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~ j .

ELSEVIER

Microelectronics Journ al28 (1997) 509-517 1997 Elsevier Science Limited

All rights reserved. Printed in Great Britain0026-2692/97/ 17.00

P H S0026-2692(96)00067-5

S i m u l a t i o n o fs i l i c o n e t c h i n g w i t hKOH C a m o n a n d Z M o k t a d i rLaboratoire d Architecture et d Analyse des Syst~mes du C N R S , 7 avenue du colonel Roche,F-31077 Toulouse Cedex, France. Tel : 33 61 33 64 67. Fax: 33 61 33 62 08

Anisotropic chem ical etching o f m onocrystallinesilicon inKO H aqueous solution is investigated. The atom ic scalemodel proposed is based on the influence of the O H groupon chemical bonds. Etch rate and activation energies arecalculated and extended to the com plete etch ra te polardiagram and compared to available experimental data.Finally, an analytical description o f etch rat e ratios isproposed. 1997 Elsevier Science Ltd.

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

e c e n t y e a r s h a v e s e e n i m p o r t a n t p r o g r e s si n t h e c o n s t r u c t io n o f m i c r o - e l e c tr o -

m e c h a n i c a l s tr u c t u re s w i t h t e c h n o l o g i e s d e r iv e df r om in t e g r a t e d c i r c u i t f a b r i c a t i on . A n i so t r op i cc h e m i c a l e t c h i n g is o n e o f t h e k e y t e c h n i q u e s f o rt e c h n o l o g i c a l e l a b o r a ti o n o f 3 D m i c r o s t r u c t u r e sl e a d i n g t o m i c r o m e c h a n i c a l d e v ic e s a n d m i c r o -sys tems [1 ,2] . S ing le c rys ta l s i l i con i s chemica l lye t c h e d u s i n g s t r o n g b as es s u c h as K O H , E D P,T M A H , e t c. th r o u g h s i l ic o n o x i d e o r n it r id emasks rea l ized wi th the c lass ica l l i thographicprocess .

T h e s e p r o c e s s e s a r e v e r y c o m p l i c a t e d a n d t h er e su lt s a r e n o t a lw a ys a c c u r a t e ly p r e d i c ta b l e .T h u s , t h e s u c c e sf u l d e s i g n a n d i m p l e m e n t a t i o no f s u c h m i c r o s t r u c t u r e s d e p e n d t o a la rg e d e g r e eo n e x p e r i e n c e o r o rt t h e d i li g e n c e u s e d i n a

t r i a l- a n d - e r r o r a p p r o a c h . To b u i l d c o m p l i c a t e dm i c r o - d y n a m i c a l s y st em s g o o d p r ed i c ti v e C A Dt o o l s b e c o m e a n e c e s s i t y. S o m e a t t e m p t s h a v eb e e n c a r ri e d o u t t o s i m u l a t e t h e e t c h i n g p r o c e s sus ing ge o me t r i c a l r u le s [ 3 - 7 ] .

T h e ge ne r a l p r ob l e m, t a k ing in to a c c o u n t a llc r y s ta l log r a ph i c d ir e c t ions , i s ve r y c o mp le x . Fo rc onc a v e c o r ne r s , t he 3D sha pe w i l l be de f i ne d b ys lowes t e tch ra tes and face ts can d isappear. Inc on t r a s t , f o r a c onv e x c o r ne r, t h e 3D sha pe w i l l b ede f ine d by f a s t e s t e t c h r a t e s , a nd ne w f a c e t s c a na pp ea r. I n o r d e r to k n o w w h e n a n d w h i c h a n e wface t wi l l appear, the t im e s tep ins ide the s im ula torha s t o be d e t e r m ine d a nd a da p t e d f ir st . A t p r e se n t ,t h is k in d o f mo de l l i ng i s va l id on ly i n som e p a r t i-cu la r cases . Some o ther s imula tors take in toa c c o u n t a n u m b e r ( t h re e o r f o u r) o f c r ys t al -l og r a ph i c d i r e c t i ons t o a vo id t h i s h igh CPUm e t h o d t o r e s e a rc h w h e n a n e w f ac e t w i l l ap p e a ra nd w h ic h one . T he r i sk s a r e m i s s ing t he r i gh to r i e n t a t i on o f f a ce t s a nd de sc r i b ing imp e r f e c t l ythe 3D sha pe . Fo r t he se r e a sons , t he ge ome t r i c a ls u r f a c e c o n s t r u c t i o n p r o g r a m r e q u i r e s c o m p l e t ee tch ra te in format ion for a l l poss ib le d i rec t ions .T h i s i s a lso tr ue f o r s imu la t i on ba se d on t h e m o d e le q u i v a le n t o f t h e s o l id o n s o li d m o d e l . M i n i m aa n d m a x i m a o f t h e e t c h r at e p o l ar d i a g r a m h a v e t ob e k n o w n i n d i re c t i o n a n d m o d u l u s .

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H . C a m o n a n d Z . M o k t a d i r /S i e t c h i n g w i t h K O H

Etch in g sp eed s a re h ig h ly d ep en d en t o n th ec ry st al li n e o r i en t a ti o n , co n cen t r a t i o n o f e t ch in gso lu t io n , t emp era tu re an d d o p in g co n cen t r a t i o nof e tche d subst ra tes (especia lly P dop ing ) . ED Pis an in teres t ing e tch an t because o f i ts an iso t ropyand select ivi ty w ith several materials. T hed ecrease o f e t ch in g r a te wi th b o ro n co n cen t r a -t ion in s i l icon i s abrup t . Never theless , i t s h ighlevel o f tox ic i ty is a g reat handicap . K O H iswi th o u t d o u b t t h e mo s t u se fu l e t ch an t fo rimp lemen ta t i o n . Th e an i so t ro p y i s q u i t e h ig h

b u t t h e d ec rease o f e t ch in g r at e wi th b o ro nco n cen t r a t i o n i s mo re smo o th . Th e se l ec t i v i t ywi th s i l icon ox ide makes i t a poor candidate fo rlo n g t ime e t ch in g . Th ere fo re , fo r so me ap p h ca-t ions , T M A H is used . Th e select iv ity w i th s i l i-co n o x id e i s h ig h er, b u t t h e an i so t ro p y lo wer.Un fo r tu n a t e ly, n o t en o u g h in fo rmat io n has b eenpubl i shed to descr ibe the complete e tch ra ted iagram. General ly, e tch ra tes have beenmeasu red an d p u b l i sh ed o n ly fo r a f ew mater ia lsan d so me e t ch an t s i n so me se l ec t ed d i r ec t i o n s :the tw o or th r ee p r incipal crys ta llographic p lanes[8-11] . In add i t ion , values o f e tch ing ra te anda c ti v at io n e n e rg ie s f o r T M A H , E D P a n d K O Ha re s ca tt er e d. T h e m o s t c o m p l e te w o r k o n K O H(values fo r TM A H are too scat tered) is due toTe l l i e r e t a l [11]. In this paper, we shall refer toTel l ier and Seidel [10] fo r expe r imen tal values .

T o ob tain physical ly p lausib le e tch ra te d iagrams,we have developed a s impl i f ied a tomic scalemo d e l o f t h e e t ch in g p ro cess .

2 A t o m i c m o d e l

As we shall see later, th is mo de ll ing is consisten tw i th t h e e l ec t ro ch emica l ap p ro ach d ev e lo p ed b ySeidel e t a l T h e e t c h i n g p r oc e ss in K O H s o l u-t i o n can b e d esc r ib ed b y th e fo l l o win g g lob a lreact ion :

Si + 2 O H - + 2 H 2 0 -- . S i ( O H 4 ) - + H 2

an d su mmar i zed fo r o u r p u rp o se b y th e fo l l o w-ing steps:

f ir st , b ind ing o f the hyd rox id e ion to theu n p a i r ed e l ec t ro n o f t h e su rf ace d an g l in gb o n d s t h ro u g h th e He lmo l t z l ay e r. Th eion izat ion ener gy of th is sur face state i s weak(near 0 .35 eV) and thus th is react ion occursvery rap id ly.

seco n d ly, b reak in g o f t h e S i -S i b ack b o n d sw h ich p ro ceed s b y e l ec t ro n t ran s fe r in to t h eco n d u c t io n b an d an d su ccess iv e b in d in g o fh y d r o x i d e i o n s w h i c h w e a k e n t h e b a c k -

bon ds s t reng th . Th is even t i s therm al lyact ivated.

Ac co rd in g to t h e p rev io u s as su mp t io n , t h emajo r k in e t i c ev en t t h a t g o v ern s t h e e t ch in gp ro cess is t h e b reak in g o f ch emica l b o n d s . Th eresu l t o f su ccess iv e b reak in g s o f t h e ch emica lb o n d s is t h e su b t r ac t io n o f a to ms f ro m th esurface . The surface d i ffus ion i s neg lected s incew e a r e d e a li n g w i t h l o w t e m p e r a t u r e c o n d i -t i o n . Th e a r ri v al o f O H o n e t ch in g su r face isas su med to h av e a p ro b ab i l i t y eq u a l t o o n e ,

d u e to t h e l o w en erg y asso c i at ed w i th t h is s t ep ,an d , i n t h e case we d o n o t t ak e i n to acco u n ts t i r r ing effects . Exper iments shows that th i sa s s u m p t i o n i s t r u e f o r K O H b u t n o t f o rT M A H . A l s o , t h i s m o d e l d o e s n o t t a k e i n t oacco u n t ex p l i c i tl y th e n a tu re o f d i f f e ren t e t ch -i n g s o lu t io n s s uc h as E D P o r T M A H . T h ee t ch an t i s t ak en in to acco u n t b y ad ap t in g th ese t o f mic ro sco p ic ac t i v a t io n en erg i es fo r eache t ch an t . A t p resen t , t h i s wo rk h as j u s t b eend o n e f o r K O H . T h e i n fl u en c e o f th e d o p i n glevel has been s tud ied in deta i l by Seidele t a l

as co n c en t r a t i o n e f fec ts . I f o u r mo d e l d o es n o tt ak e i n to acco u n t d o p in g e f f ec t s , ex p er imen t sh av e sh o w n th a t a v a r i a ti o n o f co n cen t r a t i o nd o es n o t ch an g e th e macro sco p ic ac t i v a t io nen erg i es an d th u s t h e co n cen t r a t i o n can b ein t ro d u ced as a p re -ex p o n en t i a l f ac to r i n t h ecalcu la t ion of p robabi l i t ies .

The model supposes that the p robabi l i ty fo rb reak in g a n o n -d an g l in g b o n d i s g o v ern ed b y anAr rh en iu s l aw w h o se ac t iv a t io n en erg y d ep en d s

510

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M i c r o e l e c t r o n i c s J o u r n a l Vo l.28 N o . 4

o n t h e n u m b e r o f O H g ro u p s b o u n d e d t o th e sea t o m s [ 1 2 ]. We a s s u m e t h a t i f t h e n u m b e r o fO H g r o u p s at t ac h e d to t h e t w o a t o m ss u r r o u n d i n g a c h e m i c a l b o n d i n cr ea s es , t h es t r e n g th o f t h is b o n d d e c re a s es , w h i c h l ea d s t oa n i nc r e a se o f t h e p r oba b i l i t y fo r b r e a k ing i t. T hep r oba b i l i t y f o r b r e a k ing a bond ,P i , jis:

P i j = I e x p E i , j / k T )

w h e r e I s ta n d s f o r t h e v i b r at i o n al f r e q u e n c y o f

t he c r y s t a l l a tt i ce , k Bo l t z m a nn s c o ns t a n t a nd Tt e m p e r a t u r e . E i , j i s t he mic r o sc op i c a c t i va t i one ne rg y a s soc i at e d w i th t he c o n f igu r a t i on ( i,3 )w h e r e i a n d j a re t h e n u m b e r o f n o n - d a n g l i n gb o n d s o f t h e t w o n e i g h b o u r i n g a t o m s . I n s i li co n ,t h e a t o m l ie s at t h e c e n t r e o f a t e t r a h e d r o n , t h u sn u m b e r s i a n d j a r e e q u a l to f o u r m i n u s t h en u m b e r o f a t ta c h e d O H g r o up s . T h e t i m e o fb r e a k i n g a s s oc i at ed w i t hP i , ji s g iven by:

T i ,j = - l n z ) / P i , j

w h e r e z is a r a n d o m n u m b e r e v e n l y d i s t ri b u t e dbe t w e e n 0 a n d 1 . A t t h e f ir s t pa ss , the s imu la to rc h e c k s e a c h c o n f i g u r a t i o n a n d c o m p u t e s t h ec o r r e s p o n d i n g p r o b a b i l i t y a n d t h e a s s o c i a t e dt ime . A f t e r tha t , a t e a c h pa ss , w h e n a ll th es u rf a ce is c h e c k e d , t h e c o n f i g u r a t i o n w i t h t h el ea st ti m e is re m o v e d . T h e n u m b e r o f O Hg r o u p s o f n e i g h b o u r i n g c o n f i g u r a t i o n s is c h a n -g e d a n d t h e i r n e w p r o b a b i l i t i e s a n d n e w t i m e sa r e c a l c u l a t e d . T h e ope r a to r c a n c hoose c r y s t a lo r i e n t at i o n , t e m p e r a t u r e o f e t c h i n g , s i ze o f t h ec r y s t a l s a mp le s , pe r i od i c c ond i t i ons f o r t he

la te ra l faces o f the samples o r d es ign fac il i ti es fort h e c r e a t io n o f a m a s k .

I n a p r e v i o u s m o d e l , d e s c r i b e d i n R e f . [ 1 3] ,a t o m s w e r e r e m o v e d b y t a k i n g i n t o a c c o u n tt h e n u m b e r o f b o n d s o f e a ch a t o m i n d e p e n -d e n t l y o f t h e s ta te o f th e n e i g h b o u r i n g a t o m s .To f i n d th e e x p e r i m e n t a l a n i s o t ro p i c r a t ioR{hkO)/{lO0), i t was necessary to change them i c r o s c o p i c a c t iv a t io n e n e r g y o f th r e e b o n d e da toms f o r e a c h c r y s t a l o r i e n t a t i on . L e t u s s e e

b o n d i n g s i t u a t i o n s f o r t h e t h r e e m a i n l o w -ind e x c r y s t a l p l a ne s . Fo r t he ( 100 ) p l a ne , a na t o m h a s tw o d a n g l in g b o n d s a n d t w o b o n d sw i t h a t o m s w h i c h h a v e f o u r b o n d s . T h u s t w ob o n d s h a v e t o b e b r o k e n t o r e m o v e a n a t o m .F o r t h e ( 111 ) p l a n e , w h i c h c o r r e s p o n d s t o t h el o w e s t e t c h r a t e , t h e a t o m h a s o n e d a n g l i n gb o n d a n d t h r e e b o n d s w i t h a t o m s w h i c h h a v ef o u r b o n d s . S o , t h r ee b o n d s h a v e to b e b r o k e nt o r e m o v e o n e a t o m f r o m t h e e t c h i n g s u r f a c e .I n t he c a se o f t he ( 110 ) p l a ne , a t om s a t t he

s u r f a c e h a v e o n e d a n g l i n g b o n d , t w o b o n d sw i t h a t o m s w h i c h h a v e th r e e b o n d s a n d o n eb o n d w i t h a n a t o m w h i c h h a s f o u r b o n d s . I nt h i s c a s e , t h r e e b o n d s a l s o h a v e t o b r o k e n , b u tt w o o f th e m a re c o n n e c t e d t o t h re e b o u n da t o m s i n s t ea d o f f o u r b o u n d a t o m s a s in t h e( 111 ) p la n e . T h e s e t w o b o n d s a r e c e r t a i n l yw e a k e r . I t c a n b e e x p l a i n ed b y t h e n u m b e r o fO H g r o u p s .

I n t hi s m o d e l , t h e n u m b e r o f O H g r o u p sa t t a c h e d t o a n a t o m c a n v a r y f r o m z e r o t o

t h r e e . S o t h e t o t a l n u m b e r o f c o n f i g u r a t i o n is16 . Tw o a r e u se le s s : 4 - - - 4 i s a c he m ic a l b o n db e t w e e n t w o a t o m s i n t h e s u b s t r a t e a n d 1 - - 1is a c h e m i c a l b o n d b e t w e e n t w o a t o m s i n t h es o l u ti o n . B y s y m m e t r y c o n s i d e r at i o n , w e h a v ee igh t d i f f e r e n t c on f igu r a t i on s ( s e e Ta b l e 1 ).T he y c a n be r ough ly c l a s s i f i e d i n to f i ve c a se sd e p e n d i n g o n t h e t ot al n u m b e r o f O H g r ou p s

TABLE 1 List of configurations and probabilities used: Arepresents an OH attached group andi / j the number ofbonds for the tw o atom s surrounding a bond

Probab i l i t i es t t ached i / j ) U s e dO H groups conf igu ra t ions p robab i l i ti es

Pm A - 3/4, 4/3 P~Pm A A - 2/4, 4/2 P2~P2A A -A 3/3 P 2AP3~ A A -A 2/3, 3/2 P3aP3A A A A - 1 /4 4 /1 P3AP4A A A A -A 1/3, 3/1 P4~P4A A A - A A 2 /2 P 4 APSA A A A -A A 1/2, 2/1 Psa

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H . C a m o n a n d Z . M o k t a d i r /S i e t c h i n g w i t h K O H

w i t h a n i n c r e a s i n g p r o b a b i l i ty f o r b r e a k i n gfromP 1A to P S a) - W e m a k e n o d i s t i n c t i o n f o r

t h e d i f f e re n t c o n f i g u r a t i o n s i n t h e c a se o f t h r e ea n d f o u r O H g r o u p s c o n s i d e r in g th a t th ee f fe c ts w i ll b e o f th e s e c o n d o r d e r d u e t o t h es m a l l d i f e r e n c e o f c a l c u l a t e d p r o b a b i li t i e s . B u ta d i s t i n c t i o n is m a d e f o r t h e c a se o f t w o O Ha t t a c h e d g r o u p s . I t is k n o w n t h a t t h e i n f lu e n c eo f ra d ic a ls o n a b o u n d is n o t t h e s a m e i n t h e s et w o c o n f i g u ra t i o ns ( A A - ; A - A ) . T h e r el at iv ed i f f e r e n c e s b e t w e e nE i y i e l d s t h e a n i s o t r o p y

b e t w e e n d i f fe r e n t b r e a k i n g p r o b a b i li ti e s . T h es m a l l e r t h e d e v i a t i o n i s , t h e m o r e i s o t r o p i ce t c h i n g b e c o m e s . T h i s p a r t i cu l a r p o i n t h a sb e e n v e r i f i e d .

3 Re s u l t s

3 1 Ti me d e p e n d e n c eI n F i g . 1 t h e v a r i a t i o n s o f t h e e t c h r a t e v e r s u st im e f o r ( 1 0 0 ) a n d ( 111 ) i de a l su r f a c e s i s r e p o r -t e d . W e c a n o b s e r v e t h a t e t c h r a t e v a ri e s v e r yr a p id l y a t th e b e g i n n i n g o f t h e e t c h i n g p r o c e s s

f o r ( 1 0 0 ) o r i e n t a t i o n a n d r e a c h e s a s t e a d y s t a t ev a l u e . I n o r d e r t o e x p l a i n t h i s b e h a v i o u r, w eh a v e s t u d i e d t h e e v o l u t i o n o f t h e s u rf a c em o r p h o l o g y. T h e d e c re a s e o f t h e e t c h i n g r a te isd u e t o t h e a p p e a r a nc e o f PA b o n d s o n t h e ( 1 0 0)s u rf a c e. O n t h e c o n t r a r y, f o r a ( 111 ) o r i e n t a t i o n ,w e o b s e r v e t h e i n c r e a se o f t h e e t c h i n g r a te . T h i si s d u e t o t h e a p p e a r a n c e o f P 2A b o n d s o n t h e( 111 ) su r f a c e . I n bo th c a se s, i f t h e s im u la t i o n isp e r f o r m e d u n t i l t h e r e m o v a l o f 6 0 0 0 0 0 a t o m s ,t h e v a r i a t i o n o f t h e s t e a d y st a te e t c h i n g r a t e isl es s t h a n 1 . F r o m t h is o b s e r v a t io n , w e c a n

c ons ide r t ha t : ( i ) t o c a l c u l a t e a n e t c h r a t e byc o n s i d e r i n g o n l y t h e o r e t i c a l i d e a l s u r f a c e s c a ni n t r o d u c e s o m e m i s t a k e s ; ( i i ) t h e e t c h r a t e i sc l o s e l y r e l a t e d t o t h e s p e c if ic r o u g h n e s s o f e a c ho r i e n t a t i o n .

3 2 Etch ra te and ac t iva t ion ene rg ie sO u r s i m u l a t i o n s a r e n o t a b l e t o c a l c u l a t e a b s o -l u t e v a l u e o f e t c h r a t es ; b u t a f e a tu r e o f g e n e r a li n t e r e s t f o r m a n y p r a c t ic a l a p p l i c a t io n s o f a n i so -t r o p i c s i l ic o n e t c h i n g i s t h e r a t i o o f t h e e t c h r a te s

2.2

2.0

.~ 1.8

1 6

~ 1.4

~ .2

~ 1.0

0.8

1 1

0.1 0.2

T i m e a r b i tr a r y u n i t s )

0.3

E 1.0 S0.9

0.8

z0.6 ,

0.1 d.2 0.3T i m e a r b i tr a r y u n i t s )

Fig. 1. Norm alized etch rate versus time for (100 ) and(111) orientation.

w h i c h d e t e r m i n e t h e t y p e o f 3 D s h a pe s af te re t ch i n g. F r o m e x p e r im e n t s , fo r K O H s o lu t io n ,( 11 0 ) p l a n e s a r e e t c h e d f a s te r t h a n ( 1 0 0 ) p l a n e s ,w i t h n e a r l y i d e n t i c a l m a c r o s c o p i c a c t i v a t i o ne n e r g i e s o f 0 . 6 0 a n d 0 . 5 9 5 e V, r e s p e c ti v e ly. T h em a c r o s c o p i c a c t i v a t i o n e n e r g y f o r ( 111 ) p l a n e s isa p p r o x i m a t i v e l y 0 . 7 4 e V w i t h t h e s l o w e s t e t c hr a t e . I t c a n b e s e e n t h a t t h e s l o w e r t h e e t c h r a t ei s , t h e h i g h e r t h e m a c r o s c o p i c a c t i v a t i o n e n e r g y

i s . A s a c o n s e q u e n c e , t h e e t c h r a t e r a t i o o f( 11 0 ) : ( 1 0 0 ) : ( 111 ) i n c r e as e s f r o m 5 0 :3 0 : 1 n e a rt h e b o i l i n g p o i n t o f t h e s o l u t i o n t o 1 6 0 : 1 0 0 : 1 a tr o o m t e m p e r a tu r e . O u r s i m u l a ti o n f o u n d a na n i s o t r o p i c r a t i o o f 6 0 : 4 7 :1 a t b o i l i n g p o i n t a n d1 3 0 0 : 7 5 0 : 1 a t r o o m t e m p e r a t u r e . T h i s i s ac o n s e q u e n c e o f a t o o l o w e t c h r a te f o r ( 111 ) , b u tt h e r a t i o b e t w e e n ( 11 0 ) a n d ( 1 0 0 ) i s s ti ll i n g o o da g r e e m e n t . H o w e v e r , w e c a n r e a d i n t h e l i t e r a -t u r e d i f f e r e n t v a l u e s f o r ( 111 ) e t c h r a t e a n d a c t i -v a t i o n e n e r g y.

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