SPATIAL EXPANSION OF HOT ELECTRON-HOLE PLASMA AT HIGH DENSITY IN CdSe

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SPATIAL EXPANSION OF HOT ELECTRON-HOLE PLASMA AT HIGH DENSITY IN CdSe

A. Cornet, M. Pugnet, J. Collet, Thierry Amand, M. Brousseau

To cite this version:

A. Cornet, M. Pugnet, J. Collet, Thierry Amand, M. Brousseau. SPATIAL EXPANSION OF HOT

ELECTRON-HOLE PLASMA AT HIGH DENSITY IN CdSe. Journal de Physique Colloques, 1981,

42 (C7), pp.C7-471-C7-476. �10.1051/jphyscol:1981757�. �jpa-00221694�

JOURNAL DE PHYSIQUE

Colloque C7, supplément au n°10, Tome 42, oetobve 1981 page C7-471

S P A T I A L EXPANSION OF HOT ELECTRON-HOLE PLASMA AT HIGH DENSITY IN CdSe

A. C o r n e t , M. P u g n e t , J . C o l l e t , T. Amand and M. Brousseau

Laboratoive de Physique des Solides assoaie au C.N.R.S., I.N.S.A., Avenue de Rangueil, 31077 Toulouse Cedex, France

Résumé : Nous présentons la première étude expérimentale du transitoire à I'échelle picoseconde de l'expansion d'un plasma chaud et très dense dans CdSe (en platelet) fortement excité par une impulsion d'un laser YAG (Nd

) à modes synchronisés de durée 30 ps. Nous montrons qu'au-dessus d'une densité critique,

le plasma explose à une vitesse qui est supérieure de deux ordres de grandeur à la valeur de la vitesse de diffusion à l'équilibre thermodynamique. Nous utilisons nos calculs théoriques antérieurs pour analyser les résultats.

A b s t r a c t : We r e p o r t here t h e f i r s t experimental study of t i m e resolved expan- sion in t h e picosecond time s c a l e of h o t e l e c t r o n - h o l e plasma a t very high d e n s i t y generated in CdSe p l a t e l e t s s t r o n g l y e x c i t e d by a mode locked Yag laser pulse of d u r a t i o n 30 p s . We show t h a t above a c r i t i c a l d e n s i t y , t h e plasma ex- pands a t a v e l o c i t y which is two o r d e r s of magnitude g r e a t e r than t h e thermo- dynamic e q u i l i b r i u m d i f f u s i o n v e l o c i t y v a l u e . We use our p r e v i o u s t h e o r e t i c a l work f o r t h e a n a l y s i s of t h e r e s u l t s .

I n t r o d u c t i o n . - I n d i r e c t gap semiconductors t h e e l e c t r o n hole plasma luminescence can be used as a probe f o r t e s t i n g t h e presence of t h e plasma i n a defined r e g i o n o f a sample ; we apply here t h i s i d e a t o t h e h i g h d e n s i t y plasma i n CdSe a t low temperatu- r e , using a p p r o p r i a t e experimental c o n d i t i o n s .

1. Experimental s e t u p . - A complete d e s c r i p t i o n o f o u r experimental apparatus has been p r e v i o u s l y reported [l], [2], [ 3 ] . I n t h e present e x p e r i m e n t s , a picosecond pulse (30 p s ) i s used t o e x c i t e t h e sample ( F i g . 1 ) . The i n t e n s i t y of t h e p u l s e , measured by a p h o t o d i o d e , i s i n t r o d u c e d i n t o a two l e v e l s d i s c r i m i n a t o r which defines a narrow window f o r p u l s e energy. When t h e energy o f t h e e x c i t a t i o n p u l s e f a l l s w i t h i n t h i s energy window, t h e two l e v e l s d i s c r i m i n a t o r a u t h o r i z e s t h e p r o c e s s i n g o f t h e e x p e r i - mental data by multichannel computer. Two photons a b s o r p t i o n a t 1.064 am gives r i s e t o homogeneous e x c i t a t i o n i n CdSe p l a t e l e t s , according t o recent measurements [ 4 ] . The luminescence o f t h e sample i s f o c a l i s e d i n t o a Kerr c e l l which t r a n s m i t s t h e i n - c i d e n t l i g h t o n l y when i t i s e x c i t e d by t h e pulse a t 1.064 urn, t h a t means d u r i n g 30ps, and so are o b t a i n e d the time resolved s p e c t r a . The t r a n s m i t t e d luminescence e n t e r s a monochromator and i s f i n a l l y detected by an o p t i c a l multichannel analyser monitored by t h e energy window d i s c r i m i n a t o r o f t h e e x c i t a t i o n .

The sample i s a p l a t e l e t , grown i n vapor phase, o f t y p i c a l dimensions 1 x 1 x 0.03mm

. We have choosen a t h i n sample f o r two reasons :

- f i r s t , we g e t an homogeneous e x c i t a t i o n ; t h e inhomogeneities i n t h e e x c i t a t i o n a r e less than 10 % between t h e f r o n t s u r f a c e and back s u r f a c e of the p l a t e l e t ;

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981757

C7-472 JOURNAL DE PHYSIQUE

- Secondly, the stimulation i s low i n the detector direction ( Y ) (see Fig. 2 ) and we s h a l l neglect i t i n our calculations.

1

1 kerr cell

mode-locked m

yag laser pulse chopper

I amplifier

ID- -0. ... .. -4. .-- - *.---Q--+

-4 --- - - - - -- ^7Y +-- --a!

4- - - - - - - -

'8; ph0t6iT:;~

Ker r c e l l 7 V

F i g . 1 F i g . 2

The excited region i s a parallelipipedic volume ( 1

0.3

0.03 mm 3 ) ( s e e Fig. 2 ) . The luminescence emerges through a s l i t (width 100 m) i n a black paper which covers P

a l l the back surface of the sample, but, only are detected the photons which spring i n a s o l i d angle of W/100 steradian, i n order t o increase the s p a t i a l d e f i n i t i o n of the luminescent plasma. The principle of the experiment i s t o get a time and wave- length resolution of the luminescence which springs from the back side s l i t f o r va- rious positions X of the excited region (Fig. 2) so t h a t we obtain the space and time resolved luminescence spectrum of the sample. The CdSe p l a t e l e t i s stuck on a copper cold finger i n an optical cryostat. When the incident power i s i n the range

100

P ( I. 5 G W / C ~ ' , the p1 asma density i s given by n=p~b+p~e)-'(~R~)-' (l)

where _[4], e i s the sample thickness, and h $ i s the e x c i t a t i o n photon energy. In t h i s work, i s the two photons absorption c o e f f i c i e n t ; p 2 0 . 0 3 cm/MW f o r h= 1.064 r- m the plasma density i s always calculated using the formula (1) ; when the incident po- wer increases, the exciton l i n e (present a t low e x c i t a t i o n ) disappears a t a density n = 1.5

1017 cm-3, derived i n t h i s way, which i s i n good agreement w i t h previous experimental determination f o r the Mott density 151.

When the incident power P i s lower than 1.5 GW/cm 2 , the l a t t i c e heating due t o l a s e r pulse i s always lower than 15 K [3]. The experimer~ts are performed successively a t TL z (10 - 20 K ) , TL 2: (80 - ^{90 K ) and} TL

300 K.

2. Experimental r e s u l t s and analysis .- ^A. Eipeyimg?tal r e s u l t s . - The figure 3 shows two time resolved luminescence spectra due t o recombination of electron-hole pairs i n the plasma, a s s i s t e d by the emission of an L0 phonon. In the range

300 ~ ~ / c m ~ ( P ( 1.5 ~lrl/cm', the band gap reduction induces a s h i f t of the luminescence

b u t the process i s always the same. I n a

P: I GW /cm2

delay

t 1

685 690 695 nm

wavelength

F i g . 3

Time r e s o l v e d LO-phonon a s s i s t e d plasma luminescence o r i g i - n a t i n g from a non-laser e x c i t e d r e g i o n ( X

275 rm).

I-

F i g . 4

Two p o s t - e x c i t a t i o n d i s t r i - b u t i o n s o f t i m e r e s o l v e d luminescen- ce. -

T h e o r e t i c a l f i t w i t h (8).

d e t a i l e d a n a l y s i s [ Z ] we have shown t h a t a t h i g h plasma temperature, t h e low energy edge i s the renormalized band gap E ' G minus the l o n g i t u d i n a l o p t i c phonon energy 5 m L 0

and the upper edge i s approximately the re- normalized band gap i t s e l f . Consequently, t h i s luminescence i s an evidence f o r t h e presence ( a t t h e p o i n t X) o f h i g h d e n s i t y e l e c t r o n h o l e plasma. The time r e s o l v e d s p a t i a l d i s t r i b u t i o n o f t h e detected lumi- nescence i s s t r o n g l y dependent on the e x c i - t a t i o n : under a t h r e s h o l d Pe, t h e l i g h t springs o n l y from the i n i t i a l l y e x c i t e d re- gion, w h i l e above t h i s c r i t i c a l value Pe, the l i g h t e w r g e s from the whole sample.

Fig. 4 shows the luminescence GXo a t a g i - ven wavelength i n the plasma band vers'us X f o r an i n c i d e n t - t i m e averaged-power

P = 1 GW/cm 2 a t two times tl

50 ps and t2 = 80 ps. The time o r i g i n i s d e f i n e d as the luminescence threshold. When P i s grea-

P = 0.9 ~ w x c m *

,XJC

m-

2

+ u

Y

Q,

U

c

Q, U

U) Q,

S

m-

3 E

-

F i g . 5

Time i n t e g r a t e d luminescence f o r two r e l a t i v e d i r e c t i o n s o f propa- g a t i o n w i t h r e s p e c t t o t h e c - a x i s ( t h e e f f e c t i s s i m i l a r f o r t i m e r e s o l v e d

luminescence).

0

C7-474 JOURNAL DE PHYSIQUE

t e r than a c r i t i c a l value Pe (which i s dependent on t h e r e l a t i v e d i r e c t i o n

w i t h respect t o the c-axis) the l i g h t emerges from t h e whole sample before t h e end o f t h e

2 2

l a s e r pulse. We f i n d Pe ( x / / c ) 2 : 0 . 9 GW/cm and Pe ( x I ' c ) = 0 . 8 GW/cm .

A l l these r e s u l t s a r e s i m i l a r when the experiment i s performed a t TL--10 K and TLW80 K ; on the c o n t r a r y , we cannot d e t e c t any luminescence o u t s i d e o f t h e e x c i t e d r e g i o n when TL- 300 K.

B. fila_lysls.- For a q u a n t i t a t i v e analysis, a d i f f u s i o n model i s used, i n which the d i f f u s i v i t y D i s o n l y a parameter ; the f i t o f the two curves (tl = 50 ps) and ( t 2 = 80 p s ) i n Fig.4 w i t h t h i s model, a1 lows us t o g i v e an o r d e r o f magnitude f o r D.

The s p a t i a l plasma d e n s i t y n ( x ) i n the

d i r e c t i o n depends on the photon d e n s i t y ( l u - minescence) d i s t r i b u t i o n w i t h i n t h e sample v i a t h e s t i m u l a t e d emission process [6] ; t h i s i s a very d i f f i c u l t problem because o f t h e gain s a t u r a t i o n o f s t i m u l a t e d lumi- nescence. E.O. GBbel and a l . [6] proposed a s e l f - c o n s i s t e n t model i n which n ( x ) i s a symetric bell-shaped f u n c t i o n .

Here, f o r s i m p l i c i t y , we assume :

( 2 ) _{n ( x , t} = o ) = N ^{e x p} - + 4 L 2 ^X

where a and N a r e parameters.

The d i f f u s i o n i s governed by :

(3) a 2 n ( x , t )

a t a 7

where D and r a r e t h e "ambipolar d i f f u s i v i t y " and the l i f e t i m e r e s p e c t i v e l y . The so- l u t i o n of (3) w i t h the i n i t i a l c o n d i t i o n (2) i s :

(4) n(x,t)=N &e(2+1*22X ^a ~ t ) - s e r p - { r ~ [ ~ * 2 / r ~ o g ~ ) + 4 ~ t ) )

The luminescence detected i n the Y d i r e c t i o n (Fig. 2) f o r a given wavelength A,is a f u n c t i o n o f

We c a l l IAo ( X , ti) the d i s t r i b u t i o n f u n c t i o n f o r spontaneous lumines- cence i n t e n s i t y a t t i m e t, w i t h &given by -k- EG/

c o n s t a n t ( = l l r n e V ) -

luminescence, we have X0 121 :

l,(&) ~&'+R~,,-E; -2)

(5)

where Mel-ph i s the m a t r i x element f o r t h e electron-phonon i n t e r a c t i o n , Ec i s the k i n e t i c energy o f the e l e c t r o n , fe and fh a r e the Fermi s t a t i s t i c f a c t o r s f o r e l e c - t r o n s and holes r e s p e c t i v e l y , N i s the LO-phonon occupation number a n d - K ~ ~ ~ i s the LO-phonon energy. 9

We s h a l l g i v e l a t t e r an estimate o f the plasma temperature, b u t i n a l l cases, despi- t e i t s h i g h density, t h e h o t plasma i s r a t h e r close a non degenerate s t a t e (because the h i g h e r the e x c i t a t i o n i s , t h e h i g h e r the d e n s i t y i s , b u t the h i g h e r the plasma temperature i s !). If N i s lower than u n i t y , the formula (5) gives :

(6) X , t d exp w h 4 P = ⁿ²

w h e r e y e and P'l are t h e chemical f o r e l e c t r o n s and holes r e s p e c t i v e l y , T

i s the plasma temperature, and k i s the Boltzmann constant.

With (6) and ( 2 ) we obtain :

n L

4 L , 2 2

(7) In0(x,ti)= C [ n ( x t t ~ ) ] =A(ti) e x ? - + X where i = 1 or 2 and A(t:) and C are independent of

L;

bi i s defined by bf/4LO92= (C12/8~og2)+2Dti

Through the s l i t (Fig. 2 ) , the t o t a l measured i n t e n s i t y d i s t r i b u t i o n forX, i s :

X S. @/2

V

P k J X , t i ) = ~ i / I ~ , ( x , I ~ ) =

(8) X - ^&/2

K ~ { , P c ~ ( x + + ) J - P[ F i x - 4)))

Here K, and K, a r e constants, X i s the distance between the centre of the excited

I L

zone and the centre of the s l i t (Fig. 2 ) , f i s the s l i t width and P(z) i s the tabu- lated function :

z

p ) ^{( U ) du .} The best f i t of the experimental data (Fig. 4 ) i s obtained f o r bl

187pm, b2

230ym a t tl and t2 respectively a n d T 2 1 6 0 ps. W de- e duce D 10 cm2/s. This value of 160 ps f o r the parameter 6 r cannot be associated with the spontaneous luminescence only, because the "diffusion" along

i s affected by the stimulation of l i g h t in t h i s direction. The value f o r D i s more than four order of magnitude greater than the conventionnal d i f f u s i v i t y : the electron hole plasma blows up !

3. Discussion.- The mean k i n e t i c energy of the photoexcited electron-hole pairs i s here (2 h v - E f G ) E 0 . 5 eV. When the density i s high enough to permit the internal thermalisation of the plasma, i .e. n)z 1017 cm-3 121, a temperature can be defined ; we have calculated t h e temperature k i n e t i c s , but also the time dependent non- equilibrium distributions f o r the mixed plasmon-L0 phonon modes 171 and f o r TO pho- nons modes.

Four consequences follow from the use of t h i s analysis f o r our experimental r e s u l t s :

- F i r s t l y , we can verify the previous affirmation of non degenerate plasma s t a t i s t i c s in the f i r s t 80 ps (plasma temperature i s always greater than 70 K ) .

- ^Secondly, the knowledge of the plasma temperature allows us t o estimate the thermo- dynamic equilibrium d i f f u s i v i t y , using the Einstein r e l a t i o n . The calculation gives a value f o r Do a t l e a s t four orders of magnitude lower than our experimental values of D ;

- Thirdly, we can calculate the absorption c o e f f i c i e n t (which i s a function of the plasma temperature) and see t h a t the photon t r a n s f e r t [ 8 ] cannot be considered as the iiiain mechanism i n t h i s rapid displacement of the luminescent plasma. Otherwise, the absence of hot luminescence i n the experimental spectra supports t h i s i n t e r p r e t a t i o n ;

- Fourthly, the p a r t played by the non-equilibrium d i s t r i b u t i o n s of phonons i s very important i n the cooling of high density electron hole plasma. Moreover, a t low l a t - t i c e temperature, the plasma expands out of the i n i t i a l l y excited region i n a l a t t i c e w i t h few phonons (except the ones created by plasma cooling) whereas a t high l a t t i c e temperature (TL-300 K ) i t does not expand.

M. Combescot [g] calculated the velocity f o r the expansion of a very dense plasma a t

C7-476 JOURNAL DE PHYSIQUE

T

0 K, using an hydrodynamic model ; i f we use t h i s model h e r e , we obtain a value which i s t h e t e n t h of our experimentally deduced r e s u l t V = g 1 0 . 8 10 cm/s. 8 R. Zimmermanhand M. Rosler c a l c u l a t e d t h e f r e e energy p e r p a i r F i n CdS a t d i f f e r e n t temperatures a s a f u n c t i o n of d e n s i t y [10]. We can c a l c u l a t e t h e p r e s s u r e i n t h e plasma using p

n (L) where N is t h e t o t a l number o f e l e c t r o n - h o l e p a i r s ;

a ^{i.05 n} T,N

when the d e n s i t y i s increased above t h e electron-hole l i q u i d d e n s i t y

( n o w 5.4

1017 c i 3 i n CdSe) t h i s pressure r i s e s up r a p i d l y . This f a c t i s i n good agreement with a plasma expansion.

Conclusion. - We have s t u d i e d t h e s p a t i a l expansion of t h e luminescent e l e c t r o n hole plasma a t high d e n s i t y i n CdSe, using a time, space and wavelength resolved picose- cond photo1 uminescence experiment. The main r e s u l t i s t h a t above a c r i t i c a l d e n s i t y , t h e plasma blow up a t a v e l o c i t y a t l e a s t two o r d e r s o f magnitude g r e a t e r than t h e thermodynamic equilibrium value. A model f o r plasma explosion a t T f. 0 t a k i n g i n t o account t h e non e q u i l i b r i u m d i s t r i b u t i o n o f phonons would be very complex ; we t h i n k t h a t t h e progress i n t h i s f i e l d depends mainly on the f u t u r e experiments i n various m a t e r i a l s t o approach t h e space resolved k i n e t i c s of t h e plasma temperature and non equi l i b r i um d i s t r i b u t i o n s of phonons.

References.-

1 M. Pugnet, A. Cornet, J . C o l l e t , If. Brousseau, B.S. Razbirin, G.V. Michailov, S o l i d S t a t e Comm., 36; 85 (1980)

2 M. Pugnet, These, Univ. Paul S a b a t i e r , Toulouse (1981)

3 J . C o l l e t , M. Pugnet, A. Cornet, M. Brousseau, B.S. Razbirin, G.V. Plichailov, Phys. S t a t u s S o l i d i , 103, 367 (1981)

4 J.H. Betchel and W.L. Smith, Phys. Rev., g, 3515 (1976)

5 N . Volovik and K. Strashnikova, Sov. Phys., S o l i d S t a t e , 20, 94 (1978)

6 E.O. Gtibel , 0. Hildebrand and K. Lohnert, I.E.E.E. Journal of Quantum Electro- n i c s , vol. QE-13, n" 10 (Oct. 1977)

7 J . C o l l e t , A. Cornet, M. Pugnet, T. Amand, t o be published 8 R. Bichard, ThGse, P a r i s V1 (1979)

9 M. Combescot, S o l i d S t a t e Comm., 30, 8 1 (1979)

10 R. Zimmermann and M. RGsler, Phys. S t a t . Sol. ( b ) , 2, 633 (1976).