Theory of Umklapp-assisted recombination of bound excitons in Si:P

Abstract

We present calculations for the oscillator strength of the recombination of excitonsbound to phosphorus donors in silicon. We show that the direct recombination ofthe bound exciton cannot account for the experimentally measured oscillatorstrength of the no-phonon line. Instead, the recombination process is assisted byan Umklapp process of the donor electron state. We make use of the empiricalpseudopotential method to evaluate the Umklapp-assisted recombination matrixelement in second-order perturbation theory. Our result is in good agreementwith experiment. Being potentially useful for quantum computing, the process ofUmklapp-assisted recombination can be used to detect optically the spin state of thenucleus of a phosphorus donor, which requires that the energy levels of the nuclearspin are optically resolvable. We therefore present two methods to improve theoptical resolution of the optical detection of the spin state of a single nucleus inSi:P.