Recent trends of ternary, quaternary half-Heusler thermoelectric materials and contact resistance effect on their power output efficiency

•The concept of 18, 19, and 21 valance electron count HH materials and their effect on thermal conductivity and zT.•Selection of Quaternary Half-Heusler materials based on formation energy for better thermoelectric performance.•Double Half-Heusler Materials Development by aliovalent doping approach.•Contact resistance effect on power output of thermoelectric power generator.•Prediction of power out efficiency by cumulative temperature dependence and constant property models.