Excitation cross section of erbium in semiconductor matrices under optical pumping

Based on a detailed consideration of excitation mechanisms of erbium in crystalline and amorphous matrix we present an analysis of the physical meaning of the Auger excitation cross section of Er³⁺ ions in semiconductor. It is demonstrated that large values of Auger excitation cross sections under optical pumping in semiconductor matrices are due to large values of band-to-band absorption coefficient exceeding by several orders of magnitude the absorption coefficient of erbium in dielectric SiO₂ and Al₂O₃ matrix. The Auger excitation cross section of Er³⁺ in semiconductor matrices is roughly given by the ratio of the matrix absorption coefficient to concentration of Er³⁺ ions. While the analysis of the excitation cross section is carried out for Er-doped crystalline and amorphous silicon, the results are expected to be applicable to the other rare-earth doped semiconductors. Based on low-temperature experimental results for crystalline silicon we get the Auger excitation coefficient of cAᶜʳʸˢᵗ≈7×10^-10 cm³s^-1 and the effective excitation cross section σeffᶜʳʸˢᵗ=(2-8)×10^-12 cm². For amorphous silicon at 100 K we obtain σeffᵃᵐᵒʳᵖʰ≈1.4×10^-14 cm².