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±0.0005. For a given donor, one of the C-N bond directions is a hyperfine axis with constants $A=40.8\mathrm{}$ oersteds, $B=29.2\mathrm{}$ 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 ½ has a natural abundance of 1.1%.) The hyperfine constants measured for a ${\mathrm{C}}^{13}$ atom of an N-C pair are $A^{\prime }=60.8\mathrm{}$ oersteds, $B^{\prime }=25.3\mathrm{}$ oersteds. The $s$ and $p$ contributions to all 4 measured hyperfine constants are separated to give the values $O_{\mathrm{N}}=\left(\frac{8\pi }{3}\right){{\left|\psi \mathrm{}\right(0\left)\right|}^2}_{\mathrm{N}}=2.41\mathrm{} \mathrm{atomic}\mathrm{units},$ $P_{\mathrm{N}}={〈\frac{[z^2-\frac{1}{2}(x^2+y^2\left)\right]}{r^5}〉}_{\mathrm{N}}=0.28\mathrm{} \mathrm{atomic}\mathrm{unit},$ $O_{\mathrm{C}}=\left(\frac{8\pi }{3}\right){{\left|\psi \mathrm{}\right(0\left)\right|}^2}_{\mathrm{C}}=0.78\mathrm{} \mathrm{atomic}\mathrm{unit},$ $P_{\mathrm{C}}={〈\frac{[z^2-\frac{1}{2}(x^2+y^2\left)\right]}{r^5}〉}_{\mathrm{C}}=0.25\mathrm{} \mathrm{atomic}\mathrm{unit}.$ 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.