# Calculate Minority Carrier Concentrations given the Fermi Level

1. Oct 2, 2013

### HunterDX77M

1. The problem statement, all variables and given/known data
This question is based on a previous question in the same homework:

The Problems deal with Silicon at 300K, using band gap energy Eg = 1.12 eV, electron density of states mass 0.327, hole mass 0.39, electron mobility 0.15 m2/Vs, hole mobility 0.05 m2/Vs and relative permittivity 11.8.

1) Consider a pn junction in Si at 300K (other parameters given), with doping NA = 1021/m3 and ND = 1023/m3. Assume all impurities are ionized. On this basis find the Fermi level on each side. From this find the band bending VB and make a sketch of the pn junction.

This problem has been solved and its thread is here: https://www.physicsforums.com/showthread.php?t=713644

5) Following your results for the Fermi Levels in Problem 1
a) Find the minority carrier concentrations (holes on the N-side, electrons on the P-side).
b) Repeat the calculation for the minority carrier concentrations using the mass action law and the intrinsic concentration 5.85E15/m3

2. Relevant equations
I found this equation while searching online relating minority and majority carriers
$n^{2}_{i} = n_p N_A = p_n N_D$

Where np is the minority concentration of electrons and pn is that of holes. But this leaves me with two variables and one equation.

3. The attempt at a solution

Based on the first problem, I have numbers for the Fermi level (EF) on both sides. If you are curious they are 0.974 eV (N-side) and 0.226 eV (P-side). However, I don't know of any way to relate the Fermi level with ni or the minority concentrations in the above equation.

As far as I know
$N_e \times N_h = N^2_i \neq n^2_i$

Where Ne and Nh are the majority concentrations (known).

Does anyone know a relation I can use to solve for these minority concentrations?