Femtosecond luminescence of nonequilibrium carriers in InAs

JOURNAL

OF

LUMINESCENCE ELSEVIER

Journal

Femtosecond

of Luminescence

76&77

(1998) 141

143

luminescence of nonequilibrium

carriers in InAs

Abstract

We observe a transient pre-thermalized nonequilibrium distribution of electrons in intrinsic InAs photoexcited by an ultrashort pulse, using luminescence up-conversion technique with a time resolution of about 120 fs. Luminescence has been observed between 0.9 and 1.35 eV in the Stokes side and between 1.75 and 2.15 eV in the anti-Stokes side. The time evolution after 0.5 ps (slow component) can be well understood in terms of an electron cooling model. In addition to this component. we find a fast component which decays in a few hundreds of femtoseconds. at energies close to the excitation laser line. This component is attributed to the nonequilibrium carrier distribution before thermalization. t 199X Elsevier Science B.V. All rights reserved. Kcym~ls:

InAs: Nonequilibrium

carriers;

Relaxation

in semiconductor:

Using the luminescence up-conversion technique, it is possible to obtain direct information about excited carriers with a time resolution in subpicosecond range [l]. However, carrier distribution ht@re thermalkation has not been observed clearly in luminescence measurements so far, whereas in the calculations temporal evolutions of photoexcited distribution of carriers are clearly displayed. In fact, since most of femtosecond luminescence experiments were carried out for middle-gap semiconductors such as GaAs and InP, only the luminescence near the band edge was investigated. Therefore. the whole distribution especially near the excitation laser was not clearly seen [Z]. Because of the small difference between the band gap and the excitation photon energy, it was difficult to

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0022-2313’98~519.00 I’//

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Femtosecond

luminescence

spectroscopy

generate electrons with large excess energy in such middle-gap semiconductors. On the contrary. in the case of relatively small gap semiconductor InAs, it is easier to generate high-energy electrons. In this paper we show the time-resolved luminescence measurement of InAs excited by ultrashort pulses. We find a femtosecond component which decays in a few hundreds of femtoseconds. in addition to the picosecond component which is attributed to the cooling process of the electrons. We used the luminescence up-conversion technique employing a self mode-locked Ti : sapphire laser which generates 80 fs optical pulses with a frequency of 90 MHz and an average power of 1 W. The overall time resolution is about 120 fs. Intrinsic bulk InAs sample was excited by the fundamental 1.6 eV optical pulses with an excited carrier density of 1 x 1Or8 crnm3 estimated from the one pulse energy and the absorption coefficient. As an absorption bleaching may occur in this case, this value gives the upper limit. However, the deviation will

1998 Elsevier Science B.V. All rights reserved

not be so large, because, in the case of GaAs, the transient change of absorption coefficient at the excitation energy generating carriers as much as 3.3 x lOi cm-3 was reported to be at most 6% of the initial value [3]. The inset of Fig. 2 shows the schematic scenario of the ultrafast processes which we anticipate to occur in the photoexcited InAs. During the optical excitation, electrons are excited from heavy-hole, light-hole and split-off-hole bands to the conduction band creating holes in each band. The carriercarrier scattering rate is proportional to the density of final states. Since the density of states for the holes is about 10 times larger than that for the electrons, the scattering rate for hole-hole is larger than for electron-hole and electron-electron. Through this carrier-carrier scattering, holes thermalize, i.e. become quasi-equilibrium, more quickly than electrons, e.g. within 100 fs in GaAs [2]. In 1nAs so do the holes, because the density of states for holes is the same order (two-thirds) of that in GaAs. Furthermore. holes cool down to RT through hole-LO phonon scattering much more quickly than electrons. Because, in contrast to the electron-LO phonon scattering via Frolich interaction, hole-LO phonon scattering via optical deformation potential interaction is not screened by the existing carriers [2,4]. Hence, in our case the hole distribution can be safely assumed to be constant after 1 ps. The luminescence intensity is proportional to the product of corresponding distribution and holes, L(o) c functions of electrons fe(k,,,)fh(k,,), where k,, is the wave number at which the energy difference of electron and heavy-hole equals the luminescence photon energy. Therefore, the temporal evolution of the luminescence reflects that of the electron distribution as long as we consider in picosecond region. Fig. 1 shows the temporal evolution of the luminescence ranging from 0.992.15 eV, which extends far above the excitation energy of 1.6 eV. In Fig. 1, we notice that the luminescence has two different decay components. At all energies, the luminescence decays within several picoseconds. We here name this slow-evolving component as picosecond component. At emission energies within about 0.3 eV below and above the laser energy 1.6 eV, the luminescence initially decays in hun-

0

1

2

3

4

5

6

Delay Time (ps) Fig. I. Points:

time-resolved

luminescence

of InAs

excited

using an electron

assuming

decay time 2.3 ps. See text for the

electron

temperature

cooling

at

1.6 eV. Solid lines: calculation

model

details.

dreds of femtoseconds. We name this fast-decaying component as femtosecond component in this paper. First, we refer to the picosecond component of the luminescence. This component decays in 1 or 2 ps at high energies, showing a plateau of about 1 ps before the decay at middle energies from 1.2-1.40 eV, and even increases in 1 or 2 ps at low energies around 1.O eV before decaying in 4 or 5 ps. These behaviors are understood if we simply make a cooling model of hot electrons. In Fig. 1 we plot solid lines which are calculated using an electron cooling model. The assumptions of this model are the following. First, the lifetimes of electrons and holes are so long that we need not consider decrease in total number of electrons and holes. Second, we may consider electrons are in quasiequilibrium, i.e. the electron Fermi distribution is well established so that the temperature is well defined. Third, the electron temperature decays exponentially approaching to RT. Assuming that hole distribution remains constant, the time

dependence L(PJ.

t) x,fe[k,,,,

of the luminescence

is given by

T,, p(T,. iiF)].

where T, is time-dependent electron temperature and I+ is the Fermi energy. In order to apply this to the realistic system. we need to consider decrease of luminescence intensity due to carrier diffusion from the surface into the bulk sample. We use absorption coefficients of luminescence light and ambipolar diffusion constant ( 15.6 cm2/s) for electrons and holes from literatures. We obtain the best fitting with electron temperature decay time 2.3 ps and initial electron temperature 6000 K. As we see in Fig. 1. this calculation shows a quite good agreement with the experimental data in picosecond region. Therefore. we interpret the picosecond behaviors of the luminescence as the cooling of hot photoexcited electrons. Second, we refer to the femtosecond component. As we see in Fig. 1, luminescence at 1.35 eV exhibits a fast decay of about 200 fs. The femtosecond component is regarded as ~urnirzescrnce from nonequilibrium carriers rather than scattered excitation light, because the temporal evolution has a decay evidently longer than the autocorrelation of the excitation pulse. In contrast to the case of picosecond component. when we consider subpicosecond regime, we must keep in mind that both electron and hole distributions may depend on time. Hence, the temporal evolution of the luminescence can reflect the behaviors of both electron and hole distributions. Now. the question is how the carriers distribute in subpicosecond regime. Carrier redistribution process is believed to consist of two steps. First. it evolves toward quasi-equilibrium distribution which is simply described using tmprrntuw. Before quasi-equilibrium, distribution changes drastically in the time scale of carrier carrier scattering. This process is called thermalization. After establishment of the temperature. distribution does not change at all even if carriers scatter each other often. Second, carriers cool down toward RT. temperature of the carriers being well defined. This process is called cooling. Here we have to consider four processes. that is, thermalization and cooling of electrons and holes, respectivcly. Holes are considered to cool down to RT in a few hundreds of femtoseconds in the case of GaAs

[2,5]. For InAs, we do not expect any special difference. Thermalization of holes should be much faster (i.e., in tens of femtoseconds) than the cooling. This value (tens of femtoseconds) is much smaller than the experimentally obtained decay time of a few hundreds of femtoseconds. We now have to consider two processes; hole cooling and electron thermalization for the candidate of the femtosecond component. Here we consider which can appear only near the excitation energy. Since the hole energy (110 meV) corresponding to the lowest luminescence energy of 0.9 eV is larger than the Fermi energy ( < 100 meV for our excitation intensity). hole distributions above this energy should be decreasing monotonously after excitation during cooling process. If hole cooling process were observed as the femtosecond component. it would appear in all the luminescence energies. But it does not. Thus, the hole cooling process does not explain why the femtosecond component appears only near the excitation energy. We now examine the last candidates, i.e. electron thermalization. Electrons thermalize to a quasi-equilibrium mainly through carrier-carrier scattering: electron hole intervalence-band scattering plays the most important role among them because of the large scattering rate [4--61. If we take this hole--electron collision into account, we can explain the bandwidth of the femtosecond component. A hole scattered from heavy-hole band to light-hole band gets energy’ of a few hundreds of meV from an electron and vice versa, corresponding to the splittins of heavy and light hole bands (e.g.. the splitting is about 200 meV at the wave number corresponding to the luminescence energy of 1.6 eV). Monoenergetically photogenerated electron distribution will be broadened through scattering of electrons with holes, Thcrefore. we interpret the femtosecond component which appears while and just after excitation before thermalization as the luminescence from partly redistributed nonequilibrium c~lcctum. In Fig. 2. solid lines are electron distributions calculated LISing the parameters used in the fitting of the picosecond component. Using the experimental curves in Fig. 1. we evaluated the intensity ratio of the femtosecond component to the picosecond component at the time when the total amplitude reaches maximum for each photon energy. By

T. Suemoto et al. / Journal qf Luminescence

144

Luminescence 0.5

I

I

Energy (ev) 1.5

1 .o

’

2.5

2.0

I

1

’

1.1

Electron Energy (ev)

Fig. 2. Solid lines: calculated electron distributions at 0 ps (a), 1.0 ps (b), 2.8 ps (c)and 4.8 ps (d). Circles: nonequilibrium distribution before thermalization estimated from the femtosecond component. The inset is a schematic scenario of excitation and luminescence. Arrows represents excitation and recombination. Photoexcited electrons spread over the conduction band and recombine with the relaxed heacv holes.

multiplying the magnitude of the calculated distribution (curve a in Fig. 2) by this ratio, we can estimate the distribution corresponding to the femtosecond component at each photon energy. The

76& 77 (I 998) 141~ 144

estimated total distribution corresponding to the femtosecond and picosecond components is indicated by circles connected by dots in Fig. 2. We can regard this dotted curve as the nonequilibrium distribution of electrons in the conduction band. In conclusion, we succeeded in measuring the time-resolved hot luminescence from InAs with a femtosecond temporal resolution. The temporal evolution of the luminescence is explained by using a simple cooling model of electrons in the picosecond time region. Initial fast component of the luminescence around the laser energy is now considered as from nonequilibrium electrons before thermalization. This is the first finding of a prethermalized transient nonequilibrium carrier distribution using time-resolved luminescence spectroscopy within the knowledge of the authors.

References Cl] J. Shah, IEEE J. Quantum Electron. QE-24 (1988) 276. [2] L. Rota, P. Lugli, T. Elsaesser, J. Shah, Phys. Rev. B 47 (1993) 4226. [3] Jeff F. Young. Ting Gong, P.M. Fauchet, Paul J. Kelly, Phys. Rev. B 50 (1994) 2208. [4] M.A. Osman, D.K. Ferry, Phys. Rev. B 36 (1987) 6018. [5] M. Woerner, T. Elsaesser, Phys. Rev. B 51 (1995) 17490. [6] J.H. Collet. Phys. Rev. B 47 (1993) 10279.