Optical processes in semiconductor quantum wells

Optical processes in semiconductor quantum wells

111 Surface Science 174 (1986) 111-119 North-Holland, Amsterdam OPTICAL PROCESSES C. DELALANDE IN SEMICONDUCTOR QUANTUM WELLS and M. VOOS Lab...

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Surface Science 174 (1986) 111-119 North-Holland, Amsterdam







and M. VOOS

Laboratoire de Physique de I’Ecole Normale Supkrieure, 24, rue Lhomond, 75231 Paris Cedex 05, France Received

30 July 1985; accepted

for publication

10 September


We present some results obtained on GaAs/Ga(Al)As single quantum wells by steady-state photoluminescence and excitation spectroscopy. It is shown that optical methods provide reliable information on these structures. The problems of the determination of the valence-band and conduction-band offsets, of the impurity profile at the inverted GaAlAs/GaAs interface, of the capture of photoexcited carriers by the well and of the temperature variation of the luminescence efficiency are discussed.

1. Introduction Optical probes provide reliable information on the properties of quantum well (QW) structures. In GaAs/Ga(Al)As multi-QWs, absorption measurements have been used to determine the valence-band and conduction-band offsets [l], AE, = 0.15 A EG and AE, = 0.85 AE, where AEG(x) is the difference between the band gaps of Ga,_,Al,As and GaAs. The low-temperature photoluminescence (PL) of high-quality MQWs has been attributed to excitonic recombination [2] but acceptor-related emissions have been also reported in nominally undoped structures grown by molecular beam epitaxy (MBE) [3]. On the other hand, the recombination lifetime and the carrier-capture rate by the well, when photoexcitation is provided in the Ga(Al)As barrier, have been measured by time-resolved experiments [4-61. We present here some recent results on these problems - band offsets, impurity trapping, carrier relaxation - obtained by steady-state photoluminescence and excitation spectroscopy on GaAs/Ga(Al)As single QWs, and we compare these results with other investigations reported in the literature.

2. Determination

of band offsets

GaAs and Ga,_,Al,As are two direct-gap semiconductors whose low-temperature energy gaps are well known [7] Eo(Ga,_,Al,As)

(for x < 0.435)

= 1.5192 + 1.247x eV.

0039-6028/86/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division) and Yamada Science Foundation

Excitation spectroscopy, like absorption spectroscopy is a good tool for the determination of conduction-band (A E,) and valence-band (A E, = A E,; AE,) offsets: the energy positions of the electron states E,, and of the heavy (or light) hole states H,,(L,,) which arise from the yuantization of the electronic motion along the growth direction z of the QW have been shown theoretically to be sensitive to the conductionand valence-bands offsets, because of the relative penetration of the carrier wavefunctions in the GaAlAs barrier [8]. Unfortunately, the predominant n - m = 0 optical transitions are found to be weakly sensitive to the offsets: the increase of the energy confinement of E, which is obtained when A EC is increased is compensated by the corresponding decrease of the energy confinement of H,,. The pioneer determination of Dingle [l] (obtained via a fitting of the n - nr = 0 transitions) has been recently reappraised by Miller et al. [9,10]. Using excitation spectroscopy measurements, these authors have fit the weakly allowed E,-H, transition whose energy is actually sensitive to the band offsets and determined Qc = A EC/A E, = 0.57 for x = 0.3. The structures we have investigated consist of a GaAs QW embedded in a Ga,_,,Al,,As thicker one, the latter being clad between thick Ga, _,2AI,2As layers with x2 > x,, as shown in fig. 1 [ll]. They are known as quantum well separate confinement heterostructures (QWSCH) and have been grown by





Fig. 1. Sketch of the QWSCH structures transitions described in the text.


Also shown

are the three types of optical

C. Dela~a~de, M. Yeas / O~t~e~lF~~esses

in semiconductor




MBE at CNET Bagneux by Alexandre and L&in. The aluminum concentration xi is 0.13. Three different kinds of transitions can be observed in the excitation spectrum of these QWSCHs: transitions involving quantized levels (i) both essentially localized within the narrow GaAs well; (ii) with one state (initial or final) in the barrier; (iii) both in the barrier. The calculation of the energy levels following the three band envelope function approximation [4] shows that the transitions (i) are very sensitive to the width of the GaAs QW; the tr~sitions (iii) are essentially sensitive to the aluminum concentration x,; that gives precise values of the width and of xi; the transitions (ii) are the more sensitive to the band offsets. Fig. 2 displays the theoretical dependence of the various transitions as a function of Q,, for a sample consisting of a 50 A GaAs QW inserted in a 200 A Ga,,,,Al,,,,As one. Note the appearance of an n - m = 1 odd transition in this asymmetrical structure (the QW is at 50 A from one side). By fitting three different (ii) transitions, a value of Qc = 0.59 + 0.03 was found. Similar experiments performed on symmetrical QWSCHs with comparable xi have led to the same Q, value. It is worth noting that the expe~mental 1121or theoretical 1131binding energies of the exciton have to be taken into account. The parameters used



Fig. 2. Calculated dependence of the transition energies on the ratio of the conduction-band discontinuity to the total band-gap difference for the asymmetrical QWSCH described in the text. The observed transitions, corrected for the binding energies of the excitons and with the reiated uncertainty, are indicated on the ant-hand side of the figure.


C. Delalande, M. Voos /

Opticalprocesses in semiconductor quantum WCIIS

were 341 - 66x meV for the spin-orbit energy at the r point; O.O67m,, (0.48 + 0.31x)m, and O.O94m, for the electron, heavy-hole and light-hole effective masses, respectively. The uncertainties due to the lack of precise knowledge of these parameters have been also shown to be small. This value (Q, = 0.59, x = 0.13) must be compared to the already mentioned value of Miller et al. [9] (Qc = 0.57, x = 0.3) and that of Dawson et al. [14] (Q, = 0.75, x = 0.3) both obtained by excitation spectroscopy. The measurement of the two-dimensional carriers density in modulation-doped heterostructures and a comparison with a theoretical model which needs the value of the binding energy of acceptors ]15] for p doping or donors [16] for n doping the strong has given also a value near 0.6 (x = 0.5 or 0.3). In conclusion, dependence of the optical transitions on Q, in the case of QWSCHs seems to give an accurate value of the offsets for the x = 0.13 MBE-grown samples, in accord with other recent results.

3. Impurity trapping profile at the GaAs/Ga(AI)As


The binding energy of shalow impurities varies with its localization in the QW 1171. By selectively doping the center of the well. it has been possible to measure the well-width variation of the binding energy of Si donors [IS] and Be acceptors 1191. Observation of emissions related to acceptors trapped in the well in nominally undoped GaAs QW has also been reported [3]. Except in the narrow wells, the energy of the impurity-related luminescence line showed that the impurity was mainly trapped at the QW interface, which may be due to the difference of solubility in GaAlAs and GaAs: the impurity (which may be carbon) keeps floating at the GaAlAs/vacuum interface during growth and is trapped in the first few monolayers of GaAs [20]. The low-temperature luminescence spectra of our QWSCHs display, at low excitation power, an acceptor-related emission which becomes saturated at high excitation, showing then mainly the intrinsic narrow (= 3 meV) peak associated with n = 1 electron to heavy-hole exciton recombination, as corroborated by excitation spectroscopy measurements. The measured binding energy of the acceptor, obtained by taking into account the binding energy of the exciton [13], is compared to the calculated one following Bastard’s variational approach ]17] in fig. 3. That shows that the acceptors are actually distributed at the well interfaces (probably the first Ga(AI)As/GaAs interface) even for well thickness smaller than 70 A, in contrast to other studies [3], possibly due to a different impurity concentration. In order to evaluate the extension of the impurity distribution near the interface, we have calculated the theoretical lineshape associated with the recombination of electrons to acceptors distributed in the structure. Taking a trial wavefunction of the bound hole as in ref. [17], we assume a Boltzmann

C. Delalande, M. Voos / Optical processes in semiconducror quantum wells

Fig. 3. Calculated (full line) and experimental energy on the well thickness for an aluminum

(dots) dependence of the on-edge concentration of 0.15.




electronic distribution of temperature T = 2 K. As for the holes, we suppose that they are close to the steady-state saturation regime, in which each acceptor state is filled with a hole. We believe that this condition is satisfied in our samples since (i) the integrated intensity of the acceptor-related PL is nearly independent of the excitation power density and (ii) no significant deformation of its lineshape can be detected with increasing power density. In any case, attempts to fit the observed lineshape using a thermalized hole distribution have led to a linewidth considerably narrower than the experimental one ( = 10 meV). Under these conditions, various numerical simulations have shown that the extension of the impurity distribution varies approximatively from 12 to 30 A in the GaAs QW and from 6 to 8 A in the Ga(Al)As barrier. The latter features may be due to exodiffusion processes of the in-well incorporated acceptors during growth. Fig. 4 displays the experimental and calculated electron to acceptor PL spectra for a 50 A QW sample. In addition, we have found that a fit of the acceptor-related PL lineshape of 50 A GaAs wells grown after 1500 A should involve acceptor distributions which extend at least Ga o,ssA1,,,,As twice as far in the GaAs well than that of GaAs wells grown after 500 A Ga o.ssA1,,,,As. This result is in agreement with previous results correlating the purity and roughness of the inverted GaAlAs/GaAs interface with the thickness of the preceding GaAlAs layer [21]. This corroborates the important role of thin GaAs prelayers grown before the actual structure in order to improve their luminescence properties as well as their device performance.

C. Delalande, M. Voos / Optical processes in semiconductor







quantum wells

(meV 1

Fig. 4. Experimental (full line) and calculated (dashed line) electron to acceptor photoluminescence lineshape for a 50 A QW with x = 0.15. The best fit is obtained when the center of the impurity distribution is taken at b = 6.5 A in the GaAlAs barrier; W = 12 a and Z = 28.25 A are the parameters taken in the calculation for the extension of the impurity distribution into the barrier and the well. respectively.



is thus clear that into the impurity

optical experiments trapping problem.

4. Carrier capture by the well and luminescence


give powerful




One of the most useful applications of QWs lies in the achievement of lasers which display improved performance over the conventional double heterostructure laser. One of the reasons is that the carriers injected into the Ga(Al)As barrier are efficiently collected by the QW. Time-resolved experiments have been performed at 2 K and have been interpreted in terms of carrier capture times varying from 50 ps [4] to 2 ns [5], depending perhaps on the quality of the sample and of the barrier length. Other estimates lead to a transfer time of the order of 0.1 ps [22]. An indirect method of determining the capture time consists in measuring the relative luminescence efficiencies when optical excitation is provided (1) in the GaAs QW and below !he GaAlAs barrier, (2) above the GaAlAs barrier. Fig. 5 displays the integrated intensities of the QW PL in case (1) (curve 1) and case (2) (curve 2a) as well as the GaAlAs barrier PL in case (2) (curve 2b) as a function of temperature in the 15-200 K range, for a 10 nm QW clad between

C. Delalande, M. Voos / Optical processes in semiconductor quantum wells






(K 1

Fig. 5. Integrated intensities of the luminescence of the 100 A, x = 0.16 QW localized at 500 A of the vacuum surface as described in the text. Curve I, corresponds to an excitation at 1578 meV, above the GaAs QW gap but below the Ga(A1)As gap. Curve I,, corresponds to an excitation at 1750 meV, above the Ga(Al)As gap. Also shown (curve I,,) the PL of GaAL4s in the second case.

a 300 nm and a 50 nm (near the surface) Ga,,,,Al,,,As barrier. This sample has been grown by metal-organic chemical vapor deposition by Frijlink at LEP. It can easily be observed that, in the 100-200 K range, the integrated intensity is roughly 30 times larger when the laser energy provides excitation in the barrier than when it provides excitation only in the QW. An evaluation of the ratio of the number of photoexcited carriers can be made. In case (1) we do excite the E,-H, and E,-L, optical transitions. In case (2), we evaluate to about 30 the number of two-dimensional electronic levels excited in the 350 nm GaAlAs barrier, roughly 35 meV above the gap. It is also the ratio of the integrated luminescence intensities. Thus, we find that the capture by the well is faster than the Ga(Al)As barrier luminescence process (curve 2b) and also than the non-radiative processes involving Ga(Al)As barrier. At low temperature, the ratio of the integrated luminescence intensities decreases by a factor of 2, whereas the luminescence efficiency of the barrier increases, due to impurity-related lines. That is consistent with a trapping of


C. Delalande,

M. Voos /


in semiconductor

quantum wells

the excitation on defects (or impurities) in the alloy at low temperature which prevents the carriers to reach the well, as suggested also in time-resolved experiments [5]. It is worth noting that the temperature variation of the radiative efficiency is much smaller below 100 K than in the 100-200 K range. That is consistent with a radiative nature of the recombination process at low T. As can be seen in fig. 5, when T increases from 100 to 200 K, the measured luminescence efficiency decreases by a factor of 103, indicating an increase of the non-radiative process rate. Following the usual approach, we plot in fig. 6 the same results in an Arrhenius plot. A slope of 2000 K (166 meV) is found in this 10 nm, x = 0.16 sample. Larger values are found in samples with larger X: 173 meV for a 5 nm, x = 0.28 sample and 234 meV for a 10 nm, x = 0.35 one. The larger this slope, the larger the temperature of the onset of the decrease of the radiative efficiency, indicating that the non-radiative processes need a higher temperature to be activated. What is the non-radiative process involved? It may be a recombination at the GaAs-Ga(Al)As interface which is concentration dependent. It may also be a temperature-induced de-trapping process of the carriers out of the well





Fig. 6. Arrhenius plot of the QW PL efficiencies I Za for (166 meV) a 100 k QW. x = 0.16 sample. (173 meV) a 50 A, x = 0.28 one, and (234 meV) a 100 A, x = 0.35 one. No attention has been paid to sample to sample PL efficiency variation, which means that the vertical scale is different for the three samples.

C. Delalande, M. Voos / Optical processes in semiconductor quantum wells


followed by surface recombination at the Ga(Al)As-vacuum interface which is only at a distance of 50 nm from the QW. Obviously much work is needed there but the experimental results are interesting for their own sake.

Acknowledgements We are grateful to M.H. Meynadier, J.A. Brum and G. Bastard for their contribution to this work. We wish also to thank F. Alexandre and J.L. Lievin from
References [l] R. Dingle, in: Advances in Solid State Physics, Vol. 15. Festkorperprobleme, Ed. H.J. Queisser (Pergamon/Vieweg, London/Braunschweig, 1975) p. 21. [2] C. Weisbuch, R.C. Miller, R. Dingle, A.C. Gossard and W. Wiegmann, Solid State Commun. 37 (1981) 319. [3] R.C. Miller, W.T. Tsang and 0. Munteanu, Appl. Phys. Letters 41 (1982) 374. [4] E.O. GBbel, H. Jung, J. Kuhl and K. Ploog, Phys. Rev. Letters 51 (1983) 1588. [5] T. Miyoshi, J. Aoyagi, Y. Segawa, S. Namba and M. Nunoshita, Japan. J. Appl. Phys. 24 (1985) L53. [6] Y. Masumoto, S. Shionoya and H. Kawaguchi, Phys. Rev. B29 (1984) 2324. [7] H.C. Casey and M.B. Parrish, in: Heterostructure Lasers (Academic Press, New York, 1978). [8] S.R. White and L.J. Sham, Phys. Rev. Letters 47 (1981) 879. [9] R.C. Miller, D.A. Kleinman and A.C. Gossard, Phys. Rev. B29 (1984) 7085. [lo] R.C. Miller, A.C. Gossard, D.A. Kleinman and 0. Munteanu, Phys. Rev. B29 (1980) 3740. [ll] M.H. Meynadier, C. Delalande, G. Bastard, M. Voos, F. Alexandre and J.L. Litvin, Phys. Rev. B31 (1985) 5539. [12] R.C. Miller, D.A. Kleinman, W.T. Tsang and A.C. Gossard, Phys. Rev. B24 (1981) 1139. [13] J.A. Brum, private communication, following the treatment of R.L. Greene and K.K. Bajaj, Solid State Commun. 45 (1983) 831. 1141 P. Dawson, G. Duggan, R.I. Ralph and K. Woodbridge, Superlattices Microstructures 1 (1985) 173. [15] W.I. Wang, E.E. Mendez and F. Stem, Appl. Phys. Letters 45 (1984) 639. (161 G. Bastard, private communication. [17] G. Bastard, J. Luminescence 30 (1985) 488. [18] B.V. Shanebrook and J. Comas, Surface Sci. 142 (19aq) 504. [19] R.C. Miller, J. Appl. Phys. 56 (1984) 1136. [20] R.C. Miller, A.C. Gossard and W.T. Tsang, Physica 117/118B (1983) 714. [21] W.T. Masselink, M.V. Klein, Y.L. Sun, Y.C. Chang, R. Fischer, T.T. Drummond and H. Morkg, Appl. Phys. Letters 44 (1984) 435. [22] J. Christen, D. Bimberg, A. Steckenbaum and G. Weimann, Appl. Phys. Letters 44 (1984) 84.