Vertical transport in GaAs/GaAlAs superlattices: Carrier density effects

Superlattices

and Microstructures,

VERTICAL TRANSPORT

Laboratoire

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Vol. 5, No. 3, 1989

IN GaAs/GaAlAs

SUPERLATTICES:

CARRIER DENSITY EFFECTS

D. Block, B. Boulanger, P. Edel, R. Romestain de Spectrometrie Physique, BP 87, F-38402 Saint-Martin B. Deveaud, B. Lambert, A. Regreny CNET/LAB/ICM, BP 40, F-22301 Lannion, France.

d'Heres, France.

(Received 8 August 1988)

With an all-optical technique, we have studied vertical transport in a 3nm/3nm GaAs/GaAlAs suoerlattice held at 77K. Its efficiencv is strongly dependent on the photoexcitation density. This is at ieast partly due to a decrease of the non-radiative processes in the The value of the ambipolar diffusion coefficient is superlattice. equal to 0.65 cm*/, which is due to the low mobility of holes.

The mixing of quantum and classical vertical makes transport in transport superlattices a very attractive topic. We have previously analysed the effects of the carrier density on some properties of superlattices by Here, an all-optical methodl. we present results more devoted to vertical transoort itself and obtained by the same technique. ' Me have studied a 3nmf3nm GaAs/GaAlAs superlattice (the Al composition in the alloy is about 30%). An enlaraed well (EWl of width 4.5nm is embedded in the-superlattice (SL) at a distance L=O.9 pm from the SL surface. This enlarged well, whose radiative emission is spectrally resolved from the superlattice emission, acts as a trap for the carriers The superlattice. photocreated in the photoexcitation is done with a mode-locked frequency-doubled Nd:YAG laser providina 100 DS wide pulses (repetition frequency: lOO"MHz).'A conventional time-correlated single-photon counting technique (time resolution = 250 ps) allows us to record the time evolution of the SL and of the EW emissions. The results of these measurements together with the data the time-integrated obtained on emission intensities give insight into the efficiency of vertical transport in the superlattice and its dependence on the excitation density. All experiments described here have been performed at 77 K. In figure 1 are shown two time-integrated spectra corresponding to two laser attenuations differing by a factor of ten. The calculated photocreated carrier density is about 3~10~6 cm-3 for the higher laser power (labelled 0 dB on the figure). Both spectra consist of two main emission bands corresponding respectively to the enlarged well and to the superlattice. As can be easily seen, the emission of the enlarged well is stronger. But, as will be seen

0749-6036/89/030427+04$02.00/0

later, this is not a proof that the main part of the carriers photocreated in the SL are trapped in the EW. We should note that if the spectra were corrected for the instrumental response, the relative emission of the EW would be slightly increased. The ratio R between the intensities of the enlarged well and of the superlattice decreases with the laser power (the vertical scales are different for the two laser attenuations). We have plotted separately the behavior of time-integrated the intensity of the superlattice and of-the enlarged well when the laser attenuation is chanqed (see fiaure 2). For the EW, we have performed a -spectral integration of the time-integrated intensity, and for the SL we have only displayed the timeintegrated intensity at the top of the emission band. A spectral integration would have only

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FIG 1. Luminescence spectra measured two excitation densities

O1989Academic

1 70 eV at 77K for

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Vol. 5, No. 3, 1989

30dB

20dB

10dB

-2OdB

-1OdB

OdB

Dependence of time-integrated intensities with excitation density

FIG

2.

slightly changed the results due to an increase of the width of the spectra with power. The time-integrated intensity of the superlattice has a quadratic behavior with the laser power as emphasized by the line of slope 2 drawn on the figure. The time-integrated intensity of the enlarged well has a dependence between quadratic and linear. The time evolution of the intensity also depends on the laser fluence. The results of figure 3 have been obtained with the same laser attenuations as those of figure 1. The main features of figure 3 are the following: when the laser power increases, i) the intensitv decreases more slowly for. both the enlarged well and the superlattice, ii) the intensitv rises more slowly for the.enlarged well, iii) the widths at half maximum of the signals increase, iv) the delay between the appearance of the EW intensitv relative to the appearance of the SL intensity (characterized by the times at which the EW and the SL signals have increased to their half maxima) increases. We should keep in mind that this delav is not a direct measurement of the time needed by the carriers to travel through the superlattice. Working at 77K allows one to study the transport properties of free carriers: at this temperature the excitons of the superlattice are ionized. the exciton bindino Indeed, energy2 is 4.2 meV. This is confirmed by the appearance of a Maxwell-Boltzmann tail on the high energy side of the SL emission band, as is for recombination of free expected the carriers. For instance, for the spectrum of figure 1 labelled 0 dB, the carrier temperature is about 100K. On the other hand, the EW emission band has a high energy side too steep to be due to free carrier recombination. Therefore, the emission in the enlarged well is mainly excitonic. radiative processes . the The being due to band i: band superlattice, of bimolecular nature. recombination, are Therefore, the instantaneous intensity depends on the product N.P of the photoelectron and of

FIG 3. Time evolution measured at the top of emission bands of SupyoFttlce two (SL), and Enlarged Well (EW), excitation densities the photohole densities, as lonq as the densitv of photocreated carriers is above the residual dopinq level. Once assumed this last point, let us.discuss the following model: in this model, the number of electrons (respectively holes) disappearing by non-radiative processes in a given volume of the superlattice is proportional to N (P); any transport property is also assumed to be linear. Then, if the nonradiative processes dominate the bimolecular radiative recombination, N and P are linear with the laser power at every time and at every point of the superlattice. Therefore, in this intensity the regime, the emitted by superlattice is quadratic with the laser intensity. In summary, as long as the carrier density in the superlattice is higher than the residual doping and is low enough to have a sufficiently small number of radiative recombination, it is not surorisino to find a quadratic behavior as shown on figure 2. On the other hand, in this model the number of carriers arriving in the enlarged well is linear with the laser power (aqain. all sup&lattice processes experienced by the carriers are assumed to be linear except the radiative ones). The excitonic luminescence is of monomolecular type i.e. its intensity is orooortional to the number of excitons in the EW.' If the time of formation of an exciton is short enouqh, the time-inteqrated EW intensity will be proportional to the total number of electrons or holes arriving in the well. Therefore, the luminescence intensity emitted

Superlattices

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by the enlarged well should be linear with the laser power, in total contradiction with the experimental results. As shown in figure 3, the SL intensity decays more slowly at the highest laser power. That means that the non-radiative annihilation processes in the SL are less efficient at the highest carrier density. In order to study the effect of this phenomenon on the number of carriers trapped by the EW and therefore on the intensity emitted, we have analysed a very simple diffusion model. We assume a one-dimensional diffusion in "vertical" is the the z direction which direction. The density of electrons is taken equal to the density of holes at any point of the superlattice and at any time: therefore, we only consider the ambipolar diffusion. So we introduce N(z,t) the density of electrons in the superlattice with its associated equation: aN(z,t)/&=D

+N(z,t)/az=

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-ws,N(z,t) -BN2(z,t)

where D is the diffusion constant, wgl is the non-radiative recombination rate in the SL, and B is the bimolecular radiative recombination coefficient. We have solved this equation in the regime where the bimolecular recombination can be neglected since the SL intensity has a quadratic behavior. We take N=O as the boundary condition at the interface with the enlarged well (z=L): the EW is described as an infinitely efficient trap. Now for the interface with the free surface (z=O) we consider two models. The first one assumes that there is no recombination at this surface and that the carriers are purely reflected: this implies that the spatial derivative of N is zero for z=O; this model is REF (for reflection) in the quoted as following. On the opposite, the second one (quoted as RCB for recombination) deals with an recombination at the free infinitelv fast surface, therefore N=O for z=O. The laser pulse is taken as a 6(t) Therefore at t=O, function. N(z) has an exponential dependence : N(z) = No exp(-kz) O