High-accuracy Midinfrared(450 cm-1 ' w ' 4000 cm-1)Refractive Index values of Silicon
Deane Chandler-Horowitz, Paul M. Amirtharaj
The real and imaginary parts of the refractive index, n(w) and k(w), of silicon, as a function of photon frequency w were measured by using Fourier Transform Infrared (FTIR) transmission spectral data from a double-sided-polished Si wafer. An accurate mechanical measurement of the wafer's thickness, t, was required and two FTIR spectra were used: one of high-resolution (Dw = 0.5 cm-1) yielding a typical channel spectrum dependent mainly on t and n(w), and one low resolution (Dw = 4.0 cm-1) yielding an absorption spectrum dependent mainly on t and k(w). Independent analysis of each spectrum gave initial n(w) and k(w) estimates which were then used together as starting point values for a fit to the high-resolution spectra using a previously derived transmission formula for a slightly convergent incident beam. The accuracy of n(w) and k(w) values determined using this procedure is dependent upon the measurement error in the sample thickness, the absolute transmission values obtained from a sample-in and sample-out method, and the modeling of the influence of a convergent incident light beam and any wafer thickness nonuniformity.. Our results are compared with previously published values for n(w) and k(w) in the 450 cm-1 to 4000 cm-1 spectral region. The error in n(w) is < 1 part in the 104, a factor of 10 better than published values. The k(w) values are in good agreement with previous measurements except in the vicinity of the 610 cm-1 peak feature where our values are 20% lower.