Example: Indices of refraction tests

Here we perform some tests for several indices of refraction supported by ThinFilmsTools.jl.

The complete code of this example can be found here.

First, we load the modules:

using Plots, LaTeXStrings
pyplot()
using ThinFilmsTools

Sellmeier equation

We use the Sellmeier equation to reproduce the indices of refraction of several glasses:

lg = ["BK7" "Sapphire (OW)" "Sapphire (EW)" "Fused Silica" "MgF2"]
plt = plot();
λ = float.(0.2:0.001:1.6)
B₁ = [1.03961212, 1.43134930, 1.5039759, 0.696166300, 0.48755108]
B₂ = [0.231792344, 0.65054713, 0.55069141, 0.407942600, 0.39875031]
B₃ = [1.01046945, 5.3414021, 6.5927379, 0.897479400, 0.897479400]
C₁ = [6.00069867e-3, 5.2799261e-3, 5.48041129e-3, 4.67914826e-3, 0.001882178]
C₂ = [2.00179144e-2, 1.42382647e-2, 1.47994281e-2, 1.35120631e-2, 0.008951888]
C₃ = [103.560653, 325.017834, 402.89514, 97.9340025, 566.13559]
for i in eachindex(B₁)
    n = RI.sellmeier([B₁[i], B₂[i], B₃[i], C₁[i], C₂[i], C₃[i]], λ)
    plot!(plt, λ.*1e3, real.(n), label=lg[i]);
end
xaxis!("Wavelength [nm]")
yaxis!("Sellmeier index of refraction")
gui()

Drude-Lorentz model

The Drude-Lorentz dispersion model is tested for several materials, taken the values from here:

AlGaN

ħω = 0.6:0.01:4
x = [
     [1.0], # ϵinf
     [1.0, 13.7, 7.22, 0.127], # f1, ħωₚ1, ħω₀1, Γ1
]
n = RI.drude_lorentz(x, ħω)
plot(ħω, [real.(n) imag.(n)], label=["n = ℜ{N}" "k = ℑ{N}"], line=([:solid :dashdot]))
xaxis!("Energy [eV]")
yaxis!("Drude-Lorentz AlGaN index of refraction")
gui()

SiO2

ħω = 0.6:0.01:5
x = [
     [1.0], # ϵinf
     [1.0, 12.7, 12, 0.1], # f1, ħωₚ1, ħω₀1, Γ1
]
n = RI.drude_lorentz(x, ħω)
plot(ħω, [real.(n) imag.(n)], label=["n = ℜ{N}" "k = ℑ{N}"], line=([:solid :dashdot]))
xaxis!("Energy [eV]")
yaxis!("Drude-Lorentz SiO2 index of refraction")
gui()

CuPc

ħω = 0.6:0.01:5
x = [
     [1.8], # ϵinf
     [1.34, 1.686, 1.686, 0.31], # f1, ħωₚ1, ħω₀1, Γ1
     [0.152, 3.541, 3.541, 0.292], # f2, ħωₚ2, ħω₀2, Γ2
]
n = RI.drude_lorentz(x, ħω)
plot(ħω, [real.(n) imag.(n)], label=["n = ℜ{N}" "k = ℑ{N}"], line=([:solid :dashdot]))
xaxis!("Energy [eV]")
yaxis!("Drude-Lorentz CuPc index of refraction")
gui()

Tauc-Lorentz

For the Tauc-Lorentz parameterization of the dielectric function, we use the values from Appl. Phys. Lett. 69 (3), 15 July 1996 and Erratum.

a-Si(II)

ħω = 0.8:0.01:5.9
x = [
     [1.15, 1.2],
     [122, 3.45, 2.54], # A1, E01, Γ1
]
n = RI.tauc_lorentz(x, ħω)
plot(ħω, [real.(n) imag.(n)], label=["n = ℜ{N}" "k = ℑ{N}"], line=([:solid :dashdot]))
xaxis!("Energy [eV]")
yaxis!("Tauc-Lorentz a-Si(II) index of refraction")
gui()

Si3N4

ħω = 1.5:0.01:6
x = [
     [3.10, 4.5],
     [59.2, 6.78, 0.49], # A1, E01, Γ1
]
n = RI.tauc_lorentz(x, ħω)
plot(ħω, [real.(n) imag.(n)], label=["n = ℜ{N}" "k = ℑ{N}"], line=([:solid :dashdot]))
xaxis!("Energy [eV]")
yaxis!("Tauc-Lorentz Si3N4 index of refraction")
gui()

Forouhi-Bloomer

We test the model for two materials with different numbers of oscillators, and take the parameters from Physical Review B, 38, 1865 (1988):

SiC, 1 term

ħω = 0:0.01:15
x = [
     [1.680, 2.5],
     [0.25926, 14.359, 53.747], # first oscillator
]
n = RI.forouhi_bloomer(x, ħω)
plot(ħω, [real.(n) imag.(n)], label=["n = ℜ{N}" "k = ℑ{N}"], line=([:solid :dashdot]))
xaxis!("Energy [eV]")
yaxis!("Forouhi-Bloomer SiC index of refraction (1 term)")
gui()

SiC, 2 terms

ħω = 0:0.01:15
x = [
     [1.337, 2.5],
     [0.18028, 14.222, 52.148], # first oscillator
     [0.10700, 19.397, 99.605], # second oscillator
]
n = RI.forouhi_bloomer(x, ħω)
plot(ħω, [real.(n) imag.(n)], label=["n = ℜ{N}" "k = ℑ{N}"], line=([:solid :dashdot]))
xaxis!("Energy [eV]")
yaxis!("Forouhi-Bloomer SiC index of refraction (2 terms)")
gui()

SiC, 4 terms

ħω = 0:0.01:15
x = [
     [1.353, 2.5],
     [0.00108, 13.227, 43.798], # first oscillator
     [0.19054, 14.447, 53.860], # second oscillator
     [0.00646, 19.335, 94.105], # third oscillator
     [0.05366, 21.940, 125.443], # fourth oscillator
]
n = RI.forouhi_bloomer(x, ħω)
plot(ħω, [real.(n) imag.(n)], label=["n = ℜ{N}" "k = ℑ{N}"], line=([:solid :dashdot]))
xaxis!("Energy [eV]")
yaxis!("Forouhi-Bloomer SiC index of refraction (4 terms)")
gui()

InAs, 4 terms

ħω = 0:0.01:8
x = [
     [1.691, 0.3],
     [0.18463, 5.277, 7.504], # first oscillator
     [0.00941, 9.130, 20.934], # second oscillator
     [0.05242, 9.865, 25.172], # third oscillator
     [0.03467, 13.956, 50.062], # fourth oscillator
]
n = RI.forouhi_bloomer(x, ħω)
plot(ħω, [real.(n) imag.(n)], label=["n = ℜ{N}" "k = ℑ{N}"], line=([:solid :dashdot]))
xaxis!("Energy [eV]")
yaxis!("Forouhi-Bloomer InAs index of refraction (4 terms)")
gui()

Cody-Lorentz

We test this function using the parameters from J. Appl. Phys., 92, No. 5, 2424 (2002).

Dipole option

ħω = 1.0:0.01:5
x = [
     [1.0, 1.35, 1.5, 0.7, 0.055], # ϵinf, Eg, Et, Ep, Eu
     [60, 3.7, 2.7], # first oscillator, A1, E01, Γ1
]
n = RI.cody_lorentz(x, ħω)
ϵ = n.^2
plot(ħω, [real.(ϵ) imag.(ϵ)], label=["ϵ₁ = ℜ{ϵ}" "ϵ₂ = ℑ{ϵ}"], line=([:solid :dashdot]))
xaxis!("Energy [eV]")
yaxis!("Cody-Lorentz a-Si(H) dielectric function")
gui()

Momentum option

ħω = 1.0:0.01:5
x = [
     [1.0, 1.35, 1.5, 0.7, 0.055], # ϵinf, Eg, Et, Ep, Eu
     [60, 3.7, 2.7], # first oscillator, A1, E01, Γ1
]
n = RI.cody_lorentz(x, ħω; cme=:momentum)
ϵ = n.^2
plot(ħω, [real.(ϵ) imag.(ϵ)], label=["ϵ₁ = ℜ{ϵ}" "ϵ₂ = ℑ{ϵ}"], line=([:solid :dashdot]))
xaxis!("Energy [eV]")
yaxis!("Cody-Lorentz a-Si(H) dielectric function")
gui()