Characterization of strain in $Si_1_-_xGe_x$ films using multiple angle of incidence ellipsometry

In this letter we characterize strain in $Si_1_-_xGe_x$ based heterojunction bipolar transistors and modulation doped field effect transistors grown by rapid thermal chemical vapor deposition exploiting the phenomenon of strain-induced birefringence. The technique used is multiple angle of incidence ellipsometry at a wavelength of 670 nm to measure the ordinary and extraordinary refractive indices of the $Si_1_-_xGe_x$ films. We report measurements on thin fully strained films (with thicknesses less than the critical thickness) with Ge concentration varying from 9% to 40% with an accuracy of the order of 1 part in 104 and propose an empirical relation between the difference in the ordinary and extraordinary refractive indices (\delta n) and the Ge concentration (x) given by $\delta n(x) = 0.18x-0.12x^2$