@@ -229,6 +229,13 @@ A $pn$-junction has a **depletion layer** in its middle with the potential in a
### Exercise 1: Crossover between extrinsic and intrinsic regimes
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 $n_h$ without additional assumptions.
3. Verify that your solution reproduces intrinsic regime when $|N_D - N_A| ≪ n_i$ and the extrinsic regime when $|N_D - N_A| ≫ n_i$
