Electron-Spin Resonance of Nitrogen Donors in Diamond

Abstract

Electron-spin resonance of bound substitutional nitrogen donors in diamond is observed and discussed. The $g$ factor is isotropic at 2.0024\ifmmode\pm\else\textpm\fi{}0.0005. For a given donor, one of the C-N bond directions is a hyperfine axis with constants $A=40.8$ oersteds, $B=29.2$ oersteds. There are thus four types of donors, equally abundant. A model for the donor wave function is proposed which puts the donor electron principally into an antibonding orbital located on a nitrogen atom and on one of its nearest-neighbor carbon atoms. A C-N bond distortion results which can be regarded as a manifestation of the Jahn-Teller effect. A careful search reveals the presence of an additional weak spectrum due to donors on ${\mathrm{N}}^{14}$-${\mathrm{C}}^{13}$ pairs. (The isotope ${\mathrm{C}}^{13}$ which has a nuclear spin of \textonehalf{} has a natural abundance of 1.1%.) The hyperfine constants measured for a ${\mathrm{C}}^{13}$ atom of an N-C pair are ${A}^{\ensuremath{'}}=60.8$ oersteds, ${B}^{\ensuremath{'}}=25.3$ oersteds. The $s$ and $p$ contributions to all 4 measured hyperfine constants are separated to give the values ${O}_{\mathrm{N}}=(\frac{8\ensuremath{\pi}}{3}){{|\ensuremath{\psi}(0)|}^{2}}_{\mathrm{N}}=2.41 \mathrm{atomic}\mathrm{units},$ ${P}_{\mathrm{N}}={〈\frac{[{z}^{2}\ensuremath{-}\frac{1}{2}({x}^{2}+{y}^{2})]}{{r}^{5}}〉}_{\mathrm{N}}=0.28 \mathrm{atomic}\mathrm{unit},$ ${O}_{\mathrm{C}}=(\frac{8\ensuremath{\pi}}{3}){{|\ensuremath{\psi}(0)|}^{2}}_{\mathrm{C}}=0.78 \mathrm{atomic}\mathrm{unit},$ ${P}_{\mathrm{C}}={〈\frac{[{z}^{2}\ensuremath{-}\frac{1}{2}({x}^{2}+{y}^{2})]}{{r}^{5}}〉}_{\mathrm{C}}=0.25 \mathrm{atomic}\mathrm{unit}.$ These are compared with theoretical values obtained by assuming a simple antibonding wave function composed of nitrogen and carbon tetrahedral orbitals. An increase of several percent in the N-C separation along the hyperfine axis is strongly implied by the comparison.