  We modeled the electron and hole states in Si/SiO2 quantum wells within a
basis of standing waves using the 30-band k.p theory. The hard-wall confinement
potential is assumed, and the influence of the peculiar band structure of bulk
silicon on the quantum-well sub-bands is explored. Numerous spurious solutions
in the conduction-band and valence-band energy spectra are found and are
identified to be of two types: (1) spurious states which have large
contributions of the bulk solutions with large wave-vectors (the high-k
spurious solutions) and (2) states which originate mainly from the spurious
valley outside the Brillouin zone (the extra-valley spurious solutions). An
algorithm to remove all those nonphysical solutions from the electron and hole
energy spectra is proposed. Furthermore, slow and oscillatory convergence of
the hole energy levels with the number of basis functions is found and is
explained by the peculiar band mixing and the confinement in the considered
quantum well. We discovered that assuming the hard-wall potential leads to
numerical instability of the hole states computation. Nonetheless, allowing the
envelope functions to exponentially decay in a barrier of finite height is
found to improve the accuracy of the computed hole states.
