Optical Constants of Insulators: Dispersion Relations

Abstract

The optical behavior of an optically isotropic solid (e.g., a cubic crystal) is determined by the spectral dependence of two parameters: the real and the imaginary part of the refractive index n = n r +in i (n i is usually referred to as k in the literature and called the extinction index), or the real and the imaginary part of the dielectric constant e = e r + ie i . The two spectral functions which determine the optical behavior are most readily determined by measuring the transmission and the reflection of a plane-parallel slab as a function of frequency [1]. In the region of interband transitions, however, the absorption coefficient reaches very large values (105−106 cm−1) and the preparation of single-crystal samples thin enough for transmission measurements becomes extremely difficult [2]. Because of the large number of imperfections associated with vacuum-deposited samples, thin films prepared by this method are not very trustworthy for optical measurements, although progress has been made recently by using epitaxial deposition methods [3]. Absorption in the substrate or film backing can also become a problem, especially in the far ultraviolet region, and therefore techniques based exclusively on reflection measurements have been most widely used for the determination of optical constants in the region of electronic interband transitions of metals, semiconductors, and insulators. The same considerations apply to the intraband (or free-carrier) absorption in metals [4], since the corresponding absorption coefficients are also very high.