Strong optical nonlinearities and laser emission of semiconductor microcrystals

~)

Solid State Communications, Vol. 81, No. 3, pp. 227-230, 1992. Printed in Great Britain.

0038-I098/9255.00+.00 Pergamon Press plc

STRONG OPTICAL NONLINEARITIES ANDLASER EMISSION OF SEMICONDUCTOR MICROCRYSTALS V.S.Dneprovskii, V.I.Klimov, D.K. Okorokov, Yu.V. Vandyshev Department of Physics, Moscow State University, 119899 Moscow, USSR (Received 10 October 1991 by L.V. Keldysh)

Changes in the transmission of quasi-zero-dimensional CdSe microcrystals (quantum dots) induced by ultrashort laser pulses were investigated with picosecond time resolution. The transitions between the energy levels of electrons

and holes spatially confined within micrccrystals were observed as bleaching bands in nonlinear transmission spectra, Gain registered at the transitions between the lowest levels of size quantization in microcrystals allowed to achieve the regime of laser generation in Pabry-Perot resonator made of glass containing semiconductor microcrystals.

I. Introduction

were excited bypowerful picosecond (20~ 25 ps) pulses o f the second harmonic ol Nd:YAG moae-±ocked laser.The excitation photons energy exceeded the energy corresponding to the absorption edge of SDG by about 0.5 eV. Transmlsslon of photoexclted samples was probed by the Relayed pulses ol plcosecond continuum. Optical hmltichannel analyser was. us.ed to measure differential transmlsslon (DT) spectra DT(k)=KT-To]/To, where T(k) and To(k) are the transmission spectra of excited and unexcited sample respectively. The measured DT spectra of sample I for varlous time aelays oetween the pump and the probe pulses are snQwn in flg.la (exclta~ion energy w=.2mJ/cm'): Excitation resulted in slgniflcan~ b l e a c h i n g above t h e a b s o r p t ! o n edge. Three b l e a c h i n g bands w i t h maxima a t M=(I ) 649 nm,(2) 616 nm, (3) 563 nm were observed for sample I, while these bands were not pronounced in the linear absorption spectrum. The kinetics of the absorption recovery dlfferea significantly f o r k~,~ and k3 bands ( f i g . 2 ) . B l e a c h i n g at k3 band c o m p l e t e l y r e l a x e d w i t h i n 70 ps a f t e r e x c i t a t i o n . The s l o w e r r e c o v e r y was c h a r a c t e r i s t i c of ~ band. And kl band c o u l d be seen in DT s p e c t r a up to the maximum d e l a y o f 3 ns. Spectral position of bleaching bands and their kinetics allowed to attribute the observed bleaching to filling of energy levels of spatially confined electrons and holes by photoexcltea charge carriers.

Semiconductor mlcrocrystals (MCs) in glass matrix can be treated as threedimensional potential wells for charge carriers an~ when the diameter of mlcrocrystals is reduced down to values comparable to or less than that of exclton in bulk crysta±, quantum s1~e effect begins to play significant role'. Spatial confinement results in the o_rastlc modification of the energy spectrum: the quasl-continuous spectrum of bulk seml~onductor is replaced by the discrete one ~. But usually significant Inhomogeneous broadening arising from the size distribution of mlcrocrystals in a sample smears out discrete levels and complicates the analysis. In this paper we report the results of plcosecona pump-prooe optica± experiments showing t~at levels of space quantlzatlon unreso±ved In linear absorption spectrum, can oe. ooserved in nonlinear transmss~on spectra of MCs. 2. Dynamics of nonlinear transmission spectra I n v e s t i g a t e d samples o f semicond u c t o r doped g l a s s (SDG) were p r e p a r e d by the . method of secondary heat treatment'.They contained CdSe mlcrocrystals of average radius less than 10 nm (this value was predicted from growth conditions) at concentration corresponding to approximately 0.1% semiconductor volume fractlon. The samples of SDG cooled to 80 K 227

228

SEMICONDUCTOR MICROCRYSTALS

DT,

i

i

3 E.~ E02 E2~

i

E~ "

Vol. 81, No. 3

i

Eo~ (a)

20-

-HF

//

"~,a

.~.2

" ~ I ~

~

2 I

1

DT 3

ng

580

640

t. 700

~Rm

E

F lg.2. Time-dependence of induced ca a n ~ s of absorption at ~I, ~, ~ bleaching bands: sample I, T=80 K.

(b) 2

580

64O

7~0

'Xlnm

Fig.1. Ca) Time-resolved dlfferentlal transmission spectra of ~ CdSe ~Cs: sample I, T:80~, w=2 mJ/cm, At=O (I), 70 ps (2), I ns (3), 2 ns. (4). Linear transmission spectrum zs sno~a~ oy the dashed llne.(bO Calculated spectra of differential transmission of ~dSe NCs: R=5 rim; T~=500 K (I), 80 K (2,3,4); N=12 (1,2), 4 (3), I (4). Within effective mass approximation combined wlth assumptions of infinitely deep spherical potentiai well ana negliglb]e role o f Coulomb interaction between carriers, energies of ransitl.ons between space quantlzatlon evezs in v~ience ana conauctlon bands are given by':

~

E~, ,=E~+hz~, n/2~R ~ ,

(I)

where i=0, I ,2 .... n=1,2 .... E~ -bandgap for the bulk crystal, ~=mem~/(me+~), me and ~ - effective masses of electrons and holes, R - mlcrocrystal radius, ~ , are determined by the condit ion J1+~/2(~m)=O, Ji,~/2 - Bessel function. b . The spectral position of Zl and anas agrees well wlth energles of IS-IS and IP-IP transitions - ~ and E. for R about 6 nm. ~3 band corresponds to the spectral region of transitions with energies E2~,Eo2,E~.

The dynamics of the nonlinear transmission spectra of MCs was numerically slmfilated. The adsorption speczra of the photoexclted. MCs were cazculated by summation over zransltlons with various quantum numbers i and n, for A, B, C - valence subbands of wurtzlte structure CdSe mlcrocrystals. We used the size dlstrlbution function derived by Llfshltz and Slyozov and used for SDG by Efros and E~ros 2. To take into account the effect of filling of states by photoexclted cart lets we intrgduqed population faqtors zor energy z evezs zn conauction aria vazence oanas assuming quasi - equilibrium Fermi diszrlbutlon. The results of the calculations for different electron temperatures Te (80, 500 K) and full numoer of electron hole (E~) pairs in NCj N=I-12 a r e presented in fig.lb. The mltlai stage of t h e DT spectra kinetics can oe attribuzed to the relatively fast cooling of photoexclted carriers accompanied by i n t r a b a n d t r a n s i t i o n s o f c a r r i e r s from h i g h e r to lower l e v e l s . Due to t h l s p r o c e s s ~3 - band r e l a x e s r a p i d l y while the amplitudes o f kl and - bands i n c r e a s e s - l l g h t l y ( s p e c t r a 1 and 2 i n f i g . l a and l b ) . The f i n a l s t a g e of the r e l a x a t i o n l s governed by the r e c o m b i n a t i o n o f c a r r i e r s which r e s u l t s In the r e c o v e r y of a b s o r p t i o n a t ~1 and ~ - bands ( s p e c t r a 2 , 3 , 4 i n f l g . la and I b ) . Signlflcant bleaching was observed in DT spectra for sample 2 with smaller slze mlcrocrystals. The spectral position of the bleaching band (589 rum) corresponds" to average size of mlcrocrystazs about 3.5 nm. The recovery time of the transmission was about 60 - 70 ps. The significant, shorten i~g of relaxation for smaller m~crocryszals Is probably due to the enhancement of non - radiative recombination (Auger ~rocesses a~d surface recombination may e involved~).

Vol. 81, No. 3

SEMICONDUCTOR MICROCRYSTALS

229

3. Spectra of nonlinear susceptibility. The thllxi-order Kerr-type s u s c e p t i b i l i t y XT M of SDG Is measured usually using degenerate four-wave mixing. This m e t h o d g l v e s Information only on the modulus of XT M , so a d d i t i o n a l measurements a~% necessary to provide the phase of XT M ". The DT spectra r e p o r t e d i n the p r e s e n t work can De u s e d t o eva~m~e ~he real ana imaginary parts of X T M . The changes of the absorption coefficient Aa(~) and refraction coefficient An(~) induced by the resonant monochromatic field of int~Bsity I(~) ,°,are connected with Imx T M and Rex T M respectively. For small An and Aa:

Rex(~)(~)=~iAn(~) ,

(2a)

I(~)

imx(~)(~)=--c2n~---,A~(~)

(2b)

8~2~ I ( ~ ) where no is linear refraction index. For uaslstationary conditions the radiation ntenslty I(~) is connected with N - the number of EH pairs per MC:

~

(a)

sl ~¢1). 4 3

%, v-

x

Re

2

%1

70 700 ~50

"~610 t

640

k, nm

-1 -2 -3

Im

) =," 6

~Re 64O

0

x2

670

k,nm

-2 -4

(I -T (~)-r) I(~)

N(~)~

e

,

(3)

dhmN= where N, denotes the concentration of mlcrocrystals in the glass matrix, ~, recombination time of photoexclted carriers, T(~) and r -the transmission and reflectlvlty of the sample respectively, d - its thickness. Combining equations (2) and (3) we can express the nonlinear susceptibility in terms of the ratio of absorptlon and reflection c nanges to the number of EH pairs per ~C.. The Aa(~) spectrum is ~irectly determlned by the corresponding DT spectrum A~=-ln(1+DT)/d. The induced refraction index changes can be calculated using the Kramers - Kronlg relation. T~us all values necessary to evaluate ~ ' can be obtained from the measured DT(k,At) and To spectra. It saould be noticed that the above rocedure Is valid only for small ransmlsslon changes when the third order nonlinearity is dominant. In our alculatlons we used only DT spectra for ong enough delays when absorption changes were localized in the vlclnlty of ~he transition between the lowest levels of size quantlzatlon. The resultant spectra of Re and Im X (~) are presented in fig.3a (sample I) and flg.3b (sample 2). These spectra are of clear resonant character that is due to the discrete structure of the energy spectru~,~)of ~Cs. The amplitudes of Re and _ ~ are of the same order - abou~ 5,10 -° - esu for~ larger mlcrocrystals (R=6nm) and 10 -~ esu for the smaller

~ ~

-6

Jim

'

Flg.3. Spectra of the third- order nonlinear susceptibility of CdSe MOs: T=8OK, sample I (a), sample 2 (b). ones (R=3.5nm). Strong reduction of the nonlinearity for MC of smaller size (instead of its enhancement, predicted by Schmltt-Rink wlth coauthors p) is caused mainly by the slgnlflcant shortening of the relaxation time (from 1.5-2 ns in sample I to 60-80ps In sample 3). The

oaloulatlon

of

X (3)

in

the

frames of the model of the filling of levels gives the result similar to that for th~ two - level system with saturation:

X(3)=N"

8 Idol 2 2

2

~,

(4)

2

[ (ha~Eol) +h Pol ] [h~-E o +lhFol ] where d~ is the matrix element of dipole moment for interband transition, Pol is the factor of the homogeneous broadening of the lowest transition between size quantlzatlon ±evels. The above expression shows that the value of nonlinearity is proportional to ~e and inversely proportional to the volume ol

230

SEMICONDUCTOR MICROCRYSTALS

MC V~ (assuming N~V~const). Formula (4) predicts that in the case of sample 2 ~he enhancement of nonlinearity (compared to sample I), caused by the increase in MC concentration (Nm/N~5) is compensated by the shortening of relaxatlon time (~e2/~o1-~.03) that r e s u l t s in the observed r e d u c t i o n of ~3)~ To o b t a i n q u a l i t a t i v e agreement f o r the r a t i o o f e x p e r i m e n t a l l y measured susceptibilities it is necessary to take into account the size dependence of the homogeneous broadening factor and the effects of inhomogeneous broadening. 3.Gain and laser generation semiconductor microcrystals.

in

The amplitude of the differential transmission in the spectral region of M and ~ bands (sample I) indicates that not only the bleaching of absorption but galrt. (a
Ik a.U.

3

~I

610

./

a'

650

t

690

I ,/

0

730

i

,

0,5 1,0 ~o,rnJ/cm2

770

k,nm

Fig.4 Spectra of spontaneous (I) and stimulated (2,3) emission of sample I with reflective coatings : T=~O K, w=O.08 (I), 0.5 (2), 0.8 (3) mJ/cm'. Inset: intensity of stimulated emission vs. pumping energy.

Vol. 81, No. 3

band was negative for the delays up to Ins.

To obtain laser generation we used a I mm thick Fabry-Perot resonator: dielectric coatings wlth reflection coefficients of 95~ and 100% at 650 nm were deposited on the parallel faces of sample I. The resonator was cooled to liquid nitrogen temperature. At low excitation levels a broad band of spontaneous emission (k=682 nm) was observed in the luminescence spectrum (fig.4). When the energy of excltatlo~ was increased to about 0.2 mJ/cm" stimulated emission, directed perpendicularly to the mirrors of the resonator arose at the high energy wlng of the spontaneous band. At w~-0.5 mJ/cm" intensity of the stimulated emission increased steeply (flg.4, inset) and its linewldth narrowed to about 7 nm, indicating the onset of laser generation. At pump levels more than 0.5 mJ/cm" the narrow line of laser generation dominated in the luminescence ectrum. The spectral posltlgn of the aser generatlbn line colncidea with the energy of the lowest IS-IS transition in microcrystals.

~p

4. Conclusions. In conclusion, we have studied the recovery of the transmission of CdSe MCs after intense picosecond excitation. Bleaching bands corresponding to the transitions between the levels of size tlzatlon were clearly observed in erential transmission spectra. The induced decrease of absorption was explained by filling of states in MCs by phbtoexclted carriers. Spectra of the third - order nonlinear susceptibility were calculated for MCs of ~Ifferent size. The observed decrease of nonlinearity in MCs of smaller slze was attributed to the strong shortening of the carriers lifetime. Laser generation in glass doped with CdSe mlcrocrystals was achleved[. References

~

I. A. Eklmov, AI. Efros, A. A. Onushchenko, Solid State Commun. 56,921 (19851. 2. A1.Efros,A.Efros, Flzlka i Tekhnlka Poluprovodnlkov 16,1209 (I982 ). 3. V. Dneprovskil, A. Efros ,A. Ekimov et. al. Solid State Cormmun. 74,555 (19901. 4. P. Rosslgnol, D. Ricard, C. Flytzanls, Ap l.Phys.A 44,285 (19871. 5. S.~cl'~lt t - R i n k , D . A . M l l l e r , D.S. Chemla, Phys.Rev. 35B,8113 (19871.