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simLN_7.3.py
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#Paolo Wetzl 2020
#IMPORT LIBRARIES
from numpy import linspace, array, loadtxt, exp, dot, log, log10, savetxt, transpose
import matplotlib.pyplot as plt
from fun import material_nk_fnLN, material_nk_fnLNt, material_nk_fnGaN, material_nk_fnAl2O3, make_k, make_T_int, make_T_lay, make_layer_matr, T_inc
#layer characteristics
#1: air
#2: LN
#3: GaN
#4: Al2O3
#5: air
#roughness list in microm
z_1 = 0
z_2 = 0
z_3 = 0.0151
z_4 = 0
# list of layer thicknesses in microm
d_LN = 0.23
d_GaN = 5.57
d_Al2O3 = 500
#urbach energies, urbach zero energy and zero absorption coefficient
Eu_GaN = 0.017 #in eV
E0_GaN = 3.56 #in eV
alpha0_GaN = 16e3
Eu_LN = 0.150 #in eV
E0_LN = 4.502 #in eV
alpha0_LN = 3e3
#wavelenghts for the simulation in microm
l_sx = 0.350
l_dx = 2.5
n_points = 20000
lambda_list = linspace(l_sx, l_dx, n_points)
#initialization of T matrices
T = []
Tinc = []
#angles of incidence on the layers
th_i = 0
th_f = 0
#execute the various operations for each wavelength
for lambda_vac in lambda_list:
#compute the refractive indeces of the various materials
nreGaN = material_nk_fnGaN(lambda_vac, 'o')
nimGaN = make_k(lambda_vac, alpha0_GaN, E0_GaN, Eu_GaN)
nreLN = material_nk_fnLN(lambda_vac,'o')
nimLN = make_k(lambda_vac, alpha0_LN, E0_LN, Eu_LN)
n_LN = nreLN + 1j * nimLN
n_GaN = nreGaN + 1j * nimGaN
n_Al2O3 = material_nk_fnAl2O3(lambda_vac, 'o')
#compute the transfer matrices for the various interfaces and layers, one by one
T12 = make_T_int(lambda_vac, 1, n_LN, th_i, th_f, z_1)
T2 = make_T_lay(lambda_vac, n_LN, d_LN)
T23 = make_T_int(lambda_vac, n_LN, n_GaN, th_i, th_f, z_2)
T3 = make_T_lay(lambda_vac, n_GaN, d_GaN)
T34 = make_T_int(lambda_vac, n_GaN, n_Al2O3, th_i, th_f, z_3)
T4 = make_T_lay(lambda_vac, n_Al2O3, d_Al2O3)
T41 = make_T_int(lambda_vac, n_Al2O3, 1, th_i, th_f, z_4)
#use eq 16 (Katsidis) for the computation of the transmission coefficient of the multilayer from the total transfer matrix for the stack of layers
Tinc.append(T_inc(lambda_vac, dot(dot(dot(dot(dot(T12,T2),T23),T3),T34),T4), T41, n_Al2O3, d_Al2O3))
#load the measurement datafile to compare it with the simulation
x, y = loadtxt('Dati/7.3 con bandwidth bassa 2.txt', delimiter='\t', unpack=True)
#save the result of the simulation on a file
d =array([lambda_list,Tinc]).T
savetxt('simLN_7.3.txt', d, fmt='%10.5f', newline='\n')
#plot the simulation and the measured data in the same graph
plt.figure(1)
plt.xlim(1.5, 3.5)
plt.ylim(0, 1)
plt.plot(0.4135667662 * 2.99 / lambda_list, Tinc, 'g-', alpha=0.7, linewidth=0.8)
plt.plot(0.4135667662 * 2.99 / (x/1000), y / 100, 'b-', alpha=0.5, linewidth=0.8)
plt.xlabel('Energy (eV)')
plt.ylabel('Fraction of power transmitted')
plt.title('Transmission at normal incidence')
plt.savefig('Transmission_7.3.pdf')
plt.savefig('Transmission_7.3.svg')
#plot the data in order to be able to check the slope of the absorption edge (to estimate the Urbach energy)
plt.figure(2)
plt.xlim(2.6, 3.5)
plt.plot(0.4135667662 * 2.99 / lambda_list , log(-log(Tinc)), 'g-', alpha=0.7, linewidth=0.8)
plt.plot(0.4135667662 * 2.99 / (x/1000) , log(-log(y / 100)), 'b-', alpha=0.7, linewidth=0.8)
plt.xlabel('Energy (eV)')
plt.ylabel('ln(-ln(T))')
plt.show()