add band diagram

src/14_doping_and_devices.md

@@ -5,10 +5,16 @@ import numpy as np
 from scipy.optimize import curve_fit
 from scipy.integrate import quad
 
+import plotly.offline as py
+import plotly.graph_objs as go
+
 from common import draw_classic_axes, configure_plotting
 
 configure_plotting()
 
+py.init_notebook_mode(connected=True)
+
+
 def sqrt_plus(x):
     return np.sqrt(x * (x >= 0))
 
@@ -204,7 +210,233 @@ The main idea is to plot the dependence of various energies ($E_F$, bottom of co
 
 So here is our problem for today:
 
-![](figures/band_diagram_question.svg)
+```python
+
+def trans(x, a, b):
+    x = (x-a)/(b-a)
+    return h(x)/(h(x) + h(1-x))
+
+
+def h(x):
+    return (x > 0) * np.exp(-1/x)
+
+left_cutoff = 0.3
+right_cutoff = 0.7
+x = np.linspace(0, 1, 100)
+mid_idx = (x > left_cutoff) * (x < right_cutoff)
+
+
+Ef_p = 0.5
+Ef_n = Ef_p + 0.25
+Ef_delta = Ef_n - Ef_p
+
+E_C_1 = 1
+E_V_1 = 0.25
+
+E_C = E_C_1 - trans(x, left_cutoff, right_cutoff)*Ef_delta
+E_V = E_V_1 - trans(x, left_cutoff, right_cutoff)*Ef_delta
+
+fig1 = go.Figure()
+
+fig1.add_trace(go.Scatter(
+        x = [0, left_cutoff],
+        y = [E_V_1, E_V_1],
+        line_color = 'red',
+        mode = 'lines',
+        name = r'$E_V$',
+    ))
+
+fig1.add_trace(go.Scatter(
+        x = [0, left_cutoff],
+        y = [E_C_1, E_C_1],
+        line_color = 'blue',
+        mode = 'lines',
+        name = r'$E_C$',
+    ))
+
+# n bands (button 1)
+fig1.add_trace(go.Scatter(
+        x = [right_cutoff, 1],
+        y = [E_V_1, E_V_1],
+        line_color = 'red',
+        mode = 'lines',
+        showlegend=False
+    ))
+
+fig1.add_trace(go.Scatter(
+        x = [right_cutoff, 1],
+        y = [E_C_1, E_C_1],
+        line_color = 'blue',
+        mode = 'lines',
+        showlegend=False
+    ))
+
+# p fermi
+fig1.add_trace(go.Scatter(
+        x = [0, left_cutoff],
+        y = [Ef_p, Ef_p],
+        line_color='black',
+        mode = 'lines',
+        line_dash='dot',
+        name=r'$E_F$'
+
+    ))
+
+# n fermi (button 1)
+fig1.add_trace(go.Scatter(
+        x = [right_cutoff, 1],
+        y = [Ef_n, Ef_n],
+        line_color='black',
+        mode = 'lines',
+        line_dash='dot',
+        name='r$E_f$',
+        showlegend=False
+    ))
+
+fig1.add_trace(go.Scatter(
+        x = [right_cutoff, 1],
+        y = [E_V_1-Ef_delta, E_V_1-Ef_delta],
+        line_color = 'red',
+        mode = 'lines',
+        showlegend=False,
+        visible=False
+    ))
+
+fig1.add_trace(go.Scatter(
+        x = [right_cutoff, 1],
+        y = [E_C_1-Ef_delta, E_C_1-Ef_delta],
+        line_color = 'blue',
+        mode = 'lines',
+        showlegend=False,
+        visible=False
+    ))
+
+
+fig1.add_trace(go.Scatter(
+        x = [0, 1],
+        y = [Ef_p, Ef_p],
+        line_color='black',
+        mode = 'lines',
+        line_dash='dot',
+        name='r$E_F$',
+        visible=False,
+
+    ))
+
+
+fig1.add_trace(go.Scatter(
+        x = x[mid_idx],
+        y = E_C[mid_idx],
+        line_color='blue',
+        line_dash='dot',
+        visible=False,
+        showlegend=False
+
+    ))
+
+fig1.add_trace(go.Scatter(
+        x = x[mid_idx],
+        y = E_V[mid_idx],
+        line_color = 'red',
+        line_dash='dot',
+        visible=False,
+        showlegend=False
+    ))
+
+updatemenus=list([ 
+    dict(
+        type="buttons",
+        direction="down",
+        active=0,
+        buttons=list([
+            dict(label="n and p",
+                 method="update",
+                 args=[{"visible": [True, True, True, True, True, True, False, False, False, False, False]}]),
+            dict(label="Equilibrium",
+                 method="update",
+                 args=[{"visible": [True, True, False, False, False, False, True, True, True, False, False]}]),
+            dict(label="Band Bending",
+                 method="update",
+                 args=[{"visible": [True, True, False, False, False, False, True, True, True, True, True]}]),
+        ]),
+    )
+]
+)
+
+layout = dict(
+    dragmode=False,
+    showlegend = True,
+    updatemenus=updatemenus,
+    plot_bgcolor = 'rgb(254, 254, 254)',
+    yaxis_range=[(E_V_1-Ef_delta)-0.1, 0.1+E_C_1],
+    xaxis_range=[-0.05, 1.05],
+    width = 800,
+    height = 600,
+    xaxis=dict(title=r'$x$', showticklabels=False),
+    yaxis=dict(title=r'$E$', showticklabels=False),
+    title='Band Diagram'
+)
+
+fig1.update_xaxes(showline=True, linewidth=2, linecolor='black')
+fig1.update_yaxes(showline=True, linewidth=2, linecolor='black')
+
+fig1.add_annotation(
+    x = 1.065,
+    y = -0.1,
+    xref = "x", yref = "y",
+    axref = "x", ayref = "y",
+    text = "",
+    ax = 0.9,
+    ay = -0.1,
+    showarrow=True,
+    arrowhead=3,
+    arrowsize=30,
+    arrowwidth=0.1,
+    arrowcolor='black')
+
+fig1.add_annotation(
+    x = -0.05,
+    y = 1.12,
+    xref = "x", yref = "y",
+    axref = "x", ayref = "y",
+    text = "",
+    ax = -0.05,
+    ay = 1.1,
+    showarrow=True,
+    arrowhead=3,
+    arrowsize=30,
+    arrowwidth=0.1,
+    arrowcolor='black')
+
+fig1.add_annotation(
+    showarrow=False,
+    x = 0.15,
+    y = -0.05,
+    xref = "x", yref = "y",
+    axref = "x", ayref = "y",
+    text = "p-region")
+
+fig1.add_annotation(
+    showarrow=False,
+    x = 0.5,
+    y = -0.05,
+    xref = "x", yref = "y",
+    axref = "x", ayref = "y",
+    text = "depletion region")
+
+fig1.add_annotation(
+    showarrow=False,
+    x = 0.85,
+    y = -0.05,
+    xref = "x", yref = "y",
+    axref = "x", ayref = "y",
+    text = "n-region")
+
+fig1.update_layout(layout)
+py.plot(fig1)
+fig1.show()
+
+```
 
 The main difference between $n$-type and $p$-type semiconductors is the location of the Fermi level $E_F$. 
 The Fermi level of an $n$-type semiconductor is close to the donor states.