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NONLINEARITY OF THIN-FILM
SEMICONDUCTOR INTERFEROMETERS DUE TO INTERLAYER BOUNDARY PHOTOEMF AND
ELECTROOPTIC PROCESSES
F. Karpushko
To cite this version:
F. Karpushko. NONLINEARITY OF THIN-FILM SEMICONDUCTOR INTERFEROMETERS
DUE TO INTERLAYER BOUNDARY PHOTOEMF AND ELECTROOPTIC PROCESSES. Journal
de Physique Colloques, 1988, 49 (C2), pp.C2-87-C2-90. �10.1051/jphyscol:1988219�. �jpa-00227636�
NONLINEARITY OF THIN-FILM SEMICONDUCTOR INTERFEROMETERS DUE TO INTERLAYER BOUNDARY PHOTOEMF AND ELECTROOPTIC PROCESSES
F.V. KARPUSHKO
Institute of Physics, BSSR Academy of Sciences. Minsk 220602, USSR
A b s t r a c t
-
The t h i n - f i l m semiconciuct;or i n t e r f e r o n ? c t e r s a r c co~xsiclcred a s d i m e n s i o n a l o p t i c a l and e l e c t r i c s t r u c t i l r e s . It i s s:-lovn L;Ilat i l l b j s t a b l a d e v i c e s b a s e d on ~ ~ and 7 h 3 ~ 5 3 ~serllicollductors t h i n - f i l o l i t ~ t e r f e r o n i e t e r s a s w i t c h i n g t i m e o f-
10-12 s and s w i t c h i n g erlcrgy of 104 p h o t ~ ~ ~ ~ / d e v i c e c a n b e o b t a i n e d .From t h e f i r s t p u b l i c a t i o n / I / and u p t o now / 2 / t h e t h i n - f i l m semiconductor i n - t e r f e r o ~ n e t e r s ( T F I ) b i s t a b l e d e v i c e s h a v e beer, t h e s u b j e c t o f s e r i o u s i n t e r e s t t o r e a l i z e t h e components o f t h e o p t i c a l d i g i t a l coinputers. T h i s p e r s i s t e n t i n t e r e s t i s d e t e r m i n e d by some a t t r a c t i v e p r o p e r t i e s o f o p t i c a l b i s t a b l e ( O B ) d e v i c e s baser1 on TFI /3/. But t o widen t h e p r a c t i c a l u s e of t h e TFI 0 5 d e v i c e s , i t i s n e c e s s a r y t o improve t h e i r k i n e t i c f e a t u r e s . The i n s u f f i c i e n t r e s p o n s e t i m e of t h e T F I i s t h e r e s u l t o f t h e t h e r m a l n o n l i n e a r i t y o f i t s semicorlductor l a y e r s .
The f a s t and s t r o n g n o n l i n e a r i t y o f t h e e l e c t r o n n a t u r e i n TFI c a n be r e a c h - ed o n l y a t narrow s p e c t r a l i n t e r v a l s which c o r r e s p o n d t o t h e s i n g u l a r p o i n t s of t h e e n e r g y band s t r u c t u r e a t t h e i n t r i n s i c a b s o r p t i o n t a i l o f t h e semiconductors used. The q u e s t i o n a r i s e s , what k i n d o f i n t e r a c t i o n siechanistns c o u l d a l l o w t o e x h i b i t t h e s e s i n y l a r i k i e s i n t h e b e s t way.
TO answer t h i s q u e s t i o n , it i s u s e f u l t o c o n s i d e r TFI n o t o n l y a s a dimen- s i o n a l o p t i c a l s t r u c t u r e ( a s compared w i t h t h e l i g h t wavelength) b u t a s a n e l e c - t r i c s t r u c t u r e , t o o ( a s compared w i t h t h e c h a r a c t e r i s t i c s i z e s o f t h e m a t e r i a l s ' e l e c t r i c p a r a m e t e r s ) . A s a n o p t i c a l d e v i c e , t h e TFI i s a system c o n s i s t i n g of a l - t e r n a t i n g l a y e r s w i t h d i f f e r e n t o p t i c a l c o n s t a n t s . The i n t e r n a l s e ~ n i c o n d u c t o r l a er, w i t h t h e complex r e f r a c t i v e i n d e x
3
=n -
L2 ,
h a s g e o m e t r i c a l t h i c l t n e s sI = m h r n / 2 n ,
whereA m
i s t h e wavelength o f t h e i n t e r f e r o m e t e r t r a n s - m i s s i o n peak;n, =
a r e t h e r e a l and i m a g i n a r y p a r t s o f,
r e s p e c t i v e l y ;m
i s t h e i n t e r f e r e n c e o r d e r . For TFI OB d e v i c e s M e q u a l s 1 o r 2, a s a r u l e . Thequarterwave a l t e r n a t i n g l a y e r s w i t h r e a l r e f r a c t i v e i n d i c e s
n 4
andn2
have o p t i - c a l t h i c k n e s s e s4, n, = e2 nl
=Am /4 .
They form d i e l e c t r i c m i r r o r s w i t h r e f r a c t i v i t y R c l o s e t o 1. Only t a k i n g i n t o c o n s i d e r a t i o n t h e a b s o r p t i o n i n s i d e t h e i n t e r n a l semiconductor l a y e r , t h e peak t r a n s n i s s i o n Tm and t h e s p e c t r a l h a l f w i d t h of t h e TFI A 0,s a r e g i v e nArticle published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1988219
C2-88 JOURNAL
DE
PHYSIQUEIt should b e noted t h a t
2%aern/n
( even whenae - - 10 3cm'1). The d i s p e r - s i v e b i s t a b i l i t y o c c u r s i f t h e r e f r a c t i v e i n d e x change i s
For t h e l i g h t beam of wavelength and a r b i t r a r y i n p u t power t h e absorbed power h a s a maximum i f
R -exp(- 2mem T).
Then Eqs. ( 1) and ( 2 ) r e s u l t i nT :
"- 0.25 and AhqS
c4 = X , /n .
I n t h i s c a s e , c l o s e t o t h e optimum, t h e OB o c c u r s i fThus, Eq. ( 4 ) i s a c r i t e r i o n f o r choosing n o n l i n e a r i t y mechanisms which permit r e a l i z i n g OB d e v i c e s based on TFI.
For a system of a l t e r n a t i n g d i e l e c t r i c and semiconductor l a y e r s , such a s TFI, t h e o p t i c a l and e l e c t r i c c o n s t a n t s can d i f f e r widely a s compared w i t h t h e c o r r e s - ponding p r o p e r t i e s of t h e i n i t i a l b u l k c r y s t a l s . T h i s d i f f e r e n c e i s due t o t h e energy b a r r i e r s a r i s e n a t t h e neighbouring l a y e r boundaries. A t y p i c a l example of t h e energy b a r r i e r i s t h e h e t e r o j u n c t i o n a t t h e boundary between t h e i n t e r n a l se- miconductor l a y e r and t h e neighbouring quarterwave l a y e r s . Also, one can p o i n t o u t t h e boundary between t h e semiconductor l a y e r and t h e t h i n metal l a y e r (Shot- t h y ' s b a r r i e r ) i n t h i n - f i l m i n t e r f e r e n c e systems known a s i n t e r f e r e n c e f i l t e r s w i t h induced t r a n s m i s s i o n /4,5/.
The e l e c t r i c p r o p e r t i e s of t h e b a r r i e r domain a r e formed by t h e f i e l d of t h e s p a t i a l charge r e s u l t i n g from t h e achievement of e q u i l i b r i u m between t h e c o n t a c t - i n g m a t e r i a l s / 6 / . The c h a r a c t e r i s t i c s i z e of t h e s p a t i a l charge domain ( ~ e b y e ' s r a d i u s ) i s determined by t h e c a r r i e r c o n c e n t r a t i o n i n s i d e each of t h e c o n t a c t i n g l a y e r s , by t h e i r d i e l e c t r i c p r o p e r t i e s and temperature. A t 3 0 0 ' ~ and t h e concen- t r a t i o n of 10~5-1017 cm-3, t h e t y p i c a l v a l u e s of Debyefs r a d i u s a r e about 0. lp.
It i s j u s t comparable t o t h e geometrical t h i c l t n e s s of t h e TFI l a y e r s . That i s why t h e e l e c t r i c f i e l d of 104-105 ~ / c m i s a p p l i e d t o t h e whole semiconductor l a y e r of t h e TFI. A s a r e s u l t , t h e o p t i c a l c o n s t a n t s
( n , ae
) of t h e l a y e r a r e changed a s compared t o t h e i n i t i a l bulk c r y s t a l c o n s t a n t s by means of Franz-Keldyshfs e f f e c t ( o r o t h e r e l e c t r o o p t i c mechanisns).
The i n f l u e n c e of t h e e l e c t r i c f i e l d on t h e o p t i c a l c o n s t a n t s of a semicon- d u c t o r i s b e s t observed a t s i n g u l a r p o i n t s of t h e energy band s t r u c t u r e
/7/.
A t t h e i n t r i n s i c a b s o r p t i o n t a i l such c h a r a c t e r i s t i c p o i n t s correspond t o t h e i n t r i n -s i c a b s o r p t i o n edge and e x c i t o n s t a t e s . The l a t t e r a r e u s u a l l y seen poorly a t room temperature. Note a l s o t h a t
2Saem/n
i s not l a r g e enough i n t h i s s p e c t r a l a r e a t o s p o i l t h e good f i n e n e s s of t h e TFI. I n t h e c a s e of a doped semiconductor t h e r e i s one more s i n - l a r p o i n t n e a r t h e i n t r i n s i c a b s o r p t i o n edge. T h i s p o i n t i s due t o t h e implanted impurity.The s i n y l a r i t i e s of t h e energy band s t r u c t u r e a r e expressed by s h a r p r e s o - nances and o s c i l l a t i o n s i r l t h e r e f r a c t i v e i n d e x speckrum with magnitudes cl 10'~-10'~. The e l e c t r i c f i e l d a p p l i e d t o t h e semiconductor c r y s t a l changes t h e e n e r g i e s of t h e band s t r u c t u r e c h a r a c t e r i s t i c p o i n t s . A s a r e s u l t , t h e o p t i c a l c o n s t a n t s of t h e setniconductor a r e modulated i n t h e corresponding s p e c t r a l r e g i - ons. These e f f e c t s form t h e ba.sis of t h e e l e c t r o r e f l e c t a n c e and e l e c t r o a b s o r p t i o n methods knolm i n t h e l u o d u l a t i o ~ ~ spectroscopy t e c h n i q u e /7,8/. I n p a r t i c u l a r , one oE t h e m o d i f i c a t i o n s of t h e s e methods i s phoi;oreflectance based on t h e modulation of t h e senticonductor s p a t i a l charge donlain by p h o t o c a r r i e r s g e n e r a t e d a t l i g h t a b s o r p t i o n / 9 / . Thus, t h e r c i s a pliotoinduced e l e c t r o o p t i c mechanism of nonlinea- r i t y i n t h i n - f i l m semiconductor i n t e r f e r e n c e systems. Let t h e TFI b e f a b r i c a t e d f o r
A m
t h a t corresponds t o one of t h e p h o t o r e f l e c t a n c e peaks of t h e i n t e r n a l l a y e r m a t e r i a l . A s n r e s u l t of l i g h t a b s o r p t i o n a tA,
t h e r e o c c u r s t h e genera-r i e r s a r e s e p a r a t e d by t h e f i e l d of t h e s p a t i a l b a r r i e r charge, and photoEbIF a r i s e s . The corresponding response t i m e i s about 10'12 s because t h e c h a r a c t e r i s - t i c c a r r i e r speeds, f o r i n s t a n c e i n ~ 3 semiconductor, a r e 1 0 l l p m / s . ~ 5
/lo/.
T h i s photoEb1F r e d u c e s t h e b a r r i e r p o t e n t i a l and t h e e l e c t r i c f i e l d s t r e n g t h decreases.It l e a d s t o t h e r e a l r e f r a c t i v e i n d e x change
1
h n \ a n d , consequently, t o t h e de- t u n i n g of t h e TFI t r a n s m i s s i o n peak r e l a t i v e t o t h e i n p u t l i g h t wavelength. It was p o i n t e d o u t t h a t Eq. (4) must b e s a t i s f i e d t o reach t h e OB. The a n a l y s i s of t h e d a t a f o r b o t h t h e ae(A)-spectra /11/ and t h e p h o t o r e f l e c t a n c e /12,13/ and e l e c t r o r e f l e c t a n c e /7,8/ s p e c t r a shows t h a t Eq.(4) i s s a t i s f i e d f o r a wide c l a s s of t h ea and
B~ semiconductors.A t f i r s t s i g h t , t h e mechanism of OB i n TFI under c o n s i d e r a t i o n i s based on t h e same photo and e l e c t r o o p t i c p r o c e s s e s which determine t h e o p e r a t i o n of SEEDes /14,15/. However, t h e r e i s a p r i n c i p a l d i f f e r e n c e . The SEEDes u s e t h e e l e c t r i c - f i e l d dependence of t h e a b s o r p t i o n c o e f f i c i e n t w h i l e i n our c a s e d i s p e r s i v e OB i s r e a l i z e d . We b e l i e v e t h i s p e r m i t s u s t o s u b s t a n t i a l l y d e c r e a s e t h e t o t a l power d i s s i p a t e d by t h e OB device.
Now e s t i m a t e t h e energy p r o p e r t i e s of TFI OB d e v i c e s based on t h e pho- toinduced e l e c t r o o p t i c n o n l i n e a r i t y of t h e r e a l r e f r a c t i v e index. Assume t h a t t h e n o n l i n e a r r e f r a c t i v e i n d e x change
] ~ n \
r e q u i r e d f o r t h e d i s p e r s i v e b i s t a b i l i t y i s reached when t h e photoEMF completely compensates t h e b a r r i e r p o t e n t i a lu, .
Thee l e c t r i c b a r r i e r c a p a c i t y i s
C = & E 0 - ,
S( 5 )
e
Dwhere
E,, E
a r e , r e s p e c t i v e l y , t h e vacuum d i e l e c t r i c c o n s t a n t and t h e r e l a t i v e p e r m i t t i v i t y o f t h e medium;ep
i s Debyers r a d i u s of t h e s p a t i a l charge screening, andS
i s t h e s e c t i o n o f t h e l a s e r hoam i n c i d e n t on t h e TFI. To compensate t h e p o t e n t i a l U, i n t h e c a p a c i t y C one i s t o keep t h e ~ l g h o t o l t - c l ~ a r g eHere,
e
i s t h e e l e c t r o n charge, and i s t h e number of g e n e r a t e d e l e c t r o n - h o l e couples. 111 t h e s t e a d y - s t a t e one can w r i t e f o r Nwhere
IobS
i s t h e absorbed i n t e n s i t y , C i s t h e l i g h t v e l o c i t y ,h
i s Planckl s c o n s t a n t , and i s t h e photoEPIF r e l a x a t i o n t i m e c o n s t a n t . E q s . ( 6 ) and( 7 )
g i v e f o r t h e energy absorbed i n t h e TFI d u r i n g t h e t i m e<
A t
E =lo,
U o = l V,h, =o.
8 p ~ t ~ , [,=x,/zn
=O. 1p m ,
Eq. ( 8 ) r e s u l t s i n Iobs'i:-15 2
@ 1 . 4 10 J / ~ I
.
T h i s v a l u e corresponds t o about 5 . 6lo3
absorbed p h o t ~ n s / ~ m 2 which i s c l o s e t o t11e quantum s t a t i s t i c l i m i t .The r e l a x a t i o n t i m e c o n s t a n t
<
of t h e photoE?IF i s determined by t h e pro- c e s s e s t a k i n g p l a c e i n t h e b a r r i e r a r e a of any r e c t i f y i n g e l e c t r i c c e l l a t f o r - ward b i a s v o l t a g e / 6 / . F i r s t of a l l t h e s e p r o c e s s e s a r e t h e c a r r i e r t r a n s f e r over t h e b a r r i e r , t h e t u n n e l c a r r i e r t r a n s f e r through t h e s p a t i a l charge domain, and t h e c a r r i e r recombination c o l l i s i o n s i n s i d e t h e s p a t i a l c h a r g e domain. The f i r s t and t h e second p r o c e s s e s have t h e d i f f u s i o n n a t u r e and t h e i r c h a r a c t e r i s b i c t i m e s a r e t h e t i m e s of c a r r i e r t r a n s i t over t h e d i s t a n c eeD .
For TFI l a y e r s , say f o r doped GaAs and InP l a y e r s , t h e s e t i m e s a r e of about 1 0 ' ~ ~ - 1 0 ' ~ ~ s. Tile recontbina- t i o n time i s u s u a i l y g r e a t e r tlian Lhese values. But one shoulcl n o t e t h a t t h e r e -C2-90 JOURNAL
DE
PHYSIQUEcombination p r o c e s s i t s e l f d o e s n o t change t h e photoEMF b e c a u s e t h e l a t t e r i s t h e r e s u l t o f t h e c h a r g e s e p a r a t i o n a l o n e . That i s why t h e r e c o m b i n a t i o n r a t e d o e s not c h a r a c t e r i z e t h e OB d e v i c e o p e r a t i o n r a t e . To r e a c h a h i g h o p e r a t i o n r a t e , primary c o n s i d e r a t i o n must b e g i v e n t o t h e c r e a t i o n o f b a r r i e r l a y e r s w i t h o u t d e e p t r a p s c a p a b l e of l o c a l i z i n g s e p a r a t e d c a r r i e r s . The h e t e r o - and p i n - d i o d e s w i t h t h e r e s p o n s e t i m e o f 1 0 - l 2 s a r e e x c e l l e n t examples of such f a s t s y s t e m s i n photo- e l e c t r o n i c t e c h n o l o g y
/lo/.
Tile above e s t i m a t e s o f s w i t c h i n g e n e r g y and o p e r a t i o n r a t e s o f T F I OB d e v i - c e s w i t h t h e photoinduced e l e c t r o o p t i c r e a l r e f r a c t i v e i n d e x n o n l i n e a r i t y a r e c l o s e t o t h e fundamental l i m i t s . We b e l i e v e t h i s w i l l permit them t o compete suc- c e s s f u l l y w i t h o t h e r a l l - o p t i c a l d e v i c e s and, p a r t i c u l a r l y , w i t h e l e c t r o n i c i n - f o r m a t i o n p r o c e s s i n g d e v i c e s .
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/lo/
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