Efficient tuning of the carrier capture efficiency of

Efficient tuning of the carrier capture efficiency of quantum wells by introducing a barrier asymmetry J. M. Gerard, B. Deveaud, and A. Regreny Citation: Appl. Phys. Lett. 63, 240 (1993); doi: 10.1063/1.110353 View online: http://dx.doi.org/10.1063/1.110353 View Table of Contents: http://apl.aip.org/resource/1/APPLAB/v63/i2 Published by the American Institute of Physics.

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Efficient tuning of the carrier capture by introducing a barrier asymmetry

efficiency

of quantum

wells

J. M. Gerarda France T&corn,

CXET/P.4 B, 196 Au. Henri Ruuera, 92225 Bagneux Cedq

France

B. Deveaud and A. Regreny France T&corn,

CNET/LAB,

22301 Lannion, France

(Received 8 February 1993; accepted for publication

18 May 1993)

A GaAs quantum well (QW) placed in an AlGaAs barrier layer of linearly graded composition has been studied by photoluminescence, in order to estimate experimentally the carrier capture efficiency of a QW in an electric field. The introduction of a slight compositional asymmetry (3% to 6% Al) between both sides of the QW allows to enhance or drastically reduce the capture probability. 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. Carrier capture processes play a key role in defining the ultimate performance of quantum well (QW) lasers and infrared photodetectors (QWIPs). In separate confinement multi=QW lasers, the capture time of electrons by the QWs has to be minimized in order to get an optimal threshold current and modulation frequency for this device.’ On the other hand, an inefficient transport of the captured carriers from well-to-well also results in an inhomogeneous differential gain in the various QWs, and in a reduction of the modulation bandwidth.2 Since holes are captured very efficiently by the first QWs, an optimization of the device performance presumably requires not only a minimization of the electron capture time but also an enhancement of the capture time of holes by the first QWs so as to homogenize hole injection. Concerning QWIPS,~,~ the capture by QWs limits to typically 8 ps the lifetime of the photoexcited carriers in the barriers, to be compared with ,us lifetimes in conventional HgCdTe based photodetectors. A reduction of the carrier capture efficiency is obviously highly desirable, since it would provide an enhancement of the optical gain, responsivity, and presumably detectivity’l of QWIPs. It is necessary, for lasers as well as QWIPs, to adjust the capture probability p, of carriers that drift across the QW by an electric field, in order to get an optimum performance of the device. Capture processes in absence of electric field are well modeled and understood.“-’ The dominant capture mechanism of a carrier (e.g., an electron) by the QW is mediated by LO phonon scattering. If the kinetic energy of the incoming carrier is lower than fitiLo, the emission of a single LO phonon (with energy %+o) scatters this carrier towards a quantum level confined in the QW: it will then quickly relax towards the bottom of the QW and can, therefore, be considered captured. Under E field, the efficiency of capture processes are far from being so well understood. We propose in this letter an original technique to investigate pc and show for the first time that it is possible to tune pi very efficiently (for a given E field and QW width) by means of the introduction of a slight asymmetry ‘iMrmhrr of the Direction des Recherches, Etuda et Techniques, French Ministry of Defense. 240

Appl. Phys. Lett. 63 (2), 12 July 1993

in the QW structure. More precisely, we suggest to rise or lower by typically hLo the downstream barrier height vd with respect to the upstream barrier height VU of the QW. If r;, is lowered, scattered carriers will still occupy, after emission of a single LO phonon, a &localized quantum state: as such these can be drifted by the electric field and avoid being captured by the QW. The capture now relies on less probable processes involving multiple-phonon emission and a drastic reduction of pc is expected. Since for moderate electric fields (in the 10 kV/cm range), LO phonon emission is an efficient relasation mechanism, the kinetic energy of a drifted carrier is, at most, fitiLo. When raised by &+o, the downstream barrier will act as a barrier to the drift of the carriers, and the capture probability will approach unity. Measurements of capture times in the absence of E field are generally obtained by time resolved spectroscopy, which cannot be used under E field. Up to now, only eaperimental measurements of the optical gain of QWIPs gave an (indirect) access top,. We propose as an alternate method to mimic the presence of an E field by introducing the QW in a barrier layer of linearly graded composition. The photoluminescence (PL) intensity of the QW under continuous excitation of the upstream barrier is directly relat.ed to the capture efficiency of the injected electrons by the QW. The tuning of pc resulting from the introduction of an asymmetry of the barrier heights is clearly evidenced this way, as shown hereafter. Finally, experimental estimates ofp, are in reasonable agreement with the results of a quantum calculation of the capture probability. Our test structures have been grown by molecular beam epitaxy (MBE) on GdAs (001) substrates. Their structure is sketched, from sample surface to buffer layer, in Fig. 1. The 5 nm thick GaAs/Ga,,8Alo,2As QW C, whose capture is studied? is placed at the center of a 200 nm thick Ga,AII-,As layer of graded composition (CRY/ dz= 1 pm-‘). A 0.4 pm thick Al,,,G+,,As layer fi on top, and a 12 nm broad QW Tat the bottom ofthe graded layer complete this structure, which is entirely Be-doped low p type (5 x 1Ol6 cm-‘). The growth has been performed at a

0003-6951/93/63(2)/24Oo/31$6.00

8 1993 American Institute of Physics


240

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FIG. 1. Ahm~inum composition profile of three GaAs/ Ga, ,Al,.As heterostructures, for which the capture efficiency of Q W C is studied by PI.. Solid line: reference sample, dashed line: structure enhancing the electron transfer CA-59 < 03, dotted line: structure enhancing electron capture (Ay30).

low rate (0.3 yrm/h) so as to get a perfect control of the composition protile, especially for QW C. Under continuous illumination, electron-hole pairs are generated in the absorbing cap layer A; electrons diffuse in layer A, and are drifted in the apparent electric field of the graded barrier layer. In our power density range? the valence band configuration of the p-type heterostructure is essentially flat. As a result, electrons experience an apparent electric field close to 15 kV/cm in the graded layers, i.e., in the useful range for QWIPs. 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 1: Since GaAs/GaAlAs structures have a radiative efficiency close to unity at low temperature, the PL intensity of QWs C and 7; respectively, reflect the proportions of captured and transferred electrons for QW C. In the reference sample R, the downstream barrier of QW C has a 0.7% lower Al composition than the upstream barrier, in order to mimic the potential drop across the QW for a 1.5 k-V/m electric field. “Modified” sampics have also been studied, for which the Al composition of the downstream barrier is uniformly lowered (or raised) by A-b$Ay= -=0.03,--Oo.06, or 0.03 j. One can note that for &~?=0.03, the change of the downstream barrier height (~45 meV) is slightly larger than the energy of LO phonons in GaAs (36 me13), and in the energy range of the Al&-type LO phonons in GaAlAs (47 meV). The low temperature (8 K) YL spectra obtained for sample R and two modified samples are displayed in Fig. 3, for a 500 W!cm’ power density of the exciting blue 476.5 nm line of a11 argon ion laser. We observe for each sample two PL peaks, easily attributed to the thin QW C (higher energy PL peak) and to the large QW T. For this wavelength the absorption coefficient in layer .I is zrz60 000 em- ‘. which ensures that we have no significant direct excitation of QWs 7’and C. This is confirmed experimentally: the rclative intensities of these peaks do not change for a green (514.5 nm) exciting light. On the opposite, the rrlative emission of QW T is much stronger under 647.1 nm red laser excitation (a -20 000 cm--‘), and a third peak corresponding to the emission of the GaAs buffer layer then appears: the weaker absorption of the incident light by the cap layer allows here 9 direct excitation of QWs 1’and C. 241

Appl. Phys. Mt.,

Vol. 63, No. 2, 12 July 1993

&

1.5”” ENERGY Le’.‘)

FIG. 2. PL spectra obtained at 8 K for the referense sample (Ay=O), and for two modified samples, for which the electron capture by Q W C is enhanced (Ay= -‘0.03) or inhibited (.Ay=O.O3). The intensity scale is the same for the three samples.

Except for the lower values of the excitation power (PC 100 W/cm’, typically) for which nonradiative recombination processes can eventually play a dominant role, the relative intensities of both PL. peaks remain constant when P is varied. For the power densit.ies we implement, we do not observe any significant broadening of the PL peaks. Owing to the low electron temperature, and low electron concentrations in QW C, and considering the large barrier height of this QW, we can reasonably neglect the thermoionic escape of electrons from QW C. We can therefore assume with some confidence that the relative (integrated) PL intensities of QWs C and T actually reflect the proportions of electrons which are captured by QW C or transferred to QW T. We can now discuss the impact of the design of QW C on pr. In our reference sample R? the capture probability by Q W C, PC, is typically 400%. As highlighted on Fig. 2, a slight AJ~drastically changes the PL intensity ratio of QWs C and T, whereas the total YL intensity is essentially unaffected. pr becomes close to 35% when the composition of the Al composition of the downstream barrier is raised by 0.03 (a value as large as 95% for ;1Jp-O.O5 has been mea sured for another series of samples), whereas capture probabilities as low as 15% and 10% are observed when it is lowered by 0.03 and 0.06, respectively. On the other hand, the optical transition energy of QW C is, as expected, only slightly shifted (by a few meV at most) by the modification of the structure. This suggests that capture characteristics and optical properties of a QW can essentially be optimized independently. As required for any practical application to QWIPs, this effect is also observed at 77 K: we obtain p,=20%, 45%, and 70%, respectively, for Ay= -0.03, 0, or +0.03. Thermoemission of electrons from QW C totally blurs the data obtained at 300 K (by strongly enhancing the PL intensity of QW r>, 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 for estimating pc theoGerard, Deveaud, and Regreny


241

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Ar FIG. 3. Experimental and theoretical electron capture probability pe as a function of Ay. Please note the logarithmic scale for pe.

retically, which will, despite its simplicity, satisfactorily describe the influence of Ay on pc, for our samples (and therefore, also for QWIPs under E field). We first calculate the bound states ) n) of the overall structure defined by both QWs, the layer of graded composition and a quasi-infinite barrier layer on the substrate’s side of QW T. We then compute the scattering rate r~i~for single LO phonon emission processes, for all possible initial and final electron minibands, by using Fermi’s golden rule and a Frohlich matrix element (see, e.g., Refs. 5-7). Since QW C supports a single bound state ( c), the capture probability of an electron in state ) i) can then be written as

It is obviously very difficult to describe the overall relaxation of an injected electron in the graded layer. In particular, we obviously have to take into account the finite coherence of the electrons’ state. We will simply consider an elect.ron in the upstream barrier, “just arriving” at QW C, and study its capture probability. We attribute to this electron a wave-paquet $J, decompose I/I over the bound states 1k) of the structure, and evaluate p,. as follows:

Figure 3 displays the influence of Ay on the calculated capture probability for a 20 nm broad real square wave paquet. (This size corresponds to the typical mean-free path of the electron for a 1.5 ‘x lo6 V/m electric field and a p,=2000 cm’ V-’ s-’ electron mobility in Gae,Al,,,As8.) This calculation gives a 8.5% estimate for pc in the reference sample. For a better quality barrier material, pe would be lower; for instance p,=7% for a 40 nm broad wave paquet. [We can aiso note that for pp= 2000 cm2 VI’ s-l, the average kinetic energy of an electron in GaAlAs ( 16 meV) is typically h/2. Since the kinetic energy Ek of a drifted carrier is at movt tiLc,, a reasonable distribution function for the electrons arriving at QW C is given by an equiprobability of Eh in the [0, &l>Lo] range. For this specific distribution function, the cdlcuhdted dependence of pc on Ay is very close to the one obtained in the previous model and shown in Fig. 3. The photoconductive gain g of QWIPs is simply related to pc. For detectors implementing a transition be242

Appt. Phys. Lett., Vol. 63, No. 2, 12 July 1993

tween a bound state and a continuum state, a photoexcited electron has a very large probability to be drifted by the electric field, and contribute to the current g, which is the ratio of the signal current by the number of absorbed photons, is then roughly given by l/Now pc- A more detailed derivation’ of g leads to gem’= NQw p,( 1 + p,). From numerous measurements of g for a variable number of Qws, an 8% estimate has been obtained far p. (4%gp,