@@ -627,13 +627,12 @@ In the lecture we have identified the intrinsic and extrinsic regimes.
Let us now work out what happens when the semiconductor is at the border between these two regimes, and the dopant concentration $|N_D - N_A|$ is comparable to the intrinsic one $n_i$.
1. Write down the law of mass action and the charge balance condition for a doped semiconductor.
2. Solve this system of equations for $n_e$ and $n_h$ with the additional assumption of full dopant ionization.
2. Solve this system of equations for $n_e$ and $n_h$ only assuming $E_G \gg k_B T$.
3. Verify that your solution reproduces intrinsic regime when $|N_D - N_A| ≪ n_i$ and the extrinsic regime when $|N_D - N_A| ≫ n_i$
### Exercise 2: Donor ionization
Previously we have assumed that all dopants are ionized.
Let us examine when this is a good assumption.
Let us examine when the full donor ionization is a good assumption.
For that we consider a doped semiconductor in the extrinsic regime.
1. Assume that all dopants are ionized, determine the position of the Fermi level.
