Oscillator strengths, intracenter absorption and photoionization cross sections of optical transitions of shallow donors in silicon

Abstract

Infrared photoionization and intracenter cross sections as well as oscillator strengths of intracenter transitions in silicon doped with single-electron, shallow donors are determined in research-grade crystals and compared with the corresponding values calculated by various theoretical models. The float-zone grown crystals were doped with substitutional group-V, interstitial group IA lithium and lithium-oxygen complex at concentrations of 1e12–1e17 atoms/cm3. The concentrations of electrically active impurity centers in the samples were determined from resistivity measurements. Experimentally integrated cross sections were obtained from low-temperature absorption spectra of impurities. For an isocoric substitutional donor, the oscillator strengths for intracenter transitions into the lowest odd-parity states were compared for two main crystal growth and doping methods: the float-zone and the Czochralski techniques. The applicability of the obtained calibration coefficients for various ranges of impurity concentrations is discussed. Recommendations are given for the optimal selection of optical transitions for quantifying the density of shallow donors in silicon along with experimental values for each shallow center. The oscillator strengths of transitions of shallow impurities were estimated for almost all observed donor transitions, including those into high excited, Rydberg-like atomic states, as well as for the intracenter transitions into several even-parity excited states.