dos_santos_montgomery_resistivity.py

# Final equations from Procedure for measuring electrical resistivity of anisotropic materials:
# A revision of the Montgomery method by Dos Santos et al. (2011)  in the Journal of Applied Physics
# dx.doi.org/10.1063/1.3652905

# These equations can be used to determine the electrical resistivity in the two planar directions of an anisotropic material in the form of a thin film
# They are only valid if L3/(L1*L2)^(1/2) < 0.5, note that L1, L2 and L3 are the dimensions of the isotropic mapping of the anisotropic material and can't be determined a priori
# Refer to Section III of the paper for a discussion

R2 = np.array([10, 10, 10])  # Measured resistance in direction "2" in ohms
R1 = np.array([1, 1, 1])  # Measured resistance in direction "1" in ohms

# Isotropic mapping of L2/L1 calculated from the measured resistances
L2_L1 = 1/2*(1/(np.pi) * np.log(R2/R1) + np.power((np.power(((1/np.pi) * np.log(R2/R1)), 2) + 4), 0.5))
L1_L2 = np.power(L2_L1, -1)

# thickness of the sample in metres
thickness = 1 * 10**-5

L2_prime = 1  # length of the sample in the "2" direction
L1_prime = 1  # length of the sample in the "1" direction

AR_2_1 = L2_prime/L1_prime  # aspect ratio in 2/1
AR_1_2 = AR_2_1**-1

# Equation 22
rho1_A = np.pi/8 * thickness * AR_2_1 * (L1_L2) * R1 * np.sinh(np.pi*L2_L1)
print(rho1_A)
print(f'rho1_A: {np.average(rho1_A)} ohm/m')

# Equation 23
rho1_B = np.pi/8 * thickness * AR_2_1 * (L1_L2) * R2 * np.sinh(np.pi*L1_L2)
print(rho1_B)
print(f'rho1_B: {np.average(rho1_B)} ohm/m')

# Equation 24
rho2_A = np.pi/8 * thickness * AR_1_2 * (L2_L1) * R1 * np.sinh(np.pi*L2_L1)
print(rho2_A)
print(f'rho2_A: {np.average(rho2_A)} ohm/m')

# Equation 25
rho2_B = np.pi/8 * thickness * AR_1_2 * (L2_L1) * R2 * np.sinh(np.pi*L1_L2)
print(rho2_B)
print(f'rho2_B: {np.average(rho2_B)} ohm/m')