Finite-size effects on the optical functions of silicon microcrystallites: A real-time spectroscopic ellipsometry study

We have performed real-time spectroscopic ellipsometry (SE) measurements over the photon-energy range from 1.5 to 4.0 eV during the growth of microcrystalline silicon (μc-Si:H) by plasma-enhanced chemical-vapor deposition on chromium at 250 °C. We focus on the regime when the film consists of isolated microcrystallites and intervening void volume. In this regime, the observed three-dimensional growth behavior allows us to associate the crystallite size with the physical thickness of the film. The SE measurements are self-contained in that they provide not only microstructural information, including film thickness and void-volume fraction, but also the effective optical functions of the film. From this combination of results, the optical functions of the Si crystallites, themselves, can be deduced by mathematically extracting the influence of the void-volume fraction on the effective optical functions. A critical-point (CP) analysis of the ${\mathit{E}}_1$ transitions visible near 3.3 eV in the crystallite optical functions provides information on the electronic properties as a continuous function of crystallite size. Over the physical thickness range accessible in these experiments (∼200–250 Å), the transition energy and phase deduced in the CP analysis are constant at the single-crystal values, within experimental error, while the broadening parameter decreases with increasing thickness. The latter behavior is consistent with a finite-size effect in which electron scattering at surfaces modifies the optical response of the microcrystallites.