Influence of scattering processes on electron quantum states in nanowires

Abstract

In the framework of quantum perturbation theory the self-consistent method of calculation of electron scattering rates in nanowires with the one-dimensional electron gas in the quantum limit is worked out. The developed method allows both the collisional broadening and the quantum correlations between scattering events to be taken into account. It is an alternative per se to the Fock approximation for the self-energy approach based on Green's function formalism. However this approach is free of mathematical difficulties typical to the Fock approximation. Moreover, the developed method is simpler than the Fock approximation from the computational point of view. Using the approximation of stable one-particle quantum states it is proved that the electron scattering processes determine the dependence of electron energy versus its wave vector.

Influence of surface roughness scattering on electron low-field mobility in thin undoped GaAs-in-Al2 O3 nanowires with rectangular cross-section

“…The validity of such an approximation for quantum nanowires like the nanowires being considered in this study has been justified by Calecki 24. Other scatterers are not taken into account because of their weak interaction with electrons under the conditions considered 16.…”

“…(1)–(3), (6) and (7), it is easy to derive the formulae where the averaging is carried out over all possible realizations of the random function g ( Λ , y ) specified by the autocorrelation function In Eq. (9), χ is the wave vector which corresponds to the collisional broadening factor ΔE 13 characterizing the collisional broadening of the electron energy spectrum due to all the scattering mechanisms under consideration 12–16.…”

“…The mobility is calculated numerically using where F is the longitudinal electric field strength, f is the electron distribution function and $v(k) = h^{ - 1} {\rm d}E(k)/{\rm d}k$ is the electron group velocity, where ħ is the Planck constant and E is the electron kinetic energy ($k(E) = k_E = E^{ - 1} (k) \Leftrightarrow E(k) = k^{ - 1} (E)$ 16). In turn, the function f is found by means of the direct numerical solution of the one‐dimensional Boltzmann transport equation 16 in the form of using the method of finite‐difference approximation of differential operators. In Eq.…”

“…So, for example, the physico‐mathematical basis by means of which one can create numerical models allowing the electrophysical parameters of thin GaAs quantum nanowires with rectangular cross‐section characterized by some physical (Fermi energy and temperature) and topological (geometrical) parameters to be calculated has been developed in Refs. 10–16 recently. Nevertheless there is a reason to think that this is not exactly so.…”

“…So the main purpose of the study reported here was to calculate the electron low‐field mobility in thin undoped GaAs‐in‐Al 2 O 3 quantum nanowires with rectangular cross‐section using the physico‐mathematical models developed in Refs. 10–16 and to investigate the influence of surface roughness scattering on the mobility. Moreover, it is proposed to apply the parameter Δ 2D instead of the parameter Δ 1D during the calculation of surface roughness scattering matrix elements.…”