Time‐instability measurements of the capacitance‐voltage (C‐V) characteristics of InSb MIS devices show that the flatband voltage shift followsVG=K(V)  log(1+t/&tgr;) and appears to be caused by tunneling of free carriers from the semiconductor surface into insulator traps. The analysis of such a mechanism emphasizes the influence of the semiconductor band‐gap width on the values ofKfor InSb substrates at 77 °K leading to about a 100 times larger instability than silicon sustrates at 300 °K for an equal value of the insulator trap density.