Appendix C: Selfconsistent Coupling of the Trap Equations with the Basic Semiconductor Equations



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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.



Martin Stiftinger
Sat Oct 15 22:05:10 MET 1994