Further improvements of integrated circuits depend on the continuous downscaling of MOSFET´s, well beyond the limits for which direct tunneling currents are acceptable. These leakage currents affect both the stand-by power dissipation and the formation of the inversion layer ate the semiconductor surface, i.e., the channel formation. The most promising strategy to overcome this problem is the use of high-κ insulator in substitution of or as an additional layer on the traditional silicon dioxide. The aim of this work is using a recently developed theory to describe tunneling from inversion layers for high-κ insulators or stacks and analyze the effects of tunneling current on the thermal equilibrium in these cases.