Critical investigation of the infrared-transmission-data analysis of hydrogenated amorphous silicon alloys

Abstract

Infrared-transmission spectroscopy is widely used to obtain quantitative information about hydrogen bonding in hydrogenated amorphous silicon (a-Si:H), silicon-germanium (a-SiGe:H), and silicon-carbon (a-SiC:H) alloys. To simplify the conversion of transmission spectra to absorption spectra the most commonly used methods, suggested by Brodsky, Cardona, and Cuomo (BCC) [Phys. Rev. B 16, 3556 (1977)] and Connell and Lewis (CL) [Phys. Status Solidi B 60, 291 (1973)], assume incoherent multiple reflections in the film as well as the substrate. We show that the absorption in a-Si:H alloy films on c-Si substrates is different for coherent and incoherent reflections in the film. This difference causes the BCC and CL methods to overestimate or underestimate the absorption coefficient (\ensuremath{\alpha}) in many experimental situations. The most notable feature is an overestimate of \ensuremath{\alpha} if the film thickness d is below a critical value (${\mathit{d}}_{\mathrm{min}}$). For d>${\mathit{d}}_{\mathrm{min}}$, the error in absorption coefficient is usually less than 10%. Below ${\mathit{d}}_{\mathrm{min}}$, the error in \ensuremath{\alpha} increases as d decreases. The maximum error, which occurs in the limit d\ensuremath{\rightarrow}0, increases with the refractive index of the film and is \ensuremath{\ge}30% for a-SiC:H alloys, \ensuremath{\sim}70% for a-Si:H, and \ensuremath{\le}90% for a-SiGe:H alloys. The value of ${\mathit{d}}_{\mathrm{min}}$ decreases as the refractive index of the film and the frequency of the vibrational mode increase. For a-Si:H, for example, the hydrogen content determined from the 640-${\mathrm{cm}}^{1}$ Si-H wagging-mode absorption is overestimated if d is less than \ensuremath{\sim}1 \ensuremath{\mu}m. We show that experimental data are consistent with the predictions of this analysis. In most cases it is possible to correct the results from the BCC and CL methods so that they are accurate to within 10%. For greater accuracy, infrared-transmission data should be analyzed by taking the effects of optical interference into account.