Electronic stacking-fault states in silicon

Abstract

The nonorthogonal-tight-binding (NTB) method is applied to calculate the electronic-defect states in silicon which are produced by intrinsic, extrinsic, and twin stacking faults (ISF, ESF, and TSF, respectively) along a $〈111〉$ axis. This NTB scheme, which utilizes a supercell geometry, includes $s-p$ orbitals at each atomic site and contains two-center energy-overlap parameters spanning three shells of neighbors. The NTB parameters are determined by an accurate fit (rms error≅0.1 eV) to the bulk silicon band structure of Chelikowsky and Cohen. These NTB results are also applied to calculate the stacking-fault energies $\gamma$; neglecting relaxation effects, this calculation yields a value for ${\gamma }_{\mathrm{ISF}}$ which is about twice the observed value and the relative values ${\gamma }_{\mathrm{ISF}}\approx {\gamma }_{\mathrm{ESF}}\approx {2\gamma }_{\mathrm{TSF}}$. It is shown that relaxation of the perfect-crystal interlayer spacings near the fault planes reduce the corresponding $\gamma$'s by about 50%, thereby bringing the calculated and observed values for ${\gamma }_{\mathrm{ISF}}$ into close agreement. The defect states produced by these three types of stacking faults are all qualitatively similar. They include states which are located about 0.1 eV above the valence-band maximum. However, contrary to a recent experimental study on an ESF, no fault states are found with energies below the conduction-band mimimum.