A method of growing an AlGaN semiconductor layer structure by Molecular Beam Epitaxy comprises supplying ammonia, gallium and aluminum to a growth chamber thereby to grow a first (Al,Ga)N layer by MBE over a substrate disposed in the growth chamber. The first (Al,Ga)N layer has a non-zero aluminum mole fraction. Ammonia is supplied at a beam equivalent pressure of at least 1 10-4 mbar, gallium is supplied at a beam equivalent pressure of at least 1 10-8 mbar and aluminum is supplied at a beam equivalent pressure of at least 1 10-8 mbar during the growth step. Once the first (Al,Ga)N layer has been grown, varying the supply rate of gallium and/or aluminum enables a second (Al,Ga)N layer, having a different aluminum mole fraction from the first (Al,Ga)N layer to be grown by MBE over the first (Al,Ga)N layer. This process may be repeated to grown an (Al,Ga)N multilayer structure.
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