How to find energy levels in doped silicon

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SUMMARY

This discussion focuses on determining energy levels in doped silicon semiconductors, specifically the conduction band edge (E_c), valence band edge (E_v), Fermi level (E_f), and intrinsic energy level (E_i). The user references the equation E_f - E_i = kT ln(N_D/n_i) but struggles with the values of E_i and E_f. The user estimates the bandgap energy (E_g) to be 1.12 eV and calculates E_c - E_i as 0.56 eV, seeking further guidance on deriving the remaining energy levels.

PREREQUISITES
  • Understanding of semiconductor physics
  • Familiarity with energy band diagrams
  • Knowledge of doping concentrations in semiconductors
  • Proficiency in using the equation E_f - E_i = kT ln(N_D/n_i)
NEXT STEPS
  • Research the intrinsic carrier concentration (n_i) in silicon at various temperatures
  • Study the derivation and implications of the equation E_f - E_i = kT ln(N_D/n_i)
  • Learn about the effects of doping on the energy band structure of semiconductors
  • Explore methods for calculating energy levels in semiconductors using software tools like MATLAB or Python
USEFUL FOR

Students and researchers in semiconductor physics, electrical engineering, and materials science who are working on understanding energy levels in doped silicon and related semiconductor materials.

zje
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Homework Statement


This is part of a much larger problem, but I'm stuck on trying to draw an energy band diagram for doped silicon and I'm wondering if it is possible for me to find the energy levels ( E_c, E_v, E_f, and E_i ) in a doped semiconductor knowing only the concentrations? This seems really basic to me, but I'm not getting anywhere. I've tried searching places and I can't seem to find anything.


Homework Equations


I've been looking at this:

E_f - E_i = kT ln(N_D/n_i)

But I don't seem to know E_i or E_f

The Attempt at a Solution


I think that E_g = 1.12eV, so E_c - E_i = 0.56eV, but where can I go from here?


Thank you very much for your help and sorry if this post is a little off, it's my first one


P.S.
Sorry for the poor formatting on the formula, I kept running into problems with the LaTeX formatting
 
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It seems that I can get E_f - E_i rather easily and if my assumption for E_c - E_i is correct, then E_c - E_f = (E_c - E_i) - (E_f - E_i), which is what I think I'm looking for. However, I'm somewhat hesitant to believe it's that simple.

Maybe the trick is to get more sleep :-)
 

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