AlSb quantum wells

Physica E 2 (1998) 121—125

Landau-level lifetimes in PbTe nipi superlattices, PbTe/PbEuTe and InAs/AlSb quantum wells C.J.G.M. Langerak!,*, B.N. Murdin", C.M. Ciesla#, J. Oswald$, A. Homer$, G. Springholz%, G. Bauer%, R.A. Stradling&, M. Kamal-Saadi", E. Gornik', C.R. Pidgeon# ! FOM Institute for Plasma Physics ‘Rijnhuizen+, NL-3430 BE Nieuwegein, The Netherlands " Department of Physics, University of Surrey, Guildford, GU2 SXH, UK # Department of Physics, Heriot-Watt University, Edinburgh, EH14 4AS, Scotland, UK $ Department of Physics, University of Leoben, A-8700 Leoben, Austria % Department of Physics, University of Linz, A-4040 Linz, Austria & Department of Physics, Imperial College, London, SW7 2BZ, UK ' Institut fur Festkorperelektronik, T.U. Wien, A-1040 Wien, Austria

Abstract Landau-level lifetimes are determined from saturation cyclotron resonance (CR) in wide parabolic wells, quantum wells and bulk PbTe—Pb Eu Te systems. These narrow gap structures exhibit strong band non-parabolicity necessary 1~x x to terminate the normally equi-spaced Landau-level ladder. It was not possible to saturate the bulk sample, but short lifetimes, of between 1.5 and 8 ps, were obtained for the wide parabolic well and the quantum well, respectively, utilising a multi-level rate equation model. We also report the first pump—probe cyclotron resonance result in an InAs—AlSb quantum structure. The pump—probe experiment provides a direct determination of the lifetime, giving q"40 ps in this InAs—AlSb sample. This shows good agreement with an 8]8k ) p calculation. ( 1998 Elsevier Science B.V. All rights reserved. Keywords: Landau-level lifetimes; Saturation spectroscopy

1. Introduction Electronic lifetimes in semiconductor quantum wells are of interest both for fundamental research and application in opto-electronic devices. The availability of tunable, high intensity, picosecond far-infrared pulses from free-electron lasers has * Corresponding author. Tel.: #31 30 6096999; fax: #31 30 6031204; e-mail: [email protected].

greatly improved the ability to make intra-band relaxation-time measurements. Saturation spectroscopy is a well-suited technique for the quantitative determination of carrier relaxation in quantising magnetic fields when the lifetime of interest is shorter than the length of the exciting optical pulse [1,2]. When the lifetime is longer than the optical pulse length, the more direct pump—probe measurement becomes possible. The basic requirement for both types of measurements is the bleaching of the

1386-9477/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved PII: S 1 3 8 6 - 9 4 7 7 ( 9 8 ) 0 0 0 2 7 - 7

122

C.J.G.M. Langerak et al. / Physica E 2 (1998) 121—125

absorption due to high intensity excitation between absorbing states. The bleaching is studied as a function of intensity in the saturation experiment, whilst in the pump—probe experiment the recovery of the bleaching is studied as function of delay-time between the pump and the probe. In order to achieve saturation of the cyclotron resonance, the ladder of equi-distant Landau levels needs to be truncated. In contrast with GaAs, narrow gap semiconductors (such as the PbTe- and InAs-based materials) exhibit a large band non-parabolicity, terminating the excitation of the Landau-level ladder. In this paper we report Landau-level lifetimes in PbTe—PbEuTe samples obtained by saturation spectroscopy. In addition, we present what to our knowledge are the first far-infrared pump—probe cyclotron resonance data, on an InAs—AlSb quantum structure.

period multi-quantum well structure with well width of 7 nm (MBEG214). In the MQW sample the quantum wells are separated by 56 nm wide barriers of Pb Eu Te with x"4.7%. By an anal1~x x ysis of the CR peak positions (below) at three different wavelengths we deduce that the carrier concentration is 5.5]1011 cm~2. The bulk sample is a 2.5 lm thick epilayer with a carrier concentration of 3.2]1017 cm~3, which is close to the 3D equivalent carrier concentration of the nipi structure. All PbTe samples were grown on (1 1 1) oriented BaF substrates. 2 Using a set of band parameters for PbTe as given in Ref. [5] we have calculated the fan-diagram of Landau levels of the two types of valleys, as shown in Fig. 1 for the nipi sample. To illustrate the importance of the band non-parabolicity arrows indicate the j"70 lm (17.76 meV) 0~P1~ CR transition. Subsequent higher transitions at the

2. Magneto-saturation spectroscopy on PbTe PbTe is a narrow gap (E "190 meV), IV—VI ' multi-valley semiconductor, whose conduction band minima are located at the eight L-points in the [1 1 1] directions. When a magnetic field is applied parallel to the [1 1 1] direction (which is the growth direction) two cyclotron resonances can be observed: one from the valley oriented along the [1 1 1] growth direction (longitudinal) and one from three equivalent valleys tilted by 70° from the [1 1 1] direction (oblique). Furthermore, PbTe exhibits a large spin-splitting of approx. 0.6]+u for # the lowest levels. We have studied bulk PbTe, nipi structures and quantum well samples. In the latter the second resonance is absent due to the strong confinement. The nipi structures were grown to produce wide parabolic wells, with effective channel widths of the order of 500 nm, a 2D electron concentration of N "1.2]1013 cm~2, and a mobility of 105 cm2/ 4 Vs. Novel and interesting magneto-transport phenomena have been observed in these samples [3,4]. The subband spacing for the nipi is 1.2 meV in the oblique valleys and nearly a factor of 10 less for the valley along the [1 1 1] growth direction. The results of this nipi wide parabolic well sample (B64) are compared to a bulk sample (B69) and a 40

Fig. 1. Landau levels and Fermi energy for both the longitudinal and oblique valleys. # and ! indicate the spin orientation and the vertical arrows indicate the transition energies at the resonance position of the 0!P1! transition, for j"70 lm.

C.J.G.M. Langerak et al. / Physica E 2 (1998) 121—125

same magnetic field require a far-infrared energy much smaller than the spectral width of FELIX would allow for. The Fermi-energy is also plotted in Fig. 1, showing that the nipi experiments are performed in the quantum limit, i.e. without excitation all carriers are in the lowest Landau level. In the quantum well samples this is not the case, due to the higher carrier concentration, and here we excite the 1`P2` transition (i.e. all levels below the 1`-level are full). The measurements have been performed using the far-infrared picosecond free-electron laser FELIX at Rijnhuizen [6]. FELIX delivers macropulses of typically 4 ls duration at a frequency of 5 Hz. Each macropulse consists of a train of micropulses 8—15 ps long, separated by 1 or 40 ns. The spectral range covered in this experiment (between 50 and 80 lm) was limited by the Reststrahlen band of the BaF on the short wavelength side 2 (j'50 lm) and the PbTe Reststrahlen band on the long wavelength side (j(90 lm). These photon energies are above the LO-phonon energy of PbTe (14 meV). Fig. 2 shows the result of a saturation experiment on the wide parabolic well sample at j"70 lm. From the line shape (no broadening at higher intensities) it is evident that we indeed saturate the absorption and that carrier heating does not take place [2]. The bulk sample shows a similar line shape with the two resonances present, but even at the highest intensity we do not observe any saturation. In contrast the quantum well sample

Fig. 2. Normalised magneto-transmission at different peak intensities for the nipi sample at j"70 lm. The experiment is carried out at ¹"2 K.

123

shows only the low field resonance and saturation is achieved. To allow comparison between the three samples, we have evaluated all the data using the same multi-level rate equation model [1]. For each level the following rate equation is evaluated: dN i"/[A !A ]#[N (1!N )/q] i~1 i i`1 i dt ![N (1!N )/q], i i~1 where N is the carrier concentration in Landau i level i, and q is the non-radiative relaxation time, assumed to be the same for all Landau levels. The polarisation active photon flux per electron /" I/2N+u, where N is the total carrier density. A is i the absorption coefficient from Landau level i into i#1 and is calculated from the fill-factor-dependent sheet conductivity. A also depends on the i Landau-level separation, which depends on i due to the band non-parabolicity. By solving the rate equations in the steady state, we can find the N values and hence the total absorption as a funci tion of intensity. The absorption lines are fitted to the experiment using q as a free parameter. The band non-parabolicity terminating the Landaulevel ladder is taken from Ref. [5]. For the bulk sample (B69) we do not see even an onset of saturation at the highest powers used. A 3D system in a magnetic field has a continuous density of states. Since the excitation is at energies above the LO-phonon energy, a fast relaxation involving LO-phonon scattering is always possible. This would imply saturation intensities beyond that which we can obtain. In a 2D system a perpendicular magnetic field quantises the density of states completely, and therefore the LO-phonon emission would be strongly suppressed off resonance. The nipi structures are wide parabolic wells with closely separated subband energies, well below the cyclotron resonance energy. Therefore, the suppression is not complete and it is still possible to have a fast zone boundary scattering in these samples. Thus, we have observed the same saturation intensity for the longitudinal and oblique valleys. The quantum wells have a much stronger confinement, not only leading to a larger subband separation, but also moving the lowest subband associated with the oblique valleys above the Fermi

124

C.J.G.M. Langerak et al. / Physica E 2 (1998) 121—125

Fig. 3. Intensity-dependence of the integrated absorption for a PbTe quantum well sample MBEG214. The points represent the experimental results, and the solid line the theory, fitted as described in the text.

Fig. 4. Pump—probe cyclotron resonance of a InAs/AlSb quantum well sample at a wavelength of j"70 lm and a magnetic field of 5.6 T. From these data a lifetime of q"40 ps is obtained directly.

energy. Therefore only one resonance, of the longitudinal valley, is observed. This sample has a much higher electron density, with the result that many more Landau levels are accessed (we find convergence after 15 levels) and the saturation intensity appears to be higher. In Fig. 3, the integrated CR absorption is plotted as a function of intensity, with the model fitted using q as the only adjustable parameter. We find that the measured values of q progress from q(bulk)"un-measurable, through q(nipi)"1.5 ps, to q(quantum well)"8 ps, as expected from the increasing 2D confinement. In particular, we report that the wide quantum well of the nipi sample already shows a significant 2D effect in the lifetime.

centration of 5]1011 cm~2 and a mobility of 262, 000 cm2/Vs at 4 K. On the GaAs substrate, buffer layers of GaAs and GaSb were grown followed by 500 nm GaSb, 80 nm AlSb, 20 nm GaSb, 10 periods of a GaSb(2.5 nm)/AlSb(2.5 nm) smoothing superlattice, 20 nm AlSb barrier, 15 nm InAs well, 15 nm barrier and a 12 nm GaSb cap. The InAs/AlSb interfaces forming the quantum well were grown to be InSb-like with 5 s pause times. We have measured lifetimes of q"40 ps over a small wavelength range between 70 and 90 lm. Fig. 4 shows a typical result at j"70 lm and B"5.6 T, at ¹"4 K. This lifetime is longer than expected from LO-phonon emission, and consistent with the wavelength not being at the magnetophonon resonance condition. (LO-phonon energy is 30 meV). Good agreement is obtained with an 8]8k ) p calculation. In conclusion, we have determined from CR saturation experiments the Landau-level lifetime in a wide parabolic PbTe quantum well with a Fermi energy of about 12 meV to be in the range of 1.5 ps. Since the Landau level spacing is larger than the LO-phonon energy in PbTe such a short lifetime can be expected. In the high-density quantum well sample we have found a longer lifetime (8 ps) as expected. We have presented the first cyclotron resonance pump—probe experiment on InAs—AlSb and a lifetime of 40 ps is obtained.

3. Pump—probe cyclotron resonance on InAs—AlSb InAs—AlSb is also a narrow gap material with a large band non-parabolicity, allowing CR saturation in a quantum well system. This is essential for the pump—probe technique. So far this technique has been employed in the far infrared to obtain intersubband lifetimes in quantum well samples [7]. Here we present the first pump—probe CR relaxation experiment on a 2D electron system in an InAs quantum well. The sample is a modulation doped quantum structure of InAs—AlSb with an electron con-

C.J.G.M. Langerak et al. / Physica E 2 (1998) 121—125

Acknowledgements We acknowledge EPSRC and FOM for support.

References [1] T.A. Vaughan, R.J. Nicholas, C.J.G.M. Langerak, B.N. Murdin, C.R. Pidgeon, N.J. Mason, P.J. Walker, Phys. Rev. B 53 (1996) 16481. [2] W. Heiss, P. Auer, E. Gornik, C.R. Pidgeon, C.J.G.M. Langerak, B.N. Murdin, G. Weimann, M. Heiblum, Appl. Phys. Lett. 67 (1995) 1110.

125

[3] J. Oswald, G. Heigl, G. Span, A. Homer, P. Ganitzer, D.K. Maude, J.C. Portal, Physica B 227 (1996) 360. [4] J. Oswald, G. Span, A. Homer, G. Heigl, Ganitzer, D.K. Maude, J.C. Portal, Solid State Commun. 102 (1997) 391. [5] J. Oswald, P. Pichler, B.B. Goldberg, G. Bauer, Phys. Rev. B 49 (1994) 17029. [6] D. Oepts, A.F.G. van der Meer, P.W. van Amersfoort, Infrared Phys. Technol. 36 (1995) 297. [7] B. N Murdin, W. Heiss, C.J.G.M. Langerak, S.C. Lee, I. Galbraith, G. Strasser, E. Gornik, M. Helm, C.R. Pidgeon, Phys. Rev. B 55 (1997) 5171.