296 Physica 129B ( 1985 ) 296-300 North-Holland, Amsterdam

SIMULATION OF DEEP DEPLETED SOl MOSFETS WITH BACK POTENTIAL CONTROL

Franc is BALESTRA, Jean BRINI and Pierre GENTIL

Labo ra to i r e de Phys ique des Composan ts ~ S e m i c o n d u c t e u r s , E R A - C N R S 659, ENSERG, 23 rue des Mar t y r s , 3 8 0 3 1 Grenoble Cedex, France

We c o n s i d e r SOl M O S F E T s t r u c t u r e s of N and P types fo r wh ich a c o n t r o l o f the b a c k p o t e n t i a l o f the ep i l a y e r is o b t a i n e d by u s i n g a b a c k g a t e . The a c t i o n o f the i n t e r f a c e p a r a m e t e r s on the b a c k a n d f r o n t t h r e s h o l d v o l t a g e s is a n a l y s e d in the c a s e o f a s t r o n g c o u p l i n g b e t w e e n the f r o n t a n d b a c k i n t e r f a c e ( l igh t ly doped epl l aye r ) . This ana lys is is c a r r i e d out by a n u m e r i c a l s i m u l a t i o n of Po isson 's equa t i on t h r o u g h o u t the s t r u c t u r e . We thus o b t a i n the p o t e n t i a l p r o f i l e a n d the e l e c t r o n a n d h o l e d e n s i t i e s , as a f u n c t i o n of f r o n t ( Vg f ) a n d b a c k (Vg 2) gate voltages. We a/so deduce the Id(Vg I , Vg 2) character ist ics in the case of low drain voltage. E x p e r i m e n t a l m a t e r i a l is g iven by C M O S / S O S t r a n s i s t o r s , the s a p p h i r e s u b s t r a t e of wh ich has been l o c a l l y t h i nned down. C o m p a r i s o n of the e x p e r i m e n t a l l d ( v g 2) c h a r a c t e r i s t i c s with the s i m u l a t e d c h a r a c t e r i s t i c s a l lows us to de te rmine d i rec t ly the fast s tate densi ty and the f ixed charge at the back in te r face .

t . I N T R O D U C T I O N

We s tudy C M O S / S O S t r a n s i s t o r s of bo th N and P

t ypes , the c h a n n e l s o f wh i ch a re m a d e ot the s a m e

l i g h t l y d o p e d N - s i l i c o n . The N - c h a n n e l t r a n s i s t o r

is a d e e p d e p l e t e d o n e , w h e r e a s the P - c h a n n e l

t r a n s i s t o r is o f e n h a n c e m e n t t y p e . The s a p p h i r e

s u b s t r a t e has b e e n l o c a l l y t h i n n e d down by

u l t r a s o n i c d r i l l i n g to a b o u t 501zm. A h i g h v o l t a g e

( 2 k V ) a p p l i e d on the b a c k s i d e of the t r a n s i s t o r

( t h rough a m e t a l l i s a t i o n of the s a p p h i r e ) a l lows us to

c o n t r o l the p o t e n t i a l a t the b a c k i n t e r f a c e o f the

s i l i con epi layer.

In the c a s e o f a l i g h t l y d o p e d e p i l a y e r , bo th

i n t e r f a c e s a re too s t r o n g l y c o u p l e d to be d e s c r i b e d

by a s i m p l e a n a l y t i c a l m o d e l . F o r th i s r e a s o n , we

deve loped a numer i ca l s imu la t i on of Poisson's equat ion

f o r t h i s t ype ot s t r u c t u r e . S e v e r a l a u t h o r s [ 1 - 6 ]

have g iven m o d e l s o f the t h r e s h o l d vo l t age o f t hese

d e v i c e s , b u t w i t h o u t a n a l y s i n g p r e c i s e l y the

i n f l u e n c e of the back i n t e r f a c e . Our p r o g r a m a l lows

us to g i ve a c c o u n t o f the a c t i o n o f the i n t e r f a c e

p a r a m e t e r s on bo th t r a n s f e r c h a r a c t e r i s t i c s : d r a i n

c u r r e n t ( I d ) v e r s u s f r o n t g a t e v o l t a g e (Vg 1) a n d

versus back gate voltage ( V g 2 ) .

2. PROGRAMMING CONSIDERATIONS

The p r o g r a m uses a f in i te d i f f e r e n c e me thod . For

the c a l c u l a t i o n we have c h o s e n a non - l i n e a r

ove r re laxa t ion me thod , the ove r re laxa t ion c o e f f i c i e n t

b e i n g c a l c u l a t e d p e r i o d i c a l l y . The i n p u t v a r i a b l e s

a r e . g e o m e t r y o f t r a n s i s t o r s , d o p i n g o r d o p i n g

p r o f i l e N d, f i xed c h a r g e at the two i n t e r f a c e s Q s s l

( a t the f r o n t i n t e r f a c e ) and Oss 2 ( a t the b a c k

i n t e r f a c e ) , s u r f a c e s t a t e d e n s i t y N s t ( u n i f o r m l y

d i s t r i b u t e d ) a t the b a c k i n t e r f a c e ( w i t h a c c e p t e r

s ta tes be tween the c o n d u c t i o n band and the m i d g a p ,

and d o n o r s t a tes be tween the v a l e n c e b a n d and the

m i d g a p ) , a p p l i e d ga te to s o u r c e vo l t ages at the two

g a t e s , t h i c k n e s s e s ot s i l i c o n d i o x i d e , s i l i c o n a n d

sapph i re ( eSA ) .

The p r o g r a m p r o v i d e s : p o t e n t i a l , e l e c t r o n and

h o l e d e n s i t i e s i n s i d e the f i l m t o t a g i ven va lue ot

t r e n t a n d b a c k g a t e v o l t a g e s , the I d ( V g )

c h a r a c t e r i s t i c s ( t r e n t o r b a c k Vg, the o t h e r one

b e i n g f i x e d ) o f the two t ypes ot t r a n s i s t o r . These

c u r v e s a re p l o t t e d f o r a low d r a i n v o l t a g e

( I V d I =20mY) .

The i n s u l a t o r t h i c k n e s s e s a r e , in the c a s e

which is ana lysed , 501Lm for the sapph i r e and 65nm for

0378-4363/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

F. Balestra et al. / Deep depleted SOI MOSFETS 297

the f ron t gate ox ide, with a O. 61zm s i l i con f i lm . Al l the

c h a r a c t e r i s t i c s a re p l o t t e d f o r the f r o n t and back

g a t e - c h a n n e l work f u n c t i o n s set e q u a l to z e r o . A

t r a n s l a t i o n of the va lue o t the f r o n t g a t e - c h a n n e l

work f u n c t i o n f o r f r o n t t h r e s h o l d vo l t ages mus t be

done a c c o r d i n g to the f ron t gate m a t e r i a l used. The

back g a t e - c h a n n e l work func t ion has no i m p o r t a n c e

b e c a u s e o f i ts low va lue c o m p a r e d to the a p p l i e d

back ga te v o l t a g e . The i n t e g r a t i o n of the e l e c t r o n

a n d ho le d e n s i t i e s to o b t a i n the d r a i n c u r r e n t is

worked out with a cons tan t mob i l i t y . This Is ev ident ly

wrong but a var iable mob i l i t y would not af fect p r ima r i l y

the t h r e s h o l d v o l t a g e wh ich is o u r p a r a m e t e r of

interest in this work.

We have pa r t i cu la r l y s tud ied the in f luence of f ixed

cha rge dens i ty and s u r f a c e state dens i ty at the back

i n t e r f a c e on t h r e s h o l d vo l tages . We have p l o t t e d in

f i g u r e 1 p o t e n t i a l p r o f i l e s f o r s e v e r a l back ga te

vo l t ages with a f i xed f r o n t gate vo l t age , with a non

zero back i n te r f ace state dens i ty . We can c lea r l y see

the change of f ron t su r face po ten t i a l of mo re than one

h u n d r e d m i l l / v o l t s when the back s u r f a c e p o t e n t i a l

varies f rom st rong accumu la t ion into s t rong invers ion.

The low d o p i n g is r e s p o n s i b l e f o r th is s t r o n g

coupl ing between the two interfaces.

SiOz %0

0.6

.., 0.2 - 0

-0.2 Q Q.

-0.6

-1.0 0

5i AL~O3

~~ vg2(v)

O0 -

1 -lsoo ..... i/ ,oo

e ,oo . . . . . ) :2400

01 0.2 O3 0.¢ 0.5 06 X (pro)

3. BACK THRESHOLD VOLTAGE

We have p l o t t e d the I d ( Vg 2) c h a r a c t e r i s t i c s fo r

seve ra l f i xed c h a r g e dens i t i es at the back i n t e r f a c e

and s e v e r a l d o p i n g s o f the s i l i c o n f i l m , the b a c k

i n t e r f ace s ta te dens i ty b e i n g set equa l to zero . The

t h r e s h o l d v o l t a g e s o f N - c h a n n e l and P - c h a n n e l

t r a n s i s t o r s , m e a s u r e d In the l i n e a r zone of I d ( V g )

c h a r a c t e r i s t i c s on a l i n e a r sca le in s t rong i nve rs ion

or s t rong a c c u m u l a t i o n , a re a lmos t i den t i ca l fo r the

d i f f e r e n t f ixed cha rges and d o p i n g s . The s a p p h i r e

is very th i ck and thus the t e r m s wh ich have no t the

s a p p h i r e t h i ckness as a f a c t o r in the e x p r e s s i o n o f

the t h r e s h o l d vo l tage a re n e g l i g i b l e . Thus the f ixed

c h a r g e at the back i n t e r f a c e and the d o p i n g of the

s i l i c o n f i l m have on ly s t r a n s l a t i o n e f f e c t on bo th

threshold voltages.

We show in f igure 2 an example of the dependence

of d r a i n c u r r e n t on back ga te vo l t age wi th a non

ze ro s u r f a c e s ta te d e n s i t y . We n o t i c e a s t r o n g

assymet ry of the ac t i on o f the i n te r f ace states on the

t h r e s h o l d v o l t a g e s o f N - c h a n n e l and P - c h a n n e l

1|-'/

1 0 4 T___

I I I-~

P-CHANNEL

Nst=I 510'ncm"~eV -1 " ~ " "

1 | -~ i i -2~10 -1000 -1200

V | f l V I

N-CHANNEL

.Nsr:o

i

-600

Figure 1

Variation of potential inside sil icon fi lm for various

values of V_ 2 with non zero Nst. Vg1=O ,

Nd=fO2Om-'V°i eSA=5Olzm, Q s s l / q = l o l O c m - 2 ,

O s s 2 / q = l O t 2 c m -2 , N s t = l . 5 1012cm-2eV -1

Figure 2

I d {Vg 2) character is t ics obta ined with non zero

Nst compared to Nst = O. Vgl=O, eSA=5Olzm,

Nd= 1020m-3, C/ss t / q = I 0 1 0 c m - 2 Qss2/q = f 012cm-2

298 f~ Balestra et al. / Deep depicted SO1 MOSI*'ETS

]200

>2400

t

~1600

800

i i

1012 210r2 Nst [[m-2eV -1)

F igu re 3

D i f fe rence in back threshold voltages ot N -channe l

and P-channe l transistors as a funct ion of the hack

i n te r f ace s ta te dens i ty Nst . eSA=1OOlzm.

t r a n s i t o r s . Th is is c o n f i r m e d by the p l o t o f the tsgure

3. We s h o w the d i f f e r e n c e in t h r e s h o l d v o l t a g e s as a

f u n c t i o n o f b a c k i n t e r f a c e s t a t e d e n s i t y . T h i s

d i f f e r e n c e is i n d e p e n d e n t o f t he f i x e d c h a r g e

d e n s i t y a t t he b a c k i n t e r f a c e a n d i n d e p e n d e n t o f

s i l i con d o p i n g .

We thus ob ta in a d i r e c t m e a s u r e of the s ta te dens i t y

a t t he b a c k i n t e r f a c e by t he d i f f e r e n c e o f b a c k

t h r e s h o l d v o l t a g e s f o r b o t h t y p e s o t t r a n s i s t o r . We

have a l s o a m e a n s o f d e t e r m i n i n g the f i x e d c h a r g e

d e n s i t y a t the b a c k i n t e r f a c e by u s i n g the p o s i t i o n o t

t he t h r e s h o l d v o l t a g e s o f N - c h a n n e l a n d P - c h a n n e l

t rans i s to rs c o m p a r e d to zero .

4. FRONT THRESHOLD VOLTAGE

We have s t u d i e d the f r o n t t h r e s h o l d v o l t a g e s o f

b o t h types o f t r a n s i s t o r u n d e r s a m e c o n d i t i o n s as the

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

v o l t a g e s , p a r t i c u l a r l y to e x a m i n e the i n f l u e n c e o f the

f i x e d c h a r g e s a n d t he s u r f a c e s t a t e s a t t h e b a c k

~" II.6

~ -t.2 !

~000

G s s 2 / q = l O ~ cm-7

. . . . . . . Qss~/q= lOU cm-~

V~N

~ V l p

.'1 i t I i 1 1 i J ¢

| 10 ~ 2.10 ~ Nsl" [cm-2,eV -11

F igure 4

D e p e n d e n c e of the f ron t t h resho ld vo l tages of

N - c h a n n e l and P - c h a n n e l t rans is to rs on the back

i n te r f ace s ta te dens i ty with two d i f f e r e n t back

f ixed cha rges . Vg2=O, Q s s l / q = l O l O c m - 2 ,

Nd=102Om-3

i n t e r f a c e . F i g u r e 4 is the p l o t o t the d e p e n d e n c e o t

bo th f r o n t t h r e s h o l d v o l t a g e s on b a c k i n t e r f a c e s t a te

d e n s i t y o b t a i n e d by s i m u l a t i o n . We have p l o t t e d th is

v a r i a t i o n f o r two d e n s i t i e s o f b a c k f i xed c h a r g e s . We

n o t e t h e d i f f e r e n c e in t he v a r i a t i o n o f t he f r o n t

t h r e s h o l d v o l t a g e s o t t he P - c h a n n e l t r a n s i s t o r f o r

the two b a c k f i x e d c h a r g e s . Th is is the r e s u l t o f the

d i s t r i b u t i o n o t b a c k i n t e r f a c e s t a t e s in a c c e p t o r

s ta tes and dono r s ta tes .

We c a n o b s e r v e t h a t t he b a c k i n t e r f a c e s t a t e

d e n s i t y has no m o r e e f f e c t on the t h r e s h o l d v o l t a g e

when i t is h i g h e r than 101 2 c m - 2 e V - 1. A f t e r th is l i m i t

t he b a c k s u r f a c e p o t e n t i a l no l o n g e r v a r i e s ; i t is

f i xed n e a r the F e r m i p o t e n t i a l . We can say t ha t when

the s t a t e d e n s i t y is h i g h e r than th is va lue a v a r i a t i o n

o f t h e d e n s i t y f r o m t r a n s i s t o r to t r a n s i s t o r has no

e f f e c t on t he t h r e s h o l d v o l t a g e s . Th i s l e a d s p a r a -

d o x i c a l l y to an i n c r e a s e d r e l i a b i l i t y o f t he

[~ Balestra et al. / Deep depleted SO1 MOSFETS 299

t e c h n o l o g y for a h igh value of the back i n t e r f a c e

s ta te dens i t y . This is not the case when it is

lower.

3. EXPERIMENT

The tested c i r cu i t s are P- type and N- type SOS-

MOS t ransis tors previously descr ibed. The thickness

of the sapphire after s l imming is determined by opt ical

measure, with an accuracy of 2 0 t . Back voltages are

varying between -2000V and +2000V. We study these

t r a n s i s t o r s with low d ra in vo l tages

( I V d l = 2 O m V ) (F ig , 5a and 5 b ) . We measure the

t h r e s h o l d vo l tage in the l i nea r zone of the I d ( V g )

curve, in the same way as on the s imulat ion c u r v e s .

-lO-Z

-lg-~

,<

-i= -lO-lO

-lO-'n -2 -1 0 1 2

Vg21KVI

Figure 5a

Experimental characterist ic Id(Vg 2) of P-channel

transistor. Vd=-2OmV. eSA=fOO#m.

10 -o

10 -9

-~ I0-IE

-2 -1 0 1 Vg2 I KV I

Figure 5b

Experimental character ist ic Id (Vg 2) of N-channel

transistor. Vd=2OmV. esA=lOOlzm.

The d i f f e rence of the back th resho ld vol tages of

N - c h a n n e l and P - c h a n n e l t r ans i s t o r s , which is of

2100 Vo l ts , leads ( f i g u r e 3) to a dens i t y of back

in te r face states at the s i l i c o n - s a p p h i r e in te r face of

about 1 . 5 l O Z 2 c m - 2 e V - Z W e t h u s h a v e a d / r e c t

measure of the back in ter face state density by s imple

d i f f e r e n c e in t h r e s h o l d vo l tages . I t is the gap

between the t h r e s h o l d vo l tages which give us the

value of the state densi ty , and we have a measure of

the back f ixed charge dens i ty by us ing the pos i t i on

of the t h r e s h o l d vo l tages of N - c h a n n e l and P -

c h a n n e l t r a n s i s t o r s c o m p a r e d to zero. This las t

measu re is less a c c u r a t e than that of the s ta te

dens i t y . M o r e o v e r th is value is d e p e n d e n t on the

chosen d i s t r i b u t i o n of the back i n t e r f a c e s ta tes ,

whereas the value of the s ta te dens i t y is

i n d e p e n d e n t o f i ts d i s t r i b u t i o n in a c c e p t o r s ta tes

and donor s ta tes . Never the less we can say that the

back f ixed cha rge is low, c e r t a i n l y l ower than

1011cm-2 ,

The value of the d i f f e r e n c e in t h r e s h o l d

vo l tages is d e p e n d e n t of the s a p p h i r e t h i c k n e s s ,

and we thus have an inde te rmina t ion of about 20% of

the value of the back in te r face state densi ty l ike that

of the s a p p h i r e th i ckness ( f i g . 3 ) . Neve r t he less ,

the f r on t t h r e s h o l d vo l tages are in a zone of Nst

s u f f i c i e n t l y s t r ong to be i n d e p e n d e n t of such a

var ia t ion of the dens i ty ( f i g . 4 ) . In th is zone of Nst

the f ront th resho ld vol tages are pa r t i cu la r l y s tab le ,

and a l m o s t i n d e p e n d e n t of a va r ia t i on of the back

interface state density or of the back fixed charge.

6. CONCLUSION

Our p rog ram al lows us to de te rmine d i rec t l y the

i n f l u e n c e of the i n t e r f a c e p a r a m e t e r s on the

e lec t r i ca l cha rac te r i s t i cs of a mu l t l l ayer s t ruc tu re .

For CMOS/SOS t rans is tors a high densi ty of states at

the back in te r face is ob ta ined. We can observe that

we are in a zone of Nat where the f ron t t h r e s h o l d

vo l tages are p a r t i c u l a r l y s t a b l e . This leads to an

increased re l iab i l i ty of the deep depleted CMOS/SOS

t e c h n o l o g y .

T h l s p r o g r a m is eas i l y a p p l i c a b l e to any SO/

300 t,. Balestra et al. i Deep depleted SO1 MOSI,'ETS

s t r u c t u r e l ike S IMOX, where the back gate is

constituted by the si l icon substrate.

ACKNOWLEDGEMENTS

The authors would l ike to thank M. MONTIER and

Y. "GRIS of EFCIS for t he i r e n c o u r a g e m e n t and tor

s u p p l y i n g the SOS MOSFET's used in our m e a -

surements.

REFEREN C ES

I , M. R. Splinter, IEEE Trans. Electr.

Dev. ED-25, 996 (1978)

2. D. Kranzer, K. Schlgtter and D.

Takacs, IEEE Trans. Electron. Dev.

ED-25, 890 (1978)

3.

4.

5.

6.

V. Kowshik and D .J . Dumin, IEEE

Trans. Electron. Dev. ED-28, 993

(1981)

N. Sasaki and R. Togei, Solid St.

Electron. 22, 41 7 (1979)

E. R. Worley, Solid St. Electron. 23,

1107 (1980)

H . - K . Lira and J . G . Fossum, IEEE

Trans. Electron. Dev. ED-30, 1244

(1983)