Quantum behaviour of hydrogen and muonium in vacancy-containing complexes in diamond

Abstract

Most solid-state electronic structure calculations are based on quantum electrons and classical nuclei. These calculations either omit quantum zeropoint motion and tunnelling, or estimate it in an extra step. Such quantum effects are especially significant for light nuclei, such as the proton or its analogue, µ + . We propose a simple approach to including such quantum behaviour, in a form readily integrated with standard electronic structure calculations. This approach is demonstrated for a number of vacancy-containing defect complexes in diamond. Our results suggest that for the NHV − complex, quantum motion of the proton between three equivalent potential energy minima is sufficiently rapid to time-average measurements at X-band frequencies.

Diffusion of Muonium and Hydrogen in Diamond

“…Here we will concentrate on high-resistivity diamond, where the nonparamagnetic fraction does not play an important role [1], and thus we will study neutral H and Mu.In earlier works, hydrogen diffusion in diamond has been studied theoretically in the classical (hightemperature) limit [6,8]. However, quantum effects are important for hydrogen-related defects in this material at relatively low temperatures [9]. Thus, we study in this Letter the diffusion of H and Mu in diamond by explicitly considering the impurities as quantum particles.…”

Importance of Quantum Tunneling in Vacancy-Hydrogen Complexes in Diamond

“…However, ab initio theory in which the H nuclei are treated classically predicts an equilibrium structure in which the H bonds to one of the three unsaturated C atoms at the vacancy [4], giving a defect of C 1h symmetry in clear contradiction with experiment. Quantum tunneling of the H between the three equivalent C sites could account for the observed symmetry -calculations of the tunneling time [5] indicate that the EPR measurement would indeed average the contributions from the three sites. Figure 1 shows the static nitrogen-bonded model of Ref.…”

“…In a recent paper, Kerridge et al [5] described a method for the rapid evaluation of the quantum wave function of a light interstitial (typically a proton or muon) in a variety of defect complexes. This method has been implemented so that self-consistent calculations of zero-point motion can be made in a time comparable to standard self-consistentfield approximation calculations.…”

“…We have performed calculations using the parametrized correlation model of Ref. [5] on two diamond clusters, one containing a single V 2 -H ÿ complex and the other a single V-H ÿ complex. These calculations yield a tunnel splitting energy and tunneling period of 0:1 cm ÿ1 and 320 ps for V 2 -H ÿ , respectively, and 0:6 cm ÿ1 and 50 ps for V-H ÿ .…”

Theoretical characterization of carrier compensation in P-doped diamond

“…In addition, hydrogen is a very common impurity in diamond and may influence greatly the gap states associated with defects and electronic properties [22][23][24][25]. Considering the existence of NVH and SiVH complexes in N-doped and Si-doped diamond [26][27][28][29][30], H atom may bind to P and V defects to form PVH related complexes and affect the electronic properties of P-doped diamond.…”