Experimental doping dependence of the lattice parameter in n -type Ge: Identifying the correct theoretical framework by comparison with Si

The lattice parameter of Ge films doped with phosphorus, arsenic, and antimony was measured as a function of the dopant concentration. When the observed trends are compared with similar measurements in doped Si, a clear pattern emerges in support of the Cargill-Keyes theory that computes the doping dependence of the lattice parameter as the sum of a purely electronic contribution, proportional to the absolute deformation potential for the states occupied by the dopant carriers, plus a size mismatch contribution that depends on the universal topological rigidity parameter for Si-Ge systems. It is shown that when considered from the same global perspective, ab initio calculations of the structural effects of doping are in remarkable agreement with the Cargill-Keyes theory.