We report ballistic transport measurements in a two-dimensional electron system confined to an AlAs quantum well and patterned with square antidot lattices of period $a = $0.6, 0.8, 1.0 and 1.5 $mu$m. In this system two in-plane conduction-band valleys with elliptical Fermi contours are occupied. The low-field magneto-resistance traces exhibit peaks corresponding to the commensurability of the cyclotron orbits and the antidot lattice. From the dependence of the position of the peak associated with the smallest commensurate orbit on electron density and $a$, we deduce the ratio of the longitudinal and transverse effective masses $m_l/m_t=5.2pm 0.4$, a fundamental parameter for the anisotropic conduction bands in AlAs.
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