Free-carrier electro-refraction and electro-absorption modulation predictions for silicon over the 1-14µm infrared wavelength range

We present relationships for the free-carrier-induced electrorefraction and electroabsorption in crystalline silicon over the 1-14 µm wavelength range. Electroabsorption modulation is calculated from impurity-doping spectra taken from the literature, and a Kramers-Kronig analysis of these spectra is used to predict electrorefraction modulation. More recent experimental results for terahertz absorption of silicon are also used to improve the commonly used 1.3 and 1.55 µm equations. We examine the wavelength dependence of electrorefraction and electroabsorption, finding that the predictions suggest longer wave modulator designs will, in many cases, be different from those used in the telecom range