shown in Fig. 57. To calculate the minority carrier lifetime zo from the relaxation time constant z,,it is assumed (25)that the space charge generation is the major effect and the generation rate during the whole transition period is constant at the value U

= nJso

(72)

TRANSIENT RESPONSE OF AN MIS CAPACITOR

323

C

t I

’V

FIG.56. Voltage dependence of MIS capacitance.

With this assumption the relation between

‘s,

and

to is

t, = to ND/ni (73) where NDis the impurity concentration and ni is the intrinsic concentration. On the other hand, we have learned from our numerical results (Sections IV and V) that the assumption of a constant generation rate during the transient period according to Eq. (72) is not true. Furthermore, the net recombination rates for electrons U , and holes Up are not equal and are time dependent as is shown in Figs. 4 2 4 4 . We conclude that it is not generally possible to obtain the minority carrier lifetime using Eq. (73). To verify this conclusion consider numerical calculations using the parameters ND = 1.5 x 10’’ ~ m - ~ ni = , 1.5 x 10” cmP3, N, = 5 x lOI4 ~ m - and ~ , u , ~ (= T loP8cm3 sec-’. The results of these numerical calculations would lead to a conclusion that C ( t ) has a time constant t, = 100 msec, which means, according to Eq. (73), a minority carrier lifetime T~ = 1 psec. On the other hand, the minority carrier lifetime in the stationary SRH formula is

to =

1

-

1 = 0.2 psec 5 x lOI4 x loP8

(74) N,k: which is not the same as calculated by Eq. (73). Therefore, the “lifetime” in Eq. (73) is not truly the lifetime in the stationary SRH formula for recombination-generation. It should be noted here as in Example 1 that when using this method one can obtain aJinite value T~ even in the case where the SRH lifetime is infinite. ~

FIG.57. Relaxation of MIS capacitance after pulsing from accumulation to inversion (deep depletion).

324

T. W. COLLINS ET AL.

F . Example 6 : Current-Time Product Method

Another method, using the pulsed MIS capacitor for measuring trap parameters at the surface of semiconductors, was recently described by Simmons and Wei (26). They use the ( J t )versus t plot calculated from the time varying current of the MIS capacitor after pulsing it from flatband (or accumulation) toward inversion. A typical ( J t ) versus t plot is shown in Fig. 58. From the maximum (Jt),,, they obtain the single level trap density N , from the expression (Jt)max

= qNT/e

(75)

and the energy level E , of the trap from the equation E, - E,

=kT

(76)

h(ut,QnNctrnax)

To verify this simple analytical approach, we have done some numerical calculations at low gate voltages V, . For example, consider a semiconductor with midgap terms ( E , - E , = 0.55 eV). The surface state density is 1.3 x 10'' cm-2, the bulk density of traps is N , = 5 x 1014 ~ m - and ~ ,uthcrnN , = 5 x 10" sec- '. The deep depletion layer thickness is of the order 1 pm (see Fig. 42). So the effective density of bulk traps per unit area is 5 x 10" cm-', which is smaller than the surface state density. For our example, we obtain from Eqs. (75) and (76), t,,, = 3.4 x sec and (Jt),,, = 7.7 x A cmP2 sec. From numerical calculation of ( J t )versus t , we get for the same example t,,, = 2.4 x lo-' sec and (Jt),,, = 7.1 x loP9A cm-' sec which, by using Eqs. (75) and (76), leads to E , - E , = 0.54 (instead of 0.55 eV) and N , = 1.2 x 10" cm-' (instead of 1.3 x 10" cm-'). Thus, we appear to have very good agreement between the simplified analytical method and the results from our simulation. However, the numerically calculated values (Jt),,, and t,,, increase with increasing values of applied voltage V,. This in turn [see Eqs. (75) and (76)] implies that N , and E T must

__2 S

10-1

-t

FIG.58. Current-time product of a pulsed MIS capacitor

TRANSIENT RESPONSE OF AN MIS CAPACITOR

325

vary with V, for a given semiconductor sample. This cannot be true. Therefore, further computer runs are underway to investigate the exact relationship between ( J t )versus t and the values of N, versus ET. Once again, as in the Zerbst plot (Example 3) and the Jund-Poirier method (Example 5), we find that there will be a finite (Jt),,, and t,,, even for the case of a semiconductor totally free of surface and bulk traps. Using Eqs. (75) and (76), this implies the existence of a nonzero " surface state density " NT and an " energy level" E , even when no such physical quantities are meaningful.

VII. CONCLUSION The transient response of an MOS capacitor has been analyzed in depth. Numerical techniques were used to obtain self-consistent solutions for the system of equations that describe the dynamics of the electrons, holes, traps, and the electrostatic potential throughout the MOS device. For practical reasons, a finite thick substrate was used that was thinner than that used in an actual device. This was found to be relatively unimportant if the substrate was made thicker than the depletion region and if the effective lifetime of the traps was made shorter than the effective lifetime associated with the bulk thermal leakage current. The exact trap rate equations were introduced into the transient model to synthesize results that were already established in the literature and that were based on approximate steady-state models. The results indicated that the existing theory was inadequate and approximated the exact solution only near the end of the transient. Several key results were obtained and will be discussed below. Existing theory stated that during the entire transient, minority carriers were supplied by the traps acting as generation centers throughout the depletion region. A little reflection on the situation will reveal that this can not be the case. Referring to the energy band diagram before the transient begins, reveals that the deep traps near the intrinsic energy level are well above the Fermi level for the p-type substrate and therefore are depleted of electrons (minority carriers). They cannot possibly supply electrons to the surface until they themselves receive electrons supplied from the back contact. This argument holds for both donor- and acceptor-type traps with n- or p-type substrates. (With an n-type substrate, holes are the minority carriers and the deep traps are below the Fermi level and depleted of holes.) The results of the exact model also reveal that the transient response of electrons with traps present consists of two distinct sequential events. First, during the depletion time, the trap centers are filled with electrons being supplied by the bulk electron current. Also, during this time, the dominant mechanism in the depletion region is the generation of majority carriers and

326

T. W. COLLINS ET AL.

that the generation of minority carriers near the surface is actually suppressed. The value of the electron current during this time is independent of whether traps are present or not and is only a function of the applied voltage and the conduction characteristics of the substrate. Second, due to the overextension of the depletion region during the transient, a number of trap centers near the depletion region that would not normally be filled with electrons, capture electrons in the process. As the device starts to equilibrate, these “overfilled” trap centers emit their electrons and cause a surge of electron current toward the semiconductor surface to create the surface inversion layer. This process brings the device into equilibrium sooner than if no trap centers were present. This creates the two distinct regions of the MOS capacitor transient response-the retention time and the equilibration time. Even during the whole of the equilibration time, the minority carrier generation rate of n i / T is never totally realized in the depletion region. The process is too complicated to be modeled by a single time constant 7. As shown in the results, the generation and recombination rates vary with time and are strongly dependent on the initial conditions of the system. In practical devices, the transient response is complicated by the presence of surface states. Extraneous surface states were not included in this model but deep traps at the surface were. These can be thought of as surface states near the intrinsic level and from the results presented here, minority carrier generation at the surface was never present during the entire transient. This is in direct opposition to the concept of surface generation included in the Zerbst equation.

LISTOF SYMBOLS integration constants (cm-3) semiconductor capacitance per unit area (Ficm’) oxide capacitance per unit area (F/cm2) total capacitance per unit area (F/cm2) steady state total capacitance (F/cm2) diffusion coefficient for electrons and holes. respectively (cm’ sec- ’) displacement vector (Cjcm’) electric field vector (Vicm) electric field at semiconductor surface (Vjcm) steady-state electric field (V/cm) length of energy barrier at Si/SiO, interface (joule) permittivity (F/cm) permittivity of Si and S O , , respectively (F/cm) trap, Fermi, and intrinsic energy levels, respectively (joule)

TRANSIENT RESPONSE OF AN MIS CAPACITOR

energy level of conduction band minimum and valence band maximum, respectively (joule) generation rate for electrons and holes, respectively (cm-' sec-I) carrier generation rate (cm-3 sec-l) electron and hole current densities, respectively (A/cm') Maxwell's displacement current density (A/cm') diffusion-limited current density (A cm-' sec- I ) maximum value of time-current-density product (A sec/cm') product of thermal velocity and capture or emission cross section (cm' sec- I ) thermal energy (joule) silicon thickness electron and hole mobilities, respectively (cm'/V sec) electron and hole concentrations, respectively (cm- ') effective density of states in conduction and valence bands, respectively (cm-') intrinsic carrier concentration (1.4 x 10" cm-') bulk equilibrium electron concentration (cm-') bulk equilibrium hole concentration (cm-') electron and hole surface concentrations, respectively (cm ') concentration of electrons in inversion layer (cm- ') steady state electron and hole concentrations, respectively (cm- ') incremental electron and hole concentrations, respectively (cm--') total concentration of recombination centers (cm-') concentration of positive-, neutral-, and negative-charged recombination centers, respectively (cm-') steady-state concentration of positive-, neutral-, and negative-charged recombination centers, respectively (cm-') incremental concentration of positive-, neutral-, and negative-charged recombination centers, respectively (cm-') donor and acceptor impurity concentrations, respectively (cm- ') concentration of initial donor and acceptor impurities, respectively (cm- ') frequency matrix (sec-l) components of frequency matrix (sec- l ) eigenvalues of frequency matrix (sec- I ) magnitude of electronic charge (1.6 x 10- l9 C) inversion layer charge (Cjcm') semiconductor charge (C/cm') semiconductor surface charge (Cicm') contribution to QsC due to electrons (C/cm') contribution to QsC,dueto holes (C/cm') surface gencration velocity (cmisec) measured surface generation velocity (cmjsec) capture cross sections (cm') emission cross sections (cm') time (sec)

T. W. COLLINS ET AL.

dielectric relaxation time (sec) time for which maximum in Jt occurs (sec) Shockley-Read-Hall lifetime (sec) time constants (sec) measured value of T (sec) effective lifetime (sec) calculated lifetime (sec) relaxation time (sec) unitary transformation matrix, its inverse, and its adjoint, respectively net recombination rate for electrons and holes, respectively (cm-3 sec-l) applied gate t o substrate voltage (V) thermal velocity of carriers in semiconductor (cm/sec) matrix representation of n and p in transformed coordinate system (cm- ') width of depletion layer (cm) nonequilibrium depletion layer width (cm) steady-state width of depletion layer (cm) deviation of depletion layer width from steady-state value (cm) inversion layer width (cm) oxide layer thickness (cm) electrostatic potential (V) electrostatic potential at semiconductor surface (V) electrostatic potential at gate contact (V) semiconductor surface potential (V) distance from metal/SiO, interface (cm) computational grid spacing (cm) matrix representation for incremental electron and hole concentrations

ACKNOWLEDGMENTS The authors wish to express their appreciation to Professor J. Killeen of the Applied Science Department of the University of California (LRL) for his continued guidance and advice during the development of the numerical algorithms, to Mrs. Jean Sherman of the IBM Corporation, San Jose, California for developing the computer plotting routines used in this work. and t o Dr. Noble Johnson of the Xerox Palo Alto Research Center, for his helpful suggestions concerning the format of this paper.

REFERENCES I . M. Zerbst, Z.Angew. Phys. 12, No. 1. 30-33 (1966). 2. E. P. Heiman, I E E E Trans. Electron Deuices 4-14,781-784 (1967). 3. S. R. Hofstein, I E E E Trans. Electron Deuices ed-14,785-786 (1967). 4 . J. Muller and B. Schiek, Solid-state Electron 13, No. 10 1319-1332 (1970) 5 . C. T. Sah, R. N. Noyce, and W. Shockly, Proc. IRE 45, 1228 (1957). 6 . C. T. Sah and H. S . Fu, Phys. Status Solidi A 11, Part I, 297-310 (1972).

TRANSIENT RESPONSE OF AN MIS CAPACITOR

329

7. C. T. Sah and H. S. Fu, Phys. Status Solidi A 14, Part 11, 59-70 (1972). 8. R. N. Hall, Phys. Reo. 87, 387 (1952). 9. W. Shockley and W. T. Read, Phys. Rev. 87, 835 (1952). 20. J. S. Blakemore, “ Semiconductor Statistics,” pp. 250-304. Pergamon, Oxford, 1962. 2 1 . T. W. Collins and J. N. Churchill, I E E E Trans. Electron Devices ED-22, 90-101 (1975). 12. T. W. Collins, Ph.D. Dissertation, University of California, Davis (1973). 13. J. J. Moll, “ Physics of Semiconductors,” Chapter 6. McGraw-Hill, New York, 1964. 24. S. M. Sze, “Physics of Semiconductor Devices,” pp. 26 and 27. Wiley (Interscience), New York, 1969. 15. A. S. Grove, “Physics and Technology of Semiconductor Devices,” pp. 127-136. Wiley, New York, 1967. 26. J. S. Blakemore, “ Semiconductor Statistics,” p. 288. Pergamon, Oxford, 1962. 17. S. M. Sze, “ Physics of Semiconductor Devices,” p. 426. Wiley (Interscience), New York, 1969. 18. W. Shockley, “ Electrons and Holes in Semiconductors.” p. 467. Van Nostrand Reinhold, Princeton, New Jersey, 1950. 19. H. Elschner, A. Moschwitzer, and S. Ritz, Proc. Int. Con$ Electron. Circuits, 2nd. 1976 (1976). 20. K. H. Diener, H. Elschner, M. Krauss, D. Landgrof-Dietz, A. Moschwitzer, and L. Tschernokoscheva, Nachrichtentech.-Elektron.27, 71 (1977). 22. J. Miiller and B. Schiek, Solid-state Electron. 13, 1319-1332 (1970). 22. C. T. Sah and V. G. K. Reddi, IEEE Trans. Electron. Devices E D 1 1 , 345-349 (1964). 23. S. M. Sze, “Physics of Semiconductor Devices,” p. 435. Wiley (Interscience), New York, 1969. 24. A. S. Grove, “Physics and Technology of Semiconductor Devices,” p. 275. Wiley, New York, 1967. 25. C. Jund and R. Poirier, Solid-state Electron. 9, 315 (1966). 26. J. G . Simmons and L. S. Wei, Solid-State Electron. 17, 117 (1974).

This Page Intentionally Left Blank

Author Index Numbers in italics refer to the pages on which the complete references are listed.

A Abbott, D. L. 95, 118 Abraham. M . J., 3, 5, 33, 34, 48 Abramson, N., 120 Adachi, K., 16, 17, 50 Adetunji, J., 26, 48 Almen, O., 13, 17, 18, 48 Altman, L., 118, 119 Altshuler, E. E., 167, 168. 192 Arnbrose, E. J., 47, 48 Anders, R., 144, 192 Andersen, H . H., 17, 48 Anderson, A. P., 185, 187, 188, 192,193 Anderson, G. A., 106, 118, 120 Anderson, G. S., 15, 18, 50 Andreason, M . G., 149, 195 Arnold, P. W., 156, 192 Aspinall, D., 70, 71, 72, 106, 118, 120 Azam, M . N., 5, 36,48

B Bach, H., 2, 22, 26, 28, 32, 43, 48 Ball, P. C., 45, 49 Baltz, D. J., 45, 46, 48 Barber, D. J., 2, 3, 5, 15, 19, 20, 21, 22, 23, 24, 25, 26, 29, 35, 42, 43, 44, 48, 50 Barber, M. J., 119 Bar-Lev, A., 221, 265 Barron, I . M., 120 Bass, C., 120 Bassous. E., 198, 265 Baternan, I . M., 235, 250, 265 Bates, R. H . T., 133, 192 Batzdorf, U., 47, 48 Bay, H., 17, 18, 48 Berg, R. S., 23, 48 Berglund, C. N., 225, 239, 241, 250, 265 Berz, F., 241, 242, 265 Beverage, H . H., 162, 193

Bews, M., 119 Bhojwani, H . R., 159, 193 Bilsby, C. F., 44, 48 Binham, R. F., 171, 194 Birchfield, J. L., 171, 193 Blakemore, J. S., 270(10), 271, 277(16), 329 Blakeslee, T . R., 1 I9 Boella, M., 162, 193 Booker, G. R., 41, 50 Bower, R. W., 119 Boyde, A,, 47, 49 Boyer, J. M., 161, 193 Bradshaw, P., 90,91, 118 Brammer, D., 150, 196 Brandt, W., 15, 19, 49 Brews, J. R., 233, 241, 243, 244, 245, 246, 247, 248, 254, 259, 261, 262, 264, 265, 265 Brissenden, T. H. F., 81, 118 Broux, G. L., 224, 241, 264, 265, 266 Brown, D., 61, 62, 64, 118, 120 Brown, D. M., 225, 265 Brown, G. H., 155, 193 Brown, P. J., 120 Bruce, G., 13, 17, 18, 48 Buie, J . L., 1 19 Buiocchi, C. J., 3, 5, 33, 34, 48 Bulgerin, M . A,, 164, 193 Burke, G. J., 138, 194 Burke, G. R., 120 Burrows, R. M., 171, 194 Burton, R. W., 161, 193 Butler, C. M., 141, 142, 143, 146, 148, 193, 194, 196 Butt, I. K., 189, 195 C Cain, G., 118 Cain, J. T., 120 Callendar, M . H., 179, 193 Carlson, A. D., 121 33 1

332

AUTHOR INDEX

Carteaud, A. J. P., 47, 49 Carter, G., 3, 22, 49 Castagne, R., 224, 265 Castiang, R., 2, 3, 24, 30, 31, 33, 40, 49 Chan, K. K., 137, 148, 195 Chang, D. C., 132, 136, 193 Chao, H. H., 146, 148, 193 Chaperot, D., 23,50 Chapman, J. N., 41,49,50 Chapple, K., 58, 118 Chen, J. T. C., 241, 242, 243, 248, 253, 265 Chen, K. M., 164, 166, 168, 173, 189, 193, 294 Cheng, D. K., 191, 193 Chu, L. J., 187, 188, 193 Churchill, J. N., 270( 1l), 329 Clinton, D. J., 44, 48, 49 Cobbold, R. S. C., 219, 265 Coburn, J. W., 17, 23, 49 Colebrooke, F. M., 125, 193 Colligon, J. S., 3, 22, 49 Collins, B. S., 180, 185, 193 Collins, T. W., 270(11, 12), 282, 329 Conte, G., 99, 118 Cooper, J. A,, Jr., 208, 265 Copeland, J. R., 172, 173, 193 Coutts, M. D., 3, 5, 33, 34, 48 Crockett, C. G., 8, 9, 10, 36, 49 Cugiani, C., 162, 193 Cummins, J. A,, 175, 294 Cushman, R. H., 119

D Dagless, E. L., 70, 71, 72, 118, 220 Daniel, J. P., 175, 185, 186, 187, 193 Davies, A. C., 219 Davies, A. J., 81, 228 Davies, W. S., 171, 185, 192, 293 Davis, W. D., 9, 49 Dawoud, M. M., 185, 187, 188, 192, 293 Deadrick, F. J., 144, 145, 294 Declerck, G. J., 212, 224, 241, 263, 264, 265, 266 Del Corso, D., 99, 128 Dennard, R. H., 198, 265 Denton, D. H., 160, 294 Dhariwal, R. S., 45, 49 Diener, K. H., 292(20), 329 Djordjevic, A. R., 190, 295

Dowsing, R. D., 120 Dragovic, M. B., 168, 190, 195 Drum, C. M., 23, 31, 42, 49 Dubost, G., 158, 175, 185, 186, 193 Diiker, H., 4 0 , 4 9 Duff, I. S., 152, 193 DuHamel, R. H., 157, 193 Duncan, R. H., 132, 134, 135, 136, 193 Dunn, G. R., 159, 193

E Egashira, S., 161, 293 Elschner, H., 292, 329 Enslow, P. H., 220 Evans, B. G., 157, 293 Evans, L., 90, 91, 218 Evans, W. A,, 120

F Fang, F. F., 241, 242, 247, 253, 265 Fanson, P. L., 173, 189, 193 Faulkner, D., 44,49 Ferrier, B. P., 41, 50 Ferrier, R. P., 41, 49 Ferris, J. E., 168, 195 Firestone, R. F., 3, 5, 25, 35, 42, 44, 49 Fisher, E., 99, 118 Fitch, R. K., 45, 46, 49 Flachenecker, G., 183, 184, 293 Flewitt, P. E. J., 40, 41, 49, 50 Flinn, I., 241, 242, 265 Foster, D., 163, 193 Fowler, A. B., 241, 242, 247, 253, 265 Frank, F. C . , 21, 22, 23, 24, 25, 48 Franks, J., 2, 11, 12, 21, 23, 37, 38, 45, 46, 49 Free, W. R., 171, 293 Frisch, B., 47, 49 Fu, H. S., 269, 329 Fukui, H., 182, 293 Fulker, M. J., 47, 49 Fullagar, D., 90,91, 128 G

Gaensslen, F. H., 198, 265 Galanakis, D. E., 185, 292 Gallett, 1. N. L., 133, 292 Gangi, A. F., 159, 293

333

AUTHOR INDEX

Garuin, H. L., 27, 28, 49 Gebler, P., 103, 106, 118 Gentry, B., 3, 5, 31, 40, 49 Ghander, A. M., 11, 12, 37, 49 Gibbons, J., 120 Gibson, J. J., 185, 193 Gilder, J. H., 119 Giordana, M., 99, 118 Glodeanu, F., 23, 50 Gloersen, P. G., 27, 28, 49 Goetzberger, A,, 224, 225, 233, 239, 240, 242, 265 Goodhew, P. J., 1, 49 Gordon, D., 119, 121 Gray, P. V., 225, 265 Green, H. W., 3, 5, 25, 35, 42, 44,49 Gross, M. H., 156, 193 Grove, A. S., 119, 271(15), 276(15), 306(15), 322(24), 329 Gummel, H. K., 221, 223, 265 Guzev, A. A., 225, 241, 265

H Hall, R. N., 201, 204, 220, 241, 263, 265, 269, 278, 317, 328, 329 Hallen, E., 128, 131, 132, 134, 135, 136, 137, 139, 144, 145, 146, 148, 164, 170, 193 Hamid, M. A. K., 172, 195 Hanna, K. A. K., 180, 193 Hansen, R. C., 165, 193 Harkins, P. W., 23, 50 Harot, H., 158, 193 Harrington, R. F., 127, 132, 139, 140, 141, 147, 159, 164, 190, 191, 193 Harrison, C. W., 160, 164, 194 Hassan, M. A,, 148, 193 Hauffe, W., 23, 49 Healey, M., 1 I9 Heiman, E. P., 268(2), 270(2), 317(2), 318(2), 328 Hersch, W., 157, 158, 194 Hertz, H., 123, 194 Heuer, A. H., 3, 5, 25, 35, 42. 44, 49 Hietel, B., 10, 31, 32, 49 Hilford, M. H., 82, 118 Hinchey, F. A., 132, 134, 135, 136, 192 Hirthe, W. M., 32, 43, 49 Hnatek, E. R., I19

Hockey, B. J., 3, 22, 34, 43, 49, 50 Hodges, D. A,, 119 Hodges, G. M., 47, 49 Hodgson, D., 153,194 Hofstein, S. R., 268(3), 270(3), 317(3), 318(3), 328 Hojou, K., 16, 17, 50 Holland, L., 3, 5, 6, 7, 13, 19, 36, 47, 49 Holt, O., 120 Howarth, B. A., 148, 193 Howe, R. G., 3, 5, 25, 35, 42, 44, 49 Hukin, D. A., 41, 49, 50 Hurley, R. E., 3, 5, 6, 7, 47, 49 Husson, S. S., I20 I Iasis, 1 I9 Iizuka, K., 164, 194 Imbriale, W. A,, 130, 131, 142, 194 Induni, G., 3, 50 Ingerson, P. G., 130, 131, 142, 194 Isbell, D. E., 157, 193 Iwashige, J., 162, 193

J James, J. R., 133, 171, 192, 194 Jenkins, R. W., 120 Jensen, E. D., 106, 118, 120 Jones, D. S., 133, 194 Jouffrey, B., 24, 49 Jund, C., 322, 329 K

Kalafus, R. M., 154, 155, 159, 194 Kanaya, K., 16, 17, 50 Kellogg, E. W., 162, 193 Kidd, M. W., 23, 50 Kikuchi, H., 163, 194 King, R. W. P., 132, 135, 136, 160, 161, 168, 193,194, 196 Klausmann, E., 239, 266 Kline, B., 101, 118 Knight, M. A,, 163, 194 KO, W. L., 147, 148, 194 Kominiak, G. J., 23, 48

334

AUTHOR INDEX

Kowalsky, J., 163, 194 Krauss, M., 292(20), 329 Kubina, S. J., 149, 194 Kuhn, M., 239, 249, 265 Kuo, F. F., 120 Kurishev, G. L., 225, 241, 265

L Laborie, P., 2, 3, 30, 40, 49 Laegreid, N., 14, 15, 16, 29, 50 Lamensdorf, D., 167, 171, 194 Landgrof-Dietz, D., 292(20), 329 Landstorfer, F. M., 162, 183, 194 Laubert, R., 15, 19, 49 Laurenson, L., 3, 5, 6, 7, 49 Leblanc, A. R.,198, 265 Lec, S. C., 121 Lenoir, G., 3, 49 Lewis, S. M., 45, 47, 49, 50 Lidbury, D. P. G., 41, 50 Lin, C. J., 164, 166, 194 Lin, S. M., 146, 195 Lin, Y. T., 150, 151, 194 Lindenmeier, H., 182, 183, 184, 194 Linington, P. F., 42, 50

Mayes, P. E., 173, 195 Mayne, K. D., 121 Mei, K. K., 143, 145, 196 Meindl, J. D., 59, 118, 200, 265 Meinke, H., 173, 174, 182, 183, 184, 194 Melliar-Smith, C. M., 14, 18, 19, 20, 26, 27, 28, 50 Melville, A. T., 32, 43, 49 Merkel, B. B., 23, 50 Meyerhoff, K., 10, 31, 32, 49 Middleton, D., 132, 135, 194 Mikuni, Y., 167, 194 Millar, R. F., 133, 192 Miller, E. K., 138, 144, 145, 194 Mittra, R., 147, 148, 194 Moll, J. J., 271, 329 Moore, D. A,, 44, 48 Morris, G., 176, 194 Moschwitzer, A,, 292( 19, 20), 329 Moss, M., 21, 22, 23, 24, 25, 48 Muir, M. D., 47, 49 Muller, J., 268(4), 270(4), 304, 305(21), 317(4), 318(4), 328, 329 Muller, R. S., 241, 242, 243, 248, 253, 265 Muls, P. A,, 212, 224, 263, 265, 266 Murphy, N. St. J., 241, 242, 265 N

M McAdams, H. V., 146, 195 MacDonald, A. J., 19, 50 McDonnell, D., 121 McDonough, J. A., 163, 194 McClynn, D. R.,119 McIIraith, A. H., 10, 11, SO McKendrick, W., 41, 50 McKendrick, W. H., 41, 49 Maclean, T. S. M., 167, 174, 175, 176, 177, 178. 194, 195 Maerz, M., 101, 118 Magnuson, C. D., 23, SO Magowan, J. A,, 235, 250, 265 Malech, R. G., 163, 194 Margalit, S., 221, 265 Marsland, E. A,, 45, 49 Martin, D. P., 119 Martinez. R., 120 Mason, H. P., 156, 194

Nagai, K., 167, 194 Nasu, N., 148, 193 Naufel, E. S., 120 Navez, M., 23, 50 NeH, N. P., 135, 194 Neugroschel, A., 221, 265 Newman, E. H., 171, 195 Nicholas, M., 158, 293 Nichols, A. J., 121 Nicollian, E. H., 224, 225, 232, 239, 240, 242, 249, 265, 266 Nicoud, J. D., 98, 99. 118 Nobes, M. J., 22, 49 Noyce, R. N., 269(5), 317(5), 328 Nyguist, D. P., 164. 166, 168, 194 0

Oechsner. H., 17. 19, 29, 50 Ogdin, C. A,, 119

335

AUTHOR INDEX O’Neill, B., 90,91, 118 Opdenduk, T., 120 Osborn, J. S., 45, 47, 48, 49, 50 Osbourne, A,, 119

P Pache, J. E., 121 Pao., H. C., 208, 209, 211, 215, 218, 219, 220, 223, 226, 243, 253,257. 265 Paulus, M., 3, 4, 5, 6, 15, 33, 35, 42, 45, 50 Paunovic, DJ. S., 168, 169, 194, 195 Pavlasek, T. J. F., 149, 194 Pearson, L. W., 129, 141, 143, 194 Pelletier, M., 175, 194 Pettit, H. R., 41, 50 Pfeiffer, E. A,, 121 Pizer, R., 150, 194 Pocklington, H. C., 127, 128, 129, 132, 134, 136, 137, 138, 139, 140, 141, 143, 144, 146, 147, 148, 149, 194 Poggio, A. J., 173, 195 Poirier, R., 322, 329

Pokoski, J. L., 120 Popovic, B. D., 128, 131, 135. 136, 137, 138, 164, 167, 168, 169, 190, 194. 195 Popovic, B. S., 168, 195

R Ramsdale, P. A,, 165, 166, 167, 174, 175, 176, 177, 178, 189, 194, 195 Rangole, P. K., 176, 195 Rao, B. L. J., 168, 195 Raphael, H. A., I20 Read, W. T., 269, 278, 317, 328, 329 Read, W. T., Jr., 201, 204, 220, 263, 265 Reddi, V. G. K., 318(22), 329 Reverchon, F., 3, 4, 5, 6, 15, 33, 42, 45, 50 Rice, C. W., 162, 193 Richman, P., I20 Richmond, J. H., 127, 136, 148, 150, 151, 171, 194, 195 Rideout, V. L., 198, 265 Rippin, J. F., 172, 195 Ritz, S., 292( 19), 329 Robertson, W. J., 172, 173, 193 Rodgers, T. J., 59, 118

Rosenfeld, P., 101, 118 Rushton, G. J., 46, 50 Russo, P. M., 120 Ryan, C . E., 150, 195 S Sagert, N. H., 44,49 Sah, C . T., 208, 209, 211, 215, 218, 219, 220, 223, 226, 243, 253, 257, 265, 269, 317, 318(22), 328, 329 Saini, S. P. S., 176, 195 Sanzgiri, S., 175, 194 Sarkar, T. K., 191, 195 Sayre, E. P., 147, 195 Schelkunoff, S. A., 153, 195 Schiek, B., 268(4), 270(4), 304, 305(21), 317(4), 318(4), 328, 329 Schlette, W., 40, 49 Schmidt, P. H., 13, 15, 17, 18, 19, 27, 28, 30, 50 Schuler, A. J., 171, 194 Schwartz, R. J., 208, 265 Selden, E. S., 138, 194 Sella, C., 23, 47, 49, 50 Sensiper, S., 159, 193 Sexton, E. E., 44, 49 Shen, L. C., 168, 170, 195 Shockley, W., 201,204, 220,263, 265,269, 278, 281(18), 317, 328, 328, 329 Siewiorek, D. P., 120 Sigmund, P., 13, 15, 18, 19, 22, 50 Siller, C. A., 135, 194 Silvester, P., 137, 148, 193, 195 Simmons, J. G., 324, 329 Simonne, J. J., 225, 235, 236, 237, 238, 240, 258, 264, 265 Sinitsa, S. P., 225, 241, 265 Smith, D. L., 170, 182, 195 Smith, G. S., 189, 195 Snow, J. D., 3, 5, 25, 35, 42, 44, 49 Somekh, S., 27, 28, 50 Sosin, B. M., 180, 189, 195 Soucek, B., 119, 121 Spector, M . , 47, 50 Spencer, E. G., 13, 15, 17, 18, 19, 27, 28, 30, 50 Spencer, R. D., 121 Steeds, J. W., 21, 22, 23, 24, 25, 48 Stern, F., 246, 265

336

AUTHOR INDEX

Storer, J. E., 132, 195 Storm, B., 134, 135, 195 Strait, B. J., 146, 148, 191, 193, 195 Stuart, P. R., 45, 47, 48, 49, 50 Styles, R. C., 44,49 Surutka, J. V., 129, 195 Swanson, R. M., 200, 265 Sze, S. M., 271( 14), 279( 17), 3 19(23), 329

Vapaille, A,, 224, 265 Vasiliu, F., 23, SO Veillard, J., 175, 193 Velickovic, D. M., 129, 195 Verhofstadt, P. W. J., 59, 61, 118, 120 Verjans, J . R., 221, 237, 266 Verstraete, R. G., 173, 193 Villa, A,, 162, 193 Vuille, J. P., 99, 118

T W

Tai, C. T., 132, 195 Tanner, R. L., 149, 195 Tate, A. J., 40,49 Taylor, C. D., 131, 146, 148, 195 Teodorescu, 1. A., 23, 50 Terman, L. M., 225, 266 Terret, C., 187, 193 Theis, D. J., 119 Thiele, G. A,, 127, 136, 195 Thompson, M. W., 15, 19, 50 Thompson, S. J., 41, 50 Thomson, C. P., 7, 10, 50 Thomson, J. J., 7, 10, 50 Thornley, A., 121 Tighe, N. J., 3, 22, 34, 43, 50 Tillman, J. D., 135, 194 Toki, K., 16, 17, 50 Torrerra, E. A,, 119 Towaij, S. J., 172, 195 Trillat, J. J., 14, 24, 45, 50 Tsai, L. L.. 129, 195 Tschernokoscheva, L., 292(20), 329 Tsong, 1. S . T., 15, 19, 20, 21, 22, 23, 24, 25, 29, 48, 50 Tucker, D. G., 188, 195

u Uda. S.. 157, 195

Wackman, P. H., 32,43,49 Wadbrook, D. G., 82, 118 Wakerly, J. F., 107, 118 Walters, A. B., 164, 193 Wang, J. J. H., 150, 195 Ward, A. R., 121 Ward, J. W., 5, 36, 40, 42, 45, 46, 50 Watson, D., 104, 105, 106, 118 Watson, I . M., 85, 120 Wegmann, L., 23, 50 Wehner, G . K., 14, 15, 16, 29, 50 Wei, L. S., 324, 329 Weissberger, A. J., 120, 121 Wenham, R. E., 109, 118 Wilkes, M. V., 67, 118 Wilkinson, W. C., 157, 158, 195 Williams, D., 150, 196 Williams, H. P., 170, 196 Wilson, I. H., 23, 50 Wilson, R. M., 185, 193 Wilton, D. R., 131, 141, 142, 146, 193, 195. 196

Witcomb, M. J., 23, 50 Withington, F. G.. 120 Wong, W. C., 177, 196 Wood, C., 47, 49 Woodman, K. F., 172, 196 Woodward, 0. M., 155, 193 Wright, D. W., 119, 121 Wu, T. T., 128, 132, 136, 168, 194, 196

V

Vallese, L. M., 166, 195 Vanderslice, T. A., 9, 49 van Gelder, W., 249, 266 Van Overstraeten, R. J., 212, 221, 224, 237, 241, 263, 264, 265, 266

Y

Yagi, H., 157, 162, 171, 188, 196 Yeh, Y. S., 143, 145, 196 Yu, H. N., 198, 265

AUTHOR INDEX Z

Zelby, L. W., 159, 293 Zerbst, M.,268(1), 269,270(1), 302, 304, 305,

331

312, 317(1), 318(1), 320, 321, 325, 326, 328 Zich, R., 162, 293 Ziegler, K., 239, 266 Zimmerrnan, W. E., 168, 295

Subject Index

A

B

AC conductance technique. surface state properties and. 224-225.264 Address mode direct. 68 immediate, 68 indexed, 69 indirect, 69 relative, 69 Alloys. ion etching of. 40 A L U . see Arithmetic and logic unit Analog-to-digital converter. in microprocessors. 88-95 Anode ion source. electron microscopy and. 3-12. 36-38 Antenna, .tee Dipole antenna: Monopole antenna; Wire antenna Antenna-amplifiers. . t e e Antennafier Antenna-converter. see Antennaverter Antenna efficiency long antennas, 167- 168 optimization and. 190-191 resistance and. 165-167 short antennas. 165 Antenna field patterns. for long antennas. 170 Antennafiers. use of. 172-173 Antennamitters, use of. 173 .4ntenna susceptance. impedance and. 168-169 Antenna system noise. V H F , 181-183 Antenna-transmitter. .see Antennamitter Antennaverter, integrated circuits and. 172- 173 .4rithmetic and logic unit. microprocessoi-. 63 As\ernbler, microprocessor. 83-87 Assembly language. 83-87 Asynchronous serial transmission, microprocessor, 97

Backscattering sputtering and. 13 in wire antennas, 149 Bandwidth, in wire antennas, 152. 162. 172. 188. 189 Binary operator. instruction set and. 70 Biological materials. ion beam technology and. 46-47 Bipolar integrated circuits memory and. 77 technology of. 54-56 unipolar circuits and, 60-61 Bit-slice architecture, technology of. 66-67 Brews fluctuation theory, M O S F E T mobility and, 243-248,254.262.264- 265 Bubnov-Galerkin method, foi- current distribution approximation. 137 Bulk impurity density, determination of. 249 Bulk recombination lifetime. 268 Bulk storage, in minicomputer system\. 78-80

C

Capacitance, in MOS capacitor. 225. 263. 267-326 Capacitor. MOS, .see Metal-insulatorsemiconductor capacitor Capture cross section MOS capacitor and. 271 M O S F E T model and, 224,263-264 Carrier-density fluctuation, M O S F E T nio hility and. 241-248.259-262 Carrier recommendation, theory of, 269 Cathode ion source. electi-on mici-oscopy and, 3-12,31-38.45-46 C C D , see Charge-coupled device Channel current, M O S F E T , 197-265

338

SUBJECT INDEX

Charge-coupled device, bulk storage and, 79-80 Chemical etching ion etching and, 1-2,40,47-48 surface topography and, 2 I CMOS, see Complementary metalinsulator-semiconductor Collocation, for current distribution approximation, 133-152 Communications system. antenna as part of, 188-189, 191 Complementary metal-insulatorsemiconductor memory and, 75 in multiprocessor systems, 107 technology of, 58-59, 61 in weak inversion, 200 Computer, effect on physics. 51-117 see olso Microprocessor Computer language assembly, 83-87 high level, 87-88 Conductivity mobility, MOSFET, 242 Control systems, microprocessors and, 108-109 Converters, in microprocessors, 88-91 Current continuity, interconnected wires and, 147 Current discontinuity, 144- 146 Current distribution in active antennas, 173 integral equations for, 125-132 interconnected wires and. 146-148 numerical methods for, 133-146 in wire antennas, 124-125 Current-time product method. trap density and. 324-325

D

DC conductance mobility, determination of, 253-262 DCTL. see Direct-coupled transistor logic Depletion layers, comparison of, 317-319 Depletion mode device, MOSFET, 56 Depletion region generation rate in, 319-320 MOS, 325-326

339

Depletion time in capacitor, 284-286 flatband-to-inversion transient, 288,290, 291-293,296-297,301,306-308. 325-326 Dielectric relaxation time flatband-to-inversion transient, 289-290, 294 inversion-to-flatband transient, 3 15 MOS capacitor, 284 Digital-to-analog converter, 9 Diode-transister logic, technology of. 55 Dipole antenna broadband, 152-153, 159 classical impedance of, 135 coated, 172 current distribution of, 132, 138 efficiency of, 166, 167 field patterns of. 170 folded, 167 frequency and, 124 HF, 179 printed, 157-159 resonant, 153-159 Direct access memory, in microprocessors, 75 Direct-coupled transistor logic, technology of, 55 Direct memory access analog-to-digital converter and, 92-93 processor-memory switch and, 71-72 Discone antenna, coated, 172 DMA, see Direct memory access Doping, nonuniform, 23 1 Doping density determination of, 249 MOSFET, 221-224 Doping profile MOSFET, 263 surface potential and, 252-253 Drain current model of, 201-233 MOSFET, 263 surface state density and, 224-239 in weak inversion, 264-265 Drain voltage MOSFET, l97-20l,208,21l-2l7 mobility and, 257,261 surface state density and, 224-239

340

SUBJECT INDEX

DTL, see Diode-transistor logic Dynamic circuits, power dissipation and, 197

comparison of, 47-48 surface topography and, 21-24,45 variation in, 21 for various materials, 26-28

E

EAROM, see Electrically erasable and re programmable read-only memory ECL. see Emitter-coupled logic Electrically erasable and reprogrammable read-only memory, technology of, 78 Electrolytic etching, compared with ion etching, 2,40,47-48 Electromagnetic radiation, sputtering and, 13 Electron microscopy ion beam technology and, 1-50 scanning, see Scanning electron microsCOPY

transmission, see Transmission electron microscopy Emission cross section, in MOS capacitor, 271 Emitter-coupled logic memory and, 17 speed of, 60 technology of, 55 Energy band forbidden, 200-208,228-230,264 surface state and, 227-230 Energy level, MOSFET, 197-265 Energy transfer, sputtering and, 13-20 Enhancement mode device, MOSFET, 56 EPROM, see Erasable programmable readonly memory Equr-erosion profile, surface topography and, 21 Equilibrium time flatband to inversion transient, 288-293, 296-305,307-310 MOS capacitor transient response, 284285,326 Erasable programmable read-only memory, technology of, 78 Erosion slowness, surface topography and, 21,22 Etching, see Chemical etching; Electrolytic etching; Ion etching; Thermal etching Etching rate angle ofionincidence and, l9-20,21

F

FAMOS device, see Floating-gate avalanche-injection device Fast paper tape reader, in microprocessors, 80 Fast switching, in microprocessors, 103-104 FET, see Field effect transistor Field effect transistor, technology of, 56-58 Flatband conditions, in ideal MOS structure, 279-282 Flatband-to-inversion transient depletion region, 3 19-320 model of, 277,279-282 traps excluded, 286-297 traps included, 305-313 Floating-gate avalanche-injection device memory and, 78 technology of, 57 Floppy disk, bulk storage and, 78-79 Fluctuation theory, MOSFET mobility and, 259-262 Franklin array antenna, analysis of. 170 Frank’s kinematic theory, surface topography and. 21,23 Frequency transition, MOS capacitor. 322 G

Galerkin method current distribution approximation, 133I34 wire grid modeling and, IS0 Gate voltage, MOSFET, 199,204,211. 212-216,217,225,228,241,249-253 Generation centers, model, 305-313,325 Generation rate, in depletion region, 269. 319-320 Graphic display. in microprocessors, 80-82 H

Hall-Shockley-Read statistics, surface state occupancy and, 263

341

SUBJECT INDEX

Hallen collocation, for current distribution approximation, 134-136, 137 Hallen equation, for current distribution approximation, 128, 131-132, 134-135, 144-145, 164 Hallen-Galerkin method, for current distribution approximation. 137 Harrington equation, for current distribution approximation, 127, 132, 139-140, 147, 159 High-level languages, microprocessors and, 87-88 Hummocks, surface topography and, 22

I ICE processor, see In-circuit emulation system 12L, see Integrated injection logic Image memory in microprocessors, 63 processor-memory switch and, 70-71 Impedance, in wire antennas, 153-156, 163-166 Impurity density, MOSFET, 249,263 Impurity distribution, surface state density and, 231 Impurity profile, MOSFET, 221-224 In-circuit emulation system, microprocessor development and, 101 Inductor, in short wire antennas, 164-166 Input devices, in microprocessors, 80-82 Instruction set, in microprocessors, 67-70 Integrated antenna, technology of, 173- 178 Integrated circuit technology, advances in, 52, 54-61 effect on antenna technology, 172-173 MOS, 197-265 see also Bipolar integrated circuits; Unipolar integrated circuits Integrated injection logic applications of, 61 memory and, 77 technology of, 55-56, 61, 65 Interconnected wires, in wire antennas, 146-148 Interface charge carrier-density fluctuation, 243-248 conductivity mobility and, 242-243

MOSFET, 262-265 surface state density and, 239 Interrupts, processor-memory switch and, 73-74 Inversion, ideal kiOS structure, 281,282 see also Strong inversion; Weak inversion Inversion capacitance mode, of MOS capacitor, 268 Inversion charge, MOSFET, 215,216 Inversion layer, conductivity mobility and, 242 Inversion-to-flatband transient response, in MOS capacitor, 313-316 Ion beam, angle of incidence, 19-20.21-24 Ion beam technology electron microscopy and, 1-50 ion beam production, 2-12 ion bombardment, 24-26 ion erosion, 30,45-48 ion etching rate, 26-29 ion thinning, 30-45 sputtering process, 13-29 surface topography and, 21-24 Ion bombardment, damage induced by, 24-26 Ion erosion equipment, 30,45-46 scanning electron microscopy and, 45-48 surface topography and, 21-24 Ion etching, technology of, 1-50 see also Etching rate Ion implantation, sputtering and, 13, 18 Ionization, methods of, 2-12 Ion thinning, for transmission electron microscopy, 30-45 Isolator-semiconductor interface, nonuniformities near. 241 K

Kinematic theory of crystal dissolution conical bombardment and, 23 surface topography and, 21 Kinematic wave equation, surface topography and, 22 L

Large-scale integrated circuits bipolar devices, 54-56

342

SUBJECT INDEX

technology of, 54-61 unipolar devices, 56-61 Loop coupling, in supergrain antennas, 188 LSI circuits, see Large-scale integrated circuits M

MACRO processor, advantages of, 86-87 Magnetic bubble memory, bulk storage and, 79-80 Magnetic frill current, current distribution and, 136-137, 141 Magnetic disk cartridge, bulk storage and, 78-79 Magnetic tape cartridge, bulk storage and, 79 Magnetic tape cassette, bulk storage and, 79 Master processor, in multiprocessor system 106 Memory dynamic. 199 fast switching contexts. 103-104 improvements in, 109 in microprocessor. 63.75-82 processor-memory switch, 70-75 see nlso Direct access memory; Random access read and write memory; Read-only memory Metal, ion thinning procedures for, 40-41 Metal-insulator-semiconductor memory and, 76.77 technology of, 56-58. 109 in weak inversion, 197-198 Metal-insulator-semiconductor capacitor dynamic equations for, 270-278 pulse response, 282-285 simplest-case example, 274-278 transient response in. 267-326 Metal-insulator-semiconductor field effect transistor bipolar devices and, 60-61 carrier-density fluctuation and, 243-248 channel length of, 198 drain current model of. 197-223 fabrication of, 257-259 models of, 217-221 potential fluctuation influence, 241-262 simple analytical model of, 212-217 source-drain current in. 208-212

surface state density in, 224-240 in weak inversion, 197-265 Microcomputer systems, advantages of, 110 Microprocessor applications of, 100- I10 architecture of, 61-75 choice of, 100-103 costs of, 100-103 experiments and, 88-100 failure of, 107-108 improvements in, 109-1 10 kits, 102-103 memory. 75-82 peripheral devices, 75-82 software, 83-88 technology of, 51-1 I7 Microprogramming, technology of, 66-67 Microscopic mobility, carrier-density fluctuation in, 243-248, 262 Microtoming, limitations of, 1 Minicomputer control systems and, 109 costs of, 100 physics and, 52 Minority-carrier lifetime, 269-270 Mobility low-field, 257-259 surface potential and, 254-257.259-362 see crlso DC conductance mobility Monopole antenna active loop, 174-178 coated, 171 fed-collector. emitter-loop, 174- 176 fed-emitter, collector-loop, 174- 178 field patterns of, 170- 171 folded, 166, 167 H F , 179 integrated. 173-178 long, 162 with lumped capacitors, 168 resonant. 153 short, 159, 164-167 vertical. 150 see also Antenna: Wire antenna MOS, see metal-insulatorsemiconductor MOSFET. see metal-insulatorsemiconductor field effect transistor Multichip implementation, in microprocessors, 65-67

343

SUBJECT INDEX

Multiprocessor systems, advantages of, 105-108 N n-channel metal-insulator-semiconductor applications of, 60-61 memory and, 77 in multiprocessor systems, 107 Net generation rate, for depletion region carriers, 269 NMOS, see n-channel metal-insulatorsemiconductor Nonequilibrium depletion capacitance mode, MOS capacitor, 268 Nonmetallic inorganic materials, ion thinning procedures for, 42-45 Nonsaturation region, MOSFET, 21 1, 212. 2 14-2 16 Nonuniform doping, MOSFET, 231 npn transistor, technology of, 54-61

0 Oscilloscopes, in microprocessors, 89 Output devices, in microprocessors, 80-82

P Pao-Sah model, for source drain current, 208-222.226.243, 253,263 Paschen's law, ionization and, 10 Patchwork model, MOSFET, 242-243,251, 263 Peripheral devices, in microprocessors, 70-82, 101 Pinch-off point, MOSFET, 216 p-n junction theory, depletion layers and, 3 I 7-3 I9 p i p transistor, technology of. 54-61 Pocklington collocation, for current distribution approximation, 136- 137, 140- 141 Pocklington-continuity requirement, current discontinuity and. 144 Pocklington equation, for current distribution approximation, 127, 128, 129. 131-132, 138, 146, 147-148. 149

Pocklington-Galerkin method, for current distribution approximation, 137- 138, 141-143 Pocklington-sinusoidal interpolation, for current distribution approximation, 143- 144 Pocklington-trigonometricicontinuouscurrent and derivative-collocation, for current distribution approximation, 144 Pocklington-trigonometriciextrapolated continuity-collocation, for current distribution approximation, 144 Polling, processor-memory switch and, 74-75 Power consumption, microprocessors and, 104- I 05 Power dissipation, in MOS circuits, 197-201 Priority interrupt, defined, 73 Processor-memory switch, in microprocessors, 70-75 Program counter, instruction set and, 68-69 Programmable read-only memory, technology of, 77-78 Programming, in microprocessors, 83-88 PROM, see Programmable read-only mem0rY Pulse response, MOS capacitor, 282-285

R Random access memory, microprocessor, 75-78, 107 Random cascade theory, sputtering and, 13-14 Random model, ofcharge distribution, 243-248.263-265 Read and write memory, in microprocessors, 75-77 Read-only memory high-level language and, 88 microprogramming and, 66 software and, 88 technology of, 77-78 Recombination centers, MOS capacitor modeling and, 270-274.305-313 Recombination-generation theory, energy level and, 201 Relaxation time, inversion to flatband, 315-316

344

SUBJECT INDEX

Reprogramming, in microprocessors, 78 Resistance, in loaded antennas, 163 Resonance, in wire antennas, 153-159, 164-166, 171 Retention time, MOS capacitor transient response, 326 ROM, .see Read-only memory

S

Saturation region, MOSFET, 21 1-212, 2 16-2 I9 Saturation voltage, MOSFET, 215-216 Scalar potential, current distribution approximation and, 139-140 Scanning electron microscopy limitations of, 2 ion erosion and, 45-48 Schottky diode, bipolar technology and, 54-55 Schottky transistor, bipolar technology and, 54-55 SEM, see Scanning electron microscopy Semiconductor ion thinning procedures, 41-42 potential fluctuation in, 241-245 Serial transmission. in microprocessors, 97-98 Shockley-Read-Hall theory, carrier recombination, 269-270.278, 305-313, 3 17-3 I8 Signal-to-noise ratio, in wire antennas, 165-168, 177, 190-191, 197 Silicon-on-sapphire integrated circuit, technology of, 59 Silicon-silicon oxide interface, MOSFET, 200-201,241,262 Simple interrupt, defined, 73 Single-chip implantation, in microprocessors. 65-67 Sinusoidal collocation, for current distribution approximation, 141 Sinusoidal current distribution, in wire antennas, 125 Sky noise contribution H F antenna and, 180 signal-to-noise ratio and. 177 VHF antenna and, 181 Slave processors, in multiprocessor systems, 106

Software, microprocessors, 83-88, 101, 110 SOS, see Silicon-on-sapphire integrated circuit Source-drain current carrier-density fluctuation and, 243-247 influence of nonuniformity, 243-248 model of, 208-212 Source voltage, MOSFET, 212-217.225 Sputtering cathode aperture and, 12 damage induced by, 26 defined, 13 in ionization, 10, 13-29 kinematic wave equation and, 22 surface cleaning and, 45 Sputtering rate lattice environment and, 17 surface topography and, 21-24 variation in, 17-18 Sputtering yield angle ofion incidence and, 19, 23 expression for, 13 ion bombardment damage and, 26 variation in, 13-20, 22 for various materials, 26,28-29 SRH, see Shockley-Read-Hall theory Standard instrument interface, in microprocessors, 95 Static inverter, weak inversion current and, 198

Steady state theory, MOS capacitor and. 270,274-278,281-282,307-308 Strong inversion, MOSFET operating i n , 212,214-217,218,257 Superdirectivity, in wire antennas. 188. 191 Surface barrior diode, see Schottky diode Surface generation, charge equation and, 269 Surface potential determination of, 224-230,249-253 fluctuations, 233, 241-262, 263 Surface recombination velocity, at insulator-semiconductor interface, 268 Surface states determination of, 225-239 energetic position of, 227-230 occupancy of, 201-208 transient response and, 326 Surface state charge, density fluctuations and, 243 Surface state density

345

SUBJECT INDEX

ac conductance technique and, 264 determination of, 224-239 forbidden energy gap and, 228-230 model of, 263 Surface topography, ion erosion and, 21-24 Synchronous serial transmission, in microprocessors, 97

T Teletype assembler and, 84 in microprocessors, 80 Television antenna, efficiency of, 167 TEM, see Transmission electron microsCOPY

Thermal etching, surface topography and,

22 Threshold voltage, in weak inversion, 199, 212-216,241 Time-dependent capacitance, calculation of. 268 Transient response dynamic equations for, 270-278 flatband to inversion, 277,286-297,305313,319-320 inversion to flatband, 313-316 MOS capacitator, 267-326 simplest-case example, 274-278 Transistor in active loop antennas, 173-178 noise contribution, 177 antenna system noise and, 182 field effect, see Field effect transistor technology of, 54-56 Transistor-transistor logic applications of, 61 memory and, 77 technology of, 55.65 Transition rate, MOS capacitor, 271 Transmission electron microscopy ion erosion and, 45 ion thinning and, 30-45 limitations of, 1 Transmission problens, in microprocessors, 92-95 Trapping centers, model of, 270-278, 305313 TTL, see Transistor-transistor logic Tunnel diode antenna, resistance and, 173 Turn-on voltage, in MOSFET, 212,217,218

U Unary operator, instruction set and, 70 Unipolar integrated circuits bipolar circuits and, 60-61 technology of, 56-60

Vector interrupt, defined, 73 Vector-scalar potential, current distribution approximation and, 139-140 Very large scale integrated circuits, technology of, 52 V-groove metal-insulator-semiconductor, technology of, 59-60 VLSI circuits, see Very large scale integrated circuits VMOS, see V-groove metal-insulatorsemiconductor Voltage, see Drain voltage; Gate voltage; Saturation voltage; Source voltage; Threshold voltage; Turn-on voltage Voltage transfer characteristic, MOSFET, 198 W Weak inversion drain current model of, 201-223,263 MOSFET operating in, 197-265 mobility in, 241-262 potential fluctuations, 241-262,264-265 surface state density, 224-239,263-265 Wire antenna active, 172-187, 188 analysis of, 123-152 antifading, 170- 171 aperiodic, 179 broadband, 152- 153, 167- 168 conical, 155-156 cylindrical. 155 dipole, see Dipole antenna efficiency, see Antenna efficiency electrically long, 162-163 electrically short, 159-162 frequency independent, 179 HF, 153, 155-157. 159, 162-163, 179-181, 187, 188-189

346

SUBJECT INDEX

hula hoop, 161-162 integrated, 173-178 land vehicle, 150 unloaded, 173 long, 167-171 loop, 162, 173-178, 179 MF. 162, 170-171 monopole, see Monopole antenna nonintegrated, 173, 178-187 numerical analysis of, 192 optimization of, 189-191 passive loaded, 163-172, 188-189 performance of, 187- 188 resonant length, 153-159, 160-162, 167 selection of, 187-192 short, 164-167 size, 153 supergain, 188 synthesis techniques, 189-191

in systems, 188-189 technology of, 123-192 UHF, 124. 157, 181-187 unloaded, 152-163 VHF, 157, 167. 173, 181-187 VLF, 124, 159-160 Wire grid modeling current continuity and, 147 wire antennasand, 148-152 Wires electrically long, 162-163 electrically short, 159-162 interconnected. 146-148 Word length, in microprocessors, 63-64

z Zerbst plot, 269, 320-321, 326

A B C 8 D 9

E O

F 1 6 H 1 J

2 3 4 5