Energy relaxation in disordered two-dimensional electron gas with dynamic deformation potential S.S.Z. Ashraf a , P. Tripathi b,Ã , S.T. Hasan a , A.C. Sharma b a Physics Department, Shibli National P.G. College, Azamgarh 276 001, India b Physics Department, M.S. University of Baroda, Vadodara 390 002, India article info Article history: Received 29 May 2009 Received in revised form 16 August 2009 Accepted 31 August 2009 Available online 6 September 2009 PACS: 72.10.-d 72.15.Lh 73.21.Fg Keywords: Energy loss rate Dynamic screening Deformation potential abstract We investigated the electron energy loss rate through the emission of acoustic phonons in disordered two-dimensional electron gas in the deformation coupling limit. The energy loss rate has been determined by considering dynamic screening of electrons as various earlier studies have shown that static screening underestimates the energy loss rate. We find a change in the temperature exponent as well as the pre-factor b from the earlier reported approximate temperature power law dependence bT 6 obtained under static and dynamic strong screening and impurity limit. The difference in magnitude between the approximate analytic and numerical results mounts at decreasing sub-Kelvin temperatures with the pre-factor being enhanced about three times at a temperature 100 mK and mean free path length 8 nm, and the power dependency decreasing from the analytically derived T 6 to numerically observed T 5.2 . & 2009 Elsevier B.V. All rights reserved. 1. Introduction At low temperature, scattering width acoustic phonon is an important process leading to energy loss rate of electron in low- dimensional systems [1]. When excess energy is supplied to an electron in an empty conduction band, as in the case of strong applied electric field or optical excitation, the electron becomes ‘‘hot’’ and loses energy to its surroundings, i.e. to the cold lattice, in order to achieve equilibrium (at the bottom of the band). The same situation, in a somewhat more complicated form, arises for a hot-electron gas where a finite density of electrons is excited out of equilibrium with the lattice [2]. A hot-electron gas in order to attain equilibrium with the lattice loses its energy to the surrounding usually through the emission of phonons. This energy transport between electrons and phonons at low tem- peratures continues to be a topical subject in research because of electron–phonon (e–ph) interaction being a fundamental subject in solid state physics as well as because of its relevance in the working of low temperature devices like microbolometers, calorimeters, on chip refrigerators, etc [3]. Also the e–ph energy relaxation rate governs the phonon mediated electron dephasing. A number of transport measurements techniques such as phonon drag, energy loss rate, one-dimensional thermo power, etc, give information on electron–phonon interaction [4]. The principal mechanism of electron energy losses at low temperatures is via the scattering with acoustic phonons. For the case of acoustic scattering in semiconductors, deformation potential (DP) and piezoelectric are two important types of mechanism. There has been considerable theoretical and experimental interest in hot- electron energy relaxation in polar semiconductors, particularly in two- and three-dimensional GaAs heterostructures. This subject has technological significance since actual devices work mostly in high field hot-electron conditions. The e–ph interaction in disordered semiconductors is much more complicated than in pure bulk systems. Despite the progress in theory the issue has not been settled completely yet [5]. Electron relaxation through the e–ph scattering via DP in disordered semiconductor nanostructures has drawn substantial interest in the recent past [3,6,7 and references there in]. In his paper, Prunnila considering multi-component electron systems with symmetric and asymmetric coupling constants has derived a set of formulae for pure and diffusive three- and two-dimensional electron gas systems [6]. Sergeev et al. have obtained analytical results on the e–ph scattering rates via the DP for single valley disordered semiconductor nanostructures [7]. Various tempera- ture (T) and mean free path (l) dependences have been determined in the static screening condition. However, it has been shown by Chow et al. that the phonon emission power in ARTICLE IN PRESS Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/physe Physica E 1386-9477/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.physe.2009.08.023 Ã Corresponding author. Tel.: +91265 2795339. E-mail address: ptrip71@yahoo.com (P. Tripathi). Physica E 42 (2009) 87–90