Analytical calculation of effective densities of states, intrinsic carrier concentration and ionized doping concentration in strained Si 1− xGe x alloys on (001) Si substrates at room and low temperatures

Abstract

In this paper, the effective densities of states for the conduction and valence bands, N c and N v , the intrinsic carrier concentration n i , and the ionized doping concentration in strained Si 1− x Ge x layers grown on (001) Si substrates are analytically calculated, and their temperature and Ge fraction dependence studied. It is found that whereas n i increases quasi-exponentially, the ionized doping concentration increases (carrier freeze-out is mitigated at low temperatures compared with that in Si) and N c , V v and the product N c · N v decrease rapidly due to the effect of strain in the Si 1− x Ge x layers as the Ge fraction increases. Furthermore, as the temperature becomes lower, the decrease in N c , N v and the product N c · N v become more rapid and the increase in n i becomes more evident. In addition, it is also found that for strained Si 1− x Ge x layers with low and high Ge fractions, respectively, N c , N v and the product N c · N v normalized by those in Si depend on temperature T strongly versus slightly, which is consistent with the results of Prinz et al.