The thermoelectric figure of meritz=&agr;2/&rgr;&kgr; is calculated for an extrinsic semiconductor with mixed acoustic‐mode lattice scattering and ionized‐impurity scattering. The result is compared to the value for pure acoustic‐mode scattering. As the amount of ionized‐impurity scattering is increased, the figure of merit increases by less than 10% and then falls slowly.