Flexible construction of error functions and their minimization: application to the calculation of optical constants of absorbing or scattering thin-film materials from spectrophotometric data

Abstract

A flexible numerical procedure for the calculation of thin-film optical constants from specular transmittance and reflectance data is presented. The method is based on the minimization of a quadratic error function, which may be adapted to the specifics of the optical behaviour of the given sample (or set of samples), and the given wavenumber region. The flexibility in choosing an appropriate form of the minimized error function, in combination with the powerful minimization method of conjugated gradients, allowed us to investigate the optical constants of very different types of novel thin-film material with a complicated optical loss behaviour. In particular, the results concerning the investigation of single- and two-layer systems based on the following technologically interesting optical thin film materials are presented: (1) amorphous silicon as an example of-an anorganic solar cell material; (2) as-deposited (rough) CVD diamond layers as an example of a polycrystalline protective material; (3) hydrogenated amorphous carbon, applicable as a protective long-wavelength in antireflection coating as well as a spectrally selective solar absorber; (4) copper phthalocyanine layers as an example of a molecular solid, potentially applicable as an organic solar cell material; (5) rare-earth diphthalocyanine layers, interesting because of their electrochromic behaviour.