Question about Doping and devices question 2.3

Physics Q&A
1

Hello,

Im having difficulty with the answer given by the solution model for doping and devices q2.3. It asks for the range where not all donors are ionized. So I take this range is around n_d = N_d roughly. Taking the charge balance:
n_e - n_h + n_d - n_a = N_d - N_A.
Because n_d = N_d we can say:
n_e - n_h - n_a = - N_A. However, the full answer has N_d in it. How is that possible? Also is my charge balance correct or do i need to make further assumptions?

Kind regards,

Ilia

2

The logic of the reasoning is as follows:

  1. When donors are present, the position of E_F depends on N_d.
  2. If N_d is sufficiently small (or T sufficiently large) all donors are ionized.
  3. We use that all donors are ionized as an approximation to determine E_F.
  4. The donors stop all being ionized when the approximation breaks down.

Does that help?

3

Yes I understand now! Thanks.