LUMINESCENCE STUDY OF NON-EQUILIBRIUM EFFECTS IN LASER GENERATED PLASMA

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LUMINESCENCE STUDY OF NON-EQUILIBRIUM EFFECTS IN LASER GENERATED PLASMA

B. Laurich, A. Forchel

To cite this version:

B. Laurich, A. Forchel. LUMINESCENCE STUDY OF NON-EQUILIBRIUM EFFECTS IN LASER GENERATED PLASMA. Journal de Physique Colloques, 1983, 44 (C5), pp.C5-43-C5-47.

�10.1051/jphyscol:1983505�. �jpa-00223085�

LUMINESCENCE STUDY OF N O N - E Q U I L I B R I U M EFFECTS I N LASER GENERATED PLASMA

B . Laurich and A . F o r c h e l

PhysikaZisches I n s t i t u t , TeiZ

U n i v e r s i t d t S t u t t g a r t , P f a f f e w a Z d r i n g 57, 0-7000 S t u t t g a r t 80, F.R.G.

A b s t r a c t - The p r o p e r t i e s o f s u r f a c e g e n e r a t e d e l e c t r o n - h o l e plasma i n S i l i c o n a r e s t u d i e d u s i n g l u m i n e s c e n c e s p e c t r o s c o p y . By d e t a i l e d l i n e shape a n a l y s i s we d e t e r m i n e plasma d e n s i t i e s up t o 2.1019cm-3 f o r 300K a n d ( n s - ) p u l s e e n e r g i e s o f 0.08 J/cm2. We d e m o n s t r a t e t h a t d r i f t e f f e c t s a r e e s s e n t i a l f o r t h e d e s c r i p t i o n o f t h e luminescence.

T y p i c a l plasma d r i f t v e l o c i t i e s a r e a b o u t 4.106cm/s.

F o r t h e d e s c r i p t i o n o f p u l s e d l a s e r a n n e a l i n g (PLA) t w o c o n t r o v e r s i a l models have been used. The s u p p o r t e r s o f t h e "Thermal Model" g e n e r a l l y assume t h a t t h e e x c i t a t i o n e n e r g y i s t r a n s f e r e d i m m e d i a t e l y t o t h e l a t t i c e / l , Z / . I n consequence t h e e n e r g y t r a n s p o r t b y e l e c t r o n - h o l e p a i r s i s u s u a l l y n e g l e c t e d . I n c o n t r a s t a "Nonthermal Model" has been proposed / 3 / w h i c h p r e d i c t s a s i g n i f i c a n t r e d u c t i o n o f t h e m e l t i n g t e m p e r a t u r e by a plasma w i t h a d e n s i t y of t h e o r d e r of 1021cm-3. I f t h o s e d e n s i t i e s a r e t o be a c h i e v e d i n h i g h e x c i t a t i o n e x p e r i m e n t s one has t o assume t h a t r e c o n i b i n a t i o n ( A u g e r e f f e c t ) and d i f f u s i o n a r e s t r o n g l y i n h i b i t e d / 4 / . I n o r d e r t o v e r i f y one o f t h e s e models a w e a l t h o f e x p e r i m e n t a l r e s u l t s i n c l u d i n g r e f l e c t i o n , t r a n s m i s s i o n and Raman d a t a has been p u b l i s h e d 1 5 - 7 1 . From t h e e x p e r i m e n t a l d a t a l a t t i c e and plasma t e m p e r a t u r e s as w e l l as plasma d e n s i t i e s a r e e s t i m a t e d u s i n g s i m p l e c l a s s i c a l models. However, a t t h e h i g h d e n s i t i e s o b t a i n e d i n PLA t h e c a r r i e r system approaches t h e quantum l i m i t and many body e f f e c t s as w e l l as n o n - e q u i l i b r i u m f e a t u r e s a r e e x p e c t e d t o become i m p o r t a n t .

We have used l u m i n e s c e n c e e x p e r i m e n t s o f h i g h l y e x c i t e d S i l i c o n t o s t u d y many body and n o n - e q u i l i b r i u m t r a n s p o r t p r o p e r i t e s o f t h e plasma. Emiss- i o n s p e c t r o s c o p y o f S i i s p a r t i c u l a r l y s u i t e d f o r t h i s i n v e s t i g a t i o n f o r t h e f o l l o w i n g reasons:

- H i g h e x c i t a t i o n e x p e r i m e n t s a t l i q u i d H e l i u m t e m p e r a t u r e show t h e f o r - m a t i o n o f e l e c t r o n - h o l e d r o p l e t s ( E H D ) . The s p e c t r a l shape and t h e band

r e n o r m a l i s a t i o n by many body e f f e c t s a r e i n q u a n t i t a t i v e agreement w i t h t h e o r y / 8 / .

- Above t h e c r i t i c a l p o i n t f o r a d r o p l e t c o n d e n s a t i o n (23K) a non e q u i l i - b r i u m e l e c t r o n - h o l e p l asma (EHP) i s observed/9/.

The s u b j e c t o f t h e p r e s e n t s t u d y i s t o a p p l y t h e methods o f measurement and a n a l y s i s d e v e l o p e d i n l o w t e m p e r a t u r e e x p e r i m e n t s t o PLA c o n d i t i o n s . The exp:rimental s e t u p i s d e s c r i b e d w i t h s p e c i a l emphasis on t h e l a s e r power l i m i t imposed by t h e o n s e t o f s u r f a c e damages. We d e s c r i b e t h e l i n e shape a n a l y s i s and we d e m o n s t r a t e t h a t t h e plasma e x p a n s i o n a l t e r s s i g n i f i c a n t l y t h e e m i s s i o n s p e c t r a . Our a n a l y s i s y i e l d s unexpected h i g h plasma d r i f t v e l o c i t i e s and i m p l i e s t h a t plasma e x p a n s i o n e f f e c t s must n o t be n e g l e c t e d i n any q u a n t i t a t i v e t h e o r y o f PLA.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983505

JOURNAL DE PHYSIQUE

I - Experiment

The samples o f v e r y high p u r i t y Si ( s p e c i f i c r e s i s t a n c e

8000 Qcm) a r e s i t u a t e d i n a t e m p e r a t u r e c o n t r o l l e d dewar ( t e m p e r a t u r e r a n g e 1.8K

- 400K) and e x c i t e d by a f r e q u e n c y d o u b l e d Nd-YAG l a s e r w i t h a p u l s e l e n g t h of 6 5 ns.

The sample s u r f a c e can be m o d i f i e d by s t r o n g 1 a s e r p u l s e s . For l u m i n e s - t e n c e measurements however, t h e sample must not be a l t e r e d . T h e r e f o r e t h e

h i g h e s t l a s e r power t h a t can be used i s c l o s e below t h e t h r e s h h o l d f o r s u r f a c e m o d i f i c a t i o n . Above an e n e r g y d e n s i t y o f 2.0 J/cm2 ( o n e p u l s e ) t h e s u r f a c e i s d e s t r o y e d . The t h r e s h o l d f o r a n n e a l i n g e f f e c t s i d e n t i f i e d by t h e o c c u r a n c e o f c-Si r e g i o n s i n a-Si h a s been d e t e r m i n e d a s 0.32 J/cm2.

In c o n t r a s t t o t h e s i n g l e p u l s e e x p e r i m e n t s s u r f a c e change can be o b s e r v e d a t l o w e r l a s e r p u l s e e n e r g i e s by u s i n g mu1 t i p l e p u l s e s . Hereby t h e s u r f a c e damage c o n s i s t s of r i n g s of r i p p l e s a t t h e edge o f t h e e x c i t a t i o n s p o t and t h i s i s q u i t e d i f f e r e n t t o t h e p a t t e r n s s e e n i n s i n g l e p u l s e e x p e r i m e n t s . The t h r e s h o l d f o r a m u l t i p l e p u l s e s u r f a c e change i s d e t e r m i n e d a s 0.09 J/cm2.

The l u m i n e s c e n c e r a d i a t i o n was d e t e c t e d by a s e l e c t e d i n f r a r e d s e n s i t i v e S 1 p h o t o m u l t i p l i e r and p r o c e s s e d by a photon c o u n t i n g system. The d e t e c t i o n g a t e had a l e n g t h o f 20 ns and was s i t u a t e d a t t h e maximum of t h e l a s e r p u l s e .

11 - Luminescence A n a l y s i s

Fig. 1 shows a s e r i e s of plasma lumines- c e n c e s p e c t r a r e c o r d e d a t d i f f e r e n t b a t h t e m p e r a t u r e s a t t h e e x c i t a t i o n p u l s e e n e r g y o f 0.08 J/cm2. With i n c r e a s i n g t e m p e r a t u r e t h e e m i s s i o n l i n e width i n - c r e a s e s whereas t h e e n e r g e t i c p o s i t i o n of t h e i n t e n s i t y maximum i s unchanged.

From an a n a l y s i s of t h e e x p e r i m e n t a l lumi- n e s c e n c e s p e c t r a w i t h c a l c u l a t e d e m i s s i o n bands a v e r a g e v a l u e s of t h e plasma d e n s i t y and t e m p e r a t u r e a s well a s t h e band r e n o r - m a l i z a t i o n can be d e t e r m i n e d . In t h e f o l l o w i n g a l i n e s h a p e c a l c u l a t i o n used s u c c e s f u l l y f o r t h e d e s c r i p t i o n of t h e 1 ow t e m p e r a t u r e pl asmas i s o u t 1 i ned b r i e f l y w i t h s p e c i a l emphasis on m o d i f i - c a t i o n s n e c e s s a r y f o r t h e c h a r a c t e r i z a - t i on o f t h e non-equi 1 i b r i um pl asmas under P L A c o n d i t i o n s .

1.0 1.1 1.2 1.3

Energy (eV) To a f i r s t a p p r o x i m a t i o n t h e e m i s s i o n l i n e s h a p e o f a band-to-band t r a n - s i t i o n i n an i n d i r e c t gap s e m i c o n d u c t o r i s d e s c r i b e d by t h e c o n v o l u t i o n o f t h e d e n s i t i e s o f o c c u p i e d s t a t e s i n t h e c o n d u c t i o n and t h e v a l e n c e bands.

The d e n s i t i e s of e l e c t r o n s and h o l e s i n t h e bands a r e c h a r a c t e r i z e d by quasi-Fermi l e v e l s . In t h e c a s e o f a m o d e r a t e l y d e g e n e r a t e plasma t h e sum of e l e c t r o n and h o l e q u a s i - F e r m i l e v e l s d e t e r m i n e s t h e emi s s i o n 1 i n e w i d t h whereas t h e c a r r i e r t e m p e r a t u r e can be o b t a i n e d from t h e high e n e r g y t a i l . / l o / . Note t h a t due t o t h e wide r a n g e of t e m p e r a t u r e s t u d i e d t h e e v a l u a - t i o n has t o i n c l u d e t h e e x p l i c i t t e m p e r a t u r e dependence of t h e e f f e c t i v e masses. The e f f e c t i v e masses o f e l e c t r o n s and h o l e s a t 300K a r e l a r g e r by

a b o u t 1 0 % and 30% r e s p e c t i v e l y t h a n t h e i r O K v a l u e s / l l / .

The e n e r g e t i c p o s i t i o n o f t h e low e n e r g y edge of t h e plasma l u m i n e s c e n c e r e l a t i v e t o t h e s i n g l e p a r t i c l e band gap d e f i n e s t h e band gap r e n o r m a l i - z a t i o n due t o many body e f f e c t s . E x t e n s i v e t h e o r e t i c a l and e x p e r i m e n t a l s t u d i e s i n t h e c o n t e x t of e l e c t r o n - h o l e d r o p l e t f o r m a t i o n imply t h a t t h e band r e n o r m a l i z a t i o n i s m a i n l y a f u n c t i o n o f t h e c a r r i e r d e n s i t y b u t u n - s e n s i t i v e t o t h e t e m p e r a t u r e / 8 , 1 2 / . Hence t h e plasma d e n s i t y can be d e t e r - mined from t h e band r e n o r m a l i z a t i o n i n d e p e n d e n t l y from t h e e m i s s i o n l i n e shape.

For t h e low t e m p e r a t u r e E H D e x p e r i m e n t s t h e v a l u e s o f t h e band r e n o r m a l i - z a t i o n o b t a i n e d from t h e e n e r g e t i c p o s i t i o n of t h e e m i s s i o n a r e i n good agreement w i t h t h o s e c a l c u l a t e d from t h e c a r r i e r d e n s i t y .

de have e v a l u a t e d l u m i n e s c e n c e s p e c t r a i n t h e t e m p e r a t u r e r a n g e between 30K and 300K. From t h e l i n e s h a p e f i t s we o b t a i n a plasma d e n s i t y t h a t i s a l m o s t i n d e p e n d e n t of t h e e x c i t a t i o n i n t e n s i t y b u t which i n c r e a s e s approx- i m a t e l y l i n e a r l y w i t h t e m p e r a t u r e . A s i m i l a r b e h a v i o u r h a s been o b s e r v e d f o r low t e m p e r a t u r e E H P i n a v a r i e t y o f s e r n i c o n d u c t o r s / l 3 / .

In Fig. 2 we d e p i c t t h e e x p e r i m e n t a l v a l u e s of t h e band r e n o r m a l i z a t i o n e x t r a c t e d from t h e l i n e p o s i t i o n ( t r i a n g l e s ) t o g e t h e r w i t h t h o s e ex-

p e c t e d t h e o r e t i c a l l y from t h e c a r r i e r -

d e n s i t i e s d e r i v e d from t h e f i t

( s q u a r e s ) / l 4 / . In t h e e n t i r e r e g i o n

i n v e s t i g a t e d t h e t h e o r e t i c a l v a l u e s

of E g a r e s i g n i f i c a n t l y s m a l l e r z

( d i s c r e p a n c y lOmeV - 20meV) t h a n t h e e x p e r i m e n t a l o n e s . In t h e l i g h t of t h e good agreement o f e x p e r i m e n t and p: -

t h e o r y f o r t h e e l e c t r o n - h o l e d r o p l e t s 3 t h i s d i s a g r e e m e n t i s unexpected. In c

t h e f o l l o w i n g we s h a l l d e m o n s t r a t e

t h a t t h i s d i s c r e p a n c y i s due t o t h e

u n j u s t i f i e d use of a q u a s i - e q u i l i b r i u m t h e o r y f o r t h e d e s c r i p t i o n o f t h e pl asma.

r E \ exp rn Eb theor (n exp

I I

1 2 3 L

Carrier Density ( l ~ ~ ~ c r n - ~ )

IV - D r i f t E f f e c t s

In t h e p r e v i o u s t h e o r e t i c a l c o n s i d e r a t i o n s a homogeneous and s t a t i o n a r y plasma s t a t e h a s been assumed. However t h e plasma i s c r e a t e d a t t h e s u r - f a c e of t h e sample and due t o t h e high g r a d i e n t s o f c a r r i e r d e n s i t y and t e m p e r a t u r e i t w i l l expand r a p i d l y i n t o t h e bulk. The f a s t d r i f t l e a d s t o a n e t plasma momentum and t h e r e f o r e a1 t e r s t h e d i s t r i b u t i o n f u n c t i o n s . In a f i r s t a p p r o x i m a t i o n we assume t h a t t h e Fermi s p h e r e s a r e r i g i d l y s h i f t e d i n momentum s p a c e by a v e r a g e d r i f t v e c t o r s k D :

A s t h e 1 umi n e s c e n c e i s d e t e r m i n e d mai n l y by t h e d i s t r i b u t i o n f u n c t i o n s

we e x p e c t s i g n i f i c a n t c h a n g e s f o r d r i f t v e c t o r s c o m p a r a b l e t o t h e Fermi

v e c t o r s .

JOURNAL DE PHYSIQUE

We h a v e r e e v a l u a t e d t h e l u m i n e s c e n c e s p e c t r a i n c l u d i n g t h e d r i f t e d F e r m i -

d i s t r i b u t i o n u n d e r t h e a s s u m p t i o n >

t h a t t h e d e n s i t y i s d e t e r m i n e d m o s t

r e l i a b l y f r o m t h e l i n e p o s i t i o n . T h i s % means t h a t EG i s i n d e p e n d e n t o f

kD a n d a f u n c t i o n o f t h e d e n s i t y

o n l y . T h i s i s c o n s i s t e n t w i t h t h e

v e r y weak k - d e p e n d e n c e o f t h e t h e o -

r e t i c a l b a n d r e n o r m a l i z a t i o n .

2

As shown i n F i g . 3 t h e d i s a g r e e m e n t

b e t w e e n e x p e r i m e n t a l ( t r i a n g l e s ) a n d ;

t h e o r e t i c a l v a l u e s ( s p h e r e s ) o f Eij i s s i g n i f i c a n t l y d e c r e a s e d b y i n c l u d i n g t h e c a r r i e r d r i f t i n t h e e v a l u a t i o n o f t h e s p e c t r a . We o b t a i n t y p i c a l v a l u e s o f 4.106cmIs f o r t h e p l a s m a

E n e r g y (eV

V - D i s c u s s i o n

A Eg exp.

Eb theor. In exp.1

Carrier D e n s i t y ( l ~ l ~ c r n - ~ )

e x p a n s i o n v e l o c i t y i n good a g r e e - m e n t w i t h a n i n d e p e n d e n t m e a s u r e - m e n t b a s e d o n EHP t i m e c o n s t a n t s 1151.

An e x a m p l e o f a l i n e s h a p e f i t i n - c l u d i n g t h e p l a s m a d r i f t i s shown i n F i g . 4. As t h e c a r r i e r s a r e d i s - t r i b u t e d o v e r a w i d e r e n e r g e t i c r a n g e i f d r i f t i s i n c l u d e d 1 i n e shape f i t s w i t h d r i f t e d F e r m i f u n c t i o n s y i e l d s i g n i f i c a n t l y l o w e r d e n s i t i e s a n d s l i g h t l y r e - d u c e d t e m p e r a t u r e s compared t o f i t s a s s u m i n g q u a s i e q u i l i b r i u m . N o t e t h a t t h e a v e r a g e e l e c t r o n i c t e m p e r a t u r e d e r i v e d f r o m t h e f i t

does n o t e x c e e d t h e b a t h t e m p e r a - t u r e b y m o r e t h a n 40K e v e n d u r i n g t h e e x c i t a t i o n p u l s e .

T h r e e i m p o r t a n t r e s u l t s c a n b e d e r i v e d f r o m t h e p r e s e n t s t u d y o f EHP i n S i e x c i t e d t o t h e o n s e t o f ns-PLA:

- T h e a v e r a g e p l a s m a d e n s i t i e s ob- t a i n e d f o r p u l s e e n e r g i e s w i t h i n a f a c t o r o f f o u r b e l o w t h e s i n g l e p u l s e a n n e a l i n g t h r e s h o l d a r e o f t h e o r d e r o f 1019cm-3 ( s e e F i g . 5 ) . T h e s e d e n s i t i e s a r e a p p r o x i m a t e l y t w o o r d e r s o f m a g n i t u d e l o w e r t h a n n e c e s s a r y f o r t h e o n s e t o f p l a s m a d r i v e n i n s t a b i l i t i e s i n t h e phonon s y s t e m ( n o n - t h e r m a l me1 t i n g ) / l 6 / a n d a l s o much l o w e r t h a n r e q u i r e d f o r t h e s c r e e n i n g o f t h e e l e c t r o n -

phonon coup1 i n g / l 7 / .

d u r i n g a l o p s p u l s e t h e p l a s m a o c c u p i e s a volume a b o u t t w i c e as l a r g e a s t h e one e x c i t e d by t h e l a s e r . Hence i n ns as w e l l a s i n p s l a s e r a n n e a l i n g e x p e r i m e n t s r o u g h l y 50% o f t h e e x c i t a t i o n e n e r g y ( f o r 2 Eg e x c i t a t i o n ) l e a v e t h e e x c i t e d r e g i o n . F u r t h e r m o r e t h e f a s t plasma d r i f t s u g g e s t s t h a t t h e d e n s i t y r e d u c t i o n b y d r i f t i s c o m p a r a b l e t o d e n s i t y l o s s e s b y A u g e r r e c o m b i n a t i o n .

- The s m a l l d i f f e r e n c e b e t w e e n t h e l a t t i c e a n d t h e e l e c t r o n i c t e m p e r a t u r e shows c l e a r l y t h a t on a ns t i m e s c a l e t h e e l e c t r o n - h o l e p a i r s h a v e t r a n s - f e r e d t h e i r e x c e s s e n e r g y ( ,lev) t o t h e l a t t i c e . We f i n d no e v i d e n c e o f a h o t p l a s m a p e r s i s t i n g s e v e r a l nanoseconds.

I n summary o u r s t u d y e m p h a s i z e s t h a t t h e p l a s m a c r e a t e d b y h i g h s u r f a c e e x c i t a t i o n m u s t n o t be t r e a t e d b y e q u i l i b r i u m t h e r m o d y n a m i c s b u t t h a t i t s n o n - e q u i l i b r i u m n a t u r e has t o b e c o n s i d e r e d .

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