The determination of the optical constants of thin films from measurements of reflectance and transmittance at normal incidence

Abstract

The derivation of the components n and k of the complex refractive index of a thin film from measurements, at normal incidence, of reflectance R and transmittance T is complicated by the existence of multiple solutions of the relevant equations. It is shown that, although use of Tomlin's expressions for (1 ± R)/T rather than Heavens's explicit formulae for R and T separately simplifies the problem, it is still necessary to consider very carefully the multiple solutions. A procedure is given for determining the correct solutions for n and k, and also for accurately fixing the film thickness, provided that the film is a homogeneous single layer on a substrate. Some experimental results have not yielded to this treatment and in these cases it has been found necessary to assume the presence of a surface layer (often, but not necessarily, an oxide layer) and to make use of the equations in the preceding paper which relate to a double layer on a substrate. It is shown how this may be done in such a way as to obtain the correct dispersion curve for the material, together with its thickness, and that of the surface layer.

Structural, optical and dielectric studies of lithium sulphate monohydrate single crystals

“…The large band gap and transparency shown by the crystals make them a possible choice for optoelectronic application [39,46]. The transmittance (T) is given by the relation [47]:…”

Preparation and optical characterization of Cu2ZnGeSe4 thin films

“…In order to determine n and k for each single wavelength we substituted the measured thickness d of the film and the value s = 1.45 for the s refractive index of the substrate in the equation system (4) is the existence of (n, k) multiple solutions for singular values of T exp , R exp and d. Furthermore, at some specific wavelengths n(λ)and k(λ) curves exhibit discontinuities which are typical for the method of normal incidence transmittance and reflectance [27,31]. To restict the possibility of multiple solutions we solved the equation system (3)-(4) in the region 2.5-3.5 for n and in the region 0-1.5 for k .…”

Optical Properties of Thin Germanium Films

“…If this was riot done it was found that closure of the dispersion curve (see Denton, Campbell, and Tomlin 1972) could not be achieved owing to insufficient Uniformity of film thickness. The substrate temperature could be maintained at any desired temperature between room temperature and 700°C.…”

“…It has been shown by Denton, Campbell, and Tomlin (1972) that the calculations are much simplified by using expressions for (1 ±R)/T rather than those for Rand T, and that the correct choice from the multiple solutions can be made unambiguously, together with an accurate determination of film thickness, provided measurements are made over a sufficiently wide range of wavelengths. The same paper also discusses the application of rigorous formulae, for a double layer film, to the investigation of thin surface layers and shows how to allow for the effects of such layers.…”

“…In this paper we present results for amorphous films of germanium based on the use of rigorous formulae according to the methods discussed by Denton, Campbell, and Tomlin (1972).…”