On the X-ray reflectivity of absorbing crystals

A simple relationship is reported defining the ratio of dynamical and kinematic values of the integrated reflectivity in absorbing single crystals in terms of the product μ_nξ, where μ_n is the linear absorption coefficient for depth measured along the normal to the diffracting crystal's surface and ξ is the extinction distance in a nonabsorbing crystal. This relationship is interpreted through comparison with existing (albeit mathematically complicated) expressions for the dynamical reflectivity in the two limits of negligible absorption and very strong absorption. It is shown to be valid for intermediate values of μ_nξ by comparison with calculated values of the integrated reflection from single-crystal CdTe using various wavelengths and 〈111〉-type reflections. This relationship's usefulness is discussed in the analysis of dynamical diffraction experiments commonly employed in semiconductor materials characterization.