Simulated Annealing for Ground State Energy of Ionized Donor BoundExcitons in Semiconductors

We present a global optimizationmethod, called the simulated annealing, to the ground stateenergies of excitons. The proposed method does not require thepartial derivatives with respect to each variational parameteror solving an eigenequation, so the present method is simplerin software programming than the variational method, and overcomesthe major difficulties. The ground state energies of ionized-donor-boundexcitons (D⁺, X) have been calculated variationally for all valuesof effective electron-to-hole mass ratio σ. They are comparedwith those obtained by the variational method. The results obtaineddemonstrate that the proposed method is simple, accurate, and hasmore advantages than the traditional methods in calculation.