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Defect and analysis effects in the infrared optical properties of silicon



The infrared optical properties of silicon reported by different workers disagree by far more than the precision of the measurements. Further, their extrapolations conflict with THz measurements. These inconsistencies are commonly attributed to crystal defects or impurities, but lack of reliable intrinsic silicon values hampers separation of host and defect effects. We have developed tests based on linear-response theory to address this. Tests include requiring that the refractive index is an even function of photon energy, and comparing the coefficients of a Taylor expansion of the IR index with the moments of the electronic absorption above the band gap. The latter is sufficiently well known for silicon that predictions for the intercept, slope, and curvature, of the index may be used to test infrared measurements for consistency. Thus, we identified the sources of conflict as: (i) A physically inconsistent assumption for index parity commonly made in analysis of channel-spectra. (ii) Defect and free-carrier absorption. Eliminating data sets with these shortcomings resolved the conflict between measurements and allowed us to develop a composite set of IR optical constants for silicon that is a best fit to reliable measurements from microwaves to the visible.