CHARGE CENTROID DETERMINATION IN FIELD-EFFECT EXPERIMENTS

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CHARGE CENTROID DETERMINATION IN FIELD-EFFECT EXPERIMENTS

S. Senturia, J. Rubinstein, S. Azoury, D. Adler

To cite this version:

S. Senturia, J. Rubinstein, S. Azoury, D. Adler. CHARGE CENTROID DETERMINATION IN

FIELD-EFFECT EXPERIMENTS. Journal de Physique Colloques, 1981, 42 (C4), pp.C4-503-C4-

506. �10.1051/jphyscol:19814107�. �jpa-00220722�

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CoZZoque C4, suppZ6ment au nO1O, Tome 42, octobre 1981 page C4-503

CHARGE CENTROID DETERMINATION IN FIELD-EFFECT EXPERIMENTS

S.D. S e n t u r i a , J. R u b i n s t e i n , S.J. Azoury and D. Adler

Depar-tment of EZectricaZ Engineering and Computer Science, and Center for MateriaZs Science and Engineering, Massachusetts I n s t i t u t e o f TeehmZogy, Cambridge, MA, 021 39, U . S. A.

Abstract.- T h i s paper p r e s e n t s a new method f o r making f i e l d - e f f e c t measurements i n low-conductivity m a t e r i a l s . The method complements c o n v e n t i o n a l f i e l d e f f e c t methods by p r o v i d i n g f o r t h e d e t e r m i n a t i o n o f t h e c h a r g e c e n t r o i d o f t h e f i e l d - i n d u c e d charge.

I n t r o d u c t i o n . - I n c o n v e n t i o n a l f i e l d - e f f e c t measurements, c o n t a c t s a r e a p p l i e d t o a sample, a b i a s is a p p l i e d between t h e c o n t a c t s , and a t r a n s v e r s e e l e c t r i c f i e l d i s a p p l i e d t o t h e sample through an i n s u l a t o r t o a c h i e v e modulation of t h e sample conductance. I n t e r p r e t a t i o n o f t h e f i e l d e f f e c t r e q u i r e s knowledge both o f t h e c a r r i e r m o b i l i t y and t h e s p a t i a l d i s t r i b u t i o n of t h e c h a r g e s induced i n t h e sample by t h e t r a n s v e r s e f i e l d . T h i s paper r e p o r t s a new method o f measurement t h a t complements t h e c o n v e n t i o n a l f i e l d e f f e c t by p r o v i d i n g independent measure- ment of t h e c e n t r o i d o f field-induced charge. The method can be used b o t h f o r s t a t i c and dynamic measurements; t h i s paper, however, i s concerned o n l y w i t h s t a t i c measurements.

The method i s based on t h e charge-flow t r a n s i s t o r (CFT), a d e v i c e i l l u s - t r a t e d i n Fig. 1. The CFT resembles a c o n v e n t i o n a l m e t a l - o x i d e s e m i c o n d u c t o r f i e l d - e f f e c t t r a n s i s t o r (MOSFET), e x c e p t t h a t a p o r t i o n o f t h e g a t e e l e c t r o d e i s r e p l a c e d by t h e sample m a t e r i a l ( l ) . E x t e n s i v e e x p e r i m e n t a l e x p e r i e n c e w i t h CFT1s both w i t h polymeric and c h a l c o g e n i d e g l a s s g a t e m a t e r i a l s h a s shown t h a t one can r e p r e s e n t t h e channel o f t h e CFT when o p e r a t e d i n t h e l i n e a r r e g i o n a s c o n s i s t i n g o f two p a r t s , t h e MOS r e g i o n o f t o t a l c h a n n e l l e n g t h L-W

,

f o r which t h e charac- t e r i s t i c s a r e i d e n t i c a l t o a s t a n d a r d MOSFET o f c o r r e s p o n d i n g dimensions, and t h e gap r e g i o n o f channel l e n g t h W, f o r which t h e c h a r a c t e r i s t i c s have t h e same a l g e b r a i c form a s t h e s t a n d a r d MOSFET, b u t w i t h d i f f e r e n t v a l u e s of t h r e s h o l d v o l t a g e and t r a n s c o n d u c t a n c e .

S p e c i f i c a l l y , w i t h r e f e r e n c e t o t h e e q u i v a l e n t c i r c u i t o f F i g . 2. t h e CFT can be modeled a s two FET1s i n s e r i e s , Q ~ ~ ~ w h i c h r e p r e s e n t s t h e metal-covered p o r t i o n o f t h e c h a n n e l , and QGAP, which r e p r e s e n t s t h e sample-covered p o r t i o n o f t h e channel. I f t h e gate-to-channel c a p a c i t a n c e p e r u n i t a r e a f o r QFET i s denoted by C i ( =

~ ~ d t , ,

^), and if t h e t h r e s h o l d v o l t a g e o f QFET is denoted by VT, t h e n fron, s t a n d a r d MOSFET t h r e o r y (2). t h e l i n e a r r e g i o n V-I c h a r a c t e r i s t i c .of QmT c a n be w r i t t e n a s f o l l o w s :

where Z i s t h e channel width,

u

t h e c a r r r i e r m o b i l i t y , VG t h e gate-to-source v o l t a g e , and where t h e parameter 11 d e s c r i b e s how t h e drain-to-source v o l t a g e VDD d i v i d e s between t h e two t r a n s i s t o r s . The c h a r a c t e r i s t i c f o r Q G A ~ h a s t h e same form a s Eq. 1 , b u t w i t h p a r a m e t e r s Cp r e p l a c i n g C i and V p r e p l a c i n g VT. and w i t h a p p r o p r i a t e c h a n n e l dimensions and d r a i n v o l t a g e . That i a . f o r QGM:

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19814107

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Fig. 1. CFT c r o s s s e c t i o n F i g . 2. CFT c i r c u i t model

Experimentally. 11 is determined by t a k i n g advantage o f t h e f a c t t h a t QFET and QG%

must always c a r r y t h e same c u r r e n t ID. One f a b r i c a t e s on t h e same s u b s t r a t e b o t a CFT and a n i n d e n t i c a l l y dimensioned MOSFET w i t h complete m e t a l g a t e . The MOSFET s e r v e s t o measure b o t h V T and U, s i n c e t h e channel dimensions and oxide t h i c k n e s s a r e known. By measuring I D vs. V G f o r t h e CFT f o r a s m a l l v a l u e of V D D

(100 mV is t y p i c a l ) , and by u s i n g t h e known v a l u e s o f VG, VT

,

^p, C i , L , Z , and W , one can e x t r a c t t h e v a l u e o f 17 from Eq. 1 , and can t h e n r e c a s t Eq. 2 i n t o t h e form

T h i s e q u a t i o n f o r ID/s v s VG i s l i n e a r , w i t h an i n t e r c e p t a t V p and a s l o p e from which t h e parameter Cp can be r e a d i l y determined. E x p e r i m e n t a l l y , it is always found t h a t Cp<Ci. and

lvpl

²

1 ~ ~ 1 .

Both r e s u l t s can be e x p l a i n e d by examining t h e s p a t i a l d i s t r i b u t i o n o f t h e f i e l d - i n d u c e d c h a r g e i n t h e sample m a t e r i a l , and can, i n t u r n . b e used a c t u a l l y t o measure t h e c e n t r o i d of t h e f i e l d - i n d u c e d charge.

Because t h e t h r e s h o l d v o l t a g e s VT and V p depend on a l a r g e number o f p r o c e s s r e l a t e d v a r i a b l e s such a s s u r f a c e - s t a t e d e n s i t i e s , it t u r n s o u t t h a t t h e capaci- tance-per-unit-area parameter i s t h e more r e l i a b l e s o u r c e o f i n f o r m a t i o n on t h e c h a r g e c e n t r o i d . The model f o r e x t r a c t i n g t h e charge c e n t r o i d from C p i s ex- p l a i n e d i n t h e f o l l o w i n g s e c t i o n .

Model f o r CD.- The sample m a t e r i a l i s assumed t o be c h a r a c t e r i z e d by a s c r e e n i n g l e n g t h LS determined by t h e d e n s i t y o f l o c a l i z e d s t a t e s n e a r t h e Fermi l e v e l . which is presumed t o be a t l e a s t weakly pinned n e a r midgap. T h i s s c r e e n i n g l e n g t h w i l l show up i n two p l a c e s : I f a S c h o t t k y b a r r i e r is formed a t t h e metal-sample c o n t a c t , t h e s p a c e c h a r g e a s s o c i a t e d w i t h t h e S c h o t t k y b a r r i e r w i l l e x t e n d i n t o t h e sample a d i s t a n c e o f s e v e r a l times Ls. S i m i l a r l y , f a r from t h e sample con- t a c t s , and assuming t h a t t h e sample t h i c k n e s s is g r e a t e r t h a n s e v e r a l s c r e e n i n g l e n g t h s , t h e f i e l d - i n d u c e d c h a r g e d e n s i t y i n t h e sample w i l l decay e x p o n e n t i a l l y from a maximum a t t h e sample-oxide i n t e r f a c e toward z e r o a t t h e upper s u r f a c e o f t h e sample w i t h a c h a r a c t e r i s t i c l e n g t h e q u a l t o LS. Thus, f o r a s u f f i c i e n t l y l a r g e gap width and a s u f f i c i e n t l y t h i c k sample, t h e d i s t r i b u t i o n o f f i e l d - - induced c h a r g e i n t h e sample i s e s s e n t i a l l y uniform a c r o s s t h e gap. and decays e x p o n e n t i a l l y from t h e o x i d e toward t h e upper s u r f a c e .

The s t r u c t u r e c o n s i s t i n g o f t h e gap m a t e r i a l , t h e g a t e o x i d e , and t h e semi- conductor s u r f a c e (which is presumed t o be i n s t r o n g i n v e r s i o n when t h e t r a n s i s - t o r i s c o n d u c t i n g ) forms a c a p a c i t o r w i t h a capacitance-per-unit-area t h a t is determined by t h e l o c a t i o n o f t h e charge c e n t r o i d i n t h e sample m a t e r i a l . I t is p l a u s i b l e t h a t t h i s capacitance-per-unit-area be i d e n t i f i e d a s t h e parameter Cp.

That is, i f X, i s t h e d i s t a n c e o f t h e charge c e n t r o i d above t h e sample-oxide i n t e r f a c e , and i f i s t h e sample p e r m i t t i v i t y , t h e n f o r a s u f f i c i e n t l y t h i c k sample,

We have c a r r i e d o u t a f u l l two-dimensional numerical s i m u l a t i o n o f t h e q u a s i - s t a t i c CFT c h a r a c t e r i s t i c s , and have v e r i f i e d t h a t t h i s i d e n t i f i c a t i o n o f Cp w i t h t h e c e n t r o i d i s v a l i d . F i g u r e 3 shows t h e c a l c u l a t e d r a t i o o f C p t o C i f o r two d i f f e r e n t oxide t h i c k n e s s e s , p l o t t e d a s f u n c t i o n s o f tp/LS, where t p is t h e sample t h i c k n e s s . It i s seen t h a t above a r a t i o o f 5 / L S = 2 , t h e Cp/Ci r a t i o i s c o n s t a n t , and, a l t h o u g h n o t shown e x p l i c i t l y i n t h e f l g u r e , a g r e e s w i t h t h e r e s u l t o f Eq. 3. Below tp/bS=2, however, t h e r e is a s h a r p d r o p i n Cp. i n d i c a t i n g t h a t t h e s i m p l e one-dimensional model f o r t h e f i e l d - i n d u c e d c h a r g e b r e a k s down.

The a c t u a l c e n t r o i d i n t h i s c a s e becomes c o n s t a n t a t h a l f t h e sample t h i c k n e s s , whereas t h e c e n t r o i d one would i n f e r from a n e x p e r i m e n t a l v a l u e o f Cp and t h e u s e o f Eq. 3 would a c t u a l l y f a l l above t h e sample m i d p o i n t , and could even f a l l out- s i d e t h e sample. T h i s f i c t i t i o u s r e s u l t , i n f a c t , p r o v i d e s a u s e f u l check on t h e v a l i d i t y o f t h e model. I f one f i n d s a c e n t r o i d from Eq. 3 above t h e midpoint o f t h e sample, one can assume t h a t t h e one dimensional model i s i n v a l i d . T h i s i s s u e h a s been d i s c u s s e d more e x t e n s i v e l y elsewhere ( 3 ) .

Experimental r e s u l t s . - We have c a r r i e d o u t experiments on a five-component chal- cogenide g l a s s , Te gAs36Ge7Si17P1. The d e v i c e s were p-channel enhancement mode, f a b r i c a t e d on (1009 s i l i c o n n-type s u b s t r a t e s doped 7E15 cm-3. The o v e r a l l chan- n e l dimensions were 254

urn

wide and 50.8 Pm long. Gap w i d t h s v a r i e d from 12.7 t o 38.1 Pm. Four d i f f e r e n t g a t e oxide t h i c k n e s s e s were used i n o r d e r t o

dependence o f Cp on oxide t h i c k n e s s . These were 950. 1370. 2040. and 22 d i f f e r e n t t h i c k n e s s e s o f chalcogenide g l a s s were used, 2100

I!

and 5200

d a t a were o b t a i n e d from 28 d e v i c e s w i t h 2100

1

g l a s s and from 6 d e v i c e s w i t h 5200

J1

g l a s s .

The v a l u e s o f Cp were e x t r a c t e d f o r e a c h d e v i c e a s i n d i c a t e d i n t h e I n t r o - d u c t i o n . No s i g n i f i c a n t v a r i a t i o n e i t h e r with gap w i d t h o r g l a s s t h i c k n e s s was observed. T h i s i s c o n s i s t e n t w i t h t h e assumption t h a t t h e g l a s s i s more t h a n two s c r e e n i n g l e n g t h s t h i c k and t h a t t h e gap w i d t h s a r e much l a r g e r t h a n t h e screen- i n g l e n g t h . There was, however, a s i g n i f i c a n t and s y s t e m a t i c v a r i a t i o n o f C p w i t h o x i d e t h i c k n e s s . I n o r d e r t o v e r i f y t h a t t h e v a r i a t i o n was o f t h e t y p e p r e d i c t e d i n Eq. 3 , it is u s e f u l t o r e c a s t t h a t e q u a t i o n i n t o t h e f o l l o w i n g form:

(Ci/CP)

-

^{l = c ~ ~ x ~ / E ~ ~ ~ (5) ~}

T h i s form shows t h a t a graph o f (Ci/Cp)

-

1 v e r s u s l/to, s h o u l d y i e l d a s t r a i g h t l i n e t h r o u g h t h e o r i g i n w i t h a s l o p e e q u a l t o . €

.

F i g u r e 4 shows t h e r e s u l t o f such a p l o t . w i t h o n l y t h e a v e r a g e s o f t h e O d ~ L E h r e a c h oxide t h i c k n e s s shown f o r c l a r i t y . The s l o p e o f t h e s o l i d l i n e c o r r e s p o n d s t o a v a l u e o f charge c e n t r o i d s c a l e d by t h e p e r m i t t i v i t y o f xC/cp = 119

*

⁴

1.

S i n c e t h e r e s u l t i s independent o f g l a s s f i l m t h i c k n e s s , we conclude t h a t t h e s c r e e n i n g l e n g t h must be l e s s t h a n h a l f o f 2100

1.

The p e r m i t t i v i t y o f a s i m i l a r g l g s s is r e p o r t e d t o be 8.8 ( 4 ) . Using t h i s v a l u e . we e s t i m a t e a c e n t r o i d o f 1047 A. which i s j u s t h a l f t h e 2100-1 f i l m t h i c k n e s s . and much l e s s t h a n t h e 5200-1 t h i c k n e s s , b o t h c a s e s b e i n g w i t h i n t h e range o f v a l i d i t y o f t h e charge-centroid model.

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F i g . 3. S i m u l a t i o n r e s u l t s F i g . 4 . Experimental, r e s u l t s

F o l l o w i n g t h e d e t e r m i n a t i o n o f t h e s t a t i c c e n t r o i d a s d e s c r i b e d above, a q u a l i t a t i v e e x p e r i m e n t on t h e e f f e c t o f l i g h t was performed. A f t e r measuring t h e Cp v a l u e i n t h e d a r k , t h e d e v i c e s were exposed t o a microscope l i g h t f o r s e v e r a l m i n u t e s , and t h e d e v i c e c h a r a c t e r i s t i c s were t h e n remeasured i n t h e d a r k . We found t h a t Cp i n c r e a s e d by a few p e r c e n t , c o r r e s p o n d i n g t o a s m a l l d e c r e a s e i n c e n t r o i d . T h i s r e s u l t c o r r e l a t e s w e l l w i t h t h e decay o f t h e f i e l d e f f e c t n o t e d by F r y e and A d l e r ( 5 ) .

Ackhow1edgements.- The a u t h o r s w i s h t o t h a n k Robert F r y e f o r h i s a s s i s t a n c e on t h e t e c h n i q u e s f o r d e p o s i t i n g t h e c h a l c o g e n i d e g l a s s f i l m s u s e d i n t h e e x p e r i - ments r e p o r t e d h e r e . The d e v i c e s were f a b r i c a t e d i n t h e M i c r o e l e c t r o n i c s Labora- t o r y o f t h e M.I.T. C e n t e r f o r M a t e r i a l s S c i e n c e and E n g i n e e r i n g , a f a c i l i t y sup- p o r t e d i n p a r t by t h e N a t i o n a l S c i e n c e Foundation under C o n t r a c t DMR-78-24185.

P r o j e c t s u p p o r t f o r t h i s r e s e a r c h came from t h e N a t i o n a l S c i e n c e Foundation under C o n t r a c t s DMR-78-24185 and ENG-7717219. One o f t h e a u t h o r s (J.R.) a l s o w i s h e s t o acknolwedge t h e s u p p o r t o f t h e Government o f Mexico t h r o u g h Consejo N a c i o n a l De C i e n c i a Y Technologia (CONACYT).

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(1977) 106.

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3. SENTURIA S., RUBINSTEIN J . , AZOURY S.. and ADLER D.. J. Appl. Phys., J u n e 1981. i n p r e s s .

4. RADJY N. and GREEN M.. P h i 1 Mag.

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5 . FRYE R. and ADLER D., Phys. Rev. L e t t e r s M (1981) 1027.