Material database

Define permittivity functions to be used in the GTM method.

Utility functions such as Drude or phonon models are defined at the end of the script. Some materials have different definitions according to the frequency range, you should always carefully check if they match your expectations !

All permittivities are expected to be calculated at frequency f in Hz.

Change log:

15-10-2021:

  • Fixed ordering of KRS5 tabulated permittivity data

19-03-2020:

  • Fixed various bugs in the definition of single resonance materials

(GaN, AlN, MoO3, InN, hBN) and added SiC without weak phonon modes

20-09-2019:

  • Fixed database problems for some materials and some mistakes in the

permittivity functions. Commented out helper print functions.

GTM.Permittivities.eps_KRS5(f)

Tabulated values for KRS5 material

Parameters

f (array) – frequency (array or float)

Returns

permittivity (float or len(f)-array)

GTM.Permittivities.eps_SiCx(f)

Silicon carbide (SiC) in-plane permittivity (x-y)

Parameters

f (array) – frequency (array or float)

Returns

permittivity (float or len(f)-array)

GTM.Permittivities.eps_SiCz(f)

Silicon carbide (SiC) out-of-plane permittivity (z) without weak phonon modes

Parameters

f (array) – frequency (array or float)

Returns

permittivity (float or len(f)-array)

GTM.Permittivities.eps_SiC6Hx(f)

6H-Silicon carbide (6H-SiC) in-plane permittivity (x-y)

Parameters

f (array) – frequency (array or float)

Returns

permittivity (float or len(f)-array)

GTM.Permittivities.eps_SiC6Hz(f)

6H-Silicon carbide (6H-SiC) out-of-plane permittivity (z) with weak phonon modes

Parameters

f (array) – frequency (array or float)

Returns

permittivity (float or len(f)-array)

GTM.Permittivities.eps_GaNx(f)

Gallium nitride (GaN) ordinary axis permittivity (without excitons)

Parameters

f (array) – frequency (array or float)

Returns

permittivity (float or len(f)-array)

GTM.Permittivities.eps_GaNz(f)

Gallium nitride (GaN) extraordinary axis permittivity (without excitons)

Parameters

f (array) – frequency (array or float)

Returns

permittivity (float or len(f)-array)

GTM.Permittivities.eps_AlNx(f)

Aluminium nitride (AlN) ordinary axis permittivity (without excitons)

Parameters

f (array) – frequency (array or float)

Returns

permittivity (float or len(f)-array)

GTM.Permittivities.eps_AlNz(f)

Aliuminium nitride (AlN) extraordinary axis permittivity (without excitons)

Parameters

f (array) – frequency (array or float)

Returns

permittivity (float or len(f)-array)

GTM.Permittivities.eps_hBNx(f)

Hexagonal boron nitride (hBN) ordinary axis permittivity (without excitons)

Parameters

f (array) – frequency (array or float)

Returns

permittivity (float or len(f)-array)

GTM.Permittivities.eps_hBNz(f)

Hexagonal boron nitride (hBN) extraordinary axis permittivity (without excitons)

Parameters

f (array) – frequency (array or float)

Returns

permittivity (float or len(f)-array)

GTM.Permittivities.eps_InNx(f)

Indium nitride (InN) ordinary axis permittivity (without excitons)

Parameters

f (array) – frequency (array or float)

Returns

permittivity (float or len(f)-array)

GTM.Permittivities.eps_InNz(f)

Indium nitride (InN) extraordinary axis permittivity (without excitons)

Parameters

f (array) – frequency (array or float)

Returns

permittivity (float or len(f)-array)

GTM.Permittivities.eps_MoO3x(f)

Molybdenum oxide (MoO3) first axis permittivity

Parameters

f (array) – frequency (array or float)

Returns

permittivity (float or len(f)-array)

GTM.Permittivities.eps_MoO3y(f)

Molybdenum oxide (MoO3) second axis permittivity

Parameters

f (array) – frequency (array or float)

Returns

permittivity (float or len(f)-array)

GTM.Permittivities.eps_MoO3z(f)

Molybdenum oxide (MoO3) third axis permittivity

Parameters

f (array) – frequency (array or float)

Returns

permittivity (float or len(f)-array)

GTM.Permittivities.eps_GaAs(f)

Gallium arsenide (GaAs) permittivity (without excitons)

Parameters

f (array) – frequency (array or float)

Returns

permittivity (float or len(f)-array)

GTM.Permittivities.eps_GaP(f)

Gallium phosphide (GaP) permittivity (without excitons)

Parameters

f (array) – frequency (array or float)

Returns

permittivity (float or len(f)-array)

GTM.Permittivities.eps_InAs(f)

Indium arsenide (InAs) permittivity (without excitons)

Parameters

f (array) – frequency (array or float)

Returns

permittivity (float or len(f)-array)

GTM.Permittivities.eps_Al2O3o(f)

Aluminium oxide (Al2O3) ordinary axis permittivity

Parameters

f (array) – frequency (array or float)

Returns

permittivity (float or len(f)-array)

GTM.Permittivities.eps_Al2O3e(f)

Aluminium oxide (Al2O3) extraordinary axis permittivity

Parameters

f (array) – frequency (array or float)

Returns

permittivity (float or len(f)-array)

GTM.Permittivities.eps_BaTiO3(f)

Barium titanate (BaTiO3) permittivity

Parameters

f (array) – frequency (array or float)

Returns

permittivity (float or len(f)-array)

GTM.Permittivities.eps_SiN(f)

Low-stress silicon nitride (SiN) permittivity in the far and mid-infrared.

Parameters

f (array) – frequency (array or float)

Returns

permittivity (float or len(f)-array)

Typically for SiN_x PECVD deposited layers, from Cataldo et al., Optics Letters 37, 4200 (2017)

GTM.Permittivities.eps_Au(f)

Gold (Au) permittivity.

Parameters

f (array) – frequency (array or float)

Returns

permittivity (float or len(f)-array)

Attention, two models are used: a simple Drude model with parameters from Derkachova et al., Plasmonics 11, 941 (2016) (open access) or the tabulated data from Jonhson and Christy (refractiveindex.info) You should check carefully if this works out for you.

GTM.Permittivities.eps_Ag(f)

Silver (Ag) permittivity.

Parameters

f (array) – frequency (array or float)

Returns

permittivity (float or len(f)-array)

Attention, two models are used: a simple Drude model or tabulated data. Both are taken from Yang et al., Phys. Rev. B 91, 235137 (2015) You should check carefully if this works out for you.

GTM.Permittivities.eps_BaF2(f)

Barium fluoride (BaF2) refractive index.

Parameters

f (array) – frequency (array or float)

Returns

permittivity (float or len(f)-array)

Originally from Querry, Contractor Report CRDEC-CR-88009 (1987) downloaded from RefractiveIndex.info (2019)

GTM.Permittivities.eps_CaF2(f)

Calcium fluoride (CaF2) refractive index.

Parameters

f (array) – frequency (array or float)

Returns

permittivity (float or len(f)-array)

Originally from Malitson, Applied Optics 2, 1103 (1963) downloaded from RefractiveIndex.info (2019)

GTM.Permittivities.eps_SiO2(f)

Silicium dioxide (SiO2) refractive index.

Parameters

f (array) – frequency (array or float)

Returns

permittivity (float or len(f)-array)

Originally from Popova, Opt. Spectrosc. 33, 444 (1972) and and Malitson, J. Opt. Soc. Am. 55, 1205 (1965) downloaded from RefractiveIndex.info (2019)

GTM.Permittivities.eps_drude(f, fp, gammap, epsinf=1.0)

Drude-like permittivity

Parameters

  • f (array) – frequency (Hz)

  • fp (float) – plasma frequency (Hz)

  • gammap (float) – mean collision rate (Hz)

  • epsinf (float) – high frequency permittivity

Returns

complex permittivity

GTM.Permittivities.eps_Lorentz(f, fT, fL, gammaT, eps_inf)

Single Lorentz oscillator model

Parameters

  • f (array) – frequency (Hz)

  • fT (float) – frequency of the transverse phonon

  • fL (float) – frequency of the longitudinal phonon

  • gammaT (float) – damping rate of the transverse phonon

  • epsinf (float) – high-frequency permittivity

GTM.Permittivities.eps_1phonon(f, fT, fL, gammaT, gammaL, eps_inf)

1 phonon permittivity model

Parameters

  • f (array) – frequency (Hz)

  • fT (float) – frequency of the transverse phonon

  • fL (float) – frequency of the longitudinal phonon

  • gammaT (float) – damping rate of the transverse phonon

  • gammaL (float) – damping rate of the longitudinal phonon

  • epsinf (float) – high-frequency permittivity

Returns

complex permittivity

GTM.Permittivities.eps_3phonon(f, fT, fL, gammaT, gammaL, fT1, fL1, fT2, fL2, gammaTw, eps_inf)

3 phonons permittivity model

Parameters

  • f (array) – frequency (Hz)

  • fT (float) – frequency of the transverse phonon

  • fL (float) – frequency of the longitudinal phonon

  • gammaT (float) – relaxation rate of the transverse phonon

  • gammaL (float) – relaxation rate of the longitudinal phonon

  • fT1 (float) – frequency of the weak transverse phonon 1

  • fL1 (float) – frequency of the weak longitudinal phonon 1

  • fT2 (float) – frequency of the weak transverse phonon 2

  • fL2 (float) – frequency of the weak longitudinal phonon 2

  • gammaTw (float) – damping of the transverse phonon

  • epsinf (float) – high-frequency permittivity

Returns

complex permittivity