Photoionization cross sections of a two-electron donor center in silicon

Abstract

A simple model is presented for calculating the photoionization cross-section spectra of a two-electron center in silicon. A hydrogenlike wave function is used for the ground state of the singly ionized one-electron center, and a heliumlike wave function for the ground state of the neutral two-electron center. A test of this model is provided by comparison with the observed photoionization cross-section spectra of sulfur centers in silicon, using trial wave functions obtained previously from variational calculations of the bound-state electronic energy levels. The experimental spectra were obtained by the photocapacitance transient method for sulfurdoped silicon $p^{+}$-$n$ junction diodes. Good agreement between theory and experiments is obtained without the use of empirical-effective-field ratios. Structures below the extrinsic edge in the spectra of the neutral centers were observed and are attributed to two-step photothermal transitions. The peak at about 0.285 eV is attributed to an optical transition from the [$1s\left(A_1\right), 1s\left(A_1\right)$] ground state of the neutral two-electron center to the [$1s\left(A_1\right), 1s\left(T_2\right)$] excited state, with a subsequent thermal excitation into the conduction band as the second transition step.