Hyperfine interactions at dangling bonds in amorphous germanium

Isotope-engineered amorphous germanium $(a$-Ge) films with ⁷³Ge concentrations in the range of 0.1 to 95.6 % have been investigated by electron spin resonance (ESR) and electrically detected magnetic resonance (EDMR) at microwave frequencies between 0.434 and 9.35 GHz. The hyperfine interactions of dangling bond (DB) defects with many ⁷³Ge nuclei and their spin localization radius have been extracted from the broadening of the EDMR signals in isotope enriched samples at different ⁷³Ge concentrations. Linewidths as low as ΔBₚₚᵉˣᵖ=2.6G have been observed at 0.434 GHz in a sample without ⁷³Ge nuclear spins. At low ⁷³Ge concentrations, the frequency-dependent linewidth BₚₚSO/ν=4.4G/GHz is determined by g-factor anisotropy and disorder. A frequency-independent linewidth contribution of about 1 G is attributed to dipolar broadening between the DB electronic spins. Over a large range of intermediate concentrations, the statistically distributed nuclear spins of ⁷³Ge atoms on sites close to the DB defect atom are responsible for the overall linewidth. The large linewidth ΔBₚₚᵉˣᵖ=300G of samples with ⁷³Ge concentrations of 95.6% requires a model wave function with a Fermi contact interaction of Aᵢₛₒ=29G×gμB at the defect atom, indicating that a fraction of 3.4% of the DB wave function originates from s-like orbitals there. The decay of the rest of the DB wave function can be described with a spin localization radius of 3.5 {} by a numerical model for the statistical hyperfine broadening. The delocalization of the DB spin is much smaller than that of the DB charge density determined in transport measurements.