Numerical analysis of the absorption and the refractive index change in arbitrary semiconductor quantum-well structures

A numerical method for the analysis of the absorption spectrum and the refractive index change due to an external electric field in quantum-well structures is presented. The finite-element method and the variational method are used to obtain the subband and the exciton energies in a quantum-well structure, respectively. The absorption spectrum due to the band-to-band and the excitonic transitions is then calculated, and the refractive index change is obtained using the Kramers-Kronig relations. This method is applicable to quantum-well structures with arbitrary potential profiles made of arbitrary semiconductors, because it is based on the finite-element method in which the general boundary condition for the heterointerface is employed. The validity of the method is confirmed by comparing the computed results with the measured ones.<
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