Picosecond luminescence of excitons localized by disorder in CdSxSe1−x

Journal of Luminescence 37 (1987) 45-50 North-Holland, Amsterdam

PICOSECOND S. SHEVEL

45

LUMINESCENCE

*, R. FISCHER,

OF EXCITONS

E.O. GGBEL,

Fachbereich Physik der Philipps-Unioersitiit

LOCALIZED

G. NOLL

BY DISORDER IN CdS,Se i _ x

and P. THOMAS

Marburg, Renthof 5, D-3550 Marburg. Fed. Rep. Germany

C. KLINGSHIRN Physikalisches

Institut der llniversitiit

Frankfurt, Robert-Mayer&r.

2- 4, D-6000 Frankfurt am Main, Fed. Rep. Germany

Received 31 August 1986 Revised 20 November 1986 Accepted 16 December 1986

We have investigated in Cd&Se, _-x and in pure CdSe the temporal evolution of the excitonic luminescence with 20 ps time resolution. In CdSe and in alloys with x < 0.15 the onset and decay of the luminescence can be described by time constants which are independent of the photon energy in the region of the free and bound excitons. In contrast, the time constants vary strongly over the main emission band for x > 0.15, which is attributed to the relaxation of excitons localized by compositional disorder. A simplified hopping model is presented which accounts for the experimental findings.

1. Introduction Heterostructures formed by semiconductor alloys are the base for numerous modem optoelectronic and electronic semiconductor devices [l]. The optical and electrical properties of semiconductor alloys, however, differ generally from their respective components due to the effect of compositional disorder [2-91. This compositional disorder causes localized states preferentially for anion-alloyed compound semiconductors, which result in an inhomogeneous broadening of the optical transitions and in modifications of the electronic relaxation and transport properties. Disorder-localized excitons in the II-VI alloy have been identified and studied by CdS,Se, --x selective optical pumping or by depolarization spectroscopy, e.g. [3,4,10]. Time-resolved experiments have revealed an increase of the recombination decay constant with increasing localization in Cd&Se,_, and ZnSe 1_,Te, [ll], which has been attributed to a decrease in oscillator strength with * Permanent address: Institute of Physics of the Academy of Science of the Ukrainian SSR, Prospect Nauki 144, 252650 Kiev-28, U.S.S.R.

0022-2313/87/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)

increasing localization energy. The kinetics of localized excitons in CdS,,,,Se,,d, has been studied with a time resolution of 200 ps by Kash et al. [12] demonstrating exciton transfer throughout the localized exciton band. We report here on experimental studies of the dynamics of exciton recombination in CdS,Se,_, with various alloy compositions (0 < x < 0.42) at low temperature (T = 5 K) with a time resolution of 20 ps. We find that the systematic broadening of the exciton recombination features with increasing x is accompanied by a characteristic change in the time behavior indicating the effect of localization. The high time resolution of our experiments allows one to study the very first relaxation steps of the excitons within the localized band, which are determined by single hops to lower energy sites. A hopping model thus can be applied and provides reasonable agreement with the experimental results. 2. Experiment The experiments were performed dye-laser chronously mode-locked B.V.

with a syn(Rh 6G, 76

46

S. Shawl et al. / Picosecond luminescence

MHz repetition rate, 5 ps pulse width (FWHM) pumped by the frequency doubled output of an actively mode-locked CW Nd : YAG laser for excitation and a synchroscan streak camera for time-resolved detection of the luminescence. The overall time resolution of the present experiments, including the temporal broadening due to dispersion of the luminescence with a 0.5 m grating spectrometer amounted to 20 ps. The samples used are thin platelets with a thickness of some ten urn grown by vapor-phase transport techniques. They are kept in an Heevaporation cryostat at T = 5 K. The polarization of the excitation and of the luminescence was preferentially E I C. The luminescence was observed in backward geometry to minimize reabsorption. The photon energy ttw,,, of the incident laser is situated around 2.13 eV and is thus in the band-to-band transition region for all samples investigated here.

of excitons localired hv disorder in Cd& Se, _ \-

_ 77

,z 2 d

CdS,

Se,_,

T=5K c) x O.L2 q

l_L

b) x = O.lL

a) x=0

IiS

3. Results and discussion

/

Time integrated luminescence spectra for three different samples with x = 0, x = 0.14, and x = 0.42 are depicted in fig. 1 for an average excitation intensity of 3 mW corresponding to a peak power of 4.2 kW/cm2. The spectrum for pure CdSe (x = 0) exhibits the well-known recombination lines due to free and bound exciton recombination and their phonon replicas. The emission is dominated by the I,-line, which corresponds to an exciton bound at a neutral donor. For x = 0.14 the dominant emission line is spectrally broadened with still a narrow feature at the high-energy side. Finally, for x = 0.42 an almost structureless broad band dominates the emission. For x > 0.97 and x < 0.2 one finds at low temperature preferentially excitons bound to impurities, while excitons localized by disorder fluctuations dominate in the composition range 0.2 < x < 0.97 [3,10,11]. The compositions x = 0 and x = 0.14 thus correspond to the range of mainly delocalized excitons while we expect strongly localized excitons for x = 0.42. The time behavior of the luminescence at different spectral positions within the main emission bands is depicted in fig. 2 for the three samples

GO Photon

Energy

1.62 [eV]

Fig. 1. Time-integrated luminescence spectra for CdS,Se, ox with x = 0 (a), n = 0.14 (b) and x = 0.42 (c) at T = 5 K.

shown in fig. 1. The results for the samples with x = 0 and x = 0.14 are qualitatively very similar. They show a fast initial component, which reaches its maximum at about 70 ps followed by a component with a slower rise. The decay is exponential and the decay constants are independent of photon energy in the spectral range under investigation and amount to about 320 ps for x = 0 and 650 ps for x = 0.14. The experimental results can be explained by free and bound electron-hole pair recombination. The first fast component which has disappeared after about 150 ps is attributed to recombination processes in a dense system of electron-hole pairs. If we assume that the energy per pulse is initially deposited in a layer of 1 urn thickness an electron-hole pair density up to 10” cme3 is reached. This value exceeds the Mott density in CdSe. Initially an electron-hole plasma (EHP) thus will be formed which is consistent with the fact that the fast luminescence feature is observed over the entire spectral range (up to 19

S. Shevel et al. / Picosecond luminescence

CdS,

I I I 0

0.2

1

Se,-,,T=SK

0.4

0.6

1-l

t Fig. 2. Time behavior of the luminescence positions within the main emission bands shown in fig. 1.

at different spectral for the three samples

meV) for x = 0 and x = 0.14. The plasma disappears by expansion over about 10 pm [13] and recombination in a time shorter than the EHP lifetime (about 200 ps [16]). After thermalization and capture of the free excitons and/or electronhole pairs, the bound exciton luminescence dominates [17]. Since the EHP period is short compared to the bound exciton time constant, the time-integrated spectra in fig. 1 show almost exclusively the latter one. The difference in the time constants for the decay of the I, bound exciton luminescence could be due to the increase of the binding energy and decrease of the oscillator strength with increasing x [14,15]. However, the most important point is, that the rise and decay times are independent of the photon energy within the emission band. This demonstrates that the emission is still essentially

of excitonsloculired

by disorder in Cd&Se,

~

41

due to bound exciton recombination for x = 0.14 and energy transfer amongst localized excitons is not observed. The experimental results for the luminescence dynamics in the sample with x = 0.42 (fig. 2c) differ appreciably from those for x = 0 and x = 0.14. Both the rise and decay times depend strongly on the emission wavelength and the curves deviate generally from an exponential behavior. The risetime of the luminescence is short at the high-energy side of the emission band but increases continuously at low photon energies. The decay of the luminescence is also fastest at high energies and becomes slower for lower energies. This time behavior is characteristic for the relaxation of carriers or excitons within a localized band [12,18,19] and can be qualitatively explained as follows. The population of the high-energy states decreases by recombination and relaxation to lower energy sites. The population of the states at lower energies again decreases by recombination and relaxation to sites with even lower energies, but increases on the other hand due to the relaxation from higher energies into this particular state. The relaxation between different sites is determined by hopping at low temperatures, whereas at higher temperatures thermally activated multiple trapping [20] dominates. The behavior described above is almost unchanged, if we increase the incident intensity by almost a factor of ten from 4.2 kW/cm’ to 40 kW/cm2. This finding is in agreement with highexcitation luminescence spectroscopy and with transmission measurements obtained with the pump and probe technique. It has been found that localized exciton recombination with unshifted eigenenergies remains the dominant process up to excitation intensities in the MW/cm’ range where the EHP is already formed in the pure constituents CdS and CdSe [13,21]. As a final point we want to analyze the data for x = 0.42 in fig. 2c by applying a simplified hopping model. We assume that after pulse excitation the excitons are trapped in tail states of the exciton band with uniform probability per site. This initial trapping takes place in times shorter than 50 ps as indicated by the risetime of the luminescence at the highest photon energies (cf. fig. 2~).

S. She&

48

et ul. / Picosecond luminescence

Subsequently excitons relax further by downward hops (at low temperatures) with rates

o/excitons

loculized by disorder in Cd&Se,

only the first two terms in an expansion of eq. (4): (G~(z)>Ji’iJ

(GJl(z))Ji=

lTj = y. e-2R/a,

(1)

z; > c.

J’

connecting sites i and j. ~a is the attempt to escape frequency, R the distance between site i and j and LYthe localization length. Excitons also recombine radiatively with a constant rate 7~~. The occupation of site i then develops according to the rate equation

G;(z)

= -

= Cnj(f=O)GJ,(z),

1 iz - ril

(G;(t)),=

where G,,(z) function G,,(z)=

is the frequency

(3)

dependent Green

where

n

/‘, m N(E)

n .nj/d3R

[exp( --Iv, e-2R/a I-

is dE.

with (4) k

In the time domain Gji(t) is the probability for finding an exciton at site i at time t if it started at site j at t = 0. The luminescence intensity at energy E, is proportional to the number of excitons with energy c;. The luminescence intensity can then be written in terms of GiJ(t) as

(7)

proximated by: (8)

with the average rate g = n / d3RV, ee2R/a. For longer times ( GJy(t)), follows essentially a power law t-y. Just for a qualitative illustration we briefly discuss the short time form for (GO). The calculation of the spectra, however, has been performed using eq. (7). Along similar lines the averages of the single hop term can be calculated in the time domain, leading finally to: L(ei)

aN(ci) exp[ --t(r;i X (1 + tg(l

where a random distribution of sites is assumed, uncorrelated with the site energies. ( ),j indicates the conditional average with ij fixed. N(E) is the normalized density of exciton states; / N(C) de = 1. The problem of energy relaxation and diffusion has been solved for finite T within a mean-field approach by Gri.inewald et al. [22]. A mean-field approach is not applicable for T + 0, but instead an analytical solution can be obtained as recently shown by Movaghar et al. [23]. Here we do not apply the full theory. Due to the short time interval of our experiments we may assume that just one hop makes the main contribution to the energy relaxation of the excitons. Thus we consider

1 I] ,

the density of sites, and nj = For short times this can be ap-

(Gj(?))J-exp[-t(r;l+gnj)],

-(iz-7;1+K)i1,

Kji=+cI;,.

- CI;.,

exp( -‘/ra)exp(

X

Im z>O,

(G~(Z)l;iGZ(Z>)ji,

The conditional averaging ( )/, leads to [24]:

which is formally solved by ‘i(z)

+

where

i

i

x

- n,)),

+gni)]

(9)

where once more the short-time form is used. This expression clearly displays the relaxation behavior as qualitatively discussed before. The prefactor describes the decay of excitons at energy 6, due to recombination and hops to lower energies. This happens to excitons which have been trapped at cr from the original trapping process, as given by the first term in the parentheses, and to those, which have performed a single hop from a state with energy c > E, into the state with energy C, as described by the second term. The average rate for these hops is g and the relative proportion of excitons involved is (1 - ni) = jcy N(c) de. In fig. 3 we present a set of curves calculated according to eqs. (5) and (7) (full lines) together with the experimental curves (dashed lines). An

S. Shevel et al. / Picosecond luminescence of excitons localized by disorder in CdS, Se, _ x

II

~,=4.2meV

0

I

I

0.2

0.4 t

I

0.6

bl

Fig. 3. Calculated temporal variation of the luminescence for different energies according to the model described in the text. The corresponding parameters are a3n = 5 x 10m3, ye = 10” s-l and cc = 4.2 meV. The symbols correspond to experimental data points according to fig. 2c.

I I

49

zation on their recombination kinetics. The exciton decay is determined by bound exciton recombination for small values of x and the decay of the bound exciton emission is most likely determined by radiative recombination with a decay constant of 320 ps and 650 ps for x = 0 and x = 0.14, respectively. The kinetics of the recombination changes appreciably for higher values of x. In particular the risetime of the luminescence on the low-energy side increases with decreasing photon energy which can be attributed to the exciton relaxation to lower energy states within the inhomogeneous energy distribution of the disordered localized excitons. Due to the high time resolution of 20 ps we are able to resolve the very early relaxation processes, which are governed by single hops. A simplified hopping model thus can be successfully applied and describes the data quantitatively if reasonable parameters are used. Acknowledgements

exponential density of states N(C) = ~0~ exp(c/ co); E < 0 has been assumed in the calculations. From the overall agreement between the theoretical and experimental curves we conclude that a3rr = 5 X 10e3, co = 4.2 meV, and v0 = lO”/s, which are reasonable numbers for the present system. If, e.g., n = 5 X 1017 cm -3 is assumed, we obtain for the localization length (Y= 22 A, which is of the order of the exciton Bohr radius. The agreement between theory and experiment is not perfect. Especially at the very early times the experimental data show a more gradual rise as compared to the theoretical ones. We have not attempted to fit the data more precisely by optimizing the density of states function N(c). Nevertheless, we conclude that a hopping model can describe the present experiments and that in fact we are able to resolve the very initial changes in the exciton distribution due to single hops.

4. Conclusion Time-resolved luminescence experiments with a time resolution of 20 ps in the II-VI alloys reveal the influence of exciton localiCdS,Se, --x

We acknowledge gratefully the preparation of the various samples by the crystal laboratories of the Universities of Karlsruhe, Kiev, and Leningrad. One of us (S.S.) would like to thank the Deutsche Forschungsgemeinschaft (DFG) for a research fellowship. Thanks are also due to G. Peter for the help with the experiments, to M. Preis for expert technical assistance, and to W. ElsslBer for a careful reading of the manuscript. We are indebted to M. Grtinewald for sending us the preprint of ref. [23] prior to publication.

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