Commit 88135aab authored by Isidora Araya's avatar Isidora Araya
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Update 14_doping_and_devices_solutions.md

parent b5504c08
......@@ -18,7 +18,7 @@ $$ n_e - n_h + n_D - n_A = N_D - N_A $$
$$ n_{e} = \frac{1}{2}(\sqrt{D^2+4n_i^2}+D)$$
$$ n_{h} = \frac{1}{2}(\sqrt{D^2+4n_i^2}-D)$$
where $n_i=n_{e,intrinsic}=n_{h,intrinsic}$.
where $D = N_D - N_A$ and $n_i=n_{e,intrinsic}=n_{h,intrinsic}$.
### Subquestion 3
......@@ -37,21 +37,19 @@ If all the dopants are ionized, the Fermi level gets shifted up towards the cond
This result can be obtained when using results in Exercise 1 - Subquestion 2 and the following:
$$ n_D \approx 0$$
$$ n_A \approx 0$$
$$ n_e - n_h = N_D - N_A $$
### Subquestion 2
Now,
$$ n_D^{\ast} = N_D (1-\frac{1}{e^({E_D-E_F})/k_BT+1})$$
$$ n_A^{\ast} = N_A (1-\frac{1}{e^({E_F-E_A})/k_BT+1})$$
$\ast$ indicates non-ionized concentrations.
### Subquestion 3
??? hint "how?"
Use Germianium Fermi Energy at room temperature and solve E_F
via using the n_e solution in Exercise 1 and by applying the definition of n_e.
Check [key algorithm of describing the state of a semiconductor](13_semiconductors/#part-1-pristine-semiconductor)
Check [key algorithm of describing the state of a semiconductor](/13_semiconductors/#part-1-pristine-semiconductor)
## Exercise 3: Performance of a diode
......
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