A simple model for the index of refraction of GaAs–AlAs superlattices and heterostructure layers: Contributions of the states around Γ

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Abstract
We present a simple theory of the dielectric function in superlattices. The calculation is performed separately for different symmetry points of the band structure. We assume that among the contributing states only the Γ states are influenced substantially by size quantization and the electronic states at Γ are calculated by using a simplified k⋅p method. New features of the dielectric constant of superlattices are a fine structure due to zone folding (subbands) and a small anisotropy due to the lower symmetry. Except for these finer details, the index of refraction of a superlattice is well approximated by the corresponding constant for an alloy Al x̄Ga1−x̄As where x̄ is the averaged Al mole fraction of the superlattice.