Tailoring of the carrier capture efficiency of a quantum well

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Solid-State ElectronicsVol. 37~Nos 4-6, pp. 1167-1170,1994 Copyright i,~ 1994ElsevierScienceLtd 0038-1101(93)E0036-Z Printed in Great Britain.All rights reserved 0038-1101.'94 $6.00+0.00

TAILORING OF THE CARRIER CAPTURE EFFICIENCY OF A QUANTUM WELL J. M. GERARDIi" and B. DEVEAUD2 LFranceTelecom, CNET/PAB, Laboratoire de Bagneux, 196 av. Henri Ravera, 92225 Bagneux Cedex and :France Telecom, CNET/LAB, 22301 Lannion, France Abstract--A GaAs quantum well (QW) placed in an AIGaAs barrier layer of linearly graded composition has been studied by photoluminescence, so as to estimate experimentally the carrier capture efficiencyof a QW in an electric field. The capture probability can be drastically enhanced or reduced, by introducing a slight compositional asymmetry (3-6% AI) between both sides of the QW. This tuning is efficient for temperatures as high as 77 K. Our experimental results, supported by a quantum mechanical calculation of the capture probability, suggest novel routes for optimizing QW infrared photodetectors and QW lasers.

The efficiency of carrier capture processes often define the ultimate performance of quantum well (QW) based devices. For instance, the capture of photoexcited carriers by subsequent QWs limits the optical gain, and therefore the responsivity and detectivity of QW infrared photodetectors (QWIPs)[l], whereas the capture time of electrons in the optical cavity by the QWs limits the modulai:ion bandwidth of separate confinement QW lasers[2]. The capture efficiency of a quantum well (QW) markedly depends on its design. For instance, the oscillatory dependence of the capture time as a function of the QW thickness, predicted theoretically some years ago[3], has found recently a clear experimental confirmation from time-resolved photoluminescence (PL) studies[4-7]. It is therefore necessary (and possible) to take into account capture processes in a global attempt to optimize optoelectronic QW devices. Up to now, only a minimization of the electron capture time in undoped separate confinement multi QW heterostructures has been conducted[6]. It appears now more generally highly desirable: (l) to study the capture efficiency of a QW for electrons drifted by an E-field (which is the relevant situation for vertical transport optoelectronic devices such as QWlPs or electrically pumped lasers); (2) to be able to adjust independently such electronic properties of the structure as its operating wavelength and the QW capture efficiency. We show for the first time that the capture probability Pc of a drifted electron to be captured by a QW can be tuned very efficiently by introducing a slight asymmetry of the barrier heights of the QW. For moderate E-fields the dominant capture mechanism presumably relies on LO phonon scattering, as in absence of E-field. In order to avoid the capture of a carrier (e.g. an electron), we can raise the upstream tMember of the Direction des Recherches, Etudes et Techniques, French Ministry of Defense.

barrier height Vu with respect to the downstream barrier height Vd by typically htd)LO: even after emission of a single LO phonon, the electron still occupies a delocalized quantum state and can be drifted by the electric field. Electron capture then requires multiple phonon emission, and is therefore drastically less probable. On the other hand, the capture probability Pc can also be drastically enhanced by raising Va with respect to Vu. If the barrier height difference Vd - Vu is larger than the typical kinetic energy of incoming electrons, the capture probability will become close to unity. Since time-resolved PL experiments cannot be easily conducted for QWs under E-field, we introduced a novel approach which permits an optical investigation by c.w. PL of the influence of the QW barrier asymmetry on Pc. We mimic the presence of an E-field by inserting the QW whose capture efficiency is studied in a barrier of linearly graded composition. The PL intensity of the QW under continuous excitation of the upstream barrier is then proportional to the probability for injected electrons to be captured by the QW. We describe hereafter two series of experiments which highlight the efficient tuning of Pc resulting from a slight asymmetry of the QW composition profile. Our GaAlAs/GaAs test structures have been grown by molecular beam epitaxy (MBE) on GaAs (001) substrates; their design is plotted in the insets of Figs I and 2 for the first and second series of experiments respectively. Each sample comprises, from surface to buffer layer, a thick surface absorbing GaAIAs cap layer (0.4#m), the "upstream" GayAll_yAS graded barrier (dy/dz = l/~m-I), the GaAs QW "C", whose capture efficiency is studied, the "downstream" Ga, Al~_yAS graded barrier (dy/dz = l/~m - j ) and a broad GaAs QW " T ' . A low MBE growth rate (0.3#m) has been implemented in order to ensure a perfect control of the

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Fig. 1. Normalized 8 K PL spectra for the reference sample RI (Ay = 0), and for two modified samples, for which the electron capture by QW C is enhanced (Ay = -0.05) or inhibited (Ay = 0.05). The AI composition profile of these GaAs/GaAIAs heterostructures is sketched in the inset, by solid and dashed lines respectively. composition profile. Finally, the structure is entirely Be-doped low p-type (5 1016cm-3). Our c.w. PL experiment is performed at 8 K under excitation with the blue 476.5 nm line of an argon ion laser. For this wavelength the absorption coefficient in the cap layer A is • ~ 60,000 cm- ~, so that we have no significant direct excitation of QWs T and C. The generated electron-hole pairs diffuse in layer A, and the electrons are drifted in the apparent electric field of the graded barrier layer. The valence band configuration of this p type heterostructure is essentially fiat in our power density range (typically 500Wcm-2), so that this apparent electric field is close to 15 kV/cm in the graded layers, i.e. in the useful range for QWlPs. On the other hand, majority holes move nearly freely throughout the structure. A fraction Pc of the injected electrons is captured by QW C, whereas transferred electrons are collected in QW

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Fig. 2. Same as Fig. 1, for the reference sample R2(Ay = 0), and two modified samples (Ay = -0.03 and 0.03). The Al composition profile of these GaAs/GaAIAs heterostructures is sketched in the inset, by solid and dashed lines respectively. The PL intensity scale is the same for all samples.

T. At such a low temperature (8 K), thermoemission of electrons out of QW C can be neglected: since GaAs/GaAIAs structures have furthermore a radiative efficiency close to unity at low temperature, the PL intensity of QWs C and T respectively reflect the proportions of incoming electrons which have been captured or not by QW C, i.e. p~ and 1 -PcWe study in a first experiment a 65A thick GaovsA10.25As QW. In our reference sample R~, the downstream barrier of QW C has a 0.7% lower AI composition than the upstream barrier, in order to mimic the potential drop across the QW for a 1.5 kV/m electric field. In a series of "modified" samples, the A1 composition of the upstream barrier has been uniformly lowered (or raised) by a variable Ay. The PL spectra obtained at 8 K for three samples (Ay = 0, 0.05 and -0.05) are shown on Fig. 1. We observe for each sample two PL peaks, easily attributed to the thin QW C and to the large QW T. The relative intensity of these peaks is drastically affected by the introduction of a small barrier (Ay = -0.05) or a small "jump" (Ay = 0.05) for the drifted electrons: the PL intensity of QW T is reduced by a factor of 10 in the first case, and enhanced by a factor of 2.5 in the second case, which reveals a similar change for the proportion 1 - Pc of the transferred electrons. This efficient tuning of 1 - P c is obtained for a moderate change of the composition profile [Ay =0.03 corresponds to 45 meV change of the upstream barrier height, i.e. in the energy range of the (higher energy) AlAs-type LO phonons of the GaAIAs barrier ( ~ 4 7 meV)]. In this experiment however, the capture efficiency of QW C is always very large: pc, equal to 0.85 for the reference sample, remains larger than 0.5 for all samples. The comparison with our second experiment will indicate that this large capture probability is essentially related to the presence of a high barrier on the substrate's side of QW T, i.e. in the vicinity of QW C (distance: 37 nm). A second series of samples, which mimics more closely the conduction band configuration in QWIPs, has also been grown. Their structure, sketched in Fig. 2, differs of the first series in that: (1) the high barrier on the substrate's side of QW T has been suppressed, (2) the width of the downstream barrier has been enlarged up to 100 nm, (3) our reference QW C is now a 5 nm thick GaAs/Ga0gAl02As QW. Furthermore, the "modified" samples are now obtained by changing the height of the downstream barrier. The PL spectra obtained for the reference sample R2 (Ay = 0) and two modified samples (Ay = - 0 . 0 3 and 0.03) are displayed in Fig. 2. The capture probability Pc for the reference sample is now 0.4. Here again a drastic modification of the intensity ratio of QWs C and T emissions is observed when a slight QW asymmetry is introduced. It is worth being emphasized that the total PL intensity remains, as expected, essentially constant, p~ becomes close to 0.85 when the composition of the AI composition of

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Tailoring carrier capture efficiency of quantum well the downstream barrier is raised by 0.03, whereas capture probabilities as low as 0.15 and 0.10 are observed when it is lowered by 0.03 and 0.06 respectively. On the other hand, the PL peak energy of QW C is essentially unaffected for the "modified" samples: capture characteristics and other electronic properties of QWs can be optimized independently by using this technique. As required for any practical application to QWIPs, this effect is also observed at 77 K: we obtain Pc = 0.20, 0.45 and 0.70 respectively for Ay = -0.03, 0 or +0.03. Thermoemission of electrons from QW C totally blurs the data obtained at 300K (by strongly enhancing the PL intensity of QW T), and presumably accounts for the slight differences observed between 8 and 77 K results. No quantum mechanical calculation of Pc has been conducted up to now for carriers drifted in an electric field. We propose here a novel approach, which gives, despite its roughness, a good estimate of pc in QWIPs and describes satisfyingly the influence of Ay on PcTwo major problems are the difficulty to describe the overall relaxation of the electrons in the graded layer and the fact we need to take into account the finite coherence length of the electron wave function when calculating Pc. To overcome these difficulties, we consider an electron "just arriving" at QW C; we attribute to this electron a wave-paquet W, which typical extension is defined by the electron mean free path. We then compute the bound states Ik) of the heterostructure comprising both QWs, the graded layer and a semi-infinite barrier on the substrate's side of QW T, by a transfer matrix approach in the effective mass approximation. We calculate the scattering rate W,~ for single LO phonon emission processes for all possible initial and final electron minibands, by using Fermi's golden rule and a Frrhlich matrix element. We decompose IW) over the bound states of the structure and, retaining these dominant energy relaxation processes only, we estimate Pc as: Wk,~

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where c labels the miniband originating from the single bound state [e) of QW c. Figure 3 displays for both series of samples the influence of Ay on the calculated capture probability, for a 20nm broad real square wave-paquet. (This size corresponds to the typical mean-free path of the electron for a 1.5 106V/m electric field and a /a~=2000cm:V-Js-~ electron mobility in Ga08Al0,As[8]. ) For the reference samples R~ and R 2, we respectively estimate Pc to be 0.085 and 0.4. (For a lower quality barrier material, pc is somewhat larger, e.g. p==0.1 and 0.45 for a 15nm broad wave-paquet.) On the one hand, this clear difference confirms the drastic influence of the proximity of a high barrier on the capture efficiency of QW C,

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already observed experimentally. On the other one, our theoretical value for pc in sample R., (though much larger than a previous estimate of Pc obtained by admittance spectroscopy (Pc = 0.013)[9]) accounts particularly well for the Pc = 0.08 average estimate which has been extracted from the measurement of the optical gain of numerous QWIPs[10]. Though rather crude, our model is therefore very likely to describe accurately the influence of a QW asymmetry on pc. The theoretical dependence of Pc on Ay is plotted on Fig. 3. For the second series of samples (as well as QWIPs), a small Ay (lAy[ < 0.05) allows to reduce by a factor of three (down to 0.03) or enhance pc up to 0.95. Though the experimental relative dependence of p¢ on Ay is well described for both series of samples, differences are observed between experimental and calculated values of Pc. This effect is presumably related to the ambipolar character of the transport and capture in our samples. At the initial stage of the illumination, the capture probability by QW C is much larger for the holes than for the electrons. A photoinduced electric field Evh appears between Q W C and QW T under steady-state illumination[l !], in order to favor the transport of holes across the structure toward QW T. Consequently, the capture probability of the incoming electrons by QW C is enhanced (Eph is such that electron and hole currents flowing from QW C to QW T are equal; as such, Eph, and the capture probability of electrons are independent of the excitation power). We therefore do not expect our experiment on the reference sample to give a quantitative estimate for Pc in conventional QWIPs, but reflect only qualitatively the dependence of pc on Ay. The determination becomes however quantitative when pc is large, since nearly all photocreated electron-hole pairs then recombine in QW C. To conclude, the introduction of a slight compositional asymmetry for QW barriers allows to tune very efficiently the probability for electrons, drifted by an electric field, to be captured by this QW. This opens the way to an independent optimization of

J. M. GERARD and B. DEVEAUD

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capture characteristics and optical properties of numerous Q W based optoelectronic devices.? Acknowledgements--The authors gratefully acknowledge J. Y. Marzin, G. Bastard, J. F. Palmier, A. Regreny, B. Lambert, F. Cl6rot, D. Morris, M. Voos and M. Quillec for stimulating discussions. REFERENCES

1. Intersubband Transitions in Quantum Wells (Edited by E. Rosencher, B. Vinter and B. F. Levine). Plenum Press, New York (1992).

?Patent pending.

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