Deformation potentials in AlGaN and InGaN alloys and their impact on optical polarization properties of nitride quantum wells

The deformation potentials $a_{cz}-D_1$, $a_{ct}-D_2$, $D_3$, $D_4$, and $D_5$ are determined for random AlGaN and InGaN alloys using electronic band structure calculations based on the density functional theory. A sublinear composition dependence is obtained for $a_{cz}-D_1$ and $D_3$ in AlGaN, and $D_3$ in InGaN, whereas superlinear behavior on composition is found for $a_{ct}-D_2$, $D_4$, and $D_5$ in AlGaN, and $a_{ct}-D_2$ and $D_5$ in InGaN. The optical polarization properties of nitride quantum wells are very well described by the k·p method when the obtained deformation potentials are included. In $m$-plane AlGaN/AlN and InGaN/GaN quantum wells, the difference between the interband transition energies for light polarized parallel and orthogonal to the crystalline $c$ axis compares more favorably to experimental data, than when deformation potentials previously reported in literature are used.

Figure 1

The deformation potentials in wurtzite (a) Al${}_x$Ga${}_{1-x}$N and (b) In${}_x$Ga${}_{1-x}$N alloys, as a function of alloy composition. Solid lines correspond to the parabolic parametrizations, Eq. (3), with parameters presented in Table . Open symbols in (a) represent the recent experimental results for GaN taken from Ref. 4.

Figure 2

The separation energy $\Delta E$ for $c$-plane Al${}_x$Ga${}_{1-x}$N/AlN QWs with well widths equal to 2, 4, and 6 nm, obtained using the present deformation potentials (circles), as well as the deformation potentials taken from Ref. 5 (squares). Lines are added to guide the eye.

Figure 3

The separation energy $\Delta E$, Eq. (4), for 3.8-nm-wide $m$-plane Al${}_x$Ga${}_{1-x}$N/AlN QWs obtained using the present deformation potentials (circles), as well as the deformation potentials of Refs. 5 (squares) and 1 (triangles). Lines are added to guide the eye.

Figure 4

The separation energy $\Delta E$, Eq. (4), for 3-nm-wide $m$-plane In${}_x$Ga${}_{1-x}$N/GaN QWs obtained using the present deformation potentials (circles), as well as the deformation potentials of Refs. 5 (squares) and 1 (triangles). Open circles correspond to the results obtained when the composition dependence of the elastic constants in In${}_x$Ga${}_{1-x}$N was also taken into account. A solid line represents the experimental results of the PL measurements reported in Ref. 25. Other lines are added to guide the eye.