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Calculations/rendered/Tunneling-Current-Distance.md

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+```python
+import matplotlib.pyplot as plt
+import numpy as np
+from pint import UnitRegistry
+
+# Set up unit system
+unit = UnitRegistry()
+unit.formatter.default_format = "~"
+unit.setup_matplotlib()
+
+# Physical constants
+e=-1.602176634e-19 * unit.C # electron charge
+m=9.109e-31 * unit.kg # electron mass
+hbar=6.62607015e-34/2/np.pi * unit.joule * unit.second # Planck constant
+phi=4 * unit.eV # Work function (see table)
+phi_joule=phi.to("joule")
+U=5 *unit.V
+
+# Table working functions different metals
+
+# Metal F(eV)
+# (Work Function)
+# Ag (silver) 4.26
+# Al (aluminum) 4.28
+# Au (gold) 5.1
+# Cs (cesium) 2.14
+# Cu (copper) 4.65
+# Li (lithium) 2.9
+# Pb (lead) 4.25
+# Sn (tin) 4.42
+# Chromium 4.6
+# Molybdenum 4.37
+# Stainless Steel 4.4
+# Gold 4.8
+# Tungsten 4.5
+# Copper 4.5
+# Nickel 4.6
+
+# Distance range
+Distance_tip_sample=np.linspace(10e-13,2e-10,100)* unit.m
+Tunneling_current=U*np.exp(-2*np.sqrt(2*m*phi_joule)/hbar*Distance_tip_sample) /unit.V #please note: This is not the tunneling current as this formular gives just the proportionality. Calculating the current constant is difficult as there are for us unknown parameters
+Distance_tip_sample_nm=Distance_tip_sample.to("nm")
+
+plt.plot(Distance_tip_sample_nm, Tunneling_current)
+plt.xlabel(f"Distance tip sample [{Distance_tip_sample_nm.units:~P}]")
+plt.ylabel(f"Tunneling-Proportionality [arb. Unit]")
+plt.xticks(ticks=np.linspace(0, 0.2, 5), labels=[f"{x:.2f}" for x in np.linspace(0, 0.2, 5)])
+#plt.yscale("log")
+
+```
+
+
+
+
+    ([<matplotlib.axis.XTick at 0x7e10b04929b0>,
+      <matplotlib.axis.XTick at 0x7e10b04b0310>,
+      <matplotlib.axis.XTick at 0x7e10b034ba60>,
+      <matplotlib.axis.XTick at 0x7e10b0328670>,
+      <matplotlib.axis.XTick at 0x7e10b0329360>],
+     [Text(0.0, 0, '0.00'),
+      Text(0.05, 0, '0.05'),
+      Text(0.1, 0, '0.10'),
+      Text(0.15000000000000002, 0, '0.15'),
+      Text(0.2, 0, '0.20')])
+
+
+
+
+    
+![png](Tunneling-Current-Distance_files/Tunneling-Current-Distance_0_1.png)
+    
+