Free-Carrier Electrorefraction and Electroabsorption Modulation Predictions for Silicon Over the 1–14- $\mu\hbox{m}$ 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.