E6 Semiconductors Compounds and Alloys (III-V)

Topic

The composition of this III-V semiconductor alloy—specifically the ratio of its constituent Group III and Group V elements—determines the alloy's lattice parameter in accordance with Vegard's law. This law linearly interpolates the resulting lattice parameter based on the exact proportions of the constituent binary compounds at the composition's extremes. As the alloy composition shifts closer to one of these extreme binary compounds, the lattice parameter—governed by Vegard's law—correspondingly moves closer to the lattice parameter characteristic of that specific extreme binary compound.

This same alloy composition also determines the semiconductor alloy's bandgap; however, unlike the lattice parameter's linear interpolation, the bandgap follows a markedly non-linear "bowing" relationship. Across most of the composition range, the alloy's bandgap deviates from the simple linear interpolation between the bandgaps of the extreme binary compounds. A bowing parameter specific to each pair of extreme binary compounds quantifies the extent of this deviation at any intermediate composition. A higher bowing parameter for a given pair of extreme binary compounds causes the bandgap at intermediate compositions to deviate even further from the linear interpolation between those two compounds. Consequently, this model—characterized by its specific lattice parameter and bandgap—allows the alloy composition itself to facilitate a transition between direct and indirect bandgap regimes: as the alloy composition varies, the conduction band minimum of the semiconductor alloy can shift within momentum space from the point coinciding with the valence band maximum to a different point in that same space; it is this shift in the conduction band minimum that drives the crossover between the two bandgap regimes. The fact that this alloy composition—defined by its tunable lattice parameter and bandgap—determines both parameters for each individual layer makes it the fundamental basis for the design of the heterostructures described in greater detail by two other models in this set (semiconductor layer upon semiconductor layer, each with a deliberately selected alloy composition).

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