UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Planar GaAs Gunn and field effect devices Tucker, Trevor William 1972

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Notice for Google Chrome users:
If you are having trouble viewing or searching the PDF with Google Chrome, please download it here instead.

Item Metadata

Download

Media
831-UBC_1972_A1 T82.pdf [ 14.58MB ]
Metadata
JSON: 831-1.0101454.json
JSON-LD: 831-1.0101454-ld.json
RDF/XML (Pretty): 831-1.0101454-rdf.xml
RDF/JSON: 831-1.0101454-rdf.json
Turtle: 831-1.0101454-turtle.txt
N-Triples: 831-1.0101454-rdf-ntriples.txt
Original Record: 831-1.0101454-source.json
Full Text
831-1.0101454-fulltext.txt
Citation
831-1.0101454.ris

Full Text

PLANAR GaAs GUNN AND FIELD EFFECT DEVICES by TREVOR WILLIAM TUCKER B.A.Sc. U n i v e r s i t y of B r i t i s h Columbia, 1964 M.A.Sc. U n i v e r s i t y of B r i t i s h Columbia, 1966 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of E l e c t r i c a l E ngineering We accept t h i s t h e s i s as conforming to the req u i r e d standard. THE UNIVERSITY OF BRITISH COLUMBIA J u l y , 1972 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced degree at the U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e arid s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department o f ET i . f e C fe-K< C -The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8, Canada Date ( < ^ e L P T 7 £ ABSTRACT Two types of devices, p l a n a r Gunn diodes and the negative r e s i s t a n c e f i e l d e f f e c t t r a n s i s t o r s , have been i n v e s t i g a t e d . Their f a b r i c a t i o n , t e s t i n g and p r o p e r t i e s are discussed. For the planar diode the Gunn domain v e l o c i t y i s p r e d i c t e d a n a l y t i c a l l y and shown experimentally to decrease with, decreasing product of c a r r i e r c o n c e n t r a t i o n and diode t h i c k n e s s . A p a r t i c u l a r s t r u c t u r e of GaAs FET which d i s p l a y s a s t a t i c negative d i f f e r e n t i a l r e s i s t a n c e (SNDR) c h a r a c t e r i s t i c without Gunn i n s t a b i l i t y has been made. The mechanism of the SNDR i s discussed and the device's uses i n a number of c i r c u i t s ( o s c i l l a t o r , a m p l i f i e r , phase-l o c k e d o s c i l l a t o r and b i s t a b l e l o g i c element) are de s c r i b e d . i TABLE OF CONTENTS Page ABSTRACT i TABLE OF CONTENTS i i LIST OF ILLUSTRATIONS ' v ACKNOWLEDGEMENT x I. INTRODUCTION 1 I I . PLANAR GUNN DIODES 4 2.1 Introduction 4 2.2 Background 5 2.2.1 O s c i l l a t i o n i n Experimental Planar Gunn-Diodes 5 2.2.2 O s c i l l a t i o n Suppression i n Bulk Gunn Diodes . . 9 2.2.3 Properties of S u b c r i t i c a l l y Doped Bulk Diodes . 11 2.2.4 Analyses of O s c i l l a t i o n Suppression i n Thin Diodes 12 2.2.5 Planar Diodes with Surface Capacitive Loading . 19 2.2.6 Experimentally Observed O s c i l l a t i o n Suppression i n Thin and D i e l e c t r i c a l l y Loaded Diodes . . 20 2.3 Small Signal Analysis of the Thin Gunn Diode -23 2.3.1 G\mn Domain Velocity i n a Thin Gunn Diode . . . 28 2.3.2 Condition for Zero Domain Velocity i n a Thin Gunn Diode 31 2.3.3 O s c i l l a t i o n Suppression i n Thin Gunn Diode . . 33 2.4 O s c i l l a t i o n Suppression i n a Capacitively-Loaded Thin Gunn Diode 36 I I I . DEVICE FABRICATION 39 3.1 Introduction 39 3.2 Photographic Reduction . 39 3.3 Photoresist and Etching Techniques 40 3.4 E l e c t r i c a l Contacts 43 3.4.1 Influence of Contacts • . 43 3.4.2 GaAs Cleaning 47 3.4.3 The Alloying Cycle 48 3.4.4 Low Fi e l d Contact Resistance 50 3.4.5 Current-Voltage Characteristics 54 3.4.6 The High Resistance Contact Layer. 56 3.4.7 Impact Ionization Noise Spectrum 58 3.4.8 Anode Light Emission 62 3.4.9 Anode Metal Migration and Device Failure . . . 66 3.5 Device Mounting 68 i i Page IV. PLANAR GUNN DIODE EXPERIMENTAL APPARATUS AND RESULTS . . . . 70 4.1 I n t r o d u c t i o n 70 4.2 Test Apparatus . . . 70 4.2.1 Diode C o a x i a l Holder 70 4.2.2 Test C i r c u i t 72 4.2.3 Device Geometries 74 4.3 GaAs P r o p e r t i e s . 76 4.4 Domain V e l o c i t y i n Planar Gunn Diodes . 80 4.4.1 Dependence on the nd Product 80 4.4.2 Bias Tuning of Uniform Gunn Diodes 84 4.4.3 Bias Tuning of Tapered Gunn Diodes 86 V. THE NEGATIVE RESISTANCE FIELD EFFECT TRANSISTOR (NERFET) . . 89 5.1 I n t r o d u c t i o n 89 5.2 The C o n s t r u c t i o n and C h a r a c t e r i s t i c s of the NERFET . . 89 5.2.1 NERFET St r u c t u r e and F a b r i c a t i o n 89 5.2.2 NERFET C h a r a c t e r i s t i c s 99 5.3 Related Devices 119 5.3.1 I n t r o d u c t i o n . s . . . . . . . 119 5.3.2 Conventional GaAs FETs . 127 5.3.3 GaAs FETs w i t h Negative Resistance E f f e c t s . . 128 5.3.4 Gunn Devices w i t h Three E l e c t r o d e s 132 5.3.5 Other GaAs Devices w i t h SNDR 133 5.4 On the S t a t i c Negative D i f f e r e n t i a l Resistance (SNDR) Mechanism . . . . . . . 134 5.4.1 I n t r o d u c t i o n 134 5.4.2 Thermal E f f e c t s and the NERFET Swi t c h i n g Speed 135 5.4.3 T r a v e l l i n g Gunn Domain E f f e c t s 138 5.4.4 E f f e c t of the p-n J u n c t i o n . 139 5.4.5 Other Aspects of the SNDR Phenomenon 141 5.4.6 Previous Theories of Bulk SNDR 145 5.5 C i r c u i t Performance of the NERFET 148 5.5.1 I n t r o d u c t i o n 148 5.5.2 The NERFET Equ i v a l e n t C i r c u i t . 148 5.5.3 Small S i g n a l A n a l y s i s 151 5.5.4 Non-linear A n a l y s i s 156 5.5.5 R e l a x a t i o n O s c i l l a t i o n A n a l y s i s 162 5.5.6 The NERFET as a Gate Tunable O s c i l l a t o r . . . . 164 5.5.7 The NERFET as a Phase Locked O s c i l l a t o r and as a Stabl e A m p l i f i e r 168 5.5.8 The NERFET as a B i s t a b l e L o g i c Element . . . . 169 VI. CONCLUSIONS 173 i i i Page 6.1 The Planar Gunn Diode 173 6.2 The NERFET 174 •{ v LIST OF ILLUSTRATIONS Fi g u r e Page 1.1 a) The sandwich, s t r u c t u r e and b) the pl a n a r s t r u c -ture 1 2.1 The domain v e l o c i t i e s observed by previous workers 7 2.2 Current-voltage c h a r a c t e r i s t i c o f a s u b - c r i t i c a l l y doped diode 12 2.3 C r o s s - s e c t i o n of a t h i n f i l m diode 23 2.4 The s i g n convention 23 14 2.5 D i s p e r s i o n curves f o r (a) n = 2 x 10 and (b) n = 15 -3 2 x 10 cm 29 2.6 Domain v e l o c i t y (normalized to the c a r r i e r d r i f t v e l o c i t y ) as a f u n c t i o n of diode t h i c k n e s s and surface l o a d i n g . . . 30 2.7 The growth f a c t o r 3"L as a f u n c t i o n of a f o r v a r i o u s £ I I diode lengths and c a r r i e r c oncentrations . 34 2.8 C r o s s - s e c t i o n of a th-in f i l m 'diode -with -surface capaci-t-ive l o a d i n g 36 3.1 The m i c r o p o s i t i o n e r 41 3.2 A t y p i c a l diode 42 3.3 A t y p i c a l a l l o y i n g c y c l e 49 3.4 Globules of Au-Ge a f t e r a l l o y i n g 50 3.5 Bevel showing f i l a m e n t p e n e t r a t i o n i n t o GaAs 51 3.6 Contact r e s i s t a n c e as a f u n c t i o n of a l l o y i n g temperature . . 52 3.7 Contact r e s i s t a n c e as a f u n c t i o n of a l l o y i n g time 53 3.8 I-V c h a r a c t e r i s t i c of a coherent diode 55 3.9 I-V c h a r a c t e r i s t i c of an incoherent diode . . . . . . . . . 55 3.10 Waveform w i t h both coherent and incoherent components . . . 56 3.11 I-V c h a r a c t e r i s t i c of a diode whose waveform has both co-herent and incoherent components 57 3.12 P o t e n t i a l d i s t r i b u t i o n along a diode w i t h poor contacts . . 59 v Figure Page 3.13 E l e c t r i c f i e l d d i s t r i b u t i o n along a diode w i t h poor contacts 59 3.14 Noise spectrum of a diode b i a s e d s l i g h t l y above the. t h r e s h o l d v o l t a g e 60 3.15 Noise spectrum of a diode b i a s e d at twice the t h r e s h o l d voltage . . . . . . . . 61 3.16 Diode showing emitted l i g h t at the anode 62 3.17 L i g h t spectrum measurement system . 63 3.18 Spectrum of emitted l i g h t at the anode of a GaAs diode . . . 64 3.19 R a d i a t i o n i n t e n s i t y dependence on a p p l i e d v o l t a g e 65 3.20 Metal m i g r a t i o n and anode l i g h t emission from a device undergoing breakdown 67 3.21 Bevel across a conducting f i l a m e n t a f t e r breakdown 68 3.22 A mounted diode 69 .4.1 Diode mount and ho l d e r . . . . . . . . . 71 4.2 VSWR measurement c i r c u i t 72 4.3 The diode t e s t c i r c u i t 73 4.4 Diode geometries s t u d i e d . . . . 75 4.5 Edge view of the holder used f o r b e v e l l i n g 77 4.6 The van der Pauw c l o v e r l e a f geometry 78 4.7 C a r r i e r c o n c e n t r a t i o n p r o f i l e s 79 4.8 H a l l m o b i l i t y p r o f i l e s 79 4.9 Gunn mode current waveform 80 4.10 C o r r e l a t i o n of current waveform to diode shape 81 4.11 Domain v e l o c i t y i n t h i n Gunn diodes as a f u n c t i o n of nd product 82 4.12 Bias t u n i n g of a uniform Gunn diode 85 4.13 A tapered diode 86 4.14 Bias t u n i n g of a tapered diode 87 \7T Figure Page 5.1 Types of NERFET geometries i n c r o s s - s e c t i o n 91 5.2 Capacitance-voltage measurement c i r c u i t 92 5.3 T y p i c a l capacitance-voltage c h a r a c t e r i s t i c f o r a reverse b i a s e d p-n j u n c t i o n 93 5.4 E l e c t r o n c o n c e n t r a t i o n p r o f i l e s measured by C-V and H a l l methods 94 5.5 T y p i c a l p-n j u n c t i o n c u r r e n t - v o l t a g e c h a r a c t e r i s t i c . . . . 96 5.6 A b e v e l l i n g and s t a i n e d p-n j u n c t i o n 96 5.7 NERFET s t r u c t u r e 98 5.8 NERFET t y p i c a l I-V c h a r a c t e r i s t i c s 98 5.9 The c u r r e n t - v o l t a g e c h a r a c t e r i s t i c s of a tunnel diode a) w i t h c i r c u i t s t a b i l i t y and b) w i t h c i r c u i t i n s t a -b i l i t y (from Chow 1964) 99 5.10 The c u r r e n t - v o l t a g e c h a r a c t e r i s t i c of a NERFET i n a) s t a b l e c i r c u i t o p e r ation b) and c) unstable c i r c u i t o p e r a t i o n 100 5.11 ' Current-voltage t e s t c i r c u i t 100 5.12 Current-voltage c h a r a c t e r i s t i c of a NERFET which apparently produced coherent GHz o s c i l l a t i o n i n a r e s i s t i v e c i r c u i t . 101 5.13 GHz o s c i l l a t i o n from a NERFET i n a r e s i s t i v e c i r c u i t . . . 101 5.14 Current-voltage c h a r a c t e r i s t i c of a NERFET which produced incoherent GHz o s c i l l a t i o n i n a r e s i s t i v e c i r c u i t . . . . 102 5.15 The c u r r e n t - v o l t a g e c h a r a c t e r i s t i c of a NERFET a) before and b) a f t e r a step was etched i n t o the source end . . 103 5.16 I-V c h a r a c t e r i s t i c s f o r three device thicknesses 105 5.17 Normalized I-V c h a r a c t e r i s t i c of a j u n c t i o n FET i n terms of the parameter I / I d e s c r i b i n g v e l o c i t y s a t u r a t i o n . . . 110 r o p 5.18 Representation of the cross s e c t i o n of a notched NERFET . . 110 5.19 Match of experimental and t h e o r e t i c a l I-V c h a r a c t e r i s t i c s f o r a NERFET 114 5.20 C r o s s - s e c t i o n of a NERFET 114 5.21 H y s t e r e s i s growth a f t e r i l l u m i n a t i o n ceases 116 v i i Figure Page 5.22 C i r c u i t used to measure KTFR p r o p e r t i e s 117 5.23 V a r i a t i o n of KTFR p r o p e r t i e s w i t h d r y i n g 118 5.24 H y s t e r e s i s v a r i a t i o n w i t h d r y i n g time of a KTFR covered NERFET 120 5.25 Compilation of r e l a t e d devices 122 5.26 Tuning c h a r a c t e r i s t i c as a f u n c t i o n of p-region b i a s (from P e t z i n g e t , Hahn and M a t z e l l e 1967) 130 5.27 NERFET s w i t c h i n g speed c i r c u i t 136 5.28 NERFET switching'waveforms . . . 137 5.29 Poi n t of the tungsten probe 142 5.30 Voltage p r o f i l e s i n two NERFETs 143 5.31 The NERFET and e q u i v a l e n t c i r c u i t . . .' 149 5.32 Approximate NERFET equ i v a l e n t c i r c u i t . 151 5.33 NERFET t e s t c i r c u i t 151 5.34 ac e q u i v a l e n t c i r c u i t of the NERFET t e s t c i r c u i t 152 5.35 Regions of NERFET c i r c u i t s t a b i l i t y . . . . . . . . . . . . . 155 5.36 NERFET waveforms f o r s e v e r a l p o i n t s on the s t a b i l i t y p l o t . . 155 5.37 Experimental and f i t t e d I-V c h a r a c t e r i s t i c s 159 5.38 NERFET o s c i l l a t i o n frequency as a f u n c t i o n of c i r c u i t inductance . . . . . . . 160 5.39 R e l a x a t i o n s w i t c h i n g path 163 5.40 R e l a x a t i o n o s c i l l a t i o n current waveform ( f o r tunn e l diode c i r c u i t from Ko 1961) 163 5.41 Test c i r c u i t used to show NERFET gate t u n a b i l i t y 166 5.42 Current waveforms f o r a NERFET i n a high Q c i r c u i t w i t h v a r i o u s gate v o l t a g e s 166 5.43 Gate t u n a b i l i t y of the NERFET 167 5.44 Current waveforms f o r a NERFET i n a low Q c i r c u i t w i t h v a r i o u s gate voltages 167 v i i i Figure Page 5.45 Test c i r c u i t used to show phase-locked o s c i l l a t i o n 168 5.46 Test c i r c u i t used to show s t a b l e a m p l i f i c a t i o n 169 5.47 Device c h a r a c t e r i s t i c s and l o a d l i n e showing s t a b l e o p e r a t i n g p o i n t s 170 5.48 Test c i r c u i t f o r NERFET b i s t a b l e s w i t c h i n g 171 5.49 NERFET b i s t a b l e waveforms 171 5.50 Switching waveform of the NERFET l o g i c element 172 i x ACKNOWLEDGEMENT The f i n a n c i a l support of t h i s work by the Canadian Defence Research Board (DRB Grant 5501-67) i s most g r a t e f u l l y acknowledged. I wish to thank my research s u p e r v i s o r , Dr. L. Young, f o r h i s encouragement, guidance and support during the course of the work. I would also l i k e to thank Mr. J . Stuber, Mr. H. Black and Miss B. Andersen f o r t h e i r t e c h n i c a l a s s i s t a n c e and Miss N. Duggan f o r t y p i n g the manuscript. F i n a l l y , I wish to acknowledge a s p e c i a l debt of g r a t i t u d e to my w i f e , I s a b e l l e , f o r her u n s e l f i s h support during these years of study. 1 I . I N T R O D U C T I O N Since J.B. Gunn's 1963 discover}' of u l t r a - h i g h - f r e q u e n c y cur-rent i n s t a b i l i t i e s i n n-type g a l l i u m arsenide, much research has gone I n t o understanding and e x p l o i t i n g the phenomenon. The bulk of the work which has been reported i n the l i t e r a t u r e to date deals w i t h devices of the "sandwich" s t r u c t u r e , i . e . , p l a n e - p a r a l l e l contacts on opposite faces of a GaAs c r y s t a l ( f i g u r e 1 ( a ) ) . However, the sandwich s t r u c t u r e may not be the best s t r u c t u r e from the standpoint of frequency, heat s i n k i n g and mass pr o d u c t i o n . For example, present p l a n a r t r a n s i s t o r technology has almost t o t a l l y r eplaced the o l d e r a l l o y e d and grown j u n c t i o n t r a n s -i s t o r technologies p r i m a r i l y because of the requirement to mass produce t r a n s i s t o r s and s t i l l maintain adequate c o n t r o l of device geometries •and parameters. The .refinement .of . .photolithographic and other tech-niques has enabled such c o n t r o l l e d mass production to be r e a l i z e d . The planar nature of the t r a n s i s t o r s i s a r e s u l t of s u c c e s s i v e o x i d a t i o n , m e t a l l i z a t i o n and d i f f u s i o n processes on one semiconductor surface using p h o t o l i t h o g r a p h i c techniques. / / / j _ "PI / / / /-<> / / / VY//A (a) (b) Figure 1.1 a) the sandwich s t r u c t u r e and b) the p l a n a r s t r u c t u r e The purpose of t h i s t h e s i s i s to examine t h e o r e t i c a l l y and e x p e r i m e n t a l l y some of the p r o p e r t i e s of GaAs devices i n the p l a n a r 2 structure (f i g u r e 1(b)). The term planar as applied to GaAs Gunn e f f e c t devices s i m i l a r to those studied here has previously been used by Clark, Edridge and Bass 1969; C o l l i v e r and Fray 1969; Parkes and Taylor 1971 and several others. The term Gunn e f f e c t i n th i s thesis r e f e r s to the occurence of ultra-high-frequency current o s c i l l a t i o n s caused by the formation and movement of charge dipole domains. Such charge domains occur because the GaAs possesses negative d i f f e r e n t i a l conductivity due to the i n t e r - v a l l e y transfer of electrons. This favors the accumulation of charge rather than the dispersion of charge which occurs i n p o s i t i v e conductivity materials. Some important properties of the planar GaAs devices are as follows: a) The planar structure permits heat removal i n the t h i n dimen-sio n . The frequency of Gunn o s c i l l a t i o n i s i n v e r s e l y propor-t i o n a l to the length of the device. Therefore, cooling of long devices i s s i m p l i f i e d and planar devices can operate cw at lower frequencies than sandwich type devices. b) The shape of a Gunn diode determines the shape of the o s c i l l a t i o n waveform. The planar s t r u c t u r e , being compatible with photolithographic techniques, permits easy shaping of the device. Hence high frequency function generators can be e a s i l y f a b r i c a t e d . c) The planar structure allows easy access to the act i v e region of the device and a d d i t i o n a l electrodes o r surface d i e l e c t r i c loading can be included to modify or control the Gunn in s t a b -i l i t y . d) A s u f f i c i e n t l y t h i n device suppresses Gunn i n s t a b i l i t y 3 and allows the device to be used as a s t a b l e microwave am-p l i f i e r . T his t h e s i s discusses two d i s t i n c t types of GaAs device. The f i r s t i s the planar Gunn diode which i s composed of n-type GaAs e p i t a -x i a l l a y e r s on s e m i - i n s u l a t i n g GaAs s u b s t r a t e s . Chapter Two contains a s m a l l s i g n a l a n a l y s i s of the p l a n a r Gunn diode from which c o n d i t i o n s of s t a b i l i t y are obtained. This .analysis a l s o .predicts a dependence of domain v e l o c i t y on diode t h i c k n e s s . Some p r o p e r t i e s of these diodes such as l i g h t emission, noise generation and domain v e l o c i t y which were ex p e r i m e n t a l l y observed are discussed i n the l a t t e r part of Chapter Three and i n Chapter Four. The second type of device i s the GaAs f i e l d e f f e c t t r a n s i s t o r which d i s p l a y s a negative d i f f e r e n t i a l r e s i s t a n c e c h a r a c t e r i s t i c w ithout i n s t a b i l i t y . This device i s given the name 'Negative Resistance F i e l d E f f e c t T r a n s i s t o r ' o r NERFET to d i s t i n g u i s h i t from the conventional FET's which d i s p l a y a s a t u r a t i n g current c h a r a c t e r i s t i c . Chapter F i v e contains a d i s c u s s i o n of the p r o p e r t i e s of the NERFET, a d i s c u s s i o n of the mechanism of the negative r e s i s t a n c e and a d i s c u s s i o n of c i r c u i t a p p l i c a t i o n s of the device. The f a b r i c a t i o n techniques used i n making both types of device are des c r i b e d i n the f i r s t p a r t of Chapter Three. 4 I I . PLANAR GUNN DIODES 2.1 Introduction The small l a t e r a l dimension of the planar Gunn diode gives r i s e to d i f f e r e n t e l e c t r i c a l properties of this structure diode as compared to the properties of the conventional sandwich structure Gunn diode. The most important difference i s that Gunn o s c i l l a t i o n can be completely suppressed i f the planar diode i s s u f f i c i e n t l y t h i n . This phenomenon i s s i m i l a r to one observed i n conventional structure diodes i n which os-c i l l a t i o n i s suppressed i f the diode i s s u f f i c i e n t l y short. This chapter contains a review of previous work both a n a l y t i c a l and experi-mental on the suppression of o s c i l l a t i o n i n thin Gunn diodes. Previous a n a l y t i c a l work i s extended i n this chapter by solving numerically the .equations for small signal space charge .growth. The result of this numerical solution shows that the onset of o s c i l l a t i o n as diode thickness i s increased i s abrupt and i s associated with an abrupt increase of space charge growth. This compares to the gradual increase i n space charge with diode thickness which has been predicted by previous ap-proximate solutions. The numerical solution also predicts that the frequency of Gunn o s c i l l a t i o n i s lower i n a thin diode than i n a bulk diode of the same length. This result i s consistent with the observations of many other workers as outlined i n this chapter and i s also consistent with experimental results reported i n Chapter Four of th i s thesis. Also contained i n t h i s chapter are the det a i l s of a small signal analysis of a planar Gunn diode which has a metal plate close to the surface of the diode. The resul t of this analysis i s s i m i l a r to the results quoted by other workers. 5 2.2 Background 2.2.1 Oscillation in Experimental Planar Gunn Diodes The first report of Gunn diodes made in the planar structure was that of Foxell, Summers and Wilson 1965. Their devices were operated in pulse mode, as have the majority of devices reported in the literature. Satisfactory C.W. operation in the planar structure has been difficult to obtain because this structure is susceptible to low voltage break-down and also coherent oscillation can be difficult to obtain. The practical problems associated with obtaining good performance from a planar Gunn diode and the techniques used to overcome some of the d i f f i -culties are discussed in Chapter Three. When a Gunn diode is operated in a resistive circuit the fre-quency of Gunn oscillation is the reciprocal of the time for a charge diode domain to form, transit and extinguish. In the usual case for-mation occurs at the cathode and extinction occurs at the anode hence the frequency is determined by the average domain velocity and the diode length. In bulk diodes the domain velocity is dependent on bias voltage. At bias voltages slightly in excess of the threshold voltage the domain travels at approximately 1.5 x 10^ cm/sec. When the bias is increased to several times threshold the domain velocity is slowed to approximately 0.85 x 10^ cm/sec and remains at this value for further increases in bias. This dependence of domain velocity on bias has been explained by Butcher's 1965 "equal areas rule", modified for a bias voltage which is changing with time by Kurokawa's 1967 "unequal areas rule" and made to include the effect of field dependent diffusion by Copeland 1966 and Butche^) Fawcett and Ogg 1967. Since the domain velocity is a function of bias voltage and since none of the researchers using 6 p l a n a r Gunn diodes to date appears to have s p e c i f i e d the b i a s f o r which o s c i l l a t i o n waveforms were obtained i t i s d i f f i c u l t to compare t h e i r r e s u l t s d i r e c t l y to the r e s u l t s f o r bulk diodes. However, the r e l a t i v e l y low breakdown voltage of planar Gunn diodes as discussed i n Chapter Three suggests that most r e s u l t s quoted i n the l i t e r a t u r e were obtained f o r b i a s v o l t a g e s not g r e a t l y i n excess of t h r e s h o l d . The domain v e l o c i t y i n bulk diodes f o r b i a s voltages near t h r e s h o l d should be near a value of 1.5 x 10^ cm/sec. Figure 2.1 shows the domain v e l o c i t y i n p l a n a r Gunn diodes as determined from the r e s u l t s of other workers. The r e s u l t s shown are f o r e p i t a x i a l n-GaAs l a y e r s on s e m i - i n s u l a t i n g GaAs s u b s t r a t e s . The i n i t i a l s i n t h i s f i g u r e are those of the v a r i o u s authors as given i n the reference s e c t i o n at the end of the t h e s i s . The p o s i t i o n of the i n i t i a l s on the v^ - nd plane show the value of domain v e l o c i t y (v^) as determined from the r e s u l t s quoted by those authors. The product nd (n i s the e l e c t r o n c o n c e n t r a t i o n , d i s the diode t h i c k n e s s ) i s chosen because of the importance i t i s shown to have i n s e c t i o n s 2.2.4 to 2.3.3 of t h i s t h e s i s . Some authors i n s t a t i n g t h e i r r e s u l t s quote only a range of e l e c -t r o n c o n c e n t r a t i o n , t h i c k n e s s or domain v e l o c i t y and i n such cases a bar i s shown i n f i g u r e 2.1 to i n d i c a t e that range. I t i s evident i n f i g u r e 2.1 t h a t many of the measured values of domain v e l o c i t y are s i g n i f i c a n t l y l e s s than the v e l o c i t y f o r bulk m a t e r i a l of approximately 1.5 x 10^ cm/sec. which i s expected w i t h b i a s v o l t a g e s j u s t over the t h r e s h o l d . There have been s e v e r a l r e p o r t s of domain v e l o c i t y i n p l a n a r diodes i n the range of 0.5 x 10^ cm/sec. a value which appears to be s i g n i f i c a n t l y l e s s than the domain v e l o c i t y which would occur i n b u l k diodes. Even when operated at b i a s v o l t a g e s many times t h r e s h o l d , b u l k diodes u s u a l l y 1.0 x10 -7 .8 (cm ) sec .6 •BTn "1? rtln THSn o THSgJMOp  P STHKp FHSC]fo TMr CEB, 'cw BTMp .4 .2 10 11 nd (cm~2) 10 12 Figure 2.1 The domain v e l o c i t i e s observed by previous workers. 8 don't d i s p l a y a domain v e l o c i t y of l e s s than 0.85 x 10 cm/sec. Of p a r t i c u l a r i n t e r e s t i s the observance by Boccon-Gibod and Teszner 1971 of the passage of domains i n a p l a n a r diode using a c a p a c i -t i v e probe. The domain v e l o c i t y which Boccon-Gibod and Teszner 1971 observed depended on the type of anode su r f a c e c a p a c i t i v e l o a d i n g . For the unloaded case the domain v e l o c i t y was approximately 0.5 x 10^ cm/sec. f o r a diode approximately 6.5 microns t h i c k w i t h a c a r r i e r con-15 -3 c e n t r a t i o n of 1.1 x 10 cm . They observed a domain make o n l y one t r a n s i t a f t e r turn-on and a f t e r i t a r r i v e d at the anode no other t r a v e l l i n g domains were observed. Dienst, Dean, Enstrom and Kokkas 1967 and C o l l i v e r and Fray 1969 w h i l e not r e p o r t i n g device parameters and o p e r a t i n g c h a r a c t e r i s t i c s of s p e c i f i c devices have remarked on having observed lower frequencies -for.planar diodes -than -would occur f o r bulk -diodes of the same l e n g t h . Dienst et a l 1967 r e p o r t : "The fundamental t r a n s i t time frequency f o r a l l of the samples was about 600 - 700 MHz, which i s q u i t e a b i t lower than the 1000 MHz that was expected on the b a s i s of a gap l e n g t h of 100 um. The lower t r a n s i t - t i m e frequency i n low-reactance c i r c u i t s suggests that the domains f o l l o w a curved path that i s longer than the gap l e n g t h " . C o l l i v e r and Fray 1969 s t a t e : the output frequency i s g e n e r a l l y somewhat lower than would be obtained from domain t r a n s i t d i r e c t l y across the gap. T y p i c a l l y ~ 8 GHz f o r a 10y spacing". C o l l i v e r e t a l do not provide an e x p l a n a t i o n f o r the lower frequency. 9 When they operated t h e i r p l a n a r devices i n resonant c a v i t i e s Parkes, T a y l o r and C o l l i v e r 1971 found that maximum power output occurred when the c a v i t y resonant frequency corresponded to the t r a n s i t time asso-c i a t e d w i t h a domain v e l o c i t y of approximately 0.7 x 10^ cm/sec. Parkes et a l 1971 comment: "The low value (of domain v e l o c i t y ) i s i n p a r t due to the non-uniform geometry of -the device., .but i s probably a l s o due to the hi g h o p e r a t i n g temperatures i n these l a y e r s and the consequent r e d u c t i o n i n domain v e l o c i t y " . I t i s evident from f i g u r e 2.1 t h a t there has been r e l a t i v e l y l i t t l e documentation of Gunn o s c i l l a t i o n frequency f o r t h i n diodes w i t h low e l e c t r o n c o ncentrations. There appear to be two reasons f o r t h i s . F i r s t , the problems of e p i t a x i a l l a y e r defects and contact f i e l d i n h o -mogeneities are accentuated i n very t h i n l a y e r s . Second, f o r s u f f i c i e n t l y t h i n l a y e r s , Gunn i n s t a b i l i t i e s w i l l be completely suppressed as di s c u s s e d i n d e t a i l i n s e c t i o n 2.3. 2.2.2 O s c i l l a t i o n Suppression i n Bulk Gunn Diodes The suppression of i n s t a b i l i t y i n a fundamentally unstable system by reducing the dimensions of the system i s a w e l l documented phen-omenon. For example, Johnson 1955 has found that o s c i l l a t i o n i n a backward wave o s c i l l a t o r could be suppressed by making the body of the o s c i l l a t o r s u f f i c i e n t l y s h o r t . In a conventional or "sandwich" type Gunn diode, i n s t a b i l i t i e s can be suppressed i f the product of e l e c t r o n c o n c e n t r a t i o n x device l e n g t h (nL product) i s made s u f f i c i e n t l y s m a l l . 10 -2 Kroemer 1964 f i r s t p r e d i c t e d a c r i t i c a l nL product of nL = 10 cm below which o s c i l l a t i o n would not occur. Kroemer2l965 subsequently r a i s e d h i s estimate of t h i s c r i t i c a l product to the range of n = 10^ 10 -2 cm . S i m i l a r c r i t e r i a f o r o s c i l l a t i o n suppression i n b u l k diodes have 12 -2 been p r e d i c t e d by R i d l e y 1966 (nL < 10 cm ) and McCumber and Chynoweth 11 -2 1966 (nL < 2.7 x 10 cm ). The c r i t i c a l nL product observed e x p e r i -11 -2 mentally i s i n the range of nL < 5 x 10 cm (Thim and Barber 1966) 12 -2 to nL < 10 cm (Hakki and Knight 1966). The e x i s t e n c e of a c r i t i c a l nL product below which o s c i l l a t i o n does not occur r e s u l t s from the .amount of growth a space charge wave i n c u r s i n t r a v e l l i n g the le n g t h of the diode. I f t h i s growth i s s u f f i -c i e n t l y l a r g e the c o n d i t i o n corresponds to the occurrence of Gunn i n -s t a b i l i t y . The s m a l l s i g n a l a n a l y s i s of a bulk diode c a r r i e d out by McCumber and Chynoweth 1966 and s e v e r a l others have assumed an e l e c t r i c f i e l d d i s t r i b u t i o n of the form: E = E q exp g"L exp j (tot - B'L) where: g"L i s the wave growth f a c t o r i n t r a v e l l i n g the diode l e n g t h L 3"L = KnL = en |y | L/e v n i s the e l e c t r o n c o n c e n t r a t i o n v i s the e l e c t r o n v e l o c i t y • u c z i s the negative d i f f e r e n t i a l m o b i l i t y i s the p e r m i t t i v i t y of the diode K = 1.1 x 1 0 1 1 cm 2 f o r GaAs McCumber and Chynoweth 1966 showed by examining the behaviour of the zeros of the s m a l l s i g n a l impedence t h a t i n s t a b i l i t y occurs i f B"L £ 2.09. In a c t u a l GaAs devices the c r i t i c a l growth f a c t o r necessary to produce i n s t a b i l i t y was found to be somewhat l a r g e r . McCumber and Chynoweth 1966 on the discrepancy between the s m a l l s i g n a l s t a b i l i t y c o n d i t i o n and the e x p e r i m e n t a l l y observed c o n d i t i o n s t a t e : 11 "Numerical c a l c u l a t i o n s i n c o r p o r a t i n g a l l of the d i f f u s i o n and energy-transport c o r r e c t i o n s give a c r i t i c a l nL pro-duct which i s a f a c t o r of 2 or 3 l a r g e r than nL $ 2.7 x l O ^ -2 cm and which i s i n somewhat b e t t e r agreement w i t h e x p e r i -ment ..." According to S t e r z e r 1971 the f o l l o w i n g three reasons account f o r the discrepancy: "1) In an a c t u a l device, the e l e c t r i c f i e l d i s g e n e r a l l y above t h r e s h o l d over only part of the device, and the ' a c t i v e ' device l e n g t h i s t h e r e f o r e u s u a l l y s m a l l e r than the geometric device l e n g t h . 2) The e l e c t r i c f i e l d i n an a c t u a l device i s always nonuniform, and the average value of K w i l l t h e r e f o r e always be s m a l l e r -11 2 than i t s maximum value of 1.1 x 10 cm . 3) The value of K decreases r a p i d l y w i t h i n c r e a s i n g temperature, and many p r a c t i c a l d e v i c e s , because of s e l f - h e a t i n g operate w e l l above room temperature." 2.2.3 P r o p e r t i e s of S u b c r i t i c a l l y Doped Bulk Diodes The c u r r e n t - v o l t a g e c h a r a c t e r i s t i c at the ter m i n a l s of a s t a b l e 11 -2 s u b c r i t i c a l l y doped ( i . e . nL 5 x 10 cm ) b u l k diode does not show a r e g i o n of s t a t i c negative d i f f e r e n t i a l r e s i s t a n c e i n s p i t e of negative d i f f e r e n t i a l c a r r i e r m o b i l i t y . This p o s i t i v e conductance theory of u n i -form diodes was f i r s t presented by Shockley 1954 and l a t e r g e n e r a l i z e d by Kroemer^ 1970 to i n c l u d e non-uniform, inhomogeneous diodes. The ten-dency of the c a r r i e r s to slow down at l a r g e enough f i e l d s causes c a r r i e r accumulation toward the anode. This accumulation i s s u f f i c i e n t to r e t a i n c o n t i n u i t y of current throughout the diode and negates the e x t e r n a l ob-12 s e r v a t i o n of negative conductance. Rather, the current at l a r g e a p p l i e d v o l t a g e tends to s a t u r a t e as shown i n f i g u r e 2.2. This f i g u r e was ob-2 4 6 8 10 V (volts) Figure 2.2 Current-Voltage C h a r a c t e r i s t i c of a S u b c r i t i c a l l y Doped Diode (n = 6 x 10 cm , L = 18y) ta i n e d by i n t e g r a t i n g the e l e c t r i c f i e l d -versus d i s t a n c e p l o t -which was deri v e d f o r sub c r i t i c a l diodes by McCumber and Chynoweth 1966. The previous d i s c u s s i o n a p p l i e s to the low-frequency ( q u a s i -s t a t i c ) case. I f a s u b c r i t i c a l diode w i t h a l a r g e a p p l i e d v o l tage i s al s o pumped w i t h an r f source, r i p p l e s o f space charge can propagate and grow along the diode. The r i p p l e s are s e l f - r e - e n f o r c i n g when the pumping frequency i s near harmonics o f the t r a n s i t frequency of the c a r r i e r s and the device d i s p l a y s a dynamic negative conductance at those f r e q u e n c i e s . The diode can t h e r e f o r e be used as an a m p l i f i e r i n these p a r t i c u l a r frequency bands ( f o r example,Thim and Barber 1966). 2.2.4 Analyses of O s c i l l a t i o n Suppression i n Thin Diodes In the pl a n a r s t r u c t u r e the f i n i t e c r o s s - s e c t i o n of the diode m o d i f i e s the form of the growth f a c t o r 3"L. As w i l l be shown i n d e t a i l 13 i n s e c t i o n 2.3 the parameter 3" i n p l a n a r Gunn diode i s p r o p o r t i o n a l to d/L where d i s the diode t h i c k n e s s . Hence the growth f a c t o r f3"L neces-sary f o r o s c i l l a t i o n r e s u l t s i n a product of e l e c t r o n c o n c e n t r a t i o n x diode t h i c k n e s s ( r a t h e r than diode length) below which the diode w i l l not o s c i l l a t e . P h y s i c a l l y the modified growth f a c t o r B"L i n the p l a n a r diode a r i s e s from e l e c t r i c f i e l d l i n e s spreading o u t s i d e the device from the space charge wave. Hence, the l o n g i t u d i n a l f i e l d appears to come from a reduced amount of space charge when the p l a n a r equation i s used. I f the diode i s made s u f f i c i e n t l y t h i n the growth f a c t o r can be s m a l l enough to be a s s o c i a t e d w i t h the suppression of Gunn i n s t a b i l i t i e s . The f i r s t p u b l i s h e d statement of a c r i t i c a l product of c a r r i e r c o n c e n t r a t i o n x diode thickness (nd product) below which Gunn o s c i l l a t i o n i s suppressed was that of Koyama, Ohara, Kawazura and Kumabe 1968. They s t a t e without d e r i v a t i o n that a s m a l l s i g n a l a n a l y s i s c a r r i e d out on a Gunn diode whose thi c k n e s s i s much l e s s than i t s l e n g t h produces a s t a -b i l i t y c r i t e r i o n of: n d £ I < 2 e l V l E I I ~ ^ c T ^ l where n i s the diode c a r r i e r c o n c e n t r a t i o n d i s the diode thickness Ej. i s the diode m a t e r i a l ' s p e r m i t t i v i t y i s the surrounding m a t e r i a l ' s p e r m i t t i v i t y v i s the c a r r i e r v e l o c i t y | y c z | i s the magnitude of negative d i f f e r e n t i a l m o b i l i t y ^ = 2.09 n, = 7.46 14 T h e i r c r i t e r i o n i s equivalent to a growth f a c t o r of g"L £ 2.09 f o r i n -s t a b i l i t y . The numerical value of c r i t i c a l nd product which they quote i s : , E I . , i n l l -2 nd = 1.3 x 10 cm £ I I 2 7 which i m p l i e s they used a value of u = 270 cm /v-sec ( t a k i n g v = 10 cz -12 cm/sec and e^ . = 10 f/cm f o r GaAs). The f i r s t measurement of negative d i f f e r e n t i a l m o b i l i t y (Gunn and E l l i o t t 1966) y i e l d e d a value i n t h i s range, however more recent measurements (Ruch and Kino 1967, McWhorter and Foyt 1966, and Acket and de Groot 1967) which agree more c l o s e l y w i t h t h e o r i e s (Butcher and Fawcett 1965, Conwell and V a s s e l l 1966, and Boardman, Fawcett and Rees 1968) have r e s u l t e d i n the acceptance of a value of |u ! i n the range of 2000 to 2500 cm /v-sec. The c r i t e r i o n cz E I 11 f o r o s c i l l a t i o n suppression of JKoyame et a l 1968 (nd $ 1.3 x 10 e I I -2 cm ) e x p l i c i t l y s t a t e s that not only can a s u f f i c i e n t l y t h i n diode cause Gunn o s c i l l a t i o n suppression but a l s o a l a r g e p e r m i t t i v i t y s u r f a c e d i -e l e c t r i c ( £ T T ) c a n have the same e f f e c t . Kino and Robson 1968 i n a d e t a i l e d s m a l l s i g n a l a n a l y s i s i n -d i r e c t l y produced a r e s u l t s i m i l a r to that of Koyame et a l 1968. For the case of = e T T> Kino and Robson 1968 obtained a s t a b i l i t y c r i t e r i o n of: 11 -2 nd £ 1.6 x 10 cm by equating the s m a l l s i g n a l growth f a c t o r 8"L which they d e r i v e f o r t h i n diodes to the value of B"L = 17. This l a t t e r value of growth f a c t o r gives a good match to the e x p e r i m e n t a l l y observed o s c i l l a t i o n suppression c o n d i t i o n i n b u l k diodes. Kino and Robson 1968, i n c a l c u l a t i n g a value 15 f o r a c r i t i c a l nd product, used a negative d i f f e r e n t i a l m o b i l i t y of u = 2000 cm /v-sec. ' cz Despite the d i f f e r e n t growth f a c t o r s assumed necessary f o r i n s t a b i l i t y by these two set s of authors (Koyame et aL 1968 and Kino et a l . 1968) the numerical values o f c r i t i c a l nd products which they a r r i v e d at were approximately the same because t h e i r assumed values of |y I cz compensated f o r t h i s d i f f e r e n c e . By using a simple model, Engelmann 1968 also p r e d i c t e d a r e -duced growth r a t e i n t h i n diodes. In a subsequent paper (Englemam^ 1969) he showed h i s model p r e d i c t e d a c r i t i c a l nd product o f : nde_ 2v £ T I o I < E I I e U o f£"I which n u m e r i c a l l y i s nd $ 2 x 10 cm . This i s approximately E I I the value which Koyame et a l . 1968 would have obtained had they used a value of |u . I = 2000cm /v-sec i n t h e i r c a l c u l a t i o n s . Kuru and Tajima 1969, to account f o r e l e c t r i c f i e l d leakage outside the diode i n -troduced a leakage f a c t o r y i n t o Poisson's one dimensional equation and i o 1 2 a r r i v e d at the simple o s c i l l a t i o n suppression c r i t e r i o n of nd £ — — . They d i d not determine the dependence of y on device parameters. H a r t -n a g e l 1969 and 1970 by g e n e r a l i z i n g the Kino and Robson 1968 approach to i n c l u d e magnetic f i e l d showed that not only can d i e l e c t r i c s u r f a c e l o a d i n g cause o s c i l l a t i o n suppression but f e r r i m a g n e t i c s u r f a c e l o a d i n g a l s o can cause o s c i l l a t i o n suppression. In a s i m i l a r approach Masuda, . Chang and Matsuo 1970 a l s o showed f e r r i t e s u r f a c e l o a d i n g can cause o s c i l l a t i o n suppression. Gueret^ 1970 derived the c o n d i t i o n s f o r which l o a d i n g the su r f a c e of a t h i n Gunn diode w i t h another semiconductor a l s o suppresses Gunn i n s t a b i l i t i e s . 16 H e i n l e 1971 has considered the e f f e c t of d i f f u s i o n on the growth of space-charge waves i n the Kino and Robson 1968 a n a l y s i s and has concluded that d i f f u s i o n i s the dominating e f f e c t at s u f f i c i e n t l y high frequency. Therefore, there i s a p a r t i c u l a r frequency a t which the gain i s a maximum when the device i s used as an a m p l i f i e r . This r e s u l t i s the same as that a r r i v e d at by Dean 1969 who i n c l u d e d the e f f e c t of d i f f u s i o n i n a l e s s rigorous way. In comparison, the Kino and Robson 1968 r e s u l t i n d i c a t e s the gain increases monotonically w i t h frequency. Hofmann^ 1969 showed that f o r heavy d i e l e c t r i c l o a d i n g (e^. << e T T ) one of the Kino and Robson 1968 approximations i s not v a l i d and he obtained under t h i s c o n d i t i o n a new c r i t i c a l nd product which i s 12 -2 independent of n u m e r i c a l l y equal to nd = 1.5 x 10 cm . The s t a b i l i t y c r i t e r i o n which he used was based on the study of i n s t a b i l i t i e s of waves i n plasma by Briggs 1964. Based on Hofmann's 1969 treatments the c r i t i c a l growth f a c t o r e q u i v a l e n t to the Brigg's s t a b i l i t y c r i t e r i o n i s $"L = 15. The s t a b i l i t y c r i t e r i o n used by Koyame et a l . 1968 and many others was based on the behaviour of the zeros of an e q u i v a l e n t diode im~ pedence i n the complex frequency plane. The c r i t i c a l growth f a c t o r s obtained from the v a r i o u s approaches are s i m i l a r w i t h the exception of a u s u a l l y s m a l l f a c t o r . Gueret2 1970 using the Kino and Robson approach obtained a c r i t i c a l t h i c k n e s s to l e n g t h r a t i o below which the conventional one dimensional a n a l y s i s i s not v a l i d . G i a n n i n i , O t t a v i and Salsano 1970 c a r r i e d out a s m a l l s i g n a l a n a l y s i s on a t h i n Gunn diode i n which the r f e l e c t r o n flow was assumed to be i n the dc d r i f t d i r e c t i o n only ( i . e . the one dimensional problem). This one dimensional flow was imposed by 17 a s u i t a b l e magnetic f i e l d but the growth r a t e obtained was the same as that obtained by Hartnagel 1969 and d i f f e r e n t from the Kino and Robson 1968 only by a s m a l l f a c t o r . They concluded, t h e r e f o r e , t h a t the r f motion i s only i n the d i r e c t i o n of dc d r i f t and the boundary c o n d i t i o n i n the l a t e r a l d i r e c t i o n as used by Hartnagel 1969 and Kino and Robson 1968 and others i s not necessary to the s o l u t i o n of the problem. En-gleman^ 1970, w h i l e acknowledging the growth r a t e i s i d e n t i c a l using e i t h e r boundary c o n d i t i o n , disputes G i a n n i n i ' s et a l . 1970 c o n c l u s i o n that r f flow i s laminar. Giannini„ , „ et a l . 1970 and 1971 and 2 and 3 Englemann^ 1970 i n b r i e f comments do not appear to have yet c l e a r e d the p o i n t up. The f a c t that i d e n t i c a l growth ra t e s are obtained f o r the two types of boundary c o n d i t i o n s i s however s i g n i f i c a n t because the boundary c o n d i t i o n that Kino and Robson 1968 used was that i n i t i a l l y -used by.Hahn 1939 f o r .electron .beams ..in..^vacuum. I.t i s ..not .obvious .that t h i s boundary c o n d i t i o n when a p p l i e d t o c a r r i e r flow i n a semiconductor of l i m i t e d dimensions i s c o r r e c t , e s p e c i a l l y s i n c e they ignored the e f -f e c t of d i f f u s i o n . Gueret 1970 found the s m a l l s i g n a l impedance i n t h i n Gunn diodes by extending the Kino and Robson a n a l y s i s and obtained the s t a -b i l i t y c o n d i t i o n s f o r the diode's e q u i v a l e n t c i r c u i t which, again w i t h the exception of a numerical f a c t o r , was the same as that found by Kino and Robson. Gueret 1970 al s o quoted c o n d i t i o n s f o r LSA mode ope r a t i o n i n t h i n diodes. Hofmann^ 1972 has done a numerical a n a l y s i s of the general t r a n s c e n d e n t a l d i s p e r s i o n equations f i r s t quoted by Kino and Robson 1968. His exact computations show two forms of s t a b i l i t y c r i t e r i o n £ I £ I e x i s t , dependent on the value of . For 2 1 the s t a b i l i t y c r i -E I I £ I I 18 t e r i o n i s : n d e 4 v e T o I which n u m e r i c a l l y he quotes as: nde 11 -2 <: 2.1 x 10 cm e I I and f o r the case of — << 1 the s t a b i l i t y c r i t e r i o n i s : E I I nd <: 2.7 x 10 11 -2 cm which i s independent of The former i s compatible w i t h the Kino and Robson 1968 a n a l y s i s w h i l e the l a t t e r i s compatible w i t h the pre-vious Hofmann„ 1969 a n a l y s i s . on the Kino and Robson a n a l y s i s , and the c r i t i c a l growth f a c t o r assumed f o r the onset of i n s t a b i l i t i e s i s that used by Kino and Robson ( i . e . 3" L 2 17). Note al s o that the Kino and Robson 1968 value of c r i t i c a l growth f a c t o r i s clo s e to the value of 3" L = 15 which Hofmann 1969 obtained from the Briggs 1964 s t a b i l i t y c r i t e r i o n . The f o l l o w i n g ex-tensions to the Kino and Robson a n a l y s i s have been made, and are reported i n s e c t i o n 2.3. The Kino and Robson approximate d i s p e r s i o n r e l a t i o n -s h i p i s not used, r a t h e r the more exact d i s p e r s i o n r e l a t i o n s h i p i s s o l v e d n u m e r i c a l l y . From t h i s numerical s o l u t i o n a pulse propagation v e l o c i t y i s obtained as a f u n c t i o n of the diode th i c k n e s s and i s shown to decrease w i t h decreasing t h i c k n e s s . In the Kino and Robson 1968 approximate r e l a t i o n s h i p the pulse propagation v e l o c i t y i s indepen-dent of diode t h i c k n e s s . A l s o , the growth f a c t o r (3" L) i s c a l c u l a t e d n u m e r i c a l l y and shown to have an abrupt drop near the nd product which The s m a l l s i g n a l a n a l y s i s presented i n s e c t i o n 2.3 i s based 19 Kino and Robson 1968 and most other workers have taken to be the c r i t i c a l v alue f o r o s c i l l a t i o n suppression. 2.2.5 P l a n a r Diodes w i t h Surface C a p a c i t i v e Loading Kino and Robson without d e r i v a t i o n s t a t e that conducting sheets cl o s e to the surface of the diode modify the s t a b i l i t y c r i t e r i o n t o : £ I 11 -2 ndb3 $ 1.6 x 10 cm . . E I I 2 TT Taking the value o.t g = — — as taken by Becker, Bosch and Englemann e Li 1970 the Kino and Robson 1968 c o n d i t i o n f o r i n s t a b i l i t y suppression i n a Gunn diode w i t h c a p a c i t i v e s urface l o a d i n g becomes: E I ndb 10 -2 = 2.5 x 10 cm £ I I L where b i s the d i s t a n c e between the conducting l a y e r and the diode sur-face L i s the diode l e n g t h . This i s s i m i l a r to the i n s t a b i l i t y c r i -t e r i o n obtained from a t r a n s m i s s i o n l i n e analogy by Becker, Bosch and Englemann 1970: I ndb o I < which n u m e r i c a l l y i s E I ndb 9' -2 $ 1.2 x 10 cm £ I I L B e c k e ^ and Bosch 1970 i n a subsequent paper quote another c r i t e r i o n i n which the r i g h t hand s i d e i s 6 times l a r g e r . Although the a n a l y s i s was the same t h i s f a c t o r apparently r e s u l t e d from t a k i n g a growth time f o r a domain as one r a t h e r than t h r e e , growth time constants and from 20 assuming appreciable i n t e r a c t i o n between e l e c t r o n flow and c a r r i e r wave when t h e i r v e l o c i t i e s were equal r a t h e r than when the former was twice the l a t t e r . This new s t a b i l i t y c r i t e r i o n being n u m e r i c a l l y — — $ E I I L 9 -2 7.2 x 10 cm i s c l o s e r to the value quoted by Kino and Robson(1968). Suga 1969 i n a computer s i m u l a t i o n of a t h i n diode w i t h a d i s t r i b u t e d c a p a c i t i v e e l e c t r o d e on one s i d e showed that i f the capa-c i t a n c e exceeds a c r i t i c a l v a l ue, Gunn o s c i l l a t i o n i s i n h i b i t e d and a s t a t i c high f i e l d domain i s formed at the anode. He found f o r the case —8 3 of C £ 10 f/cm the e f f e c t of the capacitance was almost n e g l i g i b l e -7 " 3 and Gunn o s c i l l a t i o n was obtained, w h i l e a capacitance of C = 10 f/cm produced o s c i l l a t i o n suppression. His meaning of capacitance per u n i t volume i s obscure but i f i t i s taken to mean capacitance per u n i t area per u n i t diode thickness then t h i s corresponds to a suppression c r i t e r i o n of the order o f : £ I I > _ - 7 . b 10 d which ( f o r h i s values of n = l O 1 ^ cm 3 and L = lOOu)is e q u i v a l e n t t o : ndb £ I , , n l l -2 S 10 cm L e T I This r e s u l t i s compatible w i t h the numbers quoted by Kino and Robson 1968, Becker, Bosch and Engelmann 1970 and Becker^ and Bosch 1970. Sec-t i o n 2.4 contains the d e t a i l s of a s m a l l s i g n a l a n a l y s i s which d e r i v e s a s t a b i l i t y c r i t e r i o n which i s s i m i l a r to that reported by these authors, 2.2.6 Experimentally Observed O s c i l l a t i o n Suppression i n Thin  and D i e l e c t r i c a l l y Loaded Diodes. Analyses such as that of Kino and Robson 1968 p r e d i c t that a diode which supports Gunn o s c i l l a t i o n may not support such o s c i l l a t i o n 21 i f the diode i s imbedded i n a h i g h p e r m i t t i v i t y m a t e r i a l . Kataoka, Tateno, Kawashima and Komamiya 1968 had indeed reported having observed t h i s behaviour one month before Koyama, Ohara, Kawazura and Kumabe 1968 quoted the r e s u l t s of t h e i r s m a l l s i g n a l a n a l y s i s which p r e d i c t e d the be-havi o u r . Kataoka et a l . 1968 p l a c e d B a T i 0 3 sheets ( e r ~ 10,000 to 15,000) along the surface of a diode and found that although the diode produced Gunn . o s c i l l a t i o n - w i t h o u t the BaT-i-0^ such o s c i l l a t i o n was suppressed-with the BaTiO^ i n p l a c e . Vlaadringerbroek, Acket, Hofmann and Boers 1968 and Kuru and Tajima 1969 have observed that the r a t e of growth of a Gunn domain was reduced when a l a y e r of high p e r m i t t i v i t y m a t e r i a l (BaTiO^ f o r Vlaardingerbroek et a l . 1968 and SrTiO^ f o r Kuru et a l . 1969) was pl a c e d on the surface of p l a n a r diodes. Such a reduced growth r a t e was p r e d i c t e d by the Kino and Robson type of s m a l l s i g n a l a n a l y s i s . By v a r y i n g the p o s i t i o n of h i g h p e r m i t t i v i t y and semiconductor s l a b s on the diodes' surfaces Katoka, Tateno and Kawashima 1969 and Tez-ner 1971 r e s p e c t i v e l y have tuned the frequency of Gunn o s c i l l a t i o n s over s e v e r a l octaves. The frequency generated by such devices corresponds to the l e n g t h of diode not covered by s u r f a c e l o a d i n g . Kuru and Tajima 1969 observed that i f the diodes were not t h i n enough, the i n f l u e n c e of a high p e r m i t t i v i t y s u r f a c e m a t e r i a l was weak and " p a r t i a l l y suppressed" domain o s c i l l a t i o n was observed. S h o j i 1967, Tataoka, Tateno and Kawashima 1969 and Hofmann^ 1969 have shown that i n -creased e f f i c i e n c y or current wave-shaping can be obtained by the p r o -per choice of d i e l e c t r i c l o a d i n g or c a p a c i t i v e s u r f a c e l o a d i n g . The f i r s t systemmatic experimental examination of the c o n d i t i o n f o r o s c i l l a t i o n suppression i n t h i n Gunn diodes was that Kumabe 1968. He v a r i e d the c a r r i e r c o n c e n t r a t i o n of specimens of s e v e r a l t h icknesses 22 by v a r y i n g the temperature of o p e r a t i o n of the specimens and observed the fo ] l o w i n g : 11 -2 1) For nd > 5 x 10 cm s t a b l e o s c i l l a t i o n occurred, 11 -2 2) For nd < 1.1 x 10 cm no o s c i l l a t i o n occurred at any b i a s , 11 -2 11 -2 3) For 1.1 x 10 cm < nd < 5 x 10 cm i n c o h e r e n t . o s c i l l a t i o n occurred and the t h r e s h o l d v o l t a g e i n c r e a s e d as nd approached 1.1 x 10 cm Kumabe 1968 also found that the t h r e s h o l d v o l t a g e i n c r e a s e d as the d i e l e c -t r i c constant of the surrounding m a t e r i a l was i n c r e a s e d . Hofmann 1969 showed that dc f i e l d inhomogeneities due to dc f i e l d leakage from or near anode and cathode due to the n o n - i n f i n i t e dim-ensions of these contacts i n the tra n s v e r s e d i r e c t i o n i n h i b i t s the usual Gunn domain o s c i l l a t i o n . T his e f f e c t i s d i f f e r e n t from the leakage i n the region of a charge d i p o l e which i s assumed to be the cause of os-c i l l a t i o n suppression i n t h i n diodes. Hofmann^ and 't Lam 1972 and Hof-mann^ 1972 used a specimen h o l d e r f o r experimental t h i n diodes i n which the contact extended i n the transverse d i r e c t i o n w e l l outside the diode thus reducing the dc f i e l d inhomogeneity. By surrounding the t h i n diode by a i r or by high p e r m i t t i v i t y l i q u i d s such as d e - i o n i z e d water (e = 81) or g l y c e r i n e (e^ = 41) they observed the f o l l o w i n g : 1) There was l i t t l e d i f f e r e n c e i n diode performance w i t h d e i o n i z e d water as compared to g l y c e r i n e s u r f a c e l o a d i n g and 2) Heavy d i e l e c t r i c l o a d i n g suppressed o s c i l l a t i o n only i f the diode was s u f f i c i e n t l y t h i n . They concluded that t h e i r experimental r e s u l t s were c o n s i s t e n t w i t h two e I d i f f e r e n t s t a b i l i t y c r i t e r i a depending on whether was l a r g e r than £ I I or s m a l l e r than u n i t y as discussed i n the previous s e c t i o n . The obser-23 va t i o n s of Hofmann^ and ' t Lam 1972 and Hofmann^ 1972 also appear to be c o n s i s t e n t w i t h the p r e v i o u s l y mentioned observations of Kuru and Tajima 1969. 2.3 Small S i g n a l A n a l y s i s of the Thin F i l m Gunn Diode For the device shown i n f i g u r e 2.3 i t i s assumed that the e l e c -t r i c f i e l d can be synth e s i z e d by a sum of s i g n a l s of the form: E = E + E E (y) e j ( u t " B z ) o 1 J (2-1) where the s u b s c r i p t o denotes dc components and the s u b s c r i p t 1 denotes s m a l l s i g n a l ac components throughout. cathode 6/ anode Figure 2.3 C r o s s - s e c t i o n of a t h i n f i l m diode In t h i s treatment the s i g n convention shown i n f i g u r e 2.4 has been used to avoid negative signs throughout which a r i s e from the e l e c t r o n i c charge. This i s a common convention i n the l i t e r a t u r e on Gunn e f f e c t ( C a r r o l l 1970, Butcher 1965, McCumber and Chynoweth 1966) and i s used throughout the t h e s i s . ^ T + v V = lEdz cathode E electron -P~ v(E) anode Figure 2.4 The s i g n convention 24 The e f f e c t i v e c a r r i e r m o b i l i t y i n the z d i r e c t i o n i s (Kino and Robson 196 8) : Sv y z = SE and i n the y d i r e c t i o n i s : v y y = E The .small s i g n a l current components are: 6p 6p. j • = V P E. - D ~ A to e T E. - I K — (2-2) l y y o l y <Sy == cy I l y oy j . = u p E- + v p - D 7 A to e T E, + v p. - D - 7 — J l z z o l z o 1 6z = cz I l z o 1 6z where D i s the d i f f u s i o n c o e f f i c i e n t v i s the dc c a r r i e r d r i f t v e l o c i t y o J p i s the space charge d e n s i t y Gj. i s the p e r m i t t i v i t y of medium I ^ p o . V o ' to = and to = cy e.j. cz e The equation of c o n t i n u i t y i s : j l + j w p l = ° ( 2 _ 3 ) and Poisson's equation i s : I Taking V • E = (2-4) 1 e. E 1 = - V ^ (2-5) assuming cj>j = A cos ay exp j (tot - Bz) (2-6) 25 and combining equations 2-1 to 2-6 r e s u l t s i n : / O O 0 0 Da + a (23 D + a> + j (w - 3v )) + 3 (D3 + w + j (to - 3v )) = 0 cy o cz o (2-7) where a i s the transverse wave number and 3 i s the l o n g i t u d i n a l wave number The c o n d i t i o n at the diode surface i s : e n E y i n " e i E y i i = p i s ( 2 _ 8 ) where p i s obtained from the Hahn 1939 boundary c o n d i t i o n : d p l s 3 p l s i T = j u p l s = p 0 v y l " Vo ^ = P v + j 3 v p o y i O -LS or P v T ° y 1 1s j(oj - V q 3 ) and i s the p e r m i t t i v i t y of the surrounding m a t e r i a l With the p o t e n t i a l continuous across the boundary * I = * I I a t 7 = ± a ( 2 _ 9 ) where a i s the diode h a l f t h i c k n e s s . Since (j)^ simultaneously s a t i s f i e s Laplace's equation and the boundary co n d i t i o n s i t must be of the form: <J>1II = C exp [ j ( u t - 3z) - 3y] (2-10) S u b s t i t u t i n g (2-10) and (2-6) i n t o (2-9) r e s u l t s i n : A cos aa = C exp (~3a) (2-11) 26 Combining equations ' (2-8), (2-5), (2-6), (2-10) and (2-11) y i e l d s : e 3 (to- 6 V Q ) cttancca = ; — : r- (2-12) But Therefore 2 aatanaa =(aa) i f |aa| < 0.4 c (to-Bv ) ( a a ) Z = - , p . ° , (2-13) provided e i l 3 a 1 < I (2-14) E I I For the case of a GaAs diode surrounded by axr = 12 and E I i n e q u a l i t y (2-14) reduces to |ga| <2. Equation (2-7) can be r e w r i t t e n : „ 3 2 (D3 2 + a) + j ( u - B v ) ) ^ - cz o ,„ a = - (2-15) D(a +23 ) + to + i ( to-3v ) cy o 2 1 2 - 1 For GaAs, D ~ 100 cm /sec and to - 2 x 10 sec i f an e l e c -cy 15 -3 t r o n c o n c e n t r a t i o n of n = 2 x 10 cm i s used. The n o n - l i n e a r i t i e s of D, to and to w i t h e l e c t r i c f i e l d are ignored i n t h i s s m a l l s i g n a l cz cy ° 2 15 a n a l y s i s . The value of to , t a k i n g u = -2400 cm /v-sec and n = 2 x 10 J cz' . z o — 3 12 —1 2 5 —1 cm i s to = -10 sec . Therefore | DB ]<< | to | i f |g| < 10^ cm CZ C Z 2 , _ 2 , i „ .. . . . I „ I . ,«5._-l cy -g. 5 -1 ' From equation (2-15), |ct| < | B | , hence |D(a +28 ) | .« co i f | B | < 10' cm Therefore, under the c o n d i t i o n | B | < 10 cm equation (2-15) can be ap proximated by: 27 2 2 + 3 ( " - g v o ) ) a = " & a, +j ( c o-3vT" ( 2 _ 1 6 ) cy o The approximation i m p l i e s d i f f u s i o n e f f e c t s are n e g l i g i b l e f o r lower order s o l u t i o n s o f 3 ( i . e . the longer wave-length s o l u t i o n s ) . This i s al s o c o n s i s t e n t w i t h the conclusions of Dean 1969 and H e i n l e 1971 who also considered the e f f e c t of d i f f u s i o n . Equations (2-13) and (2-16) can be combined under the c o n d i t i o n s that|3a| < 2 and | B | < 1 0 5 cm 1 to y i e l d : u (Ba) ( 3 c z a ) ia = — a - n-~ (2-17) v J e V T + Ba £ I where a) u n q cz z cz v v e T o o I S u b s t i t u t i n g 3=3'+ jB" i n t o equation 2-17, s e t t i n g the r e a l and imaginary p a r t s equal to zero and e l i m i n a t i n g 3" r e s u l t s i n the d i s -p e r s i o n r e l a t i o n (w versus 3') 3 e T I 2 R ' e c z X 3 ' 2 " c z 2 X - (B' + 7 ^ ) X + ~ f~ = 0 (2-18) T TT TT 1 3' + — 3' + — aEj. ae^ where X = 23' + — - — . (2-19) a e T v I o 28 Figures 2.3a and 2.3b show the d i s p e r s i o n curves (to versus \l\ — 3 15 ~*3 B ' ) computed f o r n = 2 x 10 cm and n = 2 x 10 cm r e s p e c t i v e l y f o r v a r i ous values of ac^/e^. 2.3.1 Gunn Domain V e l o c i t y i n a Thin Gunn Diode With the diode o p e r a t i n g under steady s t a t e c o n d i t i o n s i n a r e s i s t i v e c i r c u i t , o s c i l l a t i o n occurs (Englemann and Quate 1967) i f the phase s h i f t i s B n'L - 2Trn, n = 1, 2 Lower harmonic s o l u t i o n s ( i . e . |(3a| < 2) are w r i t t e n i n the form: w (B ) = + ( ^ ) - (B ' - £ M n n L op Q , _ ZTT n L where terms of —ggT2 a n d higher i n the T a y l o r expansion are n e g l e c t e d . The v e l o c i t y of energy propagation of the wave should be ( S t r a t t o n 1941) the group v e l o c i t y (TTT) 0 provided the d i s p e r s i o n i s r e l a t i v e l y L s m a l l . The curvature of the d i s p e r s i o n curves of f i g u r e s 2.5a and 2.5b i s s m a l l e s p e c i a l l y f o r the s m a l l values of B' of i n t e r e s t . Briggs 1964 de r i v e d a pulse propagation v e l o c i t y equal to V = \T | 3 ^ B ' * w n e r e S ' * i s the value of B' which corresponds to maximum wave growth. According to Engelmann . and Quate 1967, maximum space charge 2ir growth occurs f o r B' = — . The domain propagation v e l o c i t y used here ' v d = NSB"1" g' = ' l s c o m P a t l b l e w i t h these r e s u l t s . L Shown i n f i g u r e 2.6 i s the domain v e l o c i t y computed from ( - -§T) . _ 2TT (normalized by the c a r r i e r d r i f t v e l o c i t y ) as a f u n c t i o n ^ ~ I T 14 -3 of n a E j / e ^ j . This curve i s v a l i d f o r n = 5 x 10 cm and L > 20 microns. Under these c o n d i t i o n s the very weak dependence o f domain 29 10 (b) 10' 10' 14 Figure 2.5 Dispersion Curves f o r (a) n = 2 x 10 (b) n 2 x 10 -3 cm 15 .2 10™ 10" naS 1 (cm-2) VP o Figure 2.6 Domain V e l o c i t y (normalized to the c a r r i e r d r i f t v e l o c i t y ) as f u n c t i o n of diode thickness and surface l o a d i n g . 31 v e l o c i t y on n and L i s not s u f f i c i e n t l y s i g n i f i c a n t to be shown i n f i g u r e 2.4. The computed domain v e l o c i t y as shown i n t h i s f i g u r e goes to zero 10 -2 at the thickness corresponding to n a ^Jz-^_ = 5.66 x 10 cm The preceeding s m a l l s i g n a l a n a l y s i s i s s t r i c t l y v a l i d only f o r the i n i t i a l stages of domain formation when the domain i s s t i l l s m a l l . The a c t u a l domain v e l o c i t y i s probably l e s s than that p r e d i c t e d by the s m a l l - s i g n a l - a n a l y s i s . The computer s i m u l a t i o n s of Torrens 1969 i n d i c a t e that under l a r g e b i a s c o n d i t i o n s the domain v e l o c i t y i n b u l k diodes i s about 1.4 x 10 ^ cm/sec during the i n i t i a l moments of formation and reduces to a steady s t a t e value of about 0.85 x 10^ cm/sec. 2.3.2 Condition f o r Zero Domain V e l o c i t y i n a Thin Gunn Diode The mathematical d e r i v a t i o n that domain v e l o c i t y i s zero at 1 0 - 2 n a E T / £ - [ - j = 5.66 x 10 cm i s as f o l l o w s : Equation 2-19 y i e l d s the c o n d i t i o n that — -r^T = 0 ( i . e . zero v 63 o domain v e l o c i t y ) f o r -r-r-f- = 2. D i f f e r e n t i a t i n g equation 2-18 w i t h r e s -op pect to 3' and s u b s t i t u t i n g - r f f = 2 i n t o the r e s u l t y i e l d s : op x2 + 4(3' + — )x " 4(3' + — ) 2 + 3 2 = 0 (2-20) aEj. ae^. cz Rearranging, e T T I ~T~~2 1 X - 2(3' + T^-) [-1 + 2 ^ =• ] (2-21) V 4(3' +-71) a E I From equations (2-18) and (2-19), x must be r e a l p o s i t i v e s i n c e both 3' and co are r e a l p o s i t i v e . In order t h a t x he r e a l p o s i t i v e i n equation (2-21) the c o n d i t i o n ; 3 2 + 1 < J 2 — < + V2 ( 2 - 2 2 ) 4 ( 3 ' + ^ ) a E I must h o l d . Using the approximation v^ T * | (1 +X ) (2-23) f o r v^ X - 1 then equation (2-21) becomes: 2 e 0 a E X » ( 3 ' + — } (1 - . ' ( — r ) (2-24) a e I 4 e I I Combining r e l a t i o n s 2-14, 2-19 and 2-24 y i e l d s ; a £ I ~ 2 . 1 4£^2 4g' -j e T T 3 L 2 C3 ' " I T T ' I I cz cz 1 c z 1 (2-25) f o r zero domain v e l o c i t y . But I3 I >> 43' f o r GaAs devices longer than about 20 microns 1 cz' 14 - 3 and n > 5 x 10 cm . The c o n d i t i o n f o r zero domain v e l o c i t y then reduces t o : a eT o V^ ET —- -nr-r " 2 - r - V (2-26) or ae 2v e i n n- — = I °i 1 = 5.66 x 1 0 i U cm (2-27) £ I I l ^ z l q Equation (2-27) agrees w i t h the c o n d i t i o n obtained n u m e r i c a l l y f o r zero 10 -2 domain v e l o c i t y , s p e c i f i c a l l y n a e ^ / e ^ = 5.66 x 10 cm 33 2.3.3 O s c i l l a t i o n Suppression i n a Thin Gunn Diode Since the maximum s m a l l s i g n a l charge d e n s i t y at the anode (z = L) of a device i n steady s t a t e o p e r a t i o n i s : P 1 = A exp 8" L exp j(tot ~ 8' L) (2-28) l a r g e p o s i t i v e valued s o l u t i o n s of 8" 1 correspond to l a r g e space charge growth w h i l e s m a l l values correspond to s m a l l growth. S u f f i c i e n t l y s m a l l growth i s a s s o c i a t e d w i t h a n o n - o s c i l l a t i n g diode. The value of growth f a c t o r 8" L below which no o s c i l l a t i o n i s obtained i s somewhat u n c e r t a i n because, as ex p l a i n e d i n the background to t h i s chapter, the experimen-t a l l y observed o s c i l l a t i o n suppression c r i t e r i o n has i n many cases been somewhat l a r g e r than v a r i o u s p r e d i c t e d values- The value of 8" 1 as-sumed here to correspond to o s c i l l a t i o n suppression i s th a t used by Kino and Robson 1.968 (8" L = .17) and i s clos e to the value used .by Ho.fmann^ 1969 (8" L = 15). This value has been demonstrated to provide a good match to the experimentally observed c o n d i t i o n of o s c i l l a t i o n suppression. The growth term (8" L) i s obtained by combining equations 2-17, 2-18 and 2-19 y i e l d i n g : L 8" L = — (2-29) a e T v I o The dependence of to on 8' was p r e v i o u s l y determined from equations 2-18 and 2-19 and t y p i c a l p l o t s are shown i n f i g u r e s 2.5a and 2.5b. The de-pendence of the growth term 8" L on th i c k n e s s parameter as computed • £ I I from equations 2-19 and 2-29 f o r v a r i o u s diode lengths and dopant con-c e n t r a t i o n s i s shown by s o l i d l i n e s i n f i g u r e 2.7. This f i g u r e shows an abrupt drop i n space charge growth f o r s u f f i c i e n t l y t h i n diodes i n a l l 35 cases. The diagonal dashed l i n e s are those obtained from the Kino and Robson 1968 approximate a n a l y s i s and as p r e d i c t e d by them are shown to give a good match to the more exact computations at s m a l l values of ae^ aEj. . At l a r g e r values of the computed 3" L curves, being m u l t i v a l u e d e I I E I I a £ I f u n c t i o n s of , have at l e a s t one s o l u t i o n of 3" L which i s s i g n i f i -£ I I c a n t l y l a r g e r than the approximate Kino and Robson 1968 s o l u t i o n . There-f o r e , l a r g e r space charge growth occurs than they p r e d i c t e d f o r these a £ I values of . Suppression of Gunn i n s t a b i l i t i e s occurs at values of £ I I a £ I f o r which s o l u t i o n s f o r 3" 1 do not e x i s t above the h o r i z o n t a l dotted E I I l i n e shown i n f i g u r e 2.7. This l i n e corresponds to a value of 3" L = 17 which i s the Kino and Robson 1968 o s c i l l a t i o n suppression c r i t e r i o n . The computed curves show that no s o l u t i o n s w i t h 3" L ^ 17 n a E I 10 -2 e x i s t f o r — S 5.66 x 10 cm Therefore, the computations i n d i c a t e e I I an o s c i l l a t i o n suppression c r i t e r i o n o f : n a e l _ ^ , . 1 0 -2 $ 5.66 x 10 cm E I I Sections 2.3.1 and 2.3.2 of t h i s t h e s i s have shown that the Gunn domain n a £ I 10 -2 v e l o c i t y was zero a l s o at the value of = 5.66 x 10 cm E I I Therefore, a s t a t i o n a r y domain i s p r e d i c t e d to occur at the value of naEj which corresponds to suppression of o s c i l l a t i o n . This i s compatible E I I w i t h the s t a t i o n a r y high f i e l d p r e d i c t e d by McCumber and Chynoweth 1966 f o r s u b c r i t i c a l l y doped bulk GaAs diodes and observed e x p e r i m e n t a l l y i n t h i n and d i e l e c t r i c a l l y loaded diodes by Kataoka, Tateno, Kawashima 36 and Komamiya 1968, Kuru and Tajima 1969, and Hofmann 1969. 2.4 O s c i l l a t i o n Suppression i n a Capacitively-Loaded Thin Gunn Diode I f metal p l a t e s are placed c l o s e to the surfaces of the t h i n f i l m Gunn diode as shown i n f i g u r e 2.8 the f i e l d p a t t e r n i s modified from the previous case of a n o n - c a p a c i t i v e l y loaded diode. Equation (2-10) becomes where b i s the distance between the s u r f a c e of the diode and the metal p l a t e . Equation (2-11) i s then modified t o , I I I 'C exp j(tot - Bz) s i n h 3 (b + a - y) (2-30) A cos aa = C s i n h 8b (2-31) V cathode anode z f i g u r e 2.8 C r o s s - s e c t i o n of a t h i n f i l m diode w i t h surface c a p a c i t i v e l o a d i n g Equation (2-12) then becomes: 8coth 8b atan aa = (2-32) I f the diode i s s u f f i c i e n t l y t h i n and the s e p a r a t i o n between 37 diqde and metal plate i s s u f f i c i e n t l y small then b < a << TgJ" * Under these conditions coth ftb = -r^ and equation (2-13) reduces to: p b 2 e I I (2-33) Combining equation 2-15 and 2-33 y i e l d s : gaEj The l i m i t s of v a l i d i t y of equation 2-34 are | 1 << 1 and |gb| << 1. 2 I Therefore |g 1 << 1 and hence equation 2-34 can be reduced to: £ I I 8 e T T j R - l f ~- — 2 ( 2 _ 3 5 ) 6 e 6 ab gj. B 2 S u b s t i t u t i n g 8 = 8' + j 8 " i n t o equation 2-35 and rearranging y i e l d s : e T T I 28'abE 8 ? 8" - - R [ - l + / l + ( — ] (2-36) where a b e I 3 c z 2 (28' ) « 1. e I I S u b s t i t u t i n g r e l a t i o n 2-23 i n t o equation 2-36 y i e l d s : 0 abs 8 8" = -8' — — (2-37) e l l The growth fa c t o r 8" L f o r waves i n a t h i n diode with capaci-t i v e surface loading then becomes: , ,2 ab£ 8" L = - K---f B . (2-38) L e T T cz 3 8 S u b s t i t u t i n g f o r 3 , equation 2-38 becomes: cz 2 (2TT) U q n abe 3 " L = ° (2-39) L v e T e T T o I I I Using the Kino and Robson c r i t e r i o n f o r o s c i l l a t i o n s uppression, 3 " L S 17, then equation 2-39 can be rearranged t o : n abe T . _ v e T o I $ __1^ _ o _ I ( 2 _ 4 0 ) L " l l ^ (27T)2 | V - l ' q or n dbe . $ 2.5 x 10 cm . (2-41) E I I This i s the c o n d i t i o n f o r o s c i l l a t i o n suppression i n a t h i n Gunn diode w i t h c a p a c i t i v e surface l o a d i n g , and as discussed i n s e c t i o n 2.2 i s s i m i -l a r to the c r i t e r i a quoted by Kino and Robson 1968, Becker, Bosch and Engelmann 1970 and B e c k e ^ and Bosch 1970. With c a p a c i t i v e surface l o a d i n g , the c o n d i t i o n f o r o s c i l l a t i o n suppression i n a t h i n Gunn diode (as shown by equation 2.41) i s depen-dent on the device length. The form of the r e l a t i o n s h i p i s however very s i m i l a r to the n o n - c a p a c i t i v e l y loaded case except a f a c t o r of the r a t i o of d i e l e c t r i c t hickness to device l e n g t h i s intro d u c e d i n t o the l e f t hand s i d e of the r e l a t i o n s h i p . 39 I I I . DEVICE FABRICATION 3.1 I n t r o d u c t i o n The diode lengths which are needed to produce Gunn o s c i l l a t i o n s at 1 Ghz and 10 Ghz are approximately 100 microns and 10 microns respec-t i v e l y . To produce t h i n f i l m devices of these dimensions a c c u r a t e l y , hi g h r e s o l u t i o n p h o t o l i t h o g r a p h i c techniques were r e q u i r e d . The f i r s t and second s e c t i o n s of t h i s chapter o u t l i n e 'the p h o t o l i t h o g r a p h i c methods used. These techniques are t r e a t e d b r i e f l y s i n c e d e t a i l e d reviews such as that of Glang and Gregor 1970 provide a comprehensive d i s c u s s i o n of these techniques. The t h i r d s e c t i o n describes the techniques used i n making e l e c t r i c a l contact to the devices and the p r o p e r t i e s of these contacts. Since the c o n d i t i o n s of contact formation had a considerable e f f e c t on the devices' performance these are discussed i n some d e t a i l . 3.2 Photographic Reduction Photographic masks were produced by reducing artwork by a f a c t o r of 40 to 100 times by the use of p r e c i s i o n photography. The artwork was produced using K e u f f e l and Esser "Cut 'n' S t r i p " mylar-backed a r t -work sheets. This i s a two l a y e r m a t e r i a l s p e c i f i c a l l y made f o r artwork production i n m i c r o - c i r c u i t f a b r i c a t i o n . The u l t r a - v i o l e t opaque l a y e r i s s t r i p p e d o f f i n the d e s i r e d p a t t e r n l e a v i n g a sharp, s t a b l e artwork o r i g i n a l . The photographic masks were produced i n the beginning phases of the study by photographing the artwork w i t h a V o i g t l a n d e r , V i t o C (Lanthar 2.8/50 Lens) 35 mm camera. The f i l m and exposure used were Kodak H 135 ("High Contrast, Extreme Resolution") f i l m at f/5.6 f o r 1/30 seconds. The artwork was i l l u m i n a t e d using two Photoflood #2 lamps, 40 3 f e e t i n f r o n t of the artwork and at 45° to i t . A camera to artwork distance of 16 f e e t 8 inches produced a r e d u c t i o n of 100 times. The r e s u l -t i n g photomasks had a minimum l i n e width of 10 microns (approximately 1000 l i n e s per i n c h ) . The c e l l u l o i d photomasks were then glued onto 2" x 2" x 0.04" glass s l i d e s f o r use i n t h e m i c r o p o s i t i o n e r as described l a t e r . During the l a t t e r p a r t s of the study, photomasks produced d i r -. .e.c.tly on 2" x. 2" .high r e s u l t i o n g l a s s s l i d e s were obtained from Shaw Photogrammetrie Services L t d * . These s l i d e s had sharper d e f i n i t i o n and were much e a s i e r to p o s i t i o n i n the m i c r o p o s i t i o n e r than the m u l t i -l a y e r e d s l i d e s . No attempt was made to determine the minimum l i n e width p o s s i b l e w i t h these s l i d e s but i t was l i k e l y somewhat l e s s than 10 microns. 3.3 P h o t o r e s i s t and E t c h i n g Techniques The device geometry was def ined"by exposing a "t-hin l a y e r -of p h o t o - s e n s i t i v e m a t e r i a l which covered the GaAs chip through appropriate photomasks. Kodak Thin F i l m R e s i s t (KTFR) d i l u t e d i n the r a t i o of 4:5 w i t h KTFR Thinner was the p h o t o s e n s i t i v e m a t e r i a l used. I t was a p p l i e d to the chip by e j e c t i n g through a 0.4 micron M e t r i c e l f i l t e r from a s y r i n g e and then by s p i n n i n g the flooded chip at approximately 2000 rpm f o r 15 seconds. The time from r e s t to f u l l speed f o r the spinner was a p p r o x i -mately one second. The l a y e r of KTFR was then prebaked f o r 12 minutes, 6 inches beneath a General E l e c t r i c i n f r a - r e d lamp (temperature a p p r o x i -mately 85° C). This l a y e r was approximately 0.9 microns t h i c k as measured usin g a Sloan Angstrometer. The f i r s t photomask and the r e s i s t covered chip were then p l a c e d i n the m i c r o p o s i t i o n e r which i s shown i n f i g u r e * Shaw Photogrammetrie Services L t d , 30 T h o r n c l i f f e P l a c e , Ottawa 6, Ontario. 41 3.1. This m i c r o p o s i t i o n e r allowed movement of the mask i n three d i m e n s i o n s . Figure 3.1 The m i c r o p o s i t i o n e r r o t a t i o n of the chip about an axis p e r p e n d i c u l a r to the face of the chip and t i l t of the mask with respect to the ch i p . The mask was p o s i t i o n e d i n the appropriate place on the chip by simultaneously observing through a Bausch and Lomb b i n o c u l a r microscope at x30 power. The mask was lowered i n t o contact w i t h the r e s i s t l a y e r on the chip and the r e s i s t was exposed f o r about 6 minutes and 15 seconds, 6 inches beneath a General E l e c t r i c u l t r a - v i o l e t lamp (#R-40). The r e s i s t was developed by immersing w i t h gentle a g i t a t i o n i n KTFR Developer f o r 1 minute and 30 seconds. This was followed by immersing i n KTFR Rinse, again w i t h gently a g i t a t i o n , f o r 30 seconds. The r e s i s t areas which were polymerized during exposure r e -mained a f t e r developing to pr o t e c t appropriate p o r t i o n s of the chip. The unexposed r e s i s t washed away l e a v i n g p o r t i o n s of the chip unprotected. These unprotected portions of GaAs were etched down to the substrate using an etch of 3H2SO^ : : H 20 (parts by volume). The etch rate was dependent on age and method of p r e p a r a t i o n of the etch. 42 The preparation method used which gave an etch rate of approximately 2.5 microns per minute when used a f t e r .15 minutes but before 2 hours o l d was: 10 ml of ^2®2 W a S a c ^ e ^ t o x ^ m^ °* ^2^' t ^ ^ s m : * - x t u r e ' w a s placed i n a cold water bath to di s s i p a t e the heat of reaction and 30 ml of ll^SO^ were slowly added. A f t e r etching down to the substrate a mesa with a photoresist cap remained. The. width of the mesa was to be the device length. An. a l l o y of gold-germanium as described i n section 3.4.3 was then deposited i n vacuum over the e n t i r e structure usually i n two de-po s i t i o n s , each at 45° to the chip surface. This ensured deposition of Au-Ge up the mesa walls. The top of the mesa was then cleaned of i t s r e s i s t and a l l o y layers by gently rubbing with a cotton swab soaked i n t r i c h l o r e t h y l e n e . The photoresist procedure was then repeated w i t h a photomask which defined the contact land areas and the device's width. The unwanted a l l o y was removed by etching f o r several seconds i n aqua r e g i a (3 HCI : KNO^ by volume). The device edges were then smoothed by etching once again for several minutes i n 3H„S0, : H„0„ : H„0. The 2 4 2 2 2 fig u r e 3.2 A t y p i c a l diode (xlOO) W • " 43 device at t h i s stage then looked l i k e that shown i n f i g u r e 3.2, where the l i g h t e r areas at top and bottom l e f t are the Au-Ge contacts w i t h the center p o r t i o n being a r a i s e d mesa which i s the diode i t s e l f . The Au-Ge contacts were then a l l o y e d i n t o the GaAs to form an e l e c t r i c a l con-t a c t as described i n the next s e c t i o n . 3.4 E l e c t r i c a l Contacts 3.4.1 I n f l u e n c e of Contacts The importance of the anode and cathode boundary c o n d i t i o n s f o r bulk diodes i n determining whether Gunn i n s t a b i l i t i e s occur has been recognised by computer s i m u l a t i o n s (Kroemer 1968; Shaw, Solomon and Grubin 1969; Hasty, S t r a t t o n and Jones 1968; and Suga ? and Sekido 1970) and f i e l d of d i r e c t i o n analyses ( C o n w e l ^ 1970; and Boer and Dbhler 1969). A common weakness of a l l of these s t u d i e s i s that they do not t r e a t the case of imperfect contacts e x i s t i n g simultaneously at both anode and cathode. I r r e s p e c t i v e of t h i s omission the f o l l o w i n g conclusions of these papers should be v a l i d : 1) A p a r t i a l l y b l o c k i n g cathode a f f e c t s the operation of an otherwise i d e a l bulk Gunn diode by: a) Reducing the domain t r a n s i t l e n g t h and thereby i n -c r e a s i n g the frequency of Gunn o s c i l l a t i o n s (Kroemer; Suga et a l ) , b) Lowering the amplitude of Gunn o s c i l l a t i o n s (Kroemer; Suga et a l ; Hasty et a l ) , c) Reducing the s a t u r a t i o n current (Shaw et a l ; Suga et a l ; Conwell; Hasty et a l ) , d) Causing h y s t e r e s i s i n t h e c u r r e n t - v o l t a g e charac-44 t e r i s t i c (Conwell) e) .. Suppressing Gunn o s c i l l a t i o n s completely i f the contact i s s u f f i c i e n t l y b l o c k i n g (Suga et a l ; Hasty et a l ; Shaw et a l ; Conwell; Kroemer; Boer et a l ). 2) A p a r t i a l l y b l o c k i n g anode a f f e c t s the o p e r a t i o n of an otherwise i d e a l b u l k Gunn diode by: a) Lowering the amplitude of Gunn o s c i l l a t i o n s (Suga et a l ), b) Reducing the s a t u r a t i o n current (Suga et a l ) , c) Suppressing Gunn o s c i l l a t i o n s completely by formation of a high anode f i e l d which may be s u f f i -c i e n t l y l a r g e to cause impact i o n i z a t i o n (Hasty et a l ; Suga et a l ) . To ensure t h a t d i p o l e domains form completely and t r a n s i t the e n t i r e length of the device, Boer and Dohler 1969 conclude the cathode contact c o n d u c t i v i t y must be l e s s than the GaAs low f i e l d c o n d u c t i v i t y but greater than the c o n d u c t i v i t y a s s o c i a t e d w i t h the p o i n t at which the minimum s u s t a i n i n g current (as computed from the equal areas r u l e ) crosses the negative slope p o r t i o n of the J versus E c h a r a c t e r i s t i c . I n terms of the cathode e l e c t r i c f i e l d , Shaw et a l and Conwell conclude that i t must exceed the e l e c t r i c f i e l d a s s o c i a t e d w i t h the peak current i n the J versus E c h a r a c t e r i s t i c but must be l e s s than the e l e c t r i c f i e l d a s s o c i a t e d w i t h the crossover of the minimum s u s t a i n i n g current w i t h the negative slope p o r t i o n of the J versus E c h a r a c t e r i s t i c . In p r a c t i c e the Bo'er and Dohler requirement i s very s i m i l a r to that of Conwell and Shaw et a l . In the terminology of Boer and Dohler the cathode contact must be " s l i g h t l y 45 b l o c k i n g " i n order that dipole domain formation and t r a n s i t along the e n t i r e length of the device can occur. The properties of the anode contact are assumed by Boer et a l . and Conwell to have n e g l i g i b l e influence on the o v e r - a l l device p r o p e r t i e s . The computer simulations of Suga et a l . and Hasty et a l . i n d i c a t e t h i s i s not a v a l i d assumption. They both conclude that an anode contact which has one-half the c a r r i e r concentration of the body of the diode w i l l com-p l e t e l y suppress o s c i l l a t i o n by causing the formation of a stationary high f i e l d at the anode. Also, experiments performed by Harris et a l . using a vacuum deposited metal anode and an e p i t a x i a l n + cathode appear to support these computer simulations. However, the simulations i n d i c a t e that a reduction i n c a r r i e r concentration by ten percent at the anode has r e l a t i v e l y l i t t l e e f f e c t on the operation of the device and can be t o l e r a t e d . From the preceding discussion i t i s evident that the i n f l u e n c e of contacts on the performance of bulk diodes has been quite thoroughly i n v e s t i g a t e d from a t h e o r e t i c a l viewpoint. To date no s i m i l a r studies have been reported for the planar Gunn diode s p e c i f i c a l l y . I t seems probable however that the same b a s i c conclusions discussed above f o r bulk diodes also apply to planar diodes. The problem of making contacts to planar diodes appears i f anything to be more severe. A non-uniform f i e l d d i s t r i b u t i o n which can be caused by improper contacts, by the planar nature of the contacts and by surface states and other defects i n the planar e p i t a x i a l l a y e r appears to cause most of the problems. These e f -fects can combine to cause a high f i e l d at the anode which leads to l o -c a l i z e d heating and anode contact d e t e r i o r a t i o n . The most common f a i l u r e mode i n planar Gunn diodes ( C o l l i v e r and Fray 1969, Jeppsson and Marklund 1967, Dienst, Dean Enstrom and 46 Kokkas 1967, U l l r i c h . 1971, and Fallman and Hartnagel 1971) has been the m i g r a t i o n of anode metal across the diode causing the diode to be s h o r t c i r c u i t e d . A number of approaches have been used to overcome the problem of anode metal m i g r a t i o n which i s a s s o c i a t e d w i t h the simple a l l o y e d metal contact. Sekido, Takeuchi, Hasegawa and K i k u c h i 1969 have used n s o l u t i o n regrown l a y e r s covered w i t h evaporated m e t a l l i z a t i o n at both anode and cathode to o b t a i n CW o p e r a t i o n i n the 0.5 to 1 GHz range, Nakamura, Kurono, H i r a o , Toyabe and Kodera 1971 have used vapour phase I [ e p i t a x y i n preparing n contacts. Parkes, T a y l o r and C o l l i v e r 1971 used ++ a vapour phase grown n region at the anode only and an a l l o y e d metal contact at the cathode. Takeuchi, Higashisoka and Sekido 1972 and Fallman, Hartnagel and S r i v a s t a v a 1970, have used tapered diodes w i t h l a r g e r anode than cathode a n d , r e t a i n i n g the simple a l l o y e d metal contacts, found that •anode d e t e r i o r a t i o n was reduced. -Annular .structures (.which ..are i n p r i n c i p l e the same as tapered s t r u c t u r e s ) having a l l o y e d metal contacts have a l s o been shown by C o l l i v e r and Fray 1969, C l a r k e , Edridge and Bass 1969, and Jeppsson, Marklund and Olsson 1967 to be l e s s susceptible, to anode migra-t i o n than uniform devices. These devices are a l s o v o l t a g e tunable because of t h e i r taper as discussed i n s e c t i o n 4.4.3. Voltage tuning over greater than one octave has been reported by the l a t t e r two s e t s of authors. Adams 1969 found that CW o p e r a t i o n was o b t a i n a b l e w i t h a l l o y e d metal contacts by making a c o n s t r i c t i o n a t the cathode to provide a n u c l e a t i o n p o i n t f o r the Gunn domains. Boccon-Gibod, Teszner and Mautre 1972 have demonstrated that the form of Gunn i n s t a b i l i t y i n coplanar diodes i s i n -fluenced by the depth of the a l l o y e d metal c o n t a c t s . Adams 1969 and Takeuchi, Higashisaka and Sekido 1972 have observed that a diode o s c i l l a t e s at a lower frequency when operated w i t h a dc b i a s as opposed to a pulse b i a s . 47 Takeuchi et a l . 1972 have concluded that the d i f f i c u l t y i n ob-t a i n i n g coherent CW o s c i l l a t i o n i n planar Gunn diodes i s due to f i e l d d i s t o r t i o n caused by field-enhanced t r a p p i n g . The e f f e c t i s g r e a t e s t near the anode where trapped charge and f i e l d b u i l d up cummulatively w i t h successive domain passages through the t r a p s . They found t h a t t a p e r i n g the diode to have a wider anode than cathode tended to compensate f o r the field-enhanced t r a p p i n g and CW Gunn o s c i l l a t i o n was thereby o b t a i n a b l e f a i r l y r e p r o d u c i b l y . Hartnagel^ 1971 has observed t h a t the surface p r e p a r a t i o n of the p l a n a r diode a l s o a f f e c t s the coherence of the Gunn o s c i l l a t i o n s . This i s compatible w i t h the i n t r o d u c t i o n of surface s t a t e s by some surface p r e p a r a t i o n methods which may be s u s c e p t i b l e to field-enhanced t r a p p i n g e f f e c t s . Since "the a l l o y e d metal contacts -are easy'-to-make -and "there i s considerable i n f o r m a t i o n i n the l i t e r a t u r e on the p r o p e r t i e s of v a r i o u s a l l o y s t h i s c o n t a c t i n g method was chosen f o r t h i s study. 3.4.2 GaAs Cleaning P r i o r to the d e p o s i t i o n of contact metal the s u r f a c e of the GaAs was cleaned by the f o l l o w i n g s t e p s : a) Rinse i n t r i c h l o r e t h y l e n e b) Rinse i n e l e c t r o n i c grade acetone c) Rinse i n d i s t i l l e d water d) Etch i n 3 H^O^ : : H 20 e) Double r i n s e i n d i s t i l l e d d e i o n i z e d water (8 Mft -cm) f ) Rinse i n a c h e l a t i n g agent s o l u t i o n of 30 gm ethy-l e n e d i a m i n e t e t r a c e t i c a c i d (EDTA) : 20 ml 50% NaOH : 1000 ml of H 20 ( d i s t i l l e d and deionized) 48 g) Double r i n s e i n d i s t i l l e d d e i o n i z e d water. This r i n s e schedule and p a r t i c u l a r l y the r i n s e i n EDTA s o l u t i o n to remove any surface metal ions was found to be important i n o b t a i n i n g r e p r o d u c i b l e low r e s i s t a n c e contacts. 3.4.3 The A l l o y i n g Cycle Contacts to the GaAs were made by vacuum d e p o s i t i n g 88% by weight Au - 12% by weight Ge and a l l o y i n g as described by B r a s l a u , Gunn and Staples 1967 and H a r r i s , N a n i c h i , Pearson and Day 1969. To determine the optimum time and temperature a l l o y i n g c y c l e , a number of square t h i n f i l m specimens w i t h coplanar contacts were produced. These were subjected to a v a r i e t y of h e a t i n g schedules i n a molybdenum boat i n a hydrogen a t -mosphere of approximately two t o r r pressure. The temperature of the specimen was measured using an iron-constantan thermocouple cl o s e to the .specimen. The thermocouple was c a l i b r a t e d using the m e l t i n g p o i n t s of I n , Sn, Pb. Te, and A l . Near 450° C (the approximate temperature at which Au a l l o y s i n t o GaAs) the thermocouple was c a l i b r a t e d u s i n g the m e l t i n g p o i n t of AgCl (455° C). R e c a l i b r a t i o n u s i n g the m e l t i n g p o i n t of AgCl was done immediately p r i o r t o , or during the a l l o y i n g process f o r a l l devices made. The absolute accuracy of the temperature measurement i s estimated at + 5° C. The temperature as a f u n c t i o n of time f o r each a l l o y i n g c y c l e was recorded onaNesco chart recorder (Model JY1-20A-2). A t y p i c a l a l l o y i n g temperature c y c l e i s shown i n f i g u r e 3.3. The c o l o r of the Au-Ge contacts before a l l o y i n g was that of d u l l gold p l a t e . Upon h e a t i n g to 330° C, the m e l t i n g p o i n t of the Au-Ge mixture, the contacts took on a much s h i n i e r gold appearance. Upon he a t i n g to 425° C they changed to a d u l l e r s i l v e r - g o l d c o l o r . At 455° C the c o l o r became a more shiny gold c o l o r and t h i s change was accompanied 49 by a large drop i n contact resistance. Further heating to the range of 650° C to 700° C resu l t e d i n the contacts assuming a d u l l brown color which was associated with a much higher resistance. The a l l o y i n g tem-perature of 455° C + 5° C thus found was i n close agreement with the a l l o y i n g temperature of 450° C quoted by Harris et a l . zt=z ; / ! I. . ! i — zl 1= 600 500 1400 300 200 — 100 1 in/min Figure 3.3 A t y p i c a l a l l o y i n g cycle A f t e r a l l o y i n g , globules of Au-Ge had formed on the surface of the contact and occasionally were square i n shape as shown i n f i g u r e 3.4. Be v e l l i n g at approximately 5° to the surface showed that filaments of Au-Ge extended many microns i n t o the GaAs under the globules. Figure 3.5, a serie s of microphotographs at d i f f e r e n t depths of bevel , shows two filaments of a l l o y extending more than 5 microns i n t o the GaAs. To minimize the e f f e c t s of the non-uniformity of the contacts 5 0 Figure 3.4 Globules of Au-Ge a f t e r a l l o y i n g . (x400) caused by such globules and filaments, about 20% n i c k e l powder was added to the Au-Ge a l l o y and coevaporated i n a manner s i m i l a r t o that describe by Edwards, Hartman and Torrens 1972. This type of Au-Ge-Ni contact was used on devices made i n the l a t t e r p a r t of the study w i t h other a l l o y i n g steps remaining the same. 3.4.4 Low F i e l d Contact Resistance The low f i e l d r e s i s t a n c e of each t e s t specimen was measured and the contact r e s i s t a n c e was c a l c u l a t e d from the known r e s i s t i v i t y and thickness of the specimen. The r a t i o of contact r e s i s t a n c e to m a t e r i a l r e s i s t a n c e as a f u n c t i o n of a l l o y i n g temperature i s shown i n f i g u r e 3.6 and i s of the same form as reported by Paola 1970 and Knight and Paola 1968. The minimum s p e c i f i c contact r e s i s t a n c e as determined from -3 -4 2 f i g u r e 3.7 i s i n the range of 10 to 10 fi -cm . This i s comparable to the s p e c i f i c contact r e s i s t a n c e f o r a l l o y e d metal contacts to GaAs quoted by Cox and Strack 1967, Schwartz and Sarace 1966,. Knight and Paol Figure 3.5. Bevel showing filament penetration into GaAs (x 1000) D contact R material 10' / / / / / / / / / 10 0 \ / Temperature (°C) Figure 3.6 Contact r e s i s t a n c e as a f u n c t i o n of a l l o y i n g temperature 600 53 1968, and more r e c e n t l y by Edwards., Hartman and Torrens 1972. The spe-c i f i c contact r e s i s t a n c e t h e o r e t i c a l l y determined by Gupta, Sharma and Sreedhar 1971 f o r an n + -n ( n + = 5 x 10"*"^ ; n = l O ^ cm ^) GaAs j u n c t i o n —6 2 i s approximately 10 £2 -cm . Hence the measured value i s s e v e r a l orders of magnitude greater than the t h e o r e t i c a l value of Gupta et a l . Using a temperature of 465° C s e v e r a l specimens were heated f o r v a r i o u s lengths of time and t h e i r r e s i s t a n c e s measured. The contact r e s i s t a n c e as a f u n c t i o n of time at 465° C i s shown i n f i g u r e 3.7 10' 1.0' 10 0 R contact ^material 10 20 Time (sec) 30 Figure 3.7 Contact r e s i s t a n c e as a f u n c t i o n of a l l o y i n g time at 465° C. The minimum contact r e s i s t a n c e a s s o c i a t e d w i t h approximately 10 seconds a l l o y i n g time i s c l o s e to the value of 15 seconds quoted by H a r r i s et a l . and the r i s e i n contact r e s i s t a n c e upon h e a t i n g f o r longer periods has a l s o been noted by them. 54 3.4.5 Current - Voltage C h a r a c t e r i s t i c - Coherent and Incoherent  O s c i l l a t i o n Measuring the diode's low f i e l d r e s i s t a n c e as mentioned i n the previous s e c t i o n provided only a f i r s t i n d i c a t i o n of whether or not the diode would s u s t a i n Gunn o s c i l l a t i o n s . A b e t t e r i n d i c a t i o n was obtained by sweeping the device to h i g h f i e l d s w i t h a T e k t r o n i x T r a n s i s t o r Curve Tracer (575) and d i s p l a y i n g the r e s u l t i n g c u r r e n t - v o l t a g e c h a r a c t e r i s t i c . This technique a l s o enabled the o b s e r v a t i o n of approaching f a i l u r e due to avalanching without a c t u a l l y causing the f a i l u r e . Coherent o s c i l l a t i o n occurred i n devices which had a s a t u r a t i o n then a drop i n c u r r e n t at s u f f i c i e n t l y l a r g e v o l t a g e as shown i n f i g u r e 3.8. This behaviour i s c h a r a c t e r i s t i c of Gunn diodes, except the s a t -u r a t i o n current d e n s i t y observed i n a l l the coherent t h i n f i l m diodes i n t h i s study was a p p r e c i a b l y l e s s than that f o r uniform b u l k diodes. Hasty et a l . , Suga et a l . , Conwell, and Shaw et a l . have p r e d i c t e d that such a reduced s a t u r a t i o n current r e s u l t s from r e s i s t i v e contact l a y e r s . The observed reduced s a t u r a t i o n current i s t h e r e f o r e compatible w i t h the non-zero contact r e s i s t a n c e evident i n f i g u r e 3.7. Incoherent o s c i l l a t i o n i n the diode of f i g u r e 3.9 began at a b i a s of 43 v o l t s and remained u n t i l the b i a s was decreased below 36 v o l t s . Coherent waveforms w i t h a superimposed incoherent component as shown i n f i g u r e 3.10 were a l s o observed. The c u r r e n t v o l t a g e charac-t e r i s t i c r e s u l t i n g i n t h i s type of waveform showed both a tendency to s a t u r a t e and then an abrupt i n c r e a s e as shown i n f i g u r e 3.11. Figure 3 . 9 I-V c h a r a c t e r i s t i c of an incoherent diode 56 100 ma ^ f^A-^^W 7 nsec Figure 3.10 Waveform w i t h both coherent and incoherent components 3.4.6 The High Resistance Contact Layer - a cause of impact i o n i z a t i o n A t h i n r e s i s t i v e contact l a y e r has been observed by H a r r i s , N a n n i c h i , Pearson and Day 1969, Cox and Strack 1967 and has been a t t r i -buted to a high d i s l o c a t i o n density formed under the contact during a l l o y -i n g . R e l a t i v e l y t h i c k l a y e r s produced i n t h i s study by extended a l l o y i n g cycles were v i r t u a l l y i n s o l u b l e i n d i l u t e aqua r e g i a (3HC1 : HNO^ : H 20) whereas both the Au^ -Ge and GaAs i n d i v i d u a l l y were s o l u b l e . This i m p l i e s a l a y e r which was probably an i n t e r m e t a l l i c compound of the Au, Ge, Ga, and As system also forms upon a l l o y i n g . I r r e s p e c t i v e of the cause of the hi g h r e s i s t a n c e l a y e r Hasty, S t r a t t o n and Jones 1968 and Suga and Sekido 1970 have p r e d i c t e d t h a t i t s ex i s t e n c e at the anode can cause the e l e c t r i c f i e l d i n t h i s r e g i o n to be s u f f i c i e n t l y l a r g e to cause impact i o n i z a t i o n of c a r r i e r s . The i n -creased number of c a r r i e r s produced by such i o n i z a t i o n would reduce the r e s i s t a n c e at the contact and cause the jump i n current shown i n f i g u r e s 3.9 and 3.11. 57 V 20 volts Figure 3.11 I-V c h a r a c t e r i s t i c of a diode whose waveform has both coherent and incoherent components. The voltage along the specimen was probed to determine i f the anode f i e l d i n a diode w i t h poor contacts was indeed l a r g e enough to cause impact i o n i z a t i o n . Sze 1969 obtains a t h e o r e t i c a l impact i o n i z a -t i o n f i e l d i n a GaAs abrupt j u n c t i o n of approximately 3 x 10"* v/cm. Other workers(Copeland^ 1966 and Thim and Knight 1967)have used impact i o n i z a t i o n f i e l d s i n the range of 10^ to 2 x 10^ v/cm. To measure the f i e l d along the device a seven micron diameter tungsten w i r e was sup-ported i n the f o c a l plane of a m e t a l l u r g i c a l microscope and the device was moved on the microscope stage across t h i s probe w i r e . The p o s i t i o n of the probe r e l a t i v e to the device's cathode was measured using an eyepiece r e t i c l e . The voltage across the diode was a p p l i e d by sweeping w i t h a T e k t r o n i x 575 Curve Tracer which allowed simultaneous o b s e r v a t i o n 58 of the c u r r e n t - v o l t a g e c h a r a c t e r i s t i c . The probe v o l t a g e was measured on a T e k t r o n i x 515A o s c i l l o s c o p e . The p o s i t i o n a l : a c c u r a c y of the probe was estimated at +3.5 microns which was the r a d i u s of the probe w i r e . The v o l t a g e d i s t r i b u t i o n s along one diode (which was 110 microns long) f o r two values of peak a p p l i e d v o l t a g e are shown i n f i g u r e 3.12. The lower curve corresponds to an a p p l i e d v o l t a g e s l i g h t l y l e s s than t h a t corresponding to the jump i n current and consequent noise generation. The upper curve corresponds to an a p p l i e d v o l t a g e which i s c o n s i d e r a b l y l a r g e r than that necessary to i n i t i a t e noise generation. The d i s t r i b u t i o n of e l e c t r i c f i e l d f o r these two cases i s shown i n f i g u r e 3.13. The dashed p o r t i o n s of these curves are a r e s u l t of being unable to a c c u r a t e l y measure the voltage c l o s e to the anode because of the f i n i t e t h ickness of the probe w i r e . The curve i n which the e x t r a p o l a t e d p o r t i o n exceeds 10^ v/cm c o r -responds to an a p p l i e d voltage s l i g h t l y l e s s than t h a t r e q u i r e d to cause noise generation. I t appears from t h i s e x t r a p o l a t e d curve t h a t the f i e l d at the anode was indeed s u f f i c i e n t l y l a r g e to cause impact i o n i z a t i o n . The a d d i t i o n a l c a r r i e r s generated by t h i s impact i o n i z a t i o n caused the sudden jump i n cu r r e n t and the f l u c t u a t i o n s i n the cu r r e n t arose from the random nature of the generation recombination process. 3.4.7 Impact I o n i z a t i o n Noise Spectrum The noise spectrum of a diode w i t h poor contacts was found to be a f u n c t i o n of the a p p l i e d v o l t a g e . At voltages not much grea t e r than the t h r e s h o l d v o l t a g e the spectrum was u s u a l l y s i m i l a r to t h a t shown i n f i g u r e 3.14. The s p e c t r a shown here were observed on a Hewlett-Packard 855/B Spectrum Analyser which has a f l a t (+ 2db) response over the 10 MHz to 2 GHz range shown. The p a r t i c u l a r diode from which f i g u r e s 3.14 and 3.15 were obtained was approximately 105 microns l o n g and 1.25 microns F i g u r e 3.12. P o t e n t i a l d i s t r i b u t i o n along a diode w i t h poor contacts Figure 3.13. E l e c t r i c f i e l d d i s t r i b u t i o n along a diode w i t h poor cont a c t s . 60 V (mv) 100 H 0.5 1.0 1.5 frequency (GHz) Figure 3.14 Noise spectrum of a diode b i a s e d s l i g h t l y above the t h r e s h o l d v o l t a g e t h i c k . The frequency generated by a device of these dimensions should have been l e s s than one GHz i f the device were operating i n the pure Gunn mode. The peak at approximately 1.8 GHz shown i n f i g u r e 3.14 moved to the l e f t ( i . e . to lower frequency) and diminished i n amplitude as the diode b i a s was i n c r e a s e d . At a v o l t a g e of about twice the t h r e s h o l d v o l t a g e the spectrum was that shown in> f i g u r e 3.15. The movement of the peak to the l e f t i s compatible w i t h i t s major frequency component being caused by a d i p o l e domain which t r a n s i t s only p a r t of the device's l e n g t h . Such a p a r t i a l t r a n s i t according to Kroemer 1968 and Suga and Sekido 1970 can r e s u l t from a s u f f i c i e n t l y r e s i s t i v e cathode contact. I n c r e a s i n g the b i a s voltage increases the length of the t r a n s i t r e g i o n and hence lowers the o s c i l l a t i o n frequency as observed. The n o i s e spectrum due s o l e l y to generation and recombination of c a r r i e r s according to van V l i e t 1958 i s given by: (bN+P) (N+P) (l+o) T ) 61 V (mv) 100 i 10 0.5 frequency (GHz) Figure 3.15 Noise spectrum of a diode b i a s e d at twice the t h r e s h o l d voltage —2 °° where P(w) i s defined by I ( t ) = / P(to) da) I = the device t o t a l current b = e l e c t r o n m o b i l i t y / h o l e m o b i l i t y 4 N,P = t o t a l number of f r e e e l e c t r o n s and holes i n the device r e s p e c t i v e l y T = c a r r i e r l i f e t i m e Sharma and van V l i e t 1970 show that f o r m a t e r i a l s l i k e GaAs f o r which b >> 1 t h i s can be reduced to an rms n o i s e current expressed by: 2 I 2 P x ( 3 > 2 ) e q e(N+P) N(l+co 2x 2) Under c o n d i t i o n s of impact i o n i z a t i o n the values f o r N and P are d i f f i c u l t to determine e x a c t l y . Since the f r a c t i o n a l i n c r e a s e i n current at the onset of noise generation i s about 10% i t i s assumed that N = 1.1 n x device volume o = 1.1 n l t w o and P = 0.1 x N 6 2 For a c a r r i e r l i f e t i m e of 3 x 10 seconds amd the appropriate dimen-sions and e l e c t r o n concentration the noise voltage across the 50 ohm load i s c a l c u l a t e d to be the value shown by the dashed l i n e i n f i g u r e 3.15. W i t h i n the accuracy of e s t i m a t i n g the free e l e c t r o n and hole con-c e n t r a t i o n s t h i s curve provides a reasonably good match to the observed spectrum. A c a r r i e r l i f e t i m e (T) of 3 x 10 seconds i s used so that the shoulder i n the spectrum occurs at the value of 0.5 GHz as observed. I f the c a r r i e r l i f e t i m e i s 3 x 10 ^ seconds and i t s d r i f t v e l o c i t y i s about 10^ cm/sec then the mean d r i f t distance before recombining i s about 30 microns. This i s compatible w i t h U l l r i c h ' s 1971 observation by covering a p o r t i o n of h i s diodes that 80% of the recombination r a d i a t i o n i n h i s planar Gunn-effect devices occured w i t h i n 40 microns of the anode. 3.4.8 Anode L i g h t Emission The generation and recombination process also gives r i s e to the emission of low i n t e n s i t y l i g h t at the anode as shown i n f i g u r e 3.16. Figure 3.16 Diode showing emitted l i g h t at the anode (x400) curve tracer ( Tektronix 575) diode s monochromator (Bausch and L omb 33 86 03) photomultiplier (Phillips ACV 150 S1) recorder (Nesco JY1 20A 2) lock-in amplifier (PAR HR 8) Figure 3.17 L i g h t spectrum measurement system 64 The microphotograph i n figure 3.16 was taken i n two stages: f i r s t the p l a t e was exposed at f/8 f o r 1/30 sec wit h i l l u m i n a t i o n of the diode from the microscope lamp; second, w i t h the. microscope lamp turned o f f and the device operating cl o s e to breakdown the anode l i g h t emission was recorded (without moving the device) by exposing the same p l a t e f o r about one minute. The frequency spectrum of t h i s l i g h t was measured using the system shown d i a g r a m a t i c a l l y i n f i g u r e 3.17. The r e s u l t i n g emission spectrum i s shown i n f i g u r e 3.18. The peak i n t e n s i t y at 8900 + 200 A 0 corresponds to an energy of 1.40 + 0.03 eV. j... ..... INTENSE TY — r> : . l 1 resolution. ,r \:F:\. * - < * • _.,.,-0 . ... : . I . f U „ o . . ^ . - > _ -'.Hi .1. -.:,!! •ri, vi . i \~ y. a . . r ._.l...o r r f . :.n.-!r:r.".:.! «i.vi: 7.7 l z 7.0 .9 . 8 WAVELENGTH ( p ) .7 Figure 3.18 Spectrum o f emitted l i g h t at the anode of a GaAs diode, 65 The band gap i n GaAs at 300° C i s (Neuberger 1965) i n the range from 1.37 eV to 1.435 eV depending on impurity concentration. Therefore, the main recombination process occurs between states very near the conduc-t i o n and valence bands. The existence of l i g h t i n the v i s i b l e range as observed under x400 magnification, though below the s e n s i t i v i t y of the measuring apparatus, implies a c a r r i e r t r a n s i t i o n of several electron v o l t s . Therefore some recombination must also occur between excited s t a t e s . Electroluminiscence from GaAs Gunn diodes has also been observed by Acket and Sheer 1969 (8900 A°), Hasty et a l . ( 10,000 A ° ) , Heeks 1966 (9000 A°), Chang, L i u and Prager 1966 (9000 A°), Southgate 1967 (8900 A°), L i u 1966 (9000 A°), U l l r i c h 1971 (9000 A°) , and Chynoweth, Feldmann and McCumber 1966 (9000 A°). The i n t e n s i t y of r a d i a t i o n increased with applied voltage as •shown i n figure 3.20. The form of -this p l o t -is s i m i l a r .to .that .of-Ul-l r i c h 1971. V Figure 3.19 Radiation intens.ity dependence on applied voltage. The emission of l i g h t at the anode provided an i n d i c a t i o n that 66 the a p p l i e d v o l tage was c l o s e to the breakdown v o l t a g e f o r the devices as discussed i n the next s e c t i o n . 3.4.8 Anode Metal M i g r a t i o n and Device F a i l u r e Extended operation at high voltages caused f i l a m e n t s of metal to grow from the anode toward the cathode as shown i n the s e r i e s of micro-photographs i n f i g u r e 3.20. This s e r i e s covered a time span of about 20 minutes. The f i l a m e n t s u s u a l l y grew at p o i n t s at which l i g h t emission was most i n t e n s e . The growth of any p a r t i c u l a r f i l a m e n t of metal occurred too q u i c k l y to see, but was sometimes preceded by s e v e r a l seconds by darkening or v o i d i n g of the anode metal at the p o i n t at which growth was about to occur. Both of these p o i n t s have been noted by Jeppsson and Marklund 1967. The sudden appearance on the s u r f a c e of a s t r i n g of m e t a l l i c globules each up t o 2 microns i n diameter then f o l l o w e d . The anode d i s c o l o r a t i o n and the s p h e r i c a l shape of the globules i n d i c a t e the metal was molten during i t s m i g r a t i o n . The metal migrated i n the same d i r e c t i o n that p o s i t i v e metal ions would move under the i n f l u e n c e of the a p p l i e d f i e l d . Therefore, the mass t r a n s p o r t mechanism observed i n s i n g l e component metal f i l m s of e l e c t r o n s t r a n s f e r r i n g momentum to metal atoms by s c a t t e r i n g (Black 1969) was not dominant here. Furthermore, the movement of metal down a temperature gradient i s not appropriate s i n c e anode metal was scavenged from w e l l i n t o the anode area and moved over a probable temperature peak at the avalanching contact edge. I t i s concluded, t h e r e f o r e , metal m i g r a t i o n i s l i k e l y due to e l e c t r o s t a t i c a t t r a c t i o n of the cathode on p o s i t i v e metal ions which are r e l a t i v e l y mobile by v i r t u e of the metal being molten. Anode m e l t i n g has a l s o been observed by C o l l i v e r and Fray 1969 and Jeppsson and Marklund 1967. The l o c a l h e a t i n g which melted the anode metal was l i k e l y generated by a Figure 3.20. Metal migration and anode l i g h t emission from a device undergoing breakdown ( x 400) 68 combination of r e s i s t i v e heating and impact i o n i z a t i o n . During f i n a l breakdown the f i l a m e n t s of metal extending from anode to cathode were observed to be molten. B e v e l l i n g across such a f i l a m e n t showed pen e t r a t i o n beneath the surface of at l e a s t 4 microns as shown i n f i g u r e 3.21 Figure 3.21 Bevel across a conducting filament a f t e r breakdown Anode metal d e t e r i o r a t i o n under l a r g e b i a s c o n d i t i o n s has also been observed i n coplanar metal contact Gunn diodes by C o l l i v e r and Fray 1969; Dienst, Dean, Enstrom and Kokkas 1967; U l l r i c h 1971; and Jeppsson and Marklund 1967. 3.5 Device Mounting A s e r i e s of four devices on one chip were u s u a l l y f a b r i c a t e d at one time. These devices a f t e r f a b r i c a t i o n were separated by s c r a t -ching between them w i t h a hardened s t e e l s c r i b i n g t o o l , and breaking by applying l i g h t pressure from the back s i d e of the chip w i t h t e f l o n tweezers. An i n d i v i d u a l device was put on a brass mount as shown i n f i g u r e 3.22. 6 9 • y • Figure 3.22 A mounted diode The mount shown i n figure 3.22 was designed to f i t i n t o the tes t holder as discussed i n the next chapter. The mount body was e l e c -t r i c a l l y i s o l a t e d from the pins protruding from e i t h e r end of the mount. The diodes were glued to the. brass body with "Aron Alpha" Methylcyanoa-c r y l a t e adhesive. Wires were then connected between the i n s i d e ends of the mount contact pins and the diode's adjacent contact lands using "G.C. E l e c -t r o n i c s " s i l v e r paint. This s i l v e r paint was found to t o l e r a t e the device's heating during dc operation and produced quite s a t i s f a c t o r y contact to the Au-Ge contact lands. 70 IV. PLANAR GUNN DIODE EXPERIMENTAL APPARATUS AND RESULTS 4.1 I n t r o d u c t i o n The o s c i l l a t i o n frequency of p l a n a r Gunn diodes, as di s c u s s e d i n s e c t i o n 2.2, has o f t e n been observed to be l e s s than the frequency expected f o r bulk diodes of the same le n g t h . A l s o , the sm a l l s i g n a l a n a l y s i s contained i n s e c t i o n 2.3 p r e d i c t s a decrease i n Gunn domain v e l o c i t y w i t h decreasing nd product. No systematic experimental d e t e r -mination of the dependence of domain v e l o c i t y on the thic k n e s s of p l a n a r diodes has been reported i n the l i t e r a t u r e . The main purpose of the experimentation described i n t h i s chapter was to c a r r y out such a s y s -tematic examination. S e c t i o n 4.2 describes the t e s t apparatus used i n the experiments. S e c t i o n 4.3 contains a d i s c u s s i o n of the p r o p e r t i e s of the GaAs m a t e r i a l from which the diodes were made. The l a s t s e c t i o n contains the r e s u l t s e x p e r i m e n t a l l y obtained f o r diodes of va r i o u s geometries, thicknesses and doping co n c e n t r a t i o n s . 4.2 Test Apparatus 4.2.1 Diode C o a x i a l Holder To ensure t h a t the o s c i l l a t i o n s which the diodes generated were the r e s u l t of pure Gunn mode o p e r a t i o n ( i . e . charge d i p o l e formation and t r a n s i t ) i t was necessary to operate the diodes i n a r e s i s t i v e c i r -c u i t . A r e a c t i v e c i r c u i t can give r i s e to delayed or quenched mode os-c i l l a t i o n s which would confuse the e f f e c t of diode t h i c k n e s s on the os-c i l l a t i o n frequency. Since the a v a i l a b l e t e s t equipment had standard 50 ohm input terminations and s i n c e 50 ohm c o a x i a l f i t t i n g s are r e a d i l y a v a i l a b l e , the t e s t c i r c u i t was designed to have a c h a r a c t e r i s t i c im-pedence of 50 ohms. 71 The diode mount and coaxial holder used are shown i n figu r e 4.1. The outside diameter of the mount was 0.298 inches and the i n s i d e diameter of the holder was 0.696 inches, r e s u l t i n g i n a r a t i o of d i a -Figure 4.1 Diode mount and holder meters of 2.34. Elementary theory (for example Gray 1968) predicts that t h i s r a t i o of diameters i n an a i r centered c o a x i a l cable w i l l produce a c h a r a c t e r i s t i c impedence of 50 ohms. In order that the chip could be mounted, a f l a t side was made on the diode mount as shown i n figu r e 4.1. To ensure that neither this f l a t side nor the gaps between mount and the center conductor of the holder introduced appreciable r e a c t i v e components, the VSWR of the holder with a diode i n place was measured using the c i r c u i t of figure 4.2. The t r i g g e r countdown c i r c u i t i n fig u r e 4.2 i s a tunnel diode o s c i l l a t o r which generates steps with a r i s e time of les s than 40 p i c o -seconds. By observing the generated step and the r e f l e c t e d step from the diode and i t s holder on the sampling o s c i l l o s c o p e the standing wave r a t i o f o r the holder and diode was ca l c u l a t e d to be l e s s than 1.18. 72 holder 50 sampling head trigger count-down sampling oscilloscope Figure 4.2 VSWR measurement c i r c u i t T h is was only s l i g h t l y g reater than the maximum VSWR of the General Radio components (according to the GR s p e c i f i c a t i o n sheets) used i n the t e s t c i r c u i t . Since the VSWR of the -holder was comparable to that of the other components i n the t e s t c i r c u i t (low pass f i l t e r , c a p a c i t o r s and terminations) and l e s s than the VSWR of c a v i t y - t y p e holders u s u a l l y used to generate other t r a n s f e r r e d e l e c t r o n modes, i t was concluded the t e s t holder and diode assembly was s u f f i c i e n t l y n on-reactive to generate pure Gunn mode o s c i l l a t i o n s . This c o n c l u s i o n was v e r i f i e d by the success-f u l generation of pure Gunn mode o s c i l l a t i o n s as discussed i n s e c t i o n 4.4. 4.2.2 Test C i r c u i t The e n t i r e t e s t c i r c u i t i s shown s c h e m a t i c a l l y i n f i g u r e 4.3. The dc b i a s to the diode was a p p l i e d through the c o a x i a l center conductor and was i s o l a t e d from the measuring equipment by a 0.1 mfd c a p a c i t o r . Load r e s i s t o r . R-^  was the dc lo a d f o r the c i r c u i t and was a 50 ohm t e r -m i nation. Matching the diode h o l d e r assembly i n the forward d i r e c t i o n f o r microwave frequencies was accomplished by i n s e r t i n g a 3 db coupler voltage supply 4=r sampling head trigger count-down sampling oscilloscope F i g u r e 4.3 The d i o d e t e s t c i r c u i t 74 (which has a 50 ohm input at one termination i f the other terminations are loaded with 50 ohms) which allowed separation of the dc bias component from the microwave component. Matching i n the reverse dire c t i o n was ac-complished by i s o l a t i n g the power supply (which did not have a 50 ohm out-put impedence) with a 0.1 GHz low pass f i l t e r . Microwave signals were terminated i n the reverse direction through a 0.1 mfd capacitor by a 50 ohm termination (which i s l a b e l l e d i n figure 4.3). The primary measurement instrument was the Hewlett-Packard sampling oscilloscope (model 140A with a 1431A sampler head and a 1411A sampling am p l i f i e r ) . A secondary measurement instrument i n place of the 50 ohm termination marked was used i n most tests as w e l l . This se-condary instrument was variously a Hewlett-Packard power meter (model 430C) with Bolometer mount, a Beckmann frequency counter (model 6146) with model 607 or model 609 hetrodyne units, or a Hewlett-Packard spec-trum analyser* (model 855/B). Hence, t o t a l power, primary frequency component, or frequency spectrum could be measured simultaneously with the observation of current waveform. The frequencies measured on the frequency counter, the spec-trum analyser and the sampling oscilloscope a l l agreed with one another within 0.6%, and also agreed, to the same accuracy, with the s i g n a l out-put of a Hewlett-Packard sweep generator (model 8690B). 4.2.3 Device Geometries During the course of this work a number of device geometries as shown i n figure 4.4 were used. To reduce the tendency for breakdown to occur at the anode, many devices with enlarged anodes (figure 4.4(c)) and tapered devices with broader anodes than cathodes (figure 4.4(d)) * The spectrum analyser was the property of Lenkurt E l e c t r i c Co. Ltd. and was used with t h e i r consent and assistance. 75 Figure 4.4 Diode geometries studied / b were made. These l a t t e r d e vices, when they operated c o h e r e n t l y , could be v o l t a g e tuned as discussed i n s e c t i o n 4.4.3. In an e f f o r t to promote coherence many devices w i t h c o n s t r i c t e d cathodes ( f i g u r e 4.4(b)) a l s o were made. Most diodes were made i n the form o f mesas w i t h anode and ca-thode m e t a l l i z a t i o n extending up the mesa w a l l s . This was to minimize current crowding and thus avoid l o c a l h e a t i n g . These s t e p s , however, were l e s s important i n o b t a i n i n g good diodes than was ensuring that the proper c l e a n i n g and a l l o y i n g c y c l e s were used. Of more than 200 diodes made, only about 10% produced co-herent o s c i l l a t i o n , about 80% operated i n c o h e r e n t l y and the remainder d i d not o s c i l l a t e . This low y i e l d of coherently o p e r a t i n g devices was due at l e a s t i n p a r t to the low value of nd product used i n the GaAs f i l m . As pointed out i n s e c t i o n 2.2, incoherent o s c i l l a t i o n from p l a n a r diodes w i t h s m a l l nd products has been observed by a number of other workers. Devices which had a s l i g h t broadening toward the anode as shown i n f i g u r e 4.4(d) tended to operate coherently more o f t e n than the other geometries. This i s i n agreement w i t h the observations of Takeuchi, Higashisaka and Sekido 1972 as discussed i n s e c t i o n 2.2.1. 4.3 GaAs P r o p e r t i e s Since the e l e c t r o n c o n c e n t r a t i o n and the n-type e p i - l a y e r t h i c k n e s s are the parameters which determine the domain v e l o c i t y , ac-cording to the s m a l l s i g n a l a n a l y s i s contained i n s e c t i o n 2.3, these parameters were measured on a l l wafers used. The thickness was obtained by b e v e l l i n g across the e p i - l a y e r at 5° and s t a i n i n g the j u n c t i o n between the n-type l a y e r and the semi-i n s u l a t i n g s u b s t r a t e by e l e c t r o d e p o s i t i n g copper from a c u p r i c f l u o r -77 oborate s o l u t i o n ( s e c t i o n 4.2.1). The b e v e l l i n g was c a r r i e d out by mounting the chip on an aluminum h o l d e r which had a s e c t i o n sloped at 5° from the base plane of the h o l d e r as shown i n f i g u r e 4.5. holder Figure 4.5 Edge view of the h o l d e r used f o r b e v e l l i n g The p r o t r u d i n g edge of GaAs was ground down by gently rubbing i n an emulsion of 0.05 micron alumina powder i n water on a glass p l a t e . The e l e c t r o n c o n c e n t r a t i o n -was -measured by -doing-Hail-e-ffe'ct measurements (Put l e y 1960) on van der Pauw 1958 c l o v e r - l e a f geometry specimens as shown i n f i g u r e 4.6. The contacts to the specimens were made using the Au-Ge-Ni, a l l o y , s i l v e r p a i n t schedule described i n s e c t i o n 3.4. The completed contacts were covered w i t h KTFR and the center p o r t i o n was etched (3H 2SO^ : H 2 0 2 : H 20) i n stages, w i t h H a l l measure-ments being taken on the p r o g r e s s i v e l y t h i n n e r devices. I n t h i s way c a r r i e r c o n c e n t r a t i o n p r o f i l e s through the e p i - l a y e r s were obtained. A cross-check of the t h i c k n e s s measured by b e v e l and s t a i n was a l s o obtained from the t o t a l time r e q u i r e d to etch through the f i l m . The c a r r i e r con-c e n t r a t i o n p r o f i l e s obtained f o r the wafers from which diodes were made are shown i n f i g u r e 4.7. The measured H a l l m o b i l i t y p r o f i l e s are shown i n f i g u r e 4.8. The t e r m i n a t i o n p o i n t of each l i n e i n these f i g u r e s marks the thickness of each e p i - l a y e r . 78 SlSl.I Mil 1 11! 1111H 11II11 40 .1 Figure 4,6 The van der Pauw e l o v e r - I e a f geometry (x50) The parameter of p a r t i c u l a r i n t e r e s t , as discussed p r e v i o u s l y , was the product of c a r r i e r c oncentration x t h i c k n e s s . The nd product can be exx>ressed d i r e c t l y from the H a l l measurements by: nd • .10 8 BI ~ V (4-1) where n i s the e l e c t r o n concentration (cm ) d i s the l a y e r thickness (cm) B i s the magnetic f i e l d (gauss) I i s the t o t a l current (amps) V, i s the H a l l voltage ( v o l t s ) q i s the e l e c t r o n i c charge (coul) Determining the nd product from equation (4-1) e l i m i n a t e d the need to determine an "average" c a r r i e r c o n c e n t r a t i o n or even to determine the l a y e r t h i c k n e s s , although t h i s was done s e p a r a t e l y . The measured values of nd product f o r the v a r i o u s wafers (which are l a b e l l e d a f t e r the Mon-santo* n u r n b er i ng seheme) are shown i n t a b l e 4.1. ^Monsanto, P . O . Box 8, St. Peters M i s s o u r i , 63376. 79 10 16 10 15 10 14 n (cm-3) 522-46 83&VI 170-65 j n L 8 16 Figure 4 . 7 . C a r r i e r c o n c e n t r a t i o n p r o f i l e s 18 x (]JL) 7000 \ 6000 5000 4000 Mh (cm^/v-sec) 838-01 +1 522-46 + 8 -ii—'— 16 18 x (ji) Figure 4 . 8 . H a l l m o b i l i t y p r o f i l e s 80 nd (cm 2 ) 11 11 11 J-2 wafer // 838-01 2.1 x 10 552-46 4.2 x 10 422-42 6.3 x 10 170-65 2.3 x 10-Table 4.1 The measured nd product of the GaAs e p i - l a y e r s 4.4 Domain V e l o c i t y i n Pl a n a r Gunn Diodes  4.4.1 Dependence on the nd Product Modes o f o s c i l l a t i o n other than the pure Gunn mode ( i . e . d i p o l e domain t r a n s i t along the e n t i r e l e n g t h of the device) can a r i s e i f the de-v i c e i s operated i n a r e a c t i v e c i r c u i t or i f i t s cathode contact i s s u f -f i c i e n t l y b l o c k i n g as discussed i n s e c t i o n 3.4.1. To ensure t h a t the domain v e l o c i t y determination was based on pure Gunn mode o s c i l l a t i o n , only spiked c u r r e n t waveforms s i m i l a r to th a t shown i n f i g u r e 4.9 were considered r e l i a b l e . This type of waveform i s c h a r a c t e r i s t i c of domain formation and t r a n s i t ( f o r example, Foyt and McWhorter 1966). F u r t h e r -0.5 nsec Figure 4.9 Gunn mode cu r r e n t waveform more, the length of the domain t r a n s i t was checked by making use of the 81 property that a domain, i n sweeping past p r o t r u s i o n s i n the diode, r e -produces these p r o t r u s i o n s i n the current waveform ( S h o j i 1967). By cor-r e l a t i n g the shape of the current waveform to the shape of the diode, as shown i n f i g u r e 4.10, an accurate and r e l i a b l e measurement of the domain Figure 4.10 C o r r e l a t i o n of current waveform to diode shape v e l o c i t y was o b t a i n a b l e . The a p p l i e d b i a s voltage V i s ( S h o j i 1967) equal to the domain excess voltage plus the voltage drop outside the domain V = V (x) + . (4-2) ex enydb (x) where V g x ( x ) i s the excess domain voltage b(x) i s the width of the diode Assuming the domain excess voltage does not change a p p r e c i a b l y , the per-centage increase i n current ( i n equation 4-2) caused by a domain sweeping past a widened p o r t i o n of the diode i s approximately equal to the per-centage increase i n the diode width. This assumption produces a value of current increase which i s a maximum allowable value because the domain excess voltage i s reduced somewhat as the domain sweeps past the widened 1.0 Vdx10-7 8 (cm/sec) .21 I 10 n I nd (cm'2) 10 12 i- - -Figure 4.11 Domain v e l o c i t y i n t h i n Gunn diodes as a f u n c t i o n of nd product 83 p o r t i o n . The amplitude s c a l e of the waveform shown i n f i g u r e 4.10 was 100 mv/cm across a 50 fi l o a d which corresponds to 2 ma/cm. Therefore, the magnitude of the secondary peaks on the current waveform (due to the domain passing the i r r e g u l a r i t i e s ) was about 0.5 ma. This represents a change of about 6% on the dc curr e n t l e v e l of 8 ma. This 6% change i s comparable to the percentage f l u c t u a t i o n evident i n the width of the diode shown i n f i g u r e 4.10. The domain v e l o c i t y determined from the coherent waveforms of other diodes, f o r which the c o r r e l a t i o n of secondary peaks could be made, i s shown i n f i g u r e 4.11 as a f u n c t i o n of the nd product. According to the s m a l l s i g n a l a n a l y s i s presented i n s e c t i o n 2.3, the domain v e l o c i t y should approach zero as the parameter na e^/e^j approaches a value of 10 -2 5.66 x 10 cm or t a k i n g = z and d = 2a, as nd approaches 1.132 11 -2 x 10 cm . The experimental - r e s u l t s -shown i n f i-gure 4 .-11 - i n d i c a t e t h a t the domain v e l o c i t y does indeed d i m i n i s h as nd becomes s m a l l e r . The dashed l i n e i n t h i s f i g u r e i s the domain v e l o c i t y determined from the s m a l l s i g n a l a n a l y s i s and i s based on a v e l o c i t y i n bulk m a t e r i a l of 10 cm/sec. The s h i f t of the experimental p o i n t s away from the t h e o r e t i c a l curve may be at l e a s t p a r t l y e x p l a i n e d by three c o n s i d e r a t i o n s . The f i r s t i s that the sm a l l s i g n a l a n a l y s i s should r e s u l t i n a h i g h e r domain v e l o c i t y than a c t u a l l y occurs because i t i s a p p l i a b l e only during the i n i t i a l stages of domain formation, which according to Torrens 1969 i s the moment of highest domain v e l o c i t y i n bulk diodes. Secondly, the a n a l y s i s i s based on a t h i n f i l m diode symmetrically loaded w i t h m a t e r i a l s of equal p e r m i t t i v i t y . A l l o t t i n g a value to the parameter n Q a e^/e.^ i n the p r a c t i c a l case of a diode w i t h a i r l o a d i n g on one fa c e , GaAs sub-s t r a t e l o a d i n g on the other f a c e , and surface s t a t e s l i k e l y e x i s t i n g at 84 each, i s t h e r e f o r e somewhat a r t i f i c i a l . For s i m p l i c i t y was taken to be equal to e^ .. The t h i r d c o n s i d e r a t i o n i s that the a n a l y s i s does not i n c l u d e the e l e c t r o n d r i f t v e l o c i t y dependence on b i a s v o l t a g e and hence a l s o ignores the dependence of domain v e l o c i t y on b i a s . This dependence was observed experimentally and i s reported i n the next s e c t i o n . The r e s u l t s shown i n f i g u r e 4.11 were a l l obtained w i t h an a p p l i e d v o l t a g e o n l y a few percent g r e a t e r than the t h r e s h o l d v o l t a g e and . i f the diodes had been of the bulk r a t h e r than t h i n f i l m type, should have e x h i b i t e d domain v e l o c i t i e s of approximately 1.5 x IO'' cm/sec. 4.4.2 Bia s Tuning of Uniform Gunn Diodes The frequency of o s c i l l a t i o n of a diode of uniform cross s e c t i o n i n a r e s i s t i v e c i r c u i t can be tuned over a few percent bandwidth by changing the b i a s v o l t a g e . The e x p l a n a t i o n f o r t h i s tuning i s provided by Butcher's 1965 "Equal Areas Rule". A d i s c u s s i o n of the equal areas r u l e i s contained i n most t e x t s d e a l i n g w i t h the Gunn e f f e c t ( C a r r o l l 1970, Hartnagel 1969, Watson 1969, Sze 1969) and i s not repeated here. I n b r i e f , the equal areas r u l e p r e d i c t s that an i n c r e a s e i n the b i a s a p p l i e d to a bulk diode i n c r e a s e s the peak domain f i e l d , decreases the f i e l d o u t s ide the domain, and decreases the domain v e l o c i t y . The f r a c t i o n a l change i n domain v e l o c i t y , and hence o s c i l l a t i o n frequency, i s r e l a t i v e l y s m a l l compared w i t h the l a r g e change i n b i a s which causes i t . Shown i n dashed l i n e s i n f i g u r e 4.12 i s the domain v e l o c i t y i n a uniform b u l k diode as a f u n c t i o n of b i a s v o l t a g e . This p l o t i s a r e s u l t of a p p l y i n g the equal areas r u l e , which i s modified by a f i e l d dependent d i f f u s i o n term as discussed by Copeland 1966, to a h y p o t h e t i c a l diode which i s i n -f i n i t e i n c r o s s - s e c t i o n , 15 microns long and has an e l e c t r o n c o n c e n t r a t i o n 15 -3 of 2 x 10 cm . Also shown i n f i g u r e 4.12 i s the domain v e l o c i t y 1.1 -7 vdx10 1.0 (cm/sec) .9 8 \ \ \ -x-10 15 20 V (volts) Figure 4.12. Bias tuning of a uniform Gunn diode. 86 observed experimentally i n a 1.4 micron t h i c k diode which, otherwise had approximately the same l e n g t h and e l e c t r o n concentration as the h y p o t h e t i c a l bulk diode. The reduced domain v e l o c i t y and increased t h r e s h o l d voltage due to the diode's f i n i t e t hickness and imperfect contacts r e s p e c t i v e l y are evident. The amount of s h i f t i n domain v e l o -c i t y f o r a p a r t i c u l a r change i n b i a s voltage i s , however, n e a r l y i d e n t i -c a l i n the two cases. I t appears from f i g u r e 4.12, t h e r e f o r e , that frequency c o n t r o l over a small range by v a r y i n g the b i a s i s p o s s i b l e i n the t h i n f i l m diode i n a manner very s i m i l a r to that f o r the bulk diode. 4.4.3 Bias Tuning of Tapered Gunn Diodes A much l a r g e r range of frequency t u n e a b i l i t y i s p o s s i b l e i f the diode i s tapered as shown i n f i g u r e 4.13. In t h i s c o n f i g u r a t i o n , Figure 4.13 A tapered diode (x400) the f r a c t i o n of the le n g t h of the device which s u s t a i n s Gunn o s c i l l a t i o n s i s determined by the b i a s v o l t a g e . Since t h i s l e n g t h determines the o s c i l l a t i o n frequency of the diode i n a r e s i s t i v e c i r c u i t , a f a i r l y l a r g e range of voltage t u n e a b i l i t y i s p o s s i b l e . Jeppsson, Marklund and Olsson 1967, C l a r k e , Edridge and Bass 1969, S h o j i 1966, and Bhattacharya 1970, 87 a l l report having observed a v o l t a g e tuneable bandwidth of approximately one octave i n tapered Gunn diodes o r i n pl a n a r diodes w i t h c o n c e n t r i c e l e c t r o d e s . The experimental p o i n t s i n f i g u r e 4.14 show the frequency o f o s c i l l a t i o n as a f u n c t i o n of a p p l i e d v o l t a g e obtained f o r the diode of f i g u r e 4.13. This diode was 17.5 microns t h i c k and had an e l e c t r o n 2.0 freq. (GHz) 15 10 x x 4 2 U 46 V (volts) 48 50 Figure 4.14 Bias tuning of a tapered diode c o n c e n t r a t i o n of 1.65 x 10 cm . A tuning range of somewhat l e s s than one octave was observed. This diode c o n f i g u r a t i o n , however, was not optimized f o r maximum tuning. Shown as a s o l i d l i n e i n f i g u r e 4.14 i s the frequency c a l c u l a t e d according to the f o l l o w i n g model: Igno r i n g the current n o n - l i n e a r i t y as w i l l be d i s c u s s e d , the vo l t a g e at any p o s i t i o n x along the l e n g t h of the diode i s given by: 88 \V d x V ( x ) Vapp L.'' dx (4.3) o W(x) where V i s the a p p l i e d v o l t a g e app r ° and W(x) i s the diode width at p o i n t x. The e l e c t r i c f i e l d at t h i s p o i n t i s : »w • V dx (4'4) The p o i n t on the diode at which the e l e c t r i c f i e l d equals the minimum f i e l d f o r o s c i l l a t i o n determines the l e n g t h of the region of o s c i l l a -t i o n . The frequency, determined from the l e n g t h of the r e g i o n of o s c i l l a t i o n , as a f u n c t i o n of a p p l i e d v o l t a g e f o r the diode of f i g u r e 4.13, and assuming a minimum s u s t a i n i n g f i e l d of 2.7 Kv/cm and a domain v e l o c i t y of 10^ cm/sec, i s shown by the s o l i d l i n e i n f i g u r e 4.14. The t a c i t assumption i n v o l v e d i n i g n o r i n g the current non-l i n e a r i t y i n equation 4.4 i s that the r e d i s t r i b u t i o n of e l e c t r i c f i e l d w i t h i n the region of o s c i l l a t i o n upon formation of a domain, does not cause an appreciable s h i f t i n the p o i n t at which the e l e c t r i c f i e l d f a l l s below the minimum s u s t a i n i n g f i e l d . The reasonable match of the t h e o r e t i c a l r e s u l t to the experimental p o i n t s appears to add credence to t h i s assumption. 89 V. THE NEGATIVE RESISTANCE FIELD EFFECT TRANSISTOR (NERFET) 5.1 I n t r o d u c t i o n The i n i t i a l object of c o n s t r u c t i n g GaAs FETs was to determine the c o n d i t i o n s under which Gunn o s c i l l a t i o n would occur i n such FETs and to observe the e f f e c t of v a r y i n g the gate p o t e n t i a l on such o s c i l -l a t i o n . I t was found that only two devices d i s p l a y e d i n s t a b i l i t i e s apparently i n the GHz range and these were not proven to n e c e s s a r i l y be Gunn i n s t a b i l i t i e s . A l l other devices d i s p l a y e d a s t a t i c n e gative d i f -f e r e n t i a l r e s i s t a n c e (SNDR) without i n s t a b i l i t y , at v o l t a g e s g r e a t e r than a t h r e s h o l d . (The term s t a t i c a p p l i e s to the e x i s t e n c e of negative d i f -f e r e n t i a l r e s i s t a n c e down to very low f r e q u e n c i e s , i . e . q u a s i - d c ) . The FETs which d i s p l a y e d a s t a b l e SNDR c h a r a c t e r i s t i c are c a l l e d Negative Resistance F i e l d E f f e c t T r a n s i s t o r s (NERFETs) to d i s t i n g u i s h them from conventional FETs which d i s p l a y a s a t u r a t i n g current c h a r a c t e r i s t i c . This chapter i s d i v i d e d i n t o f o u r p a r t s . The f i r s t p a r t describes the devices' c o n s t r u c t i o n and c u r r e n t - v o l t a g e c h a r a c t e r i s t i c s . S e c t i o n two contains a d i s c u s s i o n of r e l a t e d devices as reporte d by o t h e r s , and l a y s the ground work f o r the d i s c u s s i o n i n the t h i r d s e c t i o n on the mechanisms which l i k e l y cause the SNDR. The f o u r t h s e c t i o n contains a d i s c u s s i o n of the o p e r a t i o n of NERFETs i n a number of c i r c u i t s . 5.2 The Co n s t r u c t i o n and C h a r a c t e r i s t i c s o f the NERFET  5.2.1 NERFET S t r u c t u r e and F a b r i c a t i o n The s t r u c t u r e s of the NERFETs were s i m i l a r to those of the diodes described i n s e c t i o n 4.2.3. The contacts were coplanar and the GaAs wafers from which the NERFET's were made were obtained from Monsanto* as n-type l a y e r s e p i t a x i a l l y deposited on p-type s u b s t r a t e s . The p-type s u b s t r a t e of the NERFETs (as opposed to the s e m i - i n s u l a t i n g *Monsanto, P.O. Box 8, St. P e t e r s , M i s s o u r i 63376 90 su b s t r a t e s of the diodes) allowed, however, gate c o n t r o l of the conducting channel i n the NERFET by the f i e l d - e f f e c t phenomenon (Shockley 1952). In p l a n view, a l l of the NERFETs, i n the source to d r a i n r e g i o n , were uniform as opposed to having notched cathodes and enlarged anodes as f o r the diodes. In c r o s s - s e c t i o n , however, s e v e r a l geometries were used as shown i n f i g u r e 5.1. The source to d r a i n distances were i n the range from 18 to 50 microns and the thicknesses i n the source to d r a i n r e g i o n were i n the range from ~ 0.1 to 5 microns. The c a r r i e r concentrations i n the n-1ayer were measured by two techniques, s p e c i f i c a l l y , H a l l e f f e c t and capacitance-voltage measurements. The H a l l e f f e c t measurements were the same as described i n s e c t i o n 4.3.2 f o r the n-type f i l m s on s e m i - i n s u l a t i n g GaAs. The e x i s t e n c e of a p-n j u n c t i o n , however, permitted the mea-surement of c a r r i e r c oncentration by measuring the ac capacitance as a f u n c t i o n of the reverse dc b i a s to the p-n j u n c t i o n . This i s a w e l l e s t a b l i s h e d (Meyer and Guldbrandson 1963, Amron 1964, Chang 1966, John-son and Panousis 1971 and D j u r i c , S m i l j a n i c and T j a p k i n 1971) technique f o r measuring doping p r o f i l e s . Provided one s i d e of the j u n c t i o n i s much more h e a v i l y doped than the o t h e r , that the m e t a l l u r g i c a l step between the two s i d e s i s abrupt, that a l l the i m p u r i t y centers are i o n i z e d and that any changes i n c a r r i e r d e n s i t y are s m a l l over a Debye le n g t h then the c a r r i e r c oncentration i s given by (Johnson and Panousis 1971): • CO - - | ff ( 5 - D where x i s the di s t a n c e from the m e t a l l u r g i c a l j u n c t i o n = e/C C i s the s m a l l s i g n a l ac c a p a c i t a n c e / u n i t area V i s the reverse dc b i a s v o l t a g e . 91 source drain yy s> S S S S S S S s n-GaAs gate p-GaAs (a) source y s / szz. drain •zzz-zzzzzzzi n-GaAs gate p- GaAs (b) source y y y ~2z dra in y s s s s n-GaAs gate p-GaAs ( c) Figure 5.1. Types of NERFET Geometries i n Cross-Section 92 The maximum depth i n t o the l a y e r which can be measured usi n g t h i s technique i s determined by the j u n c t i o n reverse breakdown v o l t a g e . The p-n j u n c t i o n s used had breakdown voltages i n the -25 to -30 v o l t range which l i m i t e d measurement to a maximum of about 1.5 microns i n t o the f i l m . The remaining thicknesses of the f i l m s were measured by p r o g r e s s i v e l y e t c h i n g H a l l specimens as discussed i n s e c t i o n 4.3.2. The capacitance-voltage measurement c i r c u i t used was that shown i n f i g u r e 5.2. The frequency at which the capacitance was measured was 1 MHz. dc voltage supply ± t [capacitance meter (Boon ton + 71A) x-y recorder Figure 5.2 Capacitance-voltage measurement c i r c u i t The capacitance versus v o l t a g e p l o t obtained f o r wafer 0856-02 from t h i s t e s t c i r c u i t i s shownin f i g u r e 5.3. The doping p r o f i l e s ob-t a i n e d using equation (5-1) from the C-V measurements f o r t h i s wafer and f o r wafer 0856-01 are shown i n f i g u r e s 5.4(a) and 5.4(b). The c a r r i e r concentrations obtained from the C-V measurements as shown by crosses i n f i g u r e 5.4 are compatible w i t h the H a l l e f f e c t measurements as shown by c i r c l e s . The c a r r i e r c o n c e n t r a t i o n was determined from the H a l l e f f e c t data by the r e l a t i o n s h i p (Putley 1960): 93 vbi Capacitance <00 (pf) 300 200 100 8 10 12 14 Reverse Bias (volts) 16 IB 20 Figure 5.3 T y p i c a l capacitance-voltage ..charac.ter,is.ti.c.-fo.r^.a..reverse b i a s e d p-n j u n c t i o n ( j u n c t i o n area = 0.0235 cm^) where: n = a/qR R = the H a l l C o e f f i c i e n t (5-2) tv. H IB (5-3) The value of a as measured by previous workers i s o n l y s l i g h t l y l a r g e r than u n i t y . W i l l a r d s o n and Duga 1960 measured a value of a = 1.07 at T = 300° K and B = 1.5 KGauss, and Hamerly. and H e l l e r 1971 measured a value of a = 1.10 under approximately the same c o n d i t i o n s . The p r o f i l e s shown i n f i g u r e 5.4 i n d i c a t e t h a t the concentrations determined from the H a l l data may be s l i g h t l y l e s s than those determined from the C-V data, hence a c a l c u l a t e d value of a s l i g h t l y g reater than u n i t y i s i m p l i e d . The scat-t e r of experimental p o i n t s however i s s u f f i c i e n t l y l a r g e to. negate the 94 Figure 5 . 4 E l e c t r o n c o n c e n t r a t i o n p r o f i l e s measured by C-V (cross and H a l l ( c i r c l e s ) methods 9 5 usefulness of making an adjustment i n the value of a. The accuracy of the measurement was t h e r e f o r e i n the range of 10 to 20%. A t y p i c a l c u r r e n t - v o l t a g e c h a r a c t e r i s t i c of a p-n j u n c t i o n had a turn-on v o l t a g e o f about 1.2 v o l t s and a very low leakage cu r r e n t as shown i n f i g u r e 5.5. (A b u i l t - i n v o l t a g e of about 1.2 v o l t s f o r a GaAs p-n j u n c t i o n of the c a r r i e r concentrations used here i s quoted by Sze 1969). Surface contamination which could cause a p p r e c i a b l e leakage current was the major problem a s s o c i a t e d w i t h the mesa s t r u c t u r e devices made i n t h i s study. Such leakage could be minimized f o r l i m i t e d p eriods ( s e v e r a l days) by c l e a n i n g the device i n the e t h y l e n e d i a m i n e t e t r a c e t i c a c i d s o l u t i o n and double r i n s i n g i n d i s t i l l e d , d e i o n i z e d water (~8 M Q -cm). Surface p a s s i v a t i o n would appear to be a b e t t e r long term s o l -u t i o n to the problem. The thickness of the e p i - l a y e r was measured by b e v e l l i n g at 5° as discussed i n s e c t i o n 4.3.1, c l e a n i n g the bevel w i t h acetone and d e i o n i z e d water and then e l e c t r o d e p o s i t i n g copper on the p s i d e of the j u n c t i o n from a 45% c u p r i c f l u o r o b o r a t e s o l u t i o n . The e l e c t r o d e p o s i t i n g 2 current of about 10 ma/cm of exposed p-type surface was a p p l i e d f o r about 5 seconds. The r e s u l t i n g j u n c t i o n looked as shown i n f i g u r e 5.6, w i t h the p-region being the dark area. The NERFETs were f a b r i c a t e d using the same b a s i c techniques which were used i n f a b r i c a t i n g the diodes as d e s c r i b e d i n s e c t i o n s 3 . 2 and 3.3. However, the type of photomasks used and the order i n which they were used was d i f f e r e n t because the s t r u c t u r e of the NERFET was d i f f e r e n t . The wafer was scribed,and broken i n t o chips about 2mm x 5 mm 9 6 F i g u r e 5 . 6 A b e v e l l e d a n d s t a i n e d p - n j u n c t i o n 97 which were l a r g e enough to allow the f a b r i c a t i o n of 4 devices on one chip. The chip was cleaned using the t r i c h l o r e t h y l e n e , acetone, d e i o n i z e d water, EDTA, d e i o n i z e d water sequence as discussed i n s e c t i o n 3.4.2. The chip was then placed i n the vacuum system and a l a y e r of Au-Ge-Ni metal was evaporated onto the chip s u r f a c e . The chip was removed from the vacuum, coated w i t h KTFR, spun and then prebaked. The f i r s t mask .consisted of a .tungsten w i r e ( i n .the .12 to 50 micron diameter range) s t r e t c h e d on a metal frame. Using t h i s mask the p h o t o r e s i s t was exposed and developed l e a v i n g a s t r i p (which was again 12 to 50 microns wide, depending on the w i r e diameter) which was f r e e of KTFR p r o t e c t i o n . (The width of the s t r i p was i n the f i n i s h e d device the source to d r a i n gap). The Au-Ge-Ni m e t a l l i z a t i o n was removed by immersion i n Metex* A u r o s t r i p at 90° C f o r 5 minutes. The n-type GaAs l a y e r i n the s t r i p r e g ion was then thinned to the d e s i r e d value by immersion i n St^SO^ •: "H^C^ : "H^ O''). The remaining n-type l a y e r corresponded to the channel t h i c k n e s s i n the FET. A notch was obtained by r e p e a t i n g the process w i t h a t h i n n e r mask w i r e . The KTFR was removed i n J-100 + at 60° C which was d i l u t e d 1:1 w i t h t r i c h l o r e t h y l e n e . The chip was again coated w i t h KTFR, spun and prebaked. The second photomask defined the s u r f a c e geometry of the de v i c e s , i n c l u d i n g contact lands. The KTFR was exposed and developed and the Au-Ge-Ni metal i n areas o u t s i d e the devices was removed i n Auro-s t r i p . These same areas were etched ( i n SH^SO^ : ^2^2 : * * 2 ^ completely through the n - l a y e r i n t o the p-type s u b s t r a t e . The r e s u l t i n g devices were i n the form of mesas as shown i n f i g u r e 5.7. _ MacDermid Inc., 526 Huntington Ave., Waterbury, Connecticut, 06720 Indust-Ri-Chem Laboratory, P.O. Box 1178, Richardson Texas, 75080 98 I n d i v i d u a l device chips were mounted on the brass holders ( s e c t i o n 3.5) i n i t i a l l y by a l l o y i n g w i t h an In-Zn a l l o y . Later, s i l v e r p a i n t was used to mount the devices because i t gave e q u a l l y good e l e c t r i c a l c ontact, a stronger bond and was e a s i e r to apply. Figure 5.7 NERFET s t r u c t u r e Figure 5.8 NERFET t y p i c a l I-V c h a r a c t e r i s t i c s 99 5.2.2 NERFET C h a r a c t e r i s t i c s The c u r r e n t - v o l t a g e c h a r a c t e r i s t i c of the NERFET i s s i m i l a r to that of the conventional JFET except i n s t e a d of the d r a i n current tending to s a t u r a t e at high s o u r c e - d r a i n voltage i t a t t a i n s a maximum and then decreases w i t h i n c r e a s i n g v o l t a g e . At s u f f i c i e n t l y h i g h v o l -tage the current may again increase and tend toward a s a t u r a t i o n v a l u e . A t y p i c a l c u r r e n t - v o l t a g e c h a r a c t e r i s t i c f o r a NERFET i s shown i n f i g u r e 5.8. A re g i o n of negative d i f f e r e n t i a l r e s i s t a n c e i n any device's c u r r e n t - v o l t a g e c h a r a c t e r i s t i c can cause c i r c u i t o s c i l l a t i o n when the device i s operated i n a r e a c t i v e c i r c u i t . The c o n d i t i o n s f o r s t a b l e c i r c u i t o p e r ation of such a negative r e s i s t a n c e device are der i v e d i n s e c t i o n 5.5.3. These c o n d i t i o n s must be met when measuring the c u r r e n t -voltage c h a r a c t e r i s t i c of the NERFET i n order to -avoid unwanted o s c i l l a t i o n e f f e c t s i n the c h a r a c t e r i s t i c . For example, the c u r r e n t - v o l t a g e charac-t e r i s t i c s of a tunnel diode when measured under the c o n d i t i o n s of c i r c u i t s t a b i l i t y and c i r c u i t i n s t a b i l i t y are shown i n f i g u r e 5.9 (taken from Chow 1964). N o t i c e the s i m i l a r i t y between these tunnel diode c h a r a c t e r --> V (a) -> V (b) Figure 5.9 The cu r r e n t - v o l t a g e c h a r a c t e r i s t i c s of a tunne l diode a) w i t h c i r c u i t s t a b i l i t y and b) w i t h c i r c u i t i n s t a b i l i t y i s t i c s and the c h a r a c t e r i s t i c s f o r the NERFET observed i n s t a b l e and unstable o p e r a t i o n as shown i n f i g u r e s 5.10(a) and (b). To avoid 100 i, I : — "I r\ 10 ma u 4 a) > # • U • 4 1 1 1 1 ib) i i 1 i /OO 1 1 1 1 ' M l M 1 1 t i l l \ 1 M M i l . . 1 1 l l ' t t i l l 1 1 1 1 1 1 1 1 1 1 1 1 2v i i > i =4-I I I ! // / 0 rrrr i / J -_ L J -JL i • uh uh uh V Figure 5.10 The cu r r e n t - v o l t a g e c h a r a c t e r i s t i c of a NERFET i n a) s t a b l e c i r c u i t o p e r a t i o n b) and c) unstable c i r c u i t o p e r a t i o n . c i r c u i t o s c i l l a t i o n the devices were operated i n the r e s i s t i v e c o a x i a l c i r c u i t shown s c h e m a t i c a l l y i n f i g u r e 5.11. The observed c u r r e n t - v o l t a g e 50 si NERFET - low pass filter 0.1 mfd ^50 J L curve-tracer (Tektronix 575) Figure 5.11 Current-voltage t e s t c i r c u i t c h a r a c t e r i s t i c across the terminals of t h e . t e s t c i r c u i t i n c l u d e d the 50 ohm load which had to be subt r a c t e d to o b t a i n the c h a r a c t e r i s t i c of the NERFET alone. N e g l e c t i n g t h i s c o r r e c t i o n r e s u l t e d i n an e r r o r of 25% or l e s s because the s m a l l e s t low f i e l d r e s i s t a n c e was about 200 ohms. 1U1 O s c i l l a t i o n i n the microwave range which may have been Gunn o s c i l l a t i o n was observed i n only two NERFETs. Both of these were t h i c k (4 to 5 microns) and short (18 to 25 microns) w i t h c a r r i e r concentrations 1 5 - 3 of about 6 x 10 cm . The f i r s t had the s t r u c t u r e shown i n f i g u r e 4.4(a), the c u r r e n t - v o l t a g e c h a r a c t e r i s t i c shown i n f i g u r e 5.12, and appeared to generate the current waveform shown i n f i g u r e 5.13 f o r zero gate b i a s . I f the o s c i l l a t i o n - s h o w n i n f i g u r e 5.13 was due to f u l l Gunn~. I !" Vg= 5 v/step h- • V Figure 5.12 Current-voltage c h a r a c t e r i s t i c of a NERFET which appar-e n t l y produced coherent GHz o s c i l l a t i o n i n a r e s i s t i v e c i r c u i t . domain formation and t r a n s i t , the domain v e l o c i t y would have been about 0.9 x 10^ cm/sec. This o s c i l l a t i o n waveform may however have been the r e s u l t of the combination of u.h.f. c i r c u i t o s c i l l a t i o n combined w i t h the tunnel diode t r i g g e r i n g o s c i l l a t i o n . This device f a i l e d before more complete t e s t i n g could be undertaken. The second device had the 1 nsec H h- J L ^ $ * i V ' ' T Figure 5.13 GHz o s c i l l a t i o n from a NERFET i n a r e s i s t i v e c i r c u i t , s t r u c t u r e shown i n f i g u r e 5.7 and the current-voltage" c h a r a c t e r i s t i c 102 shown i n f i g u r e 5.14. The incoherent o s c i l l a t i o n which occurred was observed Figure 5.14 Current-voltage c h a r a c t e r i s t i c of a NERFET which produced incoherent GHz o s c i l l a t i o n i n a r e s i s t i v e c i r c u i t on a S i n g e r - M e t r i c Model RF-4a spectrum analyser to have s e v e r a l broad peaks i n i t s n o i s e spectrum i n 1 to 4 GHz range. This o s c i l l a t i o n , as i n d i c a t e d by the noise evident i n the i n s e t of f i g u r e 5.14 occurred only f o r negative gate b i a s voltages exceeding about -9 v o l t s . A l l other devices, which were a l l l e s s than about 3 microns t h i c k d i s p l a y e d a s t a b l e , n o n - o s c i l l a t i n g c u r r e n t - v o l t a g e c h a r a c t e r i s t i c i n the r e s i s t i v e t e s t c i r c u i t . I f microwave o s c i l l a t i o n was present i n these t h i n n e r devices i t s magnitude was l e s s than the maximum s e n s i t i v i t y of the Hewlett-Packard 140A Sampling o s c i l l o s c o p e which was about 1 mv across 50 ohms . This i m p l i e s an r f power of l e s s than about -50 dbm from the NERFET as compared to the observed power from a diode of s i m i l a r dimensions o f about -7 dbm. Therefore, i f r f power e x i s t s i t i s at very low power l e v e l s . The emphasis i n the remainder of the study 103 was on the s t a b l e NERFET because: 1. The p h y s i c a l mechanism which gives r i s e to a s t a t i c negative d i f f e r e n t i a l r e s i s t a n c e (SNDR) which i s e x t e r n a l l y measurable i s unpredicted and, 2. The device has a gate-voltage c o n t r o l l a b l e negative r e s i s t a n c e which permits the device's use i n a number of unique a p p l i c a t i o n s . The s t a t i c negative d i f f e r e n t i a l r e s i s t a n c e was observed f i r s t i n the non-notched s t r u c t u r e s i m i l a r to f i g u r e 5.7, and d i s p l a y e d i t s e l f i n a cu r r e n t - v o l t a g e c h a r a c t e r i s t i c as shown i n f i g u r e 5.15, (V = 0 ) . Since the device d i d not d i s p l a y Gunn o s c i l l a t i o n a notch was introduced toward the source (cathode) end of the device i n an e f f o r t to provide a n u c l e a t i n g s i t e f o r Gunn domains. The r e s u l t was a more pronounced negative r e s i s t a n c e e f f e c t as shown i n f i g u r e 5.15 but s t i l l no measurable Gunn o s c i l l a t i o n occurred. Figure 5.15 The c u r r e n t - v o l t a g e c h a r a c t e r i s t i c of a NERFET a) before and b) a f t e r a step was etched i n t o the source end 104 The s t a t i c negative d i f f e r e n t i a l r e s i s t a n c e was observed f o r a l l thicknesses of s o u r c e - t o - d r a i n l a y e r from ~0.1 microns to 3 microns as shown i n f i g u r e 5.16. Notic e t h a t the t h i n n e s t device ( f i g u r e 5.16a) at zero gate v o l t a g e passed v i r t u a l l y zero d r a i n c u r r e n t , and that a p o s i t i v e gate voltage was r e q u i r e d to allow a p p r e c i a b l e current flow. This device, however, s t i l l d i s p l a y e d the SNDR c h a r a c t e r i s t i c . A region of negative r e s i s t a n c e e x i s t e d i n the notched devices only i f the notch was at the source (cathode) end. In the reverse b i a s , the current s a t u r a t e d l i k e that of a conventional JFET as shown i n f i g u r e 5.16b (bottom c h a r a c t e r i s t i c s ) . This e f f e c t was observed i n a l l t h i c k -nesses of so u r c e - t o - d r a i n l a y e r l e s s than about 3 microns. Some important NERFET p r o p e r t i e s and t h e i r v a r i a t i o n w i t h thickness as shown i n f i g u r e 5.16 are: 1. The maximum current decreased w i t h decreasing t h i c k n e s s , 2. The s a t u r a t i o n or t h r e s h o l d v o l t a g e decreased w i t h t h i c k n e s s and, 3. In a device of a p a r t i c u l a r t h i c k n e s s the t h r e s h o l d v o l t a g e decreased w i t h i n c r e a s i n g negative gate b i a s . Each of these p r o p e r t i e s can be e x p l a i n e d by c o n s i d e r i n g Shockley's 1952 gradual channel a n a l y s i s . Shockley's a n a l y s i s was based on two important s i m p l i f i c a t i o n s : f i r s t , the g a t e - j u n c t i o n space charge l a y e r was presumed to be completely depleted of f r e e c a r r i e r s and the edge of t h i s d e p l e t i o n l a y e r was abrupt, and secondly, a simple geometry of the device was s e l e c t e d so that the channel p o t e n t i a l d i s t r i b u t i o n could be approximated by a one dimensional equation. Using these s i m p l i f i c a t i o n s , Shockley reduced the two dimensional boundary value problem i n t o s e v e r a l one dimensional problems which could be so l v e d a n a l y t i c a l l y . These (c) Figure 5.16. I-V c h a r a c t e r i s t i c s f o r three device thicknesses (a) t~0.1 u(b) t ~ IV (c) t ~ 3y 106 s i m p l i f i c a t i o n s f o r many cases have been j u s t i f i e d by experimentation and have provided considerable i n s i g h t i n t o the o p e r a t i o n of the JFET. The Shockley a n a l y s i s was however based on a c a r r i e r m o b i l i t y which was assumed to be independent of e l e c t r i c f i e l d . For low v o l t a g e s and long channels t h i s assumption i s v a l i d but i t f a i l s when the e l e c t r i c f i e l d i n the channel i s s u f f i c i e n t l y l a r g e f o r s c a t t e r i n g v e l o c i t y s a t u r a t i o n or i n t e r v a l l e y t r a n s f e r e f f e c t s to occur. A c a r r i e r v e l o c i t y which s a t u r a t e s at l a r g e e l e c t r i c f i e l d has been i n c l u d e d i n FET analyses by us i n g piecewise l i n e a r ( T u r n e r 2 and Wilson 1968, Drangeid and Sommerhalder 1970) and e m p i r i c a l matches (Trofimenkoff 1965, Lehovec and Zuleeg 1970) to the n o n - l i n e a r v e l o c i t y -e l e c t r i c f i e l d c h a r a c t e r i s t i c . The references given above on the t o p i c of FET p r o p e r t i e s under c o n d i t i o n s of h o t - e l e c t r o n e f f e c t s are r e p r e s e n t a t i v e only. Since a number of t e x t s ( f o r example Sevin 1965, Cobbold 1970) and papers ( f o r example H o f s t e i n 1966 and Kennedy and O'Brien 1970) review many of the FET analyses they are not repeated here. Furthermore, the t o p i c of h o t - e l e c t r o n e f f e c t s i n FET's does not yet appear to be closed. Experimental GaAs MESFETs (metal-semiconductor f i e l d e f f e c t t r a n s i s t o r s ) o p e r a t i n g i n the 10 to 18 GHz range have shown gains c o n s i d e r a b l y h i g h e r than expected (Drangeid 2> Sommerhalder and Walter 1970, Baechtold 1971, B a e c h t o l d 3 > Walter and Wolf 1972, and Baechtold,, and J u t z i 1971). I t has been suggested(Baechtold 1971) that the high gain may be due to a phase s h i f t of the transconductance together w i t h the s o u r c e - t o - d r a i n feedback capacitance causing p o s i t i v e feedback, or negative impedance a m p l i f i c a t i o n due to a s t a b i l i z e d h i g h f i e l d region i n the GaAs. I t has a l s o been suggested (Ruch 21972) that the t r a n s i t - t i m e of the c a r r i e r s i s comparable to the r e l a x a t i o n time, 107 thereby a l l o w i n g the average v e l o c i t y to overshoot the steady s t a t e s a t u r a t i o n v e l o c i t y . Ruch has concluded on t h i s l a s t p o s s i b i l i t y that " t r a n s i e n t e f f e c t s on the d r i f t v e l o c i t y of GaAs are important but probably not l a r g e enough to e x p l a i n the remarkable performance of GaAs FETs". Baechtold simply says "Further i n v e s t i g a t i o n s have to be made on t h i s p o i n t " . To date no FET a n a l y s i s has considered a c a r r i e r v e l o c i t y -e l e c t r i c f i e l d c h a r a c t e r i s t i c which d i s p l a y s a region of negative d i f f e r -e n t i a l m o b i l i t y l i k e t h a t which GaAs d i s p l a y s . Rather, only s a t u r a t i n g v e l o c i t y - f i e l d c h a r a c t e r i s t i c s l i k e t hat of s i l i c o n have been considered. That no such a n a l y s i s has yet been presented i s understandable i n l i g h t of the d i f f i c u l t y of ha n d l i n g the two-dimensional problem i n v o l v i n g a gross n o n - l i n e a r i t y which i t s e l f could i n t r o d u c e i n s t a b i l i t i e s . Such i n s t a b i l i t i e s would r e q u i r e the i n c l u s i o n of time dependence as w e l l i n the equations. The e x i s t e n c e of the n o n - l i n e a r v e l o c i t y - f i e l d c h a r a c t e r i s t i c f o r GaAs does not leave the problem t o t a l l y i n t r a c t a b l e however. At low f i e l d s the c a r r i e r m o b i l i t y i s constant and the v e l o c i t y - f i e l d c h a r a c t e r i s t i c i s the c l a s s i c a l s t r a i g h t l i n e case. The Shockley a n a l y s i s i s t h e r e f o r e approximately a p p l i c a b l e i f the f i e l d everywhere i n the channel i s , l e s s than the t h r e s h o l d f i e l d f o r Gunn o s c i l l a t i o n s and al s o the j u n c t i o n d e p l e t i o n and geometry c o n s i d e r a t i o n s are met. The l a t t e r r e s t r i c t i o n s are h o p e f u l l y met f o r the devices i n t h i s study by using 15 -3 c a r r i e r concentrations of about 6 x 10 cm and by usin g a long gate on devices which have a len g t h to th i c k n e s s r a t i o of grea t e r than two to one (Kim and Yang 1970). F o l l o w i n g Turner,, and Wilson 1968 the maximum curr e n t flows 108 when the e l e c t r i c f i e l d at the d r a i n i s equal to the t h r e s h o l d and hence the c a r r i e r v e l o c i t y i s at i t s maximum. N e g l e c t i n g the j u n c t i o n b u i l t -i n p o t e n t i a l the maximum current f l o w i n g i s given by: I = I (1-u) (5-6) m o where I = nqv Za (5-7) o m (5-8) V o = drain-source voltage V = gate-source voltage V q = the c u t - o f f v o l t a g e (the gate-source v o l t a g e which p i n c h e s - o f f the channel i n the absence of d r a i n current) V = qnd 2/2e (5-9) o n = e l e c t r o n c o n c e n t r a t i o n q = e l e c t r o n i c charge Z - device width d = device t h i c k n e s s v = maximum e l e c t r o n v e l o c i t y m As the charge c a r r i e r s are j u s t e n t e r i n g v e l o c i t y s a t u r a t i o n the current can also be obtained from the Shockley 1952 theory of the unsaturated FET which g i v e s : I , = I ( 3 u 2 - 2 u 3 - 3 t 2 + 2 t 3 ) (5-10) d p where I = V nqydZ/3L (5-11) p o fv - v' t - / - v - 8 < 5 - 1 2 > v o 109 L = device l e n g t h V g = source voltage (taken to be zero here) Equating expressions 5-6 and 5-10 y i e l d s 1 2 3 2 3 o _ 3u - 2u - 3t + It I 1 - u 1 j ; P where I 6 v L 3E , L o m _ th / c i / N i " T2 " " v — ( 5 " u ) p nqyd o This equation gives the value of u (normalized drain-gate voltage) f o r a given t (normalized source-gate voltage) at which the Shockley a n a l y s i s i s no longer v a l i d . This a n a l y s i s i s no longer v a l i d because the e l e c t r i c f i e l d exceeds threshold and hence the m o b i l i t y i s no longer f i e l d i n -dependent. The p o i n t at which the Shockley a n a l y s i s i s no longer v a l i d i s obtained from the i n t e r s e c t i o n of the normalized Shockley FET curves obtained from equation 5-10 and the curves a s s o c i a t e d w i t h the onset of n o n - l i n e a r i t y obtained from equation 5-13. These two sets of i n t e r s e c t i n g curves are shown i n f i g u r e 5.17. This f i g u r e i s that provided by Turner^ and Wilson 1968. Turner and Wilson, by u s i n g a p i e c e w i s e - l i n e a r v e l o c i t y - f i e l d c h a r a c t e r i s t i c which has an abrupt v e l o c i t y s a t u r a t i o n at the t h r e s h o l d f i e l d argue that no more current can be drawn than that a s s o c i a t e d w i t h the maximum c a r r i e r v e l o c i t y o c c u r i n g j u s t adjacent to the d r a i n . They th e r e f o r e assume that the current c h a r a c t e r i s t i c s a t u r a t e s at the i n t e r -s e c t i o n of those two curves which correspond to the p a r t i c u l a r geometry parameters ( I q and I ) and the gate v o l t a g e . The s a t u r a t i o n of d r a i n current w i t h d r a i n voltage i s shown by Turner and Wilson i n f i g u r e 5.17 110 0 0-1 0-2 0-3 0-4 0 5 0 6 0-7 0-8 0-9 10 Figure 5.17 Normalized I-V c h a r a c t e r i s t i c of a j u n c t i o n F.E.T. terms of the parameter I / I d e s c r i b i n g v e l o c i t y s a t u r a t i o n . (From Turner- and Wilson 1968) V >1 *\~ <2 i f d n - GaAs 1 V \> p-GaAs Figure 5.18 Representation of the c r o s s - s e c t i o n of a notched NERFET I l l f o r the two cases of I / I = 2 by crosses and I / I = 1 by c i r c l e s . o p J o p The r e s u l t s of t h i s simple approach are q u a l i t a t i v e l y the same as the r e s u l t s of the more complicated curve f i t t i n g a n a l y s i s of Lehovec and Zuleeg 1970 and the d e t a i l e d computer s i m u l a t i o n of Kennedy and O'Brien 1970. The important m o d i f i c a t i o n s to the Shockley c u r r e n t -v o l t a g e c h a r a c t e r i s t i c s i ntroduced by each of these n o n - l i n e a r analyses are as f o l l o w s : 1) The spacing of the c h a r a c t e r i s t i c s f o r v a r i o u s gate v o l t a g e s become more uniform ( i . e . the s a t u r a t i o n transconductance becomes more uniform and not n e c e s s a r i l y a monotonic decreasing f u n c t i o n of gate v o l t a g e ) , 2) The s a t u r a t i o n current i s reduced, 3) The t h r e s h o l d voltage a s s o c i a t e d w i t h the onset of s a t u r a t i o n current i s reduced and, 4) The t h r e s h o l d voltage decreases w i t h i n c r e a s i n g n egative gate b i a s . With the exception of the f i r s t p o i n t a l l of these p r o p e r t i e s have been observed as shown i n f i g u r e 5.16 and remarked on p r e v i o u s l y . The f i r s t p o i n t (more equal spacing of device curves) i s a l s o o b t a i n a b l e from f i g u r e 5.16 by comparing these experimental c h a r a c t e r i s t i c s to the t h e o r e t i c a l c h a r a c t e r i s t i c s shown i n f i g u r e 5.17. The notched s t r u c t u r e shown i n f i g u r e 5.18 r e s u l t s i n a more complicated a n a l y s i s , the r e s u l t s of which are q u a l i t a t i v e l y the same as that presented g r a p h i c a l l y i n f i g u r e 5.17. The d e t a i l s are somewhat d i f f e r e n t however because, i f the parameters d^, d^, 1^ > and 1^ are chosen p r o p e r l y , the e l e c t r i c f i e l d w i l l reach t h r e s h o l d fit the edge of the notch f i r s t r a t h e r than at the d r a i n . R e f e r r i n g to f i g u r e 5.18 112 and again o m i t t i n g the j u n c t i o n b u i l t - i n p o t e n t i a l , the current i s given by: I i I — = {d. - [ — ] 2 [V , - V ] 2} E . (5-15) oco 1 Lqn ch g ch . v ' where a i s the GaAs low f i e l d c o n d u c t i v i t y Is the p o t e n t i a l at a p o i n t x i n the channel E ^ i s the e l e c t r i c f i e l d at the p o i n t x. I n t e g r a t i n g equation (5-15) i n the usual way r e s u l t s i n two equations, one f o r each region of d i f f e r e n t t h i c k n e s s : I I 1 1 - — 1, = d. V . . - | [ — ] 2 [ [V . . - V ] 2 - [-V ] 2 ] (5-16) au 1 1 c h l 3 qn J 1 1 c h l g g and ! i l l i h - d 2 ( V d " W - I ^ V d ~ V / ~ ^ c h l " V ' ] <~5-17> where V i s the p o t e n t i a l at the step (x = 1^) The p o t e n t i a l at the step ( i . e . can i n p r i n c i p l e be e l i m i n a t e d from equations (5-16) and (5-17). The r e s u l t i n g equation would give the d r a i n current as a f u n c t i o n of e x t e r n a l b i a s v o l t a g e s and device parameters. The s o l u t i o n of equations (5-16) and (5-17) on a Hewlett-Packard computer (which was programmed to simultaneously d e t e r -mine the f i e l d s at the step and at the drain) has been c a r r i e d out f o r a r e p r e s e n t a t i v e device. The device parameters chosen were as f o l l o w s : , , J 5 -3 n = 4 x 10 cm 1^ = 1^ = 25 microns = 3.5 microns d^ = 3.0 microns Z = 300 microns 113 The obtained c u r r e n t - v o l t a g e c h a r a c t e r i s t i c s are shown i n f i g u r e 5.19 by l i n e s superimposed on the ex p e r i m e n t a l l y obtained d c h a r a c t e r i s t i c s f o r a device of s i m i l a r parameters. The c a l c u l a t e d c h a r a c t e r i s t i c s are terminated when the f i e l d reaches 3.2 Kv/cm at some p o i n t i n the channel. The c r o s s - s e c t i o n of the device whose c h a r a c t e r i s t i c i s shown -i n - f i g u r e 5.i9 was -obtained by b e v e l l i n g -at 5° and s t a i n i n g as discussed p r e v i o u s l y and i s shown i n f i g u r e 5.20. From t h i s f i g u r e i t i s evident 1 5 - 3 that 1^ = 1 2 = 20 microns. Also n = 6 x 10 cm f o r p o i n t s f a r t h e r than about one micron removed from the s u b s t r a t e as di s c u s s e d i n s e c t i o n 5.2.1. For p o i n t s c l o s e r than one micron the c a r r i e r c o n c e n t r a t i o n as 15 -3 evident i n f i g u r e 5.4 was much l e s s than 6 x 10 cm . The m a j o r i t y of the current i s ther e f o r e c a r r i e d o u t s i d e the one micron t h i c k region adjacent to the s u b s t r a t e . The e f f e c t i v e e l e c t r i c a l t h i c k n e s s of the l a y e r at the source end of the device as obtained from f i g u r e 5.20 was about 2.9 microns w h i l e at the d r a i n end i t was about 3.65 microns. Therefore, the parameters of the h y p o t h e t i c a l device are c l o s e to those of the experimental device. The t h e o r e t i c a l and experimental c h a r a c t e r i s t i c s which are shown i n f i g u r e 5.19 are s i m i l a r to one another up to the p o i n t at which the Shockley gradual channel a n a l y s i s i s no longer v a l i d . This p o i n t , which i s marked w i t h an X, as s t a t e d before corresponds to the e l e c t r i c f i e l d reaching the t h r e s h o l d f i e l d at e i t h e r the edge of the step or at the d r a i n . The greatest d i f f e r e n c e between the t h e o r e t i c a l and experimental curves i s the degree of e f f e c t which the gate voltage had. The t h e o r e t i c a l curves p r e d i c t e d a much l a r g e r e f f e c t than was a c t u a l l y observed. The l a r g e s t gate voltage a c t u a l l y a p p l i e d was -13 v o l t s y e t 114 7 v/step Figure 5.19 Match of experimental and t h e o r e t i c a l I-V c h a r a c t e r i s t i c s f o r a NERFET Figure 5.20 Cross-section of a NERFET 115 t h i s d i d not pinch the current o f f as much as -8 v o l t s f o r the t h e o r e t i c a l case. P a r t of t h i s d e v i a t i o n may have been caused by gate leakage current which would have r e s u l t e d i n a smaller v o l t a g e drop across the gate b i a s r e s i s t o r and hence r e s u l t e d i n a s m a l l e r negative gate b i a s than s p e c i -f i e d . One s i m i l a r i t y between the experimental and t h e o r e t i c a l curves which may not be immediately evident i s the v a r i a t i o n of the d r a i n t h r e s -h o l d voltage w i t h the gate voltage (both r e l a t i v e to the source). For the experimental curves t h i s t h r e s h o l d i s taken to be the p o i n t at which the current begins to decrease w h i l e f o r the t h e o r e t i c a l curves i t cor-responds to the p o i n t at which the Shockley a n a l y s i s i s no longer v a l i d . For gate voltages near zero v o l t s both thresholds are almost independent of gate voltage w h i l e f o r l a r g e r negative gate b i a s the thresholds de-crease wi.th-increasing negative..bias. .This .i s a l s o .predicted .for the .non-notched devices as evident from the i n t e r s e c t i o n s of the two sets of curves shown i n f i g u r e 5.17. H y s t e r e s i s i n the cu r r e n t - v o l t a g e c h a r a c t e r i s t i c was observed i n almost a l l NERFETs made. This h y s t e r e s i s was shown to be a property of the device and not of the measurement c i r c u i t by i l l u m i n a t i n g the device and watching the growth of the h y s t e r e s i s loop a f t e r the i l l u m i -n a t i o n was turned o f f . White l i g h t provided by a tungsten f i l a m e n t 2 microscope i l l u m i n a t o r w i t h an i n t e n s i t y of approximately 60 mW/cm (as measured w i t h an Eppley s i l v e r - b i s m u t h thermopile) was used to i l l u m i n a t e the e n t i r e device area f o r about f i v e minutes. Immediately a f t e r the l i g h t was shut o f f the c u r r e n t - v o l t a g e c h a r a c t e r i s t i c (with zero gate voltage) as shown i n f i g u r e 5.21 (a) d i s p l a y e d no ap p r e c i a b l e h y s t e r e s i s . W i t h i n the f o l l o w i n g hour the h y s t e r e s i s loop had grown 116 I • i i r • i i i l i l t I i a • 1 I V (a) 1 1 I 1 1 1 1 1 1 1 1 1 1 1 r " i 1 1 1 1 1 1 1 u n M M M -rf 1 1 1 1 I 1 1 1 * 11 i H i i t i t i i i ' M i l 1 1 1 1 1 i --V (b) Figure 5.21 H y s t e r e s i s growth a f t e r i l l u m i n a t i o n ceases a) about 2 seconds a f t e r , b) 2 minutes a f t e r c) 8 minutes a f t e r d) 1 hour a f t e r 117 to i t s steady s t a t e value as shown by the sequence of photographs shown i n f i g u r e 5.21. The time constant of t h i s growth was observed to be about 15 minutes. P l o t t i n g the h y s t e r e s i s loop i n the c u r r e n t - v o l t a g e c h a r a c t e r i s t i c p o i n t - b y - p o i n t ( i . e . q u a s i - s t a t i c c h a r a c t e r i s t i c ) showed that the current f o l l o w e d the lower path w i t h i n c r e a s i n g v o l t a g e and returned along the upper path. This behaviour appears to be compatible w i t h c a r r i e r s being trapped as the f i e l d i s in c r e a s e d and being r e l e a s e d as the f i e l d i s decreased. I l l u m i n a t i n g the device would probably f i l l the traps and thus negate t h e i r e f f e c t . As the traps s l o w l y emptied a f t e r the i l l u m i n a t i o n was removed t h e i r e f f e c t would again be e v i d e n t . These traps were shown to l i k e l y be on the surface by covering the device w i t h Kodak Thin F i l m R e s i s t (KTFR). As the KTFR d r i e d under normal room c o n d i t i o n s the c u r r e n t - v o l t a g e c h a r a c t e r i s t i c was observed. The ' v a r i a t i o n of the" r e s i s t i v i t y and d i e l e c t r i c constant (~at l~MHz) of the KTFR as i t d r i e d under normal room c o n d i t i o n s were measured using capacitance meter Boonton 71A electrometer Keithley 600 Figure 5.22 C i r c u i t used to measure KTFR p r o p e r t i e s the c i r c u i t shown i n f i g u r e 5.22. The r e s i s t i v i t y and d i e l e c t r i c constant of the KTFR as a f u n c t i o n of d r y i n g time are shown i n f i g u r e 5.23. The d i e l e c t r i c constant was found to vary by only 20% i n d r y i n g , however the r e s i s t i v i t y i n c r e a s e d by three orders of magnitude i n the f i r s t three hours of d r y i n g . 118 I i 1_ 1 1 1 1— 1 2 3 4 5 6 Drying Time (hours) Figure 5.23 V a r i a t i o n of KTFR properties with drying 119 The v a r i a t i o n w i t h time of the c u r r e n t - v o l t a g e c h a r a c t e r i s t i c (with zero gate v o l t a g e ) a f t e r the KTFR was a p p l i e d i s shown i n the sequence of photographs of f i g u r e 5.24. The s a t u r a t i o n current was observed to be l a r g e r when the KTFR was wet and decreased as i t d r i e d . The r e s i s t i v i t y of the KTFR when wet was e i g h t orders of magnitude greater than that of the GaAs, ther e f o r e the i n c r e a s e d current should not be due to current leakage through the KTFR i t s e l f . A p o s i t i v e charge l a y e r at the GaAs-KTFR i n t e r f a c e would cause c a r r i e r accumulation i n the semi-conductor however, which could account f o r the l a r g e r c u r r e n t . The hy-s t e r e s i s loop was v i r t u a l l y non-existent f o r d r y i n g times of greater than about 10 minutes and l e s s than about 4 hours. Although not shown spe-c i f i c a l l y i n f i g u r e 5.24 the h y s t e r e s i s was again beginning to be d i s c e r -n i b l e a f t e r about 4 hours of d r y i n g . This corresponds to the KTFR f i l m n e a r i n g complete dryness as i n f e r r e d from the r e s i s t i v i t y shown i n f i g u r e 5.23. Since the a d d i t i o n of KTFR was a surface treatment, i t appears the h y s t e r e s i s was p r i m a r i l y due to sur f a c e e f f e c t s . A p o s s i b l e ex-p l a n a t i o n i s that the c o n d u c t i v i t y of the KTFR was s u f f i c i e n t l y l a r g e to conduct away e l e c t r o n s h e l d i n su r f a c e traps and thereby n u l l i f y the e f f e c t of the t r a p s . 5.3 Related Devices 5.3.1 I n t r o d u c t i o n The wide bandgap and high e l e c t r o n m o b i l i t y p r o p e r t i e s of GaAs have l e d to considerable i n t e r e s t i n usi n g t h i s m a t e r i a l to b u i l d high frequency, high power, hig h temperature f i e l d e f f e c t t r a n s i s t o r s . The negative d i f f e r e n t i a l e l e c t r o n m o b i l i t y i n GaAs under l a r g e f i e l d c o n d i t i o n s could however l e a d to Gunn or other negative r e s i s t a n c e 120 Figure 5.24 H y s t e r e s i s v a r i a t i o n w i t h d r y i n g time of a KTFR covered NERFET a) 6 minutes a f t e r covering b) 10 minutes a f t e r c) 1 hour a f t e r d) 24 hours a f t e r 121 e f f e c t s i n GaAs FETs. Such e f f e c t s have been observed i n p r a c t i c e so i t i s worthwhile to review the p r o p e r t i e s and s t r u c t u r e s of those de-v i c e s which have and those which have not d i s p l a y e d such negative r e -s i s t a n c e e f f e c t s . I t i s then p o s s i b l e to r e l a t e common features o f the va r i o u s devices to t h e i r p r o p e r t i e s and to place the NERFETs made here i n p e r s p e c t i v e . The._dis.cus.sion of r e l a t e d devices i s d i v i d e d i n t o the f o l l o w i n g s e c t i o n s : 1) a d i s c u s s i o n of conventional GaAs F i e l d E f f e c t T r a n s i s t o r s which have d i s p l a y e d no negative r e s i s t a n c e e f f e c t s , 2) a d i s c u s s i o n of GaAs F i e l d E f f e c t ' T r a n s i s t o r s which have d i s -played negative r e s i s t a n c e e f f e c t s , 3) a d i s c u s s i o n of GaAs Gunn e f f e c t devices which have a t h i r d e l e c t r o d e f o r control'purposes an'd, 4) a d i s c u s s i o n of other GaAs devices which have d i s p l a y e d ne-ga t i v e d i f f e r e n t i a l r e s i s t a n c e without i n s t a b i l i t i e s . The s e r i e s of diagrams and remarks shown on the next f i v e pages ( f i g u r e s 5.25(a) to 5.25(ee)) c o n s t i t u t e a review of experimental r e s u l t s obtained by other workers. The pr o g r e s s i o n i n these diagrams i s from conventional GaAs FETs ( f i g u r e s 5.25(a) to 5.25(m)), through FETs which d i s p l a y some negative r e s i s t a n c e e f f e c t s which are not l i k e l y due to Gunn o s c i l l a t i o n ( f i g u r e s 5.25(n) to 5.25(q)), through three t e r m i n a l devices which apparently do s u s t a i n Gunn o s c i l l a t i o n ( f i g u r e s 5.25(r) to 5.25(cc)), and ends w i t h s e v e r a l diode s t r u c t u r e s f o r which s t a t i c negative d i f f e r e n t i a l r e s i s t a n c e has been observed ( f i g u r e s 5.25 (dd) and 5.25(ee)). 122 b) Cell l.iMjlJlrr.9 CoAt t i l j..[.:!.;[TO:; •Li l.W.T'\ i I"TS .., ! ! u. ! ! ! ! i : ! ! !. 11 2 x 10 1.2 x 10 T u r t l e ^ and Wilson 12 1968 Schottky gate FET on s e m i - i n s u l a t i n g GaAs c) d) |S7ii.,|5/jin|5/im] t — S — i _ _ r ~ i t r ^ a . . n-type GoAs f i lm Semi-in iulatincj substrate u n s p e c i f i e d 2-5 50 V = 5v/step 126-7 -" ^ ~ \ I • i i i i i 5 x 10 11 Hower, Hooper, Tre-mere,Lehrer and B i t -tman 1968 Schottky gate FET on s e m i - i n s u l a t i n g GaAs. 4.5 x 10 11 vsotvoirs) Shapiro and G i o r g i o 1969 Schottky gate FET on s e m i - i n s u l a t i n g GaAs ILtUXJiLI f ) as above > T3 CO B 10 12 > • H cd 6 1 v / d i v V = 0.5 v/step P§__ _____ ••  •"'?''.'!ii.."-- • ~:u\ 10 12 1 v / d i v V = 0. g Figure 5.25 Compilation of r e l a t e d devices 5 v/step g Lehovec and Zuleeg 1970 p-n j u n c t i o n gate FET on s e m i - i n s u l a t i n g s u b s t r a t e Zuleeg~and Lehovec 1970 p-n j u n c t i o n gate FET on s e m i - i n s u l a t i n g s u b s t r a t e 123 g). h) i ) "~1 . 1 r l V / d i v V. = 0.5 v/step > ro e l V / d i v V = 1 v/step g nt (cm ) 3 x 10 11 5 x 1 0 1 1 -2 x 10 13 Authors and Remarks Doerbeck 1970 Schottky gate FET on s e m i - i n s u l a t i n g s u b s t r a t e , Driver, Kim and B a r r e t t 1971 Schottky gate FET on s e m i - i n s u l a t i n g s u b s t r a t e . CATC , SEMI-INSULATING SUOSTAATC COLO in! COLO -ro e j ) u n s p e c i f i e d k) 1) .  T il : m 1 • / • MtlM KIM t \ T 1 a. J " M 3 1 ' T I L - y - —J " T T ——1 . / Rnia MI  \ :  ...T 1 •H CO e 10 12 r 2 v / d i v 0.2 v/step V : t.....jg...... T O " i n ; r n 1-v/div Vp = 1 v/step ^ f ^ S * ^ fTJ ?*? E*S ??7 f T J s ^ J^j j j £'=«' '-rf~•-' i - T - i E l i v / d i \ V = Iv/s t e p g i ' ' KM I /.HI 3 x 10 •12 1.5 x 10 11 1.5 x 10 11 2 v / d i V V =0.5 v/step Pruniaux, North and Payer 1972 S e m i - i n s u l a t i n g gate FET on s e m i - i n s u l a r t i n g s u b s t r a t e . Drangeid2 >Sommer-halder and Walter 1970 Schottky gate FET on s e m i - i n s u l a t i n g s u b s t r a t e . Turner 1966 p-n j u n c t i o n gate FET on se m i - i n s u l -a t i n g s u b s t r a t e . Turner 1966 p-n j u n c t i o n gate FET on p-type s u b s t r a t e . Figure 5.25 Continued 124 n>) n) o) q) I- i"^ ....:„ Figure 5.25 Cont'd 1 v / d i v V„ = 2v/step nt (cm ) 2-6x10 12 :/:: l v / d i v V_ " ° - •' ' .1 H ' si?-.-...t., ..; vt. ., .... • . - ^ r . : : i : . : :' r.j tn j i: \ L i LL* .1 I. '•. • 1 / 1 v7 d i v gate f l o a t i n g u n s p e c i f i e d : / ; . ; • :. / It L 10 v / d i v V - 0 l - 3 x 10 12 1-3x10 12 2 x l 0 1 3 -5 x 10 13 2x10 i o 1 2 11 Authors and Remarks Beck, H a l l and White 1965 MOSFET w i t h d i f -fused n channel on p s u b s t r a t e . W i n t e l e r and S t e i n -mann 1966 p-n j u n c t i o n gate FET w i t h d i f f u s e d n channel on p s u b s t r a t e . W i n t e l e r and S t e i n -mann 1966 p-n j u n c t i o n gate FET from n e p i -l a y e r on p sub-s t r a t e ; uhf (30-300MHz) o s c i l l a t i o n . P e t z i n g e r , Hahn and M a t z e l l e 1967 p-n j u n c t i o n gate FET from n e p i - l a y e r on p s u b s t r a t e . C i r c u i t dependent o s c i l l a t i o n i n range 60-2500 MHz. C a l i f a n o 1969 St r u c t u r e as " r e -ported f i r s t i n Pe t z i n g e r e t a l . " . C i r c u i t and i l l u m i n -a t i o n dependent o s c i l -l a t i o n i n 80 MHz to 10.6 GHz range. Zuleeg 196 8 p-n j u n c t i o n gate FET from n e p i - l a y e r on p s u b s t r a t e . O s c i l l a t i o n observed but frequency un-s p e c i f i e d 125 Scurct _ Orotn ~ u n s p e c i f i e d nt i l l 3 x 10 2.5x10 11 12 5 v / d i v V = lOv/step 6 1-2x10 13 Authors and Remarks Z u l e e g 2 1968 p-n j u n c t i o n gate FET from n e p i - l a y e r on p-type s u b s t r a t e Gate c o n t r o l l a b l e osc. i n range 0.6-1.*2GHz. O s c i l l a t i o n quenching w i t h s u f f i c i e n t gate v o l t a g e . Doerbeck, Harp and Strack 1968. Schottky gate FET on semi-. i n s u l a t i n g s u b s t r a t e . 2x10 11 C l a r k e , Edridge G r i f f i t h and McGeeham 1971. Schottky FET on s e m i - i n s u l a t i n g sub-s t r a t e . Gunn osc. f r e q . i n c reased w i t h i n c r e a s e d negative gate b i a s . I *-e<s 10 lit J l T 13 Nahas 1971. Schottky gate FET on semi-insu-l a t i n g substrate. Gunn osc. f r e q . decreased w i t h i n c r e a s e d negative gate bi a s . C»cZbUcft r*q<.cncy lAMJ b s * ^ 6x10 12 Hashizume, Kawashima and Kataoka 1971 MISFET from bulk GaAs w i t h B a T i 0 3 gate. O s c i l l a t i o n frequency u n s p e c i f i e d . (I) 2 5 0 m < 5 m a ) 10 12 Sugeta, Y a n a i , Sekido 1971. Schottky gate FET on s e m i - i n s u l a t i n g sub-s t r a t e . Gunn o s c i l l a t i o n t r i g g e r e d by gate as shown. Figure 5.25 Cont'd 126 -4- T u n s p e c i f i e d nt 12 1.2x10 -5 x 10 12 Authors and Remarks Heime 1971. Schottky gate FET on sem i - i n -s u l a t i n g s u b s t r a t e . Gunn o s c i l l a t i o n t r i g -gered by gate. " r i c h e r puis* O T U t i t t n l n a l C»\ki n C 2.1x10 12 Hayashi 1968. Ohmic t h i r d t e r m i n a l Gunn o s c i l l a t i o n t r i g g e r i n g by current i n j e c t i o n i n t h i r d t e r m i n a l . -1. v. 10 20 10 .0 TIME IN nono iec 8X10 1 1-12 2.1x10 8X10 1 1-2.1x10 12 S h o j i 1967. Ohmic t h i r d terminal. Shaping of Gunn osc. waveform w i t h feedback r e s i s t o r to t h i r d t e r m i n a l . S h o j i 1-967. " d i s t r i b u t e d shunt contact". Shaping of Gunn osc. waveform by shunt c a p a c i t i v e c u r r e n t . .... f 1 sxio11-*• 2 . 1 X 1 0 1 2 TIKE IM <ion«i«e S h o j i 1967. "shaped d i s t r i b u t e d shunt" on bulk diode. Gunn waveform s i m i l a r to that f o r a shaped diode. J 0-16A 1 1 <_T 4.7X10 voltage 3 3 2 V Kataoka, Tateno and Kawashima 1968, surface loaded bulk diode w i t h SNDR. A C X m e l o n * • o y e r Au C t contact* L — -—1 "-v-to |» 0 • / -2-2 -SO ;  -OC -7.7x10 11 11 Figure 5.25 Cont'd Boccon-Gibod and Teszner 1971, n e p i - l a y e r diode on s e m i - i n s u l a t i n g sub-s t r a t e w i t h anode ca-p a c i t i v e l o a d , shows SNDR. 127 5.3.2 Conventional GaAs FETs The three types of f i e l d e f f e c t t r a n s i s t o r s , c l a s s i f i e d ac-cording to the type of gate, are; the metal-oxide-semiconductor (MOS) FET, the metal-semiconductor (MES) FET (which i s also c a l l e d the Schottky b a r r i e r FET), and the p-n j u n c t i o n gate FET (JFET). There has been r e l a t i v e l y l i t t l e work c a r r i e d out on the GaAs MOSFET because e a r l y work (Becke, H a l l and White 1965, Becke 2 and White 1966) i n d i c a t e d that common i n s u l a t o r s ( S i 0 2 and Si^N^) when used w i t h 12 -2 GaAs r e s u l t e d i n r e l a t i v e l y l a r g e surface s t a t e d e n s i t i e s (~ 10 cm ) which degraded device performance. Other i n s u l a t o r s could r e s u l t i n b e t t e r GaAs MOSFET performance but l i t t l e e f f o r t appears to have been exerted i n t h i s d i r e c t i o n because GaAs MESFET performances have been f a r s u p e r i o r w i t h l e s s d i f f i c u l t y i n f a b r i c a t i o n . The MESFETs and JFETs on s e m i - i n s u l a t i n g GaAs su b s t r a t e s do not appear to be fr e e of tr a p p i n g e f f e c t s , i f the h y s t e r e s i s loops i n the cu r r e n t - v o l t a g e c h a r a c t e r i s t i c s are an i n d i c a t i o n ( f i g u r e s 5.25(c), 5.25(g) and 5.25(k)). Such t r a p p i n g e f f e c t s near the i n t e r f a c e of the n-l a y e r and the s e m i - i n s u l a t i n g s u b s t r a t e c o u l d be due to s i t e s caused by the chromium dopant i n the s e m i - i n s u l a t i n g GaAs. Chromium i n GaAs provides a deep compensating l e v e l which removes most f r e e c a r r i e r s and 4 8 r e s u l t s i n the very h i g h r e s i s t i v i t y (10 to 10 0 -cm). Turner 1966 found that the h y s t e r e s i s could be almost e l i m i n a t e d by using a p-type sub-s t r a t e ( f i g u r e s 5.25(k) and 5.25 ( 1 ) ) . A common feature of a l l those devices which d i s p l a y e d the conventional s a t u r a t i n g c u r r e n t - v o l t a g e c h a r a c t e r i s t i c ( i . e . no negative r e s i s t a n c e e f f e c t s w a s that the source, d r a i n and gate x^ere a l l on one face of the n-type l a y e r and separated by at l e a s t s e v e r a l microns from one 128 another ( f i g u r e s 5.25(a) to 5.25(k)). A second f e a t u r e common to almost a l l of the devices which d i s p l a y e d the conventional FET c h a r a c t e r i s t i c was the product of c a r r i e r c o n c e n t r a t i o n x channel t h i c k n e s s (nd product) 1 2 - 2 was 10 cm or s m a l l e r . A s m a l l nd product i s a n a t u r a l consequence of pursuing a l a r g e gate c o n t r o l e f f e c t i n a conventional FET by usin g a l i g h t l y doped t h i n channel. 5.3.3 GaAs FETs w i t h Negative Resistance E f f e c t s On the other hand,when a p-type s u b s t r a t e was used,the c u r r e n t -voltage c h a r a c t e r i s t i c showed e i t h e r a very f l a t s a t u r a t i o n ( f i g u r e s 5.25(1) and 5.25(m)) or an a c t u a l r e d u c t i o n i n current w i t h i n c r e a s i n g voltage ( f i g u r e s 5.25(n) to 5.25 ( p ) ) . This l a t t e r c o n d i t i o n of negative d i f f e r e n t i a l r e s i s t a n c e can l e a d to c i r c u i t o s c i l l a t i o n s i f care i s not taken to ensure c i r c u i t s t a b i l i t y as discussed i n s e c t i o n 5.5.3. The r e l a t i v e l y low frequency -of o s c i l l a t i o n observed -by W i n t e l e r and -Stein-mann 1966 ( f i g u r e 5.25(o)), P e t z i n g e r , Hahn and M a t z e l l e 1967 ( f i g u r e 5.25(p)) and C a l i f a n o 1969 ( f i g u r e 5.25(q)) may have been due to such c i r c u i t o s c i l l a t i o n . In a l l three of these cases the devices had channel lengths i n the 10 to 25 micron range. I f the o s c i l l a t i o n was due to Gunn do-mains t r a n s i t i n g at 10^ cm/sec the frequency would have been gre a t e r than 4 GHz. I f the o s c i l l a t i o n was a c i r c u i t o s c i l l a t i o n due to s t a t i c negative d i f f e r e n t i a l r e s i s t a n c e i t s frequency would have been determined by the LC product of the c i r c u i t . None of these papers report e d the d e t a i l s of t h e i r c i r c u i t s , but assuming L ~ 1 uh (which i s a reasonable power supply output inductance) and a capacitance which i s due to the r e -verse b i a s e d p-n j u n c t i o n , the f o l l o w i n g frequencies ( c a l c u l a t e d from f = 1/2 TT i £ c ) should have been observed: 1) W i n t e l e r and Steinemann 1966 ( f i g u r e 5.25(o)): Based on a 129 contact land area of 0.015 mm the capacitance of the p-n 16 3 junction for p >> n = 10 cm would be (Sze 1969) about 2 pf. The re s u l t i n g c i r c u i t o s c i l l a t i o n frequency would be about 100 MHz, within the vhf range as reported by Winteler and Stein-mann. They apparently thought, however, the o s c i l l a t i o n was d i r -e c t l y due to the Gunn effect as indicated by thei r statement "The investigation of the vhf o s c i l l a t i o n s (Gunn Effect) has not yet been concluded Petzinger, Hahn and Matzelle 1967 (figure 5.25(p)): Based on 2 a contact are of 0.015 mm ("device size t y p i c a l l y 125 p by 250 J U " according to Petzinger et al.) the o s c i l l a t i o n frequency would again be about 100 MHz. They note a dependence of f r e -quency on the contact size and c i r c u i t inductance as follows: "However, the performance of our devices i s not ty p i c a l of transit-time Gunn diodes. The distinguishing feature of Gunn diodes i s the inverse dependence of frequency on sample length. Our frequencies do not appear to be strong functions of any dimension that might be construed as a t r a n s i t -time length. In every case, frequencies have been at least three and, i n some cases, more than 100 times lower than the Gunn frequency for an assumed transit-time length approximately equal to the width of the groove. The junction area determines the t o t a l shunt ca-pacitance between the two n terminals. Large area, and hence high capacitance units o s c i l l a t e at con-siderably lower frequencies than those of smaller 130 area. S e r i e s inductance lowers the o p e r a t i n g frequency". They observed a v a r i a t i o n of frequency w i t h gate v o l t a g e as shown i n f i g u r e 5.26. The tuning shown i n t h i s f i g u r e can be e x p l a i n e d S « J Z I O - l V B ( V O L T S ) Figure 5.26 Tuning c h a r a c t e r i s t i c as a f u n c t i o n of p-region b i a s ( t y p i c a l ) (from P e t z i n g e r , Hahn and M a t z e l l e 1967) by the v a r i a t i o n of j u n c t i o n capacitance w i t h gate v o l t a g e as shown t y p i c a l l y i n f i g u r e 5.3. For i n c r e a s i n g p o s i t i v e gate v o l t a g e (which i s l e s s than the b u i l t - i n v o l t age of about 1.2 v o l t s ) the capacitance i n c r e a s e s s t e e p l y causing the steep decrease i n frequency shown i n f i g u r e 5.26. For i n c r e a s i n g negative gate voltage the capacitance de-creases g r a d u a l l y , causing a gradual increase i n frequency a l s o as shown. 3) C a l i f a n o 1969 ( f i g u r e 5.25(q)) has apparently observed both Gunn o s c i l l a t i o n and c i r c u i t dependent o s c i l l a t i o n as i n d i c a t e d by the f o l l o w i n g : "Three-terminal Gunn devices, of the type f i r s t reported i n P e t z i n g e r et a l . , have been s u c c e s s f u l l y operated CW at room temperature between 30 MHz and 10.6 GHz. The hi g h e s t frequency i s observed w h i l e the device i s o s c i l l a t i n g i n the t r a n s i t - t i m e mode corresponding 131 to the width of the groove (~ 12 microns) between the two n b l o c k s ; the lower frequencies are ob-ta i n e d w h i l e the device i s operated i n the b i a s -c i r c u i t o s c i l l a t i o n mode. While the device i s operated i n the t r a n s i t - t i m e mode, low t u n a b i l i t y i s p o s s i b l e as f o r r e g u l a r two-terminal Gunn devices. When b i a s - c i r c u i t o s c i l l a t i o n s are used, the f r e -quency of operation can be changed over a wide range by v a r y i n g both the e x t e r n a l c i r c u i t and/or the voltage b i a s a p p l i e d to the p t e r m i n a l " . The remainder of h i s paper, however, d e a l t w i t h the i n -fluence of i l l u m i n a t i o n on the operation of devices operated i n the "bias c i r c u i t " mode. No o s c i l l a t i o n waveforms or other evidence were presented to i n d i c a t e that the 10.6 GHz o s c i l l a t i o n was a c t u a l l y due to Gunn domain t r a n s i t . None of these authors (Winteler et a l . , P e t z i n g e r e t a l . or Ca l i f a n o ) appears to have recognized that the low frequency o s c i l l a t i o n s may have been due to a s t a t i c negative d i f f e r e n t i a l r e s i s t a n c e across t h e i r device's source and d r a i n t e r m i n a l s . A l l three r e f e r o b l i q u e l y to Gunn o s c i l l a t i o n s and make no reference to SNDR c i r c u i t o s c i l l a t i o n s . The s t r u c t u r e and c i r c u i t performance of t h e i r devices however would i n d i c a t e that the devices were a c t u a l l y Negative Resistance F i e l d E f f e c t T r a n s i s t o r s (NERFETs) i n the terminology used here. Some common features of the devices of these authors are: a) a product of c a r r i e r c o n c e n t r a t i o n x th i c k n e s s which 12 -2 i s g r e a t e r than about 10 cm and 132 b) a wide p-type gate on the opposite face of the n-type layer from the source and drain contacts and overlapping each of these contacts. 5.3.4 Gunn Devices with Three Electrodes Those three terminal devices which sustain Gunn oscillations (figures 5.25(r) to 5.25(cc)) can be divided into two categories: a) GaAs FETs which happen to have nl and nd products in the right range to allow Gunn oscillation (figures 5.25(r) to 5.25(v)) and b) GaAs devices which are primarily Gunn oscillators but which have a third electrode for control or wave-shaping purposes (figures 5.25(w) to 5.25(cc)). In the first category both Zuleeg 1968 (figure 5.25(g)) and Nahas 1971 (figure 5...25(v)) found that the Gunn oscillation .frequency decreased with increasing negative gate bias while Clarke, Edridge, Griffith and McGeehan 19 71 found that i t increased with increasing negative gate bias. The frequencies observed in each case appear to be compatible with the source to drain distances used and domain velocities in the range of 10^ cm/sec. More information appears to be necessary to clear up these conflicting results. In the second category an insulated gate '(Hashizuma, Kawashima and Kataoka 1971, figure 5.25(w)) and thin Schottky gates (Sugeta, Yanai and Sekido 1971, figure 5.25(x); and Heine 1971 figure 5.25(y)) have been used to allow pinching of the field under the gate in a device which is biased just below Gunn threshold. A Gunn domain is thereby nucleated under the gate \>7hich then transits to the anode. Such devices can be used to perform sub-nanosecond logic operations (Yanai, Sugeta 133 and Sekido 1971). Gunn domains can also be triggered by injecting current through an ohmic contact near the cathode (Shoji 1967, figure 5.25(aa); Hayashi 1968, figure 5.25(x). The electric field in the region of the injecting contact is raised sufficiently by the injected current to trigger Gunn oscillation. Some common features of those devices which support Gunn os-cillation are: a) a product of carrier concentration x thickness which 12 -2 is greater than about 10 cm and, b) a narrow gate and a wide uncovered space between the gate and the anode. 5.3.5 Other GaAs Devices with SNDR Figures 5.25(dd) and 5.25(ee) depict two GaAs devices which have -displayed current-voltage characteristics with regions of stable static negative differential resistance. The significant point is that these devices, without Gunn oscillation, displayed SNDR which distin-guishes these devices from stable subcritically doped devices (i.e. 11 -2 10 -2 nl < 5 x 10 cm or nd < 5 x 10 cm ) which display a saturating current characteristic. The first device (figure 5.25(dd)) was a tapered bulk device (cathode at the narrow end) with BaTiO^ surface loading. Kataoka, Tateno and Kawashima 1968 found that Gunn oscillation was obtained in this structure i f the BaTiO^ was removed,but a non-oscillating negative differential resistance was obtained with the BaTiO^ in place. With this device, negative differential resistance was observed only for the thin and at the cathode. Kataoka et al. also found that almost a l l other elements of similar structure showed similar tendencies. 134 The second device (figure 5.25(ee)) comprised an epitaxial n-layer on a semi-insulating substrate with a capacitive surface load at the anode. With the surface load removed Boccon-Gibod and Teszner 1971 observed Gunn instabilities which gave way to a noisy instability after several domain transits. The performance of the device with the anode capacitive load in place depended on what fraction of the length of the device was covered. When a length of 500 microns (about half the length of the device) was left uncovered bistable switching between high and low current was possible with a small increase in voltage. When the surface load was moved along so that only 200 microns of the device was left uncovered a differential negative resistance without instability was observed. With the polarity reversed (i.e. the cathode loaded) the current saturated rather than decreased with increasing voltage. Some common features of thes.e devices .were: a) SNDR occurred only with a surface load in place and b) the devices geometries were unsymmetrical and showed the SNDR for only one polarity of applied voltage. The latter two devices (which were two terminal devices) are included in this discussion of primarily three terminal devices because the SNDR characteristic without instability is unusual and a feature held in common with the NERFET. 5.4 On the Static Negative Differential Resistance Mechanism  5.4.1 Introduction The discussion of possible mechanisms which could give rise to a negative differential resistance characteristic with no instability for the NERFET is divided into five sections. The first and second sections deal with the possibility of the NERFET performance arising 135 from thermal effects or travelling Gunn domain effects respectively. The third section discusses the effect of the gate p-n junction. The fourth section discusses the field probing technique used to gain insight into the mechanism and the fifth section discusses the probable mechanism in relation to previous SNDR theories. 5.4.2 Thermal Effects and the NERFET Switching Speed Negative differential resistance has been observed in silicon FETs (Todd 1965, Todd3 1968) due to heating of the device. For the FET to exhibit a voltage-stable negative resistance its drain current must have a negative temperature coefficient. This coefficient is the result of opposing effects, and may be either positive or negative. One effect is a decrease in current due to a decrease in carrier mobility by in-creased scattering at high temperatures. Opposing effects arise from "an "increase in carrier concentration and a decrease in built-in junction potential with increasing temperature. If the drain current has a nega-tive temperature coefficient, negative differential resistance is observed only i f the device is operated slowly enough to allow appreciable tem-perature swing. Todd 1965 states "The thermal time constant for a typical FET is 25 seconds" and (Todd^ 1965) "Negative resistance becomes evident only when the drain current in an FET is measured with slow discrete changes in drain-to-source voltage and the data is plotted on a graph". The possibility of the negative resistance in the NERFET characteristic arising from thermal effects can be eliminated by con-sidering the frequency at which negative resistance effects occur. The NERFET current-voltage characteristics shown throughout this thesis were observed on a Tektronix 575 Transistor Curve Tracer which sweeps at 120 times per second. The negative differential resistance which was 136 observed at this sweep rate was one thousand times faster than the thermal time constant quoted by Todd for Si FETs. Circuit oscillations which were also consistent with an SNDR characteristic have been observed at 20 MHz. Therefore, the negative resistance apparently exists up to that frequency, which is eight orders of magnitude faster than the expected thermal time constant. To measure how fast the SNDR mechanism can occur in a NERFET the device whose characteristic is shown in figure 5.16(a) was placed in the circuit shown in figure 5.27. Fifty ohm coax line was used throughout and a steep bias pulse (risetime < one nanosecond) was applied from a Hewlett Packard 140a pulse generator. The current through the sampling •oscilloscope h/p HO A pulse generator h/p 140 A - A trigger dz NERFET W \ A -20db 50 _o-sampling head h/p 1431A-Figure 5.27 NERFET switching speed circuit device was obtained from the voltage drop across the 50 fi load at the sampling head. The resulting current as a function of time is shown in figure 5.28 for two bias voltages. Figure 5.28(a) was obtained with 137 a bias voltage about 0.1 volt less than threshold, while figure 5.28(b) was obtained with a bias voltage about 1 volt greater than threshold. % 2 ma • • ( a ) 50 nsec C 6 ; Figure 5.28 NERFET switching waveforms a) 0.1 v less than threshold b) 1 v greater than threshold The spike of current on the leading edge of the pulse in these figures was probably capacitive in nature and due to the relatively large source-to-drain capacitance of the NERFET. The switch from high to low current as shown in figure 5.28(b) occurred in about 50 nanoseconds. The amount of current drop (including the 20 db power attenuator associated with the switch from high to low is about 2 ma which is consistent with the drop evident in figure 5.16(a). The switching time of 50 nanoseconds which was observed for this device was probably not limited by the mechanism of the SNDR but rather by circuit aspects. The switching time for a negative resistance device is the time required to charge the device's capacitance and is determined approximately by the time constant (Chang 1964): switching = device negative resistance x device capa-citance where for this device: r - 300 ohms C * 100 pf 138 Therefore the switching time constant determined by the charging time of the device is about 30 nanoseconds which is consistent with the observed switching time of 50 nanoseconds. To minimize this switching time and hopefully to approach the limiting switching time which is as-sociated with the mechanism for the SNDR,the capacitance must be reduced. 2 Reducing the contact area size from the value of about 1 mm used here 2 to 0.01 mm would allow a one hundred fold increase in the circuit limited switching time. Such a reduction was hot carried out here be-cause of the complicated fabrication technology involved, however i t is well within the state-of-the-art of modern integrated circuit manu-facturers . 5.4.3 Travelling Gunn Domain Effects Low frequency circuit oscillations have previously been ob-tained in Gunn diode reactive circuits -by using - the Gunn diode rather like a tunnel diode. In the presence of Gunn oscillations the average external current decreases as the bias voltage increases. Hence, circuit instabilities from this "average negative resistance" and Gunn instab-i l i t i e s can exist simultaneously. The nature of the circuit determines the.nature of the low frequency oscillations. Fleming 1966 and 1967 used an inductor in the drive circuit which caused the bias to fluctuate at a low frequency. This resulted in intermittent bursts of many cycles of the usual transit time Gunn oscillations. Fisher 1967 described a relaxation oscillator which used a resistive load to develop the pulse amplitude and a shunt inductor which determined the relaxation time. Jaskolski and Ishii 1966 reported the simultaneous generation of 12.5 MHz relaxation oscillation and 17.76 GHz Gunn oscillation without specifying the circuit. Lanza and Esposito 139 1969 described a circuit in which the switching time of the relaxation oscillation was determined by the diode capacitance. Thim^ 1967 discussed a Gunn device which he called a "travelling domain amplifier" which sim-ultaneously amplifies at frequencies other than the transit time fre-quency and oscillates in a transit mode. In the NERFET, oscillation was not usually observed in a fre-quency -range .compatible -with -Gunn oscillation. It has been concluded (section 5.2.2) that i f Gunn instability existed simultaneously with the circuit oscillation i t was of very small amplitude. The mechanism for the SNDR must therefore account for the non-existence of Gunn oscillation as discussed in the next section. 5.4.4 Effect of the p-n Junction Cawsey 1967 described an oscillator circuit using a bulk Gunn diode which generated sinusoidal waveforms in the 30 MHz to 250 MHz range which were free of higher frequency Gunn oscillation. In his circuit Gunn instability was suppressed by a 15 pf capacitor in shunt with the Gunn diode, apparently providing sufficiently low impedance in the microwave range to effectively shunt out such instability. Cawsey found that with the rf current shorted by.the shunt capacitor the slope of the negative portion of the current-voltage characteristic was steeper than when not shorted. He states "the presence of an rf voltage would affect the mean current because ofthe non-linear characteristic and would degrade the effective negative resistance". The significant point is that he ob-tained a negative differential resistance without instability by providing a capacitive shunt for any high frequency (Gunn) instabilities. The NERFETs made in this study, as described previously, had a relatively large source to drain capacitance due to the depletion 140 region between the n and p layers. The tendency of this capacitance, according to Cawsey's findings, should be to short out Gunn instability. * If a Gunn instability can exist its magnitude would probably be reduced in proportion to the ratio of the shunt and load impedances. In this case the impedence at 1 GHz of the 100 pf source-to-drain capacitance would be 1.6 ohms. This shunt would likely reduce the output amplitude across a 50 Q load by about 30 times which is a reduction of about 30 db in power. Even though this value is only an estimate i t indicates that the output rf power should be greatly reduced by the shunt capacitance. This es-timated reduction in rf power is compatible with the measurements made to determine the presence of Gunn instabilities as reported in section 5.2.2. Furthermore, the depletion region between the n and p regions, being free to distort to be compatible with the voltage distribution in the channel may allow current continuity to be retained without move-ment of any domain which may have built up. This is discussed further in section 5.4.5. It is concluded, that the cause of the SNDR without instability in the NERFET characteristic is probably due directly to distortion of the p-n junction depletion region to allow a stationary domain or indir-ectly to the capacitive shunt effect of the depletion layer or both. In either case i t is concluded the SNDR results from the depletion region which is associated with the p-n junction along one face of the conducting channel. It is worthwhile to consider the validity of this conclusion from several viewpoints. The conclusion should hold up in light of the properties of devices with similar structures made by others and in * i.e. r.f. current does not appear in the external circuit. 141 light of other theories dealing with static negative differential re-sistance. 5.4.5 Other Aspects of the SNDR Phenomenon Gunn oscillation in a conventional diode occurs most readily i f there is a constriction or high resistivity region near the cathode. The domain nucleates at such a non-uniformity because the field is highest there. The domain then travels toward the anode at a velocity which allows current continuity to be maintained. This velocity is in the usual case close to the electron drift velocity. A cathode non-uniformity which favors domain formation was recognized as being desirable by Gunn very early in the work on the Gunn Effect and had subsequently been demonstrated theoretically as discussed in section 3.4.1. Introducing a constriction or high resis-tivity layer at the anode, however, causes -a large field -at the anode which is not compatible with travelling domains. A large anode field tends to remain stationary and leads to a saturating current characteristic. If i t is sufficiently large i t can lead to impact ioni-zation as discussed in section 3.4.1, 3.4.6 and 3.4.'7. In the NERFET, a notched cathode would tend to favor formation of a domain at the cathode. The shunting capacitor, however, would tend to shunt out any rapid changes in any excess domain voltage and the field within the device should therefore be nearly static. If the excess voltage across a static cathode domain absorbs more than its share of an increase in external voltage (as is the case for a travelling domain in a conventional diode, Copeland 1966) then the device current would de-crease with increasing applied voltage. To check for the possible occurrence of a stationary domain a voltage profile was obtained for two 142 NERFETs (one notched the other not notched) by moving a probe along the surface of the NERFETs. The tungsten probe wire was polished to a point of about one microns radius as shown in figure 5.29 and mounted in a Kulicke and Soffa micromanipulator. The micromanipulator was Figure 5.29 Point, of the tungsten probe (x 100) driven with a Synchron motor and the assembly moved the probe at appro-ximately 10 microns per minute. The dc potential of the probe was measured 14 with a Keithley 602 Electrometer (input impedence > 10 ohms) to minimize the effect of probe leakage current. The resulting voltage versus distance plots were recorded on a Mosley 135 x-y recorder and are shown in figure 5.30 for various values of applied voltage. cathode drop for voltages greater than the threshold voltage in both cases. This cathode drop was larger in the notched device than in the non-notched device. Such a cathode drop is compatible with the exis-tence of a stationary dipole domain at the cathode. The larger drop in the notched device is also compatible with the greater tendency for a From figure 5.30 i t is apparent that there was an abrupt Figure 5.30 Voltage profiles in two NERFETs 144 domain to form at a constricted cathode as discussed. It is also com-patible with the accentuated negative resistance of the notched device. Another propert'y evident from figure 5.30 is a large electric field near the anode when the applied voltage exceeds threshold. This anode field exceeded the threshold field for Gunn oscillation. The anode field was larger in the non-notched device, apparently compensating for the smaller cathode drop. This also is -compatible with a-more pronounced negative resistance for the notched device. It is concluded from the voltage profile results that the static negative differential resistance probably results from the static cathode domain. The voltage across the cathode domain appears to absorb a disproportionate share of any increase in dc applied voltage in a manner similar to that of a travelling domain in a conventional Gunn diode. This disproportionate increase in domain excess voltage causes a decrease in device current which corresponds to static negative resistance. Further-more, the greater tendency for domain nucleation at a constricted cathode would explain why there is a greater tendency for negative resistance to occur \tfhen the constricted end is made the cathode rather than when i t is made the anode. Devices studied previous by Winteler and Steinemann 1966 (fig-ures 5.25(n) and 5.25(o)); Petzinger, Hahn and Matzelle 1967 (figure 5.25 (p)); and Califano 1969 (figure 5.25(q) which had similar structures to those studied here, appear to also have had surface depletion layers and relatively large source-to-drain capacitances. The circuit perfor-mance of those devices as remarked previously was similar to that observed here. The published reports of these previous devices appears to add l i t t l e extra information to confirm or deny the SNDR mechanism suggested 145 here of a stationary cathode domain caused by rf shorting or distorting of the p-n junction depletion region. The SNDR characteristics obtained from other devices as discussed in section 5.3.5 do appear, however, to be consistent with the capacitance shorting and surface depletion distortion ideas. In both devices Gunn oscillation gave way to an SNDR characteristic without instability when surface loading was added and the source-to-drain capacitance was increased. In the devices of Kataoka, Tateno and Kawashima 1968 (figure 5.25(dd)) 3 the capacitance was increased by a factor of greater than 10 by loading the device's surface with BaTiO^ (e^ > 10 ) which probably also intro-duced a surface depletion region. In the device' of Boccon-Gibod and Tes-zner 1971 the capacitance was increased by a factor of approximately 5 by moving the capacitive plate closer to the cathode while s t i l l over-lapping the anode. This plate almost certainly introduced surface de-pletion. Both of these asymmetrical devices showed SNDR in only one polarity and current saturation in the other. The tapered device of Kataoka et al. displayed SNDR when the narrow end was the cathode. This is con-sistent with the characteristics observed on notched NERFETs. The device of Boccon-Gibod et al. displayed SNDR only when the unloaded end was the cathode. Indirectly, this is also consistent with the notched NERFET characteristics because domain formation would occur more readily at an unloaded contact than at a surface capacitively loaded one. 5.4.6 Previous Theories of Bulk SNDR The possibility of static negative differential resistance existing in devices made of materials possessing negative differential mobility has been the subject of a number of papers. Shockley2 1954 showed the static differential resistance is always positive in a stable 146 uniform semiconductor which has ohmic contacts i f diffusion is ignored. Kroemer^ .1970 generalized Shockley's theorem to include arbitrary im-purity distributions and geometries and again ignoring diffusion con-cluded the static differential resistance must be positive. Kroemer0 , 3,4 1968 and 1970 also concluded that static negative differential resistance may occur i f the cathode contact is not "well behaved" as discussed further below. Hauge 1971 in a computer study and Dohler 1971 in a "field of directions" study concluded that static negative differential resistance may occur i f a field dependent diffusion coefficient of the proper form exists in the material. Sterzer 1971 in a more general approach con-cluded static negative differential resistance may occur for any case in which the electric field distribution through the device can be a multi-valued function of current. Sterzer stated that mathematically the necessary condition for the electric field distribution to be a multi-value function of current is that the differential equation relating field and current be of higher order than unity. The approximate equations relating field and current for the NERFET are coupled, non-linear equations in two dimensions which would be difficult to solve. Even i f they could be solved they would demon-strate only the necessary condition for SNDR and not the sufficient condition, and so this approach was not pursued further. For the structure used in this study i t seems possible that the depletion region along one face of the device, being free to distort to be compatible with the voltage distribution in the conducting channel, may allow more than one stable voltage distribution to exist for a par-ticular value of device current. Specifically the two types of voltage 147 distributions which were observed and discussed in section 5.4.5, (one with a cathode drop for voltages above threshold and the other with no such drop for voltages below threshold) appear to be allowed. Hence, according to the requirements stated by Sterzer these devices do not appear to be disallowed from showing a static negative differential re-sistance characteristic. Kroemer^ 1970 states "... . as long .as the cathode boundary conditions are 'well-behaved', that is > 0 ... static negative 6 j conductance cannot occur under the assumed conditions irrespective of N(x)". Tateno and Kataoka 1971 suggest that one of Kroemer's^ 1970 conditions, that of the colinearity of incremental field and current density lines, is not met i f the semiconductor is surrounded by a dielec-tric of relatively high permittivity. In this case they state "... a considerable component of the electric field perpendicular to the boundaries should be produced as a result of accumulation or depletion of electrons". Kroemer's^ 1971 reply is very important with regard to pro-viding a possible explanation for the SNDR phenomenon observed here. He states: "... for an isotropic mobility, the local static current density and the local static electric field must be colinear, except possibly in regions with zero carrier (and current) density. The latter exception could occur inside a sur-face depletion layer, which is presumably the situation Tateno and Kataoka have in mind. If the thickness of such a depletion layer did not vary as the current is increased, the depletion layer could be considered as being outside the conducting medium, and the proof would continue to hold. A changing depletion layer thickness in effect intro-duces a current-dependent boundary shape, and in structures whose transverse dimensions 148 are not large, compared to depletion layer thicknesses, this could conceivably lead to a static negative conductance. Whether this can indeed happen appears to be unknown at this time, but strictly speaking the proof is contingent on the negligibility not only of diffusion effects but also of surface depletion layers with current-dependent thickness". Kroemer^ 1971 has specifically allowed the existence of SNDR in a device which has a surface depletion layer, the thickness of which is current dependent. His statement describes exactly the situation for the NERFET. Furthermore, i t is essentially the same statement as that made above that "the depletion region along one face of the device, being free to distort ... may allow more than one stable voltage dis-tribution in the conducting channel". 5.5 Circuit Performance of the Negative Resistance Field Effect  Transistor (NERFET) 5.5.1 In't roduc t ion The current-voltage characteristic of a NERFET with a set gate voltage is similar to that of a tunnel diode in that both display regions of positive, negative and again positive differential resistance upon increasing the source to drain voltage. The circuit properties and uses of a device with such a characteristic have been quite thoroughly re-viewed in the literature for the tunnel diode (for examples Chow 1964, Chang 1964, Dunn 1969, Sze 1969). Therefore, circuit performance of such a device is reviewed only in sufficient detail to show that the observed circuit performance of the NERFET is compatible with the devices' para-meters. The emphasis in this section is on the special properties which the NERFET has as a result of the third electrode (i.e. the gate electrode). 5.5.2 The NERFET Equivalent Circuit Figure 5.31 shows diagramatically the cross-section of a NERFET 149 and an equivalent circuit superimposed on i t . Many parasitic elements which may be important at microwave frequencies such as lead resistances — gate Figure 5.31 The NERFET and equivalent circuit and inductances and terminal capacitances have been omitted. The notation used in figure 5.31 is as follows: 1) R and R, are the contact resistances of the source and *s d drain respectively. The specific resistivity of these -3 2 contacts is about 10 -cm as discussed in section 3.4. Because of the non-uniformity of the field due to the planar contacts the value of this resistance is difficult to establish but is probably less than 100 0. 2) C and C, are the capacitances associated with the gs dg source and drain respectively. The values of these capacitances are dependent on the contact areas, carrier concentration and source to drain and gate to drain 2 voltages. For contact lands of 1 mm area and carrier 15 -3 concentration in the n layer of about 5 x 10 cm (as appropriate to the devices made here) these capacitances vary from about 200 pf at zero volts 150 to 85 pf at 25 volts. 3) R and R, are the total resistances of the bulk gs dg material and gate contact for gate to source and drain to gate respectively and are probably less than 100 fi. Because they are in series with capaci-tors and are small in value they are neglected in .further consideration. 4) g the trans conductance is a function of the device's. m dimensions and carrier concentration. Transconduc-tances for the NERFETs made in this study have been often in the 6000 umho range with no attempt having been made to obtain a maximum value. This value i s , however about twice that of many commercially avail-able Si JFETs. 5) g_ the output conductance is the slope of the drain current-drain voltage characteristic and is the feature which distinguishes the NERFET from the or-dinary JFET. For the NERFET5 g_ can have a negative value for some voltages, while for an ordinary JFET i t is always positive. Output conductances in the range from ~5 to -0.01 mmhos have been observed in this study. An approximate equivalent circuit for the NERFET is shown in figure 5.3.2. 151 gate drain source source •0 Figure 5.32 Approximate NERFET equivalent circuit 5.5.3 Small Signal Analysis When a negative resistance device is used in a circuit i t is usually of paramount interest to know i f the circuit will be stable or not. If the circuit is to be used as an oscillator, instability is sought, while i f i t is to be used as an amplifier, a stable situation is desired. It is usual to consider the small signal conditions of the circuit on the grounds that i f i t is stable to small signal perturbations i t will remain stable, while i f i t is unstable the instabilities will grow into large signal conditions. The NERFET can be shown to behave predictably by considering its performance in the simple series circuit shown in figure 5.33. v W L Figure 5.33 NERFET test circuit 152 The symbol chosen for the NERFET is similar to that for the JFET except and "N", to signify the negative resistance property, is placed adjacent to the drain terminal. The^ac equivalent circuit of figure 5.34 , as-suming dc bias supplies, is shown in figure 5.34. Figure 5.34 ac equivalent circuit of the NERFET -test circuit where r = 1—1 C = series combination of C. and C dg gs are the external circuit inductance and resistance R " *E + RC The differential equation describing this circuit is: 2 T d i ,L di , R - r n z c I O N ~1 rC ~ dt 1 = ° ( 5 " 1 8 ) dt The solution of this equation is of the form: i = exp s^t + exp s^t (5-19) v s 2 " -1 <r - „ ± Jx <? - h?2 - • <5-20) 153 The exponential factors s^ and s^ may be real, complex or imaginary de-pending upon the choice of circuit parameters. If either value has a positive real part the circuit will be unstable. If the s's are real, any i n i t i a l disturbance will either decay or grow exponentially. If the s's are complex, the transient waves will be growing or decaying sinu-soids . Rearranging equation 5-20 to express the right hand side R 1 in terms of the two parameters — and —r— yields: r 2„ J r C r - - f « t - - r ? ± h <! - x ) 2 " \ a - $ • ( 5 ~ 2 1 > r C v r C r C The regions of the various forms of solution are separated by the lines: R L .r ..2._ r C (5-22) and r C r C Equation 5-23 can be rewritten: f = 2(-^-) 2 - -4}- (5-24) r r C r C From equation 5.24 i t is apparent that the largest allowable value of R L R — is unity and occurs for —~- = 1. Larger values of — are physically r C possible however and correspond to operation in one of two stable states as discussed in section 5.5.8. The small signal analysis applies only R to the case — £ 1. r 154 The various areas defined by equations 5-22 and 5-24 correspond to different types of solutions as listed in table 5.1 and shown gra-phically in figure 5.35 condition I condition II solution type Mode of operation 1 > L r r 2C 1_ r K 2 } ~2~ decaying r~C r C sinusoid Amplifier R > L r r 2C R 1 L ,2 > 2 H H r 2 ' r C r 2C decaying exponential Stable — < L r r 2C - < 2 (—) 2 r C r 2C growing sinusoid quasi-sinusoidal oscillation — < L r 2C - > 2 C — ) 2 r C -y- growing r C exponential relaxation oscillation Table 5.1 Conditions of stability and instability The exponentially growing solutions are limited by the non-linear form of the current-voltage characteristic of the diode. Because of this non-linearity, the waveforms are not pure sinusoids in the region designated "growing sinusoids" in figure 5.35. They become more R L sinusoidal as the real part of s goes to zero. At — = —r- , Re(s) = 0 r r C and this corresponds to steady (i.e. not growing or decaying) sinusoidal oscillation. Therefore, the large signal oscillation becomes more sin-usoidal as the R r 2C line is approached. To demonstrate that the operation of an actual device is com-patible with this small signal analysis the device whose characteristic is shown in figure 5.12 was used in the series arrangement shown in fig. 5. Figure 5.36 NERFET waveforms for several points on the stability plot 156 The gate was tied to the source and 11 volts applied from drain to source, resulting in a drain capacitance of C = 85 pf and a negative resistance of -r = -300 Q. The circuit resistance was 50 Q, and by putting various inductances in the circuit the waveforms inset in figure 5.36 were ob-tained. The waveform scales in this figure are 0.5 v/large div. vertically and 0.2 usec/large div. horizontally. The lowest inductance at which oscillation was observed was 2.5 uh; at 1 yh the circuit was stable. '.('This device was also made to operate in the "decaying sinusoid" region as an amplifier as discussed in section 5.5.7). The waveforms shown in figure 5.36 demonstrate the following points, a l l of which are predicted by the small signal analysis: a) For L = 1 uh no oscillation occurred, corresponding to the R L condition — > — — • r C b) For L = 2.5 uh the oscillation was quasi-sinusoidal, corresponding R L to the condition r r 2C c) As L was increased the waveform became less sinsusoidal until for large L i t was of the relaxation oscillation type, corres-' . R L , R o/ 1 sl/2 L ponding to the conditions — < — , and — > 2( „ ) ^— . r r C r r C r C 5.5.4 Non-linear Analysis A common approach (Chang 1964, Chow 1964, Cunningham 1958, Anner 1967, Schuller and Gartner 1961) for obtaining analytic expressions for the large signal operation of negative resistance devices is to- match the current-voltage characteristic of the device with an expression 3 of the form: i = -av + bv 157 The resulting differential equation which describes the device operation in a series inductive circuit (figure 5.33) is (Cunningham 1958): 2 3 d v a , 3b 2. dv v R ,dv av by. _ , c ... " c ( 1 " -_ V > dl + LC + l^-~C + "C"} = ° ( 5 _ 2 5 ) dt which, under the condition of sufficiently small external resistance R, can be reduced to the well known van der Pol equation: 2 — £ - a (1 - (Bv2) to ^ + to 2 v = 0 (5-26) j^2 o dt o v dt where a = — — , 8 = — and to = — Cto a o LC o Since the methods of solving this equation and the results ob-tained under various conditions have been well documented elsewhere these detailed solutions are not included. Only the results which contribute to an understanding of the circuit operation of a NERFET are quoted. One property of a NERFET operating in an inductive circuit which is of interest is the amplitude of oscillation. Using the pertur-bation method of solving equation 5.26, the peak to peak amplitude can be shown to second order approximation (Cunningham 1958) to be given by: 1 V = 4 ( a / 3 b ) 2 (5-27) Fitting the NERFET characteristic with the equation i = -.0025 v + .0067 v 3 as shown in figure 5.37 results in a calculated peak-to-peak amplitude across the NERFET of 4.4 volts. The resulting peak-to-peak amplitude across a series load of 50 Q should be 0.93 volts. This is compared to the observed amplitude across a 50 Q load for this NERFET of approximately 158 Ms 1/ Figure 5.37 Experimental and fitted I-V characteristics 0.5 volts as shown in figure 5.36. The difference between calculated and observedamplitudes may be partly a result of ignoring the contact resistance of the device. Note that the peak-to-peak amplitude given by expression 5-25 is independent of the circuit parameters and is a function of the device characteristic only. This independence is de-monstrated by the waveforms shown in figure 5.36 for the various in-ductances. A second property of interest is the frequency .of oscillation as a function of circuit inductance. The zeroth order approximation (which is the linear negative resistance case) predicts (Schuller and Gartner 1961) a frequency of: 159 1 - — f = — • (5-28) 2ir /L~C The first order approximation in the limit of small inductance predicts (Schuller and Gartner 1961 and Cunningham 1958) a frequency of: 2-rr^ /LC [1 + ^ -( ~ 2 - — ) ] r and in the large inductance limit predicts (Schuller and Gartner 1961) f = 1761871: • <5-30> Shown in figure 5.38 are: a) the experimental points for a NERFET (C = 85 pf, -r => -300ft) operated in a high Q (~ 200) circuit with various values of inductance (power supply irapedence: 0.5 ft, 1 uh), b) the zeroth order approximation assuming R = 0. R c) the zeroth order approximation assuming — = 0.5 (which may be possible considering the uncertainty in the value of contact resistance, and d) the first order approximations for both large and small induc-tance assuming R = 0. Linearity of the experimental points of the ln(f) vs ln(L) plot over 3 decades of inductance is evident in figure 5.38. The slope of these points is approximately -1/2, indicating a dependence of fre--1/2 quency on inductance of the form f a L . I t was observed that with the exception of inductances in the 1000 uh range the waveforms were sinusoidal. This is compatible with operation in a high Q circuit and R L infers operation near the condition — = — a s discussed in section 5.5.3. r 2_ r C 160 L (j4h) 1 order approximation (large L) 0th order approximation ( R/r= 0 ) 0 order approximation ( R/r =0.5) 1st order approximation (small L) \ -1 10 0 10 f ( M H z ) Figure 5.38 NERFET oscillation frequency as a function of circuit inductance 161 The frequency under this condition should be given by the zeroth order approximation: 1 - * f = (5-28) 2TT JLC It is shown in figure 5.38 that choosing a value of R = 0 (i.e. zero contact resistance and zero external resistance) although giving the proper slope is not a very good match to the observed points. Choosing a value of R/r = 0.5 is shown to match the experimental points much better, indicating the contact resistance was about 150 fi. This value as stated previously is quite possible. A reasonable match of experimental points to the first order approximations in the high and low inductance limits is also shown in this figure. The error bars shown in figure 5.38 at high frequency are based on a + 2.5% error. This error may arise from equipment calibration errors and error in measurement of frequency from the oscilloscope photographs. At low frequencies and large inductances the waveforms were appreciably non-sinusoidal and bias dependent, resulting in larger possible errors as shown in figure 5.38. The waveforms obtained from a non-linear analysis of the Van der Pol equation become less sinusoidal and more of the relaxation type as the circuit inductance is increased. This trend has been observed here as shown in figure 5.36. Rather than carry out this analysis which has been done by many authors (for example; Cunningham 1958 and Schuller and Gartner 1961), greater physical significance can be obtained by con-sidering the relaxation between high and low voltage states of a piece-wise linear current-voltage characteristic as discussed in the next section. 162 5.5.5 Relaxation Oscillation Analysis The analysis of the negative resistance relaxation oscillator by approximating the non-linear current-voltage characteristic by a piecewise-linear characteristic has been discussed for the tunnel diode by a number of authors (for example; Ko 1961, Chow 1964). The perfor-mance of a NERFET with a grounded gate should be similar to that of a tunnel diode when operated as the negative resistance element in a re-laxation oscillator circuit. A simple relaxation oscillation circuit is shown in figure 5.33. The basic operation of the circuit is as follows: The circuit current increases exponentially after the power is applied, and when i t reaches the peak current of the characteristic (point 1 in figure 5.39) the device switches to the high voltage state (point 2). Since .the voltage drop-across the NERFET is larger than the supply voltage, the current begins to decrease exponentially. However, when the current reaches the valley (point 3), the device switches to the low voltage state (point 4). The current again begins to increase and the cycle is repeated. The current and voltage therefore trace the path 1234 as shown in figure 5.39. If the capacitance C is sufficiently small the switching time between states 1 and 2 and also 3 and 4 will be much less than the growth and decay times of the other two sections (4-1 and 2-3). The resulting current waveform is typified by that given by Ko 1961 as shown in figure 5.40. The time constant for the exponential growth segment of the current waveform is given by: Vowth = L / RT1 1 6 3 80 70 60 (ma) 1 6,4 9.6 12.8 V (volts) Figure 5 . 3 9 Relaxation switching path Figure 5 . 4 0 Relaxation oscillation current waveform (for tunnel diode circuit from Ko 1 9 6 1 ) . where L is the circuit inductanct R is the circuit resistance R^ is shown in figure 5 . 3 9 . *T1 = R + R d l The time constant for the exponential decay portion of the cycle is given by: decay L / R T : where R ^ 2 is shown in figure 5 . 3 9 . R^ - R + R d2 164 For the device whose characteristic is shown in figure 5.16a operated in the circuit of figure 5.34 with L = 25 yh and R = 50 the calculated time constants are: T = 0.08 usee growth T , = 0.025 ysec decay The actual time constants observed for this device in an inductive cir-cuit as determined from figure 5.36 are: T _, - 1 ysec growth x , < 0.02 ysec decay ~ The decay time constant is difficult to measure in figure 5.36 because the total decay time per cycle appears to be less than one time constant and is about 0.02 ysec. A comparison of the calculated and obeserved time constants shows that the two sets of values are compatible. 5.5.6 The NERFET as a Gate Tunable Oscillator In a high Q(200) circuit a negative resistance element gen-erates a quasi-sinusoidal waveform at a frequency of approximately (section 5.5.3 and 5.5.4) i - * f = (5-28) 2ir /L~C For the NERFET, the source to drain capacitance C is due to the depletion region between the n and p layers and is composed of the series com-bination of the source to gate and gate to drain capacitances. The width of the depletion region and therefore the source to drain capacitance is a function of the reverse bias on the gate (p-region) as described in section 5.2.2. The frequency of oscillation is therefore a function of the gate voltage. 165 The circuit shown in figure 5.41 was used to observe the gate tunability of the NERFET in a high Q circuit. The current waveforms observed for gate voltages in the 0 to -7 volt range are shown in f,igure 5.42. Two distinct waves which existed simultaneously in the -1 to -2 volt range are evident in this figure. Schuller and Gartner 1961 in a large signal analysis of a negative resistance diode have shown that two such waves can exist. They state: •-"... the reason seems to be that when the device is not biased at the voltage with the highest slope, there exist two limit cycles, a smaller and a bigger one. ... Thus, for the same inductance two oscillations with different amplitudes may exist". The frequency tunability of the higher frequency, lower amplitude one is shown -in -figure 5.43. The solid line in this figure was determined from equation 5-28 using R/r = 0 and C obtained from the series combination of the source to gate and gate to drain capacitances. More investi-gation would be necessary before one could take advantage of the larger amplitude mode in a systemmatic way. When the NERFET was used in a low Q (-10) circuit the waveform was also tunable as evident in figure 5.44, however i t was not as simple to analyse. The largest portion of the cycle was that associated with the exponential growth as discussed in section 5.5.5. This growth time is given by (Ko 1961) (also refer to section 5.5.5) . T = In — 2. growth R T 1 . I a - I v where \ = V a P P / R T l I = the peak current 166 voltage supply oscilloscope] Tektronix 561A 5jnh Figure 5.41. Test c i r c u i t used to show NERFET gate t u n a b i l i t y Vr 0.5 v ^ U i W W W W W W -A h-O.ljusec Figure 5.42 Current waveforms f o r a NERFET i n a high Q c i r c u i t w i t h v a r i o u s gate v o l t a g e s (L=5uh) 167 19 18 17 16 15 (MHz) Vg (volts) -2 - 4 - 6 -8 Figure 5.43 Gate tunability of the NERFET V V9 -6 JL 0.5 v T Figure 5.44. Current waveforms for a NERFET in a low Q circuit with various gate voltages (L=200yh) 168 I = the valley current. When I - I =1 - I as is the case for the NERFET used here, the a p a v I - I a p term, In - — ^ , is a rapid function of the bias conditions and gives a v rise to a large tuning effect with small change in bias voltage. Figure 5.44 shows greater than one octave tuning for a change in gate voltage of 7 volts. The pulses near the beginning of the growth portion of each cycle shown in this figure were observed to correspond to a pulse of gate current. 5.5.7 The NERFET as a Phase-Locked Oscillator and as a Stable  Amplifier The device whose characteristic is shown in figure 5.16(a) was used in the circuit shown in figure 5.45 to demonstrate phase-locking of circuit oscillations to an rf signal on the gate. rf voltage supply dc voltage supply 1 50jxhy oscilloscope Tektronix 561 A Figure 5.45 Test circuit used to show phase-locked oscillation Phase-locking to the gate signal was observed over about a 2% variation of gate signal at about 2 MHz, The gate voltage needed for locking was about 0.2 volts peak to peak while the oscillation output voltage was about 0.5 volts peak to peak. Hence, a relatively large gate 169 voltage was required because the device was operating near the cut-off frequency for gate control. This cut-off frequency as obtained from simple transistor theory (for example, Sze 1969) is given by: f o v = g /C = 5 MHz max m g = the transconductance m where ~m = 500 ymhos for this particular device C = 100 pf for this device Note that the maximum frequency (1/rC) of circuit oscillation using the negative resistance property of this device was about 30 MHz (r = 300ft, C = 100 pf) and was considerably greater than the cut-off frequency for gate control (5 MHz). The same NERFET was used in the circuit shown in figure 5.46 and with the gate tied to the drain (i.e. acting as a two terminal ne-gative resistance amplifier) a voltage gain of about 13 db at 20 MHz was observed. rf voltage supply 0.1 Mf I f— dc voltage supply -± 1000 j4h 200-n-< oscfl loscope Tektronix ~. 561 A Figure 5.46 Test circuit used to show stable amplification 5.5.8 Tile NERFET as a Bistable Logic Element If the load resistance and device bias conditions are adjusted so the load line intersects the device characteristic as shown in figure 170 5.47 the device may operate .s.tably • at the two points labelled A and B. Switching from A to B can occur by applying a negative pulse to the gate and driving the characteristic down so that only the intersection i + I Figure 5.47 Device characteristics and load line showing stable operating points near B occurs. The device is forced to switch to this single intersection point and remains there even though the gate pulse is removed. Switching from B back to A can occur by applying a positive pulse to the gate by similar reasoning. The circuit shown in figure 5.48 was used to demonstrate swit-ching between these stable states. Figure 5.49 shows typical gate voltage (top trace) and source to drain voltage (bottom trace) waveforms when operated as a bistable logic element. This figure shows that a negative gate pulse causes switching from a low source-drain voltage (state A) to a high source-drain voltage (state B) as explained. The device remains in stage B until a positive gate pulse drives i t into state A. The switching speed of the device operated in a resistive cir-cuit, as discussed in section 5.4.2 is approximately: 171 delayed trigger pulse generator Tektronix 115 dc voltage supply pulse generator Tektronix 115 A A A _ J ~ L JV7_L oscilloscope Tektronix . 567 /I Figure 5.48 Test circuit for NERFET bistable switching V 1 msec t Figure 5.49 NERFET bistable waveforms 172 T = X C • switching For the device used in this experiment (figure 5.47) r = 105 C * 100 pf Therefore T . . . =10 usee. As shown in figure 5.50 this is close switching to the value observed experimentally for this device. Note that the 4> V .  _ L 0.5 v T 2 v T Figure 5.50 Switching waveform of the NERFET logic element magnitude of the negative resistance was very large for this device (r - lO^ft) and the resulting switching time was relatively long. Ne-gative resistances of r = 300 ohms have been observed in this study in thicker devices, which would improve the switching speed by a factor of about 300. Furthermore, i f reduced contact lands had been used as dis-cussed in section 5.4.2 the capacitance could possibly have been reduced to about 3 pf. The switching speed of such a device would then be about one nanosecond which would appear to make i t an attractive possibility for high speed logic circuits. 173 VI. CONCLUSIONS 6.1 The Planar Gunn Diode Gunn diodes in the planar structure have been fabricated and operated cw in resistive circuits. It has been observed that as the product of electron concentration x diode thickness (nd product) was de-creased, the frequency of oscillation decreased for diodes of the same length. To ensure that the oscillation was due to the formation and transit of charge domains (i.e. pure Gunn mode) the shapes of the wave-forms were correlated to the shapes of the devices. The results indicated that the oscillation was due to domain transit and that the domain velocity decreased with decreasing nd product. This is as compared to the case for bulk diodes (i.e. sandwich structure diodes) in which the domain velocity is independent of geometry and doping. A small signal analysis was carried out (section 2.3) which predicts that the pulse propagation velocity decreases' as the nd product 11 -2 decreases and at a value of nd = 1.132 x 10 cm the domain velocity 11 -2 is zero. This analysis also predicts that at nd = 1.132 x 10 cm the space charge growth is abruptly reduced and corresponds to an os-cillation suppression condition. Hence, zero domain velocity and os-cillation suppression which are physically identical have been shown analytically to occur at the same value of nd product. Gunn oscillation has been experimentally observed in devices 11 -2 with nd product as small as 2.1 x 10 cm . At this value the domain velocity was measured to be approximately 0.55 x 10^ cm/sec at a bias just above threshold. This is a factor of 2 or 3 less than the corres-ponding domain velocity for bulk diodes. The uncertainty in this factor is a result of the bias dependence of the domain velocities in each case. 174 The practical problems associated with the tendency for co-herent oscillation from planar Gunn diodes and the tendency for anode deterioration have not yet been overcome. A systematic; approach to minimizing these difficulties would be more naturally carried out by an industrial concern interested in making planar Gunn diodes on a mass pro-duction basis. Basically, however, the problems appear to arise from the materials used and do not appear to be inherent to the structure itself. The solution to these problems probably lies in using low defect material, I | shaping the diode appropriately and using n regrown GaAs contacts. 6.2 The NERFET A new device which is given the acronym NERFET (negative re-sistance field effect transistor) has been fabricated. The structure of the device consists of planar source and drain contacts on an n-type GaAs layer which has been-epitaxially-grown on a >p-type -substrate. -The p region provides gate control of the n-type epi-layer. The current-voltage characteristic of the NERFET has a region of static negative differential resistance (SNDR) without Gunn instability. This is compared to the saturating current characteristic of the conven-tional field effect transistor. Such a SNDR characteristic is not gen-erally observable (Shockley2 1954, Kroemer^ 1970) for bulk devices, even those prepared from materials such as GaAs which have negative dif-ferential conductivity. The static negative differential resistance without instability is concluded to result either directly or indirectly from the depletion layer associated with the junction which exists between the n-type epi-layer (source to drain channel) and the p-type substrate (gate). The negative resistance property of the NERFET has been utilized 175 in a number of circuits to demonstrate the device's usefulness in many applications. It has been used as two terminal (by connecting the gate to the source) negative resistance oscillators and amplifiers. The third terminal (the gate) has allowed the device to be used in unique appli-cations such as; a negative resistance oscillator which can be phase-locked to an rf gate signal, and a bistable element for which switching between the stable states is accomplished by pulsing the gate. In light of much effort to use oscillating (Hartnagel^ 1969, Hartnagel,. 1971, and Sugeta, Yanai and Sekido 1971) and non-oscillating (Thim^ a n <^ ^ 1971) GaAs devices as logic elements, this bistable NERFET application is particularly worthy of further investigation. Other applications for the NERFET such as the negative resistance amplifier with gate con-trolled gain also appear to be possible. The• NE-RFET-s -which were made--here, using simple •contact-materials and process steps, have not been as prone to breakdown as planar Gunn diodes because the negative resistance property can be obtained at much lower current and voltage levels. As is the case with the first reporting of almost any new type of device a considerable area remains unexplored. The NERFETs made here were not optimized for any particular application. For example, in making an oscillator or amplifier i t may be desirable to use a thick device which operates at high voltage and current levels, while i t may be desirable to use a thin device for low power consumption for logic applications. Optimization of the NERFET to obtain better performance would appear to be a worthwhile step. Varying such parameters as the device's geometry and carrier densities may allow the realization of a character-ist i c which has a peak to valley current ratio of two to one as observed 176 for related two terminal devices (Boccon-Gibod and Teszner 1971). Reducing the source-to-drain capacitance may allow switching times of nanosecond or less to be attained. Each of these improvements could be attempted with many possible applications in mind. 177 BIBLIOGRAPHY Acket, G.A. and J . de Groot, "Measurements of the c u r r e n t - f i e l d s t r e n g t h c h a r a c t e r i s t i c of N-type g a l l i u m arsenide using v a r i o u s h i g h power microwave techniques", I.E.E.E. Trans, on E l e c t r o n Devices, ED-14, pp 505-511, Sept. 1967. Acket2» G.A. and J . J . Scheer, " R e l a x a t i o n o s c i l l a t i o n s due to impact i o n i z a t i o n i n e p i t a x i a l sheet-type Gunn o s c i l l a t o r s " , E l e c t r o n i c s  L e t t e r s , 5_, pp 160-161, 17 A p r i l 1969. Adams R.F., "CW o p e r a t i o n of GaAs pl a n a r Gunn diodes w i t h evaporated cont a c t s " , Proc. I.E.E.E., 57, pp 2164-2165, Dec. 1969. Amron, I . , ""A s l i d e r u l e f o r computing dopant p r o f i l e s i n e x p i t a x i a l semiconductor f i l m s " , Electrochem. Tech. 2^ , pp 327-333, Nov. 1964. Anner, G.E., Elementary Nonlinear E l e c t r o n i c C i r c u i t s , P r e n t i c e - H a l l Inc., Englewood C l i f f s , N.J., 1967. Baechtold, W., "Q band GaAs FET a m p l i f i e r and o s c i l l a t o r " , E l e c t r o n i c s  L e t t e r s , J7> pp 274-275, 20 May 1971. Baechtold2, W., and W. J u t z i , " P r e a m p l i f i e r s near 18 GHz w i t h GaAs f i e l d e f f e c t t r a n s i s t o r s " , Proceedings of 1971 European Microwave  Conference, Stockholm, -Sweden, Aug. 1971. B a e c h t o l d 3 , W., W. Walter and D. Wolf, "X and Ku band GaAs MESFET", E l e c t r o n i c s L e t t e r s , 8, pp 35-37, 27 Jan. 1972. Baechtold^, W., "Noise behaviour of GaAs f i e l d e f f e c t t r a n s i s t o r s " , I.E.E.E. Trans, on E l e c t r o n Devices, ED-19, pp674-680, May 1972. Bhattacharya, T.K., "A simple a n a l y s i s of tapered Gunn o s c i l l a t o r s " , P h y s i c a Status S o l i d i , a , . l , pp 757-764, 16 A p r i l 1970. Becke, H., R. H a l l and J . White, "Gallium arsenide MOS t r a n s i s t o r s " , S o l i d State E l e c t r o n i c s , 8, pp 813-824, Oct. 1965. Becke2> H., and J . White, " G a l l i u m arsenide i n s u l a t e d gate f i e l d e f f e c t t r a n s i s t o r s " , Proceedings of the I n t e r n a t i o n a l Symposium on  GaAs, pp 219-227, Reading, Oct. 1966. Becker, R., B.G. Bosch and R.W.H. Engelmann, "Domains and guided electromagnetic waves i n GaAs S t r i p l i n e " , E l e c t r o n i c s L e t t e r s , 6^ , pp 604-605, 17 Sept. 1970. B e c k e ^ , R., and B.G. Bosch, "Power-frequency l i m i t a t i o n s of p l a n a r -type GaAs t r a n s f e r r e d e l e c t r o n d e vices", proceedings of the I n t e r -n a t i o n a l Symposium on GaAs, pp 163-171, Aachen, Oct. 1970. Black , J.R., " E l e c t r o m i g r a t i o n - A b r i e f survey and some recent r e s u l t s " , 178 I.E.E.E. Trans, on Electron Devices, ED-16, pp 338-347, A p r i l 1969. Boardman, A.D., W. Fawcett and H.D. Rees, "Monte Carlo c a l c u l a t i o n of the v e l o c i t y - f i e l d r e l a t i o n s h i p f o r gallium arsenide", S o l i d  State Comm. , <6, pp 305-306, May 1968. Boccon-Gibod, D., and J.L. Teszner, " L a t e r a l c a p a c i t i v e probing of an anode-loaded e p i t a x i a l coplanar gallium arsenide diode", E l e c - tronics L e t t e r s , ]_, pp 469-472, 12 Aug. 1971. Boccon-Gibod2> D., and J.L. Teszner, "Experimental evidence of b i -stable switching i n a Gunn e p i t a x i a l coplanar diode by anode surface loading"., E l e c t r o n i c s L e t t e r s , ]_., pp 468-469, 12 Aug. 1971. Boer, K.W. and G. Dohler, "Influence of boundary conditions on high f i e l d domains i n Gunn diodes", Physical Review, 186, pp 793-800, 15 Oct. 1969. Braslau, N., J.B. Gunn and J.L. Staples, "Metal-Semiconductor contacts for GaAs b u l k - e f f e c t devices", S o l i d State E l e c t r o n i c s , 10, pp 381-385, May 1967. Briggs, R.J., Electron-Stream I n t e r a c t i o n with Plasmas, Research Monograph #29, MIT Press, Cambridge, Mass., 1964. Butcher, P.N., "Theory of stable domain propagation i n the Gunn e f -f e c t " , Physics Letter's, '19, pp 546-547, 15 Dec. 1965. Butcher2, P.N. and W. Fawcett, " C a l c u l a t i o n of the v e l o c i t y - f i e l d c h a r a c t e r i s t i c f o r gallium arsenide", Physics L e t t e r s , 21, pp 489-490, 15 June 1966. Butcher-^, P.N., W. Fawcett and N. Ogg, " E f f e c t of f i e l d dependent d i f f u s i o n on stable domain propagation i n the Gunn e f f e c t " , B r i t . J. Appl. Phys., 18, pp 755-759, 1967. Califano, R.P., "Frequency modulation of three terminal Gunn devices by o p t i c a l means", I.E.E.E. Trans, on Ele c t r o n Devices, ED-16, pp 149-151, Jan. 1969. C a r r o l l , J.E., Hot Electron Microwave Generators, Edward Arnold Publishing Ltd., London 1970. Cawsey, D., "VHF and UHF Gunn-effect o s c i l l a t o r s " , E l e c t r o n i c s L e t t e r s , 3, pp 550-551, Dec. 1967. Chang, K.K.N., Parametric and Tunnel Diodes, Prentice H a l l Inc. Engle-wood C l i f f s , N.J., 1964. Chang2, K.K.N., S.G. L i u and H.J. Prager, "Infrared r a d i a t i o n from bulk GaAs", Applied Physics L e t t e r s , 8, pp 196-198, 15 A p r i l 1966. 179 Chow, W.F., P r i n c i p l e s of Tunnel Diode C i r c u i t s , John Wiley and Sons I nc. N.Y., 1964. Chynoweth, A.G., W.L. Feldman and D.E. McCumber, "Mechanism of the Gunn e f f e c t " , 8th I n t e r n a t i o n a l Conference on Semiconductor P h y s i c s , pp 514-521, Kyoto, 1966. Clar k e , G.M., A.L. Edridge, and J.C. Bass, "Planar Gunn-effect o s c i l -l a t o r s w i t h c o n c e n t r i c e l e c t r o d e s " , E l e c t r o n i c s L e t t e r s , 5_, pp 471-472, 2 Oct. 1969. C l a r k e 2 , G.M., A.L. Edridge, I . G r i f f i t h , and J.P. McGeehan, "The e l e c t r o n i c tuning e f f e c t s of a c o n t r o l e l e c t r o d e on tra n s v e r s e Gunn o s c i l l a t o r s " , 1971 European Microwave Conference, Stockholm, Sweden Aug. 1971. Cobbold, R.S.C., Theory and A p p l i c a t i o n s of F i e l d E f f e c t T r a n s i s t o r s , W i l e y - I n t e r s c i e n c e Inc., 1970. C o l l i v e r , D.J. and A.F. Fray, " L i m i t a t i o n s to the performance of pl a n a r Gunn e f f e c t d evices", S o l i d State E l e c t r o n i c s , 12, pp 671-674, Sept. 1969. Conwell, E.M., and M.O. V a s s e l , " H i g h - f i e l d d i s t r i b u t i o n f u n c t i o n i n GaAs", I.E.E.E. Trans, on E l e c t r o n Devices, ED-13, pp 22-27, Jan. 1966. Conwell2, E.M., "Boundary c o n d i t i o n s and h i g h - f i e l d domains i n GaAs", I.-E.-E.-E. Trans, on E l e c t r o n Devices, -ED-17, pp 262-270, A p r i l 1970. Copeland, J.A., " E l e c t r o s t a t i c domains i n two-valley semiconductors", I.E.E.E. Trans, on E l e c t r o n Devices, ED-13, pp 189-191, Jan. 1966. Copeland2, J.A., "Switching and low f i e l d breakdown i n n-GaAs bulk diodes", A p p l i e d Physics L e t t e r s , 9_ pp 140-142, Feb 1966. Cox, R.H., and H. Strack, "Ohmic contacts f o r GaAs d e v i c e s " , S o l i d  State E l e c t r o n i c s , 10, pp 1213-1218, Dec. 1967. C 0 X 2 , R.H. and T.E. Hasty, " M e t a l l u r g y of a l l o y e d ohmic contacts f o r the Gunn o s c i l l a t o r " , Ohmic Contacts to Semiconductors, B. Schwartz, Ed., pp 88-94, E l e c t r o c h e m i c a l S o c i e t y , N.Y., 1969. Cunningham, W.J., I n t r o d u c t i o n to Non-linear A n a l y s i s , McGraw-Hill, N.Y., 1958. Dean, R.H., "Optimum design of t h i n l a y e r GaAs a m p l i f i e r s " , I.E.E.E. Proc., 57, pp 1327-1328, J u l y 1969. Dea ^ , R.H., A.B. Dreeben, J.F. Kaminisky and A. Triano, " T r a v e l l i n g - . wave a m p l i f i e r using t h i n e p i t a x i a l GaAs l a y e r " , E l e c t r o n i c s L e t t e r s , 6, pp 775-776, 26 Nov. 1970. Dienst, J.F., R. Dean, R. Enstrom and A. Kokkas, "Coplanar contact Gunn-effect devices", RCA Review, 28, pp 585-594, Dec. 1967. 180 Djuric, A., M. Smiljanic arid D. Tjapkin, "p-n transition capacitance", Solid State Electronics, 14, pp 457-466, June 1971. Doerbeck, F.H., E.E. Harp and H.A. Strack, "Study of GaAs devices at high temperature", International Symposium on GaAs, Dallas, pp 205-212, Oct. 1968. Doerbeck2, F.H., "A planar GaAs Schottky barrier field-effect trans-istor with self-aligned gate", International Symposium on GaAs, Aachen pp 251-258, Oct. 1970. Dohler, G., "Shockley's positive conductance theorem for Gunn materials with field-dependent diffusion", I.E.E.E. Trans, on Electron Devices, ED-18, pp 1190-1192, Dec. 1971. Drangeid, K.E. and R. Sommerhalder, "Dynamic performance of Schottky-barrier field effect transistors", IBM J of R and D, 14, pp 82-94, March 1970. Drangeid2> K.E., R. Sommerhalder, and W. Walter, "High speed gallium arsenide Schottky-barrier field-effect transistors", Electronics  Letters, _6, pp 228-229, 16 April 1970. Driver, M.C., H.B. Kim and P.L. Barrett, "Gallium arsenide self-aligned Schottky-barrier field-effect transistors", Electronics Letters, 6^  pp 228-229, 16 April 1970. Dunn, C.N., "Tunnel diodes", Microwave Semiconductor Devices and Their  Circuit Applications, Ed. H.A. Watson, McGraw-Hill Inc., 1969. Edwards, W.D., W.A. Hartman, and A.B. Torrens, "Specific contact resistance of ohmic contacts to gallium arsenide", Solid State Elec- tronics, 15, pp 387-392, April 1972. Engelmann, R., "Simplified model for the domain dynamics in Gunn-effect semiconductors covered with dielectric sheets", Electronics  Letters, 4_, pp 546-547, 29 Nov. 1968. Engelmann2, R., "On the transverse surface boundary effect in Gunn devices", Proc. I.E.E.E., 57, pp 818-819, May 1969. Engelmam^, R. "Comment on 'Laminar electron flow in thin GaAs slabs'", Proc. I.E.E.E., 58, p 1869, Nov. 1970. Fallman, W.F., H.L. Hartnagel, and G.P. Srivastava, "Microwave pulse processing using Gunn diodes", International Symposium on GaAs, Aachen, pp 148-152, Oct. 1970. Fallman2, W.F., H.L. Hartnagel, and G.P. Srivastava, "New results of cw coplanar Gunn diodes for pulse processing", Physica Status  Solidi, _3, pp 227-228, 16 Dec. 1970. Fallman3, W.F., H.L. Hartnagel, and P.C. Mathur, "Experiments on heat sinking of semiconductor devices", Electronics Letters, 7_, pp 512-513, 9 Sept. 1971. 181 Fallman^, W.F. and H.L. Hart n a g e l , "Aspects of p l a n a r Gunn diodes f o r high cw output power", S o l i d State E l e c t r o n i c s , 14, pp 909-912, Oct. 1971. Fallman^, W.F. and H.L. H a r t n a g e l , " M e t a l l i c channels formed by h i g h surface f i e l d s on GaAs planar d e v i c e s " , E l e c t r o n i c s L e t t e r s , 1_, pp 692-693, 18 Nov. 1971. F i s h e r , R.E., "Generation of subnanosecond pulses w i t h b u l k GaAs", Proc. I.E.E.E., 55, pp 2189-2190, Dec. 1967. Fleming, P.L., "Self-modulation of pulsed GaAs o s c i l l a t o r s " , Proc. T.E.E.E., 54, pp 799-800, May 1966. Fleming2> P.L., "Further observations above and below twice the Gunn t h r e s h o l d " , Proc I.E.E.E., 55, pp 1538-1539, Aug. 1967. F o x e l l , C.A.P., J.G. Summers, and K. Wilson, " S u r f a c e - o r i e n t e d Gunn e f f e c t o s c i l l a t o r " , E l e c t r o n i c s L e t t e r s , 1_, p 217, Oct. 1965. G i a n n i n i , F. , CM. O t t a v i and A. Salsano, "Laminar flow i n t h i n GaAs s l a b s " , Proc. I.E.E.E., 58, pp 259-260, Feb. 1970. G i a n n i n i 2 , F., C.M. O t t a v i and A. Salsano, "Authors r e p l y to 'Comment on "Laminar e l e c t r o n flow i n t h i n GaAs s l a b s ' " , Proc. I.E.E.E., 58, p 1.8.6.9, Nov. 1970.. G i a n n i n i ^ , F. , C M . O t t a v i and A. Salsano, " C o r r e c t i o n to 'Comment on "Laminar e l e c t r o n flow i n t h i n GaAs s l a b s ' " , Proc. I.E.E.E., 59, p 1136, J u l y 1971. Glang, R. and L.V. Gregor, "Generation of pa t t e r n s i n t h i n f i l m s " , Handbook of Thin F i l m Technology, Ed. L . I . Massel and R. Glang, McGraw H i l l , N.Y., 1970. Gray, D.A., Handbook of C o a x i a l Microwave Measurements, General Radio Co., West Concord, Mass., 1968. Gueret, P., " S m a l l - s i g n a l 2-terminal impedence of a t h i n Gunn diode", E l e c t r o n i c s L e t t e r s , 6^ , pp 213-215, 2 A p r i l 1970. Gueret2> P.> " L i m i t s of v a l i d i t y of the 1-dimensional approach i n space-charge-wave and Gunn e f f e c t t h e o r i e s " , E l e c t r o n i c s L e t t e r s , 6, pp 197-198, 2 A p r i l 1970. Gueret-}, P - j " S t a b i l i z a t i o n of Gunn o s c i l l a t i o n s i n l a y e r e d semi-conductor s t r u c t u r e s " , E l e c t r o n i c s L e t t e r s , 6_, pp 637-638, 1 Oct. 1970. Gunn, J.B., and B.J. E l l i o t t , "Measurement of the negative d i f f e r e n t i a l m o b i l i t y of e l e c t r o n s i n GaAs", Physics L e t t e r s , 22, pp 369-371, 1 Sept. 1966. 182 Gupta, S.C., B.L. Sharma, and A.K. Sreedhar, "Specific resistance of n -n junctions", Solid State Electronics, 14, pp 427-428, May 1971. Gurney, W.S.C., "Contact effects in Gunn diodes", Electronics Letters, 7_, pp 711-713, 2 Dec. 1971. Hahn, W.C., "Small signal theory of velocity modulated electron beams", General Electric Review, 42, pp 258-270, June 1939. Hakki, B.W., and S. Knight, "Microwave phenomena in bulk GaAs", I.E.E.E. Trans, on Electron Devices, ED-13, pp 94-105, Jan. 1966. I-Iamerly, R.G. , and M.W. Heller, "Space charge scattering and electron transport in GaAs", J. of Applied Physics, 42, pp 5585-5589, Dec. 1971. Harris, J.S., Y. Nannichi, G.L. Pearson and G.F. Day, "Ohmic contacts to solution-grown gallium arsenide", J. of Applied Physics, 40, pp 4575-4581, Oct. 1969. Hartnagel, H.L., "Gunn instabilities with surface loading", Electronics  Letters, 5_, pp 303-304, 10 July 1969. Hartnagel2, H.L., "Magnetic surface loading of Gunn oscillators and resulting new devices", Solid State Electronics, 13, pp 931-936, July 1970. Hartnagel~, H.L., Semiconductor Plasma Instabilities, Heinemann Edu-cational Books Ltd., London, 1969. Hartnagel^, H.L., "Effect of surface etching on domains in Gunn diodes for pulse processing", Solid State Comm. , 9_, pp 831-833, 15 June 1971. Hartnagel,-, H.L., "Three level Gunn effect logic", Solid State Elec- tronics , 14, pp 439-444, June 1971. Hashizume, N., M. Kawashima, and S. Kataoka, "Nucleation and control of departure of a high-field domain by a gate electrode", Electronics  Letters, 1_, pp 195-197, 22 April 1971. Hasty, T.E., R. Stratton and E.L. Jones, "Effect of nonuniform con-ductivity on the behaviour of Gunn effect samples", J. of Applied  Physics, 39, pp 4623-4632, Sept. 1968. . " Hauge, P.S., "Static negative resistance in Gunn effect materials with field-dependent carrier diffusion", I.E.E.E. Trans, on Electron  Devices, ED-18, pp 390-391, June 1971. Hayashi, T., "Three-terminal GaAS switches", I.E.E.E. Trans, on Electron Devices, ED-15, pp 105-110, Feb. 1968. Heeks, J.S., "Some properties of the moving high field domain in Gunn effect devices", I.E.E.E. Trans, on Electron Devices, ED-13, pp 68-78, Jan. 1966. 183 Heime, K., "Planar Schottky-gate Gunn d e v i c e s " , E l e c t r o n i c s L e t t e r s , ]_, pp 611-613, 7 Oct. 1971. He i n l e , W., " I n c l u s i o n of d i f f u s i o n i n the space-charge theory of KinO and Robson", E l e c t r o n i c s L e t t e r s , 7_, pp 245-256, 20 May 1971. Hofmann, H.R., "Some aspects of Gunn o s c i l l a t i o n s i n t h i n d i e l e c t r i c -loaded samples", E l e c t r o n i c s L e t t e r s , 5, pp 227-228, 29 May 1969. Hofmann2, H.R., "Gunn o s c i l l a t i o n s i n t h i n samples w i t h c a p a c i t i v e surface l o a d i n g " , E l e c t r o n i c s L e t t e r s , .5, pp 289-290, 26 June 1969. .Hofmann-}, H.R.., " S t a b i l i t y c r i t e r i o n f o r Gunn o s c i l l a t o r s w i t h heavy surface l o a d i n g " , E l e c t r o n i c s L e t t e r s , 5^ pp 469-470, 2 Oct. 1969. Hofmann^, H.R., and W.H. ' t Lam, "Suppression of Gunn domain o s c i l -l a t i o n s i n t h i n GaAs diodes w i t h d i e l e c t r i c surface l o a d i n g " , E l e c - t r o n i c s Letters > 8, pp 122-124, 9 March 1972. Hofmann^, H.R., " S t a b i l i t y theory f o r t h i n Gunn diodes w i t h d i e l e c t r i c s u r f a c e l o a d i n g " , E l e c t r o n i c s L e t t e r s , JS, pp 124-125, 9 March 1972. H o f s t e i n , S.R., " F i e l d e f f e c t t r a n s i s t o r theory", F i e l d - e f f e c t Trans- i s t o r s , P h y s i c s , Technology and A p p l i c a t i o n s , Ed. J.T. Wallmark, H. Johnson, P r e n t i c e - H a l l Inc., Englewood C l i f f s , N.J., 1966. Kower, P.L., W.W. Hooper, "D."A. Tremer, W. Lehrer and C.A. 'Biftman, "The Schottky b a r r i e r g a l l i u m arsenide f i e l d - e f f e c t t r a n s i s t o r " , I n - t e r n a t i o n a l Symposium on GaAs, D a l l a s , pp 187-194, Oct. 1970. J a s k o s k i , S., and T. I s h i i , "Simultaneous low-frequency r e l a x a t i o n and high-frequency microwave o s c i l l a t i o n of a bulk GaAs cw o s c i l l a t o r " , E l e c t r o n i c s L e t t e r s , 3_, pp 12-13, Jan. 1967. Jeppsson, B., and I. Marklund, " F a i l u r e mechanisms i n Gunn diodes", E l e c t r o n i c L e t t e r s , _5, pp 213-214, May 1967. Jeppsson2, B., I . Marklund and K. Olsson, "Voltage tuning of c o n c e n t r i c p l a n a r Gunn diodes", E l e c t r o n i c L e t t e r s , 3_, pp 498-500, Nov. 1967. Johnson, H.R., "Backward wave o s c i l l a t o r s " , Proc. I.E.E.E., 43, pp 684-697, June 1955. Johnson, W.C., and P.T. Panousis, "The i n f l u e n c e of Debye len g t h on the C-V measurement of doping p r o f i l e s " , I.E.E.E. Trans, on E l e c t r o n  Devices, ED-18, pp 965-973, Oct. 1971. Kataoka, S., H. Tateno, M. Kawashima and Y. Komamia, "Microwave o s c i l -l a t i o n and a m p l i f i c a t i o n i n a long bulk GaAs diode w i t h BaTiO^ sheets on the s u r f a c e " , Proc. Conf. on Microwave and O p t i c a l Generation and  A m p l i f i c a t i o n , Hamburg, pp 454-460, Sept. 1968. Kataoka2, S., H. Tateno and M. Kawashima, "Suppression of t r a v e l l i n g 184 high field domain mode oscillation in GaAs by dielectric surface loading", Electronics Letters, 5_, pp 48-50, 6 Feb. 1969. Kataokao, S., H. Tateno and M. Kawashima, "Observations of current instabilities in a dielectric-surface-loaded n-type GaAs bulk element", Electronics Letters, 5_, pp 114-116, 20 March 1969. Kataoka^, S., H. Tateno, and M. Kawashima, "Improvements in efficiency and tunability of Gunn oscillators by dielectric-surface loading" Electronics Letters, 5_, pp 491-492, 2 Oct. 1969. Kennedy, D.P., and R.R. O'Brien, "Computer aided two-dimensional analysis of-the junction field effect transistor", IBM J. of R. and D., 14, pp 95-116, March 1970. Kino, G.S. and P.N. Robson, "The effect of small transverse dimensions on the operation of Gunn devices", Proc. I.E.E.E. 56, pp 2056-2057, Nov. 1968. Kim, C.K., and E.S. Yang, "On the validity of the gradual channel approximation for field effect transistors", Proc. I.E.E.E. , 58, pp 841-842, May 1970. King. G. , M.P. Wasse and CP. Sandbank, "An assessment of epitaxial gallium arsenide for use in Gunn effect devices", International  Symposium on GaAs, Reading, pp 184-188, Oct. 1966. Ko, W.H., "Designing tunnel diode oscillators", Electronics, 34, pp 68-72, 10 Feb. 1961. Koyama, J., S. Ohara, S. Kawazura and K. Kumabe, "Bulk GaAs travelling-wave amplifier", International symposium on GaAs, Dallas, pp 167-172, Oc Oct. 1968. Knight, S., and C. Paola, "Ohmic contacts for gallium arsenide bulk effect devices", Symposium on Ohmic Contacts to Semiconductors, B. Schwartz, Ed., pp 102-114, Electrochemical Society, N.Y. 1969. Kroemer, H., "Theory of the Gunn effect", Proc. I.E.E.E., 52, p 1736, Dec. 1964. Kroemer2, H., "External negative conductance of a semiconductor with negative differential mobility", Proc. I.E.E.E. , 53, p 1246, Sept. 1965. Kroemero, H., "The Gunn effect under imperfect cathode boundary con-ditions", I.E.E.E. Trans, on Electron Devices, ED-15, pp 819-837, Nov. 1968. Kroemer^, H., "Generalized proof of Shockley's positive conductance theorem", Proc. I.E.E.E., 58, pp 1844-1845, Nov. 1970. Kroemer^, H., "Authors reply to 'Comments on "Generalized proof of Shockley's positive conductance theorem"1", Proc. I.E.E.E. , 59, p 1283, Aug. 1971. 185 Kumabe, K., "Suppression of Gunn oscillations by a two dimensional effect", Proc. I.E.E.E., 56, pp 2172-2173, Dec. 1968. Kurokawa, K., "The dynamics of high field propagating domains in bulk semiconductors", Bell System Tech. J., 46, pp 2235-2261, Dec. 1967. Kuru, I., and Y. Tajima, "Domain suppression in Gunn diodes", Proc. I.E.E.E., 57, pp 2115-1216, June 1969. Lanza, C., and R.M. Esposito, "Bulk negative resistance device operated in a relaxation mode", Solid State Electronics, 12, pp 463-467, June 1969. Lehovec, K. , and R. Zulleg, "Voltage-current characteristics of GaAs JFET's in the hot electron range", Solid State Electronics, 13, pp 1415-1426, Oct. 1970. Liu, S.G., "Infrared and microwave radiation associated with a current controlled instability in GaAs", Applied Physics Letters, 9_, pp 79-81, 15 July 1966. Masuda, M. , N.S. Chang, and Y. Matsuo, "Suppression of Gunn-effect domain formation by ferrimagnetic materials", Electronic Letters, J3, pp 605-606, .17 Sept. 1970. Mead, C.A., "Schottky barrier field effect transistor", Proc. I.E.E.E., 54, pp 307-308, Feb. 1966. Meyer, N.I., and T. Guldbrandsen, "Method for measuring impurity distributions in semiconductor crystals", Proc. I.E.E.E., 51, pp 1631-1637, Nov. 1963. McCumber, D.E. and A.G. Chynoweth, "Theory of negative-conductance amplification and of Gunn instabilities in 'Two-valley' semiconductors", I.E.E.E. Trans, on Electron Devices, ED-13, pp 4-21, Jan. 1966. McWhorter, A.L., and A.G. Foyt, "Bulk GaAs negative conductance am-plifiers", Applied Physics Letters, 9_, pp 300-302, 15 Oct. 1966. Nahas, J.J., Design, Fabrication and Testing of Tunable Gunn Effect  Devices, Ph.D. Thesis, Purdue University, Jan. 1971. Nakamura, M., H. Kurono, M. Hirao, T. Toyabe and H. Kodera, "High-speed pulse response of planar type Gunn diodes", Proc. I.E.E.E., 59, pp 1039-1040, June 1971. Neuberger, M., Gallium Arsenide Data Sheets, Electron Properties Information Center, Hughes Aircraft Co., Culver City, Calif., April 1965. Owens, J.M., "Gallium arsenide on sapphire Gunn effect devices", Proc. I.E.E.E., 58, pp 930-931, June 1970. Paola, C., "Metallic contacts for GaAs", Solid State Electronics, 13, pp 1189-1191, Sept. 1970. 186 Parkes, E.P., B.C. Taylor and D.J. Coliver, "The performance of planar Gunn oscillators in x-band", I.E.E.E. Trans, oh Electron  Devices, ED-18, pp 840-843, Oct. 1971. Petzinger, K.G., A.E. Hahn, and A. Matzelle, "CW three-terminal GaAs oscillator", I.E.E.E. Trans., on Electron Devices, ED-14, pp 403-404, July 1967. Pruniaux, B.R., J.C. North and A.V. Payer, "A semi-insulated gate gallium arsenide field effect transistor", I.E.E.E..Trans, on Elec- ,tron Devices, ED-19, pp 672-674, May 1972. Putley, E.H., The Hall Effect and Related Phenomena, Butterworth Scientific Pubs., London 1960. Ridley, B.K., "The inhibition of negative resistance dipole waves and domains in n-GaAs", I.E.E.E. Trans, on Electron Devices, ED-13, pp 41-43, Jan. 1966. Ruch, J.G., and G.S. Kino, "Measurement of the velocity-field charac-teristics of gallium arsenide", Applied Physics Letters, 10, pp 40-42, Jan. 1967. Rucln^ , J.G., "Electron dynamics in short channel field-effect trans-istors", I.E.E.E. Trans, on Electron Devices, ED-19, pp 652-654, May 1972. Schuller, M. , and W.W. Gartner, "Large-signal theory for negative-resistance diodes, in particular tunnel, diodes", Proc. IRE, 49, pp 1268-1278, Aug. 1961. Schwartz, B. and J.C. Sarace, "Low temperature alloy contacts to gallium arsenide using metal halide fluxes", Solid State Electronics, 9_, pp 859-862, Oct. 1966. Sekido, K., T. Takeuchi, F. Hasegawa and S. Kikuchi, "CW oscillations in GaAs planar-type bulk diodes", Proc. I.E.E.E. , 57, pp 815-816, May 1969. Sevin, L.J., Field Effect Transistors, McGraw H i l l , 1965. Sliapilro, J.S. and V. Giorgio, "An expitaxial GaAs field effect trans-istor", Proc. I.E.E.E., 57, pp 2085-2086, Nov. 1969. Sharma, R.N. and K.M. van Vliet, "Generation-recombination fluctuations in mercury-cadmium telluride", Physica Status Solidi, (A), 1_, pp 765-773, 16 April 1970. Shaw, M.P., P.R. Solomon and H.L. Grubin, "The influence of boundary conditions on current instabilities in GaAs", IBM J. of R. and D., pp 587-590, Sept. 1969. 187 Shockley, W., "A unipolar 'field effect' transistor", Proc. IRE, 40, pp 1365-1376, Nov. 1952. Shockley2> W., "Negative resistance arising from transit time in semi-conductor diodes", Bell System Tech J., 33, pp 799-826, July 1954. Shoji, M. , "Functional bulk semiconductor oscillators", I.E.E.E. Trans  on Electron Devices, ED-13, pp 535-546, Sept. 1967. Shoji2» M. , and P.W. Dorman, "Capacitively coupled GaAs current waveform generator", Proc. I.E.E.E., 56, pp 1613-1614, Sept. 1968. Solomon, P.R., M.P. Shaw and H.L. Grubin, "Analysis of bulk negative mobility element in a circuit containing reactive elements", J. of Applied Physics, 43, pp 159-171, Jan. 1972. Southgate, P.D., "Recombination processes following impact ionization by high field domains in gallium arsenide", J. of Applied Physics, 38, pp 4589-4595, Nov. 1967. Sterzer, F., "Static negative differential resistance in bulk semi-conductors", RCA Review, 32, pp 497-502, Sept. 1971. Suga, M., "Field distribution in a Gunn diode with a distributed capacitance electrode", Proc. I.E.E.E.,57, pp 253-254, Feb. 1969. Suga2» > and K. Sekido, "Effects cf doping profile upon electrical characteristics of Gunn diodes", I.E.E.E. Trans on Electron Devices, ED-17, pp 275-281, April 1970. Sugeta, T., H. Yanai, and T. Ikoma, "Switching properties of bulk effect digital devices", I.E.E.E. Trans, on Electron Devices, ED-17, pp 940-942, Oct. 1970. Sugeta2, T., H. Yanai and K. Sekido, "Schottky-gate bulk effect digital devices", Proc. I.E.E.E., 59, pp 1629-1630, Nov. 1971. Swartz, G.A., A. Gonzalez and A. Dreeben, "ELectric-field profile and current control of a long epitaxial GaAs n-layer", Electronics  Letters, _8, pp 93-94, 24 Feb. 1972. Sze, S.M. , Physics of Semiconductor Devices, Wiley-Interscience, 1969. Takeuchi, M. A. Higashisaka and K. Sekido, "GaAs planar Gunn diodes for dc biased operation", I.E.E.E. Trans on Electron Devices, ED-19, pp 125-127, Jan. 1972. Tateno, H. and S. Kataoka, "Comments on 'Generalized proof of Shockley's positive conductance theorem'", Proc I.E.E.E. , 59, pp 1282-1283, Aug. 1971. Teszner, J., "Tunable Gunn oscillator by semiconductor surface loading", Electronics Letters, pp 147-148, 8 April 1971. 188 Thim, H.W. and M.R. Barber, "Microwave A m p l i f i c a t i o n i n a GaAs bulk semiconductor", I.E.E.E. Trans on E l e c t r o n Devices, ED-13, pp 110-114, Jan. 1966. Thin^, H. , "Experimental v e r i f i c a t i o n of b i s t a b l e s w i t c h i n g x j i t h Gunn diodes", E l e c t r o n i c s L e t t e r , ]_, pp 246-247, 20 May 1971. Thim3, H., " S t a b i l i t y and s w i t c h i n g i n o v e r c r i t i c a l l y doped Gunn diodes", Proc. I.E.E.E., 59_, pp 1285-1286, Aug. 1971. Thim^, H., "Linear microwave a m p l i f i c a t i o n w i t h Gunn o s c i l l a t o r s " , I.E.E.E. Trans on E l e c t r o n Devices, ED-14, pp 517-522, Sept. 1967. . Todd, C.D., "Presence of negative r e s i s t a n c e i n FET output c h a r a c t e r -i s t i c s " , Proc. I.E.E.E., 53, p 503, May 1965. Todd2, C.D., "Negative r e s i s t a n c e i n FET's: an a i d or an ailm e n t " , . E l e c t r o n i c s , 38, pp 57-61, J u l y 1965. Todd-}, C.D. , J u n c t i o n F i e l d E f f e c t T r a n s i s t o r s , John Wiley and Sons Inc., N.Y., 1968. Trofimenkoff, F.N., "Field-dependent m o b i l i t y a n a l y s i s of the f i e l d e f f e c t t r a n s i s t o r " , Proc. I.E.E.E., 53, pp 1765-1766, Nov. 1965. Torrens, A.B., Negative D i f f e r e n t i a l C o n d u c t i v i t y E f f e c t s i n Semi- conductors , Ph.D. Thesis, U n i v e r s i t y of B r i t i s h Columbia, Feb. 1969. Tucker, T.W., "Domain v e l o c i t y i n t h i n Gunn diodes", Proc. I.E.E.E., 59_, pp 1116-1117, J u l y 1971. Turner, J.A., "G a l l i u m arsenide f i e l d e f f e c t t r a n s i s t o r s " , I n t e r - n a t i o n a l Symposium on GaAs, Reading pp 213-218, Oct. 1966. Turner2> J.A. and B.L. Wilson, " I m p l i c a t i o n s of c a r r i e r v e l o c i t y s a t -u r a t i o n i n a g a l l i u m arsenide f i e l d - e f f e c t t r a n s i s t o r " , I n t e r n a t i o n a l  Symposium on GaAs, D a l l a s , pp 195-204, Oct. 1968. U l l r i c h , P., "Observation of recombination r a d i a t i o n i n p l a n a r Gunn e f f e c t d e vices", E l e c t r o n i c s L e t t e r s , 7, pp 193-194, 22 A p r i l 1971. van der Pauw, L . J . , "A method of measuring s p e c i f i c r e s i s t i v i t y and H a l l e f f e c t of d i s c s of a r b i t r a r y shape", P h i l l i p s Res. Reports, 13, pp 1-9, Jan 1958. van V l i e t , K.M., "Noise i n semiconductors and photoconductors", Proc. IRE, 46, pp 1004-1018, June 1958. Vlaardingerbroek, V.T., G.A. Acket, K. Hofmann and P.M. Boers, "Re-duced b u i l d - u p of domains i n sheet-type g a l l i u m arsenide Gunn o s c i l -l a t o r s " , Physics L e t t e r s , 28A, pp 97-98, 4 Nov. 1968. 189 Waldner, M. and I.D. Rouse, "Gallium arsenide on sapphire field-effect transistor", Proc. I.E.E.E., 57, p 2066, Nov. 1969. Watson, H.A., Microwave Semiconductor Devices and Their Circuit Ap- plications, McGraw-Hill, N.Y. 1968. Willardson, R.K., and J.J. Duga, "Magnetoresistance in gallium arsenide", Phys. Soc. Proc, 75, pt 2, pp 280-290, Feb. 1960. Winteler, H.R. and A. Steinemann, "Gallium arsenide field effect trans-istors", International Symposium on GaAs, Reading pp 228-232, Oct. 1966. Yamashita, A., and T. Tsuzaki, "Negative resistance in evaporated GaAs films", Proc. I.E.E.E., 58, p 1876, Nov. 1970. Yanai, H., T. Sugeta and K. Sekido, "Schottky-gate Gunn effect digital device", presented at I.E.E.E. Int. Elec. Devices Meeting, Washington, D.C., Oct. 1971. Zuleeg, R., "Expitaxial GaAs p-n junction field effect transistors", Proc. I.E.E.E., 56, pp 879-880, May 1968.' Zuleeg2j R., "A GaAs pn-junction FET and gate-controlled Gunn effect device , International Symposium on GaAs, Dallas pp 181-186, Oct. 1968. Zuleeg.^ ., .R. and K. .Lehovec, "High frequency and .temperature ..charac-teristics of GaAs junction field-effect transistors in the hot elec-tron range", International Symposium on GaAs, Aachen, pp 241-250, Oct. 1970. 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            data-media="{[{embed.selectedMedia}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
https://iiif.library.ubc.ca/presentation/dsp.831.1-0101454/manifest

Comment

Related Items