High-accuracy, midinfrared (450cm−1⩽ω⩽4000cm−1) refractive index values of silicon

The real and imaginary parts of the refractive index, n(ω) and k(ω), of silicon were measured as a function of photon frequency ω using Fourier transform infrared (FTIR) transmission spectral data. An accurate mechanical measurement of the wafer’s thickness, t, was required, and two FTIR spectra were used: one of high resolution (Δω=0.1to0.5cm−1) yielding a typical channel spectrum (Fabry–Perot fringes) dependent mainly on t and n(ω), and one of low resolution (Δω=4.0cm−1) yielding an absorption spectrum dependent mainly on t and k(ω). A procedure was developed to first get initial estimates for n(ω) for the high-resolution spectrum and then calculate k(ω) from the faster low-resolution spectrum with minimal measurement drift. Then both initial n and final k values were used together as starting point data for a fit to the high-resolution spectrum. A previously derived transmission formula for a convergent incident beam was used for the fit. The accuracy of n(ω) determined using this procedure is mostly dependent upon the measurement error in the sample thickness t and k(ω) is dominated by the accuracy of the absolute transmission values obtained from a sample-in and sample-out methods. Our results are compared with previously published values for n(ω) and k(ω) in the 450–4000-cm−1 spectral region. The reported uncertainty in n(ω) is ±10−4 absolute, a factor of 10 better than published values. The values of n(ω) range from 3.4400 at 4000cm−1 (λ=2.5μm) to 3.4169 at 450cm−1 (λ=22.222μm). The k(ω) values had a standard deviation of ⩽±3% and are in good agreement with previous measurements.