The MOFSET as an acoustic surface wave detector

Item Type text; Thesis-Reproduction (electronic)

Authors Kawamoto, Roy Tadashi, 1944-

Publisher The University of Arizona.

Rights Copyright © is held by the author. Digital access to this materialis made possible by the University Libraries, University of Arizona.Further transmission, reproduction or presentation (such aspublic display or performance) of protected items is prohibitedexcept with permission of the author.

Download date 03/06/2018 19:47:19

Link to Item http://hdl.handle.net/10150/554554

THE MOSFET AS AN ACOUSTIC

SURFACE WAVE DETECTOR

by

Roy T ad ash i Kawamoto

A T h e s i s S ubm itted to th e F a c u l ty o f th e

DEPARTMENT OF ELECTRICAL ENGINEERING

I n P a r t i a l F u l f i l l m e n t o f th e R equ irem en ts For th e D egree o f

MASTER OF SCIENCE

I n th e G ra d u a te C o lleg e

THE UNIVERSITY OF ARIZONA

1 9 7 2

STATEMENT BY AUTHOR

T his t h e s i s has been s u b m it te d i n p a r t i a l f u l f i l l m e n t o f r e ­q u irem en ts f o r an advanced d eg ree a t The U n iv e r s i t y o f A r izo n a and i s d e p o s i t e d in th e U n iv e r s i t y L ib r a ry t o be made a v a i l a b l e to b o rrow ers under r u l e s o f th e L ib ra ry *

p e r m i s s i o n s p ro v id e d t h a t a c c u r a t e acknowledgment o f s o u rc e i s made. R eq u es ts f o r p e rm is s io n f o r ex ten d ed q u o ta t i o n from o r r e p ro d u c t io n o f t h i s m a n u sc r ip t in whole o r i n p a r t may be g ra n te d by th e head o f th e m ajor d ep a r tm en t o r th e Dean o f th e G rad u a te C o lleg e when i n h i s ju d g ­ment th e p ro p o sed use o f th e m a t e r i a l i s in th e i n t e r e s t o f s c h o l a r ­s h ip * In a l l o th e r i n s t a n c e s , how ever, p e rm is s io n must be o b ta in e d from th e au thor*

B r ie f q u o ta t io n s from t h i s t h e s i s a r e a l lo w a b le w i th o u t s p e c i a l

SIGNED:7

APPROVAL BY THESIS DIRECTOR

Ttli-S t h e s i s h a s been approved on th e d a te shown below:

VERN RZJOHNSONA s s o c ia te P r o f e s s o r o f E l e c t r i c a l E n g in e e r in g

ACKNOWLEDGEMENTS

The w r i t e r w ish es to e x p re s s h i s a p p r e c i a t i o n to Dr. Vem

R. Johnson f o r h i s i n t e r e s t and g u id a n ce d u r in g t h i s s tu d y , and to

Dr. R e g in a ld L. C a l l f o r th e use o f th e f a c i l i t i e s o f th e S o l id S t a t e

E n g in e e r in g L a b o ra to ry . A lso a p p r e c i a t i o n to Mrs. F r e id a Long f o r

h e r h e l p f u l s u g g e s t io n s on ty p in g th e t h e s i s .

i l l

TABLE OF CONTENTS

LIST OF ILLUSTRATIONS

LIST OF TABLES

ABSTRACT

CHAPTER

1. INTRODUCTION

o o o e o o o e o o o o o e o o o o

o o o o o o o o o o o o o o e o o e o o o

o e o e o o o G G o o o o c o o o o o o o o o o

O O O C 0 0 6 0 0 0 0 0 0 6 0 0 0 0

S e le c t i o n and D e s c r ip t i o n o f th e MOSFET Developments 6 6 O C 0 - 0 C O O O O 6 6 O O O O

RAYLEIGH WAVES o e o c o o o e e o o e o o o o

Xll fclTO (ItlC fcXOXl 0 6 6 0 0 6 0 0 0 c o o e o o o e

X t i e O i r y o o o e o o e o o e o o e o o e G o o e

c- N um erica l S o lu t io n f o r S i l i c o n o o o o o o o o

PIEZORESISTIVITY 0 0 0 0 0 0 0 0 6 0 6 0 0 6 6 0

I n t r o d u c t i o n © o o o o o o o o o o o o o o o oBackground © e o o e o o o o o o o o c e e o o

TheoryI n t e r a c t i o n w i th I n v e r s io n L ay e rs

O O C O O O O O 6 0 0 6 0 0 0 0 0 6 0 0

6 0 0 0 0 0

MOSFET o c o o o o o o o o o o o o o o o o o ©

I n t r o d u c t i o n o o o o o o o o o o o o e o o © ©Theory o o o o e o e e o o o © © © © © © © © ©

F a b r i c a t i o n and C h a r a c t e r i s t i c s o f th e MOSFET

EXPERIMENTAL RESULTS 0 6 0 0 0 0 0 0 6 0 0 0 0

6 0 0 0 0 0 0 0 0 0 6 0 0

REFERENCES

E x p e r im e n ta l Method E x p e r im e n ta l R e s u l t s and D is c u s s io n o f R e s u l t s C onc lus ion e e e o o o o o e o o o e e e o e o

o 0 O 0 O 0 6 0 O 6 0 O O 0 0 0 O O © O O 6 0

LIST OF ILLUSTRATIONS

Figure

2 . 1

2,2

2 . 3

2 . 4

2.5

3.1

3.2

3.3

3.4

4.1

4.2

Page

C o o rd in a te sy s tem f o r e l a s t i c wave p r o p a g a t in gon a f r e e s u r f a c e c . , , . , - . . , . . , , . , , . . . 6 ■

Phase v e l o c i t y and r e l a t i v e pow er-f low d i r e c t i o n v e r s u s p r o p a g a t io n v e c t o r d i r e c t i o n on th e(1 0 0 ) p la n e o f s i l i c o n . . . . . . . . . . . . . . . . . 18

Phase v e l o c i t y and r e l a t i v e pow er-f low d i r e c t i o n v e r s u s p ro p a g a t io n v e c t o r d i r e c t i o n on th e(110) p la n e o f s i l i c o n 19

P hase v e l o c i t y and r e l a t i v e pow er-f low d i r e c t i o n v e r s u s p ro p a g a t io n v e c t o r d i r e c t i o n on th e(111) p la n e o f s i l i c o n . . . . . . . . o . 2 0

N orm alized l e n g th r e q u i r e d f o r su r fa c e -w a v e en e rg y to decay to t e n p e r c e n t o f th e s u r f a c e v a lu e v e r s u s p r o p a g a t io n v e c t o r d i r e c t i o n on th e ( 1 0 0 ) ,(1 1 0 ) , and ( 1 1 1 ) p la n e s o f s i l i c o n * . . . . . . . . . . 2 2

P i e z o r e s i s t i v e i n t e r a c t i o n o f a s u r f a c e wave w i tha tw o -d im e n s io n a l i n v e r s i o n l a y e r . . . . . . . . . . . 28

Power n o rm a l iz e d gauge f a c t o r s v e r s u s p r o p a g a t io n v e c t o r d i r e c t i o n on th e ( 1 0 0 ) p la n e o f s i l i c o n 0 58 0 ^ , 0 , and 90 , . . . . . © * © . * . . . . . ". ■ ., 32

Power n o rm a l iz e d gauge f a c t o r s v e r s u s p r o p a g a t io n v e c t o r d i r e c t i o n on th e ( 1 1 0 ) p la n e o f s i l i c o n 0 s® 0^ , 0 ° , and 90° . . . . . . . . . . . . . . . . . . 33

Power n o rm a l iz e d gauge f a c t o r s v e r s u s p r o p a g a t io nv e c t o r d i r e c t i o n on th e ( 1 1 1 ) p la n e o f s i l i c o n0 ® 0 . 0 , and 90 , . . . . . . . . . . . . . . . . * * 34

PS u rfa c e ene rg y band d iagram s f o r i n v e r s i o n l a y e r s . . . . . 37

C r o s s - s e c t io n o f p - ty p e i n v e r s i o n l a y e r MOSFETshowing d e p l e t i o n and I n v e r s io n l a y e r s . . . . . . . . . 39

v

v i

Figure

4 . 3

4 .4

4.5

4.6

4.7

4.8

4.9

4.10

4.11

5.1

5.2

5 .3

5.4

5.5

5.6

5.7

5 .8

LIST OF ILLUSTRATIONS— Continued

Page

C o n s tan t en e rg y s u r f a c e s i n k - s p a c e . . . . . . . . . . . . 41

C r o s s - s e c t io n o f HOSFET used i n t h i s i n v e s t i g a t i o n . . . . 42

P ro c e s s in g s t e p s n e c e s s a r y to f a b r i c a t e th e MOSFET . . . . 43

Layout o f th e f i v e photom asks superim posed to showto show r e l a t i v e d im ensions . . . . . . . . . . . . . . 45

P ho tog raphs o f com pleted w a fe r w i th MOSFETs . . . . . . . . 46

E x p e r im en ta l t r a n s c o n d u c ta n c e i n th e s a t u r a t i o n r e g io n v e r s u s e f f e c t i v e g a t e v o l t a g e f o r th e (110) p la n e * . . . . . . . . . @ @ . . . . . . . . . . 48

E x p e r im e n ta l ch an n e l conduc tance i n th e l i n e a r r e g io n v e r s u s e f f e c t i v e g a t e v o l t a g e f o r th e (110) p la n e . . . . . . . . . . . . . . . . . . . . . . 50

N orm alized e x p e r im e n ta l c h an n e l conduc tance i n th e s a t u r a t i o n r e g io n v e r s u s e f f e c t i v e g a te v o l t a g e f o r th e (110) p la n e . . . . . . . . . . . . . . . . . . 51

Simple e q u i v a l e n t c i r c u i t o f a MOSFET w i th s o u rc eand s u b s t r a t e common . . . . . . . . . . . . . . . o o o o 52

Wedge co u p l in g method used to m easure th e i n s e r t i o nl o s s o f MOSFET s u r f a c e wave d e t e c t o r . . . . . . . . . . 59

Wedge c u t t o a n g le 6 ^ w i th mounted p l a t e t r a n s d u c e r . . . . 60

Block diagram o f e x p e r im e n ta l a r rangem en t f o r i n s e r t i o n lo s s measurement o f a MOSFET s u r f a c e wave d e t e c t o r . . . . . . . . o . . . . . . . . . . . . 62

MOSFET c i r c u i t u sed f o r i n s e r t i o n l o s s m easurem ents . . . . 64

C i r c u i t a n a l y s i s o f MOSFET s u r f a c e wave d e t e c t o r . . . . . 65

Mounted MOSFET a r r a y on t e s t f i x t u r e . . . . . . . . . . . 6 8

O utput o f th e MOSFET . . . . . . . . . . . . . . . . . . . 70

E x p e r im en ta l i n s e r t i o n l o s s v e r s u s t h e o r e t i c a l PNGF . . . . 73

LIST OF TABLES

Table

3 e l P i e z o r e s i s t a n c e c o e f f i c i e n t s i n p - ty p e in v e r s i o nl a y e r s 0 0 * 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

4 .1 E le m e n ta l v a lu e s f o r th e HOSFET e q u i v a l e n t c i r c u i t . «

5 .1 E x p e r im e n ta l i n s e r t i o n l o s s e s f o r MOSFET s u r f a c ewave d e t e c t o r s 0 0 0 0 0 0 * 0 0 0 0 , 0 0 0 0 0 0

v i i

Page

* * 27

o * 54

. . 71

ABSTRACT

The p u rp o se o f t h i s t h e s i s was t o s tu d y th e m e ta l - o x i d e -

semi c o n d u c to r f i e l d - e f f e e t - t r a n s i s t o r (MOSFET) as a d e t e c t o r o f a c o u s t i c

s u r f a c e w aves . A p - c h a n n e l enhancement-mode MOSFET was u sed to d e t e c t

th e a c o u s t i c s u r f a c e w aves . The d e t e c t i o n was b ased on th e m o d u la t io n

o f e l a s t i c s u r f a c e waves w i th an i n v e r s i o n l a y e r which m o d u la te s th e

d r a i n c u r r e n t th ro u g h th e MOSFET. T h is i s known as th e p i e z o r e s i s t a n c e

phenomenon which was d e f in e d a s th e change i n r e s i s t a n c e f o r a change

i n s t r e s s .

The a n a l y s i s o f s u r f a c e wave i n t e r a c t i o n w i th th e MOSFET con­

s i s t s o f th e com b in a tio n o f th e tw o -d im en s io n a l p i e z o r e s i s t a n c e t e n s o r

f o r p - ty p e i n v e r s i o n l a y e r s w i th th e R a y le ig h s u r f a c e wave s o l u t i o n s to

y i e l d a t h e o r e t i c a l pe rfo rm ance in d e x . The pe rfo rm an ce in d e x , power

n o rm a l iz e d gauge f a c o r e (PNGF), was a p p l i e d t o th e (110) p la n e o f

s i l i c o n . The e x p e r im e n ta l r e s u l t s w ere th e n compared f o r th e MOSFETs

o p e r a t in g i n th e s a t u r a t i o n r e g io n .

v i i i

CHAPTER 1

INTRODUCTION

In th e p a s t a c o u s t i c s u r f a c e waves were d e t e c t e d u s in g

p i e z o e l e c t r i c d e v ic e s . A new method o f d e t e c t i n g a c o u s t i c s u r f a c e

waves i s to u se an a c t i v e d e v ic e . From a s e l e c t i o n o f v a r io u s

d e v ic e s th e MOSFET was found to m eet th e re q u ire m e n ts o f d e t e c t i n g

o n ly a s u r f a c e wave and n o t a com bina tion o f b o th b u lk and s u r f a c e

w aves .

The p i e z o r e s i s t a n c e t e n s o r f o r in v e r s i o n l a y e r s was an a ly z e d

and combined w i th th e s u r f a c e wave s o l u t i o n to o b ta in a power

n o rm a l iz e d gauge f a c t o r , PNGF. The s u r f a c e wave i n t e r a c t i o n w i th

th e i n v e r s i o n l a y e r o f th e MOSFET was modeled w i th a c u r r e n t g e n e r a to r

c h a r a c t e r i s e d by th e PNGF o f th e i n v e r s i o n l a y e r . The MOSFET was

e x p e r im e n ta l ly v e r i f i e d w i th th e PNGF.

S e l e c t i o n and D e s c r ip t i o n o f th e MOSFET

The s e l e c t i o n o f s i l i c o n as a s u b s t r a t e m a t e r i a l a l lo w s a

w ide ch o ice i n d e t e c t o r s . The f i v e m a jo r d e v ic e s a s d e t e c t o r s w ere:

th e p i e z o r e s i s t o r ; j u n c t i o n d io d e ; b i p o l a r t r a n s i s t o r ; 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 (JFET); and th e MOSFET. The p i e z o r e s i s t o r and th e

j u n c t i o n d iode do n o t r e p r e s e n t a c t i v e t h r e e t e r m in a l d e t e c t o r s so th e y

1

w ere n o t c o n s id e re d i n t h i s i n v e s t i g a t i o n . The b i p o l a r t r a n s i s t o r i s

an a c t i v e t h r e e t e r m in a l d e v ic e ; however R ln d n e r , D o e r in g , and Wonson

(1965) show t h a t a s t r e s s - b i a s was n e c e s s a r y f o r e f f i c i e n t s t r e s s

d e t e c t i o n . The s t r e s s - b i a s was an e x t e r n a l l y a p p l i e d s t r e s s . The JFET

was n o t an enhancement-mode d e v ic e and would be awkward t o use i n l o g i c

c i r c u i t s w hich was an a p p l i c a t i o n o f t h i s ty p e o f d e t e c t o r . The

enhancement-mode d e v ic e i s one which i s n o rm a l ly o f f f o r ze ro g a te

v o l t a g e . I n a d d i t i o n , th e p hase o f th e a c o u s t i c s u r f a c e wave was n o t

c o n s t a n t w i th d ep th (W hite , 1967) and t h i s would in t r o d u c e n o n l i n e a r i t y

i n t o th e JFET d e t e c t i o n which r e s u l t s i n d e t e c t i n g c o n t r i b u t i o n s from

b o th b u lk and s u r f a c e w aves .

The MOSFET used was an a c t i v e enhancement-mode d e v ic e . I t was

f a b r i c a t e d on an n - ty p e s i l i c o n s u b s t r a t e u s in g a p r o c e s s s i m i l a r to

t h a t used to p ro d u ce i n t e g r a t e d c i r c u i t s ' . A n e g a t iv e g a t e v o l t a g e was

r e q u i r e d to form an i n v e r s i o n l a y e r a t th e o x id e -s e m ic o n d u c to r i n t e r f a c e

w hich forms a c o n d u c t in g p a th from th e d r a in to s o u r c e . , F o r a f i x e d

g a t e v o l t a g e t h e .MOSFET was o p e ra te d i n th e s a t u r a t i o n mode.

The c u r r e n t i n t e r e s t i n th e u s e o f e l a s t i c s u r f a c e waves was

due to th e r e l a t i v e l y low wave v e l o c i t y as compared w i th t h a t o f an

e l e c t r o m a g n e t i c wave. T y p ic a l e l a s t i c s u r f a c e wave v e l o c i t i e s on s o l i d s

3 3range form 0 .5 x 10 to 4 .0 x 10 m e te r s / s e c o n d . These v e l o c i t i e s w ere

5a p p ro x im a te ly 10 t im es low er th a n t h a t o f e l e c t r o m a g n e t i c w aves. . This

im p l ie s t h a t th e s u r f a c e wave d e v ic e s a r e i d e a l f o r d e la y l i n e s «

A p p l ic a t io n o f th e MOSFET as a v a r i a b l e ta p p e d d e la y l i n e and a

c o r r e l a t i o n f i l t e r o f p h ase -co d ed waveform was shown by C la ib o rn e ,

S t a p l e s , H a r r i s , and Mize (1971). O th e r a p p l i c a t i o n s o f s u r f a c e wave

d e v ic e s w ere d e s c r ib e d by C la ib o rn e , Hartmann, and Jo n es (1970) and by

W hite (1970) .

A c o u s t ic s u r f a c e waves a r e a c c e s s i b l e f o r i n p u t - o u t p u t s i g n a l

co u p l in g on a s i n g l e s u r f a c e which can in c o r p o r a t e th e use o f i n t e g r a t e d

c i r c u i t te ch n o lo g y i n p r o v id in g n e c e s s a r y c i r c u i t r y to a m p lify th e o u t ­

p u t s i g n a l . T h is cou ld l e a d to s m a l l e r - s i z e d d e v ic e s f o r low lo s s

d e la y l i n e s ,

CHAPTER 2

RAYLEIGH WAVES

I n t r o d u c t i o n

A c o u s t ic s u r f a c e waves w ere r e f e r r e d to as R a y le ig h waves named

a f t e r th e E n g l is h s c i e n t i s t Lord R ay le ig h (1885)$ who d em o n s tra ted

t h e o r e t i c a l l y t h a t waves can be p ro p a g a te d on an e l a s t i c h ^ l f - s p a c e .

These waves r e p r e s e n t e l a s t i c p e r t u r b a t i o n s p ro p a g a t in g on th e p la n e

boundary betw een an e l a s t i c h a l f - s p a c e and vacuum. The a m p li tu d e o f th e

p a r t i c l e d is p la c e m e n t goes to ze ro a t an i n f i n i t e d ep th i n th e e l a s t i c

h a l f - s p a c e .

Butchwald (1961) and Lim and P a r n e l l (1969) d i s c u s s th e fo rm al

prob lem o f s u r f a c e wave s o l u t i o n s f o r an a r b i t r a r y , a n i s o t r o p i c c r y s t a l

and C la ib o rn e , Hartmann, and Jo n es (1970) b r i e f l y d i s c u s s th e s o l u t i o n

o f th e a n i s o t r o p i c wave e q u a t io n . A com plete s o l u t i o n to th e wave

e q u a t io n was a r r i v e d a t by u s in g a mode summation te c h n iq u e . The

s t r e s s e s and s t r a i n s w ere n o rm a l iz e d to a p a r t i c u l a r s t r a i n v a lu e and

th u s used i n o b ta in in g a power v e c t o r . I n th e work t h a t fo l lo w s the

d i r e c t i o n o f power flow was c a l c u l a t e d from th e power v e c t o r and th e

d i f f e r e n c e between th e p ro p a g a t in g d i r e c t i o n and power f low was shown

as a f u n c t i o n o f th e p ro p a g a t io n d i r e c t i o n .

4

5

Theory

The a n a l y t i c a l problem c o n s id e re d was t h a t o f an e l a s t i c wave

p ro p a g a t in g on th e s u r f a c e o f a s o l i d . A c o o r d in a te system

F ig . 2 .1 , was chosen so t h a t X^ was th e d i r e c t i o n o u t o f th e s o l i d . The

d i r e c t i o n o f p ro p a g a t io n forms an a n g le 0 ^ w ith r e s p e c t to X^.

The d e fo rm a tio n o f a s o l i d r e s u l t s in p a r t i c l e s a t a p a r t i c u l a r

p o i n t b e in g d i s p la c e d in c o o r d in a te s p a c e . The change i n th e d i s p l a c e ­

ment component was r e l a t e d to th e s t r a i n component by

3ui 3uj 3uk 3uk S = ----- + ----- + -------------------- » (2 .1)

3Xj 9x_£ 3x^ 9Xj

where u ^ ,U j ,u ^ a r e th e d is p la c e m e n t components and i s th e component

o f th e s t r a i n t e n s o r . The t e n s o r has symmetry s in c e

s i j - s j i • ( 2 - 2)

and r e t a i n i n g on ly l i n e a r te rm s , th e s t r a i n t e n s o r was reduced to

i / 8ui 8unS = f ----- + — " ) . (2 .3 )

l j 2 V 3xj 9x1 /

The s t r a i n t e n s o r w r i t t e n i n m a t r ix form w i th s i n g l e s u b s c r i p t s

becomes,

6

F ig . 2 .1 C o o rd in a te system f o r e l a s t i c wave p ro p a g a t in g on a f r e e s u r f a c e

7

w here .

K

i s

2 s 6

2 SA

11

22

2 S5

2 S2 ( 2 .4 )

33

S4 " S23 32

S13 ” S31

S6 - S12 21

The f a c t o r s o f ^ were used in o r d e r to p r e s e n t c e r t a i n b a s i c e q u a t io n s

o f e l a s t i c i t y th e o ry i n a s im p le form (A uld, i n p r e p a r a t i o n ) .

As th e s o l i d d e fo rm s , th e i n t e r n a l p a r t i c l e s i n th e s o l i d were

d i s p la c e d c r e a t i n g an i n t e r n a l s t r e s s which te n d s to r e s t o r e th e p a r ­

t i c l e s to t h e i r o r i g i n a l p la c e m e n t . The s t r e s s components were d e f in e d

as f o r c e p e r u n i t a r e a a c t i n g in p a r t i c u l a r d i r e c t i o n s , and can be

r e p r e s e n t e d in m a t r ix form a s .

T

T T TXX yx xz

T T Tyx yy yz

T T Tzx zy zz

(2 .5 )

where T ^ a r e th e s t r e s s components w i th i , j « x , y , z .

For no r o t a t io n a l m otion, the s t r e s s ten so r was symmetric,

Ti j " Tj i(2 . 6 )

and th e s t r e s s t e n s o r can be r e p r e s e n t e d a s .

(2 .7 )

w here ,

T - T 1 xx

T3 ” Tz Z

T4 = Tyz

T5 = Txz

zy

zx

T 6 ‘ Txy yx

For s m a l l d e fo rm a t io n s , s t r e s s and s t r a i n w ere l i n e a r i l y r e l a t e d

by Hooke’ s la y

Ti j = Ci j k l Sk l (2 . 8)

where c^^^^ a r e th e s t i f f n e s s c o e f f i c i e n t s . These c o e f f i c i e n t s form

th e f o u r th rank s t i f f n e s s t e n s o r which c h a r a c t e r i z e s th e e l a s t i c p ro ­

p e r t i e s o f the c r y s t a l . E qua t ion 2 .8 in th e s i m p l i f i e d m a t r ix n o t a t i o n

becom es,

Ti “ • Ci j Sj ' ( 2 .9 )

o r in expanded form i t becomes,

C11 C12 C13 C14 C15 C16

c 12 c22 c23 c24 C25 C26

c 13 C23 c 33 C34 c 35 c 36

c 14 c 24 c 34 c 44 c 45 C46

c 15 C25 C35 C45 c55 C56

'16 C26 c36 C46 c 56 C6 6

(2 . 10)

where a s i m i l a r t r a n s f o r m a t io n to t h a t used on th e s t r e s s and s t r a i n

t e n s o r s was used h e re to reduce th e s t i f f n e s s c o e f f i c i e n t s to a s i x by

s i x m a t r ix form.

The wave e q u a t io n which th e a l low ed e l a s t i c wave must s a t i s f y

was.

8 2U

a t '

axi j

a

dx( Ci j k l Sk l ) , (2 . 11)

j

whe r e ; p i s the d e n s i t y , i s th e p a r t i c l e d is p la c e m e n t i n the

d i r e c t i o n , i s th e s t r a i n t e n s o r , and i s th e s t r e s s t e n s o r .

10

The s o l u t i o n to th e wave e q u a t io n must a l s o s a t i s f y boundary c o n d i t i o n s .

For s u r f a c e w aves , the boundary c o n d i t io n s on a s t r e s s f r e e s u r f a c e

r e q u i r e s t h a t .

= 0x 3=0

(2 . 12)

o r in term s of s t r e s s ,

/3U 3 U N

i * i T -x 3=°

(2 .1 3 )

T his amounts t o ,

TA - T5 (2 .14 )

A d e s i r e d s o l u t i o n to th e wave e q u a t io n has th e form,

U, Aj, exp ~ [j (cos0 x 0 + s in 0 x _ - V t ) - sJC.l Vp L P 2 p 3 p 1J(2 .1 5 )

where w i s th e p ro p a g a t in g f req u en cy and i s th e p h ase v e l o c i t y .

For decay o f th e wave w i th d e p th , th e r e a l p a r t o f th e decay c o n s ta n t ,

s , must be n e g a t iv e .

S u b s t i t u t i o n o f Eq. 2 .15 i n t o Eq. 2 .13 r e s u l t s i n a l i n e a r

homogeneous system of t h r e e e q u a t io n s w i th th e unknowns, A^. In

m a t r ix form, th e d e te rm in a n t o f th e c o e f f i c i e n t s must be ze ro f o r a

n o n - t r i v i a l s o l u t i o n to e x i s t , t h e r e f o r e

11

H1 1 H1 2 «13

d o t f 2

pH1 2 " 2 2 ,!23 = 0

Hn "23 "33

(2 .1 6 )

where th e e lem en ts a r e ,

H . = c . . s - 2 js (c . cs l n 6 4- c . , c o s 6 ) - 2 cc ,c o s0 s in 011 11 15 p 16 p 56 p p2 2 2 - C f .co s 0 - C rcS in 0 4- V p

6 6 p 55 p pK

H12 = °16S " j s ( c l 2 = c6 6 )c o s0 p " J s ( c lA + c 56) s l n 6 p2 2 - ( c , , 4- c O£. ) s l n 0 cos0 - c 0 , cos 0 - c . , s l n 046 25 p p 26 p 45 p

H13 C15S - js(<:i4 + c45)c o s 9 p - j s ( c 13 + c55) s i n 6 p

2 2 - (c^ , 4- c . c ) s in 0 cos0 - c // :cos 0 - c_ rS ln^036 45 p p 46 p 35 p

22 C6 6 S - 2 j s ( c o ,co s0 4- c . , s l n 0 ) - 2cn , cosO sinO 26 p 46 p 24 p p2 2 2- c . . s i n 0 - c 00cos 0 4- V p44 p 22 p p r

H23 c56s - J s ( c 25 + c 46)c o s 0 p - j s ( c 45 + C36) s in 0 p2 2 - (c_ 0 4- c . . ) s in 0 cos0 - c . . s i n 0 - c 0/ cos 023 44 p p 34 p 24 p

H33 C55S - 2 j s (c . ,c o s 0 4- c _ r S i n 0 ) - 2 c _ , s in 0 cosO 45 p 35 p 34 p p

- c . . cos^O - c__sin^0 4- V^p 44 p 33 p p

and j

The procedure fo r f in d in g a s o lu t io n was to f in d the roots o f

the s ix t h order polynom ial in s formed by the expansion o f the

12

d e te r m in a n t , Eq. 2 .1 6 , i n t o the form,

K + k 2 s 5 + K3 s 4 + K^s3 + K5 s 2 + K6s + K? = 0 (2 .1 7 )

where th e c o e f f i c i e n t s were r e a l f u n c t io n s o f th e e l a s t i c c o n s ta n t s and

phase v e l o c i t y . For a g iv en v e l o c i t y and s e t o f e l a s t i c c o n s t a n t s ,

th e c o n ju g a te p a i r s o f r o o t s to Eq. 2 .17 can be found from (Campbell

and J o n e s , 1968). The t h r e e r o o t s w i th n e g a t iv e r e a l p a r t s were chosen

s in c e th e d isp la c e m e n ts must be bound o r go to zero as goes to

i n f i n i t y . T here were t h r e e r o o t s ( s n , n = l , 2 ,3 ) c o r re s p o n d in g to the

e x i s t e n c e o f t h r e e modes o f p r o p a g a t io n w i th d i f f e r e n t d e la y c o n s t a n t s .

For each mode, t h e r e e x i s t s a complex decay c o n s t a n t , s ^ ,

and th r e e am p litu d e c o n s t a n t s , The am p li tu d e c o n s ta n t s were

w eig h ted by l e t t i n g e q u a l u n i t y , th en s o lv in g Eq. 2 .16 f o r the

o t h e r two, ^ and A ^ n \ A mode summation te c h n iq u e was used to

form th e com plete s o l u t i o n ,

Ui “ ^ Fn Ai (n) exp1=1 n”7 [j (cos0 X0+ s i n 8 X_ - V t ) - s X.] V p 2 p J p n l j (2 .1 8 )

where F^ i s th e complex m ode-w eigh ting f a c t o r used to m atch the

boundary c o n d i t io n o f a s t r e s s f r e e s u r f a c e .

S u b s t i t u t i n g th e com plete s o l u t i o n , Eq. 2 .1 8 , i n t o Eq. 2 .13

r e s u l t s in a s e t o f t h r e e homogenous e q u a t io n s f o r th e w e ig h t in g

f a c t o r s , F^,

13

0)V

D 1 1 D 1 2 D13 F 1

D2 ! D2 2 D23 . F 2

D31 D32 D33 F 3

(2 .1 9 )

where th e e lem en ts of th e m a t r ix a re g iv e n by.

and

D

D

D

In = 2 c l i Si< n)

■ I 6

3n = C6 i Si (n)1=1

(2 . 20)

( n = l , 2 ,3 )

q (n) bl - S n

q (n) 2

= j Ag ^^cosOp

q (n)3 = jAg^^sinOp

q (n)4 j ( A 0 n ^sinO + A_^n ^cos6 ) Z p 3 p

q (n)5 j s i n e p " A3 (n )s n

q (n) 6 j c o s 6 p - A2 (n )s n

aT = 1

(2 . 21 )

The determinant o f the c o e f f i c i e n t s o f the unknowns must be equal to

zero in order that a n o n - t r i v i a l s o lu t io n e x i s t , i . e . ,

14

d e t = 0 . (2 . 2 2 )

The decay c o n s ta n t s and am p li tu d e w e ig h t in g te rm s , A ^ n \ were

d e te rm in e d by choosing a p p r o p r i a t e e l a s t i c c o n s ta n t s and phase

v e l o c i t i e s . A s im u l ta n e o u s s o l u t i o n o f Eq. 2 .16 and Eq. 2 .22 y i e l d s

th e s o l u t i o n to th e s u r f a c e wave boundary v a lu e p rob lem . The mode

w e ig h t in g f a c t o r s , , were d e te rm in e d in th e same manner as t h a t f o r

th e a m p li tu d e w e ig h t in g f a c t o r s , i . e . , was s e t to u n i t y , and the

o th e r two, F^ and F^, were found by s o lv in g th e d e t e r m in a n t , Eq. 2 .1 9 .

For an a p p r o p r i a t e c h o ice i n phase v e l o c i t y th e d isp la c e m e n ts

were g iv e n by Eq. 2 .1 8 . In th e fo l lo w in g e q u a t io n s , th e p ro p a g a t in g

p o r t i o n s were s u p p re s s e d . Then Eq. 2 .1 8 ta k e s th e form ,

3

u = f FnAi (n) exp (“ V SnXl ) * (2 .2 3 )1 n = l p

The s t r a i n which was norm al to th e s u r f a c e ( e v a lu a te d a t the

s u r f a c e ) was o b ta in e d from Eq. 2 .2 3 and Eq. 2 .3 ,

sn - SN f (2 .2 4 )Xj-O p

w here ,

SN = % Fn= l n Sn

I t was c o n v e n ie n t to n o rm a l iz e th e d is p la c e m e n ts , s t r a i n s , and s t r e s s e s

15

t o th e (X^=0) v a lu e o f s t r a i n . The n o rm a l iz e d s o l u t i o n s w ere ,

U,V

__ E“ SN

3I

n= lFn A1 (n) exp (

N

3I

n = lFn Si (n) exp( 7 SnXl ^

P(2 .2 5 )

where

A power v e c t o r , ana logous to the P o y n tin g v e c t o r o f e l e c t r o ­

m ag n e tic t h e o r y , e x i s t s f o r e l a s t i c wave p ro p a g a t io n (H a v l ic e , Bond, and

W igton, 1970). The components o f th e power v e c t o r , P , has components

d e f in e d by,

i j / (2 .2 6 )3 t /

which g iv e s th e d i r e c t i o n and m agn itude o f power f low . S ince R ay le ig h

s u r f a c e waves a re n o n - d i s s i p a t i v e , P has no component p e r p e n d i c u la r to

th e f r e e s u r f a c e a t any d e p th .

n= lX r „ I , ' r J - r < - $ >

(n) . s (n)

16

S u b s t i t u t i n g Eq. 2 .25 i n t o Eq. 2 .26 and i n t e g r a t i n g y i e l d s th e

power p e r u n i t w id th n o rm a l ize d to th e norm al s u r f a c e s t r a i n s q u a re d .

A new c o n s t a n t , K, was formed by m u l t ip l y in g th e r e s u l t by freq u en cy U).

The power v e c t o r c o n s t a n t , K, has com ponents ,

K2 = *2 Pe

jV.

N

3 Fn T<n > e x p ( - n = l p /

Fn A<n) e x p ( - - n- ) j n= l p /

+ ( 3 Fn T2 n) exP<" ¥ - '> ) ( 3 Fn exP (" T ^ ))\ n = l p / \ n = l p /

(n)

+ L - i F" Ta e x p ( - V y v n - i 1 - 1' 3

s ^ \ / 3nIPn x W F exp ( - 7p~~) dC

and

K = 1 Re r "3 2SN 'o . x n = l

F T_ n 5(n) , nexp ( - Sn5

PFn eXp(" t ' )n= l p /

* i 3 f » p < - & ) ( V „ *i"> • •»<- "n= l P / X n = 1 P 1

> „ # ) ) ( \ 4 - ’ • - < -m =l p / xn = l p >

dC (2 .2 7 )

where

C = w x1

17

The a c o u s t i c power p e r u n i t w id th , P/V , in th e s u b s t r a t eac

was r e l a t e d to th e power v e c t o r c o n s ta n t by

s 2P 11 ' —

“ = I T K <2*28>ac

where th e s t r a i n , S ^ , i s e v a lu a te d a t = 0. The d i r e c t i o n o f

power flow can be g iv e n as

, K6 = ta n ( z — ) . (2 .2 9 )

S ^ 2

The s o l u t i o n to th e R ay le ig h wave e q u a t io n i s now com ple te .

A mode summation te c h n iq u e has been used to s o lv e th e boundary v a lu e

p rob lem , and th ro u g h s t r a i n n o r m a l i z a t io n , e x p r e s s io n s have been

d e r iv e d f o r th e p ro p a g a t in g s t r e s s e s , d i s p la c e m e n ts , and s t r a i n s .

Then a power v e c t o r c o n s ta n t was d e r iv e d u s in g th e s e e x p r e s s io n s .

N um erical S o lu t io n f o r S i l i c o n

A com puter te c h n iq u e was used to s o lv e th e R a y le ig h s u r f a c e

wave problem to d e te rm in e th e c o r r e c t phase v e l o c i t y ( S t a p l e s , 1971).

The r e s u l t s a r e shown in F ig . 2 .2 , F ig . 2 .3 , and F ig . 2 .4 f o r the

s u r f a c e wave v e l o c i t y as a f u n c t io n o f th e p r o p a g a t io n v e c t o r d i r e c t i o n

on th e (1 0 0 ) , (110 ) , and (111) p la n e s o f s i l i c o n , r e s p e c t i v e l y . Also

shown i s th e d i f f e r e n c e between th e p ro p a g a t io n d i r e c t i o n and power-

flow d i r e c t i o n , 0 ^ - 0 ^ , which was im p o r ta n t f o r s u r f a c e wave d e t e c t o r

p e rfo rm a n ce . A d e t e c t o r has f i n i t e w id th , U, and a s s o c i a t e d s p a t i a l

bandw id th . The power p a t t e r n f o r a s u r f a c e wave d e t e c t o r (C la ib o rn e ,

(10

CM/S

EC)

18

20

10

5 .0

x

4 .60 10 20

CD

I(

CD

tc

<010> 0 (DEGREES) P

F ig . 2 .2 Phase v e l o c i t y and r e l a t i v e power-flow d ir e c t io nversus propagation v e c to r d ir e c t io n on the (100)p lane o f s i l i c o n

(DEG

REES

)

(10

CM/S

EC)

19

10

6 . 0

5.0

— 204.0

CD

800640200 CD

<110> 6 (DEGREES)P

F ig . 2 .3 Phase v e l o c i t y and r e l a t i v e power-flow d ir e c t io nversus propagation v e c to r d ir e c t io n on the (110)plane o f s i l i c o n

(DEG

REES

)

(10

CM/S

EC)

20

4 .7

4 .6

4 .5

0 10 20 30

<110> 6 (DEGREES)P

F ig . 2 .4 Phase v e l o c i t y and r e l a t i v e power-flow d ir e c t io nversu s propagation v e c to r d ir e c t io n on the (111)p lane o f s i l i c o n

(DEG

REES

)

21

Hartmann, and J o n e s , 1970) was

b n ) 2

where

X = ~ W s i n ip

and ip i s th e an g le between th e p r o p a g a t io n v e c t o r on th e s u r f a c e and

th e d e t e c t o r no rm al. A narrow s p a t i a l beamwidth r e s u l t s from a

d e t e c t o r w id th , W, much l a r g e r than th e w a v e le n g th , X. I f th e d e t e c t o r

i s norm al to the d i r e c t i o n o f power flow and th e a n g u la r d i f f e r e n c e ,

Gp - Gg, exceeds th e beamwidth o f such a d e t e c t o r , s e r i o u s l o s s e s can

r e s u l t . An optimum o p e r a t in g c o n d i t io n was when G - 6 ^ was a t a

minimum o r ze ro w i th th e d e t e c t o r norm al to th e d i r e c t i o n of power f low .

A s a t i s f a c t o r y method to examine th e decay o f th e s u r f a c e wave

i n t o th e s o l i d was to p r e s e n t o n ly one e x t i n c t i o n le n g th f o r th e t o t a l

s o l u t i o n ( S ta p l e s , 1971). The e x t i n c t i o n le n g th was d e f in e d as the

dep th f o r a p ro p a g a t in g mode to decay to te n p e r c e n t o f i t s s u r f a c e

v a lu e .

F ig u re 2 .5 shows th e n o rm a l iz e d e x t i n c t i o n le n g th v e rs u s the

p ro p a g a t io n v e c t o r , G^, f o r th e t h r e e p la n e s o f s i l i c o n . This

d i s t a n c e was n o rm a l ize d to f req u en cy and thus v a r i e s w i th f requency

o f th e wave. For th e (100) p la n e th e decay l e n g th becomes very

l a r g e f o r 6 ^ exceed ing 30*. T h is was due to th e s u r f a c e wave de­

g e n e r a t in g i n t o a b u lk wave.

EXTI

NCTI

ON

LENG

TH

wX.x

lO

(m/s

)

70.0

60 .0

5 0 .0

4 0 .0

30.0

20 .0

22

(1 0 0 )

( 111)

(110)

0 10 20 30 40

6 (DEGREES)P

F ig . 2 .5 N orm alized le n g th r e q u i r e d f o r s u r fa c e -w a v e energy to decay to te n p e r c e n t of the s u r f a c e v a lu e v e r s u s p ro p a g a t io n v e c t o r d i r e c t i o n on th e ( 1 0 0 ) , (1 1 0 ) , and (1 1 1 ) p la n e s o f s i l i c o n

CHAPTER 3

PIEZORESISTIVITY

I n t r o d u c t i o n

The p i e z o r e s i s t i v i t y e f f e c t h as th e same r e p r e s e n t a t i o n as

th e c l a s s i c a l p h o t o e l a s t i c i t y e f f e c t * S t r e s s i s th e in d e p e n d e n t

v a r i a b l e and th e dependen t v a r i a b l e s a r e changes i n r e s i s t i v i t y and

d i e l e c t r i c c o n s t a n t 5 r e s p e c t i v e l y e

By u s in g th e p r o p e r t i e s o f symmetry th e f o u r t h - r a n k p ie z o ­

r e s i s t a n c e t e n s o r can be reduced to a s e c o n d - ra n k t e n s o r f o r a c u b ic

c r y s t a l such as s i l i c o n * P i e z o r e s i s t a n c e was d e f in e d f o r s i l i c o n

in v e r s i o n l a y e r s s in c e th e MOSFET ( d e s c r ib e d i n C h ap te r 1) was made

on a s i l i c o n s u b s t r a t e * I t s geom etry was such t h a t c u r r e n t f low s i n

an in v e r s i o n l a y e r n e a r th e s u r f a c e w here i t i n t e r a c t s w i th an

a c o u s t i c s u r f a c e wave * The r e s i s t i v i t y v a r i a t i o n s w ere due to p ro p ­

a g a t in g s t r e s s waves i n t h i s i n v e r s i o n la y e r*

A pe rfo rm ance in d e x was d e r iv e d which was u sed to d e s c r ib e

th e s t r e n g t h o f th e p i e z o r e s i s t i v e i n t e r a c t i o n on s i l i c o n * S ince th e

ex p e r im en t was conduc ted on ( 1 1 0 ) p la n e s i l i c o n , p r e v io u s e x p e r im e n ta l

r e s u l t s w i l l be used to make a com parison between a l l t h r e e s i l i c o n

p la n e s .

23

Background

The f i r s t p i e z o r e s i s t i v e measurement was conduc ted by Bridgman

(1925) on s i n g l e and p o l y c r y s t a l l i n e m e ta l s . A lthough some work

was done by A l le n (1932) and Cookson (1935) , i t was n o t u n t i l 1953

t h a t C. S. Smith (1954) made m easurem ents on th e p i e z o r e s i s t a n c e

t e n s o r f o r b o th n - and p - ty p e germanium and s i l i c o n . Smith found t h a t

the p i e z o r e s i s t a n c e c o e f f i c i e n t s o f s em ico n d u c to rs w ere much h ig h e r

than t h a t f o r m e ta l s .

Theory

P i e z o r e s i s t i v i t y was d e f in e d as th e change in e l e c t r i c a l

r e s i s t a n c e o f a co n d u c to r when i t was s u b je c t e d to an e x t e r n a l s t r e s s .

The r e s i s t i v i t y o f an u n s t r e s s e d co n d u c to r can be d e s c r ib e d by a

sym m etric s e c o n d - ra n k t e n s o r w i th a s e t of s i x in d e p e n d e n t c o e f f i c i e n t s

(Sm ith , 1954). As an exam ple, th e e l e c t r i c f i e l d v e c t o r E in a

c r y s t a l i s r e l a t e d to th e c u r r e n t d e n s i t y J by

Ek “ P k lJ l (3 -1 )

where i s th e r e s i s t i v i t y t e n s o r and a l l s u b s c r i p t s have the

range 1 to 3. For an i s o t r o p i c m a t e r i a l , = p ^2 = P 3 3 = P and

a l l o th e r components a re z e ro . This was th e case f o r u n s t r e s s e d

germanium and s i l i c o n , which p o s s e s s a cu b ic c r y s t a l s t r u c t u r e .

For a s t r e s s e d c o n d u c to r th e change in r e s i s t i v i t y , 6 p_^ ,

was g iv e n by th e p i e z o r e s i s t a n c e e q u a t io n a s ,

25

where tt. n i s th e p i e z o r e s i s t a n c e t e n s o r and T. . i s th e s t r e s s t e n s o r , i j k l r k l

The p i e z o r e s i s t a n c e e q u a t io n f o r s i l i c o n and germanium i s ,

a i j Li = I j + ^ i j k A l (3e3)

where i s th e a p p l ie d e l e c t r i c f i e l d , i s th e c o n d u c t iv i t y t e n s o r ,

and 1^ i s th e c u r r e n t a long th e c r y s t a l axes (Mason, 1958).

From Eq. 3 .1 , th e components o f the r e s i s t i v i t y t e n s o r were

Pk l = 7 1 • ( 3 '4 )

Then th e r e l a t i o n s h i p f o r th e components o f th e p i e z o r e s i s t a n c e

e q u a t io n a re

(6 E)(Sp)1j = — 1 . ( 3 . 5 )

where (6 E)^ i s th e change in e l e c t r i c f i e l d f o r a c o n s t a n t c u r r e n t

d e n s i t y , J ^ .

A reduced n o t a t i o n f o r Eq. 3 .2 has been dev e lo p ed by Smith

(1958) and i s g iven by,

(6p) i = TT jTj , ( 3 . 6 )

where i s a s e c o n d - ra n k t e n s o r and T^ i s a f i r s t - r a n k t e n s o r .

The most g e n e r a l form f o r a tw o -d im en s io n a l p i e z o r e s i s t a n c e

t e n s o r a p p l i c a b l e to an i n v e r s i o n l a y e r on a c r y s t a l s u r f a c e was

(Colman, B a te , and M ize, 1968),

26

* 1 1 * 1 2 *14

7T = * 2 1

CMCMt=

*24 ( 3 .7 )

*41 *42 *44

where th e c o e f f i c i e n t s were r e l a t e d to th e t e n s o r q u a n t i t i e s by

*11 “ *1111

*12 " *1122

*14 ” 2*1112

*21 * *2211

*22 “ * 2 2 2 2

*24 ” 2*2212

*41 e *1211

*42 “ *1222

*44 ” 27T1 2 i2

I t can be shown by a p p ly in g symmetry o p e r a t io n s on each p la n e t h a t

fo u r o f th e p i e z o r e s i s t a n c e c o e f f i c i e n t s were z e ro . T ab le 3 .1 l i s t s

th e p i e z o r e s i s t a n c e c o e f f i c i e n t s f o r a p - ty p e i n v e r s i o n l a y e r

(Colman, B a te , and M ize, 1968).

I n t e r a c t i o n w i th I n v e r s io n L avers

The i n t e r a c t i o n o f a s u r f a c e wave w i th an i n v e r s i o n l a y e r was

shown in F ig . 3 .1 . The e f f e c t was d e f in e d by th e e l e c t r i c f i e l d

TABLE 3 .1

P i e z o r e s i s t a n c e c o e f f i c i e n t s i n p - ty p e i n v e r s i o n l a y e r s *

110 PLANE

- 2 3 .8 38 .2 0 .0

- 1 4 .3 5 8 .0 0 . 0

0 .0 0 .0 6 7 .7

111 PLANE

44 .7 - 1 5 .3 0 .0

- 1 5 .3 4 4 .7 0 . 0

0 . 0 0 . 0 60 .0

100 PLANE

- 1 . 0 2 3 .8 0 .0

2 3 .8 - 1 . 0 0 .0

0 .0 0 .0 127 .8

”*12 2A l l c o e f f i c i e n t s xlO cm / dyne

(

28

INVERSIONLAYER

F ig . 3 .1 P i e z o r e s i s t i v e i n t e r a c t i o n of a s u r f a c e wave w ith a tw o -d im en s io n a l i n v e r s i o n l a y e r

29

d i r e c t i o n , 0, a p p l i e d norm al to th e i n v e r s i o n l a y e r . A d i s c u s s io n on

th e p h y s ic s o f the i n v e r s i o n l a y e r i s g iv en in c h a p te r 4.

For a s i l i c o n s u b s t r a t e i n g e n e r a l , th e c o n d u c t iv i t y o f th e

i n v e r s i o n l a y e r was n o t i s o t r o p i c and th e c u r r e n t was n o t in the d i r e c ­

t i o n o f th e a p p l ie d v o l t a g e (Colman, e t a l . , 1968). S im i l a r l y , the

change in c u r r e n t d e n s i t y , AJ, w i l l a l s o be a n i s o t r o p i c w i th change

i n v o l t a g e .

E q u a t io n 3 .3 can be w r i t t e n f o r th e i n v e r s i o n l a y e r as

AI1 A11 I 1 + A12 I 2

AI2 A12 T1 + A22 I 2

(3 .8 )

where

A11 7T12T2 + 7T13T3 + ^14^4

A 2 2 ’FT23T3 + 1T22T2 + 7r24T4

A12 7T42T2 + 7T43T3 + 7T44T4

The change in c u r r e n t i s now d e te rm in e d s in c e th e it’ s a r e g iven by

Table 3 .1 and th e s t r e s s e s (n o rm alize d to s t r a i n ) w ere g iv en by

Eq. 2 .2 5 .

The c u r r e n t and change i n c u r r e n t can be t r a n s fo rm e d to the

d e s i r e d 0 d i r e c t i o n by ,

AJ = (A^^ c o s 6 + A ^ s in 0 ) + ( A ^ cosO + sinO ) (3 .9 )

30

= J 9 COS0 + J . s in O . (3 .1 0 )6 J

The c u r r e n t components were r e l a t e d to th e e l e c t r i c f i e l d , by th e

c o n d u c t iv i t y t e n s o r ,

J 0 = C00E cosO + a 0 .E sinO I zz o 23 o

= cr E cosO + CT--E s in 0 3 32 o 33 o

(3 .1 1 )

S u b s t i t u t i n g Eq. 3 .10 i n t o Eq. 3 .8 and Eq. 3 .9 y i e l d s th e d e s i r e d

r e s u l t s ,

AJJ

(3 .1 2 )

2 2a i l ^ l l COS ® + a 2 2 A2 2 s ^n ® + a i l + Cr2 2 ^A1 2 COS®s ^n ®

2 2 a^ ^co s 0 + c ^ s i n 0 + (a 1 2 + a 2 ^ )c o s 0 s i n 0

2 2^1 2 a 2 i cos ® + a i 2 S^n + ^ n a i2 + ^22a 21^COS®s ^n®

+ 2 2a ^ ^ c o s 0 + a 22s i n 0 + ( a ^ 2 + O2 ^ ) c o s 0 s i n 0

E q u a tio n 3 .12 y i e l d s th e f r a c t i o n a l change in c u r r e n t w i th

th e a p p l i e d v o l t a g e in th e 0 d i r e c t i o n norm al to th e i n v e r s i o n l a y e r .

I t a l s o c o n ta in s a s t r a i n n o r m a l iz a t io n s in c e th e s t r e s s e s were

o r i g i n a l l y n o rm a l iz e d t o th e norm al s u r f a c e s t r a i n i n Eq. 2 .2 5 .

A p e rfo rm ance in d e x used to e v a l u a t e th e i n v e r s i o n l a y e r

i n t e r a c t i o n was d e f in e d as the power n o rm a l ize d gauge f a c t o r , PNGF

( S ta p l e s , 1971). I t ta k e s i n t o acc o u n t th e power and f req u en cy of

th e s u r f a c e wave and was d e f in e d to be

The PNGF i s o b ta in e d n u m e r ic a l ly by e v a l u a t i n g th e t o t a l p o w e r -v e c to r

c o n s ta n t whose components were g iv en i n Eq. 2 .2 7 . The t o t a l power

c o n s ta n t was

+ K32

(3 .1 4 )

The perfo rm ance in d e x f o r an i n v e r s i o n l a y e r was r e p r e s e n te d by ,

E q u a t io n 3 .15 r e l a t e d th e f r a c t i o n a l o u tp u t c u r r e n t to th e freq u en cy

and a c o u s t i c power i n th e s u r f a c e wave.

Eq. 2 .25 i n t o i t a long w i th th e p i e z o r e s i s t a n c e d a t a from Table 3 .1 .

The PNGF was c a l c u l a t e d from Eq. 3 .15 f o r th e (1 0 0 ) , (1 1 0 ) , and (111)

p la n e s o f s i l i c o n and a r e shown in F ig . 3 .2 , F ig . 3 .3 , and F ig . 3 .4 ,

r e s p e c t i v e l y . The PNGF i s shown f o r t h r e e d i f f e r e n t a n g le s o f th e

a p p l ie d e l e c t r i c f i e l d v e r s u s th e p r o p a g a t io n v e c t o r d i r e c t i o n 0 ^ .

I t sh o u ld be n o ted t h a t th e r e was an e x p e r im e n ta l measurement e r r o r o f

20 p e r c e n t r e p o r t e d w i th th e d a t a o f T ab le 3 .1 (Colman, e t a l . , 1968).

s i l i c o n . This was due to the s u r f a c e wave d e g e n e ra t in g i n t o a b u lk

G A J/J (3 .1 5 )P

E qua t ion 3.12 was e v a lu a te d by s u b s t i t u t i n g th e s t r e s s e s from

The PNGF decays r a p i d l y beyond 6 ^ = 30° on th e (100) p la n e

wave as was shown in F ig . 2 .2 . A peak o c c u rs f o r 0 = 6 , the c o l i n e a r

CM-S

ECW

ATT

32

ot—fX

o <

5

4

3

2

1

03010 200

<010> 0 (DEGREES) P

F ig . 3 .2 Power norm alized gauge fa c to r s versu s propagationv e c to r d ir e c t io n on the (100) p lane o f s i l i c o n ,6 = 6 , 0 ° , and 90°

P

CM-S

ECW

ATT

33

5

0=04

3

2

901

040 6020 800

<110> 0 (DEGREES) <001>P

F ig . 3 .3 Power n o rm a l ize d gauge f a c t o r s v e r s u s p ro p a g a t io n v e c t o r d i r e c t i o n on th e (1 1 0 ) p la n e o f s i l i c o n ,0 = 0 , 0 ° , and 90°

CM-S

EC

34

<N

H

S

o

o

4

6=63

2

1

03020100

<110> 6 (DEGREES)P

F ig . 3 .4 Power normalized gauge fa c to r s versus propagationv e c to r d ir e c t io n on the (111) p lane of s i l i c o n ,6 = 6 , 0», and 90°

c a s e , when 0^ was a p p ro x im a te ly 2 7 ° , i n d i c a t i n g a maximum i n t e r a c t i o n .

The (110) p la n e shows e q u a l ly s t r o n g i n t e r a c t i o n w i th a s l i g h t l y

b r o a d e r peak f o r th e c o l i n e a r c a s e . The (111) p la n e shows a PNGF of

abou t 40 p e r c e n t l e s s than th e (100) o r (110) p l a n e s . I t a l s o shows

t h a t th e a n i s o t r o p y was n o t s t r o n g as i n th e o t h e r two p la n e s s in c e

th e e l e c t r i c a l and p i e z o r e s i s t i v e p r o p e r t i e s were i s o t r o p i c on t h i s

p la n e .

CHAPTER 4

MOSFET

I n t r o d u c t i o n

The re g io n o f i n t e r e s t i n th e MOSFET was th e p-fcype s u r f a c e

i n v e r s i o n l a y e r formed when t h e r e was s u f f i c i e n t g a t e b i a s to cause

t h e d e v ic e to c o n d u c t . T h is i n v e r s i o n l a y e r was d i s c u s s e d by means o f

th e e n e rg y band d iagram th e o r y » When i n s a t u r a t i o n , th e MOSFET i s an

a c t i v e , n o n - l i n e a r d e v ic e w hich can be d e s c r ib e d by an e q u i v a l e n t

c i r c u i t . The MOSFET f a b r i c a t i o n was d is c u s s e d and th e e l e c t r o n i c

c h a r a c t e r i s t i c s o f th e d e v ic e w ere a n a ly z e d .

Theory

The i n v e r s i o n l a y e r can be u n d e rs to o d by s tu d y in g th e energy

band d iagram s under v a r io u s b i a s c o n d i t io n s (Sah, 1 9 6 4 ) . The MOSFET

under i n v e s t i g a t i o n was an enhancement mode d e v ic e which has no

co n d u c t in g ch an n e l betw een th e two p - r e g io n d r a in and s o u rc e c o n t a c t s

f o r ze ro g a t e v o l t a g e . Due to th e f a c t t h a t t h e r e w ere sm a l l amounts

o f c o n tam in a n ts i n th e g a t e o x id e , t h i s causes n e g a t iv e s u r f a c e s t a t e s

to e x i s t a t th e o x id e -s e m ic o n d u c to r i n t e r f a c e . S in ce p o s i t i v e s u r f a c e

s t a t e s o r h o le s w ere needed to form th e i n v e r s i o n l a y e r , a n e g a t iv e

g a t e v o l t a g e was needed to overcome th e i n i t i a l n e g a t iv e s u r f a c e s t a t e s .

I n F ig . 4 . 1 ( a ) th e en e rg y bands a r e bend ing downward a t th e o x id e -

semi co n d u c to r i n t e r f a c e . For a n e g a t iv e g a te v o l t a g e s m a l l enough to

36

37

OXIDE

METAL I I SEMICONDUCTOR

• E.

V <0

(a) (b)

V <0

(c) (d)

F ig . 4 .1 S u r fa c e energy band d iagram s f o r i n v e r s i o n l a y e r s

38

d e p l e t e th e n e g a t iv e s u r f a c e s t a t e s s an e q u i l i b r i u m c o n d i t io n e x i s t s

a t th e sem ico n d u c to r i n t e r f a c e so t h a t a f l a t band c o n d i t io n was

c r e a te d as shown i n F ig . 4 . 1 ( b ) . For a l a r g e n e g a t iv e g a t e v o l t a g e th e

n e g a t iv e s t a t e s a r e d e p le te d to a maximum dep th i n t o th e sem ico n d u c to r

and th e s u r f a c e a t th e o x id e -se m ic o n d u c to r i n t e r f a c e e x h i b i t s an

i n t r i n s i c c o n d i t io n f o r th e energy l e v e l s shown i n F ig . 4 . 1 ( c ) . T h is i s

th e o n s e t f o r th e i n v e r s i o n l a y e r and a t y p i c a l d e p l e te d l a y e r i s

shown in Fig* 4*2. For l a r g e r n e g a t iv e g a te v o l t a g e s $ th e i n v e r s i o n

l a y e r was formed a t th e o x id e -s e m ic o n d u c to r s u r f a c e which c o n s i s t s o f

p o s i t i v e s u r f a c e s t a t e s . The p o s i t i v e s u r f a c e s t a t e s w ere c r e a te d when

th e i n t r i n s i c energy l e v e l c ro s s e d th e Fermi l e v e l i n th e sem ico n d u c to r

as shown in F ig . 4 . 1 ( d ) . A c r o s s - s e c t i o n a l view o f th e MOSFET w ith th e

i n v e r s i o n l a y e r i s shown i n Fig* 4 .2 .

When t h i s i n v e r s i o n l a y e r was c re a te d ^ a s t r e s s c o n d i t io n d id

o c c u r a t th e o x id e -se m ic o n d u c to r i n t e r f a c e . T h is s t r e s s changes th e

m o b i l i t y o f th e h o le s i n th e i n v e r s i o n l a y e r to ab o u t h a l f t h a t o f

th e m o b i l i t y o f th e b u lk s i l i c o n (Colman, e t a l . $ 1968).

Th is change i n m o b i l i t y can be e x p la in e d i n te rm s of th e

energy s u r f a c e s i n k - s p a c e by c o n s id e r in g th e energy s t a t e o f an

e l e c t r o n i n o r above th e c o n d u c t io n band i n s i l i c o n . I t was p o s s i b l e

f o r an e l e c t r o n to a c h ie v e a minimum e n e rg y , which i t r e q u i r e d to

rem ain i n th e co n d u c t io n band, by s e v e r a l com bina tions o f th e wave

numbers k ^ , k ^ , and k^ (G eyling and F o r s t , 1960). These com b in a tio n s

were r e f e r r e d to as band edge p o i n t s , s i n c e they form lo w er bounds f o r

th e energy r e q u i r e d o f a f r e e e l e c t r o n . A fam ily o f such s u r f a c e s .

DRAINSOURCE ‘ GATE

INVERSION LAYERDEPLETION LAYER

N -type SUBSTRATE

F ig . 4 .2 C r o s s - s e c t io n o f p - ty p e i n v e r s i o n l a y e r MOSFET showing d e p l e t i o n and in v e r s i o n l a y e r s

• 40

c e n te r e d on a band edge p o i n t , d e s c r ib e s an energy v a l l e y i n k - s p a c e .

For s i l i c o n and germanium, th e s e f a m i l i e s c o n s i s t o f e l l i p s o i d s o f

r e v o l u t i o n t h a t were a l ig n e d w i th th e c r y s t a l a x e s . F ig u re 4 .3 shows

th e c o n s ta n t energy s u r f a c e i n k - s p a c e f o r n - ty p e s i l i c o n , where th e

sp ace was r e s o lv e d i n t o components co r re sp o n d in g to th e c r y s t a l a x e s .

The c o n s ta n t energy s u r f a c e p o s s e s s e s p r i n c i p a l axes o f u n e q u a l

le n g th i n d i c a t i n g t h a t th e components o f mass and m o b i l i t y , y , o f

an e l e c t r o n (o r components o f c o n d u c t i v i t y , a ) i n such a v a l l e y were

d i f f e r e n t i n th e t h r e e p r i n c i p a l d i r e c t i o n s . C o n seq u en tly , th e s e

e l e c t r o n s c o n t r i b u t e a n i s o t r o p y to th e t o t a l c o n d u c t iv i t y o f the

l a t t i c e . I f a l l e l l i p s o i d s have th e same p r o p o r t i o n s and a l l v a l l e y s

w ere e q u a l ly p o p u la te d w i th e l e c t r o n s , th e n th e o v e r a l l c o n d u c t iv i t y

o f th e l a t t i c e w i l l be i s o t r o p i c .

F a b r i c a t i o n and C h a r a c t e r i s t i c s o f th e MOSFET

The MOSFET used i n th e i n v e s t i g a t i o n was a p - c h a n n e l , enhance­

ment mode d e v ic e . A c r o s s - s e c t i o n a l view o f th e MOSFET's f a b r i c a t e d

f o r t h i s i n v e s t i g a t i o n i s shown i n F ig . 4 .4 . Th is geom etry was s i m i l a r

to t h a t used by S ta p le s (1971), The d e v ic e c o n s i s t e d o f an n - ty p e

s i l i c o n s u b s t r a t e o f 1 to 3 ohm-cm r e s i s t i v i t y w i th two p - ty p e

d i f f u s e d r e g io n s f o r th e d r a in and s o u r c e . An a d d i t i o n a l n d i f f u s e d

re g io n was p ro v id e d f o r ohmic c o n t a c t to th e s u b s t r a t e . The w afe rs

used i n t h i s i n v e s t i g a t i o n w ere a p p ro x im a te ly 40 m i l s t h i c k to i n s u r e

t h a t o n ly a R ay le ig h s u r f a c e wave was g e n e r a te d .

Shown in F ig . 4 .5 a r e th e p r o c e s s in g s t e p s in v o lv e d in6

f a b r i c a t i n g th e MOSFET. The w a fe r was f i r s t c le a n e d and a 5000 A o x id e

41

P iiL ► -

BAND EDGE

BAND EDGE

F ig . 4 .3 C o n s ta n t energy s u r f a c e s in k - s p a c e

42

SOURCE GATE DRAIN

N -type SUBSTRATE

OXIDE

F ig . 4 .4 C r o s s - s e c t io n o f MOSFET used in t h i s i n v e s t i g a t i o n

43

STEP

" 1 ---------------------------------- r .......I " " '

2 7

I—---J I---- J

..... n "■.........

3 8

p = ^ 7 ^ y

4 9

5 10

F ig . 4 .5 P ro c e s s in g s t e p s n e c e s s a ry to f a b r i c a t e th e MOSFET

44

was grown in p r e p a r a t i o n f o r the p - ty p e d i f f u s i o n . The p - ty p e

d i f f u s i o n was perform ed w ith d ib o ra n e gas (E^H^) a t a te m p e ra tu re o f

1050°C f o r 60 m in u te s . No p - ty p e d r i v e - i n was n e c e s s a ry a t t h i s t im e .

The n e x t s te p was to e t c h away th e rem a in ing ox ide o v e r th e g a te a r e a .

The w afe r was c a r e f u l l y c le a n e d , and a 2000 A ox ide was grown a t 1100°C

in dry 0^ f o r 120 m in u te s . Next th e g a te ox ide was e tc h e d back to

ap p ro x im a te ly 1300 A. Then a window was e tc h e d in p r e p a r a t i o n f o r the

n+ d i f f u s i o n ( s te p 7 ) . The n - ty p e d i f f u s i o n was perfo rm ed w ith

phosph ine gas (PII^) a t a te m p e ra tu re o f 1050°C f o r 15 m in u te s . Windows

were then e tc h e d o v er th e d r a i n , s o u r c e , and n+ re g io n s in p r e p a r a t i o n

f o r th e m e ta l c o a t in g . At t h i s time th e w afe r was e t c h e d in 10:1 HF

(H y d ro f lo u r ic a c id ) f o r 60 seconds which e tc h e s th e g a t e ox ide toO

1000 A, Aluminum was then e v a p o ra te d o v e r th e s u r f a c e o f th e w afe r in

a vacuum b e l l j a r . The f i n a l s te p in v o lv e d s e l e c t i v e removal o f th e

aluminum and s i n t e r i n g o f the w afe r to form good ohmic c o n t a c t s .

F ig u re 4 .6 shows th e mask l a y o u t o f a s i n g l e MOSFET used in

t h i s i n v e s t i g a t i o n . The f i v e masks were superim posed to show the

r e l a t i v e d im en s io n s . The MOSFETs have a c e n t e r - t o - c e n t e r sp ac in g o f

15.5 m i l s , and the ch an n e l le n g th p r i o r to d i f f u s i o n was 1 m il and the

w id th was 93 .5 m i l s . The com pleted mask p a t t e r n c o n s i s t s o f th r e e

a r r a y s o f the MOSFET (shown in F ig . 4 . 6 ) . F ig u re 4 .7 ( a ) shows the

f i n i s h e d w a fe r , and F ig . 4 .7 (b ) shows a c lo s e up o f th e MOSFET a r r a y .

The MOSFET w i l l n o t be used in th e norm al manner as a sm a l l

s i g n a l a m p l i f i e r , t h e r e f o r e , th e DC and RF e l e c t r o n i c c h a r a c t e r i s t i c s

d e s c r ib e d w i l l app ly on ly to the MOSFET as an a c o u s t i c s u r f a c e wave

45

93 .5 MILS

S 3

SCALE: MIL

CONTACT HOLES

PHOSPHOROUS DEPOSITION AND CONTACT HOLE

BORON DEPOSITION

F ig . 4 .6 Layout of th e f i v e photomasks superim posed to show r e l a t i v d im ensions

46

(a) Completed wafer w ith an array o f MOSFERs cut from another wafer

(b) Micro-photograph o f a MOSFET array

F ig . 4 .7 Photographs o f completed wafer w ith MOSFETs

47

d e t e c t o r . The DC c h a r a c t e r i s t i c s c o n s i s t o f the t r a n s c o n d u c ta n c e ,

gmsat» *n th e s a t u r a t i o n re g io n which was d e f in e d as

= 3id^msat 3V

. 8(4 .1 )

V = c o n s ta n t d

where V i s th e g a te v o l t a g e , V, i s th e d r a in v o l t a g e , and I i s th eg d d

d r a in c u r r e n t . E x p e r im e n ta l ly o b ta in e d g _ v a lu e s f o r the MOSFET‘ J m satused a r e shown in F ig . 4 .8 . The d e v i a t i o n from th e l i n e a r b e h a v io r was

due to a g a t e v o l t a g e dependen t m o b i l i t y (Colman, B a t e , and Mize, 1968)

and a f i n i t e c o n t a c t r e s i s t a n c e in s e r i e s w i th th e s o u rc e (G rove, 1967).

In th e l i n e a r r e g io n the ch an n e l conductance i s d e f in e d as

g ch a v ,d(4 .2 )

V = c o n s ta n t 8where th e p a ra m e te rs a r e d e f in e d above and i s th e ch an n e l

co n d u c tan ce . The ch an n e l conduc tance was th e p a ra m e te r r e l a t i n g th e

p h y s i c a l d ev ic e c h a r a c t e r i s t i c s to th e e l e c t r i c a l p a r a m e te r s . I t has

been shown (G rove, 1967) t h a t f o r s m a l l v a lu e s o f V^, g ^ i s g iven by

Wee

8ch = Uh " (V VT) (4l3)

where

i= e f f e c t i v e h o le m o b i l i t y

W = ch an n e l w id th

msa

t

48

4 .0

3 .0 -

2 . 0

1 .0

4 620 8 10 12 14 16

F ig . 4 .8 E x p e r im en ta l t r a n s c o n d u c ta n c e in th e s a t u r a t i o nre g io n v e r s u s e f f e c t i v e g a te v o l t a g e f o r the (1 1 0 ) p la n e

49

L ch an n e l le n g th

CG = ox ide d i e l e c t r i c c o n s ta n tO

x = o x id e th i c k n e s so

VT " th r e s h o ld v o l t a g e

This im p l ie s t h a t th e channe l conduc tance obeys a l i n e a r r e l a t i o n s h i p

w i th g a t e v o l t a g e and was d i r e c t l y r e l a t e d to th e d e v ic e geometry and

m o b i l i t y . T y p ic a l v a lu e s of g ^ in the l i n e a r re g io n a r e shown in

F ig . 4 .9 .

The channe l conduc tance i s r e l a t e d to the a b i l i t y o f the

MOSFET to t r a n s f e r power to an e x t e r n a l c i r c u i t e le m e n t . The maximum

power t r a n s f e r o cc u rs when th e load a d m it ta n c e e q u a ls th e complex

c o n ju g a te o f th e o u tp u t co n d u c tan ce . The com plex ity o f c a l c u l a t i n g th e

o u tp u t conductance of th e MOSFET can be reduced by n o rm a l iz in g the

s a t u r a t i o n ch an n e l conduc tance to th e l i n e a r ch an n e l conduc tance

(Frohman-Bentchkowsky and Grove, 1969). The r e s u l t i s a l i n e a r

r e l a t i o n s h i p between th e n o rm a l iz e d conduc tance and e f f e c t i v e g a te

v o l t a g e . Optimum power t r a n s f e r can th en be d e te rm in e d from the

n o r m a l iz a t io n method. T y p ic a l n o rm a l iz e d e x p e r im e n ta l conduc tances

f o r th e MOSFET used a re shown in F ig . 4 .1 0 .

The RF c h a r a c t e r i s t i c s o f th e MOSFET were r e p r e s e n t e d by a

s im ple e q u i v a l e n t c i r c u i t an a ly zed by W. F i s c h e r (1 9 6 6 ) . The

e q u i v a le n t c i r c u i t i s shown in F ig . 4 .1 1 where th e e le m e n ts r e p r e s e n t

b o th e x t r i n s i c and i n t r i n s i c e f f e c t s . For the c i r c u i t o f F ig . 4 .11 i t

has been shown (W. F i s c h e r , 1966) t h a t i f

(MM

HO)

50

3 .0

2 . 0

1 .0

04 6 148 10 12 1620

F ig . 4 .9 E x p e r im e n ta l c h an n e l conduc tance i n th e l i n e a rre g io n v e r s u s e f f e c t i v e g a te v o l t a g e f o r th e (1 1 0 ) p la n e

51

1 .5

1 .0

0 .5

060 2 4 8 10 12

F ig . 4 .10 N orm alized e x p e r im e n ta l channe l conduc tance in the s a t u r a t i o n r e g io n v e r s u s e f f e c t i v e g a t e v o l t a g e f o r th e (1 1 0 ) p la n e

52

GATE DRAIN

gs

gs

SOURCE

(COMMON)

F ig . A .11 Simple e q u i v a l e n t c i r c u i t o f a MOSFET w ith so u rc e and s u b s t r a t e common

i

53

wC R « 1 gs gs

and

o)C, R, « 1 d d

th en th e common s o u rc e a d m it ta n c e p a ra m e te rs were g iv e n by

*11 - V ^ g / + J“(Cgs + Cgd)

5 ,1 2 ‘ T C8d g (4 .4 )

“ w " j u ( c ^ +

* 2 2 = 7 7 “ + (MCd)2Rd + J “ (Cgd + c d) •ds

The v a lu e o f th e e lem en ts o f th e e q u i v a l e n t c i r c u i t was

c a l c u l a t e d from th e HOSFET p a ra m e te rs such as geom etry and ox ide

th i c k n e s s . The c a p a c i t a n c e , C ^ , was th e o v e r - la p o f th e g a te m e ta l -

i z a t i o n o v e r th e d r a in d i f f u s i o n . C and C, were th e g a te to so u rc egs d

and d r a i n c a p a c i t a n c e , r e s p e c t i v e l y . The g a te to s o u rc e c a p a c i ta n c e

was dependen t on th e g a te ox id e t h i c k n e s s , and th e d r a in c a p a c i ta n c e was

due to c a p a c i t a n c e i n th e r e v e r s e b i a s e d d r a in d iode and th e d r a ino

bonding p ad . The g a te o x id e th i c k n e s s was a p p ro x im a te ly 1000 A. T h is

y i e l d s a g a te to s o u rc e c a p a c i t a n c e o f 31 p f , a g a t e to d r a in

c a p a c i t a n c e o f 4 .1 p f , and a d r a in c a p a c i t a n c e o f 8 .5 p f . Table 4 .1

shows th e v a lu e s o b ta in e d f o r th e e lem en ts o f the e q u i v a l e n t c i r c u i t

u sed . The v a lu e s o f th e c a p a c i t a n c e s were m easured u s in g th e Boonton

RX m e te r and th e T e k t ro n ix LC m e te r .

TABLE 4 .1

E lem en ta l v a lu e s f o r th e MOSFET E q u iv a le n t C i r c u i t

Geometry Z z Cgs

ACd R

gs Rd r ds gm T .

(m ils) (m ils) Pf ' p f P f . . o £2 VSl mmhos nsec

S t . L ine 90 1 27 .5 2 .5 7 .5 14 8 10 3 .0 : 1 .2

* Vj) = - 1 0 v o l t s

** (V -v_ ) = -7 v o l t sg I

55

The r e s i s t a n c e s R and R „ were due p r im a r i ly to th e gs dr e s i s t i v i t y o f th e g a te and d r a in m e t a l i z a t i o n s , r e s p e c t i v e l y . The

aluminum f i lm has a r e s i s t i v i t y o f 2 .8 x 10 ^ ft-cm. The g a te

d im ensions were 100 m i ls by 1 m il which y i e l d s an R o f 14 ohms. Thegsd r a in d im ensions were 100 m i ls by 1 .75 m i l which y i e l d s an o f 8 ohms.

The t r a n s i t t im e , T, of th e MOSFET was r e l a t e d to th e geometry

and m a t e r i a l p a ra m e te r s and was g iv en by

T = w - " Y . w - 5)

The t im e , T , was d e f in e d as t h a t tim e in which th e change in th e d r a in

c u r r e n t makes up th e change in th e t o t a l charge on the g a t e . An

es t im a te o f T can be made from the knowledge of the d ev ice parameters

and t e s t c o n d i t i o n s . The e f f e c t i v e m o b i l i t y was a p p ro x im a te ly 200 2

v o Y t-sec an< the e f f e c t i v e gate v o lta g e was approxim ately 7 v o l t s .

The channe l le n g th was ap p ro x im a te ly 1 m i l . S u b s t i t u t i n g in t o Eq 4 .5

y i e l d s a t r a n s i t tim e o f 0 .8 3 nanoseconds which a g re e s r e a s o n a b ly w e l l

w i th th e measured tim e o f 1 . 2 0 n an o se c o n d s .

The f i n a l p a ra m e te r to be d i s c u s s e d i s the e l e c t r i c a l n o is e

g e n e ra te d by th e MOSFET. The t h r e e main ty p es of n o i s e w ere : 1) Johnson

( th e rm a l) n o is e g e n e ra te d in th e c h a n n e l ; 2 ) s h o t n o i s e in t ro d u c e d by

th e g a t e ; and 3) " l / f " n o is e due to th e g e n e r a t io n and reco m b in a t io n

p ro c e s s e s in the c h a n n e l . S ince th e use o f th e MOSFET a t RF

f r e q u e n c ie s ex c lu d e s th e " l / f " n o i s e , t h i s n o is e component was n o t

c o n s id e re d . The use of th e MOSFET in a common g a te c o n f ig u r a t io n

56

red u ce s th e s h o t n o i s e , and th e s h o t n o is e was shown (Cobbold, 1970) to

be s m a l l when th e MOSFET was o p e r a t in g below th e c h a n n e l c u t - o f f

f re q u e n c y . Thus th e p redom inan t cause o f n o is e was o f th e rm a l o r i g i n

o r Johnson n o i s e . The Johnson n o i s e can be r e p r e s e n t e d by an e q u i v a l e n t

n o i s e r e s i s t o r . For s a t u r a t i o n c o n d i t i o n s th e v a lu e o f th e in p u t

n o is e r e s i s t o r was g iv e n by

Rh „ 2 _ L . . ( 4 .6 )3 8m

The t y p i c a l t r a n s c o n d u c ta n c e v a lu e s a t h ig h c u r r e n t l e v e l s-3

f o r th e MOSFETs were 3 .0 x 10 mho. T h is y i e l d s a n o i s e r e s i s t a n c e

o f 220 ohms. Assuming a 5 MHz bandw id th and a c e n t e r f req u en cy of

30 MHz, th e e q u i v a l e n t n o is e v o l t a g e was g iv e n by

VN «= (AkTI^Af) 1 7 2 = 3 .8 y v o l t s . ( 4 .7 )

For th e o u tp u t o f th e MOSFET te rm in a te d i n 50 ohms th e o u tp u t n o is e

power was 2 .4 x 10 w a t t , o r - 9 6 .2 dbm (Odbm = 1 m i l l i w a t t ) .

A ttem pts to m easure th e n o is e power o f t h i s m agnitude w ere f u t i l e

due to n o is e g e n e ra te d by th e d e t e c t i n g and a m p l i fy in g equ ipm ent.

The minimum d e t e c t a b l e a c o u s t i c s i g n a l o f th e MOSFET s u r f a c e wave

d e t e c t o r w i l l be l i m i t e d by th e n o i s e g e n e ra te d w i t h i n th e MOSFET

and th e e f f i c i e n c y o f th e MOSFET d e t e c t o r .

CHAPTER 5

EXPERIMENTAL RESULTS

The power n o rm a l iz e d gauge f a c t o r s (PNGF) w ere e x p e r im e n ta l ly

e v a lu a te d and compared to the t h e o r e t i c a l v a lu e i n t h i s chap t e r » The

PNGF i s a perfo rm ance in d e x which r e l a t e d th e e f f i c i e n c y o f an i n v e r s i o n

l a y e r to th e f req u en cy and power d e n s i t y o f an a c o u s t i c s u r f a c e wave.

The t e s t i n g p ro c e d u re was g iv e n i n th e f i r s t s e c t i o n o f t h i s chap ter*

The e l e c t r i c a l t e s t i n g c i r c u i t was examined under th e c o n d i t io n s which

th e i n s e r t i o n lo s s e s were m easured . The n e x t s e c t i o n examines and

d i s c u s s e s th e r e s u l t s * The c o n c lu s io n which fo l lo w s i n d i c a t e s t h a t

th e MOSFET can be p ro m is in g i n f i e l d o f s u r f a c e wave d e t e c t i o n .

E x p e r im e n ta l Method

This s e c t i o n d e s c r ib e s th e p ro c e d u re used to e x p e r im e n ta l ly

e v a l u a t e th e e f f i c i e n c y o f th e MOSFET in v e r s i o n l a y e r to d e t e c t

a c o u s t i c s u r f a c e waves * The e f f i c i e n c y was e x p re s s e d i n term s o f

i n s e r t i o n l o s s between th e RF power i n th e a c o u s t i c wave and th e RF

power coup led o u t o f th e MOSFET. The MOSFET d e t e c t o r s were f a b r i c a t e d

on th e 110 p la n e s i l i c o n * The i n s e r t i o n l o s s o f a MOSFET d e t e c to r

depends on th e e f f i c i e n c y o f the i n v e r s i o n l a y e r , and th e e l e c t r i c a l

ne tw ork to t r a n s f e r th e d e t e c te d RF s i g n a l from th e i n v e r s i o n l a y e r to

th e lo a d .

F ig u re 5*1 shows th e method used to o b ta in th e e x p e r im e n ta l

data* The R ay le igh s u r f a c e waves were e x c i t e d on th e s i l i c o n

57

58

s u b s t r a t e by th e wedge co u p l in g method ( I . A. V ik to ro v , 1967).

E x c i t a t i o n o f s u r f a c e waves u s in g the wedge method was b ased on th e

c o n v e rs io n o f l o n g i t u d i n a l b u lk waves i n t o R ay le igh mode s u r f a c e waves.

The wedges were made from c h a lc o g e n id e g l a s s (K rause , K u rk j ia n ,

Pinnow, and S ig e ty , 1970) which has a low v a lu e o f a c o u s t i c lo s s and

3a c o u s t i c v e l o c i t y o f 2 .518 x 10 m /se c . The wedge i s c u t to an a n g le 0^

w i th a p i e z o e l e c t r i c p l a t e t r a n s d u c e r mounted on th e f a c e which forms

th e an g le 0^ w ith r e s p e c t to th e s u b s t r a t e as shown in F ig . 5 .2 . The

an g le 0 ^ was chosen f o r optimum e x c i t a t i o n c o n d i t io n w hich o ccu rs when

where and a re th e l o n g i t u d i n a l wave v e l o c i t y i n th e wedge and

th e s u r f a c e wave v e l o c i t y on the s u b s t r a t e , r e s p e c t i v e l y .

The p i e z o e l e c t r i c p l a t e t r a n s d u c e r s were 36° Y -cu t L i th ium

N io b a te (Warner, Onoe, and Coquin, 1967) bonded to th e wedges w ith

Phenyl S a l i c y l a t e . The wedges were th en coup led to th e s u b s t r a t e

w i th s i l i c o n h ig h vacuum g r e a s e . A p u ls e d ( 1 - 2 y s e c ) RF s i g n a l o f

30 MHz was a p p l ie d to th e p l a t e t r a n s d u c e r which e m its p la n e

l o n g i t u d i n a l waves to the w e d g e - s u b s t r a te i n t e r f a c e . At t h i s boundary

th e p la n e l o n g i t u d i n a l waves c r e a t e p e r i o d i c p e r t u r b a t i o n s w ith a

s p a t i a l p e r io d e q u a l to th e R ay le ig h w ave leng th in s i l i c o n . The p e r ­

t u r b a t i o n s e x c i t e s R ay le igh waves w hich p ro p a g a te s tow ards th e MOSFET.

The wedge method c o n v e r t s a p p ro x im a te ly 0 .1 p e r c e n t o f th e a v a i l a b l e

en e rg y to s u r f a c e wave en e rg y .

59

RF*

W2

DRAIN

RF*W1

GATE

SOURCE

SILICON BAR

* INPUT/OUTPUT

F ig . 5 .1 Wedge co u p l in g method used to m easure th e i n s e r t i o n lo s s o f MOSFET s u r f a c e wave d e t e c t o r

60

PLATE TRANSDUCER

WEDGE

F ig . 5 .2 Wedge cut to angle 6^ w ith mounted p la t e transducer

61

F ig u re 5 .3 shows an o v e r a l l b lo c k d iagram o f th e t e s t i n g

system . The d e t e c t i o n c i r c u i t r y in c lu d e s the n e c e s s a ry a t t e n u a t o r s

and a m p l i f i e r s to cover th e dynamic range o f the sy s tem which was

a p p ro x im a te ly 100 db. The o u tp u t r e f e r e n c e was o b ta in e d by n o t in g the

v o l t a g e l e v e l d i s p la y e d on th e o s c i l l o s c o p e when th e p u ls e d BF s i g n a l

was o p e r a t in g in th e a t t e n u a t o r . The i n s e r t i o n lo s s measurement was

perfo rm ed by m easuring th e n e t l o s s betw een: 1) tv and th e MOSFET;

2) and the MOSFET; and 3) and The RF was a p p l i e d to e i t h e r

o r # 2 and th e amount o f a t t e n u a t i o n needed to o b t a in th e r e f e r e n c e

v o l t a g e on th e o s c i l l o s c o p e was n o te d .

The n e t i n s e r t i o n lo s s o f the MOSFET and i t s e x t e r n a l c i r c u i t r y

can now be c a l c u l a t e d s in c e t h r e e measurements in t h r e e unknowns have

been made. I f the v a lu e s of a t t e n u a t i o n o b se rved betw een th e in p u t

and o u tp u t p o r t s a re ^ , and then

N1

W1 + MOSFET N2

W2 + MOSFET N3

The n e t i n s e r t i o n lo s s o f th e MOSFET y i e l d s ,

MOSFET I .E .N2 + N3 - H1

(5 .1 )2

The lo s s between and i s composed o f a c o u s t i c as w e l l as e l e c t r i c a l

mismatch l o s s . L ikew ise th e m easured lo s s o f the MOSFET was composed

62

MOSFET

SYNC

PULSE

RF PULSE GENERATOR

EXTERNALCIRCUITRY

OSCILLOSCOPE

30 MHz RECEIVER ATTENUATOR,

AND AMPLIFIER

F ig . 5 .3 Block d iagram o f e x p e r im e n ta l a r ran g em en t f o r i n s e r t i o n lo s s measurement o f a MOSFET s u r f a c e wave d e t e c t o r

63

of a c o u s t i c ( in v e r s io n l a y e r e f f i c i e n c y ) as w e l l as th e e l e c t r i c a l

(mismatch o f th e e q u i v a l e n t c i r c u i t to th e 50 f2 o u t p u t ) .

The e x t e r n a l c i r c u i t r y connec ted to th e MOSFET s u p p l i e s th e

n e c e s s a ry o p e r a t in g v o l t a g e s and p ro v id e s a p a th f o r th e d e t e c te d RF

o u tp u t s i g n a l . The c i r c u i t used to e v a l u a te th e MOSFET i n s e r t i o n

lo s s i s shown in F ig . 5 .4 . The c o u p l in g c a p a c i t o r s were 0 .1 p f which

r e p r e s e n t e d e f f e c t iv e , s h o r t s to th e RF s i g n a l . A load r e s i s t o r of

200 was s e l e c t e d . The i n s e r t i o n lo s s measurements were taken w ith

th e MOSFET o p e r a t in g in th e s a t u r a t i o n r e g io n w ith a d r a in c u r r e n t o f

20 ma. The RF o u tp u t was te rm in a te d w i th a 50 c o a x i a l system . The

g a te sup p ly and d r a in su p p ly w ere RF b ypassed w i th 0 .1 p f

c a p a c i t o r s .

The MOSFET i s a. h ig h impedance d ev ic e w i th v a r io u s p a r a c i t i c

c a p a c i t i v e e lem en ts (U. F i s c h e r , 1966). The e x t e r n a l c i r c u i t r y o f

F ig . 5 .4 i s in c lu d e d in a now e q u i v a l e n t c i r c u i t which i s shown in

F ig . 5 . 5 ( a ) . The e f f e c t s o f th e bypass and co u p l in g c a p a c i t o r s a re

r e p r e s e n t e d by s h o r te d c o n n e c t io n s . The m agnitude o f the c u r r e n t

g e n e r a to r , *ge n » was r e p r e s e n t e d by th e p e rc e n ta g e o f m odu la tio n

induced by th e a c o u s t i c s u r f a c e wave. This m odu la tion was r e l a t e d to

th e f req u en cy and power in th e a c o u s t i c wave by means o f th e PNGF.

The o u tp u t o f th e MOSFET was te rm in a te d in a low o u tp u t

impedance of 50 T his e f f e c t i v e l y s h o r t s o u t th e h ig h impedance

e lem en ts o f the MOSFET e q u i v a l e n t c i r c u i t and avo id s a co m p lica ted

s tu d y o f th e MOSFET e q u i v a l e n t c i r c u i t . The e q u i v a l e n t c i r c u i t

s i m p l i f i e s to the c i r c u i t o f F ig . 5 .5 (b ) u s in g th e e l e m e n ta l v a lu e s

64

O .ly f

200 ft

RF OUTPUTO .ly f

GG MOSFET

O .ly f

F ig . 5 .4 MOSFET c i r c u i t used f o r i n s e r t i o n lo s s measurements

DRAINGATE

LOAD/ OUTdsgs

gen

gs

(a) E q u iv a le n t c i r c u i t and e x t e r n a l c i r c u i t components

J-Opfgen

(b) S im p l i f i e d c i r c u i t u s in g e le m e n ta l v a lu e s

gen(39 . 8 - j 3 ) 0

(c) R e s u l t in g impedance as s een by c u r r e n t g e n e r a to r a t 30 MHz

F ig . 5 .5 C i r c u i t a n a l y s i s o f MOSFET s u r f a c e wave d e t e c t o r

66

g iven in C hap te r 4. Combining im pedances a t 30 MHz r e s u l t s in the

c i r c u i t o f F ig . 5 . 5 ( c ) . The lo ad impedance as s een by th e c u r r e n t

g e n e r a to r was (3 9 .8 - j 3 . 0)ft. To a good ap p ro x im a tio n t h i s impedance

can be c o n s id e re d as th e p a r a l l e l com bina tion o f Z (50 ft) and theo u t

lo a d r e s i s t o r Z^oad (200 ft) which g iv e s 40 ft. Thus th e e f f e c t s o f

th e MOSFET can be n e g l e c te d when d r iv i n g 50 ft a t 30 MHz.

The RF power g e n e ra te d i n th e i n v e r s i o n l a y e r was d i s s i p a t e d

in th e lo a d r e s i s t o r and th e e x t e r n a l d e t e c t o r . The t o t a l power

g e n e r a te d , p out;» was g iv e n by

Po u t ' 2 Re (A1 ) 2 ^ (5 .2 )

where was 37 .8 ft. The RF power a c t u a l l y m easured was t h a t p o r t i o n

o f th e t o t a l power which was d i s s i p a t e d i n th e 50 ft o u tp u t . In term s

o f th e g e n e ra te d c u r r e n t , i g e n » th e d e t e c te d RF power was

P . = i 2 7 . 1 Zloa<i ^d e t gen "out vZ +Z I . ( 5 .3 )X lo a d ou t /

A c o u s t i c a l l y , th e i n s e r t i o n lo s s o f the MOSFET depends upon

th e f req u en cy and power d e n s i ty ° f the a c o u s t i c wave. I f the

channe l w id th W was n o t f u l l y i l l u m i n a t e d by th e a c o u s t i c beam (W^^<W),

a g e o m e t r ic a l f a c t o r must be in c o r p o r a t e d i n t o the i n s e r t i o n lo s s

e x p r e s s io n . This was ta k e n i n t o acc o u n t by c o n s id e r in g t h a t f r a c t i o n

o f th e dc c u r r e n t b e in g m odulated as opposed to th e t o t a l dc c u r r e n tW

b e in g m odu la ted . The p o r t i o n o f the dc c u r r e n t m odu la ted was I (jc~ y “

where I ^ c was th e t o t a l dc c u r r e n t . The e x p re s s io n f o r th e i n s e r t i o n

67

lo s s was g iven by

I .L . = -10 log

= - 1 0 log

r p in»

o u t -

2 Wac

G2 P w p dc

(5 .4 )

where P ^ = I i s th e dc power d i s s i p a t e d in and W ^ i s the w id th

o f the a c o u s t i c beam. By in c lu d in g th e m o d i f i c a t io n s to Eq. 5 .4

th e i n s e r t i o n lo s s o f th e MOSFET was g iv en by

I .L . = -10 log 2 W W (^load ^ ^out)

l G2 wI2 Wac Z Z2i- p dc o u t load

2

(5 .5 )

The above e x p re s s io n was used f o r com parison o f the e x p e r im e n ta l and

t h e o r e t i c a l r e s u l t s .

E x p e r im en ta l R e s u l t s and D is c u s s io n o f R e s u l t s

The r e s u l t s of ap p ly in g th e p ro c e d u re s of the p re v io u s

s e c t i o n to th e MOSFET a re p r e s e n te d in t h i s s e c t i o n . The MOSFET

a r r a y was mounted on a g l a s s s l i d e so t h a t e x t e r n a l c o n n e c t io n s to

th e MOSFET could be made e a s i l y . The g l a s s s l i d e was then mounted on

a b r a s s b lo c k w ith th e mounted t r a n s d u c e r s as shown in F ig . 5 .6 .

S ince on ly one o r i e n t a t i o n was used th e measured i n s e r t i o n lo s s u s in g

the wedge te c h n iq u e c o n s i s t s o f th e av e ra g e i n s e r t i o n lo s s m easured

on s e v e r a l MOSFETs in the a r r a y . The o p e r a t in g f re q u e n c y was

68

Fig. 5 .6 Mounted MOSFET array on te s t f ix tu re

ap p ro x im a te ly 30 MHz and th e t e s t was perfo rm ed w i th I , = 30 ma indcth e s a t u r a t i o n r e g io n o f the MOSFET. F ig u re 5 .7 shows th e o u tp u t

o b ta in e d from the MOSFET.

The wedges used to g e n e r a te th e a c o u s t i c s u r f a c e wave had

an a p e r a tu r e (V o f 125 m i ls and were a l ig n e d as shown in F ig . 5 .1 .

The w av e fro n t was p a r a l l e l to th e a p p l i e d e l e c t r i c f i e l d in the

MOSFET. The e x p e r im e n ta l u n c e r t a i n t y in the m easurem ents of , N0 ,

and was t l . O db and was due to th e accu racy l i m i t a t i o n s o f the

equipm ent used .

The p ro p a g a t io n v e c to r was d e f in e d to be in th e 0^ d i r e c t i o n

and power flow in th e 0^ d i r e c t i o n . In g e n e ra l the w a v e fro n t o f the

a c o u s t i c wave was n o t p e r p e n d i c u la r to th e d i r e c t i o n o f power f low .

Thus a c o r r e c t i o n must be made. The r e s u l t was a beams t e e r i n g

c o r r e c t i o n shown in T ab le 5 .1 f o r o r i e n t a t i o n where 0 - 0 ^ 0 .P 8

E r r o r s w ere in t r o d u c e d i n t o th e measurement o f th e w ed g e- to -

wedge i n s e r t i o n l o s s , N . , due to th e b e a m s te e r in g e f f e c t . S ince the

power flow d i r e c t i o n 0 was n o t a long th e a x i s o f th e b a r , wedge W-

was n o t f u l l y i l l u m i n a t e d by the a c o u s t i c beam of wedge W^. The wedg

were s e p a r a t e d by a d i s t a n c e o f ap p ro x im a te ly 0 .5 in c h . The l a t e r a l

d isp la c e m e n t o f th e a c o u s t i c beam f o r t h i s d i s t a n c e was ap p ro x im ate ly

8 m i ls p e r d eg ree o f the a n g u la r d i f f e r e n c e 0^ - 6 ^ . In th e above

ex p e r im en t the wedges were a d ju s t e d l a t e r a l l y t 2 0 m i ls p roduc ing

ap p ro x im a te ly 2 .5* o f a n g u la r d i f f e r e n c e . The c o r r e c t e d i n s e r t i o n

lo s s i s shown in Tab le 5 .1 .

70

HORIZONTAL; 1 y s e c /d i v VERTICAL; 0 .1 v o l t / d i v

FEEDTHROUGH FROM OUTPUT OFINPUT RF PULSE MOSFET

F ig . 5 .7 Output o f the MOSFET

71

O r i e n t a t i o n

(110) 50*

TABLE 5 .1

E x p e r im e n ta l I n s e r t i o n L osses f o r HOSFET S u r fa c e Wave D e te c to r s

M easured B eam steering C o r re c te dI n s e r t i o n Loss C o r r e c t io n I n s e r t i o n Loss

- 6 5 .0 db + 1 .0 db - 6 4 .0 db

72

The e x p e r im e n ta l PNGF can be o b ta in e d from th e i n s e r t i o n lo s s

d a ta o f Table 5 .1 t o g e th e r w ith Eq. 5 . 5 . S ince in th e above ex p er im en t

0 = 0 , th e t h e o r e t i c a l PNGF used was o b ta in e d from C hap te r 3 f o r theP

case o f c o l i n e a r d e t e c t i o n . The d a t a o b ta in e d from th e t e s t c o n d i t io n s

w ere:

Zo u t = 50 Q

Id c= 30 ma

W = 90 m i ls

Wac= 125 m i ls

load= 2 0 0 a

f - 30 MHz

F ig u re 5 .8 shows th e e x p e r im e n ta l PNGF o b ta in e d and th e s o l i d l i n e

r e p r e s e n t s th e t h e o r e t i c a l PNGF.

C onc lus ion

In t h i s t h e s i s th e p -c h a n n e l MOSFET has been shown to be a

d e t e c t o r o f a c o u s t i c s u r f a c e waves on th e (110) p la n e of s i l i c o n . The

e f f i c i e n c y o f th e i n v e r s i o n l a y e r to d e t e c t s u r f a c e waves has been

c h a r a c t e r i z e d by the tw o -d im en s io n a l p i e z o r e s i s t a n c e t e n s o r combined

w ith th e s u r f a c e wave s o l u t i o n s to o b ta in a perfo rm ance in d e x , l a b e le d

power n o rm a l ize d gauge f a c t o r (PNGF).

The i n t e r a c t i o n o f th e s u r f a c e wave w ith th e i n v e r s i o n l a y e r

r e s u l t s in m o d u la tio n o f th e d r a in c u r r e n t . This i n t e r a c t i o n may be

modeled by an e q u i v a l e n t c i r c u i t w i th an RF g e n e r a to r c h a r a c t e r i z e d by

th e PNGF o f th e i n v e r s i o n l a y e r and amount o f the c u r r e n t b e in g

INSE

RTIO

N LO

SS

(db)

73

-70

—60

4 .0 5 .03.02 . 01 .5

= „ » ( W 1 /2

F ig . 5 .8 E x p e r im en ta l i n s e r t i o n lo s s v e rs u s t h e o r e t i c a l PNGF

74

m odulatedo Using such a model th e PNGF has been v e r i f i e d f o r th e (110)

p la n e s i l i c o n .

Improvements can be made to th e m odeling o f th e MOSFET such as

tu n in g th e o u tp u t to th e f req u en cy o f o p e r a t i o n . T h is w i l l r e s u l t i n

a low er MOSFET i n s e r t i o n lo s s which may be d e s i r a b l e f o r c e r t a i n

a p p l i c a t i o n s .

REFERENCES

A l l e n , M ild re d . "The E f f e c t o f T en s io n on th e E l e c t r i c a l R e s i s ta n c e o f S in g le Bismuth C r y s t a l s , " P h y s« R e v . , V ol. 42, 1932.

A uld , B e r t A. " A c o u s t ic F i e l d s and Waves i n . S o l i d s , " S ta n fo rd U n i v e r s i t y , i n p r e p a r a t i o n .

Bridgman, P . W. " E f f e c t o f T ens ion on th e R e s i s t a n c e o f M e ta l s ," P ro c .Am. Acad. A r ts and S c i . . V ol. 60 , 1925. •

B utchw ald, V. T, "R a y le ig h Waves i n T ra n s v e r s e ly I s o t r o p i c M ed ia ," Q u a r t . J . Mech. Appl^ M a th . . V ol. 14 , 1961.

Cam pbell, James J , and W ill iam R. J o n e s . "A Method f o r E s t im a t in gO ptim al C r y s t a l Cuts and P ro p a g a t io n D i r e c t io n s f o r E x c i t a t i o n o f P i e z o e l e c t r i c S u r fa c e W aves," IEEE T ra n s . S on ic and U l t r a s o n . . V ol. SU-15, No. 4 , O c to b e r 1968.

C la ib o rn e , Lewis T . , C. S. Hartmann, and W. S. J o n e s . "AnnualT e c h n ic a l R ep o r t f o r S u r fa c e Wave D e v ic e s : 15 Ja n u a ry 1969- 15 J an u a ry 197 0 ," Texas In s t ru m e n t s C o . , D a l l a s , T exas , ONR C o n tra c t N 00014-69-C -0173 , March 1970.

C la ib o rn e , Lewis T . , Edware J . S t a p l e s , J . L. H a r r i s , and J . P . M ize. "MOSFET U l t r a s o n i c Surface-W ave D e te c to r s f o r Programmable Matched F i l t e r s . " Appl. P hys . L e t t . . V ol. 19, No. 3, August 1971.

Cobbold, R ic h a rd S. Theory and A p p l ic a t i o n s o f F i e l d - E f f e c t T r a n s i s t o r s . New York; W i l e y - I n t e r s c i e n c e , 1970.

Colman, D . , R. T, B a te , and J , P . M ize. " M o b i l i ty A n is o tro p y andP i e z o r e s i s t a n c e i n S i l i c o n p-Type I n v e r s io n L a y e r s , " J . A ppl. P h y s . , V ol. 39$ March 1968.

Cookson, J . W. "Theory o f th e P i e z o r e s i s t i v e E f f e c t , " P hys . R e v . . V ol. 47, 1935.

F i s c h e r , W. " E q u iv a le n t C i r c u i t and G ain o f MOS F i e l d E f f e c tT r a n s i s t o r s , " S o l i d - S t a t e E l e c t r o n i c s . V ol. 9 , J a n u a ry 1966.

75

76

Frohman-Bentchkowsky, D. and Ao S, G rove« "C onductance o f MOST r a n s i s t o r s i n S a t u r a t i o n , " IEEE T r a n s . E l e c t r o n Dev»«, V ol. ED-16, No. 1 , J a n u a ry 1969.

G e y l in g , F. T. and J . J . F o r s t . "S em iconduc to r S t r a i n T r a n s d u c e r s , "Tech. J . , May I9 6 0 .

G rove, A. S. P h y s ic s and Technology o f Sem iconductor D e v ic e s .New York; John W iley and Sons, 1967.

H a v l i e e , J . F . , W. L. Bond, and L. B. W igton. " E l a s t i c P o y n tin g V ec to r i n P i e z o e l e c t r i c Medium," IEEE T ra n s . S on ics and U l t r a s o n . . V ol. SU-17, No. 4 , O c to b e r 1970.

K rau se , J . T . , C. R. K u r k j ia n , D. A. P innow, and E, A. S ig e t y . "LowA c o u s t ic Loss C ha lcogen ide G la s s e s - A New C atego ry o fM a te r i a l s f o r A c o u s t ic and A c o u s to -O p t ic A p p l i c a t i o n s ," Appl. Phvs . L e t t . . V ol. 17, No. 9 , November 1970.

Lim, T. C. and G. W. F a r n e l l . " C h a r a c t e r o f Pseudo S u r fa c e Waves onA n is o t r o p ic C r y s t a l s , " J . A cous t. Soc. Am., V ol. 45 , No. 41969.

Mason, Warren P . P h y s i c a l A c o u s t ic s and th e P r o p e r t i e s o f S o l id s . P r i n c e t o n , N. J . : D. Van N o s t ra n d , 1958.

R a y le ig h , L ord . "On Waves P ro p a g a te d Along th e P la n e S u r fa c e o f an E l a s t i c S o l i d , " P ro c . London M ath. S o c . « V ol. 17, November 1885.

R in d n e r , W., G. D o e r in g , and R. Wonson. " S t r u c t r a l and O p e r a t io n a l C h a r a c t e r i s t i c s o f P i e z o - T r a n s i s t o r s and A l l i e d D e v ic e s ," S o l i d - S t a t e E l e c t r o n i c s , V ol. 8 , March 1965.

Sah , C. T. " C h a r a c t e r i s t i c s o f th e M eta l -O x id e -S em ico n d u c to rT r a n s i s t o r s , " IEEE T ra n s . E l e c t r o n D e v . . V ol. ED-11, J u ly 1964.

S m ith , C h a r le s S. " P i e z o r e s i s t a n c e E f f e c t i n Germanium and S i l i c o n , "Phvs . R e v . , V ol. 94 , No. 1 , A p r i l 1954.

. "M acroscop ic Symmetry and P r o p e r t i e s o f C r y s t a l s , " i nl i e s . V ol. 6 , F . S e i t z and D. T u r n b u l l , E d s . ,

New York; Academic P r e s s , 1958.

S t a p l e s , Edward J . " D e te c t io n o f R a y le ig h S u rfa c e Waves on S i l i c o n With th e MOSFET," Ph. D. D i s s e r t a t i o n , S o u th e rn M e th o d is t U n i v e r s i t y , May 1971.

V ik to ro v , I g o r A le k s a n d ro v ic h . R ay le igh and Lamb Waves. New York: Plenum P r e s s , 1967.

Warner

W hite ,

A. W., M. Onoe, and G. A. Coquin. " D e te rm in a t io n o f E l a s t i c and P i e z o e l e c t r i c C o n s ta n ts f o r C r y s ta l s in C la ss (3m),"J . A cous t. Soc. Am., Vol. 42, No. 6 , 1967.

R ic h a rd M. " S u rfa c e E l a s t i c Wave P ro p a g a t io n and A m p l i f ic a t io n IEEE T ra n s . E l e c t r o n D e v . . Vol. ED-14, No. 4 , A p r i l 1967.

" S u r fa c e E l a s t i c Waves," P ro c . o f th e IEEE. Vol. 58, No. 8 , August 1970.

■