Optical properties of amorphous multilayer structures

Abstract

The Tauc-law extrapolation has been recently applied to obtain the band gap of the hydro-genated amorphous silicon ($a-\mathrm{Si}:\mathrm{H}$) component of $\frac{a-\mathrm{Si}:\mathrm{H}}{a-\mathrm{Si}{\mathrm{N}}_x:\mathrm{H}}$ alternating layer structures. An increase in the deduced band gap of the $a-\mathrm{Si}:\mathrm{H}$ layer as its thickness is reduced below 30 Å has been attributed to quantum confinement in the $a-\mathrm{Si}:\mathrm{H}$ sublayers. The Tauc law has proven inadequate, however, in fitting optical absorption data of $a-\mathrm{Si}:\mathrm{H}$ over a wide range of photon energy, and thus may introduce systematic errors in the gap determinations for the multilayers. In this paper, we describe the results of exact classical calculations of the transmission spectra of a series of $\frac{a-\mathrm{Si}:\mathrm{H}}{a-\mathrm{Si}{\mathrm{N}}_x:\mathrm{H}}$ alternating layer structures which are employed to obtain an estimate of the possible errors. We find a systematic increase in the $a-\mathrm{Si}:\mathrm{H}$ band gap of about 150 meV as the thickness of the $a-\mathrm{Si}:\mathrm{H}$ layer is reduced from 150 to 5 Å, attributable to the use of the constant-index-of-refraction Tauc-law formalism. Our calculations also suggest that interface roughness between the layers can enhance this effect in certain circumstances. As a result, we believe that the optical absorption data should be applied with care in the evaluation of quantum confinement effects.