Application of sum rule to the dispersion model of hydrogenated amorphous silicon

• An approach based on sum rule is used to construct dispersion model of amorphous Si.
• The model is expressed fully analytically and it is computationally efficient.
• It covers spectral range from phonon absorption to core electron excitations.
• Material parameters such as mass density are determined using optical measurements.
• It is shown that excitonic effects play an important role in interband transitions.

Optical data obtained for a-Si:H films by ellipsometry and spectrophotometry in the wide photon energy range 0.046–8.9 eV are fitted using the analytical dispersion models based on the application of the sum rule. The models include all absorption processes ranging from phonon absorption in IR region to core electron excitations in X-ray region. They take into account the existence of extended and localized states of valence electrons and distinguish transitions to conduction band and higher energy electron states. It is demonstrated that a combination of optical measurements over the wide range, combined with reasonable assumptions about the optical response in regions where no experimental data are available can lead to dispersion models enabling to determine the mass density of the film. Comparing the density of states determined by tight-binding method with that obtained from optical data, it is shown that an excitonic effect is significant in a-Si:H and causes a redistribution of transition probability from higher energies to the broad peak centered at 3.5 eV. Moreover, it is suggested how to apply the sum rule in the commercial ellipsometric software implementing the Tauc–Lorentz model.