Bound and quasibound state calculations for biased/unbiased semiconductor quantum heterostructures

A complex transcendental equation valid for a wide range of electron energies for semiconductor quantum heterostructures under unbiased or biased conditions is derived. Its complex roots have as real parts the structure eigenenergy levels, and their imaginary parts are directly related to the lifetime of the corresponding eigenenergies. A numerical method is presented that is capable of extracting all these complex eigenenergies. The method is based on the argument principle theorem from complex number theory. Therefore, all the energy levels and lifetimes of bound and quasibound states can be determined. Energy levels and lifetimes can also be calculated in the presence of scattering events when these are modeled with an energy broadening imaginary potential. Extensive comparisons between this numerical method and other currently used techniques are included, proving the generality and the accuracy of this new method