Model-free determination of optical constants: Application to undoped and Ga-doped ZnO

For single slabs of uniform material, such as bulk semiconductors, we derive closed-form expressions for absorption and reflection coefficients, ∝ and R, respectively, in terms of measured reflectance and transmittance, Rm and Tm. The formula for α can replace the several commonly used approximations for ∝ as a function of Tm, and in particular does not require ∝d >> 1, where d is the thickness. Thus, it can be applied to weak impurity absorptions, such as Fe absorption in Fe-doped GaN. Finally, the real (η) and imaginary (κ) parts of the index of refraction (n = η + iκ) can be obtained from ∝ and R and agree well with η and κ results obtained from other experiments. For multi-layer structures, "effective" values of ∝, R, η, and κ are obtained, but they can often be assigned to a particular layer. This new technique has been successfully applied to many bulk and layered structures.