diff --git a/src/14_doping_and_devices_solutions.md b/src/14_doping_and_devices_solutions.md index 578d3af98171c14b0bec3025325b1cc754c67950..48851fc1e75547df501ea6edac07f3dbe3ff79a4 100644 --- a/src/14_doping_and_devices_solutions.md +++ b/src/14_doping_and_devices_solutions.md @@ -19,7 +19,7 @@ $$ n_e - n_h + n_D - n_A = N_D - N_A $$ Since $E_G \gg k_B T$, we can only use the law of mass action. But the question offers us another piece of information - we are around $|N_D-N_A| \approx n_i$. That means that we are near the transition between extrinsic and intrinsic regimes. -However, we also know that dopants energies are quite small such that $E_C-E_A \ll E_G$ and $E_A-E_V \ll E_G$. +However, we also know that dopants energies are quite small such that $E_C-E_D \ll E_G$ and $E_A-E_V \ll E_G$. That means that we expect $n_i \ll n_D$ and $n_i \ll n_A$ (since both $n_i$ and dopant ionazition depends exponentially of the corresponding energy differences). Therefore, we can confidently say that $N_D \gg n_D$ and $N_A \gg n_A$ so we esentially recover the dopant ionization condition. Thus, neglecting $n_D$ and $n_A$ such that they are both 0, the solutions to the charge balance are: