SIMULATION AND MODELING OF EVAPORATE DEPOSITION … · SIMULATION AND MODELING OF EVAPORATED...
74
p SIMULATION AND MODELING OF EVAPORATE DEPOSITION PROFILES I by Chiakang Sung Memorandum No. UCB/ERL MS1/8 SAMPLE Report No. SAMD-4 17 February 1981
Transcript of SIMULATION AND MODELING OF EVAPORATE DEPOSITION … · SIMULATION AND MODELING OF EVAPORATED...
p SIMULATION AND MODELING OF EVAPORATE
DEPOSITION PROFILES I
by
Chiakang Sung
Memorandum No. UCB/ERL MS1/8
SAMPLE Report No. SAMD-4
17 February 1981
SIMULATION AND MODELING
OF EVAPORATED DEPOSITION PROFILES
bY
Chiakang Sung
Memorandum No. UCB/ERL M81/8
17 February 1981
ELECTRONICS RESEARCH LABORATORY
College of Engineering University of California, Berkeley
94720
SIMULATION A N D M O D E L I N G OF EVAPORATED DEPOSITION PROFIL
b y
Ch iakang Sung
I. ABSTRACT
T h i s r e p o r t p r e s e n t s a p rogram f o r t h e s i m u l a t i o n o
t a l i z a t i o n . The s i m u l a t i o n i s u s e d t o i n v e s t i g a t e meta
c o v e r a g e f o r a v a r i e t y o f source and s u b s t r a t e c o n f i g u r a t
The models u s e d f o r d e p o s i t i o n combine a n a l y t i c and
i c a l s u m m a t i o n s . The d e p o s i t i o n r a t e i s d e r i v e d a s a n a n
f u n c t i o n , and t h e s i m u l a t i o n p r o c e e d s b y summing t h e d e p
t h r o u g h a s e r i e s o f f i n i t e t i m e - s t e p s . S i m u l a t i o n s hav
made t o model m e t a l i z a t i o n o v e r s t e p s w i t h t h e f o l
s o u r c e - s u b s t r a t e g e o m e t r i e s : ( 1 ) u n i d i r e c t i o n a l s o u r c
I
ZS
' me-
s t e p
o n s .
umer-
l y t i c
st i o n
! b e e n
owing
' , ( 2 )
d u a l e v a p o r a t i o n s o u r c e s , ( 3 ) h e m i s p h e r i c a l v a p o r s o u r c e 1 ( 4 )
p o i n t s o u r c e w i t h p l a n e t a r y - m o u n t e d s u b s t r a t e . The m o d e l i n g
t e c h n i q u e h a s a l s o b e e n e x t e n d e d t o d e p o s i t i o n processes w i t h
e l e v a t e d s u b s t r a t e t e m p e r a t u r e .
Research sponsored by the National Science Foundation under Grant EN 77-14660-A01, Hughes Ai rc ra f t , INTEL, S igne t ics , Hewlett-Packard and IBM Corporati n .
The following is a reproduction of the authors M.S. Thesis , Plan 11. I -1 -
C O N T E N T S
,Page
I . A B S T R A C T .......................................... 1
I1 . I N T R O D U C T I O N ..................................... 2
1I.I. A S S U M P T I O N S ..................................... 3
T V . S O U R C E C O N F I G U R A T I O N S ............................ 4
V . T E Y P E R A T U R E E F F E C T ................................ 7
V I . P R O G R A Y O R G A N I Z A T I O N ............................. 8
V I 1 . U S E R D O C U M E N T A T I O N .............................. 10
V I 1 1 . S I M U L A T I O N R E S U L T S ............................. 12
I X . COYMON B L O C K D O C U M E N T A T I O N ....................... 1 4
X . E X P E R I Y E N T ......................................... 18
X I . C O N C L U S I O N ....................................... 19
A P P E W D I X : P R O C E S S I N G S E Q U E N C E ........................ 20
R E F E R E N C E S ............................................ 23
S O U R C E CODE ........................................... 26
11. I N T R O D U C T I O N
D u r i n g t h e p a s t d e c a d e , many i n v e s t i g a t i o n s were c r r i e d
o u t t o e x p l o r e t h e c o v e r a g e of e v a p o r a t e d f i l m s o v e r s t p s i n .I ei
s u b s t r a t e s [ 1 ] - [ 9 ] . I n p a r t i c u l a r , B l e c h d e r i v e d a model /wh ich
c a n be a p p l i e d t o a n y source g e o m e t r y and s t e p p r o f i l q c11.
The s i m u l a t o r d e s c r i b e d i n t h i s r e p o r t e x t e n d s B l e c h ' s model t o
s u r f a c e m i g r a t i o n s u c h a s would o c c u r i n an e l e v a t e d t e q p e r a -
t u r e e n v i r o n a e n t . I
The p rob lem of t h e s t e p c o v e r a g e i s g e o m e t r i c i n n q t u r e .
E v e r y p o i n t on t h e s u b s t r a t e views t h e source s u b t e n d i n g 4 cer-
t a i n s o l i d a n g l e . The g r o w t h r a t e o f t h e e v a p o r a t e d f i q m a t
e a c h p o i n t i s s t r o n g l y d e p e n d e n t on t h e a s s o c i a t e d s o l i d q n g l e .
Depending on t h e s u r f a c e t o p o l o g y and t h e s o u r c e c o n f i g u r q t i o n ,
t h e shadow e f f e c t c a n occur . As a r e s u l t o f s h a d o w i n q , t h e
s o l i d a n g l e v a r i e s i n t ime and so d o e s t h e g r o w t h r a t e / ( F i g .
1 ) . Therefore , a f t e r a c e r t a i n amount o f t i m e , some p o i n t s on
t h e s u b s t r a t e c a n be c o m p l e t e l y shadowed b y o t h e r f a s t gqowing
points. T h i s can g i v e r i s e t o a c r a c k o r a poor s t e p c o v T r a g e .
The p rogram s i m u l a t e s t h e g r o w t h o f a d e p o s i t e d t h i n f i l m
w i t h v a r i o u s s o u r c e - s u b s t r a t e c o n f i g u r a t i o n s . Two d i m e n $ i o n a l
s u r f a c e g e o m e t r i e s w i t h a r b i t r a r y s h a p e a r e s p e c i f i e d a s i n p u t .
The s i m u l a t o r g e n e r a t e s a l i n e - e d g e p r o f i l e o f t h e f i l m c o v e r -
a g e b a s e d on a u s e r - d e f i n e d s o u r c e . By c o m p a r i n g t h e S t e p cov-
e r a g e s f o r v a r i o u s sources , t h e user can o p t i m i z e t h e s q u r c e -
s u b s t r a t e c o n f i g u r a t i o n s i n t h e d e p o s i t i o n a p p a r a t u s . I
-2-
111. ASSUMPTIONS
The f o l l o w i n g a s s u n p t i o n s a r e made i n t h e s i m u l a t i o n : /
( 1 ) The mean f r ee p a t h o f atoms i s l a r g e r t h a n t h e d i s -
t a n c e b e t w e e n source and s u b s t r a t e .
( 2 ) The s o u r c e - t o - s u b s t r a t e d i s t a n c e i s l a r g e compareld t o
t h e s t e p h e i g h t . I
( 3 ) The m a g n i t u d e of f i l m g r o w t h r a t e f o l l o w s t h e d o s i n e
d i s t r i b u t i o n l a w , t h a t i s , t h e t h i c k n e s s o f t h e f i l m grows/ a t a
r a t e p r o p o r t i o n a l t o COSUI, where u1 i s t h e a n g l e b e t w e e n t e va- i I por s t r e a m and s u r f a c e n o r m a l . I
( 4 ) The d i r e c t i o n i n w h i c h t h e f i l m g rows i s t o w a r d 4 t h e
v a p o r stream.
(5) I n case o f a c o l d s u b s t r a t e , t h e s t i c k i n g c o e f f i c i e n t
i s assumed t o b e u n i t y .
( 6 ) I n an e l e v a t e d t e m p e r a t u r e e n v i r o n m e n t , s u r f a c e m i g r a -
t i o n occur s on t h e s u b s t r a t e . It i s assumed t h a t t h e s u r f a c e
m i g r a t i o n obeys a random wa lk l a w . The m i g r a t i o n d i s t a n c e i n -
c r e a s e s w i t h t h e i n c r e a s e of t h e s u b s t r a t e t e m p e r a t u r e .
-3-
I V . SOURCE CONFIGURATIONS
The e v a p o r a t i o n s o u r c e s s i m u l a t e d i n t h i s p r o g r a
d e s c r i b e d a s f o l l o w s :
U N I D I R E C T I O N A L SOURCE
A s shown i n F i g . 2 , t h e unshadowed r e g i o n o f t h e s u b
sees t h e a r r i v a l o f t h e v a p o r streams i n o n e d i r e c t i o n
The g r o w t h r a t e o f t h e d e p o s i t e d f i l m i n t h e shadowed r e g
e q u a l t o z e r o . A c c o r d i n g t o o u r a s s u m p t i o n s , t h e g r o u t
on t h e s u b s t r a t e c a n b e e x p r e s s e d a s :
.
r a t e ( x , z ) = 0 ; i f p o i n t ( x , z ) i s shadowed
a r e
t r a t e
o n l y .
on i s
r a t e
r a t e ( x , z ) = Csinud + C c o s d ; i f p o i n t ( x , z ) i s unshadowed
where UJ i s t h e a n g l e b e t w e e n z -ax i s and t h e v a p o r s t ream, f and
Tz a r e t h e u n i t v e c t o r i n t h e x and z d i r e c t i o n r e s p e c t i v e l y ,
and C i s g r o w t h r a t e o f an unshadowed s u r f a c e n o r m a l t o tthe va-
por s t r e a m .
D U A L E V A P O R A T I O N SOURCES
I n t h i s t y p e o f s o u r c e s , each p o i n t i n t h e unshadowed re-
g i o n v i e w s t h e v a p o r s t r e a m s a r r i v i n g from t w o d i f f e r e n t d i r e c -
t i o n s ( F i g . 3 ) . The g r o w t h r a t e i s g i v e n a s :
r a t e ( x , z ) = 0 ; i f p o i n t ( x , z ) is c o m p l e t e l y shadowed
r a t e ( x , z ) = C s i n u f + CCOSU R or CsinLu f + Ccosu R ; if j ( x , z ) 1 1 2 2 l is p a r t i a l l y shadowed
r a t e ( x , z ) = C(s inu1 + s i n u ) P + C(cosu +COSUI )R; i f ( x z ) i s I 1 2 1 2 un shadowed 1
where u1, and u1 a r e t h e i n c i d e n t a n g l e s . 2
HEMISPHERICAL VAPOR SOURCE 1
-4 -
#
The f l u x of v a p o r i s c o n t i n u o u s l y d i s t r i b u t e d i n a t a n g e
o f d i r e c t i o n s ( F i g . 4 ) . The g r o w t h r a t e can b e c a l c u l a t e d a s :
r a t e ( x , z ) = C ( c o ~ t u ~ - c o s w 2 )'I + C ( s i n u 2 - s i n w 1 )R; I
w h e r e u1 and w a r e t h e lower and t h e u p p e r b o u n d s o f the1 i n -
c i d e n t a n g l e s o f t h e v a p o r s t r e a m s , r e s p e c t i v e l y . 2 I
PLANETARY SOURCE I
The p l a n e t a r y e v r a p o r a t i o n s y s t e m i s shown i n F i g . 5. ' By
i n s p e ' c t i n g t h i s s y s t e m , o n e c a n b e c o n v i n c e d t h a t t h e r o t a t i o n
o f t h e p l a n e t a l o n g t h e s y s t e m c e n t r a l a x i s h a s no e f f e c t on
t h e d e p o s i t i o n r a t e . F o r t h e p u r p o s e o f s i a p l i c i t y , t h e g r o w t h
r a t e c a n be c a l c u l a t e d b y h o l d i n g t h e p l a n e t s t a t i o n a r i l y and
b y r o t a t i n g o n l y t h e s o u r c e a l o n g t h e a x i s o f t h e p l a n e t , a s
shown i n F i g . 6 . The g r o w t h r a t s i s d e r i v e d s i m i l a r l y t o t h a t
o f B l e c h [ 2 ] :
~ r a t e x ( x , z ) 2 C-Lsec (d-8) 1 2 2 C R -r - r L t a n ( 4-8) +LW 1
= f 2 ( R 2 + W 2 ) 0 * 5 [R2-r2+L2-2rLtan(d-B)3 ., d4 [ L t a n ( d - p ) sin!B-Lcos@l t a n d
[ R 2 - ( r + L t a n ( d - p ) ) 2 1 0 ' r a t e z ( x , z )
2 C-Lsec (4-p) 1 [R2- r2+L2-2 rL tan (d -p ) I2
2 2 C R -r -rLtan(d-B)+LWI = r -7 ( R 2 + W 2 ) 0 ' 5
0 bdd [ L t a n ( d - ~ > s i n $ 3 - L c o s ~ l
r ~ ' - ( r + ~ t a n ( d - p ) ) ~ ~ where i s t h e i n c i d e n t a n g l e o f t h e v a p o r stream, g i s
t i l t a n g l e o f t h e p l a n e t p l a n e , r i s t h e d i s t a n c e b e t w e e n t h e
t h e p o s i t i o n o f t h e w a f e r and t h e p l a n e t a x i s , R , L , and W a r e
t h e p a r a m e t e r s d e p e n d e n t on t h e s y s t e m d i m e n s i o n s a s shobn i n I F i g . 5. ~ CONE SOURCE: A SPECIAL CASE OF PLANETARY SOURCE
-5 -
I f b o t h ;B and r a r e z e r o , t h e s u b s t r a t e a l w a y s sees a1 sym-
m e t r i c a l c o n e s o u r c e . I n t h i s t y p e o f c o n f i g u r a t i o n , t h
t s g r a l o f t h e a b o v e two e q u a t i o n s c a n b e e v a l u a t e d
l y , and expres sed i n t h e f o l l o w i n g s i m p l e close form:
r a t e , ( x , z )
r a t e ( x , z > 2
-1 L - 1 L - - L ( R ~ + L W ) ,C sin ( R t a n d m a x ) - s i n (Wtandmin) 3 (R2+V2)o'5(R2+L2) I
- 6 -
V . TEMPERATURE EFFECT
S u r f a c e m i g r a t i o n o n a h o t s u b s t r a t e i s p r e s u m a b l y
b l e owing t o thermal m o t i o n o f t h e d e p o s i t e d p a r t i c l e s .
random wa lk p r o c e s s i s a s s u m e d , t h i s p a r t i c l e r e d i s t r i
from a n y i n f i n i t e s i m a l a r e a on t h e s u r f a c e c a n be c h a r a c t
b y a G a u s s i a n f u n c t i o n o f wh ich t h e v a r i a n c e d e p e n d s on
p e r a t u r e . The g r o w t h r a t e f o r a n y time i n t e r v a l /\t - c a n b
Iossi-
I f a
I u t i o n
!r i zed
tern-
! c a l -
c u l a t e d b y f i r s t c a l c u l a t i n g t h e d e p o s i t i o n o f t h e m a t e r i e l a r -
r i v i n g f r o a t h e s o u r c e a t e a c h s u r f a c e p o i n t ( x , z ) and t h b n t h e
d i f f u s i o n t o and from t h e a d j a c e n t r e g i o n . Each p o i n t t h u s
sou rces a G a u s s i a n f u n c t i o n , and t h e sum o f t h e G a u s s i a n f u n c -
t i o n s is t h e m o d i f i e d d e p o s i t i o n r a t e . 2 -r
where r a t e ' ( x , z ) i s t h e g r o w t h r a t e o f p o i n t ( x , z ) on t h e h o t
s u b s t r a t e , i i s summed o v e r a l l p o i n t s on t h e s u p f a c e ,
r a t e ( x i , z . ) is t h e g r o w t h r a t e o f p o i n t ( x i , z i ) b u t o n a c o l d 1
s u b s t r a t e a s d e s c r i b e d b e f o r e , r i s t h e d i s t a n c e a l o n g t h e s u r -
face b e t w e e n ( x , z ) and ( x i , z i > , and e i s t h e v a r i a n c e of t h e
G a u s s i a n f u n c t i o n . F o r c o n v e n i e n c e , t h e l i m i t s a t t h e summa-
t i o n a r e t e r m i n a t e d a t t h e e x t e n t o f t h r e e - v a r i a n c e r a n g e .
-7 -
I
VI. PROGRAM ORGANIZATION
T h i s p r o g r a m is d e v e l o p e d a s a p o r t i o n o f SAMPLE [ l o ]
i s s i m i l a r i n s t r u c t u r e t o t h e SAMPLE " d e v e l o p mach ine"
C121. The s t r i n g mode l C13J is a l s o u s e d i n t h i s p r o
A n a l y t i c f u n c t i o n s a r e u s e d w h e r e v e r a v a i l a b l e i n o r d e r t
t a i n a c c u r a c y and t o s a v e c o m p u t e r time. The a c c u r a c y o f
p r o f i l e c a n b e improved b y r e d u c i n g t h e time s t e p o r t h e
ment l e n g t h , a t t h e c o s t o f l o n g e r c o m p u t a t i o n t ime. A t y
p r o f i l e , g e n e r a t e d w i t h 10 t o 20 a d v a n c e s , composed o f
100 l i n e s e g m e n t s , c a n g i v e a r e s o n a b l e a c c u r a c y .
It
1 1 1 ,
ram.
a t -
t h e
s e g -
i c a l
0 t o
The m o d u l a r f l o w c h a r t o f t h i s s i m u l a t o r i s shown i n F i g .
7. S u b r o u t i n e s PLOT, P U N C H , CHEKER, and DELOOP a r e t h o s e u s e d
i n SAMPLE, e x c e p t some s l i g h t m o d i f i c a t i o n s . The CONTRIOLLER I
r e c e i v e s i n p u t p a r a m e t e r s , w h i c h d e s c r i b e t h e t y p e o f spurce
and t h e s u b s t r a t e s t e p . Then t h e PROFIL s u b r o u t i n e g e n e l r a t e s l
t h e i n i t i a l s t e p p r o f i l e .
The whole p r o c e s s i n g p r o c e d u r e s a r e now u n d e r c o n t r o l 1 o f
t h e s u b r o u t i n e D P M A I N . F i r s t , s u b r o u t i n e I N I T L Z i n i t i a l i z e s
v a r i o u s i n t e r n a l p a r a m e t e r s . Then s u b r o u t i n e DPMESG e c h o e s t h e
p a r a m e t e r s o f t h e d e p o s i t i o n c o n f i g u r a t i o n , a s r e c o g n i a e d b y
t h e s i m u l a t o r . If n o f a t a l e r r o r s o c c u r , s u b r o u t i n e $HADOW
d e t e r m i n e s , o n a p o i n t - b y - p o i n t b a s i s , t h e r a n g e o f t e i n -
c i d e n t a n g l e s o f t h e i n c o m i n g f l u x t h a t t h e s u b s t r a t e iews.
C a l l e d b y s u b r o u t i n e A D V N C E , s u b r o u t i n e EVRATE t h e n e v a u a t e s 1 t h e g r o w t h r a t e p o i n t b y p o i n t a c c o r d i n g t o t h e d e p o s i t i o
tem and t h e shadow c o n d i t i o n . If h o t s u b s t r a t e h a s b e e n
-8-
f i e d , s u b r o u t i n e ADVNCE w i l l c a l l a n o t h e r s u b r o u t i n e DIFf t o
h a n d l e sur face m i g r a t i o n . The a d v a n c e o f e a c h p o i n t or t h e
l i n e - e d g e p r o f i l e i s p e r f o r m e d s t e p b y s t e p u n d e r t h e c o h t r o l
o f s u b r o u t i n e A D V N C E . D u r i n g a d v a n c i n g , t h e s t r i n g s e g h e n t s
may become v e r y l o n g w h i c h r e d u c e s a c c u r a c y , o r v e r y b h o r t
w h i c h was te s c o m p u t e r t ime. To a v o i d t h i s , a f t e r each a d v g n c e ,
s u b r o u t i n e CHEKER i s c a l l e d t o a d j u s t s e g m e n t l e b g t h .
S u b r o ' u t i n e C H E K E R may c a l l two o t h e r s u b r o u t i n e s , ADb and
DELETE w h i c h r e s p e c t i v e l y p e r f o r m s t h e t a s k t o add anb t o
d e l e t e p o i n t s a s t h e a d j u s t m e n t o f t h e s t r i n g s e g m e n t l e h g t h s
i s n e e d e d . The p u r p o s e o f s e p a r a t i n g ADD and DELETE from b H E K -
E R i s t o a l l o w t h e u s e o f more s o p h i s t i c a t e d a l g o r i t h m s f o l ad- ,
I
d i n g o r d e l e t i n g p o i n t s , i f n e e d e d i n t h e f u t u r e .
A s t h e s t r i n g a d v a n c e s , s p u r i o u s l o o p s may form and t h e y
c a n be d e t e c t e d and d e l e t e d b y c a l l i n g t h e s u b r o u t i n e DELOOP.
F i n a l l y , t h e o u t p u t i s p r o d u c e d b y c a l l i n g a l i n e - p r i h t e r -
p l o t t i n g s u b r o u t i n e PLOT a n d / o r a c a r d - p u n c h i n g s u b r o i u t i n e
P U N C H . Some o the r s u b r o u t i n e s and f u n c t i o n s , s u c h a s GRIOTBL,
E V A L U E , E V I N T G , SUM, A N O R M , and A M I G R a r e u s e d o n l y f o r i n t e r -
m e d i a t e c a l c u l a t i o n s . They a r e s e l f - e x p l a n a t o r y w i t h comhnents
o n t h e s o u r c e c o d e and t h e r e f o r e , t h e y a r e n o t d i s c u s s e d h'ere.
-9 -
V I I . USER DOCUMENTATION
t a i n e d by a n H P - p l o t t e r w i t h d a t a c a r d s p r o d u c e d b y t h e
F i g . 8 shows a t y p i c a l o u t p u t o f a n asymm
e r a g e f o r a p l a n e t a r y r o t a t i n g source [23. j , ~ ob-
p r o -
t r i c a l s t
The p l o t
2 . ) , ......, and ( X ~ ~ , Z , ~ ) = ( 6 - , 2.)
R U N METAL
-10-
I
t h i s r u n s t h e m e t a l i z a t i o n m a c h i n e t o g e n e r a t e t h e l i n k - e d g e
p r o f i l e s o f t h e f i l m c o v e r a g e .
O the r d e p o s i t i o n s o u r c e s c a n b e s p e c i f i e d i n t h e f o l l o w i n g
formats :
S O U R C E M E T A L U N I D I R E C T I O N (45 . ) (0 .005) ~
s p e c i f i e s a p o i n t s o u r c e w i t h a n i n c i d e n t a n g l e o f 45'. The
d e p o s i t i o n r a t e i s 0.005 m i c r o n s / s e c o n d . I
S O U R C E Y E T A L D U A L ( -45 . , 4 5 . ) (0 .005) ~
s p e c i f i e s t h e m e t a l i z a t i o n s o u r c e s h a s d u a l i n c i d e n t a n g l k s
-45' and 45' w i t h d e p o s i t i o n r a t e = 0.005 m i c r o n s / s e c o n d .
o f
S O U R C E M E T A L H E M I S P H E R E ( -go. , 9 0 . ) (0 .005) I s p e c i f i e s a h e m i s p h e r i c a l s o u r c e w i t h i n c i d e n t a n g l e s d k s t r i -
b u t e d c o n t i n u o u s l y from -90' t o 90'. The d e p o s i t o n rB te i s
0.005 m i c r o n s / s e c o n d .
S O U R C E M E T A L CONE (56 . ) ( 1 ! 3 . , 7 . 5 ) (0.0051 I
s p e c i f i e s a c o n e s o u r c e w i t h p a r a m e t e r s : Y = 56', c e n t r a l a x i s
l e n g t h = 18" , p l a n e t a x i s l e n g t h = 7 . 5 " , and d e p o s i t i o n r a t 2 =
0.005 m i c r o n s / s e c o n d .
+
However t h e i n t e r f a c e b e t w e e n t h i s p r o g r a m and t h e t o p
l e v e l c o n t r o l l e r o f S A M P L E w i l l n o t b e r e a d y u n t i l thie v e r y
n e a r f u t u r e .
- 1 1-
?
Some s i m u l a t i o n r e s u l t s a r e g i v e n below w h i c h
t h e c a p a b i l i t i e s o f t h e p r o g r a m . F i g . 9 shows t h e
VIII. SIMULATION RESULTS
i l l u s t r a t e
d e p o s i t i o n
f o r 3 e q u a l time s t e p s . B e c a u s e o f t h e v e r t i c a l s t e p , a
d e v e l o p s n e a r t h e i n s i d e c o r n e r .
I n F i g . 1 0 ( a ) a h e m i s p h e r i c a l s o u r c e i s assumed
c o r r e s p o n d i n g f o r e x a m p l e t o c e r t a i n s p u t t e r i n g sources .
p h e r i c a l s o u r c e , on a h o t s u b s t r a t e . I n c r e a s e d mobi:
a luminum a t o m s i n t h e g r o w i n g f i l m on t h e h o t s u b s t r a t e
t o a r e d u c t i o n of f i l m s u r f a c e a r e a and a f i l l i n g of t h e
c r a c k
C141,
T h i s
i t y o f
l e a d s
c r a c k .
-1 2-
F i g . 1 5 ( a ) shows a s y m m e t r i c a l s t e p c o v e r a q e , u s i n g a cer-
t a i n p l a n e t a r y s o u r c e . F i g . 1 5 ( b ) shows t h e same d e p o s i t b o n on
a h o t s u b s t r a t e . S i n c e s u r f a c e d i f f u s i o n t e n d s t o f i l l t he un-
f a v o r a b l e c r a c k s , d e p o s i t i n g t h e lnetal on a h e a t e d s u b f j t r a t e
t h e r e f o r e may c a u s e t h e d i s a p p e a r a n c e o f c r a c k s . Howeve1 t o o
h i g h a s u b s t r a t e t e m p e r a t u r e may a l s o r e s u l t i n e x t e n s i v e / g r a i n
b o u n d a r y g r o o v i n g w h i c h i s o f t e n u n d e s i r a b l e . The t e c h n i u e t o
i m p r o v e s t e p c o v e r a g e b u t a v o i d g r a i n s i s use o f d i f f e r e n tem-
p e r a t u r e s f o r two l a y e r m e t a l i z a t i o n [ 161 . As shown
1 5 ( c ) , t h e f i r s t l a y e r of m e t a l was d e p o s i t e d , u s i n g a plane-
I
I t a r y s o u r c e , i n room t e m p e r a t u r e . Then t h e s e c o n d l a y e r was
d e p o s i t e d i n t h e same c o n d i t i o n s e x c e p t s u b s t r a t e t e m p e r g t u r e .
By c o m p a r i n g F i g . 1 5 ( c ) w i t h F i g . 1 5 ( a ) , and ( b ) , o n e may, f i n d
t h e optimum c o n d i t i o n f o r s t e p c o v e r a q e w i t h o u t t h e o c c u r r e n c e
of s u r f a c e i r r e s u l a r i t y o r s r a i n s . I
- 1 3-
_ _ . . .
IX. COMMON B L O C K D O C U M E N T A T I O N
T h i s s e c t i o n l i s t s t h e common b l o c k s o f t h e p r
p h a b e t i c a l o r d e r .
/ C H K R /
gram
coTnmon t o C O N T R O L L E R , P R O F I L , C H E K E R , and D E L O O P .
S M I N X t h e minimum x s t r i n g s e g m e n t l e n g t h a l l o w e d b y CH
S Y I N Z t h e minimum z s t r i n g s e g m e n t l e n g t h a l lowed b y CH
S Y A X X t h e maximum x s t r i n g s e g m e n t l e n g t h a l l o w e d by CH
SMAXZ t h e maximurll z s t r i n g s e g m e n t l e n g t h a l l o w e d b y CH
X Z D E L T t h e i n i t i a l s t r i n g s e g m e n t l e n g t h .
/ C R A C K /
common t o SHADOW, and E V R A T E
n a l -
K E R .
K E R .
K E R .
K E R .
a r r a y c o n t a i n i n g t h e minimum i n c i d e n t a n g l e s o f h e i n -
coming f l u x f o r t h e 4 5 0 p o s s i b e s t r i n g p o i n t s .
WF a r r a y c o n t a i n i n g t h e maximum i n c i d e n t a n g l e s o f d h e i n -
coming f l u x f o r t h e 4 5 0 p o s s i b l e s t r i n g p o i n t s .
/ D I F U S N /
1 WI
common t o CONTROLLER, A D V N C E , E V R A T E , DIFF, ANORM, and
A M I C R .
RATE complex array c o n t a i n i n g t h e x and z componen t Q f t h e
g r o w t h r a t e for t h e 450 p o s s i b l e s t r i n g p o i n t s .
a p a r a m e t e r c o n t r o l s t h e e x t e n t o f s u r f a c e m i g r a b i o n . I
S I G M A
/ E T C H 1 1
E T C H 1 i s t h e o n l y common b l o c k u s e d i n t h e o t h e r pa t s of
S A M P L E p r o g r a m . In t h i s s i m u l a t o r , i t is common t o t I e CON-
T R O L L E R , P R O F I L , D P M A I N , SHADOW, A D V N C E , E V R A T E , DIFF, 1 ANORM,
I
-1 4-
A M I G R , C H E K E R , D E L E T E , A D D , D E L O O P , P L O T , and P U N C H
xz complex a r r a y c o n t a i n i n g t h e x and z p o s i t i o n s o t t h e
450 p o s s i b l e d e p o s i t i o n s t r i n g - p o i n t s . ~
XMAX t h e maximum v a l u e of x .
ZMAX t h e maximum v a l u e o f z.
N P T S t h e c u r r e n t nulnber of d e p o s t i o n s t r i n g - p o i n t s .
~
C X Z L n o t u s e d .
C X Z R n o t u s e d .
Y 9 D C H K n o t u s e d .
NCKOUT n o t u s e d .
/ M E T A L /
colnmon t o C O N T R O L L E R , D P M A I N , I N I T L Z , D P M E S G , SIHADOW,
A D V N C E , E V R A T E , G R O T B L , P L O T , and P U N C H
T E T C H R d e p o s i t i o n g r o w t h r a t e ; m i n u s s i g n m e a n s f i l m g r o w s t o -
w a r d s n e g a t i v e - z ( u p w a r d ) d i r e c t i o n .
T Y O U T tilne of t h e l a s t o u t p u t .
NMOUT t o t a l number o f t h e o u t p u t s .
A N G L E a r r a y c o n t a i n i n g t h e minimurn and maximum i n c i d e n t an-
g l e s o f t h e i n c o m i n g f l u x .
D E L T t h e tirne s t e p b e t w e e n a d v a n c e s .
N T O T A L t h e t o t a l number o f a d v a n c e s .
/ M T F L A G /
coamon t o C O N T R O L L E R , D P M A I N , A D V N C E , D I F F , G A U S S N , ANORM,
and A M I G R .
Y C O U N T t h e c u r r e n t number o f a d v a n c e s .
M D I F F f l a g u s e d t o c a l l D I F F ; 1 means r c y e s r r , 0 means rrfi
MPLTFIP f l a s u s e d t o c a l l P U N C H ; 1 means I t y e s r t , 0 means ’’
I
- 1 5-
MDLOOP f l a g used t o c a l l DELOOP; 1 means r f y e s f l , 0 means
MTYPE f l a g used t o s p e c i f y d i f f e r e n t t y p e s o f s o u r c e s ;
means '!dual e v a p o r a t i o n sources" , 2 means " h e m i s
c a l v a p o r s o u r c e f 1 , 3 means " c o n e s o u r c e f 1 , 4
D R , D L , DW f r e q u e n t l y used i n t e r n a l p a r a m e t e r s ; t o ca lcu-
l a t e t h e g r o w t h r a t e i n p l a n e t a r y s o u r c e .
t f n o f f .
1
s h e r i -
means
RSL o n l y used i n p l a n e t a r y sou rce , t h e d i s t a n c e be tween t h e
p o s i t i o n of t h e s u b s t r a t e and t h e p l a n e t r o t a t i n g a x i s .
AIM, CSTHET f r e q u e n t l y used i n t e r n a l p a r a m e t e r s ; t o b a l c u -
l a t e t h e g r o w t h r a t e i n p l a n e t a r y source.
/PRFILE/
common t o CONTROLLER, and PROFIL
T X Z c o n p l e x a r r a y c o n t a i n i n g t h e x and z p o s i t i o n s o k t h e
4 0 p o s s i b l e t u r n i n g p o i n t s u s e d t o s e t t h e i n i t i a l pro-
f i l e .
NT number o f t u r n i n g p o i n t s o f t h e i n i t i a l p r o f i l e .
/ SAVE RT/
common t o GROTBL, and EVALUE I ~
X P , XY o n l y used i n p l a n e t a r y s o u r c e , a r r a y c o n t a i n i n b t h e
t e m p o r a r y r e s u l t s o f g r o w t h r a t e i n x d i r e c t i o n .
Z P , ZM o n l y u s e d i n p l a n e t a r y sou rce , a r r a y c o n t a i n i n g t h e
t e m p o r a r y r e s u l t s o f g r o w t h r a t e i n z d i r e c t i o n . ~
1 /SUMCON/
common t o I N I T L Z , and SUM
-16-
#
c1, c2, c4, c5 f r e q u e n t l y u s e d i n t e r n a l p a r a m e t e r s ; t o
c u l a t e t h e g r o w t h r a t e i n p l a n e t a r y s o u r c e .
/SYSTEM/
common t o CONTROLLER, I N I T L Z , DPMESG, and EVRATE.
GAMMA
BETA
P H I
sw
RP
MRSL
o n l y u s e d i n p l a n e t a r y s o u r c e , t h e a n g l e betweel
sys t em c e n t r a l a x i s and t h e p l a n e t r o t a t i n g a x i s .
o n l y u s e d i n p l a n e t a r y s o u r c e , t h e t ilt a n g l e 01
p l a n e t p l a n e .
o n l y u s e d i n p l a n e t a r y s o u r c e , t h e a n g l e betweei
p o s i t i o n of t h e s u b s t r a t e and t h e p l a n e t a x i s .
o n l y used i n p l a n e t a r y s o u r c e , t h e l e n g t h o f t h e :
c e n t r a l a x i s .
o n l y used i n p l a n e t a r y s o u r c e , t h e l e n g t h o f t h e 1
ca l -
t h e
t h e
t h e
i s t en
- ane -
t a r y r o t a t i n g a x i s .
f l a g used t o c o n t r o l i n p u t f o r m a t i n p l a n e t a r y sou rce ;
1 means l l s p e c i t - y t n e p o s i t i o n 01- S u D s t r a c e D Y rmii i , u
means " s p e c i f y t h e p o s i t i o n of s u b s t r a t e b y RSL".
-17-
X . EXPERIMENT
I n an e f f o r t t o v e r i f y t h e m o d e l s u s e d i n t h e
A 1 e v a p o r a t i o n s were p e r f o r m e d i n vacuum a t room t e m p e r a t u r e .
The p r o c e s s i n g s e q u e n c e i s shown i n F i g . 1 6 , and a l s o i n
a p p e n d i x . A p h o t o l i t h o g r a p h i c m a s k i n g p a t t e r n ( F i g . 17)
s i s t i n g of v a r y i n g l i n e w i d t h s and spaces (1-50ym) was u s e d
t h i s e x p e r i m e n t .
1
s i m u l a t o r ,
t h e
con-
i n
r i ed o u t a t 1 2 O O 0 C and u s e d d r y o x y g e n - w a t e r v a p o r g a s e s
s e q u e n t i a l l y . After d e l i n e a t i o n , t h e S i s u b s t r a t e waiS p r e -
f e r e n t i a l l y e t c h e d t o form < 1 1 1 > s t e p s . Then t h e o x i d e o l t o p
o f t h e s u b s t r a t e was r emoved . Aluminum l a y e r (0.6-l .Op/n) was I
e v a p o r a t e d on t o p o f t h e s u b s t r a t e wh ich was mounted on a
p l a n e t a r y f i x t u r e . The S i s t e p s were o r i e n t e d e i t h e r p a i r a l l e l
or p e r p e n d i c u l a r t o t h e A 1 f l u x .
S a m p l e s were c l e a v e d a c r o s s s i l i c o n s t e p s t o examine1 s t e p
a n g l e s and d e p o s i t i o n p r o f i l e s . S c a n n i n g e l e c t r o n micr loscope
was used i n e x a m i n i n g c r o s s s e c t i o n s and s u r f a c e topogi raphy.
The SEM p h o t o g r a p h s and c o r r e s p o n d i n g s i m u l a t i o n r e s u l i t s a r e
shown i n F i g . 18 .
-1 8-
XI. C O N C L U S I O N
I n t h i s r e p o r t , t h e p r o b l e m of s t e p c o v e r a g e is ex4mined
t h r o u s h a s i m u l a t i o n p r o g r a m . A good s t e p c o v e r a g e may qe ob-
t a i n e d by t h e o p t i m i z a t i o n o f s o u r c e - s u b s t r a t e c o n f i g u r a t i o n i n
a d e p o s i t i o n a p p a r a t u s , b y t h e u s e of e l e v a t e d s u b s t r a t $ tem-
p e r a t u r e , and by t h e c o n t r o l of t h e s u b s t r a t e s t e p p r o f i l e s .
I
- 1 9-
A P P E N D I X : PROCESSING SEQUENCE
1 . S t a r t w i t h < l o o > , 1-5 ohms-cm, p - t y p e , 2" d i a m e t e r S i 1 a f e r
2 . Wafer C l e a n i n g :
3. 10 m i n u t e d i p i n p i r a n h a e t c h (H2SO4:H2o2 5 : 1 )
b . r i n s e i n d e i o n i z e d water f o r 2 m i n u t e s
' c . 20 second d i p i n a q u e o u s e t c h (H*O:HF 1,0:1)
d . r i n s e i n d e i o n i z e d water f o r 2 m i n u t e s
e . blow d r y w i t h N 2
3 . O x i d e Growth: ( t h i c k n e s s : 0.6pm, t e m p e r a t u r e : 1000°C)
a . 5 m i n u t e p u s h i n N2 a t 4 .0 cm
b . 5 m i n u t e d r y O2 a t 6 . 5 cm
c . 100 m i n u t e wet o2 a t 2.0cm (water : 9 7 ' ~ )
d . 10 m i n u t e a n n e a l i n N 2 a t 4 .0 cm
I
e . 5 m i n u t e p u l l i n N 2 a t 4 . 0 cm 1
4 . S t a n d a r d C l e a n :
a . d i p i n p i r a n h a e t c h f o r 3 m i n u t e s
b. r i n s e , blow d r y ( p e r f o r m s t e p 2 ( d ) and ( e ) )
5 . P r e b a k e :
SO°C f o r 15 m i n u t e s
6 . HMDS T r e a t m e n t :
a . 10 m i n u t e HMDS v a p o r b a t h
b. 5 m i n u t e N2 f l o w
7 . P h o t o r e s i s t C o a t i n g :
-20-
ACKNOWLEDGEMENTS
I I w i s h t o e x p r e s s my s i n c e r e t h a n k s t o t h e p e r s o n s a l s soc i -
a t e d w i t h t h e SAMPLE p r o g r a m . I w i s h t o t h a n k P r o f e s s o i r Andy
N e u r e u t h e r who h a s e n c o u r a g e d me and g i v e n me i n s p i r a t i i o n i n
t h i s r e p o r t . Also t h a n k s a r e d u e t o S h a r a d Nandgaonkar ?or h i s
h e l p and s u g g e s t i o n s . I am a l s o d e e p l y g r a t e f u l t o d i c h a e l
O ' T o o l e , S h a n k a r S u b r a m a n i a n , and J o h n R e y n o l d s f o r t h e i i r a s -
s i s t a n c a .
I
~
I e s p e c i a l l y w i s h t o t h a n k my a d v i s o r , Professor i l l i a r n
5 . Oldham, f o r h i s s u p p o r t , g u i d a n c e , and i n s p i l r a t i o n
t h r o u g h o u t my o , r a d u a t e yea r . H i s e n t h u s i a s m and i n d i s p e n s a b l e
a i d were o f 3 r e a t v a l u e t o me.
q
R e s e a r c h s p o n s o r e d b y t h e N a t i o n a l S c i e n c e F o u n d a t i o n
g r a n t ENG77-14560-AOl.
a . s q i r t p h o t o r e s i s t ( A Z 1 3 5 0 5 ) on wafer
b . w a i t f o r 1 0 s e c o n d s
c . s p i n a t 6000 rpm f o r 30 s e c o n d s
d . r emove wafer a f t e r 1 0 s e c o n d s
n o t e : ( i ) o x i d e e t c h r a t e : O.lpm/min
( i i ) water s h e e t s o f f u n p r o t e c t e d s u r f a c e
13. S o f t b a k P :
8 O o C i n N2 f o r 1 5 m i n u t e s
I
9 . Expose : ( c o n t a c t p r i n t i n g )
a . l o a d mask and wafer
b . s e t a u t o m a t i c timer a c c o r d i n g t o l a m p i n t e n s i t y
c . expose
d . u n l o a d wafer and mask
10. D e v e l o p :
a . d i p i n H 0 : A Z D e v e l o p e r 1 : l f o r 1 m i n u t e ( a t 21°C)/
b . r i n s e , b l o w d r y 2
1 1 . I n s p e c t wafers u n d e r m i c r o s c o p e and n o t e c o n d i t i o n :
n o t e : i n case of s e v e r e d e f e c t s , r emove p h o t o r e s i s t and
r e s t a r t from p r e b a k e
12 . P o s t b a k e :
1 2 0 ' ~ f o r 20 m i n u t e s
1 3 . O x i d e E t c h : ~
-21-
1 4 . I n s p e c t wafers u n d e r m i c r o s c o p e : I
n o t e : o x i d e o f u n p r o t e c t e d r e g i o n h a s b e e n e t c h e d cor$-
p l e t e l y b e f o r e r e m o v i n g p h o t o r e s i s t
15. P h o t o r e s i s t S t r i p p i n g :
a . 5 m i n u t e a c e t o n e s t r i p
b. r i n s e , b l o w d r y
15. P r e f P r e n t i a l E t c h :
a . immerse w a f e r i n p r e f e r e n t i a l e t c h a n t o f s i l i c o n
(NH2(CH2)2NH2:C6H4(0H)2:H20 255ml:45g: 120ml) f o r ,3
m i n u t e s a t 115 C 0
b . r i n s e , b l o w d r y
n o t e : (i) use an a s p i r a t o r f o r v a p o r r e f l u x i n g [ 1 7 1 , C181,
[ 191
( i i ) e t c h r a t i o s f o r < 1 1 1 > : < 1 1 0 > : < 1 0 0 > 3:30:50
-7 17. A l u m i n u m E v a p o r a t i o n : ( p r e s s u r e : 8x10 mmHg, c o l d sub-
s t r a t e )
a . rllount w a f e r on a p l a n e t a r y f i x t u r e
b . t u r n on d r i v i n g motor
c . d e p o s i t a luminum f i l m 0 .7 -1 .0 pm
1 3 . S c r i b i n g
1 9 . I n s p e c t d i c e u n d e r s c a n n i n g e l e c t r o n m i c r o s c o p e :
a . s t e p c o v e r a g e p r o f i l e s
b. t h i c k n e s s d i s t r i b u t i o n
c . h i l l o c k s
-22-
I I REFERENCES I
1. I. A . B l e c h , " E v a p o r a t e d F i l m P r o f i l e s o v e r S t e p s i n Sub-
s t r a t e s " , T h i n S o l i d F i l m s , 6 , 113, ( 1 9 7 0 )
2 . I . A . B l e c h , D . B . F r a s e r , S. E . Haszko , I l O p t i r n i z a t i n of
A1 S t e p C o v e r a g e t h r o u g h Computer S i m u l a t i o n and S c a n n i n g Elec-
t r o n M i c r o s c o p y t 1 , J . Vac. S c i . T e c h n o l . , 15, 13, (1978)
3. T . C . T i s o n e , J . B. B i n d e l l , " S t e p Coverage i n t h e yacuurn
D e p o s i t i o n o f T h i n Metal F i l m s t 1 , J . Vac. S c i . T e c h n o l . , 11, 72,
( 1 9 7 4 )
, I
,
4 . J. B. B i n d e l l , T. C . T i s o n e , " S t e p Coverage from an Ex tend-
e d S p u t t e r i n g Source11 , T h i n S o l i d F i l m s , 23, 31, ( 1 9 7 4 )
5. K . H . B e h r n d t , " T h i c k n e s s D i s t r i b u t i o n and S t e p Coverdge i n
a New P l a n e t a r y S u b s t r a t e H o l d e r Geometry1' , J . Vac. S c i . Tech-
n o l . , 9 , 2 , ( 1 9 7 2 )
I I
6 . F . H e g n e r , A . F e u e r s t e i n , l lAluminum-Si l icon M e t a l l i q a t i o n
b y R a t e C o n t r o l l e d Dual EB-Gun E v a p o r a t i o n r 1 , S o l i d S t a t e ,Tech-
n o l . , 21, 49, ( 1 9 7 8 )
7 . J . S. Logan , F. S. Maddocks, P. D . D a v i d s e , " M e t a l Edge
C o v e r a g e and C o n t r o l o f C h a r g e A c c u m u l a t i o n i n RF S p u t t e r q d In -
s u l a t o r s V 1 , IBM J . Res. & D e v e l o p . , 14, 182, ( 1 9 7 0 )
I
8. T . N . Kennedy, l l s p u t t e r e d I n s u l a t o r F i l m C o n t o u r i n g o v e r
S u b s t r a t e Topographyv1 , J . Vac. S c i . T e c h n o l . , 13, 6 , ( 1 9 7 1 6 I
-23-
9 . V. J . S i l v e s t r i , V. L. R i d e o u t , V. M a n i s c a l c o , " A 1 C o v e r a g e
of S u r f a c e S t e p s a t S i 0 2 I n s u l a t e d P o l y c r y s t a l l i n e S i eoun-
d a r i e s : A 1 E v a p o r a t i o n i n Vacuum and Low P r e s s u r e Ar", J . Elec-
t r o c h e m . S O C . , 1 2 6 , 1335, ( 1 9 7 9 )
1 0 . W . G . Oldham, S. N. Nandgaonkar , A . R . N e u r e u t h e r , MI. M .
O ' T o o l e , ,'A G e n e r a l S i m u l a t o r f o r VLSI L i t h o g r a p h y and Et lching
ProcGsses: P a r t I --- A p p l i c a t i o n t o P r o j e c t i o n L i t h o g r d p h y " ,
I E E E T r a n s . E l e c t r o n Devices, ED-26, 717, ( 1 9 7 9 )
1 1 . M . M . O I T o o l e , l l S i m u l a t i o n of O p t i c a l l y Formed Image ~ Pro-
f i l e s i n P o s i t i v e P h o t o r e s i s t " , E l e c t r o n i c Res. L a b . , D d p a r t -
m e n t of E E C S , U . C . B e r k e l e y , ( 1 9 7 9 )
1 2 .
fo r
U . C . B e r k e l e y , ( 1 9 7 8 )
S. N. N a n d g a o n k a r , ' IDesign of a S i m u l a t o r Program ( S h M P L E )
I C F a b r i c a t i o n " , E l ec t ron ic Res. L a b . , D e p a r t m e n t o f ' EECS,
1 3 . R . E . J e w e t t , P . I . H a g o u e l , A . R . N e u r e u t h e r , T . Van
Duzer , " L i n e - P r o f i l e Resist Development S i m u l a t i o n T e c h n i q u e s " ,
Palmer E n g i n e e r i n g and S c i e n c e , 17, 6 , ( 1 9 7 7 )
1 4 . W . G . Oldham, C . S u n g , A. R . N e u r e u t h e r , t l S i m u l a t i o n o f
E v a p o r a t e d D e p o s i t i o n Prof i les1 ' , F i f t e e n t h Symp. o n E l e c t r o n ,
I o n and P h o t o n Bean T e c h n o l o g y , Ex tended A b s t r a c t No. 931 (May
1 9 7 9 )
15. S. N. Lee, R . A. K j a r , l 'SOS I s l a n d Edge P r o f i l e s Fo l o w i n g f O x i d a t i o n " , T h i r t e e n t h Annual P r o c e e d i n g s R e l i a b i l i t y
I S y a p o s i u m , ( 1 9 7 5 ) I
-24-
s
1 6 . S. S. B a i r d , llHot and Cold S u b s t r a t e A 1 Evaporat ionf1
c e s s i n 3 Seminar , Department o f EECS, U. C . Be rke ley , (0
1979)
17. P. I . Hagouel, "X-Ray L i t h o g r a p h i c F a b r i c a t i o n of + lazed
D i f f r a c t i o n G r a t i n g s " , Ph. D. D i s s e r t a t i o n , Department o f EECS,
U. C . Be rke ley , (1976)
18 . Reso iu t ion
Resist f o r Submicron I n t e g r a t e d C i r c u i t s 1 1 , M . S. Tdesis ,
Department o f EECS, U . C . B e r k e l e y , (1977)
19. K . E . Bean, l l A n i s o t r o p i c Etching of S i l i c o n 1 1 , I E E E T rans .
~
'R. Sud , llModelinq and C h a r a c t e r i z a t i o n of High I
E l e c t r o n Devices , ED-25, 1185, (1978)
-25-
SOURCE CODE
program netaln
c *****this version is for f4p compiler on unix pdp 11/70 sys em***** c this program simulates the line edge profile of metalizatioj with c various source-substrate configurations
common/metal/ tetchr,tmout,nmout,angle(2),delt,ntotal 1 common/etchl/ xz(450) ,xmax ,zmax ,npts,cxzl ,cxzr ,nadchk,n/ckout common/mtflaq/ mcount ,mdiff ,mplthp,mdloop,mtype comaon/difusn/ rate(450),siqma common/prfile/ txz(40) ,nt cornmon/chkr/ sminx ,sminz, smaxx ,smax z, x zdelt cownon/system/ gamma,beta,phi ,sw,rp,qrsl comnon/planet/ dr,dl,dw,rsl,aiw,csthet complex xz,cxzl ,cxzr ,txz,rate
xmax=2.0 zrnax=O. SO00
xzdelt=O. 05 sminx=O. 2*xzdelt sminz=0.2*xzdelt smaxx= 1.8*xzdelt smaxz=l .g*xzdelt
n%=4 txz(l)=crnplx(O. ,zaax/2.) tx z ( 2 1 = cmpl x ( xmax / 2 . , zmax / 2 . ) txz( 3)=crnplx(xmax/2. ,zmax) txz( 4 )=cmplx( xmax , zmax) tetchr=-0.005 tmout=30. nmout=3 ntotal=l9/nmout*nmout qpl thp= 1
c mtype: = 1-dual, 2-hemispherical, 3-cone, 4-planetary, c 5-unidirectional source
mtype=2 md iff = 0 sigma= 1 .S*xzdelt rndloop= 0
angle( 1 )= -go . angle(2)=90.
gamrna=30. beta=Q. phi= 15.
-25-
c rnrsl=0 e n a b l e s r s l ; 1 e n a b l e s p h i m r s l = O rsl=O. ~ ~ = 2 5 . r p = 2 5 .
c a l l p r o f i l c a l l dpmain
s t o p end
s u b r o u t i n e p r o f i l
coarnon/etchl/ x z ( 4 5 0 ) ,xmax ,zmax , n p t s , c x z l , c x z r , n a d c h k , corllmon / c h k r / s r n i n x , s m i n z , smaxx , smax z, x zd e l t c o r n m o n / p r f i l e / t x z ( 4 0 ) , n t comDlex x z . t x z . u n i t
c t h i s s e c t i o n c r e a t e s a p i e c e w i s e l i n e a r p r o f i l e c k o u t
2
1
w r ike ( 6 , 1 0 0 ) sminx , s m i n z , smaxx , smax z , x z d e l t 100 f o r ~ a t ~ l h l , / / , 3 x , 6 h s m i n x = , f 7 . 4 , / , 3 x , 6 h s r n i n z ~ , f 7 . 4 , / , 3 ~ ~
h Shsmaxx= , f 7 . 4 , / , 3 x ,dhsmaxz= , f 7 . 4 , / ,3x , 7 h x z d e l t = t f 7 . 4 ) n t empzn t -1 i s t a r t z l do 1 i = l , n t e r n p u n i t = ( t x z ( i + l ) - t x z ( i ) ) / c m p l x ( c a b s ( t x z ( i + l ) - t x z ( i ) ) ,O.)
n = i n t ( c a b s ( t x z ( i + l ) - t x z ( i ) ) / x z d e l t - 0 . 5 ) i f ( ( i s t a r t + n ) .%e. 4 5 0 ) go t o 5 x z ( i s t a r t ) = t x z ( i ) d o 2 j = l , n x z ( i s t a r t + j ) = x z ( i s t a r t + j - 1 ) + u n i t * c r n p l x ( x z d e l t , O . 1 c o n t i n u e i s t a r t = i s t a r t + n + l c o n t i n u e n p t s z i s t a r t x z ( n p t s ) = t x z ( n t ) w r i t e ( 5 , 2 0 ) n t f o r m a t ( / / , 3 x , 3 l h t o t a l n u a b e r of t u r n i n g p o i n t s = , i 5 ) do 3 i = l , n t u x = r e a l ( t x z ( i ) ) u z = a i q a q ( t x z ( i) 1 w r i t e ( 5 , 3 0 ) i , u x , u z
I
c g u a r d a g a i n s t r o u n d i n g e r r o r , f i g u r e 0 . 5 i s a r b i t r a r i l y cho$en
30 f o r m a t ( 3 x , 1 4 h t u r n i n g p o i n t , i 4 , 4 h x = , f 7 . 4 , 4 h z = , f 7 . 4 ,
20
% 7 hm i c r on s 1 3 c o n t i n u e
40 f o r m a t ( 3 x , 1 3 h t o t a l p o i n t s = , i 5 )
5 w r i t e ( 6 , 5 0 > 50 f o r m a t ( 3 x , 3 8 ( l h * ) ,15htoo many p o i n t s )
s t o p end
w r i t e ( 6 , 4 0 ) n p t s
r e t u r n
-27-
2
na s t e p= n t o t a 1 / nmout d e l t= t m o u t / f l o a t ( n t o t a l ) nadv=O
i f ( m p l t h p . e q . 1 ) c a l l p u n c h ( 0 ) c p r o d u c e c a r d s o f t h e i n i t i a l p r o f i l e f o r a h p - p l o t t e r
5
s u b r o u t i n e i n i t l z ( m t y p e 1
comrnon/system/ gamma,beta,phi,sw,rp,mrsl common/rnetal/ t e t c h r , t m o u t , n a o u t , a n q l e ( 2 ) , d e l t , n t o t a l c o m m o n / p l a n e t / d r , d l , d w , r s l , a i w , c s t h e t cornmon/surncon/ c l , c 2 , c 4 , c 5
d e t r a d z 3 . 1 4 15926/180. i f ( m t y p e . n e . 1 ) go t o 2
a n g l e ( 1 ) = d e t r a d * a n g l e ( 1 )
c i n i t i a l i z e a l l t h e p a r a m e t e r s u s e d i n t h e s u b s e q u e n t s e c t i o n s
c “ d e t r a d ” is a c o n s t a n t t o c o n v e r t d e g r e e s t o r a d i a n s I
~
c t h i s i s d u a l - d i r e c t i o n a l d i s c r e t e sources
a n g l e ( 2 ) = d e t r ad* a n q l e ( 2 ) 1
-28-
2 C
if (mtype .ne. 3 ) go to 4
gamma: de t r ad* gamma dr=sw*sin( gamma) dw=sw*cos( gamma) d I= d w+r p aiw=(dr**2+dl*dw)/(sqrt(dr**2+dw**2)*((dr**2+dl**2)**1.5)) csthet=dl/((dr**2+dl**2)**0.5) angle(1) =-atan(dr/dl) angle(2) =-ansle( 1) return
this is a cone source (betaso, rsl=O), a special case of 3 C planetary
4 C
C
5 C
10 1 1
I return I
if (mtype .ne. 2) go to 3 this is a hemispherical vapor source
angle( 1 )=detrad*angle( 1) angle( 2 ) =detr ad* angle( 2 ) return
if (mtype .ne. 4) go to 5 this is a planetary rotating source
g amm a= de tr ad * g a m a beta= detr ad* beta phi= de tr ad* phi I
dr= sw* sin( gamma) dw=sw*cos(gamma) if (mrsl .eq. 1) rsl=rp*tan(phi) dl=dw+rp aiw=(dr**2+dl*dw)/(sqrt(dr**2+dwri2)*((dr**2+dl**2)**l~5)) csthet=dl/((dr**2+dl**2)**0.5) angle( 1 ) =-abs( atan( (dr-rsl)/dl) )-beta I
angle(2) =atan((dr+rsl)/dl)+beta constants cl ,c2,c4,c5 are evaporation systerll dependent paradeters
cl=(dr**2+dw**2)**0.5 c2=dr**2-rs l**2 c4=dl*cos( beta) c5=sin ( beta) call grotbl return
if (mtype .ne. 5 ) go to 10 this is a unidirectional source
angle( 1 )=detrad*angle( 1) angle(2)=angle( 1) return
write(5,ll) format(3x,l5(lh*) ,16hundefined source) stop end
I
I
i
-29-
subroutine
comnon/system/ gamma,beta,phi ,sw,rp ,mrsl common/planet/ dr ,dl ,dw,rsl ,aiw,csthet conmon/metal/ tetchr,tmout,nrnout,angle(2),delt,ntotal detrad=3.1415926/180. write(5,lO)
fornat(//,70(lh-) ,//,2Ox,ghversion 1,5x,l7hseptember 8, 1979, write(5,15)
write ( 6,20)
write( 6,25 1 tetchr
anql=angle(l)/detrad anq2=angle(2)/detrad if (mtype .ne. 5) write(6,30) angl,ang2
30 foraat(5x,l5hincident angle=,f5.1,2x,f5.1,8h degrees,//) if (mtype .eq. 5 ) write(6,31) angl
31 foraat(5x,l5hincident angle=,f5.1,8h degrees,//)
c print pertinent information about the source-substrate configuration
35 foraat(Sx,24hdual evaporation sources,//)
d pm esg ( mt ype ) c echo-print pertinent evaporation-system messages
10 format(////////,20~,38(lh*) ,15h run machine 6 ,38(lh*))/
15
9 1 ) 20 foraat(///,20~,42h--------- system message(runmc6) ---4-----
25 format(5x,l7hdeposition rate= ,f8.5,12h microns/sec,//)i
I h / / ,70 (lh-) )
if (mtype .ne. 1) go to 2 write(5,35>
return
2 if (rntype .ne. 2) go to 3
40 format(5~,2Shhemispherical vapor source ,111 write(5,40)
return
3
45
50 R, .sr sr h
51 52
,e
if (rntype .ne. 3 ) go to 4 write(6,45) format(5x 1 lhcone source , / / I beteap=0. 5 at emp= gamma/ det r ad rsl=O. write(5,SO) sw,rp,rsl,betemp,gatemp foraat(5x, 20hsystea axis length= , f6.1,3h in ,//
5x,20hplanet axis length= ,f6.1,3h in,//, 5x,l5hplanet radius= ,f4,1,3h int//, I
5x,6hbeta= ,f5.1,8h degrees,//, 5x, 6hgama= , f 5.1,8h degrees , / / )
if (gaama .eq. 0.) go to 51 return
format(3x,5(lh*) ,37hfatal error: this is a unidirectio write(5,52)
stop 22h source, input ignored,5(lh*))
-30-
I i f ( m t y p e . n e . 4 ) go t o 5 w r i t e ( 5 , 5 5 ) f o r m a t ( 5 ~ , 2 5 h p l a n e t a r y r o t a t i n g s o u r c e , / / ) w r i t e ( S , 6 0 ) s w , r p f o r m a t ( 5 x , 2 0 h s y s t e m a x i s l e n g t h = , f 6 . 1 , 3 h i n , I / ,
5 x , 2 0 h p l a n e t a s i x l e n g t h = , f 6 . 1 , 3 h i n , / ) ph t em p= ph i / d e t r ad i f (mrsl . e q . 1 ) w r i t e ( 6 , 6 5 ) p h t e q p f o r m a t ( 5 x , 5 h p h i = , f 5 . 1 , 8 h d e g r e e s , / ) I i f (mrsl . e q . 0) w r i t e ( 6 , 7 0 ) rs l
b e t e a p = b e t a / d e t r a d g a tempz ganrma/d e t r ad w F i t e ( 6 , 7 5 ) b e t emp, g a t emp f o r a a t ( S x , 6 h b e t a = , f 5 . 1 , 8 h d e g r e e s , / / ,
5x ,6hqama= , f 5 . 1 , 8 h d e g r e e s , / / ) i f ( (qamma.eq. 0 . ) . a n d . ( b e t a . e q . 0.1 ) go t o 7 6 r e t u r n
format(3~,5(lh*),37hfatal e r r o r : t h i s i s a u n i d i r e c t i o
i f ((mrsl . e q . 1 ) .and . ( p h i .eq.O.) go t o 77 i f ((mrsl . eq . O ) . a n d . ( r s l .eq. 0 . ) go t o 77 r e t u r n w r i t e ( 6 , 7 8 )
s t o p
~ f o r m a t ( 5 x , l 5 h p l a n e t r a d i u s = , f 4 . 1 , 3 h i n , / ) 1
22h s o u r c e , i n p u t i g n o r e d , 5 ( l h * ) )
4
55
60 h
6 5
70
75 &
7 5
77 75
b
5 i f ( m t y p e . n e . 5 ) go t o 90
80 f o r m a t ( 5 x , 2 l h u n i d i r e c t i o n a l s o u r c e , / / I c
w r i t e ( 5 , S O )
a n g l e ( 1 ) = a n g l e ( 1 ) - d e t r a d * 0 . 5 angle(2)=angle(2)+detrad*O. 5 r e t u r n
s p l i t i n c i d e n t a n g l e a p a r t so t h a t shadow e f f e c t c a n b e d e t q c t e d
9 9 85
w r i t e ( 6 , 8 5 ) f o r m a t ( 3 x , 1 6 h s o u r c e u n d e f i n e d ,38 ( 1 h* ) ) stop end
s u b r o u t i n e shadow c c a l c u l a t e r a n g e o f i n c i d e n t a n g l e f o r e v e r y p o i n t o n t h e p r c n o r m a l l y w i ( i ) i s n e g a t i v e , and w f ( i ) i s p o s t i v e
c o m m o n / e t c h l / x z ( 4 5 0 ) , x a a x ,zmax , n p t s , c x z l , c x z r , n a d c h k , common/metal / t e t c h r , t m o u t ,nmout , a n g l e ( 2 ) , d e l t , n t o t a l common/crack/ w i ( 4 5 0 ) , w f ( 4 5 0 ) complex x z , c x z l , c x z r
d e t r a d = 3 . 1 4 1 5 9 2 6 / 1 8 0 . p i = d e t r a d * l 8 0 . d o 2 i = l , n p t s x i = r e a l ( x z ( i ) )
c p i i s c a l c u l a t e d f o r g u a r d i n g a g a i n s t round ino , e r r o r
I
) f i l e ;
r c k o u t
-31-
C C
C C
3
2
C C
C
C C
C C
4
z i = aimag ( x z ( i) ) w i ( i ) = a n g l e ( 1 ) w f ( i ) = a n g l e ( 2 ) do 2 j = l , n p t s x j = r e a l ( x z ( j)) z j = a i m a g ( xz( j ) 1 i f ( j .aq. i ) go t o 2 temp=(xj-xi)/sqrt((xi-xj)**2+(zi-zj)**2) i f ( a b s ( t emp) . g t . 1 .) t e m p = t e m p / a b s ( t e m p ) w t e m p = a s i n ( t e m p ) i f ( j . g t . i ) go t o 3
i f ( z j . g t . z i ) wtemp=-pi-wtemp i f ( w t e m p . g t . w i ( i ) ) w i ( i ) = w t e m p i f ( w i ( i ) . g t . w f ( i ) ) w i ( i ) = w f ( i ) go t o 2
c a l c u l a t e i n i t i a l i n c i d e n t a n g l e , w i ( i ) , m e a s u r e d b e t w e e n z and x z ( j ) t o x z ( i ) ; whose u p p e r l i m i t i s w f ( i )
c a l c u l a t e f i n a l i n c i d e n t a n g l e , w f ( i ) , m e a s u r e d be tween z-a and x z ( j) t o x z ( i ) ; whose lower l i m i t i s w i ( i )
.ax i s
: i s
i f - ( z j . g t . z i ) wtempzpi-wtemp i f (wtemp . I t . w f ( i ) ) w f ( i ) = w t e r n p i f ( w f ( i ) . I t . w i ( i ) ) w f ( i ) = w i ( i ) c o n t i n u e r e t u r n end
I
I
s u b r o u t i n e a d v n c e sum up t h e i n c r e m e n t o f e a c h p o i n t i n x - and z- d i r e c t i o n f b r a s i n g l e t i m e - s t e p
' co!nmon/e t ch l / x z ( 4 5 0 ) ,xmax ,zmax , n p t s , c x z 1 , c x z r , n a d c h k , n c k o u t cornmon/metal/ t e t c h r , t m o u t , n a o u t , a n g l e ( 2 ) , d e l t , n t o t a l c o m m o n / a t f l a g / mcount , m d i f f , m p l t h p ,md loop ,mtype common/d i fusn / r a t e ( 4 5 0 ) , s i g m a complex x z , c x z l , cxzr , r a t e q c o u n t=mcoun t+ 1 c a l l e v r a t e ( m t y p e ) i f ( m d i f f . e q . 1 ) c a l l d i f f
g u a r d a g a i n s t o v e r f l o w i f ( a b s ( a i m a g ( r a t e ( 1 ) ) ) . l t . l . O e - 3 8 ) go t o 1
c a l c u l a t e d e p o s i t i o n r a t e i n t e r n a l l y f o r a c c u r a c y ; d e s p i t e ' t e t c h r '
if (mcount.eq.l)tetchr=tetchr/aimag(rate(l)) a d j u s t l e f t b o u n d a r y a s g r o w t h r e f e r e n c e ; t h i s i m p l i e s a t t f i r s t t ime-step g r o w t h r a t e a t t h i s p o i n t i s ' t e t c h r '
was g i v e n
z t 1 = a i m a s ( r a t e ( 1 1) r a t e ( 1 ) = cmplx ( 0 . , z t 1 1
do 4 i = l , n p t s x z ( i ) = x z ( i)+cmplx(-tetchr*delt*real(rate(i)) , c o n t i n u e
& t e t c h r * d e l t * a i ! n a g ( r a t e ( i) 1 )
ne
-32-
I
r e t u r n 1 wr i t e ( 6 , 2 0 1 mcount 20 f o r m a t ( 3 x , l O ( l h * ) , 3 7 h n o r m a l r a t e i s t o o S m a l l t o e v a p o r a t e ,
4 l x , 7 h a t a d v = , i 3 , 1 6 h a d v a n c e i g n o r e d ) r e t u r n e n d
s u b r o u t i n e e v r a t e ( mtype )
c o m m o n / e t c h l / x z ( 4 5 0 ) ,xmax ,zmax , n p t s , c x z 1 , c x z r , n a d c h k , n c k o u t c e v a l u a t e g r o w t h r a t e f o r v a r i o u s s o u r c e s
i f ( i f l a g . e q . 1 ) go t o 21 i f ( w i ( i ) . g t . a n g l e ( 1 ) ) go t o 2 2 r a t e ( i ) = r a t e ( i ) + c m p l x ( s i n ( a n g l e ( l ) ) , c o s ( a n g l e ( l ) ) )
22 i f ( w f ( i ) . I t . a n g l e ( 2 ) ) go t o 20
2 i f ( m t y p e . n e . 2 ) go t o 3 c h e a i s p h e r i c a l v a p o r s o u r c e
d o 30 i = l , n p t s r a t e ( i) = c m p l x ( ( c o s ( w i ( i ) )-cos( w f ( i> 1 ) /2. ,
!e ( s i n ( w f ( i ) ) - s i n ( w i ( i ) ) / 2 . ) 30 c o n t i n u e
r e t u r n
3 i f ( m t y p e . n e . 3 ) go t o 4 I
-33-
c c o n e s o u r c e , o r a s p e c i a l case o f p l a n e t a r y s o u r c e c = d l / d r d o 35 i = l , n p t s t em= a i w* c s t h e t c t a n w f = c * t a n ( w f ( i ) 1 if ( a b s ( c t a n w f ) . g t . 1 . ) ctanwf=ctanwf/abs(ctanwf) c t a n w i = c * t a n ( w i ( i ) 1 i f ( a b s ( c t anwi ) . g t . 1 . ) c t a n w i = c t a n w i / a b s ( c t a n w i ) dz=abs(asin(ctanwf)-asin(ctanwi1) dx=(l.-(ctanwf)**2)**0.5-(l.-(ctanwi)**2~**0.5 r a t e ( i ) = c m p l x ( - t e m * d x / c , t em*dz)
r e t u r n 35 c o n t i n u e
4 if ( m t y p e . n e . 4 ) go t o 5 c p l a n e t a r y r o t a t i n g source c c a l c u l a t e t h e i n t e g r a t i o n o f e t c h r a t e from s u b s t e n d i n g sol
d o 40 i = l , n p t s d x 2 = e v a l u e ( w i ( i) , O ) + e v a l u e ( w f ( i ) , O > d z 2 = e v a l u e ( w i ( i ) , l ) + e v a l u e ( w f ( i ) , 1 ) r a t e ( i) =crnplx(dx2 , d z 2 )
r e t u r n
do 5 0 i = l , n p t s r a t e ( i) = cmplx ( 0 . , 0 . I i f ( ( w i ( i ) . e q . a n g l e ( l ) ) . a n d . ( w f ( i ) . e q . a n g l e ( 2 ) ) )
40 c o n t i n u e
5 i f ( m t y p e .ne. 5 ) go t o 6
& r a t e ( i ) = c m p l x ( sin((angle(l)+angle(2))/2.), & cos((angle(l)+angle(2))/2.) 1
50 c o n t i n u e r e t u r n
5 w r i t e ( 6 , 4 5 ) 45 f o r m a t ( 3 x , 1 6 h s o u r c e u n d e f i n e d , 3 8 ( l h * ) )
s t o p end
s u o r o UT; i n e c c r e a t e t h e g r o w t h r a t e t a b l e f o r p l a n e t a r y r o t a t i n g s o u r c e
common/rnetal/ t e t c h r , t rnout ,nmout , a n g l e ( 2 ) , d e l t , n t o t a l common/savert/ xp( 1 6 ) , z p ( 1 6 ) , x m ( 1 6 ) ,zm( 1 6 )
d e t r a d = 3 . 1 4 1 5 9 2 6 / 1 8 0 . angmax=gO.*det rad i f ( ( abs ( a n g l e ( 1 ) ) . g t .angmax) .o r . ( abs ( a n g l e ( 2 ) 1 . g t . an
c i f t h e s o l i d a n g l e s u b t e n d e d o n t h e s o u r c e i s 0 , t h e n r a t e
g r 0 r ; o i
c t h e d a t a a r e s t o r e d i n a r r a y s : x p , z p , x m , and zm
& g o t o 5
d o 10 i = 1 , 1 6 xp( i) = O . z p ( i) = O .
.d a n g l e
;max) 1
i s 0
-34-
f ~
I ,
zm( i ) = O . c o n t i n u e i f ( a n g l e ( l l . g e . 0 . ) go t o 30 iangl=-int(an~le(l)*lO.)+l do 20 i = l , i a n q l x m ( i) = e v i n t g ( - f l o a t ( i) /IO., 0. , 0) zm(i)=evintg(-float(i)/lO. ,O., 1 ) c o n t i n u e i f ( a n g l e ( 2 l . l e . O . ) go t o 1 5 i a n g 2 = i n t ( a n g l e ( 2 ) * 10. ) + 1 do 25 i = l , i a n g 2 x p ( i ) = e v i n t g ( O . , f l o a t ( i ) / l O . ,O) zp( i ) = e v i n t g ( O . , f l o a t ( i ) / l O . , 1) c o n t i n u e
f o l l o w i n g s t a t e m e n t s g u a r d a g a i n s t s p u r i o u s g r o w t h r a t e d u e n u m e r i c a l summation e r ro r s , s o t h a t cu rves seen smoother
1 0
t o
20
30
25 C C 1 5
40 35
45
5 50
f u n c t i o n e v a l u e ( wang , i 1 c e v a l u a t e t h e g r o w t h r a t e b y l o o k i n g up and i n t e r p o l a t i n g c t h e d a t a t a b l e c rea ted b e f o r e
c i = O means x - d i r e c t i o n , 1 means z - d i r e c t i o n I
I c ommon/save r t / xp( 1 5 ) , z p ( 1 6 ) , x m ( 1 6 ) ,zm( 1 6 )
i f (wang . I t . 0.1 go t o 10 i a n g = i n t ( wang* 10.) i f ( i . e q . 1 ) go t o 5 v lumax=xp( i a n g + l ) i f ( i a n g .eq. 0) vlumin=O. i f ( i a n g .%e. 1) v l u r n i n = x p ( i a n g ) d v a l u e = a b s ( v lumax-vlumin) * ( a b s ( wang*lO. ) - f l o a t ( i a n g ) i f (vlurnax . g t . 0.) e v a l u e = v l u m i n + d v a l u e i f (v lumax . l e . 0 . ) e v a l u e = v l u m i n - d v a l u e r e t u r n
i f ( i a n g . e q . 0) vlumin=O. i f ( i a n g . g e . 1 ) v l u m i n = z p ( i a n g )
I
~
15
5 vlurnax=zp( i a n g + l )
-35-
go t o 15
i f ( i . e q . 1 ) go t o 20 v l u a a x = x m ( i a n g + l ) if ( i a n g . e q . 0 ) vlumin=O. i f ( i a n 3 . g e . 1) v l u m i n = x m ( i a n g ) go t o 15
20 v lurnax=za( i a n g + l ) i f ( i a n q . e q . 0) vlumin=O. i f ( i a n g . g e . 1 ) v l u m i n = z m ( i a n g ) qo t o 15 end
10 i a n q = i n t ( - w a n g * l O . )
f u n c t i o n e v i n t g ( b e g i n , e n d , i ) c n u n e r i c a l s u a m a t i o n i s u s e d , a c c u r a c y i s p r o p o r t i o n a l t o n a s well c a s c p u t ime; f i g u r o 3 i s a r b i t r a r i l y c h o s e n
n = 3 d e l a = 0 . d n = (end-beg i n ) / f l o a t ( n ) l = n - 1 do 3 j = l , l a = b e g i n + d n * f l o a t ( j) d e l a = d e l a + s u m ( a , i ) c o n t i n u e d e l a r = d e l a + ( sua( b e g i n , i +sum( e n d , i) ) / 2 . ev i n t q = d e l a r * d n r e t u r n end
3
f u n c t i o n s u r n ( a , i )
c o m m o n / p l a n e t / d r ,dl ,dw,rsl , a i w , c s t h e t c o m q o n / s y s t e a / gamrna,beta , p h i , s w , r p ,rnrsl comaon / suacon / c l , c 2 , c 4 , c 5
u p ~ ( c 2 - c ~ * r s l + d l * d w ) * ( c 5 * c ~ - d l * c 4 ) * ( ~ d l / ~ c o s ( a - b e t a ~ ~ * 2 ) b t = c l * ( (c2+d1**2-2.*~3*rsl)**2)*( ( a b s ( c 2 - c 3 * r s l t 2 . - c 3 ! *2)) c 3 = d l * t a n ( a - b e t a )
i f ( a b s ( b t ) . I t . 1 .0e -38) go t o 1
r e t u r n
c c a l c u l a t e t h e g r o w t h r a t e f u n c t i o n i n x- or z- d i r e c t i o n w i t h c t h e g i v e n i n c i d e n t angle
c i = O means x - d i r e c t i o n , 1 means z - d i r e c t i o n ; ' a T is i n c i d e n t a n g l e
& * *0 .5 ) I c n e g l e c t a n y s p u r i o u s r e su l t t h a t may c a u s e o v e r f l o w i
i f ( i .eq . 0 ) s u m = u p * t a n ( a ) / b t I i f ( i . e q . 1 ) s u m = u p / b t I
I
1
C
C C
C
C 3 2
34
C
5 2
50 1
sum=O. r e t u r n end
t h i s s u b r o u t i n e d i f f s e c t i o n h a n d l e s s u r f a c e m i g r a t i o n r e s u l t i n g from h o t s c o m m o n / e t c h l / x z ( 4 5 0 ) ,xmax ,zmax , n p t s , c x z l , c x z r , n a d c h k , common/mtf lag / mcount , m d i f f , m p l t h p , m d l o o p , m t y p e common/d i fusn / r a t e ( 4 5 0 1 , s i g m a d i m e n s i o n t e m ( 4 5 0 ) complex x z , c x z l , c x z r , r a t e , s e g m t l , t e m , a n o r m , t n o r m d e v = 3 . * s i g m a
b s t r a t e c k o u t
d n + a n g e = n p t s / 2
d o 30 i = l , n p t s I
a d j u s t r a t e b y c o n s i d e r i n g m i g r a t i o n d u e t o a d j a c e n t p o i n t s w h e r e v e r w i t h i n 3-s igma r a n g e , i n c l u d i n g b o t h l e f t and r i g h s i d e s
off1 and o f f r d e f i n e volume c e l l a t l o c a l p o i n t x z ( i ) i f ((i.eq.l).or.(i.eq.npts)) go t o 3 2
o f f l = c a b s ( xz( i ) - x z ( i - 1 ) ) / 2 . o f f r = c a b s ( x z ( i ) - x z ( i + l ) ) / 2 .
ad j u s t b o u n d a r y p o i n t s b y m i r r o r image go t o 34
if ( i . eq . 1 ) of f r = c a b s ( x z ( 2 ) - x z ( 1 ) / 2 . i f ( i . e q . 1 ) o f f l z o f f r i f ( i . e q . n p t s ) o f f l = c a b s ( x z ( n p t s ) -xz ( n p t s - 1 ) ) 1 2 . i f ( i . e q . n p t s ) o f f r z o f f l
t e m p l = g a u s s n ( o f f l , s i g m a ) I t e m ( i ) = r a t e ( i)-tnorm*cmplx(cabs(rate(i)) ,O.>
I
segmt=O. c a l c u l a t e d i s t r i b u t i o n from l e f t s i d e ( w i t h i n 3-s igma r a n g e ]
do 5 0 k = l , n r a n g e i f ( i . l e .k) i n d e x l = k - i + 2 i f ( i .le .k) i n d e x r z i n d e x l - 1 i f ( i . 1 e . k ) go t o 5 2 i n d e x l z i - k I i n d e x r = i n d e x l + l I s e g m t l = x z ( i n d e x 1 ) - x z ( i n d e x r ) s e g m t = s e g m t + c a b s ( s e g m t l ) I
w a t e = t e m p l - g a u s s n ( se8mt , s i g m a ) t e m p l = g a u s s n ( s e g n t , s i g m a ) tem( i)=tem(i)+tnorm*cmplx(cabs(rate(indexl)) ,O.>
& * c m p l x ( w a t e , O . ) if ( s e g m t . g t . d e v ) go t o 1 0 c o n t i n u e I
t n o r m = c m p l x ( r e a l ( anorm( i ) ) , -a i rnag( anorm( i ) ) 1
t empr = g a u s s n ( off r , sigma) I
1
& * cmplx ( ( t e m p l + tem pr ) , 0 . )
I
I
f o r m a t ( 3 x , 3 8 ( 1 h * ) , 3 4 h m i g r a t i o n r a n g e o r s igma t o o g r e wr i te ( 6 , 100)
s t o p
c c a l c u l a t e d i s t r i b u t i o n from r i g h t s i d e ( w i t h i n 3-s igma r a n g
100
10 s e q m t = 0 .
-37-
do 70 k = l , n r a n g e i f ( ( i + k ) . g t . n p t s ) i n d e x r z n p t s - ( i + k - n p t s ) i f ( ( i + k ) . g t . n p t s ) i n d e x l = i n d e x r + l i f ( ( i + k ) . g t . n p t s ) go t o 72
7 2
i n d e x r = i + k i n d e x l = i n d e x r - 1 s e g m t l = x z ( i n d e x r l - x z ( i n d e x 1 1 s e g m t = s e g m t + c a b s ( s e g m t l ) wa t e = tern p r - gau s s n ( segm t , s i g m a ) t e m p r = g a u s s n ( s e g m t , s i g m a ) t e m ( i ) = t e ~ ( i ) + t n o r m * c m p l x ( c a b s ( r a t e ( i n d e x r ) ) P O - )
& * c m p l x ( w a t e , O . ) if ( s e g m t . g t . d e v ) go t o 30
go t o 1 70 cdn t i n u e
30 c o n t i n u e
12
d o 1 2 i = l , n p t s r a t e ( i ) = t e ! n ( i ) c o n t i n u e r e t u r n end
f u n c t i o n g a u s s n ( r , s i g m a ) c c
b y u s i n g a p r e s t o r e d d a t a t a b l e found i n a mathematic t e x t b b o k , t h i s s e c t i o n c a l c u l a t e s t h e v a l u e o f g a u s s i a n f u n c t i o n w i t h g i v e n
c ' r ' and ' s i g m a ' common/mtf lag / mcount , m d i f f , m p l t h p ,md loop ,mtype d i m e n s i o n a r e a ( 3 0 ) d a t a a r ea /0 .4602 ,0 .4207 ,0 .~821 ,0 .3446 ,0 .3085 ,0 .2743 ,0 . /2420 ,
h 0.2119,0.1841,0.1587,0.1357,0.1151,0.Og68,0~0808, br 0.0658,0.0548,0.0446,0.0359,0.0287,0.022~,0~0179, h 0.0139,0.0107,0.0082,0.0062,0.0047,0~0035,0.0026, % 0 . 0 0 1 9 , 0 . 0 0 1 3 /
c a l c u a l t e a r e a u n d e r s t a n d a r d d i s t r i b u t i o n c u r v e ( g a u s s i a n c u r v e ) c i f ( r . I t . 0 . ) go t o 3 x = r / s i g m a * l O .
i f ( i x . g e . 30) go t o 1 d a r e a = ( a r e a ( i x ) - a r e a ( i x + l ) ) * ( 1 . - x + f l o a t ( i x ) g a u s s n = a r e a ( i x + l )+dares r e t u r n
r e t u r n
r e t u r n wr i te ( 6 , 200) mcount f o r m a t ( 3 x , 3 8 ( l h * ) , 3 2 h f a t a l e r r o r i n s e g m t c a l c u l a t i o i ,
h l l h a t xadv = , i s>
i x = i n t ( x ) ~
i f ( i x . e q . 0 ) go t o 2 I
2 gaussn=0.4602+0.0398*(1.-~) I 1 g a u s s n = O .
3 200
I
-35-
C
C
C
C C
3
1
2
s t o p end
f u n c t i o n anorm( i)
c o m m o n / e t c h l / ~ ~ ( 4 5 0 ) ,xmax ,zmax , n p t s , c x z l , c x z r , n a d c h k , l c o a r n o n / a t f l a g / mcount , m d i f f , m p l t h p , m d l o o p , m t y p e common / d i f u s n / r a t e ( 4 5 0 ) , s i g m a corllplex x z , c x z l , cxz r , r a t e , a n o r m , x z l , xz r , x z t j = i i f ( j .eq. 1) j = j + l i f ( j .eq. n p t s ) j = j - 1 x z l = x z ( j ) - x z ( j - 1 ) x z r = x z ( j + l ) - x z ( j) x z t = ( x z l + x z r * cmplx ( 0 . , -1 . ) a n o r a = x z t / c a b s( x z t 1 r e t u r n end
c a l c u l a t e normal u n i t v e c t o r a t l o c a l p o i n t i c k o u t
f u n c t i Q n arn iqr ( i ) I
c o m a o n / m t f l a g / mcount , m d i f f , m p l t h p ,md loop ,mtypa I
complex x z , c x z l , cxz r , r a t e , a n o r m j amigr=abs(real(rate(i)*anorm(i))) I r e t u r n I
c a l c u a l t e t h e normal componet o f r a t e ( i ) c o n m o n / e t c h l / x z ( 4 5 0 ) ,xmax ,zmax , n p t s , c x z l , c x z r , n a d c h k , l c k o u t
common/d i fusn / r a t e ( 4 5 0 ) , s i g m a ,
end
s u b r o u t i n e cheker a d j u s t s t r i n g l e q t h s o f t h e p r o f i l e b y a d d i n g or d e l e t i n g p'
c o a m o n / e t c h l / x z ( 4 5 0 ) ,xmax ,zmax , n p t s , c x z l ,cxzr , n a d c h k , common / c h k r / sminx , smin z , smaxx , smax z , x z d e l t complex x z , c x z l , cxz r
remove t h o s e p o i n t s w h i c h a r e o u t s i d e o f t h e l e f t o r r i g h t b o u n d a r i e s
segmtr=real(xz(2)-xz(l)> i f ( s e g m t r . g t . 0 . ) go t o 2 n t m p = n p t s - 1 do 1 i = 2 , n t m p x z ( i ) = x z ( i + l ) c o n t i n u e n p t s z n p t s - 1 \
go t o 3 s e g a t l = x m a x - r e a l ( x z ( n p t s ) 1
i n t s c k o u t
-39-
i f ( s e g m t l . g t . 0.) go t o 4 n p t s z n p t s - 1
C C 4
a s s f o r
go t o 2 uae e a c h t ime checker a d d s l e s s t h a n
c o n v e n i e n c e , f i g u r e ' n p t s / 2 ' is a r b n t e m p = n p t s + n p t s / 2 do 1 0 i = 2 , n t e m p
h a l f o f i t r a r i l y
t h e t o t a l pP c h o s e n
I
) c a l l deleit c a l l add( ill i f - ( ( s e g m t x . l t . s m i n x ) . a n d . ( s e g m t z . l t . s m i n z
i f ( ( segmtx .g t . s rnaxx) . o r . ( s e g r n t z . g t . s a a x z ) 10 c o n t i n u e 6 i f ( ( x m a x - r e a l ( x z ( n p t s ) ) ) . g t . smaxx) go t o 5
5 n p t s = n p t s+l r e t u r n
x n p t s= ( r e a l ( xz( n p t s - 1 ) ) +xmax) / 2 x z ( npts) = c m p l x ( x n p t s ,airnag( xz( n p t s - 1 ) 1) r e t u r n end
i n t s
,e( i)
s u b r o u t i n e d e l e t e ( i)
c o m m o n / e t c h l / x z ( 4 5 0 ) ,xmax ,zmax , n p t s , c x z l , c x z r , n a d c h k , n c k o u t complex x z , c x z l , c x z r if ( i .eq. n p t s ) go t o 16 i e n d = n p t s - 1 d o 1 4 j = i , i e n d x z ( j ) = x z ( j + l )
c d e l e t e l o c a l p o i n t x z ( i ) , and u p d a t e a l l o t h e r p o i n t s
1 4 c o n t i n u e 16 n p t s z n p t s - 1
r e t u r n end
s u b r o u t i n e a d d ( i)
c o m o n / e t c h l / x z ( 4 5 0 ) ,xmax ,zmax , n p t s , c x z l ,cxzr , n a d c h k b n c k o u t complex x z , c x z l , cxz r d o 15 k = i , n p t s l = n p t s + i - k if ( ( 1 + 1 ) . g t . 450) go t o 20 x z ( 1 + 1 ) = x z ( 1) ~
c add o n e p o i n t b e t w e e n x z ( i) and x z ( i - 1 1 , and u p d a t e a l l o t h e r p o i n t s
15 con t i n ue x z ( i ) = ( x z ( i + l )+xz( i -1 ) ) * c m p l x ( O . 5 , 0 . ) I n p t s= n p t s + 1
i = i + l I r e t u r n
f o r m a t ( 3 x , 3 8 ( l h * ) , 2 6 h c a n n o t add a n y more p o i n t s )
c
20 w r i t e ( 6 , 2 5 ) 25
s k i p t h e n e x t p o i n t f o r c h e c k i n g t o a v o i d p o s s i b l e i n f i n i t k v e l o o p
-40-
1
s u b r o u t i n e d e l o o p d e l e t e a l l p o s s i b l e l o o p s ( a f t e r l l d e v e l o p mach ine" ) s p u r i o u s l o o p s v e r y s e l d o r n l y e x i s t ; f o r s a v i n g c o m p u t e r t i m e ! , u s e r s h o u l d n o t u s e it u n t i l h e f i n d s l o o p s i n o u t p u t ; o n l y f o r c o m p l e t e n e s s , this s e c t i o n i s here!
c o v m o n / e t c h l / xz( 450) ,xmax ,zmax , n p t s , c x z l , cxz r , n a d c h k , r coamon/ c h k r / sminx , s m i n z , smax x , smax z , x z d e l t complex x z , c x z l , cxz r n s t a r t= 4 n e n d = 4 n s t e p = l n = n s t a r t n = n + l i f ( n .%e . ( n p t s - n e n d ) ) r e t u r n
C 2
t h e
c k o u t
C
i f ( ( x i n t e r . I t .amax1 ( a m i n 1 ( x n , x n p l ) , a m i n 1 (xm , x m p l ) ) ( x i n t e r . g t .amin 1 (amaxl ( x n , x n p 1 ) , amax 1 ( x m , x m p l ) ) ( z i n t e r .l t . amax 1 ( amin 1 ( zn , z n p 1 ) , amin 1 ( zm , zrnp 1 ) ) ) ( z i n t e r . g t .amin 1 (amax 1 ( z n , z n p 1 ,amax 1 ( zm , zmpl ) )
& & L
x z ( n + l ) = c m p l x ( x i n t e r , z i n t e r )
j s t a r t = n + 2 j s t o p = n p t s - (m- ( n + l ) ) do 3 j z j s t a r t , j s t o p
d e l t e l o o p and u p d a t e o t h e r p o i n t s C
. o r .
.or - o r 1 go t o 2
end
-41-
3 c o n t i n u e n p t s = j s t o p n = n + l
end go t o 1 I
I I I s u b r o u t i n e p l o t ( i o u t p t ) I
c p l o t t h e o u t p u t p r o f i l e s ( a f t e r l * d e v e l o p m a c h i n e " ) common/e t ch l / xz( 450) ,xmax ,zmax , n p t s , c x z l ,cxzr , n a d c h k , b c k o u t c o a m o n / a e t a l / t e t c h r , t a o u t ,nmout , a n g l e ( 2 ) , d e l t , n t o t a l 1 common/ scr a c h/ x ( 450 ) , z ( 450 1 conmon i p l t ( 1 2 3 , 9 9 1
I c!
c t h e o t h e r c o m p u t e r s t h e n e x t s t a t e m e n t works o n pdp-11 c o m p u t e r , i t may n o t work on
I
l o g i c a l * l i p l t i I colnplex x z , c x z l , c x z r I
d i a e n s i o n
d a t a i b l a n k , i p l u s , i s t a r , i z e r o / l h , l h+ , lh* , l hO/ d a t a ichar/lha,lhb,lhc,lhd,lhe,lhf, l h g , l h h , l h i , l h j , l h , l h l , lhm,
i f ( i o u t p t . g t . 26) go t o 99 i f ( i o u t p t . n e . 0 ) go t o 1
o u t t i r n ( 2 6 ) , i c h a r ( 2 6 )
& l h n , l h o , l h p , l h q , l h r , l h s , l h t , l h u , l h v , lhw, l h x , l h y , l hz / k z t = r ) . zb= zaax xr= xmax x 1 = 0 . x a x i s = ( znax /xmax)*96 . i f ( x a x i s . 3 t . 96 . ) x a x i s = 9 6 . nxax i s= i n t ( x a x i s + 3 . 5 ) do 2 1 = 1 , 9 9 do 2 k = 1 , 1 2 3 i p l t ( k , 1) = i b l a n k c o n t i n u e d o 3 k = 1 , 1 2 3 i p l t ( k , l ) = i s t a r i p l t ( k , nxax i s ) = i s t a r c o n t i n u e d o 4 1 = 2 , n x a x i s i p l t ( 1 , l ) = i s t a r i p l t ( 1 2 3 , l ) = i s t a r c o n t i n u e i p l t ( 2 ,2) = i z e r o
i f ( i o u t p t . n e . O ) o u t t i m ( ioutpt)=tmout/float(nmout)*float( i o u t p t ) do 8 k = l , n p t s I
t e m p z = a i l n a g ( x z ( k ) ) - z t i f ( telnpz . qe . zmax 1 nzf l g = 1
-42-
8
9
20
22
99 95
C
I
nz=int((tempz/(zb-zt))*xaxis+2.00001) if ( ( ioutpt .eq .O) .and. ( nx .gt . 1 .and. ( tempx .le .xmax) .and.
if((ioutpt.ne.O).and.(nx.gt.l).and.(tempx.le.xmax)
continue
if( ioutpt .ne.nmout) return write(6,g) xl,xr,zt,zb,(ichar(iout) ,outtim(iout) format(lhx,ghx left = , f8.4,8h microns,/
&
&
. and . ( tern pz . 1 e . zm ax ) ) ipl t ( nx , n z) = ipl us
.and. (tenpz. le .zmax) ) ipl t( nx ,nz) =ichar ( ioutpt)
1 8
( nz.gt . 1 .and.(nz.gt.l)
,iout=l,nmout)
10
2
3
I
subroutine punch( ioutpt) ~
conmon/etchl/ xz(450) ,xmax ,zmax ,npts,cxzl ,cxzr ,nadchk,dckout common/metal/ tetchr ,tmout ,nmout ,angle(2) ,delt ,ntotal 1
common/scrach/ ~(450) ,z( 450) complex xz,cxzl ,cxzr x1z.o zb= - zm ax zt=.O if (ioutpt.ne.0) go to 8 nternp=nmout+ 1 rnout=float( ntemp) I
write(6,l) x1,xmax ,zb,zt ,rnout I format(/ ,4( 1 x ,f8. 5) ,/ , lx ,f8.5) do 10 i=l,npts I x( i) =real( xz( i) ) z ( i)=-aimag( xz( i) ) continue rnpts=float(npts) write(6,2) rnpts format ( 1 x , f9.5) write(6,3) ((x(i) ,z(i)) ,i=l,npts) format( 1 1 (1 x ,f6.3)) return end
I
produce cards for a hp-plotter (after Itdevelop machine11)
I
-43-
x
I
N
c aJ s
a d d 0 m
ail .d F
SOURCE SOURCE
t
I
I I I I I
I D
Z
Fig. 3. A s t e p p r o f i l e with dual evaporation sources
-
Fig. 4. A step profile with a hemispherical vapor source
L
SOURCE
Fig. 5. Schematic planetary evaporator geometry
Z
SUBSTRATE
I
1
Fig. 6. Geometric re la t ionship of source t o substratel
i n a planetary evaporator
1
0
! a C 0
,
0 0
a3 0 5 L
I
I
al 0 k 5 0 v1
a al a E: 3 0 k
ffl al k
CN rl
M R -d
I
3.0um i
Al
3.0um 0
__- --me. l 3 ( a f zwep is deposited wi_tha planetary source. Discontinuities occur at . Si0 island edge caused by the shadowing effect.
2
Fig. 13 (b ) Simulation r e s u l t of two l e v e l metalization. in a unidirectional. smree with v e r t i c a l incidence. evaporated with a planetary source.
The f i r s t l e v e l i s deposited The second l eve l i s
A void i s formed a t the base of the s tep.
e . I
-e .200
-8.488
-8.688
-0.808 0 .
Fig. 14. Simulation result of a step in a hemispherical vapor source. under room temperature. temperature.
Solid line is the deposition Dash line is the same deposition but with elevated substrate
The crack is filled by material migration. ~- _ _ _
-~ ~ ~ ~~
- _ _
i I I 1 I I 1 1 I 1 I 1 I I I I 1 1 I I
- --
-
--
I I I I I I I I I I 1 I I I I
I 1 I I I 1
I I I I I I 1 1 I
I I I I 1
2.000 1.500 0.50e 1.000
........ .......
...... ...
< ................................ ;\:
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....................................
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.....................
..................... .... ...
...................... ..............
....................................
....................................
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... .. ,. . ...........
~-
. . . e .................
....................
;...
. CI
Q)
a
* .
cu .
.
Q
d
a, +J aJ k c, m 5 VI
cd k 0
............
............
.................
. 03 .
(............. .................
.................
.............
.............
.....................
- d
.....................
..
..
..
..
..
.....................
.....................
(u .
3
3
t k 0
rl
" h
d
c v
.I4
v1 d
I
m
Si02
S i
( a ) oxide growth
Si02
Si
(b ) delineate-etch
( c ) p re fe ren t i a l e tch
S i
( d ) oxide removal
( e ) ~l evaporation
Fig. 16. Processing Sequence
2.5"
am B
R -__I_..
. - .--
Fi6. 17- Photolithographic masking pattern
Fig. 18(a) SEM micrograph and computer simulation of asymmetrical step coverage
aluminum
i
Fig. 18(b) SEM micrograph and computer simulation of symmetrical aluminum step coverage
