AlxGa1-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 band-diagram strip marks this transition.
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 / Eg (nm, eV). This 2D view is a projected cross-section of the same zinc-blende lattice the 3D scene renders in full: cations sit on a square-ish projected grid and are randomly assigned Al or Ga with probability x on every reseed, anions are always As sitting at the bond mid-offsets, and each cation bonds to its four tetrahedral nearest neighbours in the true 3D structure (two of which project forward/back and are drawn shorter and dimmer here).