Dielectric properties of heavily doped crystalline and amorphous silicon from 1.5 to 6.0 eV

Extremely uniform, microscopically smooth, large-grained polycrystalline Si films saturation doped with phosphorous to a carrier concentration $n=3.3\mathrm{}\times {10}^{20}$ ${\mathrm{cm}}^{-3\mathrm{}}$ were prepared by a combination of low-pressure chemical-vapor-deposition and heat-treating processes to obtain samples suitable for measuring the small effects of large impurity concentrations on the above-band-gap dielectric properties of Si. From 1.5 to 2.5 eV, the effects of heavy doping are described by the Drude free-carrier model with lifetimes determined by scattering from lattice vibrations. Above 3 eV, the dielectric function spectrum of heavily doped Si is remarkably similar to that of undoped material except that the $E_1$ and $E_2$ structures are broadened and shifted to lower energies. The impurity-induced broadening is much larger for $E_1$ than for $E_2$, indicating that a metastable excitonic resonance is well developed for the former but not for the latter. Present and previous data of the authors, together with previous data of Viña and Cardona, are consistent with an approximately linear shift of the threshold energy with impurity concentration. This indicates that the dominant mechanism responsible for the shifts is the effect of the random impurities on the crystal potential. While the possibility of electron-electron and electron-ion interactions on the electron and hole self-energies cannot be ruled out, comparison with recent calculations of Berggren and Sernelius show that these effects must be much smaller at higher interband transitions than at the fundamental indirect band gap. Using our data as a reference, we show that the anomalous absorption observed by Jellison and co-workers for As-implanted and laser-annealed $c-\mathrm{S}\mathrm{i}$ is due to microscopically rough surface layers on their samples. Consequently, the differences that they observe between P and As dopants must involve differences in recrystallization and regrowth. Dielectric-function spectra for amorphous Si films doped in situ with phosphorus are essentially identical within microstructural effects to those of undoped material, indicating no significant influence from heavy doping. At energies below 3.2 eV, the data expressed as ${\left(\alpha nE\right)}^{\frac{1}{3}}$ or as ${\left({\epsilon }_2\right)}^{\frac{1}{2}}$ both vary nearly linearly with energy, suggesting nondirect transitions between simple parabolic bands with momentum matrix elements linearly proportional to $E$ or with dipole elements independent of $E$.