Intervalley-Scattering-Induced Electron-Phonon Energy Relaxation in Many-Valley Semiconductors at Low Temperatures

Abstract

We report on the effect of elastic intervalley scattering on the energy transport between electrons and phonons in many-valley semiconductors. We derive a general expression for the electron-phonon energy flow rate at the limit where elastic intervalley scattering dominates over diffusion. Electron heating experiments on heavily doped n-type Si samples with electron concentration in the range 3.5 − 16.0 × 10 25 m −3 are performed at sub-1 K temperatures. We find a good agreement between the theory and the experiment. Since the low temperature hot electron experiments by Roukes et al.[1], the energy transport between electrons and phonons has continued to be a topical subject. Recently, there has been significant experimental and theoretical interest in the electron-phonon (e-ph) energy relaxation in metals and semiconductors at low temperatures [2,3,4,5,6,7,8]. The understanding of thermal e-ph coupling is important for several low temperature devices such as microbolometers, calorimeters and on chip refrigerators [4,9]. This coupling plays also an important role in correct interpretation of low temperature experiments [5] and the e-ph energy relaxation rate gives direct information about phonon mediated electron dephasing [10].Interaction between electrons and phonons is strongly affected by the disorder of the electron system and, therefore, the problem is commonly divided into two special cases: pure and impure (or diffusive) limit of e-ph interaction. The cross-over between these two regions is defined as ql = 1 , where q is the phonon wavevector and l the electron mean free path. If the whole phonon system is to be considered then the phonon wavevector can be conveniently replaced by the thermal phonon wave vector q T = k B T / v, where T is the temperature of the lattice and v the sound velocity. Recent theory for single-valley semiconductors [8] predicts that the e-ph energy relaxation is strongly enhanced when the system enters from the pure limit (ql > 1) to the diffusive limit (ql < 1). The behavior is the opposite in comparison to metals where it is well known, since the pioneering work by A. B. Pippard [11], that the disorder of the electron system tends to suppress the e-ph energy relaxation (see also Ref.[2]). In semiconductors, due to small electron density, the e-ph interaction can be described by deformation potential coupling constants, which do not depend on the electronic variables, while in metals the coupling strongly depends on the electron momentum [12]. This fundamental difference eventually leads to disorder enhancement of the relaxation in the diffusive limit in single-valley semiconductors [8].In many-valley semiconductors the situation is further altered due to intervalley scattering, which is the topic of our work. Due to lack of screening the e-ph energy flow rate is strongly enhanced in many valley semiconductors in comparison to single valley ones at diffusive low temperature limit. We approach the e-ph energy transport problem by first considering the phonon energy attenuation r...

Ab initio calculations of the deformation potentials for intervalley phonon-assisted transitions in А III В V crystals with sphalerite structure

“…The experimental values of the electron-phonon interaction constants presented in the literature are widely scattered and their maximum difference can reach an order of magnitude [11]. This is obviously caused by the fact that the electron-phonon processes in crystals are combined with many other scattering channels and cannot be unambiguously separated for processing of various experiments.…”

“…For some scattering mechanisms, the probabilities are considered to be known and serve as initial data; for other scattering channels, the probabilities play the role of the adjustable parameters. This simple model contains too many simplifying assumptions and faces the problem of many phenomenological parameters; as a result, the uncertainty in determining the scattering characteristics reaches 100% [11]. To provide reliable initial data for Monte Carlo simulations, exact theoretical calculations of at least some scattering channels are required, which will allow the quality of adjustment of other parameters to be improved.…”

Micrometre-scale refrigerators

“…Theoretically, this power law was expected for (single-valley) semiconductors in two dimensions at the diffusive limit [88] but the theoretical prefactor was several orders of magnitude smaller than measured. In [89,90], the fact that multiple conduction band valleys exist in Si was included into the theoretical analysis. Phonons can lift the degeneracy between the different valleys so that the valley degree of freedom starts to play a role in the low temperature e − p coupling.…”

Recovery of SINIS turnstile accuracy in a strongly nonequilibrium regime

“…For this cooling power, a variety of expressions is available in the literature, which were derived microscopically in different regimes determined by the system dimensionality, the shape of the Fermi surface, the relation between the phonon wavelength, island size, and the electron mean free path. [39][40][41][42][43][44] All these expressions can be represented in the form…”