Jun Huang

Finite Difference Schemes for k.p Models: A Comparative Study

Finite Difference Schemes for k.p Models: A Comparative Study Jun Z. Huang, KuangChung Wang, Michael Povolotskyi, William R. Frensley, and Gerhard Klimeck

Objective:

  • To have a reliable k.p method in N5.

Problem:

  • The k.p method has spurious solutions
  • Some finite difference schemes are numerically stable while others are not.

Approach:

  • Adjust the parameters with Foreman's strategy
  • Comparative study of four cases:
    1. centered difference for symmetrized (SYM) Hamiltonian
    2. centered difference for Burt-Foreman (BF) Hamiltonian
    3. one-sided differences for SYM Hamiltonian, and
    4. one-sided differences for BF Hamiltonian

Results:

  • (1) and (2) are not stable
  • (3) and (4) are stable
  • (3) has wave function slope discontinuities at material interfaces
  • (4) has artificial spatial spin polarization
  • (3)(4) are tricky to implement
  • Published in IWCE 2015



 
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