Appendix C

Selfconsistent Coupling of the Trap Equations with the Basic Semiconductor Equations

The procedure for the selfconsistent solution of the basic semiconductor equations with the trap-dynamics equations is presented for the time-dependent Gummel algorithm defined by 3.23 - 3.25 in Section 3.2.2. The index denotes the known solution at the previous time step and denotes the solution at the actual time step.

1. Solve steady-state problem including traps. Use the solution as an initial condition for the step 2.
2. Solve 3.20 - 3.22 including traps. Use the solution , , as an initial condition for the step 3.
3. Trap-dynamics equations;
   Input: , ,
   Output: , and its derivative with respect to .
4. Continuity-equation for the majorities (holes);
   Input: , , and its derivative.
   Output:
5. Trap-dynamics equations;
   Input: , ,
   Output: , and its derivative with respect to .
6. Continuity-equation for the minorities (electrons);
   Input: , , and its derivative.
   Output:
7. Trap-dynamics equations;
   Input: , ,
   Output: , and its derivative with respect to
8. Poisson's equation;
   Input: , , , and its derivative.
   Output:
9. Repeat from 3 to 8 until the given accuracy is achieved.
10. Terminal-current calculation for time step .
11. Choose new time step; repeat from 2 to 10.

At the beginning of every new time step we use the Mock algorithm (step 2. above) which consists of expressions 3.20 - 3.22 given in Section 3.2.2. Trap-dynamics equations are coupled with this system in an analogous manner as done for the Gummel algorithm.