Calculation of the ortho-para conversion of hydrogen in a p-type silicon lattice using a dwell time approach

Quantitative spectroscopic studies of hydrogen in a p-type silicon lattice at room temperature and at reduced temperature have led to rates for the ortho-para conversion process. The characteristic relaxation time at room temperature is about 8 hours. Explanations of this rate on the basis of the interaction between the interstitial H₂ and naturally occurring ²⁹Si using the Wigner rate expression encounter several difficulties, the principal being that the decay would involve multiexponential decay, in contradiction to observation. In an earlier work we calculated the rate assuming that the ortho-para conversion was effected during scattering of holes from the hydrogen molecules. The result was smaller than observed by several orders of magnitude. In the present work it is assumed that sp_z holes diffuse randomly throughout the Si lattice, dwelling on effective areas associated with sp_z sites. The transition matrix elements are the same as for the scattering mechanism. The resultant characteristic time at room temperature we find to be 1000 hr. Considering the uncertainties in the calculation the discrepancy between our result and observation is not sufficient as to negate our physical picture.