Optical characterization of dielectric and semiconductor thin films by use of transmission data.
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.
Cisneros
J I
JI