- #1

HunterDX77M

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## Homework Statement

This question is based on a previous question in the same homework:

The Problems deal with Silicon at 300K, using band gap energy E

_{g}= 1.12 eV, electron density of states mass 0.327, hole mass 0.39, electron mobility 0.15 m

^{2}/Vs, hole mobility 0.05 m

^{2}/Vs and relative permittivity 11.8.

1) Consider a pn junction in Si at 300K (other parameters given), with doping N

_{A}= 10

^{21}/m

^{3}and N

_{D}= 10

^{23}/m

^{3}. Assume all impurities are ionized. On this basis find the Fermi level on each side. From this find the band bending V

_{B}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/m

^{3}

## Homework Equations

I found this equation while searching online relating minority and majority carriers

[itex]n^{2}_{i} = n_p N_A = p_n N_D[/itex]

Where n

_{p}is the minority concentration of electrons and p

_{n}is that of holes. But this leaves me with two variables and one equation.

## 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 n

_{i}or the minority concentrations in the above equation.

As far as I know

[itex]N_e \times N_h = N^2_i \neq n^2_i [/itex]

Where N

_{e}and N

_{h}are the majority concentrations (known).

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