Spatially correlated distributions of local metallic properties in bulk and nanocrystalline GaN

We compare local electronic structure at different atom types of a metallic semiconductor in bulk and nanocrystalline form. Multinuclear magic-angle-spinning nuclear magnetic resonance (MAS NMR) establishes that GaN synthesized as an intentionally doped bulk powder or as annealed nanocrystalline particles exhibits metallic behavior and a wide distribution of differing electronic environments in both forms. Bulk polycrystalline wurtzite GaN doped with 0.13% Ge as a shallow donor exhibits a temperature-independent distribution of $^{71}\mathrm{Ga}$ Knight shifts over the temperature range 123--473 K. Each Knight shift frequency in the inhomogeneously broadened spectrum is characterized by a $^{71}\mathrm{Ga}$ spin-lattice relaxation time ${T}_{1}$ that is in good agreement with the value predicted by the Knight-Korringa relation across the broad range of temperatures. The $^{14}\mathrm{N}$ spectrum shows a slightly smaller Knight shift distribution with spin-lattice relaxation time ${T}_{1}$ values at 295 K across the distribution also in good agreement with the Knight-Korringa relation. Similarly, annealed nanocrystalline wurtzite GaN (50--100 nm, and without Ge) exhibits a $^{71}\mathrm{Ga}$ Knight shift distribution and ${T}_{1}$ values (at 295 K) that follow the same Knight-Korringa behavior. Thus, both bulk and nanocrystalline forms of GaN are n type and well above the metal-insulator transition (MIT), the nanocrystals most likely as a result of incorporation of shallow donor oxygen atoms during synthesis. Carriers in both forms of samples exhibit the near-ideal characteristics of a degenerate Fermi gas of noninteracting spins. The observation of NMR signals from both atom types, Ga and N, allows for the direct spatial correlation of the local electronic structure at the two sites in the lattice, specifically the $s$-orbital character of the electronic wave function of conduction band electrons at the Fermi edge. The relative values of these carrier wave-function probabilities (nearly twice as great for the N atom as for the Ga) are in line with theoretical predictions. Analyses of $^{71}\mathrm{Ga}, ^{14}\mathrm{N}$, and $^{15}\mathrm{N}$ NMR results, including double-resonance 2D $^{15}\mathrm{N}{^{71}\mathrm{Ga}}$ measurements, reveal electronic disorder in the form of broad distributions of local metallic properties (Knight shifts) that are shown to be spatially correlated on a subnanometer scale.