Optical anisotropic dielectric response of GaN studied by generalized variable angle spectroscopic ellipsometry

Anisotropic dielectric response of gallium nitride (GaN) has been studied by generalized variable angle spectroscopic ellipsometry (VASE). The GaN films were grown by atmosphere pressure metal organic vapor phase epitaxy (MOVPE) and molecular beam epitaxy (MBE) on c-plane sapphire substrates (alpha-Al2O3), respectively. Room temperature isotropic and anisotropic mode VASE measurements were made, in the range of 0.75 to 6.5 eV, at the angles of incidence between 25 and 80 degrees. Evidence of anisotropy is observed especially in the spectral range under the band gap (similar to 3.4 eV), reflecting the nature of wurtzite crystal structure of GaN. The sizable off-diagonal elements (Aps and Asp) of Jones matrix indicates that the optical axis <c> of the c-plane sample are slightly off from the surface normal due to the miscut of substrates. The anisotropic mode measurement also shows that the off-diagonal elements depend strongly on the angle of incidence. (Fig. 1) In the angle-range of 50 degrees to 75 degrees, the off-diagonal elements are detectable, and reach maximum around 60 degrees to 65 degrees. While outside this angle-range the Aps and Asp are almost zero, and in such condition the isotropic and anisotropic mode measurement are identical. Thus the ordinary dielectric functions are uniquely and completely determined by eliminating the anisotropic effect. (Fig. 2) A Kramers-Kronig-consistent parametric semiconductor model was used for the VASE data analysis. The thicknesses of these GaN films are accurately determined via the analysis as well.