Analytical model of electron transport in polycrystalline, degenerately doped ZnO films

Abstract

An analytical description of the charge carrier transport, valid for non-degenerated and degenerated semiconductors, was developed, critically reviewed, and fitted to the temperature-dependent Hall mobility data of magnetron sputtered, degenerately doped ZnO:Al films. Our extended model for grain boundary scattering in semiconductors of arbitrary degeneracy is based on previous models from literature and suitable to describe the Hall mobility of the carriers as a function of the free carrier concentration and the temperature at the same time. It is mathematically simple enough for a fast fit procedure, which is not possible with most of the previous models. Applying a combined transport model consisting of ionized impurity scattering, phonon scattering, and grain boundary scattering in degenerate semiconductors, we were able to determine the trap density at the grain boundaries Nt ≈ 3 × 1013 to 5 × 1013 cm−2 and the deformation potential Eac in the range of 5 eV to 9 eV depending on the details of the transport model.

Comparison of chemical bath-deposited ZnO films doped with Al, Ga and In

“…In polycrystalline ZnO films, the grain boundary trap density is estimated to be in the range of 10 12 cm -2 for undoped ZnO [40] and reaches 1.5-3 9 10 13 cm -2 for sputtered AZO materials [38].…”

“…Thus, the optical DC conductivity, calculated from Eq. 10, does not take into account the grain boundary scattering, which has a major influence on the mobility of polycrystalline ZnO materials [38].…”

Deposition of Al-doped ZnO films by high power impulse magnetron sputtering

“…Ionized impurity scattering is scattering of the free carriers due to the Coulomb interaction with the dopants or other defects [18]. This leads to a decrease of the mobility at high charge carrier concentrations.…”

“…Above the plasma frequency, the absorption coefficient of the material is given by 6) with N the refractive index, c the speed of light and τ the relaxation time that describes the mean time between scattering events [16, p. 194 As can be seen from Equation 2.6, the absorption close to the plasma frequency is decreasing with the frequency, but depends on both the charge carrier concentration and the relaxation time. In order to keep this free charge carrier absorption low, there are therefore limits in increasing the charge carrier concentration if the material needs to be transparent [18]. The different mechanisms that limit the transparency of TCOs are summarized in Figure 2.2.…”

“…The displacement of atoms causes both a dipole electric moment and local changes in the band structure, which are responsible for optical and acoustical phonon scattering, respectively [18]. Additional scattering mechanisms include neutral impurity scattering and dislocation scattering [21].…”