Abstract
We solve the transport equations of the electrons and phonons to understand the thermoelectric behaviour of the technologically important half-Heusler alloys MNiSn (M: Ti, Zr, Hf). Doping is simulated within the rigid band approximation. We clarify the origin of the electron dominated thermoelectric response and determine the carrier concentrations with maximal figures of merit. The phonon mean free path is studied to calculate the grain size below which grain refinement methods can enforce ballistic heat conduction to enhance the figure of merit.