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Investigating Bandgap energies

As a practical matter, GaAs and GaP are soluble in all proportions, and the band gap of the alloy increases nearly linearly with the molar additions of GaP. The band gap of pure GaP is 2.25 eV. Calculate the molar fraction of GaP required to produce the 1.78 eV band gap.

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The way I see it

Bandgap energy {E(b)} is linearly proportional to Molar concentration of GaP (M) in the GaAs,GaP alloy. Let us call this constant of proportionality {p}

Then we can ...

Solution Summary

Using data on the bandgap energies of pure GaAs and given information on linear relationship of bandgap energy with addition of GaP molar concentration the estimated molar concentration of GaP required to bring the concatentated bandgap of mixed GaAs doped with GaP to 1.78 eV is deduced