Inversion criteria for the metal-insulator-semiconductor tunnel structures

Abstract

The conditions of strong surface inversion in the semiconductor surface of a metal-insulator-semiconductor (MIS) tunnel structure are studied. By employing the voltage equation which governs the potential distribution in the MIS diode and by defining a parameter θ which indicates the energy separation between the semiconductor minority-carrier quasi-Fermi level and the metal Fermi level at the insulator–semiconductor interface, the values of θ(inv) under strong surface inversion are calculated in terms of oxide thickness, metal work function, oxide and interface state charges, semiconductor doping concentration, and reverse bias voltage. There are three conditions, namely, (1) without the external injection of the minority-carrier current density Jinj (i.e., Jinj=0), (2) with it (i.e., Jinj is positive), and (3) where Jinj is negative (i.e., carrier extraction). The second condition can be attributed to the critical insulator thickness dcri below which the semiconductor surface cannot be inverted solely by applying a reverse bias voltage, hence an externally injected minority-carrier current Jinj(inv) is required to achieve strong surface inversion at certain bias and oxide thickness. It also reveals that Jinj(inv) increases with decreasing insulator layer thickness and is strongly dependent on the oxide and interface state charges. For the Al–SiO2–Si tunnel structure, the calculated value of dcri is about 30 Å, which is in good agreement with the reported experimental results of 28–35 Å.