Energy band diagram

An MOS system involves a Schottky barrier between a metal and an insulator, and a heterojunction between the insulator and a semiconductor. The energy band diagram of such a combination is shown in Fig. 2.1. One important feature of the structure is the voltage partition between these different components. When a voltage is applied, part of it falls across the insulator and part is taken up in the semiconductor depending on differences in dielectric constants, oxide thickness and charge distributions in the oxide and in the semiconductor. As mentioned in Chapter 1, this voltage division is important for the function of a MOSFET, where the structure in Fig. 2.1 represents the gate. The requirement is that the applied gate voltage, VG, should be transferred as effectively as possible to the semiconductor in order to create efficient band bending for opening a conducting channel in the silicon.

The imperfections of the insulator and of both interfaces give rise to charge carrier traps that become sources of charge and influence the potential distribution. The energy distance, ΦB, between the metal Fermi level, μM in Fig. 2.1, and the conduction band of the insulator depends on the difference in work functions between the two materials, but also on dipole charges created at that interface, as will be further discussed in Chapters 3 and 12. Connected with the insulator and the insulator/semiconductor interface, the origins of charge carrier traps are traditionally divided into four different classes, a–d, as shown in the figure (Deal, 1980). Class a are energy states occurring at energy levels within the interval defined by the energy bandgap of the semiconductor. Due to their physical position close to the semiconductor, they interact with free charge carriers in the semiconductor energy bands. For silicon at room temperature, they adopt thermal equilibrium with the semiconductor with decay times in the range of nano- to milliseconds depending on their positions in the bandgap. They are found to have energy levels tightly distributed across the whole bandgap and are treated as quasi-continuous distributions, Dit, when modeling the interface. Furthermore, they appear as donors as well as acceptors with charge states that are positive or neutral, respectively, for energies above the semiconductor Fermi level, μ, and neutral or negative, respectively, for energies below μ.