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 $s\ensuremath{-}p$ 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\ensuremath{\cong}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 $\ensuremath{\gamma}$; neglecting relaxation effects, this calculation yields a value for ${\ensuremath{\gamma}}_{\mathrm{ISF}}$ which is about twice the observed value and the relative values ${\ensuremath{\gamma}}_{\mathrm{ISF}}\ensuremath{\approx}{\ensuremath{\gamma}}_{\mathrm{ESF}}\ensuremath{\approx}{2\ensuremath{\gamma}}_{\mathrm{TSF}}$. It is shown that relaxation of the perfect-crystal interlayer spacings near the fault planes reduce the corresponding $\ensuremath{\gamma}$'s by about 50%, thereby bringing the calculated and observed values for ${\ensuremath{\gamma}}_{\mathrm{ISF}}$ 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.