typo fixes

src/13_semiconductors.md

@@ -141,8 +141,8 @@ fig, ax = pyplot.subplots()
 n_F = 1/(np.exp(2*(E - E_F)) + 1)
 g_e = m_e * sqrt_plus(E - E_C)
 g_h = m_h * sqrt_plus(E_V - E)
-ax.plot(E, g_h, label="$g_e$")
-ax.plot(E, g_e, label="$g_h$")
+ax.plot(E, g_e, label="$g_e$")
+ax.plot(E, g_h, label="$g_h$")
 ax.plot(E, 10 * g_h * (1-n_F), label="$n_h$")
 ax.plot(E, 10 * g_e * n_F, label="$n_e$")
 ax.plot(E, n_F, label="$n_F$", linestyle='dashed')
@@ -238,7 +238,9 @@ $n_i$ is the **intrinsic carrier concentration**, and for a pristine semiconduct
 1. Recall from the [Drude model](/3_drude_model/) that electrons give rise to a negative Hall coefficient. Explain why the Hall coefficient is positive if holes are the charge carriers in a material.
 2. What would be the Hall coefficient if both carriers with equal concentration are present? Assume that both electrons and holes can move freely and have the same scattering time.
 
-    Recall that the dispersion relation of a [1D single orbital tight binding chain](/7_tight_binding/) is given by $$E(k)=\varepsilon + 2t \cos(ka),$$ where $a$ is the lattice constant and $\varepsilon$ and $t$ are tight binding parameters.
+    Recall that the dispersion relation of a [1D single orbital tight binding chain](/7_tight_binding/) is given by
+    $$E(k)=\varepsilon + 2t \cos(ka),$$
+    where $a$ is the lattice constant and $\varepsilon$ and $t$ are tight binding parameters.
 
 3. What is the group velocity and effective mass of this band for holes compared to that of electrons?
 4. Give an integral expression of the hole concentration in this band given the chemical potential $\mu$ and temperature $T$.