High entropy alloy (HEA) thin films are potential candidates to act as diffusion barrier between Cu and Si in microelectronics. To evaluate the suitability of refractory HEAs, six different HEA thin films based on the MoNbTaW system and alloyed with Ti, V, Cr, Mn, Zr or Hf have been deposited by high power impulse magnetron sputtering with a thickness of 20 nm on Si substrates. The bi-layer architecture was completed by a 150 nm thick top-layer of Cu. The microstructure of the bi-layers before and after annealing in vacuum up to 800 °C was investigated by X-ray diffraction to observe possible phase changes or formations. In addition, resistance measurements and confocal laser scanning microscopy were employed to check for potential barrier failure. The lowest onset temperature for barrier failure of 600 °C was found for MoNbTaWZr, whereas the highest of 700 °C was observed for CrMoNbTaW. The obtained results for the failure temperature are discussed in terms of microstructure, strain and cohesive energy of the HEA films as well as the enthalpy of mixing between the elements in the HEA and Cu. A direct correlation between the mixing enthalpy of the fifth alloying element with Cu and the barrier failure temperature was observed.