Suppressed Incomplete Ionization of Shallow Donors in Germanium

For doping levels $N_{d}$ \textgreater 10$^{\mathrm{17}}$ cm$^{\mathrm{-3}}$, an elementary analysis indicates that shallow donors should not be completely ionized in germanium at room temperature. The predicted degree of incomplete ionization (I.I.) represents a fundamental limitation in the quest for ultra-low sheet resistances, as required in Ge-based nMOS devices. Unfortunately, the experimental verification of the predictions is made difficult by the possible presence of inactive dopants, which also lead to free carrier concentrations $n$ \textless $N_{d}$. In this work, we prepared $n$-type Ge films on Ge-buffered Si substrates using novel synthetic approaches that are expected to minimize the presence of inactive dopants. Higher-order germanes (Ge$_{\mathrm{3}}$H$_{\mathrm{8}}$ and Ge$_{\mathrm{4}}$H$_{\mathrm{10}})$ were used as the source of Ge for growth at low temperatures. Phosphorus atoms were furnished via P(MH$_{\mathrm{3}})_{\mathrm{3}}$ (M $=$ Ge, Si) compounds in which the P atom is already bonded to three group-IV atoms in a way that is expected to promote substitutional incorporation. Spectroscopic ellipsometry and SIMS were used to determine $n$ and $N_{d}$, respectively. The results indicate no observable I.I. Within experimental error, $n=N_{d}$, in contradiction with the elementary theory. These findings are compatible with the model developed by Altermatt \textit{et al}. to explain I.I. phenomena in silicon.