We study by means of full quantum simulations an asymmetric double-barrier semiconductor heterostructure refrigerator combining resonant tunneling filtering and thermionic emission. By varying the quantum well thickness, we first investigate the influence of the activation energy W on the coefficient of performance (COP) and cooling power. We show that the best performances are obtained when W equals the polar optical phonon energy of the material. However we also emphasize that cooling power and COP are severely limited by tunneling current at high bias. We then propose an original structure with a tilted potential barrier to reduce this degrading effect. Quantum simulations demonstrate that cooling properties of such tilted barrier device are significantly improved in out-of-equilibrium regime, where the thermionic cooling concept offers its best efficiency.