new file: vdP.py

vdP.py

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+# -*- coding: utf-8 -*-
+"""
+Created on Sun Mar 10 15:13:19 2019
+@author: Hezy Amiel
+"""
+
+"""
+find the sheet resistance Rs from R1 = R_AB,CD and R2 = R_BC,AD
+the solution is from the equation in a paper L. J. van der Pauw "A method of measuring the resistivity and hall coefficients of Lamellae of arbitrary shape", Philips Technical Review, Vol 26, 220.
+"""
+
+import numpy as np
+import matplotlib.pyplot as plt
+from scipy import optimize
+
+# these are the resistance R_AB,CD and R_BC,AD respectivly
+R1 = 65
+R2 = 89
+
+# define the equation
+def fun(Rs):
+    return np.exp(-np.pi*R1/Rs) + np.exp(-np.pi*R2/Rs) - 1
+
+# plot the fuction
+Rs = np.linspace (0, 10*np.sqrt(R1*R2), 200)
+# Rs = np.linspace (0, 10000, 200)
+plt.plot(Rs,fun(Rs))
+plt.axhline(color = "r")
+plt.show()
+
+# find the solution
+root = optimize.root(fun, [1])
+
+print (root)