THE v-E RELATION AND THE FIELD DISTRIBUTION IN SUBMICRON MOSFET'S

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THE v-E RELATION AND THE FIELD DISTRIBUTION IN SUBMICRON MOSFET’S

J. Leburton, G. Dorda

To cite this version:

J. Leburton, G. Dorda. THE v-E RELATION AND THE FIELD DISTRIBUTION IN SUBMICRON MOSFET’S. Journal de Physique Colloques, 1981, 42 (C7), pp.C7-193-C7-200.

�10.1051/jphyscol:1981722�. �jpa-00221659�

THE v-E RELATION AND THE FIELD DISTRIBUTION IN SUBMICRON MOSFET'S

J.P. Leburton and G. Dorda

Siemens AG., Research Laboratories, Munich, FRG

Abstract. - A new model for the description of the I-U characteristics in submicron MOSFET's is reviewed. It is shown that the familiar

"pinch-off" concept which does not hold anymore in such small struc- ture, can be replaced by a field relation factor f = Ey/Ex. On the basis of this model it is demonstrated that the intensity of the late- ral electric field at the source side plays a determinant role in the transport properties of MOS transistors. A new v-E relation is propo- sed which is a surface modification of Scharfetter-Gummel's formula and which takes into account the pronounced role of warm electrons.

In this latter regime, the remote interface polar phonon scattering in the Si-inversion layers is considered and the contribution of this relaxation mechanism to the warm electron mobility reduction is dis- cussed.

1. Introduction. - In the past the understanding of operating mode of MOS field effect transistors was essentially explained by Shockley's model which introduced the "pinch off" concept / l / . The T a t t e r is de- fined as the channel point where the gate induced charge vanishes.

This condition is realised when the drain voltage U

- is equal to the effective gate voltage UVy. In this framework the zone defined bet- ween the source and the "pinch off" is described by the "gradual chan- nel approximation" ( G . C . A . ) . This approximation neglects the lateral variation of the electrical potential 3 U / 3 x in the two-dimensional (2-D) Poisson equation. Within this a s s u m p t i o n , the mobile carrier concentration changes linearly with the potential drop u ( x ) along the channel from the source to the drain (see Fig. 1 ) , i.e.

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Colloque C7, supplément au n°10, Tome 42, octobre 1981 page C7-193

Résumé. - Un nouveau modèle qui décrit les caractéristiques I-U dans les nûSFET's de dimensions submicroniques, est revu. Il est montre' que le concept familier de "pinch off" q u i ,

dans ces petites struc- tures n'est plus v a l a b l e , peut être remplace' par un facteur de rap- port de champs .f = Ey/Ex. Sur la base de

ce m o d è l e , il est démontré que l'intensité' du champ e'iectrique late'ral à la source joue un rôle déterminant dansles propriétés de transport des transistors M O S . Une nouvelle relation v-E est proposée qui est une modification de la formule de Scharfetter-Gummel adaptée aux conditions de s u r f a c e , et qui prend en considération le rôle prononcé des électrons tièdes.

Dans ce régime, la diffusion des électrons de la couche d'inversion du silicium par les phonons polaires interfaciaux lointains est con- sidérée et la contribution de ce mécanisme de relaxation à la mobi- lité des électrons tièdes est discutée.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981722

JOURNAL DE PHYSIQUE

n ( X I

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Y Y

t e r a l e l e c t r i c f i e l d , r e s p e c t i v e l y . T h e h o t e l e c t r o n e f f e c t s a r e t a -

k e n i n t o a c c o u n t u s i n g a m o d i f i e d S c h a r f e t t e r - G u m m e l ' s v - E r e l a t i o n

/ 7 / a d a p t e d t o s u r f a c e c o n d i t i o n s . F u r t h e r i t i s d e m o n s t r a t e d t h a t

o n l y t h i s e m p i r i c a l r e l a t i o n i s v a l i d f o r t h e d e s c r i p t i o n o f t h e I-u

c h a r a c t e r i s t i c s a n d t h a t t h e i n t e n s i t y o f t h e l a t e r a l e l e c t r i c f i e l d

a t t h e s o u r c e p l a y s a d o m i n a n t r o l e i n t h e t r a n s p o r t p r o p e r t i e s o f

M O S - t r a n s i s t o r s / 6 / . I n t h i s p a p e r t h e a n a l y t i c a l m o d e l f o r t h e h o t

e l e c t r o n t r a n s p o r t i n s m a l l s i z e MOSFET's i s s h o r t l y p r e s e n t e d . M o r e -

o v e r a d e r i v a t i o n o f t h e l a t e r a l e l e c t r i c f i e l d p r o f i l e s a t t h e s o u r -

c e s i s g i v e n a n d c o m m e n t s o n t h e v a l i d i t y o f S c h a r f e t t e r - G u m m e l - 1 i k e

f o r m u l a a r e m a d e . T h e e f f e c t o f t h e r e m o t e p o l a r i n t e r f a c e p h o n o n

( R . I . P . ) modes o n t h e v - E r e l a t i o n i s a l s o d i s c u s s e d .

2. A n a l y t i c a l m o d e l f o r s u b m i c r o n MOSFET's. - I n a r e c e n t p a p e r / 5 / we d e v e l o p e d an a n a l y t i c a l m o d e l f o r t h e c u r r e n t i n s h o r t c h a n n e l t r a n s i s t o r s ( L e f f

l / u m ) . T h i s t h e o r e t i c a l a n a l y s i s i s p r o v i d e d 1 - D a n d t h e g o o d a g r e e m e n t w i t h e x p e r i m e n t s a n d w i t h 2-D n u m e r i c a l c a l c u l a t i o n s p r o v e s t h a t t h i s a p p r o a c h d e s c r i b e s t h e c u r r e n t t r a n s - p o r t i n s m a l l s i z e t r a n s i s t o r s i n a r e a l i s t i c way. I n t h i s model t h e c h a n n e l i s d e v i d e d i n t o t w o p a r t s ( F i g . 1 ) . N e a r t h e s o u r c e t h e G.C.A.

h o l d s b e c a u s e t h e l a t e r a l f i e l d Ex a n d i t s x - v a r i a t i o n a E x / a x

( P o i s s o n e q u . ) a r e much s m a l l e r t h a n t h e t r a n s v e r s a l f i e l d Ey a n d i t s y - v a r i a t i o n a E y / 3 y . r e s p e c t i v e l y . On t h e o t h e r h a n d , n e a r t h e d r a i n t h e e l e c t r o n v e l o c i t y i s c l o s e t o i t s s a t u r a t i o n v a l u e a n d t h e G.C.A.

f a i l s . I n t h i s s e c o n d r e g i o n a p a r a b o l i c d i s t r i b u t i o n i s u s e d t o d e s - c r i b e a p p r o x i m a t i v e l y t h e p o t e n t i a l p r o f i l e s . A c h a r a c t e r i s t i c r a t i o b e t w e e n t h e l a t e r a l f i e l d a n d t h e t r a n s v e r s a l f i e l d i s d e f i n e d

E , c L E

s 7 ^{( 2 )}

w h e r e f i s a c o n s t a n t f a c t o r . T h i s l a s t r e l a t i o n d e t e r m i n e s t h e b o u n d a r y b e t w e e n b o t h r e g i o n s i n d e p e n d e n c e o f t h e d i f f e r e n t p h y s i c a l p a r a m e t e r s UGT, UDS, L e f f , ( e f f e c t i v e c h a n n e l l e n g t h ) , W e f f ( e f f e c - t i v e c h a n n e l w i d t h ) , e t c . . .. A t y p i c a l v a l u e o f t h e f - f a c t o r h a s b e e n f o u n d t o b e f = 5.

On t h i s b a s i s , t h r e e d i f f e r e n t v - E r e l a t i o n s a r e c o n s i d e r e d ( F i g . 2 ) : The h y p e r b o l i c r e l a t i o n ( c u r v e a ) , t h e s o - c a l l e d s q u a r e r o o t r e l a t i o n

( c u r v e b ) a n d a m o d i f i e d S c h a r f e t t e r - G u m m e l e x p r e s s i o n / 5 - 6 1

H = H, ( 3 t e, U,, ) ( 3 b )

H e r e t h e e f f e c t i v e m o b i l i t y / u e f f i s d e t e r m i n e d b y m e a s u r e m e n t s a n d

r e l a t e s t h e s a t u r a t i o n v e l o c i t y v s t o t h e c r i t i c a l f i e l d Ec w i t h

v s = / u e f f E c w h e r e v S = 1 0 m/s e q u a l s t h e b u l k v a l u e . Ho i s a c o n - 7

s t a n t w e a k l y d e p e n d e n t o n ,ueff a n d i t s v a l u e i s a p p r o x i m a t i v e l y 0 . 1 5 .

The e m p i r i c a l p a r a m e t e r 19, i s f i t t e d w i t h t h e e x p e r i m e n t a l I - U c h a -

r a c t e r i s t i c s a n d i t s v a l u e i s e s t i m a t e d t o b e 0 . 3 5 / V .

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F i g . 2: T h r e e d i f f e r e n t n o r m a l i- F i g . 3 : I - U c h a r a c t e r i s t i c s f o r a z e d v - E d e p e n d e n c e s a c c o r d i n g MOSFET w i t h a c h a n n e l l e n g t h t o a ) t h e h y p e r b o l i c r e l a t i o n ; L - 0 . 6 6 um: s o l i d l i n e - c a l - b ) t h e s q u a r e r o o t r e l a t i o n ; c g f i t e d f r o k E q u . ( 3 a ) a n d ( 3 b ) ; c ) Equ. ( 3 ) . v i s t h e s a t u r a - - - - f r o m Equ ( 3 a ) w i t h 8,= 0 ; t i o n v e l o c i t y S a n d Ec t h e c r i t i - , . - f r o m t h e h y p e r b o l i c r e l a -

c a l f i e l d t i o n ; .... f r o m t h e s q u a r e r o o t

r e l a t i o n ; A e x p e r i m e n t a l d a t a . U G S i s t h e g a t e v o l t a g e ,

UT i s 0 . 1 V

The c h o i s e o f o n e o f t h e t h r e e v-E r e l a t i o n s m e n t i o n e d a b o v e h a s i m - p o r t a n t c o n s e q u e n c e s on t h e I - U c h a r a c t e r i s t i c s o f s h o r t c h a n n e l MOS- F E T ' s . To d i s t i n g i s h t h e e f f e c t o f t h e s e r e l a t i o n s o n t h e s l o p e o f t h e I - U c h a r a c t e r i s t i c s , t h e o r e t i c a l r e s u l t s a n d e x p e r i m e n t a l d a t a f o r a MOSFET w i t h a c h a n n e l l e n g t h o f 0.66,um a r e p r e s e n t e d o n F i g . 3 . The u s e d t r a n s i s t o r h a d an o x i d e t h i c k n e s s to, o f 25 nm, t h e c h a n n e l

16 3

w i d t h was 25,um, t h e c h a n n e l a c c e p t o r c o n c e n t r a t i o n was 1 . 5 ~ 1 0 /cm

I

2

a n d t h e e f f e c t i v e m o b i l i t y ,ueff i n t h e c h a n n e l was 590 cm / V . s . As c a n b e s e e n , t h e s q u a r e r o o t e x p r e s s i o n o v e r e s t i m a t e s t h e e x p e r i m e n - t a l d a t a b y a b o u t 1 5 - 2 0 % , w h e r e a s t h e h y p e r b o l i c r e l a t i o n g i v e s a n u n d e r e s t i m a t i o n o f a b o u t 1 5 % . The b e s t a g r e e m e n t i s o b t a i n e d w i t h Equ. 3, w h e r e t h e B,, - p a r a m e t e r h a s b e e n i n t r o d u c e d . The s l i g h t d i s c r e - p a n c y a t h i g h d r a i n v o l t a g e s i s due t o a n i n a c c u r a c y i n t h e e x p e r i m e n - t a l d e t e r m i n a t i o n o f t h e t h r e s h o l d v o l t a g e d e p e n d e n c e on t h e d r a i n vo 1 ta g e .

3 . L a t e r a l f i e l d p r o f i l e a t t h e s o u r c e . - E x c l u d i n g c h a r g e g e n e r a t i o n

a n d r e c o m b i n a t i o n p r o c e s s e s t h e c h a n n e l c u r r e n t i s o b t a i n e d b y s o l -

v i n g t h e c o n t i n u i t y e q u a t i o n , w h i c h f o r s t e a d y s t a t e y i e l d s t h e u s e -

f u l r e l a t i o n

$3 = en,,, b ^{vfiune ( 4 )}

W h e r e n s o u r c e i s t h e f r e e s u r f a c e c h a r g e c o n c e n t r a t i o n , a n d v s o u r c e i s t h e c a r r i e r v e l o c i t y a t t h e s o u r c e . I n t h e G.C.A. t h e c h a r g e d e n -

Si ty e n s o u r c e h a s t h e f o l l o w i n g e x p r e s s i o n

en,,,,, = & ^{( 5 )}

w h e r e e,, - .. i s t h e o x i d e d i e l e c t r i c c a p a c i t y . I n t h i s f r a m e w o r k t h e d r a i n c u r r e n t , e v e n i n p r e s e n c e o f h o t e l e c t r o n s , i s d e f i n i t e l y d e - t e r m i n e d b y t h e c a r r i e r v e l o c i t y a t t h e s o u r c e / 8 / . I n o t h e r w o r d s , t h e m a g n i t u d e o f t h e c h a n n e l c u r r e n t i s a f u n c t i o n o f t h e f i e l d p r o - f i l e a t t h e s o u r c e . We h a v e c a l c u l a t e d t h e l a t e r a l f i e l d p r o f i l e a t t h e s o u r c e i n d e p e n d e n c e o n t h e a p p l i e d d r a i n v o l t a g e f o r MOSFET's w i t h t h r e e d i f f e r e n t e f f e c t i v e c h a n n e l l e n g t h s L e f f = 0 . 6 6 um, 2 . 1 6 um

/ /

a n d 4 . 6 6 / u m ( F i g . 4 ) . As c a n b e e x p e c t e d f r o m t h e s c a l i n g l a w s , t h e

s o u r c e f i e l d p r o f i l e d e p e n d s s t r o n g l y o n t h e c h a n n e l l e n g t h s w i t h a

v a r i a t i o n o f n e a r l y o n e o r d e r o f m a g n i t u d e f o r t h e s e l e c t e d l e n g t h s .

M o r e o v e r i t c a n b e s e e n t h a t t h e l a t e r a l f i e l d p r o f i l e a t t h e s o u r c e

d e p e n d s s t r o n g l y o n t h e g a t e v o l t a g e . I n g e n e r a l , t h e c u r v e s p r e s e n t

a q u a s i - s a t u r a t i o n f o r h i g h d r a i n v o l t a g e s a n d we c o u l d p o i n t o u t

t h a t t h e c u r r e n t s a t u r a t i o n i n t h e I - V c h a r a c t e r i s t i c s d o e s n o t a r i s e

f r o m t h e s a t u r a t i o n o f t h e c a r r i e r v e l o c i t y , b u t f r o m t h e s a t u r a t i o n

o f t h e f i e l d a t t h e s o u r c e . I n d e e d f o r a c r i t i c a l f i e l d Ec 2 x 1 0 V/cm, 4

t h e s a t u r a t i o n o f t h e f i e l d a t t h e s o u r c e o c c u r s f o r f i e l d v a l u e s

s m a l l e r t h a n o r e q u a l t o t h e c r i t i c a l f i e l d , i . e . w h e n t h e v e l o c i t y v

a t t h e s o u r c e i s s t i l l n o t s a t u r a t e d . A s p o i n t e d o u t o n F i g . 2, t h e

d i f f e r e n c e b e t w e e n t h e t h r e e v - E r e l a t i o n s i s m o s t l y p r o n o u n c e d i n t h e

r e g i o n o f t h e c r i t i c a l f i e l d Ec. I n t h e l o w f i e l d r e g i o n ( E S , < E c / l O )

t h e s e r e l a t i o n s a r e a l m o s t i d e n t i c a l d u e t o t h e same e f f e c t i v e m o b i l i -

ty, w h e r e a s a t h i g h f i e l d ( E s > 1 0 E c ) t h e i d e n t i t y i s c a u s e d b y t h e s a -

t u r a t i o n v e l o c i t y . C o n s e q u e n t l y f o r s h o r t c h a n n e l t r a n s i s t o r s ( L e f f \ < l / u )

t h e source l a t e r a l f i e 1 d r e a c h e s t h e c r i t i c a l f i e l d a n d t h u s t h e c h o i c e

o f a c o r r e c t v - E r e l a t i o n b e c o m e s v e r y i m p o r t a n t f o r t h e t r a n s p o r t i n

t h e i n v e r s i o n l a y e r s . T h e p r e s e n c e o f t h e t e r m 2 H E / E c i n E q u . 3 d e s -

c r i b i n g t h e b e h a v i o u r o f v i n t h e t r a n s i t i o n r e g i o n b e t w e e n t h e o h m i c

r e g i m e a n d t h e r e g i m e o f s a t u r a t i o n v e l o c i t y e x p r e s s e s t h e r o l e o f

w a r m e l e c t r o n s i n t h e c r i t i c a l f i e l d r e g i o n . We s u p p o s e t h a t t h i s t e r m

a c c o u n t s f o r n o n - l i n e a r e n e r g e t i c p r o c e s s e s , i . e . f o r t h e p h o n o n d i s -

s i p a t i o n s a t t h e S i - S i 0 2 i n t e r f a c e . T h u s t h i s f a c t o r a l l o w s u s t o c o n -

s i d e r t h e r o l e o f a d d i t i o n a l s u r f a c e p h o n o n m o d e s / 9 - l O / , w h i c h a r e a b l e

t o c h a n g e t h e c u r v a t u r e o f t h e v - E r e l a t i o n w i t h o u t m o d i f y i n g t h e

v a l u e o f t h e s a t u r a t i o n v e l o c i t y . T h e n , we c a n e x p e c t t h a t t h e s e m o -

JOURNAL DE PHYSIQUE

F i g . 4 : L a t e r a l e l e c t r i c f i e l d p r o f i l e s E a t t h e s o u r c e a s a f u n c $ i o n o f t h e d r a i n v o l t a g e f o r t h r e e d i f f e r e n t g a t e v o l t a g e s U = 1, 3 a n d 5 V a n d f o r t f i ? e e d i f f e r e n t e f f e c t i v e l e n g t h s L e f f = 0 . 6 6 , 2 . 1 6 a n d 4.66,um

d e s i n f l u e n c e t h e s l o p e o f t h e I - U c h a r a c t e r i s t i c s . T h i s e f f e c t ,

e x p r e s s e d w i t h t h e h e l p o f t h e @ # - f a c t o r , d e s c r i b e s t h e d e p e n d e n c e

o f t h e s u r f a c e p h o n o n r s : a x a t i o n m e c h a n i s m s on t h e i n v e r s i o n l a y e r

d e p t h , i e . t h e r e l a t i o n b e t w e e n H i n Equ. 3b a n d t h e e f f e c t i v e g a t e

v o l t a g e UGT A p o s s i b l e r e l a x a t i o n m e c h a n i s m c a n b e t h e R . I . P . s c a t -

t e r i n g / l o / . R e c e n t l y M o o r e a n d F e r r y /11/ h a v e i n v e s t i g a t e d t h e e f -

f e c t o f s u c h a r e l a x a t i o n m e c h a n i s m o n t h e t r a n s p o r t i n i n v e r s i o n

l a y e r s . T h e y f o u n d a s m a l l e f f e c t c o m p a r e d t o t h e s u r f a c e r o u g h n e s s

s c a t t e r i n g . We h a v e c a l c u l a t e d i n a s i m p l e way / 1 2 / t h e i n f l u e n c e o f

R . I . P . s c a t t e r i n g on t h e c a r r i e r d r i f t v e l o c i t y f r o m Equ. 3a, u s i n g

P a l s ' s e x p e r i m e n t a l d a t a f o r t h e mean d i s t a n c e d o f t h e i n v e r s i o n l a -

y e r / 1 3 / a n d u s u a l d a t a o f t h e e l e c t r o n i c t e m p e r a t u r e i n f u n c t i o n o f

t h e e l e c t r i c f i e l d / 1 4 / . On F i g . 5 t h e r e l a t i v e c h a n g e o f t h e d r i f t

v e l o c i t y i s p l o t t e d a s a f u n c t i o n o f t h e l a t e r a l e l e c t r i c f i e l d f o r

t w o d i f f e r e n t e l e c t r o n s u r f a c e d e n s i t i e s a n d f o r d i f f e r e n t e f f e c t i v e

m o b i l i t i e s . As e x p e c t e d t h e l a r g e r t h e c o n c e n t r a t i o n t h e l a r g e r t h e

e f f e c t o f t h e R . I . P . s c a t t e r i n g b e c a u s e o f t h e s h o r t e r o v e r a g e d i s t a n -

c e d. A maximum o c c u r s a n d c a n b e e x p l a i n e d a s f o l l o w s : A t l o w e l e c -

t r i c f i e l d ( ~ ~ < 1 0 ~ ~ / c m ) t h e R. I . P . s c a t t e r i n g i n c r e a s e s w i t h t h e

f i e l d b e c a u s e m o r e e l e c t r o n s h a v e s u f f i c i e n t e n e r g y t o e m i t o n e R . I . P .

f o r h i g h f i e l d , t h e e f f e c t o f t h e b u l k o p t i c a l p h o n o n s i n S i becomes

F i g . 5 : R e l a t i v e c h a n g e i n t h e d r i f t v e l o c i t y v e r s u s t h e e l e c t r i c f i e l d f o r d i f - f e r e n t e f f e c t i v e m o b i l i t i e s :

-. . - , / U e f f = 9 3 0 c m ; / ~ . s ;

- - . / u T f f = 5 6 0 cm / V . S ; ~ s o l i d 1 n e , = 2 4 7 0 c m / V s

- . ^-, l U e f f = / : 5 6 ^cm / v . s ; a ) n s = l o 1 3 / c m 2 a n d 6 - 2 7 8 ,

1 2

b ) n s = 5 1 0 /cm2 a n d d - 3 3 R

p r e d o m i n a n t a n d t h e e f f e c t i v n e s s o f t h e R . I . P . s c a t t e r i n g d e c r e a s e s . T h e i n f l u e n c e o f / u e f f o n t h e c o n t r i b u t i o n o f t h e R . I . P . s c a t t e r i n g i s a l s o s h o w n . A t l o w f i e l d t h e r e l a t i v e p a r t o f t h e R . I . P . t o t h e t o t a l r e l a x a t i o n p r o c e s s i n c r e a s e s w i t h t h e m o b i l i t y b e c a u s e t h e e l e c - t r o n s b e c o m e f a s t e r h o t a n d a r e t h u s e a r l i e r a b l e t o e m i t o n e i n t e r - f a c i a l p h o n o n . H o w e v e r , t h i s s i t u a t i o n i s a l s o f a v o r a b l e f o r t h e o n - s e t o f S i - o p t i c a l p h o n o n s w h i c h l e a d s t o t h e s a t u r a t i o n v e l o c i t y . T h e r e f o r e w i t h E x > E c , t h e c o n t r i b u t i o n o f t h e R . I . P . s c a t t e r i n g i s e a r l i e r r e d u c e d a n d t h e l o w m o b i l i t y c u r v e s c r o s s t h e h i g h m o b i l i t y p r o f i l e s . T h e r e s u l t s a r e i n g o o d a g r e e m e n t w i t h t h e c a l c u l a t i o n s p r o v i d e d b y M o o r e a n d F e r r y , i f t h e m o b i l i t y / u e f f 4 3 5 0 cm / V . s . 2

C o n s i d e r i n g t h a t t h e R. I .P. s c a t t e r i n g i s m o s t l y p r o n o u n c e d f o r f i e l d

3 4

r a n g e s b e t w e e n 5x10 V / c m a n d 2x10 V / c m i . e . i n t h e w a r m e l e c t r o n r e - g i m e , we c a n s u p p o s e t h a t t h i s R . I . P . e f f e c t i s r e l a t e d t o t h e e , - f a c - t o r ( E q u . 3b), w h i c h s h o w s t h e same b e h a v i o u r i n t h e same f i e l d r a n g e a n d w h i c h c o n t r i b u t e s t o t h e v - E r e l a t i o n s w i t h t h e same o r d e r o f mag- n i tu d e .

4. Conclusions. - I n submicron MOSFET1s t h e f a m i l i a r " p i n c h o f f " c o n c e p t f a i l s due t o a d i f f e r e n t p h y s i c a l s i t u a t i o n caused by t h e h o t e l e c t r o n regime. Thus a new concept f o r t h e d e s c r i p t i o n o f t h e I - U c h a r a c t e r i s t i c s i s f o r m u l a t e d based on t h e f a c t o r f = Ey/Ex which devides t h e t r a n s i s t o r channel i n t o a G.C.A. r e g i o n and a

" s a t u r a t i o n v e l o c i t y " r e g i o n . The a n a l y s i s o f t h e o b t a i n e d I - U c h a r a c t e r i s t i c s and

C7-200 JOURNAL DE PHYSlQUE

t h e comparaison w i t h e x p e r i m e n t a l d a t a shows t h a t t h e s e l e c t i o n o f an a c c u r a t e v-E r e l a t i o n f o r t h e d e s c r i p t i o n o f t r a n s p o r t p r o p e r t i e s i s i m p o r t a n t . On t h e b a s i s o f o u r a n a l y t i c a l model t h e s i g n i f i c a n c y o f t h e f i e l d d i s t r i b u t i o n a t t h e source o f MOS devices has been elucidated,which demonstrates t h a t t h e c u r r e n t s a t u r a t i o n i s caused by t h e l a t e r a l f i e l d s a t u r a t i o n and n o t by t h e v e l o c i t y s a t u r a t i o n . Thus i t can be concluded t h a t t h e t r a n s p o r t p r o p e r t i e s and p a r t i c u l a r l y t h e r o l e o f t h e d i f f e r e n t s c a t t e r i n g mechanisms f o r MOSFET's i n steady s t a t e , i s m a i n l y determined a t t h e source. I n t h i s framework, t h e R.I.P. r e l a x a t i o n mechanism has been taken i n t o account and i t s c o n t r i b u t i o n t o t h e warm e l e c t r o n regime seems t o be 5-10%

depending on /ueff and nS.

Acknowled ements:- The a u t h o r s a r e v e r y i n d e b t e d t o Dr. H. Gesch f o r making a v a i - l a b l e e x p z r i m e n t a l I-U d a t a and would express thank t o Miss R. S c h r e i t e r f o r programming a s s i s t a n c e .

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/4/ S-R H o f s t e i n and G. W a r f i e l d : IEEE Trans. E l e c t r . Devices E, 129 (1965) /5/ J.P.Leburton, H. Gesch and G. Dorda: S o l i d S t a t e E l e c t r . i n p r e s s

/6/ J.P.Leburton and G. Dorda: t o be p u b l i s h e d

/7/ D.L. S c h a r f e t t e r and K.L. Gummel: IEEE Trans. E l e c t r . Devices ED-16, 64 (1969)

/8/ W. M i l l e r and I. E i s e l e : S o l i d S t a m r n m . 34. 447 (1980) /9/ H. Ezawa: S u r f . S c i 58, 25 (1976)

/ l o / K. Hess and P. Vogl: S o l i d S t a t e Comm. 30, 807 (1979) /11/ B.T. Moore and D.K. F e r r y : J . Appl . ^Phys. 51, 2603 (1980)

J . Vac. S c i . Technol. 2, 1037 (1980) /12/ The R.I.P. e f f e c t upon t h e e l e c t r o n d r i f t v e l o c i t y i s c a l c u l a t e d by a

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