4.2.3 Trap-Assisted Tunneling

For the calculation of trap-assisted tunneling, several additional quantities are necessary. These are

• the trap charge state,
• the trap concentration,
• the trap energy level, and
• the trap occupancy.

The trap charge state is constant -- either positive, neutral, or negative. The trap concentration and the trap energy level are also constant and can be specified by the user (see Appendix D). These quantities are initialized at startup and do not change.

The trap occupancy $\ensuremath{f_\mathrm{T}}$ is also initialized at startup. In each iteration the charge of occupied traps is included in the right hand side of the POISSON equation according to

$$\ensuremath{{\mathbf{\nabla}}}(\kappa \ensuremath{{\mathbf{\nabla... ... \ensuremath{N_\mathrm{T}}\ensuremath{f_\mathrm{T}}\ensuremath{Q_\mathrm{T}}\ ,$$ (4.5)

where $\ensuremath{N_\mathrm{T}}$ is the trap concentration, $f_\mathrm{T}$ the trap occupancy, and $Q_\mathrm{T}$ the trap charge state. If a trap-assisted tunneling model is evaluated in a transient simulation, the values of the trap occupancy change according to (3.150). For electron tunneling occupied neutral or positive traps become negative or neutral. For hole tunneling occupied neutral or negative traps become positive or neutral. This mechanism is shown in Fig. 4.4. However, a trap is only allowed to capture one carrier, so a negative trap cannot become positive and vice versa. For stacked segments, the trap occupancy and the trap charge state are transferred back to their segments after the evaluation of the tunneling model.

Figure 4.4: Positive, neutral, and negative trap charge states. Positive traps cannot become negative and vice versa.

A flow chart of the tunneling model in MINIMOS-NT is shown in Fig. 4.5. The functionality has been implemented in several steps. First, the tunneling segments, stacks, boundaries, and master segments are identified. Then, the neighbor quantities are transferred to the master segment, which is done by special interface models.

After this step the tunneling model is evaluated for all boundary node - partner node pairs. Interface routines transfer the calculated tunnel current density to the continuity equation of the neighboring segments, or directly add it to the contact current if the neighboring segment is a metal.

Figure 4.5: Flowchart of the tunneling model in MINIMOS-NT.

A. Gehring: Simulation of Tunneling in Semiconductor Devices