No abstract

We have investigated the formation energies and electronic structure of native defects in ZnO by a first-principles plane-wave pseudopotential method. When p-type conditions are assumed, the formation energies of donor-type defects can be quite low. The effect of self-compensation by the donor-type defects should be significant in p-type doping. Under n-type conditions, the oxygen vacancy exhibits the lowest formation energy among the donor-type defects. The electronic structure, however, implies that only the zinc interstitial or the zinc antisite can explain the n-type conductivity of undoped ZnO.

The kinetic electron trapping process in a shallow defect state and its subsequent thermal- or photo-stimulated promotion to a conduction band, followed by recombination in another defect, was described by Adirovitch using coupled rate differential equations. The solution for these equations has been frequently computed using the Runge-Kutta method. In this research, we empirically demonstrated that using the Runge-Kutta Fourth Order method may lead to incorrect and ramified results if the numbers of steps to achieve the solutions is not “large enough”. Taking into account these results, we conducted numerical analysis and experiments to develop an algorithm that determines the smallest non-critical number of steps in an automatic way to optimize the application of the Runge-Kutta Fourth Order method. This algorithm was implemented and tested in a variety of situations and the results have shown that our solution is robust in dealing with different equations and parameters