An alternative to the usual infinite boundary condition is obtained for free-standing quantum films in the framework of effective-mass approximation. This alternative is applied to silicon quantum film to arrive at the confinement conditions in terms of envelope functions. The confinement conditions contain surface effects as well. The present boundary condition yields the energy gap of the film that is comparable to that by ab initio calculation. The approach is also applicable to quantum films embedded by high-energy barriers.
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Kim et al. (2000) studied this question.
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