3.8.2.3 Steady-State Current

The total steady-state tunneling current is derived as the sum of the trap-assisted tunneling current (3.122) and the direct tunneling current computed from the TSU-ESAKI formula (3.13)

$$J = \ensuremath{J_\mathrm{TAT}}+ \ensuremath{J_\mathrm{Tsu-Esaki}}\ .$$ (3.149)

Fig. 3.20 shows the dependence of the gate current density on the model parameters ${\mathcal{E}}_\mathrm{T}$ (trap energy level) and $S\hbar\omega$ for a fixed phonon energy of $\hbar \omega$=10meV in an MOS capacitor. For a low trap energy level traps are located near the conduction band edge in the dielectric, and direct tunneling prevails. With increasing trap energy level, the trap-assisted component becomes stronger and exceeds the direct tunneling current for low bias. The current density shows a peak at low bias which is due to the alignment of the trap energy level with the cathode conduction band edge. The HUANG-RHYS factor has only a minor influence on the results, as shown in the right part of Fig. 3.20.

Figure 3.20: Dependence of the tunneling current on the trap energy level (left) and on the HUANG-RHYS factor for a fixed phonon energy of 10 meV (right).

A. Gehring: Simulation of Tunneling in Semiconductor Devices