elli.dispersions package

Submodules

elli.dispersions.base_dispersion module

Abstract base class and utility classes for pyElli dispersion

class elli.dispersions.base_dispersion.Dispersion(*args, **kwargs)[source]

Bases: ABC

Dispersion (abstract class).

Functions provided for derived classes: * dielectric_function(lbda) : returns dielectric constant for wavelength ‘lbda’

add(*args, **kwargs)[source]

Adds a set of parameters to the dispersion.

Returns: The current object with the additional parameters added.
Return type: Dispersion

abstract dielectric_function(lbda)[source]

Calculates the dielectric function in a given wavelength window.

Parameters: lbda (npt.ArrayLike) – The wavelength window with unit nm.
Returns: The dielectric function for each wavelength point.
Return type: npt.NDArray

get_dielectric(lbda)[source]: Returns the dielectric constant for wavelength ‘lbda’ default unit (nm) in the convention ε1 + iε2.

get_dielectric_df(lbda=None, conjugate=False)[source]

Returns the dielectric function as a pandas dataframe

Parameters

lbda (npt.ArrayLike, optional) – The wavlength range to use. If this parameter is not given a default spectral range from 200 to 1000 nm with 801 points is used. Defaults to None.
conjugate (bool, optional) – Per default the convention ε1 + iε2 is returned. If this flag is set to True, the ε1 + iε2 convention is returned. Defaults to False.

Returns

A pandas dataframe containing the wavelength as index and two rows containing ε1 and ε2.

Return type

pd.DataFrame

get_mat()[source]: Returns this dispersion as an isotropic material

get_refractive_index(lbda)[source]: Returns the refractive index for wavelength ‘lbda’ default unit (nm) in the convention n + ik.

get_refractive_index_df(lbda=None, conjugate=False)[source]

Returns the refractive index as a pandas dataframe

Parameters

lbda (npt.ArrayLike, optional) – The wavlength range to use. If this parameter is not given a default spectral range from 200 to 1000 nm with 801 points is used. Defaults to None.
conjugate (bool, optional) – Per default the convention n + ik is returned. If this flag is set to True, the n + ik convention is returned. Defaults to False.

Returns

A pandas dataframe containing the wavelength as index and two rows containing n and k.

Return type

pd.DataFrame

abstract property rep_params_template: Specifies the repeated parameters of the model and its default values.

abstract property single_params_template: Specifies the single parameters of the model and its default values.

class elli.dispersions.base_dispersion.DispersionFactory[source]

Bases: object

A factory class for dispersion objects

static get_dispersion(identifier, *args, **kwargs)[source]

Creates a DispersionLaw object identified by its string name and initializes it with the given parameters.

Parameters: identifier (str) – Identifier of the DispersionLaw object, e.g. DispersionCauchy.
Returns: The DispersionLaw object initialized with the given parameters.
Return type: DispersionLaw

class elli.dispersions.base_dispersion.DispersionSum(*disps)[source]

Bases: Dispersion

Representation for a sum of two dispersions

dielectric_function(lbda)[source]

Calculates the dielectric function in a given wavelength window.

Parameters: lbda (npt.ArrayLike) – The wavelength window with unit nm.
Returns: The dielectric function for each wavelength point.
Return type: npt.NDArray

rep_params_template = {}

single_params_template = {}

exception elli.dispersions.base_dispersion.InvalidParameters[source]

Bases: Exception

Exception for invalid dispersion parameters.

elli.dispersions.dispersions module

The dispersions are the central part of pyElli and the transfer-matrix method. They describe the change of dielectric function or refractive index with wavlength. In pyElli the default wavelength unit is nm. Each dispersion has two distinct sets of parameters:

Parameters which can be given only once (single parameters).

Parameters which can be given in multiple sets (repeated parameters), e.g.
a set of oscillator parameters.

The syntax for each of the parameter sets is different. For the single parameters they are given in the class constructor:

Cauchy(n0=1.458, n1=3.54e-3, n2=0, k0=0, k1=0, k2=0)

Repeated parameters are added via the add() function:

Sellmeier().add(A=1, B=1).add(A=1, B=2)

For dispersions having single and repeated parameters both are used:

TaucLorentz(Eg=2).add(A=10, E=2.5, C=0.1)

If parameters are not fully provided, they are set to their respective default values. The available parameters and their respective default values are given in the respective class documentation.

class elli.dispersions.dispersions.Cauchy(*args, **kwargs)[source]

Bases: Dispersion

Cauchy dispersion.

Single parameters:

n0: Defaults to 1.5. n1: Defaults to 0. Unit in nm^2. n2: Defaults to 0. Unit in nm^4. k0: Defaults to 0. k1: Defaults to 0. Unit in nm^2. k2: Defaults to 0. Unit in nm^4.

Repeated parameters:

–

Output:

ε(λ)^2 = (: n0 + 100 * n1/λ² + 10^7 n2/λ^4 + 1j * (k0 + 100 * k1/λ² + 10^7 k2/λ^4)

)

dielectric_function(lbda)[source]

Calculates the dielectric function in a given wavelength window.

Parameters: lbda (npt.ArrayLike) – The wavelength window with unit nm.
Returns: The dielectric function for each wavelength point.
Return type: npt.NDArray

rep_params_template = {}

single_params_template = {'k0': 0, 'k1': 0, 'k2': 0, 'n0': 1.5, 'n1': 0, 'n2': 0}

class elli.dispersions.dispersions.ConstantRefractiveIndex(*args, **kwargs)[source]

Bases: Dispersion

Constant refractive index.

Single parameters:: n: 1
Repeated parameters:: –
Output:: ε(λ) = `n`^2

dielectric_function(_)[source]

Calculates the dielectric function in a given wavelength window.

Parameters: lbda (npt.ArrayLike) – The wavelength window with unit nm.
Returns: The dielectric function for each wavelength point.
Return type: npt.NDArray

rep_params_template = {}

single_params_template = {'n': 1}

class elli.dispersions.dispersions.DrudeEnergy(*args, **kwargs)[source]

Bases: Dispersion

Drude dispersion model with parameters in units of energy. Drude models in the literature typically contain an additional epsilon infinity value. Use EpsilonInf to add this parameter or simply do DrudeEnergy() + eps_inf.

Single parameters:: A: Amplitude of Drude oscillator (eV^2). Defaults to 0. gamma: Broadening of Drude oscillator (eV). Defaults to 0.
Repeated parameters:: –
Output:: ε(E) = A / (E^2 - 1j * gamma * E)

dielectric_function(lbda)[source]

Calculates the dielectric function in a given wavelength window.

Parameters: lbda (npt.ArrayLike) – The wavelength window with unit nm.
Returns: The dielectric function for each wavelength point.
Return type: npt.NDArray

rep_params_template = {}

single_params_template = {'A': 0, 'gamma': 0}

class elli.dispersions.dispersions.DrudeResistivity(*args, **kwargs)[source]

Bases: Dispersion

Drude dispersion model with resistivity based parameters. Drude models in the literature typically contain an additional epsilon infinity value. Use EpsilonInf to add this parameter or simply do DrudeEnergy() + eps_inf.

Single parameters:: rho_opt: Optical resistivity (Ω-cm). Defaults to 1. tau: Mean scattering time (s). Defaults to 1.
Repeated parameters:: –
Output:: ε(E) = hbar / (eps0 * rho_opt * tau E^2 - 1j * hbar * E) where hbar is the planck constant divided by 2pi and eps0 is the vacuum dielectric permittivity.

dielectric_function(lbda)[source]

Calculates the dielectric function in a given wavelength window.

Parameters: lbda (npt.ArrayLike) – The wavelength window with unit nm.
Returns: The dielectric function for each wavelength point.
Return type: npt.NDArray

rep_params_template = {}

single_params_template = {'rho_opt': 1, 'tau': 1}

class elli.dispersions.dispersions.EpsilonInf(*args, **kwargs)[source]

Bases: Dispersion

Constant epsilon infinity.

Single parameters:: eps: 1
Repeated parameters:: –
Output:: ε(λ) = eps

dielectric_function(_)[source]

Calculates the dielectric function in a given wavelength window.

Parameters: lbda (npt.ArrayLike) – The wavelength window with unit nm.
Returns: The dielectric function for each wavelength point.
Return type: npt.NDArray

rep_params_template = {}

single_params_template = {'eps': 1}

class elli.dispersions.dispersions.Gauss(*args, **kwargs)[source]

Bases: Dispersion

Gauss dispersion law.

Single parameters:

–

Repeated parameters:

A: Amplitude of the oscillator E: Central energy (eV) sigma: Broadening of the Gaussian (eV)

Output:

ε(E) = Σi 2 * `A`i / sqrt(π) *: (D(2 * sqrt(2 * ln(2)) * (E + E`i) / `sigma) - D(2 * sqrt(2 * ln(2)) * (E - E`i) / `sigma) +1j * (A * exp(-(4*ln(2) * (E - E`i)/ `sigma)^2 - A * exp(-(4*ln(2) * (E + E`i)/ `sigma)^2)

D is the Dawson function.

References

D. De Sousa Meneses, M. Malki, P. Echegut, J. Non-Cryst. Solids 351, 769-776 (2006) K.-E. Peiponen, E.M. Vartiainen, Phys. Rev. B. 44, 8301 (1991) H. Fujiwara, R. W. Collins, Spectroscopic Ellipsometry for Photovoltaics Volume 1, Springer International Publishing AG, 2018, p. 137

dielectric_function(lbda)[source]

Calculates the dielectric function in a given wavelength window.

Parameters: lbda (npt.ArrayLike) – The wavelength window with unit nm.
Returns: The dielectric function for each wavelength point.
Return type: npt.NDArray

rep_params_template = {'A': 1, 'E': 1, 'sigma': 1}

single_params_template = {}

class elli.dispersions.dispersions.LorentzEnergy(*args, **kwargs)[source]

Bases: Dispersion

Lorentz disperison law with parameters in units of energy.

Single parameters:: –
Repeated parameters:: A: Amplitude of the oscillator. Defaults to 1. E: Resonance energy (eV). Defaults 0. gamma: Broadening of the oscillator (eV). Defaults to 0.
Output:: ε(E) = 1 + Σi `A`i / (E²-`E`i²+1j * `gamma`i * E)

dielectric_function(lbda)[source]

Calculates the dielectric function in a given wavelength window.

Parameters: lbda (npt.ArrayLike) – The wavelength window with unit nm.
Returns: The dielectric function for each wavelength point.
Return type: npt.NDArray

rep_params_template = {'A': 1, 'E': 0, 'gamma': 0}

single_params_template = {}

class elli.dispersions.dispersions.LorentzLambda(*args, **kwargs)[source]

Bases: Dispersion

Lorentz disperison law with parameters in units of wavelengths.

Single parameters:: –
Repeated parameters:: A: Amplitude of the oscillator. Defaults to 1. lambda: Resonance wavelength (nm). Defaults to 0. gamma: Broadening of the oscillator (nm). Defaults to 0.
Output:: ε(λ) = 1 + Σi `A`i * λ² / (λ² - `lambda`i² + 1j * `gamma`i * λ)

dielectric_function(lbda)[source]

Calculates the dielectric function in a given wavelength window.

Parameters: lbda (npt.ArrayLike) – The wavelength window with unit nm.
Returns: The dielectric function for each wavelength point.
Return type: npt.NDArray

rep_params_template = {'A': 1, 'gamma': 0, 'lambda': 0}

single_params_template = {}

class elli.dispersions.dispersions.Poles(*args, **kwargs)[source]

Bases: Dispersion

Disperion law for an UV and IR pole, i.e. Lorentz oscillators outside the fitting spectral range and zero broadening.

Single parameters:: A_ir: IR Pole amplitude (eV^2). Defaults to 1. A_uv: UV Pole amplitude (eV^2). Defaults to 1. E_uv: UV Pole energy (eV). Defaults to 6.
Repeated parameters:: –
Output:: ε(E) = A_ir / E^2 + A_uv / (`E_uv`**2 - E**2)

dielectric_function(lbda)[source]

Calculates the dielectric function in a given wavelength window.

Parameters: lbda (npt.ArrayLike) – The wavelength window with unit nm.
Returns: The dielectric function for each wavelength point.
Return type: npt.NDArray

rep_params_template = {}

single_params_template = {'A_ir': 1, 'A_uv': 1, 'E_uv': 6}

class elli.dispersions.dispersions.Sellmeier(*args, **kwargs)[source]

Bases: Dispersion

Sellmeier dispersion.

Single parameters:: –
Repeated parameters:: A: Coefficient for n² contribution. Defaults to 0. B: Resonance wavelength (µm^-2). Defaults to 0.
Output:: ε(λ) = 1 + Σi Ai × λ²/(λ² - Bi)

dielectric_function(lbda)[source]

Calculates the dielectric function in a given wavelength window.

Parameters: lbda (npt.ArrayLike) – The wavelength window with unit nm.
Returns: The dielectric function for each wavelength point.
Return type: npt.NDArray

rep_params_template = {'A': 0, 'B': 0}

single_params_template = {}

class elli.dispersions.dispersions.Table(*args, **kwargs)[source]

Bases: Dispersion

Dispersion specified by a table of wavelengths (nm) and refractive index values. Please not that this model will produce errors for wavelengths outside the provided wavelength range.

Single parameters:: lbda (list): Wavelengths in nm. Defaults to []. epsilon: Complex refractive index values in the convention n + ik.

Defaults to [].
Repeated parameters:: –
Output:: The interpolation in the given wavelength range.

Create a dispersion law from a refraction index list.

‘lbda’ : Wavelength list (in nm) ‘n’ : Complex refractive index values.

(n > 0 for an absorbing material)

dielectric_function(lbda)[source]

Calculates the dielectric function in a given wavelength window.

Parameters: lbda (npt.ArrayLike) – The wavelength window with unit nm.
Returns: The dielectric function for each wavelength point.
Return type: npt.NDArray

rep_params_template = {}

single_params_template = {'lbda': array([ 0. , 3.003003 , 6.00600601, 9.00900901, 12.01201201, 15.01501502, 18.01801802, 21.02102102, 24.02402402, 27.02702703, 30.03003003, 33.03303303, 36.03603604, 39.03903904, 42.04204204, 45.04504505, 48.04804805, 51.05105105, 54.05405405, 57.05705706, 60.06006006, 63.06306306, 66.06606607, 69.06906907, 72.07207207, 75.07507508, 78.07807808, 81.08108108, 84.08408408, 87.08708709, 90.09009009, 93.09309309, 96.0960961 , 99.0990991 , 102.1021021 , 105.10510511, 108.10810811, 111.11111111, 114.11411411, 117.11711712, 120.12012012, 123.12312312, 126.12612613, 129.12912913, 132.13213213, 135.13513514, 138.13813814, 141.14114114, 144.14414414, 147.14714715, 150.15015015, 153.15315315, 156.15615616, 159.15915916, 162.16216216, 165.16516517, 168.16816817, 171.17117117, 174.17417417, 177.17717718, 180.18018018, 183.18318318, 186.18618619, 189.18918919, 192.19219219, 195.1951952 , 198.1981982 , 201.2012012 , 204.2042042 , 207.20720721, 210.21021021, 213.21321321, 216.21621622, 219.21921922, 222.22222222, 225.22522523, 228.22822823, 231.23123123, 234.23423423, 237.23723724, 240.24024024, 243.24324324, 246.24624625, 249.24924925, 252.25225225, 255.25525526, 258.25825826, 261.26126126, 264.26426426, 267.26726727, 270.27027027, 273.27327327, 276.27627628, 279.27927928, 282.28228228, 285.28528529, 288.28828829, 291.29129129, 294.29429429, 297.2972973 , 300.3003003 , 303.3033033 , 306.30630631, 309.30930931, 312.31231231, 315.31531532, 318.31831832, 321.32132132, 324.32432432, 327.32732733, 330.33033033, 333.33333333, 336.33633634, 339.33933934, 342.34234234, 345.34534535, 348.34834835, 351.35135135, 354.35435435, 357.35735736, 360.36036036, 363.36336336, 366.36636637, 369.36936937, 372.37237237, 375.37537538, 378.37837838, 381.38138138, 384.38438438, 387.38738739, 390.39039039, 393.39339339, 396.3963964 , 399.3993994 , 402.4024024 , 405.40540541, 408.40840841, 411.41141141, 414.41441441, 417.41741742, 420.42042042, 423.42342342, 426.42642643, 429.42942943, 432.43243243, 435.43543544, 438.43843844, 441.44144144, 444.44444444, 447.44744745, 450.45045045, 453.45345345, 456.45645646, 459.45945946, 462.46246246, 465.46546547, 468.46846847, 471.47147147, 474.47447447, 477.47747748, 480.48048048, 483.48348348, 486.48648649, 489.48948949, 492.49249249, 495.4954955 , 498.4984985 , 501.5015015 , 504.5045045 , 507.50750751, 510.51051051, 513.51351351, 516.51651652, 519.51951952, 522.52252252, 525.52552553, 528.52852853, 531.53153153, 534.53453453, 537.53753754, 540.54054054, 543.54354354, 546.54654655, 549.54954955, 552.55255255, 555.55555556, 558.55855856, 561.56156156, 564.56456456, 567.56756757, 570.57057057, 573.57357357, 576.57657658, 579.57957958, 582.58258258, 585.58558559, 588.58858859, 591.59159159, 594.59459459, 597.5975976 , 600.6006006 , 603.6036036 , 606.60660661, 609.60960961, 612.61261261, 615.61561562, 618.61861862, 621.62162162, 624.62462462, 627.62762763, 630.63063063, 633.63363363, 636.63663664, 639.63963964, 642.64264264, 645.64564565, 648.64864865, 651.65165165, 654.65465465, 657.65765766, 660.66066066, 663.66366366, 666.66666667, 669.66966967, 672.67267267, 675.67567568, 678.67867868, 681.68168168, 684.68468468, 687.68768769, 690.69069069, 693.69369369, 696.6966967 , 699.6996997 , 702.7027027 , 705.70570571, 708.70870871, 711.71171171, 714.71471471, 717.71771772, 720.72072072, 723.72372372, 726.72672673, 729.72972973, 732.73273273, 735.73573574, 738.73873874, 741.74174174, 744.74474474, 747.74774775, 750.75075075, 753.75375375, 756.75675676, 759.75975976, 762.76276276, 765.76576577, 768.76876877, 771.77177177, 774.77477477, 777.77777778, 780.78078078, 783.78378378, 786.78678679, 789.78978979, 792.79279279, 795.7957958 , 798.7987988 , 801.8018018 , 804.8048048 , 807.80780781, 810.81081081, 813.81381381, 816.81681682, 819.81981982, 822.82282282, 825.82582583, 828.82882883, 831.83183183, 834.83483483, 837.83783784, 840.84084084, 843.84384384, 846.84684685, 849.84984985, 852.85285285, 855.85585586, 858.85885886, 861.86186186, 864.86486486, 867.86786787, 870.87087087, 873.87387387, 876.87687688, 879.87987988, 882.88288288, 885.88588589, 888.88888889, 891.89189189, 894.89489489, 897.8978979 , 900.9009009 , 903.9039039 , 906.90690691, 909.90990991, 912.91291291, 915.91591592, 918.91891892, 921.92192192, 924.92492492, 927.92792793, 930.93093093, 933.93393393, 936.93693694, 939.93993994, 942.94294294, 945.94594595, 948.94894895, 951.95195195, 954.95495495, 957.95795796, 960.96096096, 963.96396396, 966.96696697, 969.96996997, 972.97297297, 975.97597598, 978.97897898, 981.98198198, 984.98498498, 987.98798799, 990.99099099, 993.99399399, 996.996997 , 1000. , 1003.003003 , 1006.00600601, 1009.00900901, 1012.01201201, 1015.01501502, 1018.01801802, 1021.02102102, 1024.02402402, 1027.02702703, 1030.03003003, 1033.03303303, 1036.03603604, 1039.03903904, 1042.04204204, 1045.04504505, 1048.04804805, 1051.05105105, 1054.05405405, 1057.05705706, 1060.06006006, 1063.06306306, 1066.06606607, 1069.06906907, 1072.07207207, 1075.07507508, 1078.07807808, 1081.08108108, 1084.08408408, 1087.08708709, 1090.09009009, 1093.09309309, 1096.0960961 , 1099.0990991 , 1102.1021021 , 1105.10510511, 1108.10810811, 1111.11111111, 1114.11411411, 1117.11711712, 1120.12012012, 1123.12312312, 1126.12612613, 1129.12912913, 1132.13213213, 1135.13513514, 1138.13813814, 1141.14114114, 1144.14414414, 1147.14714715, 1150.15015015, 1153.15315315, 1156.15615616, 1159.15915916, 1162.16216216, 1165.16516517, 1168.16816817, 1171.17117117, 1174.17417417, 1177.17717718, 1180.18018018, 1183.18318318, 1186.18618619, 1189.18918919, 1192.19219219, 1195.1951952 , 1198.1981982 , 1201.2012012 , 1204.2042042 , 1207.20720721, 1210.21021021, 1213.21321321, 1216.21621622, 1219.21921922, 1222.22222222, 1225.22522523, 1228.22822823, 1231.23123123, 1234.23423423, 1237.23723724, 1240.24024024, 1243.24324324, 1246.24624625, 1249.24924925, 1252.25225225, 1255.25525526, 1258.25825826, 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1459.45945946, 1462.46246246, 1465.46546547, 1468.46846847, 1471.47147147, 1474.47447447, 1477.47747748, 1480.48048048, 1483.48348348, 1486.48648649, 1489.48948949, 1492.49249249, 1495.4954955 , 1498.4984985 , 1501.5015015 , 1504.5045045 , 1507.50750751, 1510.51051051, 1513.51351351, 1516.51651652, 1519.51951952, 1522.52252252, 1525.52552553, 1528.52852853, 1531.53153153, 1534.53453453, 1537.53753754, 1540.54054054, 1543.54354354, 1546.54654655, 1549.54954955, 1552.55255255, 1555.55555556, 1558.55855856, 1561.56156156, 1564.56456456, 1567.56756757, 1570.57057057, 1573.57357357, 1576.57657658, 1579.57957958, 1582.58258258, 1585.58558559, 1588.58858859, 1591.59159159, 1594.59459459, 1597.5975976 , 1600.6006006 , 1603.6036036 , 1606.60660661, 1609.60960961, 1612.61261261, 1615.61561562, 1618.61861862, 1621.62162162, 1624.62462462, 1627.62762763, 1630.63063063, 1633.63363363, 1636.63663664, 1639.63963964, 1642.64264264, 1645.64564565, 1648.64864865, 1651.65165165, 1654.65465465, 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class elli.dispersions.dispersions.TableEpsilon(*args, **kwargs)[source]

Bases: Dispersion

Dispersion specified by a table of wavelengths (nm) and dielectric function values. Please not that this model will produce errors for wavelengths outside the provided wavelength range.

Single parameters:: lbda (list): Wavelengths in nm. Defaults to []. epsilon: Complex dielectric function values in the convention ε1 + iε2.

Defaults to [].
Repeated parameters:: –
Output:: The interpolation in the given wavelength range.

Create a dispersion law from a dielectric constant list.

‘lbda’ : Tuple with (Wavelength list, unit), or Wavelength list (in nm) ‘ε’ : Refractive index values (can be complex)

dielectric_function(lbda)[source]

Calculates the dielectric function in a given wavelength window.

Parameters: lbda (npt.ArrayLike) – The wavelength window with unit nm.
Returns: The dielectric function for each wavelength point.
Return type: npt.NDArray

rep_params_template = {}

single_params_template = {'epsilon': array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 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2846.84684685, 2849.84984985, 2852.85285285, 2855.85585586, 2858.85885886, 2861.86186186, 2864.86486486, 2867.86786787, 2870.87087087, 2873.87387387, 2876.87687688, 2879.87987988, 2882.88288288, 2885.88588589, 2888.88888889, 2891.89189189, 2894.89489489, 2897.8978979 , 2900.9009009 , 2903.9039039 , 2906.90690691, 2909.90990991, 2912.91291291, 2915.91591592, 2918.91891892, 2921.92192192, 2924.92492492, 2927.92792793, 2930.93093093, 2933.93393393, 2936.93693694, 2939.93993994, 2942.94294294, 2945.94594595, 2948.94894895, 2951.95195195, 2954.95495495, 2957.95795796, 2960.96096096, 2963.96396396, 2966.96696697, 2969.96996997, 2972.97297297, 2975.97597598, 2978.97897898, 2981.98198198, 2984.98498498, 2987.98798799, 2990.99099099, 2993.99399399, 2996.996997 , 3000. ])}

class elli.dispersions.dispersions.Tanguy(*args, **kwargs)[source]

Bases: Dispersion

Fractional dimensional Tanguy model. This model is an analytical expression of Wannier excitons, including bound and unbound states.

Single parameters:

A: Amplitude (eV). Defaults to 1. d: Dimensionality 1 < d <= 3. Defaults to 3. gamma: Excitonic broadening (eV). Defaults to 0.1. R : excitonic binding energy (eV). Defaults to 0.1. Eg : optical band gap energy (eV). Defaults to 1. a : Sellmeier coefficient for background dielectric constant (eV²).

Defaults to 0.

bSellmeier coefficient for background dielectric constant (eV²).: Defaults to 0.

Repeated parameters.

–

Output:

The Tanguy dispersion. Please refer to the references for a full formula.

References

C. Tanguy, Phys. Rev. Lett. 75, 4090 (1995). Errata, Phys. Rev. Lett. 76, 716 (1996). C. Tanguy, Phys. Rev. B. 60. 10660 (1990).

dielectric_function(lbda)[source]

Calculates the dielectric function in a given wavelength window.

Parameters: lbda (npt.ArrayLike) – The wavelength window with unit nm.
Returns: The dielectric function for each wavelength point.
Return type: npt.NDArray

static g(xsi, d)[source]

rep_params_template = {}

single_params_template = {'A': 1, 'Eg': 1, 'R': 0.1, 'a': 0, 'b': 0, 'd': 3, 'gamma': 0.1}

static xsi(z, R, Eg)[source]

class elli.dispersions.dispersions.TaucLorentz(*args, **kwargs)[source]

Bases: Dispersion

Tauc-Lorentz dispersion law. Model by Jellison and Modine.

Single parameters:: Eg: Bandgap energy. Defaults to 1.
Repeated parameters:: A: Strength of the absorption. Typically 10 < A < 200. Defaults to 20. E: Lorentz resonance energy (eV). Always keep Eg < E!!. Defaults to 1.5. C: Lorentz broadening (eV). Typically 0 < Ci < 10. Defaults to 1.
Output:: The Tauc lorentz dispersion. Please refer to the references for a full formula.

References

G.E. Jellision and F.A. Modine, Appl. Phys. Lett. 69 (3), 371-374 (1996) Erratum, G.E. Jellison and F.A. Modine, Appl. Phys. Lett 69 (14), 2137 (1996) H. Chen, W.Z. Shen, Eur. Phys. J. B. 43, 503-507 (2005)

dielectric_function(lbda)[source]

Calculates the dielectric function in a given wavelength window.

Parameters: lbda (npt.ArrayLike) – The wavelength window with unit nm.
Returns: The dielectric function for each wavelength point.
Return type: npt.NDArray

static eps1(E, Eg, Ai, Ei, Ci)[source]

rep_params_template = {'A': 20, 'C': 1, 'E': 1.5}

single_params_template = {'Eg': 1}

elli.dispersions package

Submodules

elli.dispersions.base_dispersion module

elli.dispersions.dispersions module

Module contents