Commit 09f3cec5 authored by Isidora Araya's avatar Isidora Araya
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Update 13_semiconductors_solutions.md

parent 65d75e87
......@@ -41,13 +41,12 @@ Write the [Hall Effect Equations](/3_drude_model/#hall-effect) for holes and con
### Subquestion 2
In general,
$$\rho_{xy} = \frac{B(B^2R_e R_h(R_e + R_h)+R_h r_e^2 + R_e r_h^2}{B^2(R_e+R_h)^2+(r_e+r_h)^2}$$
where $r=n\mu$ and $R=q/n$. This result can be obtained by using $1/\rho = 1/\rho_e + 1/\rho_h$.
Analyse by considering equal concentrations.
where $r=n\mu$ and $R=q/n$ for both electrons and holes. This result can be obtained by using $1/\rho = 1/\rho_e + 1/\rho_h$.
When considering equal concentrations, $\rho_{xy}=0$.
### Subquestion 3
Holes will have an effective mass and group velocity with the same sign as electrons. For [electrons](/7_tight_binding/#electrons_1)
a taylor expansion around $k=0$ is done. For holes, a taylor expansion around $k=\pi/2$ is needed, and positive charge to take into account.
The effective masses will be of opposite sign. The group velocities will be the same.
### Subquestion 4
......@@ -102,7 +101,7 @@ For holes, do a taylor expansion around $k=0$ (max) of $E_{vb} = 2 t_{vb} [\cos(
### Subquestion 4
$$n = \int_{E_{cb}}^{E_{cb}+4t_{cb}} f(\varepsilon)g_c(\varepsilon)d\varepsilon$$
$$p = \int_{-4t_{vb}^{0} (1-f(\varepsilon))g_h(\varepsilon)d\varepsilon$$
$$p = \int_{-4t_{vb}}^{0} (1-f(\varepsilon))g_h(\varepsilon)d\varepsilon$$
### Subquestion 5
For an intrinsic semiconductor the number of electrons excited into the conduction band must be equal
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