High-resolution, high-accuracy, mid-IR (450 cm−1⩽ω⩽4000 cm−1) refractive index measurements in silicon

The real and imaginary parts of the refractive index of silicon, n(ω) and k(ω), have been measured by using Fourier Transform Infrared (FTIR) transmission spectral data from a double-sided-polished grade Si wafer. An accurate mechanical measurement of the wafer thickness, t, was required and two FTIR spectra were used: a high-resolution (Δω=0.5 cm−1) yielding a typical channel spectrum dependent mainly on t and n(ω), and a low resolution (Δω=4.0 cm−1) yielding an absorption spectrum dependent mainly on t and k(ω). Independent analysis of each spectrum gave initial n(ω) and k(ω) estimates which were then used together as starting point values for an iterative fit of the high- and low-resolution spectra successively. The accuracy of n(ω) and k(ω) 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 wafer thickness nonuniformity and the degree of incident light beam collimation. Our results are compared with previously published values for n(ω) and k(ω) in the 450 cm−1 to 4000 cm−1 spectral region. The error in n(ω) is <1 part in the 104, a factor of 10 better than published values. The k(ω) 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.