Electronic structure calculations for substitutional copper and monovacancies in silicon

Abstract

Two different computer program packages based on the self-consistent local-spin-density approximation- and -are employed in this study of substitutional copper Cu Si and monovacancies V Si in silicon, including the effects of their charge state. The programs differ in the types of basis sets and pseudopotentials they use, each with their own relative merits, while being similar in overall quality. This approach aims to reduce uncertainty in the results, particularly for small or subtle effects, where the risk is greatest that the conclusions are affected by artifacts specific to a particular implementation. The electronic structures of the two defects are closely related, hence they are expected to behave in a similar manner. For both defects structural distortions resulting in lower point group symmetries than T d (the highest possible) are found. This is in good agreement with the results of previous studies of V Si . Much less is known about symmetry-lowering effects for Cu Si ; however, the electronic levels of Cu Si have been measured accurately, while those for V Si are less accessible. Calculating them is a challenging task for theory. The strategy we adopt, based purely on comparing total energies of supercells in different charge states, with and without model defects, reproduces the three known levels for Cu Si reasonably well. Satisfactory results are also obtained for V Si , so far as can be judged for this more complex case.

Modeling the momentum distributions of annihilating electron-positron pairs in solids

“…We use the 216-atom supercell and the ⌫ point, begin from the structure obtained as a result from the isotropic relaxation ͑see Table II͒ and break the T d symmetry by displacing the nearest-neighbor atoms of the vacancy in order to create a symmetry-breaking relaxation with the expected D 2d symmetry. We confirm the fact pointed out by several earlier studies [42][43][44][45] that a supercell with at least 216 atoms is needed in order to obtain a convergence with respect to the supercell size.…”

Hybrid-Functional Calculations of the Copper Impurity in Silicon

“…We find a donor level (+/0) at 0.20 eV, an acceptor level (0/-) at 0. 54 These results agree with previous DFT calculations [49,52,57], except that we find that the triple acceptor charge state, Cu −3 Si , is unstable, i.e., it occurs well above the CBM. This is in contrast to early DFT calculations [49], and a previous experimental report [18].…”

“…While the experimental data for the transition levels lie in a relatively narrow range, the calculated transition levels for Cu Si are spread in a too wide energy range [49,52,54,57], as shown in center of Fig.1. For instance, the reported values for the acceptor (0/-) level of Cu Si vary in a range of 0.5 eV, which is about half of the band gap of crystalline Si.…”

“…The behavior of Cu in Si has been considered extensively by experimentalists [40][41][42][43][44] as well as by theoreticians [45][46][47][48][49][50][51][52][53][54][55][56][57]. For a long time, the Cu concentration that was detrimental to device performance was uncertain, and reliable techniques for measuring the Cu contamination level was unavailable [19].…”