The errors arising in ab initio density functional theory studies of semiconductor point defects using the supercell approximation are analyzed. It is demonstrated that (a) the leading finite size errors are inverse linear and inverse cubic in the supercell size and (b) finite size scaling over a series of supercells gives reliable isolated charged defect formation energies to around +-0.05 eV. The scaled results are used to test three correction methods. The Makov-Payne method is insufficient, but combined with the scaling parameters yields an ab initio dielectric constant of 11.6+-4.1 for InP. Gamma point corrections for defect level dispersion are completely incorrect, even for shallow levels, but realigning the total potential in real-space between defect and bulk cells actually corrects the electrostatic defect-defect interaction errors as well. Isolated defect energies to +-0.1 eV are then obtained using a 64 atom supercell, though this does not improve for larger cells. Finally, finite size scaling of known dopant levels shows how to treat the band gap problem: in < or = 200 atom supercells with no corrections, continuing to consider levels into the theoretical conductin band (extended gap) comes closest to experiment. However, for larger cells or when supercell approximation errors are removed, a scissors scheme stretching the theoretical band gap onto the experimental one is in fact correct.
The basic properties of point defects, such as local geometries, positions of charge-transfer levels, and formation energies, have been calculated using density-functional theory, both in the bulk and on the (110) surface of InP, InAs, and InSb. Based on these results we discuss the electronic properties of bulk and surface defects, defect segregation, and compensation. In comparing the relative stability of the surface and bulk defects, it is found that the native defects generally have higher formation energies in the bulk. From this it can be concluded that at equilibrium there is a considerably larger fraction of defects at the surface and under nonequilibrium conditions defects are expected to segregate to the surface, given sufficient time. In most cases the charge state of a defect changes upon segregation, altering the charge-carrier concentrations. The photothresholds are also calculated for the three semiconductors and are found to be in good agreement with experimental data.
The diffusion mechanism of Zn in GaP and InP has been investigated using first-principles computational methods. It is found that the kickout mechanism is the favored diffusion process under all doping conditions for InP, and under all except n-type conditions for GaP. In n-type GaP the dissociative mechanism is probable. In both p-type GaP and InP, the diffusing species is found to be Zn. The activation energy for the kickout process is 2.49 eV in GaP and 1.60 eV in InP, and therefore unintentional diffusion of Zn should be a larger concern in InP than in GaP. The dependence of the activation energy both on the doping conditions of the material and on the stoichiometry is explained, and found to be in qualitative agreement with the experimentally observed dependencies. The calculated activation energies agree reasonably with experimental data, assuming that the region from which Zn diffuses is p type. Explanations are also found as to why Zn tends to accumulate at pn junctions in InP and to why a relatively low fraction of Zn is found on substitutional sites in InP.
We have theoretically studied the possibility to control the equilibrium solubility of dopants in semiconductor alloys, by strategic tuning of the alloy concentration. From the modeled cases of C-0 in SixGe1-x, Zn- and Cd- in GaxIn1-xP it is seen that under certain conditions the dopant solubility can be orders of magnitude higher in an alloy or multilayer than in either of the elements of the alloy. This is found to be due to the solubility's strong dependence on the lattice constant for size mismatched dopants. The equilibrium doping concentration in alloys or multilayers could therefore be increased significantly. More specifically, Zn- in a GaxIn1-xP multilayer is found to have a maximum solubility for x=0.9, which is 5 orders of magnitude larger than that of pure InP.