Distributions of conduction electrons as manifested in MAS NMR of gallium nitride

A strategy is demonstrated for identifying unambiguously and characterizing quantitatively the effects of distributions of conduction electron concentrations arising from intentional or unintentional dopants in semiconductors by magic-angle spinning (MAS) NMR. The 71Ga MAS NMR spectra of a number of chemically synthesized GaN samples with no intentional doping show inhomogeneously broadened absorptions to high frequency of the main peak. These broad signals are shown, from spin-lattice relaxation time measurements as a function of shift position in a single sample, to be due to Knight shifts arising from degenerate conduction electrons. For a GaN sample with Ge as an intentional dopant at the 0.13% (wt) level, the spectrum is dramatically broadened and shifted to high frequency by up to several hundred parts per million. Analysis of the inhomogeneously broadened line shape yields a quantitative probability density function for electron carrier concentration in the bulk sample that reflects significant compositional heterogeneity due to a variety of possible sources.