def test_belitsky2006_fig2():
"""Recreate Figure 2 from:
V. Y. Belitsky and E. L. Kollberg, “Superconductor–insulator–
superconductor tunnel strip line: Features and applications,” J. Appl.
Phys., vol. 80, no. 8, pp. 4741–4748, Oct. 1996.
"""
# Parameters
T = 4.0
Vgap = 2.53e-3 # Gap voltage is not specified in the paper!!!
param = dict(sigma_n=1.739e7, Tc=8.1, Vgap0=2.65e-3, lambda0=85 * sc.nano)
# Calculate sigma_1
filename = 'validation-data/belitsky2006/belitsky2006-fig2-sigma1.txt'
fghz, lit_sigma1 = np.genfromtxt(filename, delimiter=',').T
sigma = mb.conductance(fghz * 1e9, T, Vgap, **param)
max_difference = np.abs(lit_sigma1 - sigma.real / param['sigma_n']).max()
assert max_difference < 0.02
# Calculate sigma_2
filename = 'validation-data/belitsky2006/belitsky2006-fig2-sigma2.txt'
fghz, lit_sigma2 = np.genfromtxt(filename, delimiter=',').T
sigma = mb.conductance(fghz * 1e9, T, Vgap, **param)
max_difference = np.abs(lit_sigma2 + sigma.imag / param['sigma_n']).max()
assert max_difference < 0.2
# Calculate E-field penetration
filename = 'validation-data/belitsky2006/belitsky2006-fig2-lambda.txt'
fghz, lit_lambda = np.genfromtxt(filename, delimiter=',').T
d = 500e-9 # The thickness is not specified in the paper!!!
zs = mb.surface_impedance(fghz * 1e9, d, T, Vgap, **param)
_lambda = mb.efield_penetration(zs, fghz * 1e9) / mb._lambda0(**param)
max_difference = np.abs(_lambda - lit_lambda).max()
assert max_difference < 0.1
# Calculate H-field penetration
filename = 'validation-data/belitsky2006/belitsky2006-fig2-delta.txt'
fghz, lit_delta = np.genfromtxt(filename, delimiter=',').T
d = 500e-9 # The thickness is not specified in the paper!!!
zs = mb.surface_impedance(fghz * 1e9, d, T, Vgap, **param)
_delta = mb.hfield_penetration(zs, fghz * 1e9) / mb._lambda0(**param)
max_difference = np.abs(_delta - lit_delta).max()
assert max_difference < 0.1
def test_compare_simple_and_MB_models():
"""Compare the surface impedance that is calculated from Mattis-Bardeen
theory to the results from [1]."""
# Frequency
f = np.arange(100, 1000, 100) * 1e9
# Surface impedance (using both models)
zs_simple = mb.surface_impedance(f, 250e-9, 4., 2.75e-3, method='simple')
zs_mb = mb.surface_impedance(f, 250e-9, 4., 2.75e-3, method='MB')
# Below ~fgap/2, both models should be roughly the same
mask = f < 350e9
# Check real values
assert (zs_simple.real == 0.).all()
assert (zs_mb[mask].real < 0.01).all()
# Check imaginary values
error_imag = (zs_simple.imag - zs_mb.imag) / zs_mb.imag * 100.
max_error = np.abs(error_imag[mask]).max()
assert max_error < 5. # below 5% relative error
import numpy as np
import matplotlib.pyplot as plt
import scipy.constants as sc
# Optional
plt.style.use(['science', 'notebook'])
# Properties of the superconducting material, i.e., normal-state conductance,
# critical temperature, gap voltage at T=0K, and penetration depth
param = dict(sigma_n=1.74e7, Tc=8.1, Vgap0=2.65e-3, lambda0=86 * sc.nano)
# Properties of the specific superconductor
d = 100e-9 # thickness of the superconducting film in [m]
T = 4. # ambient temperature in [K]
Vgap = 2.8e-3 # gap voltage at temperature T in [V]
# Frequency in [Hz]
f = np.linspace(0, 1000, 201) * 1e9
# Surface impedance [ohm / sq.]
Zs = mb.surface_impedance(f, d, T, Vgap, **param)
# Plot results
fig, ax = plt.subplots()
ax.plot(f / 1e9, Zs.real, label='Real')
ax.plot(f / 1e9, Zs.imag, 'r', label='Imaginary')
ax.legend()
ax.set(xlabel='Frequency (GHz)', xlim=[0, 1000])
ax.set(ylabel=r'Surface impedance ($\Omega$/sq.)', ylim=[0, 1.1])
plt.savefig("example.png", dpi=600)