Empirical Correlation for Minority Carrier Lifetime to Defect Density Profile in Germanium on Silicon Grown by Nanoscale Interfacial Engineering

High-quality Ge-on-Si heterostructures have been explored for many applications, including near infrared photodetectors and integration with III-V films for multijunction photovoltaics. However, the lattice mismatch between Ge and Si often leads to a high density of defects. Introducing annealing steps prior to and after full Ge island coalescence is found to reduce the defect density. The defect density in Ge is also found to decrease with increasing dopant density in Si substrates, likely due to the defect pinning near the Ge-Si interface by dopants. The authors establish an empirical correlation between the minority carrier lifetime (τ_G) and the defect density in the Ge film (ρ_D) as a function of distance from the Ge-Si interface: τ_Ge = C/ρ_D, where C is a proportionality constant and a fitting parameter which is determined to be 0.17 and 0.22 s/cm² for Ge films grown on low-doped, high-resistivity Si substrates and high-doped, low-resistivity Si substrates, respectively. The effective minority carrier lifetime measured as a function of Ge film thickness is then related to the recombination velocity on Ge film surface, average minority carrier lifetime within Ge film, and recombination velocity at the Ge-Si interface. Using this relation, the authors estimate the Ge-Si interface recombination velocity for Ge films grown on low-doped, high-resistivity and high-doped, low-resistivity Si substrates to be 220 and 100 cm/s, respectively.