diff --git a/src/14_doping_and_devices.md b/src/14_doping_and_devices.md index 502513198e01e0e5a38909f14d7165b381906870..54871e9c5bbc2e1669e707010548441fde0eb066 100644 --- a/src/14_doping_and_devices.md +++ b/src/14_doping_and_devices.md @@ -74,7 +74,7 @@ draw_classic_axes(ax, xlabeloffset=.2) ``` All donor/acceptor states at the same energy: -$$g_A(E) = N_A \delta(E-E_A),\quad g_D(E) = N_D \delta(E- (E_G - E_D))$$ +$$g_A(E) = N_A \delta(E-E_A),\quad g_D(E) = N_D \delta(E- E_D)$$ How large can $N_D/N_A$ be? The distance between donors should be such that the states don't overlap, so the distance must be much larger than 4 nm. Therefore **maximal** concentration of donors before donor band merges with conduction band is $N_D \lesssim (1Ã…/4\textrm{nm})^3 \sim 10^{-5}\ll N_C$. @@ -86,7 +86,7 @@ $$n_e - n_h + n_D - n_A = N_D - N_A$$ We already know $n_e$ and $n_h$. -$$n_D = N_D \frac{1}{e^{-(E_D-E_F)/kT} + 1}, n_A = N_A \frac{1}{e^{-(E_A+E_F)/kT} + 1}$$ +$$n_D = N_D \frac{1}{e^{(E_D-E_F)/kT} + 1}, n_A = N_A \frac{1}{e^{-(E_A+E_F)/kT} + 1}$$ Simplification: