Optical phonon modes and interband transitions in cubic Al_xGa_1-xN films

We present a comprehensive study of the phonon mode behavior and the optical interband transitions of cubic Al_xGa_1-xN films (0≤x≤0.20) using spectroscopic ellipsometry from the midinfrared to the vacuumultraviolet spectral range (0.05-8.5 eV). The ≈0.5-μm-thick Al_xGa_1-xN layers were grown by radiofrequency plasma-assisted molecular-beam epitaxy and possess free-electron concentrations in the range of 6 × 10¹⁹-1 × 10²⁰ cm^-3. A two-mode behavior for the transverse-optical phonon of Al_xGa_1-xN is observed, which is consistent with theoretical predictions. Due to the high free-electron concentration, the observed Al_xGa_1-xN fundamental band-gap energy E₀ is subject to a strong Burstein-Moss shift and band-gap renormalization. We quantify the amount of both band-gap shifting mechanisms, and provide an estimate for the composition dependence of the Al_xGa_1-xN band-gap energy E₀, which depends approximately linearly on the alloy composition with E₀ (eV) = 3.19 + 2.77x at room temperature and for carrier-depleted material. For cubic GaN, the L-point interband transition E₁ shifts to lower energies with increasing free-electron concentration, whereas the interband transition E₂ remains unshifted. Increasing A1 content induces a blueshift (redshift) of the E₁ (E₂) transition of Al_xGa_1-xN for x≤0.12. Due to strong broadening effects, both transitions cannot be differentiated anymore for x≥0.16.