use inline code execution

docs/lecture_7.md → src/lecture_7.md

+```python
+from matplotlib import pyplot
+
+import numpy as np
+from scipy.optimize import curve_fit
+from scipy.integrate import quad
+
+from common import draw_classic_axes, configure_plotting
+
+configure_plotting()
+
+def sqrt_plus(x):
+    return np.sqrt(x * (x >= 0))
+
+# Band structure parameters.
+E_V, E_C, E_F = -1.2, 1.8, .4
+E_D, E_A = E_C - .7, E_V + .5
+m_h, m_e = 1, .5
+```
+
 # Semiconductor physics
 
 ## Review of band structure properties
@@ -102,7 +122,27 @@ Observe that because we are describing particles in the valence band as holes, $
 
 ### Part 1: pristine semiconductor
 
-![](figures/intrinsic_DOS.svg)
+```python
+E = np.linspace(-3, 3, 1000)
+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, 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')
+ax.set_ylim(top=1.5)
+
+ax.set_xlabel('$E$')
+ax.set_ylabel('$g$')
+ax.set_xticks([E_V, E_C, E_F])
+ax.set_xticklabels(['$E_V$', '$E_C$', '$E_F$'])
+ax.legend()
+draw_classic_axes(ax, xlabeloffset=.2)
+```
 
 Electrons
 $$ E = E_G + {p^2}/{2m_e}$$
@@ -198,7 +238,26 @@ Likewise an acceptor adds an extra state at $E_A$ (close to the top of the valen
 
 ### Density of states with donors and acceptors
 
-![](figures/doping.svg)
+```python
+E = np.linspace(-3, 3, 1000)
+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="$g_h$")
+
+sigma = 0.01
+g_D = np.exp(-(E_D - E)**2 / sigma**2)
+g_A = .7 * np.exp(-(E_A - E)**2 / sigma**2)
+ax.plot(E, g_D, label='$g_D$')
+ax.plot(E, g_A, label='$g_A$')
+ax.legend()
+ax.set_xticks([E_V, E_C, E_A, E_D])
+ax.set_xticklabels(['$E_V$', '$E_C$', '$E_A$', '$E_D$'])
+draw_classic_axes(ax, xlabeloffset=.2)
+```
 
 All donor/acceptor states at the same energy:
 $$g_A(E) = N_A \delta(E-E_A),\quad g_D(E) = N_D \delta(E- (E_G - E_D))$$
@@ -336,7 +395,9 @@ See the book for details.
 
 Density of states in a doped semiconductor:
 
-![](figures/doping.svg)
+```python
+fig
+```
 
 Charge balance determins the number of electrons and holes as well as the position of the Fermi level.
 

docs/lecture_8.md → src/lecture_8.md

+```python
+from matplotlib import pyplot
+
+import numpy as np
+from scipy.optimize import curve_fit
+from scipy.integrate import quad
+
+from common import draw_classic_axes, configure_plotting
+
+configure_plotting()
+```
+
 # Lecture 8 – Magnetism
 
 _Based on chapters 19 and 20 of the book_
@@ -81,7 +93,18 @@ $$
 
 with $C$ a constant. This is known as the _Curie law_, and it shows that at high temperature a paramagnetic material becomes less susceptible to magnetisation.
 
-![](figures/curie.svg)
+```python
+B = np.linspace(-2, 2, 1000)
+fig, ax = pyplot.subplots()
+
+ax.plot(B, np.tanh(B * 3), label="low $T$")
+ax.plot(B, np.tanh(B), label="high $T$")
+
+ax.legend()
+ax.set_ylabel("$M$")
+ax.set_xlabel("$B$")
+draw_classic_axes(ax, xlabeloffset=.2)
+```
 
 ### Paramagnetism: free spin $J$
 For an atom with magnetic moments $L$ and $S$ the Hamiltonian will become:
@@ -193,4 +216,4 @@ $$
 {\mathcal H}=\sum_i \left( -J \sigma_i \sigma_{i+1}+ g\mu_{\rm B}B\sigma_i\right)
 $$
 
-where $\sigma_i=\pm S$.
\ No newline at end of file
+where $\sigma_i=\pm S$.