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of free excitons

B. Deveaud, F. Cl&rot Centre ~~atianul d ‘Etudes des T~i~comm~nicut~on~~22300 tannion,

France

N. Roy, B. Sermage Centre National d’Etudes des Tt%communications, 92120 Bagneux, France

and D.S. Katzer * Natal Research Laboratory, Washington, DC 20375, USA

Received 31 May 1991; accepted for publication 26 August 1991

Radiative properties of free excitons in a single GaAs quantum well are studied under resonant excitation. Superradiant decay of the excitons is evidenced by the very short lifetime as well as by the strong intensity of the signal. Dephasing mechanisms, by destroying the phase coherence of the excitons. increase the observed lifetime. Quantitative agreement between the lifetime, the intensity and the homogeneous broadening is obtained. We deduce a radiative lifetime of 8 ps in the absence of dephasing mechanisms.

2D confinement of an exciton in a quantum well leads to a shrinkage of the exciton Bohr radius accompanied by an increase of the oscillator strength and of the binding energy [1,2]. This leads to the observation of strong resonances up to room temperature, allowing a large number of potential applications [3]. The amount of work, theoretical as well as experimental, devoted to the behaviour of excitons in quantum wells has therefore been considerable [4]. Amongst the possible techniques, luminescence, due to its simplicity and sensitivity, due also to the fact that luminescence transitions in QWs are dominated by excitonic recombination, has been quite widely used 15-91. * ONT Post Doctoral Fellow. 0039~6028/92/$05.00

In 3D, the time-resolved behaviour of excitonic polaritons has been extensively studied (see ref. [lo] for a review). Excitonic polaritons are stationary states of an infinite dielectric medium (and should not therefore exhibit any temporal evolution). Decay is either observed through phonon scattering [ll] (as evidenced for example by Brillouin scattering [12]), or due to the existence of crystal surfaces where poIaritons can transform into external photons (radiative decay). The above description, however, relies on the translational invariance of the crystal, and implies the conservation of momentum from the exciton to the photon. For excitons confined in quantum wells, the coupling to photons is profoundIy modified by the breakdown of translational symmetry in the growth direction (hereafter labelled z).

0 1992 - Elsevier Science Publishers B.V. and Yamada Science Foundation.

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This coupling is now very strong for excitons with a wavevector 1k 1 < nw,,/c, as they can couple to a whole 1D distribution of photons (here CO,)is the frequency of the photon at the exciton cnergy, II the material refractive index and c the speed of light). The decay rate for those excitons has been predicted [13-151 to be enhanced by factor: 247r(h/a,)’ where A is the radiation wavelength and a, the cxciton Bohr radius. This amounts to 8 X 10’ in GaAs quantum wells, and radiative decay of near k = 0 excitons should be very fast [ 161. This rnhanced decu~ rute. which relies on the coherent nature of the movement of the exciton center of mass, is only possible in the absence of perturbations and in particular if the phase coherence of the exciton is preserved long enough. As noted by different authors [ 15-171, the loss of phase coherence (for example due to the scattcring by acoustical phonons if temperature is too high) will prevent radiative recombination and thus increase the radiative lifetime. An important point has to be raised, as it is generally neglected: the ratio of the luminescence intensity I,,,,,(t = 0) to the excitation power 4 should be inversely proportional to the radiative lifetime [16,18]. Although luminescence measurements do not allow for an absolute measurement of the intensity, relative measurements bring information of great importance. Apart from temperature effects, other perturbations may alter the fast decay of excitons: exciton-exciton or exciton-carrier scattering [18], but also any kind of imperfection in the quantum well and in particular interface roughness. As a result, and this was pointed out by Hanamura [14], enhanced decay of excitons should be very difficult to observe as it requires one single QW of the highest quality. Here, we demonstrate for the first time the enhanced decay of free excitons in a single quantum well. Not only do we monitor the decay of the luminescence intensity, but also the relative value of this intensity and the homogeneous linewidth. Under resonant excitation at 2 K, we observe a radiative decay time as short as 40 ps in a high quality GaAs/AlAs quantum well and show that temperature (above 3 K), excitation density (above 3 X 10” cmP2), as well as excita-

tion detuning (by only 2 mcV), by allowing phase breaking mechanisms, increase the luminescence lifetime and the linewidth, and decrease the intcnsity. Quantitative agreement between all measured quantities is obtained. WC have studied a single GaAs/AIAs QW grown by molecular beam epitaxy using growth interruption techniques [ IY]. This sample shows a splitting of the excitonic transitions induced by the occurrence of large growth islands at the interface [20]: each of the excitonic lines then corresponds to the recombination of excitons in portions of the well with a well defined thickness. The well width is 45 A, the exciton splitting 12 meV. The full width at half maximum of the lines is 2 meV only, and no Stokes shift is observed between luminescence and luminescence excitation: therefore, the interface roughness can be considered to be minimal. Three lines respectively corresponding to N. N - 1 and N + I monolayer (ML) wide regions are generally prcsent at each spot position. By carefully mapping the sample, it has been possible to find a zone where the N ML transition is dominant, the two other regions representing less than 10% of the signal. All experiments are carried out on such a zone, where scattering of the exciton to (or from) other zones of different thickness (which leads to heating of the exciton [21]). may be neglected. The sample is excited with picosecond pulses generated by a synchronously pumped dye laser. and the luminescence is detected by a streak camera. The overall resolution of the system is of the order of 20 ps (see the dashed line in fig. 1). The sample is immersed into superfluid helium for the measurements at 2 K. and is placed on the cold finger of a closed cycle cryostat for the measurements at higher temperatures. Let us first describe our experimental findings. We show on fig. 1 the time decay of the excitonic luminescence for an excitation density of 3 x IO" cm-‘, as a function of the detuning between the pump and the exciton energies. All curves arc plotted in absolute number of counts recorded under the same conditions. For resonant cxcitation, the decay time is non-exponential, the long time decay being of the order of 40 ps and the intensity is quite high. The short time transient

493

B. Deveaud et al. / Radiatitle properties of free excitons in a GaAs QW

DETUNINGlmeVI

100

0

DELAY

200

lps)

Fig. 1. Exciton luminescence decays for different detunings AE between the laser and the exciton energy. The same scale is used for the different measurements: an intensity decrease is observed together with the increase of the lifetime. The laser time behaviour is plotted as a dashed curve. Insert: risetime of the excitonic luminescence for different detunings.

(t < 20 ps) may be due to residual diffused laser light. As soon as the laser is detuned from the exciton (above resonance), the lifetime increases and simultaneously the intensity decreases. The same qualitative behaviour is observed for resonant excitation when the temperature is raised above 2 K, or when 4 is increased above 1O’O crnv2. In this last case, due to the change in excitation power, we do not observe a decrease of the plum but a decrease of the ratio Z,,,,Jf = O)/C#B. When the detuning is increased, a long risetime develops which has already been observed by different authors 122,231and attributed to exciton relaxation and cooling. We observe the same increase of the risetime, but with different features (see the insert of fig. 1): the absolute value of the risetime is rather short in our case; we consider that this is partly a consequence of the high quality of the sample, preventing the heating of the exciton subsequent to the trapping into larger portions of the well. The risetime is then only due to thermalization of initially hot excitons, and not to trapping of the exciton into lower energy regions of the well. Lineshapes of the excitonic transition, recorded 50 ps after resonant excitation at various densi-

ties, are reported on fig. 2. The fit is a convolution of a constant Gaussian linewidth (1.7 meV) and a density dependent Lorentzian linewidth. The increase of the linewidth, and the Lorentzian contribution to the lineshape are clearly evidenced. At low temperature and low density, the linewidth is mainly Gaussian as a result of residual inhomogeneous broadening (for example potential fluctuations due to impurities in the barriers or at the interface). A small Lorentzian contribution can be resolved giving an homogeneous width of 0.3 meV. At higher densities, a good fit to the lineshape is obtained by keeping the Gaussian contribution constant and increasing the Lorentzian linewidth (see the fits in fig. 2). A moderate temperature increase, up to 30 K, also leads to a similar Lorentzian broadening. We have checked that the above behaviour cannot be explained by the effects of exciton localization [24]. We now discuss our results: at low temperature, under resonant excitation, upon increase of the excitation density c$, the dephasing time decreases because of exciton-exciton collisions [ 191. The observed increase of the radiative lifetime of the exciton T,,J~) can only be explained if excitons are prevented to recombine for some time

u

-Lorcntzian:

Z IA

Z v, 3 E -

Lorentzian: 0.34

meV

735

130 WAVELENGTH

740 lnm)

Fig. 2. Excitonic lineshapes at different densities. The fits are obtained using a constant Gaussian width of 1.7 meV convoluted with an adjustable Lorentzian contribution.

after a scattering event. Introducing a delay time T’ after each dephasing event allows us to dcscribe the increase of the decay time which is now given by: T,ad(d)

= %( J + ~‘/~,k,,hW).

(1)

decay rate in the where 1/T,, is the radiative abscence of scattering mechanisms, and 1/T~,~,,,, is the dephasing rate. The contribution of the nonradiative lifetime has also to bc taken into account: the high quality of our samples is obtained through the growth of very thin AlAs barriers (50 A). Hence our sample structure is tunneling diodes” analogous to the “resonant studied by Tsuchiya ct al. [25], and tunneling phenomena are included through an “exciton lifetime” s,,,,, inside the double barrier. The mcasured luminescence lifetime T,,,,,, is given by: 1/~,un, = ~/~,.,‘I + 1/Ttun

(2)

In agreement with ref. [26], our measurements at large densities and dctunings indicate a value of 250 ps for ‘T,~,,,. Experimental results are given in table 1. First WC notice that, in agreement with ref. [19], the Lorcntzian broadening varies with density approximately at a rate of 0.1 meV/lO” cm ‘. From the cxperimcntal luminescence decay and from the value of s,~,,, = 350 ps, WC time TV,,,,,, deduce through cq. (2) the measured T,~,,,(&). As wc also measure T~,~,,,,(&) from the cxpcrimental linewidth. we finally use cq. ( 1) to determine T,,. The best agreement is obtained for 7,) between 7 and 9 ps, T’ being of the order of IO ps. The values of the luminescence decay time T,,,,~, calculated for T,) = 8 ps, the measured value of T,,~,,,,. in the last an d TM,, = 250 ps. are reproduced column of table 1. The agreement with the measured values is quite good. The value of S ps that

WC obtain for 7,) is in quite good agreement with the theoretically predicted value of 8.4 ps: for OUI sample structure, the infinite well is a good approximation and we only correct Hanamura’s value of 2.X ps 1141 by a factor of 3 to account fat the refractive index of GaAs [ 151. Temperature effects arc mot-c difficult to model. If we follow ref. [ 171 or [ 151, and ~SSUIIIC ;I thcrmalized cxciton distribution, the variation ot the luminescence decay time should be linear in 7.. rrflccting the proportion of excitons with wavevcctor / k 1 < r~w,,/c. However, the phonon scattering time is cxpcctcd to bc a few pa at low temperatures [14] (wc cstimatc 1.5 ps at 0 K and 0.5 ps at IS K from the cxperimcntal linewidth at low density). As a consequcncc. for resonant cxcitation, low temperature and low density. we cannot safely assume a thermalized distribution at early times. In our experiments, the lifetime variation is not linear with temperature [26] but slower (400 ps at 2 K and 65 ps at 9 K) probably heca~~se the excitons arc initially cold and cannot hc considercd to be at lattice temperature just aftcl- the excitation pulse. At short times. the scattering by phonons should rather bc modellcd as ;I phase breaking mechanism. As a conclusion, WC:have clearly evidenced the enhanced decay rate of excitons brought by the breakdown in translational symmetry in quantum wells. The deduced radiative lifetime is 8 ps in quite good agreement with theory. Our results easily explain the obvious difference bctwecn bulk GaAs samples where bound transitions dominate the spectrum even in the highest quality samples, and GaAs QWs where fret exciton transitions dominate even in medium quality samples.

The authors cxpreas their thanks to I. Bat Joseph, G. Bastard. A. Chomette. B. Lambcrt. A. Regrcny and C. Wcisbuch for useful discussions.

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f feh.

my\.

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B. DeLjeaud et al. / Radiative properties of free excitons in a GaAs QW [3] D.S. Chemla, D.A.B. Miller, A.C. Gossard and W. Wiegmann, IEEE J. Quantum Electron. QE-20 (1984) 265. [4] For a review, see for example, C. Weisbuch, in: Semiconductors and Semimetals, Ed. R. Dingle (Academic Press, New York, 1987) p. 1; S. Schmitt Rink, D.S. Chemla and D.A.B. Miller, Adv. Phys. 38 (1989) 89. [5] C. Weisbuch, R.C. Miller, R. Dingle, A.C. Gossard and W. Wiegmann, Solid State Commun. 37 (1981) 29. [6] E.O. Gobel, H. Jung, J. Kuhl and K. Ploog, Phys. Rev. Lett. 51 (1983) 1588. [7] R.C. Miller and D.A. Kleinmann, J. Lumin. 30 (1985) 512. [8] J. Lee, E.S. Koteles and M.O. Vassel, Phys. Rev. B 33 (1986) 512. [9] J. Feldmann, G. Peter, E.O. Gobel, P. Dawson, C.T. Foxon and R.J. Elliott, Phys. Rev. Lett. 59 (1987) 2337. [lo] J. Aaviksoo, J. Lumin. 48 & 49 (1991) 57. [ll] Y. Toyozawa, Suppl. Theor. Phys. 12 (1959) 111. [12] C. Weisbuch and R.G. Ulbrich, Phys. Rev. Lett. 39 (1977) 654. [13] M. Orrit, C. Aslangul and P. Kottis, Phys. Rev. B 25 (1982) 7263. [14] H. Hanamura, Phys. Rev. B 38 (1988) 1228. [IS] L.C. Andreani, F. Tassone and F. Bassani, Solid State Commun. 77 (1990) 641.

495

1161 The same is true for surfaces: see, J. Aaviksoo, J. Lippmaa and T. Reinot, Opt. Spectrosc. 62 (1987) 706. [17] See, for example, A. Honold, L. Schultheis, J. Kuhl and C.W. Tu, Phys. Rev. 40 (1989) 6442. [18] B. Sermage, F. Alexandre, J. Beerens and P. Tronc, Superlattices Microstruct. 6 (1989) 373; see also ref. [17]. 1191 D. Gammon, B.V. Shanabrook and D.S. Katzer, Appl. Phys. Lett. 56 (1990) 2710. [20] B. Deveaud, J.Y. Emery, A. Chomette, B. Lambert and M. Baudet, Appl. Phys. Lett. 45 (1984) 1078. [21] B. Deveaud, J. Shah, T.C. Damen and C.W. Tu, Appl. Phys. Lett. 51 (1987) 828. [22] J.I. Kusano, Y. Segawa, Y. Aoyagi, S. Namba and H. Okamoto, Phys. Rev. B 40 (1989) 1685. [23] T.C. Damen, J. Shah, D.Y. Oberli, D.S. Chemla, J.E. Cunningham and J.M. Kuo, Phys. Rev. B 42 (1990) 7434. [24] B. Deveaud, F. Cl&rot, N. Roy, B. Sermage and D.S. Katzer, to be published. [25] M. Tsuchiya, T. Matsutsue and H. Sakaki, Phys. Rev. Lett. 59 (1987) 2356. [261 Our experiment differs from that of Feldmann et al. [9] in the fact that we use resonant excitation, and our finding of a different behaviour is not astonishing.

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