Alloy scattering of $n$-type carriers in $\mathrm{Ga}{\mathrm{N}}_x{\mathrm{As}}_{1-x}$

A tight-binding model of the electronic structure of substitutional nitrogen in GaAs, together with a variational description of quasilocalized nitrogen-induced electronic states near the conduction band edge, is used to calculate the nitrogen-related alloy scattering of conduction band electrons in the dilute nitride alloy, $\mathrm{Ga}{\mathrm{N}}_x{\mathrm{As}}_{1-x}$. The electron mobility in the nondegenerate and degenerate doping regimes is calculated for bulk and quantum well geometries from the energy-dependent scattering rate using the Boltzmann transport equation in the relaxation-time approximation. Nitrogen cluster states are found to dominate the scattering near the conduction band edge and play a crucial role in limiting the electron mobility. In the experimentally relevant regime of degenerate doping and at nitrogen concentrations of 1 to 2%, the room-temperature mobility is found to be limited to values less than $300{\mathrm{cm}}^2{\left(\mathrm{V}\mathrm{s}\right)}^{-1}$, in agreement with experimental measurements.

Figure 1

(Color online) The density of states for localized LCINS states, weighted by ${\beta }^2∕N_a$, the square of the interaction matrix element with the GaAs conduction band-edge state, for each state vs energy (referred to the valence band edge at room temperature). Each curve refers to a different nitrogen concentration, $x$, with $x=0.1\%$, 0.36%, 0.5%, 1.2%, and 2.0%. To smooth the spectra, each energy level is broadened to a Gaussian of width 5 meV.

Figure 2

(Color online) The carrier scattering rate vs energy for nitrogen concentrations, $x=0.1\%$, 0.36%, 0.5%, 1.2%, and 2.0%. The carrier energy is referred to the conduction band edge $E_c\left(x\right)$ at room temperature.

Figure 3

(Color online) The calculated room temperature $n$-type carrier mobility vs carrier concentration for various nitrogen concentrations, $x=0.1\%$, 0.36%, 0.5%, 1.2%, and 2.0%.

Figure 4

(Color online) The calculated $n$-type carrier mobility, at temperature $30\mathrm{K}$, vs carrier concentration for various nitrogen concentrations, $x=0.1\%$, 0.36%, 0.5%, 1.2%, and 2.0%.

Figure 5

(Color online) The calculated room temperature $n$-type carrier mobility for a $10\mathrm{nm}$ quantum well vs carrier concentration for various nitrogen concentrations, $x=0.1\%$, 0.36%, 0.5%, 1.2%, and 2.0%.

Figure 6

(Color online) The calculated $n$-type carrier mobility, at temperature $30\mathrm{K}$, for a $10\mathrm{nm}$ quantum well vs carrier concentration for various nitrogen concentrations, $x=0.1\%$, 0.36%, 0.5%, 1.2%, and 2.0%.

Figure 7

(Color online) The calculated $n$-type carrier mean-free-path $l$ vs energy for nitrogen concentrations, $x=0.1\%$, 0.36%, 0.5%, 1.2%, and 2.0%. The carrier energy is referred to as the conduction band edge $E_c\left(x\right)$.