The influence of interface states

The ideal MOS structure as described in Chapter 2 was considered as a pure capacitive system, which means that no internal delay times were involved in the charging quantities as influenced by external electrical perturbation. At the interface between gate insulator and semiconductor, an amorphous material is in intimate contact with a crystal. This gives rise to a certain atomic disorder, which creates electron states of type a as described earlier in relation to Fig. 2.1. Such states communicate with charge carriers in the energy bands of the semiconductor as depicted in Fig. 4.1. For a system including these charge carrier traps, one has to take into account their charging and discharging processes. This gives rise to decay times and an additional capacitance component for the system admittance which is important for the electrical function of the MOS system.

Dealing with a large number of electrons and holes embedded in a “temperature bath” set up by the semiconductor crystal, the method to quantify such influence is by using reasoning from statistical thermodynamics. For this purpose, we first take a general approach in Sections 4.2–4.4 to quantify the probabilities for particles in isolated systems occupying energy states given by the potentials determining their quantization. This will lead us to formulate the dynamics of charge carrier traffic at traps in Section 4.6 and then to expressions for the admittance of MOS systems with interface states in Chapter 6. Since measurements are usually performed on sample volumes with macro-dimensions, the energy quantities obtained need to be considered as thermodynamic quantities. Heat stored by local phonons will be discussed and demonstrated to influence the interpretation of energy quantities, depending on the measurement technique used. At the end of the chapter, we will study the statistics of single traps to find out how such systems can be treated in the same thermodynamic language as trap ensembles.