Behavior of phosphorus donors in bulk single-crystal monoisotopic $^{28}$Si$_{1-x}$ $^{72}$Ge$_{x}$ alloys

The behavior of phosphorus donors in bulk single-crystal monoisotopic Si$_{1-x}$Ge$_{x}$ alloys ($x$ = 0.0039–0.05) enriched by zero-spin isotopes $^{28}$Si (99.998%) and $^{72}$Ge (99.984%) by the electron-spin-resonance method is investigated. The hyperfine structure of the donor-electron spectrum giving information on the density of the donor wave function in the ground state on the $^{31}$P nucleus ($I$ = 1/2) as well as the temperature dependences of the spin-relaxation rate ($T$ = 3.5–30 K), which make it possible to analyze the longitudinal component $T_1$ relaxation mechanism and magnitude of the valley–orbit splitting of the donor state, are investigated. Interest in these investigations is also caused by the fact that the Si$_{1-x}$Ge$_{x}$ alloy enriched by zero-spin isotopes ($^{28}$Si $^{\operatorname{iso}}$Ge, $\operatorname{iso}$ = 70, 72, 74, 76) is a poorly known material when compared with $^{28}$Si. The irregular arrangement of germanium atoms in the lattice of the SiGe solid solution and local distortions formed by it can level isotopic effects under isotopic enrichment. However, despite broadening of the lines of the electron-spin resonance of donor electrons due to random deformations formed by dissolved germanium atoms in silicon, narrower lines of the spectra of the electron-spin resonance are observed in isotopically pure Si$_{1-x}$Ge$_{x}$ single crystals at $x$ = 0.39, 1.2, 2.9 at.% when compared with similar crystals with the natural composition of silicon and germanium isotopes.