Multiphonon Relaxation of the 1s(T₂) States of a Singly Ionized Selenium Donor in Silicon

Abstract

The rate of the multiphonon relaxation of the 1s(T₂) level in Se⁺ donors in silicon is estimated. The calculation comprises the initial approach to the problem, in which the most simplified form of wave functions is used. To evaluate the transition probability, the Pässler expression known from publications is used [R. Pässler, Czech. J. Phys. B 24, 322 (1974)]. This expression was derived in terms of the so-called static approximation. The deformation potentials of optical and acoustic phonons were determined by the fitting procedure using published data on the luminescence spectrum of Se⁺ donors at the 1s(T₂)–1s(A₁) transition and Franck–Condon principle. Evaluation for the relaxation rate of 10³ s^–1 turned out to be five orders of magnitude smaller than the rate corresponding to the experimentally measured lifetime. The cause of disagreement with the experiment is the excessively simplified model, which does not taking into account several factors, the main one being the presence of quasi-local oscillatory modes. Analysis of the luminescence spectrum based on the mentioned transition leads to the conclusion that the energies of such oscillatory modes lie in the range from 26 to 61 meV. To attain satisfactory agreement with the experiment, the model should be made more complex taking into account the interaction with these modes.