vdP.py

# -*- coding: utf-8 -*-
"""
Created on Sun Mar 10 15:13:19 2019
@author: Hezy Amiel
"""

import numpy as np
import matplotlib.pyplot as plt
from scipy import optimize


"""
find the sheet resistance Rs from R1 = R_AB,CD and R2 = R_BC,AD
the solution is from the equation in a paper by 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.
"""


# define the equation
def fun(Rs):
    return np.exp(-np.pi*R1/Rs) + np.exp(-np.pi*R2/Rs) - 1


# these are the resistance R_AB,CD and R_BC,AD respectivly
R1 = 65
R2 = 89

# 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)