THE ELECTRONIC STRUCTURE OF HEAVILY DOPED ION IMPLANTED LASER ANNEALED SILICON : ELLIPSOMETRIC MEASUREMENTS

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THE ELECTRONIC STRUCTURE OF HEAVILY DOPED ION IMPLANTED LASER ANNEALED SILICON : ELLIPSOMETRIC MEASUREMENTS

L. Viña, C. Umbach, A. Compaan, M. Cardona, A. Axmann

To cite this version:

L. Viña, C. Umbach, A. Compaan, M. Cardona, A. Axmann. THE ELECTRONIC STRUC- TURE OF HEAVILY DOPED ION IMPLANTED LASER ANNEALED SILICON : ELLIPSO- METRIC MEASUREMENTS. Journal de Physique Colloques, 1983, 44 (C5), pp.C5-203-C5-208.

�10.1051/jphyscol:1983532�. �jpa-00223117�

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THE ELECTRONIC STRUCTURE OF HEAVILY DOPED ION IMPLANTED LASER

ANNEALED SILICON : ELLIPSOMETRIC MEASUREMENTS

L . Viiia, C . Umbach, A . cornpaan+, M. Cardona and A. Axmann*

Max-PZanck-Insti-tut f a r FestkOrperforschung, H e i s e n b e r g s t r . 1, 7000 S t u t t g a r t 80, F.R.G.

' F r a u n k o f e r - I n s t i t u t f a r Angewandte F e s t k O r p e r p k y s i k , E c k e r s t r . 4 , 7800 F r e i b u r g , F.R.G.

R'esum5

-

Les s t r u c t u r e s El e t E2 des c o n s t a n t e s optiques du s i l i c i u m o n t Gt'e abondamment u t i l i s ' e e s durant l e s v i n g t d e r n i e r e s annges pour + t u d i e r l e s ' e t a t s 'electroniques ( s t r u c t u r e s de bandes) de c e semi-conducteur. Nous avons mesur'e c e s s t r u c t u r e s dans l e s i l i c i u m dop6 type n e t p par implantation ionique e t r e c u i t au l a s e r e t dans l e s i l i c i u m dope en volume en f o n c t i o n de l a concentration de p o r t e u r s l i b r e s . Les mesures o n t 6 t 6 r g a l i s g e s avec un e l l i p s o m e t r e automatique d analyseur tournant dans l e domaine 2-6 eV. Les s t r u c t u r e s s o n t d'eplac'ees vers l e rouge e t Glargies avec l'augmentation de l a concentration des p o r t e u r s , mais de facon ind'ependante du type

n

ou p.

Les 5 c h a n t i l l o n s implant& e t r e c u i t s conduisent .S des r 6 s u l t a t s qui c o r r e s - pondent d ceux du matsriau dopg en volume. 11s nous permettent d ' a t t e i n d r e des niveaux de dopage bien plus elevgs que ceux du mat@riau dope en volume.

A b s t r a c t

-

The El and E2 s t r u c t u r e s i n t h e o p t i c a l c o n s t a n t s of s i l i c o n have been profusely used during t h e l a s t 20 y e a r s f o r studying t h e e l e c t r o n i c s t a t e s (band s t r u c t u r e ) of t h i s semiconductor. We have measured these s t r u c - t u r e s i n bulk and ion implanted l a s e r annealed n- and p-type s i l i c o n a s a f u n c t i o n of c a r r i e r concentration. The measurements were performed with an automatic r o t a t i n g a n a l y s e r e l l i p s o m e t e r i n t h e range 2-6 eV. The s t r u c t u r e s r e d - s h i f t and broaden with increasing c a r r i e r c o n c e n t r a t i o n , but independently of type.

The l a s e r annealed samples y i e l d r e s u l t s which j o i n smoothly with those f o r t h e bulk samples. They enable us t o reach doping l e v e l s much higher than those f o r bul k samples.

INTRODUCTION

In r e c e n t y e a r s much i n t e r e s t has a r i s e n i n obtaining high concentrations of impuri- t i e s i n semiconductors s i n c e t h i s a f f e c t s t h e c h a r a c t e r i s t i c s and performances of d e v i c e s . From another point of view i t i s very i n t e r e s t i n g t o study t h e changes i n t h e band s t r u c t u r e with doping and t o compare t h e experimental r e s u l t s with theore- t i c a l p r e d i c t i o n s . This could be done with bulk doped m a t e r i a l s up t o c a r r i e r concen- t r a t i o n s of about loz0

,

f o r n-type Ge a c t u a l l y only 4

x

lo1' Such r e l a - t i v e l y low dopings y i e l d changes i n band e n e r g i e s which a r e only of t h e o r d e r of experimental e r r o r s /1,2,3/.

f Permanent a d d r e s s :

Von Humboldt Foundation Fellow, on l e a v e from Kansas S t a t e U n i v e r s i t y , Dept. of Physics, Cardwell H a l l , Manhattan, Kansas 66506, U.S.A.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983532

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C5-204 JOURNAL DE PHYSIQUE

With t h e technique o f i o n i m p l a n t a t i o n and l a s e r annealing one can reach doping con- c e n t r a t i o n s , one o r d e r of magnitude l a r g e r than t h e concentrations o f e l e c t r i c a l l y ac- t i v e i m p u r i t i e s achievable by conventional techniques. We have measured the El

( ~ 3 . 4 eV) and E ( 4 . 2 5 eV) s t r u c t u r e s i n t h e o p t i c a l constants i n pure, b u l k doped, and implanted l i s e r annealed n- and p-type S i as a f u n c t i o n o f c a r r i e r concentration.

A t these h i g h photon energies t h e f r e e c a r r i e r c o n t r i b u t i o n s a r e v e r y small compared t o t h e interband e f f e c t s and do n o t a l t e r t h e p o s i t i o n s o f c r i t i c a l p o i n t s . Thus, d i - r e c t o b s e r v a t i o n o f t h e e f f e c t o f h i g h doping on t h e band s t r u c t u r e and a comparison of t h e e f f e c t o f donors and o f acceptors a r e possible.

EXPERIMENTAL

S i l i c o n s i n g l e c r y s t a l s o f v a r i o u s surface o r i e n t a t i o n s were implanted w i t h As a t doses ranging from 1 t o 5 x 1016 a t 100 t o 350 keV, and B a t doses from 1 x 1015 t o 3 x 10 a t 30 t o 100 keV. The c r y s t a l s were annealed w i t h a XeCl e x c i - 6 mer l a s e r a t 308 nm. The beam was focused i n spots o f about 0.5 x 1.5 mm2. The annealed s u r f a c e was obtained by mu1 t i p l e overlapping l a s e r spots as described i n Ref. 4.

D i e l e c t r i c f u n c t i o n spectra S(w) = f ~ E * ( w ) _- were measured a t room temperature between 2 and 6 eV w i t h an automatic r o t a t i n g analyser e l l i p s o m e t e r s i m i l a r t o t h a t described by Aspnes and Studna /5/. I n b r i e f

-

i t c o n s i s t s o f a l i g h t source (75 X s h o r t - a r c lamp), a 314 m Spex monochromator, Rochon prisms o f c r y s t a l quartz as p % l a r i z i n g elements, a p h o t o m u l t i p l i e r w i t h an S20 response as d e t e c t o r and m i r r o r o p t i c s f o r c o l l i m a t i n g and f o c u s i n g t h e l i g h t . The o u t p u t signal o f t h e p h o t o m u l t i -

p l i e r i s d i g i t i z e d and l a t e r analyzed w i t h t h e help of a mogel 9845 B HP computer.

The measurements were made a t an angle o f incidence o f 67.5

.

The samples were mounted i n a windowless c e l l i n f l o w i n g d r y N t o minimize s u r f a c e contamination. P r i o r t o measurement they were etched i n - s i t u

f g l

lowing t h e p r e s c r i p - t i o n i n Ref. 6. The treatment was repeated u n t i l r e a l - t i m e e l l i p s o m e t r i c measurements showed no more changes and t h e h i g h e s t values o f c 2 a t the E2 s i n g u l a r i t y were obtained /7/. The s p e c t r a were taken immediately afterwards. P s e u d o d i e l e c t r i c func- t i o n s were then c a l c u l a t e d from t h e complex r e f l e c t a n c e r a t i o s u s i n g t h e two-phase model /8/ i n which t h e surface i s t r e a t e d as a simple plane boundary between two homogeneous media.

Some o f t h e spectra o f i o n implanted samples show i n t e r f e r e n c e f r i n g e s i n t h e low energy range up t o 3 eV due t o back r e f l e c t i o n from t h e substrate, b u t t h i s problem i s n o t present i n t h e s p e c t r a l range above t h i s energy. From t h e f r i n g e s we e s t i m a t e t h e t h i c k n e s s o f t h e doped l a y e r t o beQ400 nm. The c a r r i e r c o n c e n t r a t i o n was d e t e r - mined from i n f r a r e d r e f l e c t i o n measurements.

RESULTS AND DISCUSSION

The d i s o r d e r i n t r o d u c e d by doping w i t h "hydrogenic" i m p u r i t i e s s h i f t s and broadens t h e s i n g u l a r i t i e s ( c r i t i c a l p o i n t s ) o f t h e fundamental e l e c t r o n i c spectra o f semiconductors /1-3,9-12/. I n o r d e r t o compare t h e s h i f t s and broadenings we c a l c u l a t e

,,

n u m e r i c a l l y t h e t h i r d d e r i v a t i v e spectra, d' o f t h e complex d i e l e c t r i c f u n c t i o n w i t h r e s p e c t t o t h e photon energy from o u r - e l 1 ip s o m e t r i c data. The r e s u l t s f o r h i g h

z

r e s i s t i v i t y

,. .

^{S i ,}

-

b u l k h e a v i l y B-doped ( p = 4 x

loz0

~ m - ~ ) , and As-implanted ( n = 3 x

loL1

cm-') samples a r e shown i n F i g u r e 1. The spectrum of t h e As-implanted sample i s enlarged by a f a c t o r o f 10. The d e r i v a t i v e s show c l e a r l y a r e d s h i f t o f t h e ener- g i e s o f t h e E and t h e E c r i t i c a l p o i n t s from t h e pure t o t h e h i g h e s t doped sample, w i t h a corresbonding inc6ease i n t h e i r L o r e n t z i a n width,

r .

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t o g e t a good f i t we a l s o account f o r e x c i t o n i c e f f e c t s . U s u a l l y one assumes t h a t t h e e x c i t o n i c e f f e c t mixes a c r i t i c a l p o i n t w i t h another /13/. A m i x t u r e of a two dimen- s i o n a l minimum and saddle p o i n t was used t o f i t t h e

El

data.

F o r t h e E, s i n g u l a r i t y we have used as c r i t i c a l p o i n t a one-dimensional maximum. Both, d3"

r e a l and imaginary p a r t o f

-2,

were f i t t e d . dw3

50 ~ 1 0 ' ~ 1

fl Si pure

Si

As doped, implanted

n = 3 x 1 0 ~ '

-

"El

F i g . 1

-

T h i r d d e r i v a t i v e spectra o f c 2 o f f o l l o w i n g S i samples: pure, B-doped 4 x loz0 ~ m - ~ , As-implanted 3 x loz1 ~ m - ~ .

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C5-206 JOURNAL DE PHYSIQUE

The r e s u l t s f o r t h e sample o f F i g u r e 1 a r e summarized i n T a b l e 1. The s h i f t s a r e w i t h r e s p e c t t o t h e c r i t i c a l e n e r g i e s f o r t h e p u r e sample. The s h i f t s t h a t we ob- t a i n e d agree w i t h t h e e a r l i e r r e s u l t s o f Ref. 9 and w i t h s i m i l a r r e s u l t s f o r GaAs

/ l o / .

T a b l e 1

-

C r i t i c a l p o i n t s e n e r g i e s o f t h e Si-samples of F i g . 1

The s h i f t s o f t h e c r i t i c a l p o i n t s El and E2 found f r o m measurements o f many b u l k and i m p l a n t e d samples a r e shown i n F i g . 2. They a r e p l o t t e d v e r s u s 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 a l o g - l o g s c a l e . The e f f e c t o f d o p i n g becomes n o t i c e a b l e f o r c o n c e n t r a t i o n s above 10'' The l a s e r annealed samples p r o v i d e d o p i n g l e v e l s much h i g h e r t h a n t h o s e f o r b u l k samples. They y i e l d r e s u l t s which j o i n smoothly w i t h t h o s e o f t h e b u l k sampl es.

The s h i f t s were f i t t e d t o a power l a w dependence on t h e doping c o n c e n t r a t i o n (AE1,2 ^aN!). I n F i g . 2 t h e b e s t f i t s a r e shown a l s o . They y i e l d a s h i f t p r o p o r t i o - n a l t o N ~ o ? ' ~ f o r El and ~ f o r t h e E2 s i n g u l a r i t y . i ~ ' ~ ~

AEl (meV) 10

Si- El shift

1o17 lol8 lot9 loz1 1022

F i g . 2

-

E n e r g i e s o f t h e El and E2

lrn

100 AE2 (meV) l o -

1

c r i t i c a l p o i n t s o f S i a t room tem- p e r a t u r e vs. doping. The dashed l i n e i s t h e b e s t f i t t o a

: N

power 1 aw.

0 p-type bak A n-type bulk m p- type Ion implanted

-

.

n-type ion imptanted ^{a / -}

@..o- -. 4.

.,f-:-"2

I <ope= 0.36t0.03 Si - E 2 shift AE2 = E2PUrL- E2,

lo,~i17

^I-f9 ^io20 i : j i i z 2

0 p-lype bu\k Si -El broadening

r n-type bulk & r l = rli

-

^FlPu,.

n p- type ion implanted

.

n- type ion irnpl~nled

1017 lot9 1020 loz1 loz2

Ni t c m 3 )

F i g . 3

-

L o r e n t z i a n broadening parameters

( r l

and r 2 ) of t h e El and E2 c r i t i c a l p o i n t s o f S i a t room t e m p e r a t u r e vs. dop- i n g . The dashed l i n e i s t h e b e s t f i t t o a ~ " o w e r law.

1

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a r e measured w i t h r e s p e c t t o t h e l i n e w i d t h o f t h e p u r e sample a t room temperature.

They a r e a l s o p l o t t e d i n a l o g - l o g s c a l e . The broken l i n e s correspond t o t h e b e s t

f i t s t o a

N;

l a w and y i e l d a ~ dependence f o r El and a ~i ~ . ~ ~ f o r E2. The r e - i ~ ' ~ ~ s u l t s f o r t h e samples o f F i g . 1 a r e summarized i n

able

^{2 .}

T a b l e 2

-

L o r e n t z i a n broadening parameters o f t h e Si-samples o f F i g . 1.

We s h o u l d p o i n t o u t , however, t h a t t h e w i d t h s o f F i g . 3 and T a b l e 2 depend on t h e t y p e o f c r i t i c a l p o i n t chosen f o r t h e f i t . They a r e s m a l l e r by n e a r l y a f a c t o r o f two i f a t h r e e - d i m e n s i o n a l

M2

s i n g u l a r i t y i s t a k e n f o r t h e f i t ( t h i s f i t , however, i s s l i g h t l y worse t h a n t h e 1-dimensional o n e ) .

F o r B-implanted S i t h e r e i s some evidence f o r t h e e f f e c t o f t h e s h r i n k a g e o f t h e l a t t i c e c o n s t a n t w i t h d o p i n g on t h e gaps /15/. It i s seen as an a d d i t i o n a l b l u e s h i f t , o f t h e o r d e r o f 10 meV, o f t h e El peak. T h i s e f f e c t i s n o t seen i n t h e

E2

-

s t r u c t u r e due t o t h e s m a l l e r p r e s s u r e dependence o f t h i s gap: t h e p r e s s u r e c o e f f i -

dE1 dE2

c i e n t s o f t h e two gaps a r e /14/:

a p

⁼5.2 x eV/bar and

a p

= 2.9 x eV/bar.

The e f f e c t i s a l s o n o t seen f o r t h e o t h e r dopants due t o t h e i r s m a l l e r e f f e c t on t h e l a t t i c e c o n s t a n t .

The l o w e s t o r d e r c o n t r i b u t i o n s t o t h e s h i f t s o f F i g . 2 a r i s e f r o m t h e change i n t h e

" v i r t u a l c r y s t a l " p o t e n t i a l ( f i r s t o r d e r p e r t u r b a t i o n ) . T h i s term, p r o p o r t i o n a l t o i m p u r i t y c o n c e n t r a t i o n N i , c o n t r i b u t e s a n o n r i g i d s h i f t o f t h e bands w i t h no l i f e - t i m e broadening. I t has been e s t i m a t e d by p s e u d o p o t e n t i a l c a l c u l a t i o n s u s i n g f o r t h e p e r t u r b a t i o n p o t e n t i a l t h e a n t i s y m m e t r i c p o t e n t i a l o f GaAs /16/. I t s h o u l d be n o t e d t h a t t h i s c o n t r i b u t i o n should change s i g n g o i n g f r o m p- t o t h e n - t y p e case. There i s no e v i d e n c e f o r such an e f f e c t i n F i g . 2. I n a d d i t i o n t h e c a l c u l a t i o n shows t h i s s h i f t t o be an o r d e r o f magnitude s m a l l e r t h a n t h e s h i f t s o f F i g . 2.

The n e x t t e r m i n v o l v e s a second o r d e r p e r t u r b a t i o n v i a a v i r t u a l i n t e r m e d i a t e s t a t e 1171. I n a d d i t i o n t o t h e s h i f t i n t h e c r i t i c a l p o i n t s t h i s t e r m produces a decrease i n 1 if e t i m e ( i n t e r m e d i a t e s t a t e becomes r e a l ) . From n u m e r i c a l c a l c u l a t i o n s o f t h i s t e r m we o b t a i n s h i f t s and broadenings which agree w i t h t h e e x p e r i m e n t a l r e s u l t s . The c o n t r i b u t i o n o f t h i s t e r m i n t h e p e r t u r b a t i o n expansion t o t h e energy s h i f t s and broadenings can b e d i v i d e d i n two extreme c a t e g o r i e s : terms w i t h l a r g e q - t r a n s f e r and w i t h s m a l l q - t r a n s f e r t o t h e v i r t u a l s t a t e . Because o f s c r e e n i n g of t h e f r e e c a r r i e r s ( a t l o w t e m p e r a t u r e s so t h a t kT

-

.- < EF) t h e f o r m e r y i e l d s a s h i f t p r o p o r t i o n a l t o Ni and t h e l a t t e r a N:'%ontribution. Our e x p e r i m e n t a l r e s u l t s f a l l i n between, b u t c l o s e r t o N:l3, i n agreement w i t h o u r c a l c u l a t i o n s /18/.

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C5-208 JOURNAL DE PHYSIQUE

ACKNOWLEDGEMENTS

We would l i k e t o acknowledge t h e h e l p o f Messr. G. K i s e l a i q t h e sample p r e p a r a t i o n , M. B l e e d e r and H. B i r k n e r i n t h e c o n s t r u c t i o n o f t h e d a t a p r o c e s s i n g hardware.

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,

B e r l i n , 1982)

,p.

45.

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- -

17. ALLEN P.B., Phys. Rev. B 18 (1978) 5217.

18. VINA L . , ALLEN P.B. and CARDONA M., t o be p u b l i s h e d .