Impurity-Scattering Limited Electron Mobility in Free Standing Quantum Wires: Image Charge Effect

Abstract

We calculate the impurity-scattering limited mobility of the one-dimensional electron gas in a rectangular GaAs quantum wire confined in the vertical (growth) direction by n-modulation doped AlGaAs layers and free standing along the transverse direction. The scattering potential of the ionized impurity is obtained by solving the Poisson equation with z-dependent electrostatic permittivity in order to take into account the image charge effect due to the abrupt permittivity change at the GaAs/air interfaces. We show that the "image impurity" scattering tends to drastically reduce the electron mobility for sufficiently small ( 10 nm) transverse wire widths.PACS numbers: 73.50.-h, 73.50.BkThe nanolithographic patterning and etching of 1ayered AlGaAs/GaAs/ AlGaAs structures have made possible to fabricate a rectangular GaAs quantum wire confined in the vertical (growth) direction ( y) by AlGaAs 1ayers, and free standing along the transverse direction (z) [1]. Nowadays there is a trend to produce free standing wires with transverse widths close to 10 nm in order to enhance the quantum confinement of the carriers. In this paper we calculate the impurity-scattering limited electron mobility in free standing GaAs wires. The scattering potential of the ionized impurity is obtained by solving the Poisson equation with z-dependent electrostatic permittivity in order to take into account the image charge effect due to the abupt permittivity change at the GaAs/air interfaces. We compare the electron mobility in the free standing GaAs wire with the mobility in the GaAs wire buried in the AlGaAs material, in which the image charge is negligible. Due to scattering by the image potentials of ionized impurities, the electron mobility in free standing quantum wires of small enough ( ≈ 10 nm) transverse width is found to be intrinsically limited to a value substantially lower . than in buried quantum wires.We consider an undoped GaAs wire of the infinite length in the x direction and of the rectangular cross-section in the y-z plane. The wire is confined in the vertical ( y) direction by AlGaAs layers. In the transverse (z) direction (1103)