Relaxation of a two-dimensional electron gas in semiconductor thin films at low temperatures: Role of acoustic phonon confinement

Abstract

We study the effect of acoustic-phonon confinement on the energy and momentum relaxation of a twodimensional electron gas in thin films. The interaction via the deformation and piezoelectric potentials with a complete set of phonon modes in films with stress-free and rigid surfaces is taken into account. We demonstrate that in thin films the modification of the phonon properties and screening brings about substantial changes of the electron relaxation rates in comparison to the case of interaction with bulk phonons at low temperatures, where the effective reduction of the phonon spectrum dimensionality takes place. For suspended films, relaxation rates are substantially enhanced: the temperature dependence of the momentum and energy relaxation rates, in films with nonmetallized ͑metallized͒ surfaces, is found to be T 7/2 (T 5/2) for both deformation potential and piezoelectric mechanisms. The reason for such an enhancement is the strong scattering of electrons by flexural phonons having quadratic dispersion and a high density of states at low frequencies. Conversely, for films with rigid surfaces the low-temperature relaxation of electrons is exponentially suppressed due to the formation of a gap in the phonon spectrum.

Electron–phonon heat exchange in layered nano-systems

“…The principal characteristic of the electron gas is that due to the quantization of the wavevector component perpendicular to the film surfaces the electron gas forms quasi 2D sub-bands, which are specific to a quantum well (QW) formalism. 16,21,22,26 In an accompanying paper we describe the electrons as a 3D Fermi gas. We choose a range of parameters L, T e (electrons temperature), and T ph (lattice temperature) such that the phonon gas has a quasi two-dimensional distribution (for L = 100 nm we took T e, T ph ≤ 0.2 K).…”

“…Such a sharp oscillatory behavior is a characteristic of the QW description of the electronic states in the metallic films 16,21,22,26 and could be useful for applications, like thickness variation detection or surface contamination. Moreover, by varying the thickness of the membrane one might vary dramatically the electronphonon coupling and, through this, the thermalisation or the noise level in the system.…”

“…Below this temperature one may expect a quasi-2D behavior of the phonon system (rigorously, for T T C ), whereas above it (rigorously, at T T C ) a 3D model would suffice. We carry out our analysis employing a QW picture of the metallic film 16,21,22,26 by taking into account the discretization of the components of the electrons wavenumbers perpendicular to the membrane's surfaces, whereas the 3D Fermi gas picture of the electron system is used in an accompanying paper. We work in a temperature range T < 200 mK in which the phonon gas is quasi-2D and we observe that the electron-phonon heat flux P cannot be simply described by a single power-law dependence, P ∝ T ph , in general the heat flux has a very strong oscillatory behavior as a function of d. At certain regular intervals the power flux increases sharply with the film thickness by at least one order of magnitude ( Fig.…”

Laterally pumped GaAs/AlGaAs quantum wells as sources of broadband terahertz radiation

“…4 It has also been previously used, in form of a shifted Fermi-Dirac ͑FD͒ distribution, in single-subband electron-transport calculations in quantum wells. 5 In this work we apply such a model to systems with a number of size-quantized subbands and assume that each of them will have the same form of shifted-MB distribution over the inplane wave vectors, which is then used to evaluate the distribution-averaged intersubband scattering rates, Eq. ͑9.153͒ from Ref.…”

Enhanced quantum interference transport in gold films with random antidot arrays

“…31,32 Hu et al 33 reported the enhancement of electron coherence transport when Nb 3 SiTe 6 crystals were reduced to below a few unit cells in thickness. This is because of a phonon dimension crossover from 3D to 2D in ultra-thin films, which leads to a weakening of the e-ph interactions.…”