The Curie temperature TC is investigated as a function of the hole concentration p in thin films of ferromagnetic semiconductor (Ga,Mn)As. The magnetic properties are probed by transport measurements and p is varied by the application of an external electric field in a field-effect transistor configuration. It is found that TC is proportional to p^{gamma}, where the exponent gamma = 0.19 pm 0.02 over a wide range of Mn compositions and channel thicknesses. The magnitude of gamma is reproduced by a p-d Zener model taking into account nonuniform hole distribution along the growth direction, determined by interface states and the applied gate electric fields.
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