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

The 30-band k.p modeling of electron and hole states in silicon quantum wells