PHYSICAL REVIEW B 89, 045311 (2014) Combined effect of electron and lattice temperatures on the long intersubband relaxation times of Ge/Si x Ge 1-x quantum wells Michele Virgilio, 1, 2 , * Michele Ortolani, 3, 4 Martin Teich, 5, 6 Stephan Winnerl, 5 Manfred Helm, 5, 6 Diego Sabbagh, 7 Giovanni Capellini, 7, 8 and Monica De Seta 7 1 Dipartimento di Fisica “E. Fermi”, Universit` a di Pisa, Largo Pontecorvo 3, 56127, Pisa, Italy 2 NEST, Istituto Nanoscienze-CNR, Piazza San Silvestro 12, 56127 Pisa, Italy 3 Dipartimento di Fisica, Universit` a di Roma “La Sapienza”, Piazzale A. Moro 2, 00185 Rome, Italy 4 CNR—Istituto di Fotonica e Nanotecnologie, Via Cineto Romano 42, 00156 Rome, Italy 5 Institute of Ion Beam Physics and Materials Research “Helmholtz-Zentrum Dresden-Rossendorf”, 01314 Dresden, Germany 6 Technische Universit¨ at Dresden, 01062 Dresden, Germany 7 Dipartimento di Scienze, Universit` a di Roma Tre, Viale Marconi 446, 00146 Rome, Italy 8 IHP, Im Technologiepark 25, 15236 Frankfurt (Oder), Germany (Received 19 September 2013; revised manuscript received 13 November 2013; published 27 January 2014) In this paper, we have experimentally and numerically studied the nonradiative intersubband (ISB) relaxation in n-type Ge/SiGe quantum well (QW) systems. Relaxation times have been probed by means of pump-probe exper- iments. An energy balance model has been used to interpret the experimental differential transmission spectra and to assess the relevance in the nonradiative relaxation dynamics of both electron and lattice temperature as well as of the carrier density. The comparison between experimental data and theoretical simulation allowed us to calibrate the interaction parameters which describe the electron-optical phonon scattering in two-dimensional (2D) Ge systems. Characteristic relaxation times has been calculated and compared with those of GaAs QWs as a function of the 2D electron density, of the subband energy separation, and of the lattice and electronic temperature. We found that ISB relaxation times for the Ge/SiGe systems are generally shorter than that previously calculated when the electron distribution was neglected. Nonetheless, our main result is that the relaxation time in Ge/SiGe QW systems is longer than 10 ps, also for transition energies above the Ge optical phonon energy, up to 300 K. Further- more, we obtained that the relaxation times are at least one order of magnitude longer than in GaAs-based systems. DOI: 10.1103/PhysRevB.89.045311 PACS number(s): 78.67.De, 73.50.Gr I. INTRODUCTION Two-dimensional electron gases (2DEG) formed in silicon- germanium multiquantum wells (MQW) have recently at- tracted considerable attention for a number of photonic appli- cations, such as quantum cascade lasers, emitters, modulators, and detectors [1–6], and also for energy harvesting devices based on thermoelectric [7] or photovoltaic effect [8]. The operation of these innovative unipolar devices exploits the tran- sitions occurring between quantized states formed in the con- duction or valence band of heterostructures, the subbands (SB). In view of possible applications, Ge/SiGe heterostructures have the practical advantage that can be grown directly on Si (001) substrates by using strain-balanced heteroepitaxy and thus are compatible with the mainstream Si-based microelec- tronic technology. In particular, n-type Ge/SiGe MQWs, with SBs confined in the conduction band, are particularly attractive owing their low values of confinement and tunneling effective mass, comparable to those of III-V systems. Qualitative differ- ences due to the nonpolar nature of group-IV semiconductor lattices and to the presence of degenerate anisotropic valley minima at the L point in the conduction band offer the opportunity for entirely new heterostructure design concepts. The modeling of the electronic properties of these systems requires, though, a nontrivial extension of the intersubband (ISB) transition theory, which was initially developed to * virgilio@df.unipi.it describe polar III-V heterostructures with a single isotropic conduction-band minimum located at the Ŵ point [9–11]. The main peculiarity of the Ge/SiGe system is that the electron- phonon scattering, responsible for the nonradiative relaxation of electrons from the first-excited to the fundamental subband (|1〉→|0〉), takes place only via the deformation potential coupling and not also through the long-range dipole Fr¨ ohlich interaction, as it happens in III-V polar structures [12,13]. As a consequence, relatively long intersubband relaxation times of the order of tens of picoseconds, which are beneficial for the achievement of population inversion, have been predicted up to room temperature, making n-type Ge/SiGe heterostructures very attractive for designing ISB unipolar lasers [14–18]. How- ever, these predictions are based on empty-band calculations, thus neglecting the effect of the 2DEG distribution in the subbands, which defines the actual population of the upper and lower “states” of the optical transition. Indeed, relying on Raman and microphotoluminescence measurements, it has been demonstrated [19] that, in III-V based ISB-based photonic devices, the electrons do populate different subbands following a thermal distribution characterized by an electron temperature T e higher than the local lattice temperature T L . Moreover, it has been clearly shown by time-resolved ISB spectroscopy that, for high enough T e , the relaxation time of 2DEG in excited SBs is much shorter than that expected by empty-band calculation of the electron-phonon scattering rate, especially for subband separation lower or equal to the optical phonon energy [11]. This is attributed to the thermal activation of nonradiative |1〉→|0〉 ISB transitions via optical phonon 1098-0121/2014/89(4)/045311(8) 045311-1 ©2014 American Physical Society