Cisneros J I
Appl Opt. 1998 Aug 1;37(22):5262-70. doi: 10.1364/ao.37.005262.
A method to calculate the optical functions n(lambda) and k(lambda) by use of the transmission spectrum of a dielectric or semiconducting thin film measured at normal incidence is described. The spectrum should include the low-absorption region and the absorption edge to yield the relevant optical characteristics of the material. The formulas are derived from electromagnetic theory with no simplifying assumptions. Transparent films are considered as a particular case for which a simple method of calculation is proposed. In the general case of absorbing films the method takes advantage of some properties of the transmittance T(lambda) to permit the parameters in the two regions mentioned above to be calculated separately. The interference fringes and the optical path at the extrema of T(lambda) are exploited for determining with precision the refractive index and the film thickness. The absorption coefficient is computed at the absorption edge by an efficient iterative method. At the transition zone between the interference region and the absorption edge artifacts in the absorption curve are avoided. A small amount of absorption of the substrate is allowed for in the theory by means of a factor determined from an independent measurement, thus improving the quality of the results. Application of the method to a transmission spectrum of an a:Si(x)N(1-x):H film is illustrated in detail. Refractive index, dispersion parameters, film thickness, absorption coefficient, and optical gap are given with the help of tables and graphs.
描述了一种通过使用在正入射下测量的介电或半导体薄膜的透射光谱来计算光学函数n(λ)和k(λ)的方法。该光谱应包括低吸收区域和吸收边缘，以得出材料的相关光学特性。这些公式是从电磁理论推导出来的，没有简化假设。透明薄膜被视为一种特殊情况，并提出了一种简单的计算方法。在吸收薄膜的一般情况下，该方法利用透射率T(λ)的一些特性，允许分别计算上述两个区域中的参数。利用T(λ)极值处的干涉条纹和光程来精确确定折射率和薄膜厚度。通过一种有效的迭代方法在吸收边缘计算吸收系数。在干涉区域和吸收边缘之间的过渡区，避免了吸收曲线中的伪像。通过从独立测量中确定的一个因子，在理论中考虑了衬底的少量吸收，从而提高了结果的质量。详细说明了该方法在a:Si(x)N(1-x):H薄膜透射光谱中的应用。借助表格和图表给出了折射率、色散参数、薄膜厚度、吸收系数和光学带隙。
