AlGaAs Ternary Alloy Bandgap Engineering

Alloy Composition

Al fraction x in Al_xGa_1-xAs 0.30

Temperature 300 K

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Al Ga As

Bandgap E_g(x,T)

1.42 eV

Band type

Direct (Γ)

Emission wavelength

873 nm

Lattice constant (Vegard)

5.6533 Å

E_g vs composition

How it works

Al_xGa_1-xAs is the textbook III-V ternary alloy: aluminium and gallium share the cation sublattice of a zinc-blende crystal in fraction x, while every anion site stays arsenic. Two conduction-band minima compete for the smallest gap, and each bows with composition (empirical fits, 300 K):

E_Γ(x) = 1.424 + 1.247x                    [eV]   (direct, Γ valley)
E_X(x) = 1.900 + 0.125x + 0.143x²          [eV]   (indirect, X valley)
E_g(x) = min( E_Γ(x), E_X(x) )

Below x ≈ 0.45 the Γ valley is lower and the alloy is a direct-gap semiconductor — efficient light emission, used in LEDs and laser diodes. Above that crossover the X valley wins and it becomes indirect-gap, like silicon, where emission requires a phonon and is far weaker. The 3D scene marks this transition on the band-diagram strip.

Temperature shifts the gap via the Varshni relation (shown here for the Γ valley):

E_Γ(x,T) = E_Γ(x) − αT² / (T + β)
α = 5.405×10⁻⁴ eV/K,  β = 204 K

The lattice constant follows Vegard's law — a linear interpolation between the end members, which is why AlGaAs can be grown epitaxially on GaAs substrates across the whole composition range with almost no strain (a(GaAs) = 5.6533 Å, a(AlAs) = 5.6611 Å):

a(x) = (1 − x)·a(GaAs) + x·a(AlAs)

Emission wavelength converts the gap through λ = 1239.84 / E_g (nm, eV). The 3D lattice shows a 3×3×3 zinc-blende supercell: cations are randomly assigned Al or Ga with probability x on every reseed, anions are always As, and each cation bonds to its four tetrahedral nearest neighbours.

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