Si material model

1. Introduction

This page contains the OghmaNano material model for Si (Si).

Bulk crystalline silicon

The model is written in Lua and provides simulation-ready material parameterisations for use within OghmaNano. For documentation, licensing, references, and information about the scope and accuracy of these models, see the material scripting documentation.

2. Lua material model

Supporting definitions

-- See end of file for copyright, licensing and documentation links.

local material = {}

function material.name()
	local enabled = true

	return "Si", enabled
end

function material.description()
	local enabled = true

	return "Bulk crystalline silicon", enabled
end

function material.formula()
	local enabled = true

	return "Si", enabled
end

function material.Eg(state)
	-- Units: eV
	--
	-- Reference:
	-- Y. P. Varshni,
	-- "Temperature dependence of the energy gap in semiconductors",
	-- Physica, 34, 149-154, 1967.
	--
	-- Parameter set (Eg(0) = 1.170 eV, alpha = 4.73e-4 eV/K, beta = 636 K)
	-- as tabulated in S. M. Sze, "Physics of Semiconductor Devices",
	-- and the Ioffe NSM database. Gives Eg(300 K) = 1.124 eV.

	local enabled = true
	local T = state.T
	local value = 1.170 - 4.730e-4*T*T/(T + 636.0)

	return value, enabled
end

function material.Xi(state)
	-- Electron affinity
	-- Units: eV
	--
	-- Reference:
	-- S. M. Sze and K. K. Ng, "Physics of Semiconductor Devices",
	-- 3rd ed., Wiley, 2007.

	local enabled = true
	local value = 4.05

	return value, enabled
end

function material.me(state)
    local enabled = true
    -- (001) ground-subband confinement mass = m_l = 0.98 (2 z-valleys).
    -- WARNING: multivalley material; 4 in-plane valleys (m_t=0.19) ignored here.
    -- Use the multivalley solver for full subband structure / DOS. Ref: Green JAP 67,2944(1990).
    local value = 0.98
    return value, enabled
end

function material.mh(state)
    local enabled = true
    -- HH[001]: g1=4.22 g2=0.39 -> 1/(4.22-0.78). Warped VB; approximate. (Lawaetz 1971)
    local value = 0.29
    return value, enabled
end

function material.Nc(state)
	-- Effective conduction-band density of states
	-- Units: m^-3
	--
	-- Reference:
	-- M. A. Green,
	-- "Intrinsic concentration, effective densities of states, and
	-- effective mass in silicon", J. Appl. Phys. 67, 2944-2954, 1990.
	-- Recommended Nc(300 K) = 2.86e19 cm^-3 = 2.86e25 m^-3.
	--
	-- Note: the (T/300)^1.5 form is the simple parabolic-band model;
	-- Green gives a weak additional T-dependence via the effective mass.

	local enabled = true
	local T = state.T
	local value = 2.86e25*(T/300.0)^1.5

	return value, enabled
end

function material.Nv(state)
	-- Effective valence-band density of states
	-- Units: m^-3
	--
	-- Reference:
	-- M. A. Green,
	-- "Intrinsic concentration, effective densities of states, and
	-- effective mass in silicon", J. Appl. Phys. 67, 2944-2954, 1990.
	-- Recommended Nv(300 K) = 3.10e19 cm^-3 = 3.10e25 m^-3.

	local enabled = true
	local T = state.T
	local value = 3.10e25*(T/300.0)^1.5

	return value, enabled
end

function material.mu_e(state)
	-- Low-field electron mobility
	-- Units: m^2 V^-1 s^-1
	--
	-- Reference:
	-- C. Jacoboni, C. Canali, G. Ottaviani, A. Alberigi Quaranta,
	-- "A review of some charge transport properties of silicon",
	-- Solid-State Electronics, 20, 77-89, 1977.
	-- Lattice-limited mu_n(300 K) = 1417 cm^2/V/s = 0.1417 m^2/V/s,
	-- temperature exponent -2.5.
	--
	-- Note: this is the intrinsic (lattice) mobility only; no
	-- doping / ionised-impurity dependence is included.

	local enabled = true
	local T = state.T
	local value = 0.1417*(300.0/T)^2.5

	return value, enabled
end

function material.mue_x(state)
	return material.mu_e(state)
end

function material.mue_y(state)
	return material.mu_e(state)
end

function material.mue_z(state)
	return material.mu_e(state)
end

function material.mu_h(state)
	-- Low-field hole mobility
	-- Units: m^2 V^-1 s^-1
	--
	-- Reference:
	-- C. Jacoboni, C. Canali, G. Ottaviani, A. Alberigi Quaranta,
	-- "A review of some charge transport properties of silicon",
	-- Solid-State Electronics, 20, 77-89, 1977.
	-- Lattice-limited mu_p(300 K) = 470.5 cm^2/V/s = 0.04705 m^2/V/s,
	-- temperature exponent -2.2.

	local enabled = true
	local T = state.T
	local value = 0.04705*(300.0/T)^2.2

	return value, enabled
end

function material.muh_x(state)
	return material.mu_h(state)
end

function material.muh_y(state)
	return material.mu_h(state)
end

function material.muh_z(state)
	return material.mu_h(state)
end

function material.epsilonr(state)
	-- Relative static permittivity
	-- Dimensionless
	--
	-- Reference:
	-- S. M. Sze and K. K. Ng, "Physics of Semiconductor Devices",
	-- 3rd ed., Wiley, 2007.

	local enabled = true
	local value = 11.7

	return value, enabled
end

function material.free_to_free_recombination(state)
	-- Radiative (band-to-band) recombination coefficient
	-- Units: m^3 s^-1
	--
	-- Reference:
	-- T. Trupke, M. A. Green, P. Wurfel, P. P. Altermatt, A. Wang,
	-- J. Zhao, R. Corkish,
	-- "Temperature dependence of the radiative recombination
	-- coefficient of intrinsic crystalline silicon",
	-- J. Appl. Phys. 94, 4930-4937, 2003.
	-- B(300 K) = 4.73e-15 cm^3/s = 4.73e-21 m^3/s.
	--
	-- Silicon is an indirect-gap semiconductor, so B is small.
	-- Trupke et al. give a full T-dependence (B decreases with T);
	-- only the 300 K value is used here to match the file format.

	local enabled = true
	local value = 4.73e-21

	return value, enabled
end

function material.auger_Cn(state)
	-- Electron Auger recombination coefficient (eeh process)
	-- Units: m^6 s^-1
	--
	-- Reference:
	-- J. Dziewior and W. Schmid,
	-- "Auger coefficients for highly doped and highly excited
	-- silicon", Appl. Phys. Lett. 31, 346-348, 1977.
	-- Cn = 2.8e-31 cm^6/s = 2.8e-43 m^6/s.
	--
	-- Note: for high-quality Si solar cells, injection- and
	-- doping-dependent (Coulomb-enhanced) parameterisations are more
	-- accurate, e.g. Richter et al., Phys. Rev. B 86, 165202 (2012).

	local enabled = true
	local value = 2.8e-43

	return value, enabled
end

function material.auger_Cp(state)
	-- Hole Auger recombination coefficient (ehh process)
	-- Units: m^6 s^-1
	--
	-- Reference:
	-- J. Dziewior and W. Schmid,
	-- "Auger coefficients for highly doped and highly excited
	-- silicon", Appl. Phys. Lett. 31, 346-348, 1977.
	-- Cp = 0.99e-31 cm^6/s = 0.99e-43 m^6/s.

	local enabled = true
	local value = 0.99e-43

	return value, enabled
end

function material.ss_srh_trap_energy(state)
	-- SRH trap energy relative to the middle of the band gap.
	-- Units: eV
	--
	-- Positive values are above mid-gap (towards the conduction band).
	-- Negative values are below mid-gap (towards the valence band).

	local enabled = true
	local value = 0.0

	return value, enabled
end

function material.ss_srh_Nt(state)
	-- SRH trap density
	-- Units: m^-3
	--
	-- This is entirely material-quality dependent and should be set
	-- from the intended bulk lifetime. The value below is a
	-- representative placeholder for device-grade silicon.

	local enabled = true
	local value = 1.0e21

	return value, enabled
end

function material.ss_srh_sigma_n(state)
	-- Electron capture cross section
	-- Units: m^2
	--
	-- Representative value ~1e-15 cm^2 = 1e-19 m^2.

	local enabled = true
	local value = 1.0e-19

	return value, enabled
end

function material.ss_srh_sigma_p(state)
	-- Hole capture cross section
	-- Units: m^2
	--
	-- Representative value ~1e-15 cm^2 = 1e-19 m^2.

	local enabled = true
	local value = 1.0e-19

	return value, enabled
end

function material.thermal_kl(state)
	-- Thermal conductivity
	-- Units: W m^-1 K^-1
	--
	-- Reference:
	-- C. J. Glassbrenner and G. A. Slack,
	-- "Thermal conductivity of silicon and germanium from 3 K to the
	-- melting point", Phys. Rev. 134, A1058-A1069, 1964.
	-- kappa(300 K) ~ 148 W/m/K; near room temperature kappa decreases
	-- with T with an effective exponent of about -1.35.

	local enabled = true
	local T = state.T
	local value = 148.0*(300.0/T)^1.35

	return value, enabled
end

function material.heat_capacity(state)
	-- Specific heat capacity
	-- Units: J kg^-1 K^-1
	--
	-- Reference:
	-- A. S. Okhotin et al., "Thermophysical Properties of
	-- Semiconductors", Atom Publ. House, Moscow, 1972;
	-- also standard tables. c_p(300 K) ~ 700 J/kg/K.

	local enabled = true
	local value = 700.0

	return value, enabled
end

function material.density(state)
	-- Mass density
	-- Units: kg m^-3
	--
	-- Reference:
	-- S. M. Sze and K. K. Ng, "Physics of Semiconductor Devices",
	-- 3rd ed., Wiley, 2007. rho = 2.329 g/cm^3.

	local enabled = true
	local value = 2329.0

	return value, enabled
end

function material.lattice_constant(state)
	-- Cubic lattice constant
	-- Units: m
	--
	-- Reference:
	-- Y. Okada and Y. Tokumaru,
	-- "Precise determination of lattice parameter and thermal
	-- expansion coefficient of silicon between 300 and 1500 K",
	-- J. Appl. Phys. 56, 314-320, 1984.
	-- a(300 K) = 5.43102 A; linear expansion ~2.6e-6 /K near 300 K.

	local enabled = true
	local T = state.T
	local a300 = 5.43102e-10
	local expansion = 2.6e-6
	local value = a300*(1.0 + expansion*(T - 300.0))

	return value, enabled
end

function material.thermal_tau_e(state)
	-- Electron energy relaxation time towards the lattice temperature
	-- Units: s
	--
	-- Value basis: Conventional semiconductor estimate
	-- Confidence: Medium
	--
	-- Reference:
	-- https://doi.org/10.1109/16.381985
	--
	-- Comments:
	-- Representative sub-ps energy relaxation for a conventional semiconductor
	-- near room temperature. Actual value is field and carrier-energy
	-- dependent.

	local enabled = true
	local value = 3.000000e-13

	return value, enabled
end

function material.thermal_tau_h(state)
	-- Hole energy relaxation time towards the lattice temperature
	-- Units: s
	--
	-- Value basis: Conventional semiconductor estimate
	-- Confidence: Medium
	--
	-- Reference:
	-- https://doi.org/10.1109/16.381985
	--
	-- Comments:
	-- Representative sub-ps energy relaxation for a conventional semiconductor
	-- near room temperature. Actual value is field and carrier-energy
	-- dependent.

	local enabled = true
	local value = 3.000000e-13

	return value, enabled
end

------------------------------------------------------------------------
-- SIX-BAND LUTTINGER-KOHN VALENCE PARAMETERS (Silicon)
------------------------------------------------------------------------

function material.gamma1(state)
	-- Luttinger valence-band parameter gamma1 (dimensionless).
	--
	-- Full reference:
	-- P. Lawaetz,
	-- "Valence-Band Parameters in Cubic Semiconductors",
	-- Physical Review B 4, 3460-3467 (1971).
	-- DOI: 10.1103/PhysRevB.4.3460
	-- (Reproduced in O. Madelung, "Semiconductors: Data Handbook",
	--  3rd ed., Springer, 2004.)

	local enabled = true
	local value = 4.22

	return value, enabled
end

function material.gamma2(state)
	-- Luttinger valence-band parameter gamma2 (dimensionless).
	-- Quoted positive (|gamma2|). Some works tabulate -gamma2; use magnitude
	-- consistent with your Hamiltonian assembly.
	--
	-- Full reference:
	-- P. Lawaetz,
	-- "Valence-Band Parameters in Cubic Semiconductors",
	-- Physical Review B 4, 3460-3467 (1971).
	-- DOI: 10.1103/PhysRevB.4.3460

	local enabled = true
	local value = 0.39

	return value, enabled
end

function material.gamma3(state)
	-- Luttinger valence-band parameter gamma3 (dimensionless).
	--
	-- Full reference:
	-- P. Lawaetz,
	-- "Valence-Band Parameters in Cubic Semiconductors",
	-- Physical Review B 4, 3460-3467 (1971).
	-- DOI: 10.1103/PhysRevB.4.3460

	local enabled = true
	local value = 1.44

	return value, enabled
end

function material.delta_so(state)
	-- Spin-orbit split-off energy delta_so (eV).
	-- Splitting of the J=1/2 SO band below the J=3/2 HH/LH edge.
	--
	-- Full reference:
	-- O. Madelung (Ed.),
	-- "Semiconductors: Data Handbook", 3rd ed.,
	-- Springer, Berlin, 2004, Si section.
	-- (Original: L. D. Laude, F. H. Pollak, M. Cardona,
	--  Physical Review B 3, 2623 (1971); DOI: 10.1103/PhysRevB.3.2623.)

	local enabled = true
	local value = 0.044

	return value, enabled
end

function material.av(state)
	-- Valence-band-average HYDROSTATIC deformation potential a_v (eV).
	-- Convention: Delta Ev,av = a_v * Tr(epsilon), tensile positive, a_v > 0.
	-- Rigidly shifts the 6x6 block; does not split HH/LH/SO. See header note *.
	-- MEDIUM confidence: absolute VB hydrostatic potentials are convention- and
	-- reference-level dependent (literature spread ~2.1-2.5 eV for Si).
	--
	-- Full reference:
	-- C. G. Van de Walle,
	-- "Band lineups and deformation potentials in the model-solid theory",
	-- Physical Review B 39, 1871-1883 (1989).
	-- DOI: 10.1103/PhysRevB.39.1871

	local enabled = true
	local value = 2.46

	return value, enabled
end

function material.b(state)
	-- Tetragonal (uniaxial [001]) shear deformation potential b (eV).
	-- Bir-Pikus convention, b < 0. Splits HH from LH under [001] strain.
	-- MEDIUM confidence (well established; ~ -2.1 eV widely used).
	--
	-- Full reference:
	-- G. L. Bir and G. E. Pikus,
	-- "Symmetry and Strain-Induced Effects in Semiconductors",
	-- Wiley, New York, 1974.
	-- Value: O. Madelung (Ed.), "Semiconductors: Data Handbook", 3rd ed.,
	-- Springer, 2004, Si section (b = -2.1 eV).

	local enabled = true
	local value = -2.10

	return value, enabled
end

function material.d(state)
	-- Trigonal (rhombohedral, [111]) shear deformation potential d (eV).
	-- Bir-Pikus convention, d < 0. Couples to off-diagonal shear (eps_xy,...).
	-- MEDIUM confidence: literature spread for Si is ~ -4.8 to -5.3 eV.
	--
	-- Full reference:
	-- G. L. Bir and G. E. Pikus,
	-- "Symmetry and Strain-Induced Effects in Semiconductors",
	-- Wiley, New York, 1974.
	-- Value: O. Madelung (Ed.), "Semiconductors: Data Handbook", 3rd ed.,
	-- Springer, 2004, Si section (d ~= -4.85 eV).

	local enabled = true
	local value = -4.85

	return value, enabled
end

------------------------------------------------------------------------
-- SHARED STRUCTURAL PARAMETERS (Silicon) -- used by BOTH solvers
------------------------------------------------------------------------

function material.lattice_a(state)
	-- Cubic lattice constant (metres), 300 K.
	--
	-- Full reference:
	-- O. Madelung (Ed.),
	-- "Semiconductors: Data Handbook", 3rd ed., Springer, 2004, Si section.
	-- (a_Si = 5.4310 Angstrom at 300 K.)

	local enabled = true
	local value = 5.431e-10

	return value, enabled
end

function material.C11(state)
	-- Elastic stiffness C11 (Pa), 300 K.
	--
	-- Full reference:
	-- J. J. Wortman and R. A. Evans,
	-- "Young's Modulus, Shear Modulus, and Poisson's Ratio in Silicon
	--  and Germanium", Journal of Applied Physics 36, 153-156 (1965).
	-- DOI: 10.1063/1.1713863
	-- (C11 = 165.8 GPa; consistent with McSkimin ultrasonic data.)

	local enabled = true
	local value = 165.8e9

	return value, enabled
end

function material.C12(state)
	-- Elastic stiffness C12 (Pa), 300 K.
	--
	-- Full reference:
	-- J. J. Wortman and R. A. Evans,
	-- "Young's Modulus, Shear Modulus, and Poisson's Ratio in Silicon
	--  and Germanium", Journal of Applied Physics 36, 153-156 (1965).
	-- DOI: 10.1063/1.1713863
	-- (C12 = 63.9 GPa.)

	local enabled = true
	local value = 63.9e9

	return value, enabled
end

------------------------------------------------------------------------
-- SIX-DELTA-VALLEY CONDUCTION PARAMETERS (Silicon)
-- Six valleys along +/-x, +/-y, +/-z (near the X points).
------------------------------------------------------------------------

function material.qw_ml(state)
	-- Longitudinal effective mass of the Si Delta valleys (units of m0).
	-- HIGH confidence. Precise cyclotron-resonance value.
	-- NOTE: coarser textbooks quote ml = 0.98 m0; 0.916 m0 is the more
	-- accurate stress-cyclotron-resonance figure and matches your validated
	-- solver.
	--
	-- Full reference:
	-- J. C. Hensel, H. Hasegawa, M. Nakayama,
	-- "Cyclotron Resonance in Uniaxially Stressed Silicon. II. Nature of the
	--  Covalent Bond", Physical Review 138, A225-A238 (1965).
	-- DOI: 10.1103/PhysRev.138.A225

	local enabled = true
	local value = 0.916

	return value, enabled
end

function material.qw_mt(state)
	-- Transverse effective mass of the Si Delta valleys (units of m0).
	-- HIGH confidence.
	--
	-- Full reference:
	-- J. C. Hensel, H. Hasegawa, M. Nakayama,
	-- "Cyclotron Resonance in Uniaxially Stressed Silicon. II.",
	-- Physical Review 138, A225-A238 (1965).
	-- DOI: 10.1103/PhysRev.138.A225

	local enabled = true
	local value = 0.190

	return value, enabled
end

function material.qw_Xi_d(state)
	-- Dilatation deformation potential Xi_d of the Si Delta valleys (eV).
	-- Convention: Delta Ec = Xi_d*Tr(eps) + Xi_u*(n.eps.n). HIGH confidence.
	-- This is the value your existing solver was validated against (1.1 eV).
	--
	-- Full reference:
	-- M. V. Fischetti and S. E. Laux,
	-- "Band structure, deformation potentials, and carrier mobility in
	--  strained Si, Ge, and SiGe alloys",
	-- Journal of Applied Physics 80, 2234-2252 (1996).
	-- DOI: 10.1063/1.363052
	-- (Convention originally: C. Herring and E. Vogt, Phys. Rev. 101, 944
	--  (1956); DOI: 10.1103/PhysRev.101.944.)

	local enabled = true
	local value = 1.1

	return value, enabled
end

function material.qw_Xi_u(state)
	-- Uniaxial (shear) deformation potential Xi_u of the Si Delta valleys (eV).
	-- Convention as in qw_Xi_d. MEDIUM confidence: authoritative values span
	-- ~8.5-9.3 eV (Balslev 8.6; Fischetti-Laux-cited 9.16; first-principles
	-- 8.8-9.0). 9.16 eV chosen to match your validated solver and lies within
	-- the accepted range.
	--
	-- Full reference:
	-- I. Balslev,
	-- "Influence of Uniaxial Stress on the Indirect Absorption Edge in
	--  Silicon and Germanium", Physical Review 143, 636-647 (1966).
	-- DOI: 10.1103/PhysRev.143.636
	-- (See also C. Herring and E. Vogt, Phys. Rev. 101, 944 (1956).)

	local enabled = true
	local value = 9.16

	return value, enabled
end

function material.C44(state)
    -- Elastic stiffness constant C44
    -- Units: Pa
    --
    -- Crystal phase: diamond (Oh), listed under zincblende profile.
    --
    -- Reference:
    -- M. Levinshtein, S. Rumyantsev, M. Shur (eds.),
    -- Handbook Series on Semiconductor Parameters, Vols. 1 and 2
    -- (World Scientific, 1996 and 1999), as reproduced in the Ioffe
    -- Institute NSM archive (www.ioffe.ru/SVA/NSM/Semicond/).
    -- (room-temperature data of McSkimin (1953) and Nikanorov et al. (1971)).
    --
    -- Notes:
    -- 7.96e11 dyn/cm^2 = 79.6 GPa -> 79.6e9 Pa (300 K).

    local enabled = true
    local value = 79.6e9

    return value, enabled
end

function material.ac(state)
    -- Hydrostatic conduction-band deformation potential ac
    -- Units: eV
    --
    -- Reference:
    -- C. G. Van de Walle,
    -- "Band lineups and deformation potentials in the model-solid theory,"
    -- Phys. Rev. B 39, 1871 (1989).
    -- DOI: 10.1103/PhysRevB.39.1871
    -- Delta-valley values Xi_d = 1.10 eV, Xi_u = 9.16 eV as quoted from this
    -- paper in arXiv:2604.13435 (SiGe/Si(111) qubit study).
    --
    -- Notes:
    -- Silicon's conduction minimum is the Delta valley. The hydrostatic
    -- conduction deformation potential for that valley in the model-solid
    -- (absolute) convention is ac = Xi_d + Xi_u/3 = 1.10 + 9.16/3 = 4.15 eV.
    -- Van de Walle's band-gap combination Xi_d + Xi_u/3 - a_v = 1.72 eV with
    -- a_v = 2.46 eV gives the same 4.18 eV within rounding.
    -- Sign convention: model-solid/absolute (dE_c = ac * Tr(eps)).
    -- This is NOT a Gamma-valley ac as used for direct-gap III-Vs.

    local enabled = true
    local value = 4.15

    return value, enabled
end

function material.phonon_lo_energy(state)
    -- Representative LO phonon energy for polar optical (Frohlich) scattering
    -- Units: eV
    --
    -- Reference:
    -- M. Levinshtein, S. Rumyantsev, M. Shur (eds.),
    -- Handbook Series on Semiconductor Parameters, Vols. 1 and 2
    -- (World Scientific, 1996 and 1999), as reproduced in the Ioffe
    -- Institute NSM archive (www.ioffe.ru/SVA/NSM/Semicond/).
    -- (nu_LTO(Gamma) = 15.5 THz at 300 K; dispersion data of Dolling (1963)).
    --
    -- Notes:
    -- Si is non-polar: LO and TO degenerate at Gamma, NO Frohlich coupling
    -- (eps_s = eps_inf). Value given only as the zone-centre optical phonon
    -- energy (non-polar optical DP scattering).
    -- 15.5 x 4.135667e-3 = 0.06410 eV (Raman ~520 cm^-1 = 64.5 meV).

    local enabled = true
    local value = 0.06410

    return value, enabled
end

function material.epsilon_static(state)
    -- Static relative dielectric constant (lattice + electronic)
    -- Dimensionless
    --
    -- Reference:
    -- M. Levinshtein, S. Rumyantsev, M. Shur (eds.),
    -- Handbook Series on Semiconductor Parameters, Vols. 1 and 2
    -- (World Scientific, 1996 and 1999), as reproduced in the Ioffe
    -- Institute NSM archive (www.ioffe.ru/SVA/NSM/Semicond/).
    --
    -- Notes:
    -- Si: 11.7 (300 K).

    local enabled = true
    local value = 11.7

    return value, enabled
end

function material.epsilon_inf(state)
    -- High-frequency (electronic) relative dielectric constant
    -- Dimensionless
    --
    -- Reference:
    -- M. Levinshtein, S. Rumyantsev, M. Shur (eds.),
    -- Handbook Series on Semiconductor Parameters, Vols. 1 and 2
    -- (World Scientific, 1996 and 1999), as reproduced in the Ioffe
    -- Institute NSM archive (www.ioffe.ru/SVA/NSM/Semicond/).
    --
    -- Notes:
    -- Non-polar diamond lattice: eps_inf = eps_s = 11.7 (no IR-active
    -- lattice polarisation; Frohlich coupling vanishes).

    local enabled = true
    local value = 11.7

    return value, enabled
end

function material.e14(state)
    -- Zincblende piezoelectric stress coefficient e14
    -- Units: C m^-2
    --
    -- Reference:
    -- J. F. Nye, Physical Properties of Crystals
    -- (Oxford University Press, 1957) - piezoelectric tensor vanishes
    -- identically in centrosymmetric point groups.
    --
    -- Notes:
    -- Si is diamond structure (m-3m, centrosymmetric): bulk piezoelectricity
    -- vanishes identically; e14 = 0 exactly by symmetry.

    local enabled = true
    local value = 0.0

    return value, enabled
end

function material.print()
	local state = {
		T = 300.0,
		x = 0.0,
		y = 0.0,
		z = 0.0,
		photon_density = 0.0,
	}

	print(string.format("Material:               %s", material.name()))
	print(string.format("Description:            %s", material.description()))
	print(string.format("Formula:                %s", material.formula()))
	print(string.format("Temperature:            %.2f K", state.T))
	print(string.format("Position:               %.6e, %.6e, %.6e m", state.x, state.y, state.z))
	print(string.format("Photon density:         %.6e m^-3", state.photon_density))

	print(string.format("Band gap:               %.6f eV", material.Eg(state)))
	print(string.format("Electron affinity:      %.6f eV", material.Xi(state)))
	print(string.format("Electron mobility:      %.6e m^2/V/s", material.mu_e(state)))
	print(string.format("Hole mobility:          %.6e m^2/V/s", material.mu_h(state)))
	print(string.format("Nc:                     %.6e m^-3", material.Nc(state)))
	print(string.format("Nv:                     %.6e m^-3", material.Nv(state)))
	print(string.format("Relative permittivity:  %.6f", material.epsilonr(state)))

	print(string.format("Radiative coeff.:       %.6e m^3/s", material.free_to_free_recombination(state)))
	print(string.format("Electron Auger coeff.:  %.6e m^6/s", material.auger_Cn(state)))
	print(string.format("Hole Auger coeff.:      %.6e m^6/s", material.auger_Cp(state)))

	print(string.format("SRH trap energy:        %.6f eV", material.ss_srh_trap_energy(state)))
	print(string.format("SRH trap density:       %.6e m^-3", material.ss_srh_Nt(state)))
	print(string.format("SRH sigma n:            %.6e m^2", material.ss_srh_sigma_n(state)))
	print(string.format("SRH sigma p:            %.6e m^2", material.ss_srh_sigma_p(state)))

	print(string.format("Electron energy relax.:  %.6e s", material.thermal_tau_e(state)))
	print(string.format("Hole energy relax.:      %.6e s", material.thermal_tau_h(state)))

	print(string.format("Thermal conductivity:   %.6e W/m/K", material.thermal_kl(state)))
	print(string.format("Heat capacity:          %.6e J/kg/K", material.heat_capacity(state)))
	print(string.format("Mass density:           %.6e kg/m^3", material.density(state)))
end

return material

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-- All rights reserved.
--
-- This file is part of the OghmaNano Materials Model Library.
--
-- Website:
-- https://www.oghma-nano.com
--
-- Documentation and accuracy statement:
-- https://www.oghma-nano.com/manual/material-scripts.html
--
-- These material models are provided to support scientific research and
-- semiconductor device simulation. If you find them useful, please cite
-- OghmaNano where appropriate. Please do not redistribute these files or
-- incorporate them into other software or databases without permission.
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