Optimisation of the envelope method for characterisation of optical thin film on substrate specimens from their normal incidence transmittance spectrum

The spectroscopic ellipsometry is the main tool for optical characterisation of a thin film in its spectral region of strong absorption, where its transmittance spectrum does not contain interference pattern. The envelope method (EM) is the main tool for accurate optical characterisation of a thin film with thickness typically in the range [500, 5000] nm on a substrate, in the spectral regions of medium and weak absorption and quasi-transparency of the film, where interference pattern is observed in the transmittance spectrum T(λ) of the film on substrate specimen. However, the EM algorithms have been devised and verified only for films with a wide spectral region of quasi-transparency. Moreover, the performance of the most credible EM algorithm assuming non-uniform film thickness contains three subjectively chosen parameters Δd, N1, and N2. The optimised EM algorithm (OEM algorithm) proposed here for the optimisation of EM, accurately characterises both quasi-transparent and absorbing films, and computes optimised values of Δd, N1, and N2. This is achieved by the correct differentiation of the film absorption from thickness non-uniformity in the film, and minimisation of the value of an error metric introduced to assess the film characterisation error. The OEM algorithm is validated for four model specimens, using films with dissimilar absorption and non-uniformity. Results are presented for film characterisation using both the EM algorithm and the OEM algorithm, for two specimens containing a-Si films with dissimilar film thicknesses. A comparison with thickness measurements by scanning electron microscope shows that using the EM algorithm leads to errors in the average film thickness d¯ of 25% and 38% for these a-Si films, due to the incorrect ascribing of film absorption to additional non-uniformity in film thickness. In contrast, an analysis of the characterisation results using the OEM algorithm indicates that d¯ is computed with an error of 0.1%, and the refractive index error is 0.15%. Using the OEM algorithm virtually guarantees accurate film characterisation in the wavelength region containing interference pattern of T(λ), regardless of whether the film has or does not have a wide spectral region of quasi-transparency, as well as whether the film is uniform or non-uniform.