4.2.1 Single Segment Tunneling

In MINIMOS-NT the tunneling current density is calculated between two boundaries of a segment which has been specified by the user (see the description of the user interface in Appendix D). Unlike other models, however, the tunneling current density formulae outlined in Section 3 depend on physical quantities from neighboring segments. Therefore, the concept of neighbor quantities has been introduced: First, the segment where tunneling is calculated is -- arbitrarily -- assigned a reference and an opposite boundary, see Fig. 4.2. Interface models are called which transfer the necessary quantities of the reference and opposite segment to the tunneling segment. This is done by additional equations in the system matrix. The neighbor quantities are

• the electrostatic potential,
• the electron and hole concentration,
• the conduction and valence band edge,
• the lattice temperature,
• the electron and hole temperature (for energy-transport simulation),
• the electron and hole effective density of states, and
• the dielectric permittivity (for calculation of the image force correction energy).

In the tunneling model the tunneling current density is calculated by one of the models presented above for all points along a boundary node - partner node pair. The resulting current density is added as a generation or recombination term to the continuity equations of the reference and opposite segments as described above. For neighboring metal segments, the tunneling current is directly added to the contact current. Again, this step is achieved by means of additional matrix entries.

Figure 4.2: Tunneling through a single segment. After identifying the reference and opposite boundary, neighbor quantities are handed over to the tunneling model.

A. Gehring: Simulation of Tunneling in Semiconductor Devices