Self consistent calculations in quantum well. Mixing by electron density?

Question

I'm challenging the problem of calculating energy structure of InAs/GaAs quantum well. One part of the task is to perform self consistent calculations in order to include potential that comes from carriers on the ground state. So the algorithm behaves as follows:

1. Calculating initial ground state and resolving poisson equation to obtain initial potential distribution from carriers.
2. Add this distribution to initial potential and calculate energy of ground state with new potential.
3. Check difference between old energy of ground state and the new one.
4. If small enough break, else calculate poisson equation again, and mix the old potential that comes from carriers with new one as follows: phi = mix_param * phi_old - (1-mix_param) * phi_new Where phi is potential distribution taken to calculations in iteration, phi_old is potential distribuion from previous iteration, and phi_new is calculated in iteration.

Professor who asked me to do this task, gave me additional one. He asked me to check the difference between potential mixing and electron density mixing. I have no clue. Literally I can not undestand what he means. Do you guys have any clue?

Answer 1

In your self-consistent cycle, you find a new potential and admix it to the old one with 'mix_param'.

However, you also find in each cycle a new electron density distribution. Alternatively to your approach above, you could also admix the new density distribution to the old one, and then continue the cycle.