CdSe material model

1. Introduction

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

Bulk crystalline cadmium selenide (wurtzite)

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 "CdSe", enabled
end

function material.description()
	local enabled = true

	return "Bulk crystalline cadmium selenide (wurtzite)", enabled
end

function material.formula()
	local enabled = true

	return "CdSe", 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.
	--
	-- Wurtzite CdSe parameter set (Eg(0) = 1.84 eV, alpha = 5.5e-4
	-- eV/K, beta = 230 K); representative II-VI compilation values
	-- (e.g. Landolt-Boernstein). Gives Eg(300 K) = 1.75 eV. Direct gap.
	--
	-- Note: reported CdSe room-temperature gaps span ~1.70-1.75 eV
	-- depending on crystal form and film quality. Bulk value; note that
	-- quantum-confined CdSe (nanocrystals) has a size-dependent gap
	-- well above this, which is a confinement effect not described by a
	-- bulk material file.

	local enabled = true
	local T = state.T
	local value = 1.84 - 5.5e-4*T*T/(T + 230.0)

	return value, enabled
end

function material.Xi(state)
	-- Electron affinity
	-- Units: eV
	--
	-- Reference:
	-- Device literature.
	--
	-- Note: reported CdSe electron affinity scatters (~4.5-5.0 eV);
	-- 4.5 eV used here. For heterojunctions, fix the band offset from a
	-- measured alignment rather than affinity differencing.

	local enabled = true
	local value = 4.5

	return value, enabled
end

function material.me(state)
    local enabled = true
    local value = 0.13    -- wurtzite, near-isotropic; c-axis confinement (Adachi 2005)
    return value, enabled
end

function material.mh(state)
    local enabled = true
    -- HH; anisotropic (in-plane ~0.45, along-c heavier). Approximate scalar.
    local value = 0.45
    return value, enabled
end

function material.Nc(state)
	-- Effective conduction-band density of states
	-- Units: m^-3
	--
	-- Reference:
	-- From electron effective mass m_e* ~ 0.13 m0 (CdSe).
	-- Nc(300 K) ~ 1.2e18 cm^-3 = 1.2e24 m^-3.
	--
	-- Note: the (T/300)^1.5 form is the simple parabolic-band model.

	local enabled = true
	local T = state.T
	local value = 1.2e24*(T/300.0)^1.5

	return value, enabled
end

function material.Nv(state)
	-- Effective valence-band density of states
	-- Units: m^-3
	--
	-- Reference:
	-- From the (heavy) hole effective mass m_h* ~ 0.9 m0 (CdSe).
	-- Nv(300 K) ~ 2.0e19 cm^-3 = 2.0e25 m^-3.

	local enabled = true
	local T = state.T
	local value = 2.0e25*(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:
	-- CdSe experimental compilation.
	-- Representative mu_n(300 K) ~ 500 cm^2/V/s = 0.05 m^2/V/s,
	-- temperature dependence approximately (300/T)^1.5.
	--
	-- IMPORTANT: strongly process dependent. Single-crystal CdSe
	-- reaches ~650-720 cm^2/V/s; polycrystalline / thin-film CdSe is
	-- much lower (grain-boundary scattering). Set from your film.

	local enabled = true
	local T = state.T
	local value = 0.05*(300.0/T)^1.5

	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:
	-- CdSe experimental compilation.
	-- Representative mu_p(300 K) ~ 50 cm^2/V/s = 0.005 m^2/V/s,
	-- temperature dependence approximately (300/T)^1.5.
	--
	-- Note: CdSe is intrinsically n-type and hard to make p-type; hole
	-- transport is poorly constrained and rarely dominant.

	local enabled = true
	local T = state.T
	local value = 0.005*(300.0/T)^1.5

	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:
	-- CdSe compilation.
	-- Static value ~10.2 (high-frequency value ~6.2).
	--
	-- Note: wurtzite CdSe is anisotropic about the c-axis; a
	-- representative value is used.

	local enabled = true
	local value = 10.2

	return value, enabled
end

function material.free_to_free_recombination(state)
	-- Radiative (band-to-band) recombination coefficient
	-- Units: m^3 s^-1
	--
	-- Reference:
	-- Representative direct-gap II-VI value,
	-- ~1e-10 cm^3/s = 1e-16 m^3/s.
	--
	-- CdSe is direct-gap, so B is significant. Poorly characterised in
	-- bulk; adjust by hand.

	local enabled = true
	local value = 1.0e-16

	return value, enabled
end

function material.auger_Cn(state)
	-- Electron Auger recombination coefficient
	-- Units: m^6 s^-1
	--
	-- Reference:
	-- Representative placeholder, ~1e-30 cm^6/s = 1e-42 m^6/s.
	--
	-- Note: bulk CdSe Auger coefficients are poorly characterised.
	-- (Auger is prominent in CdSe nanocrystals, but that is a
	-- confinement effect, not a bulk coefficient.) Placeholder only.

	local enabled = true
	local value = 1.0e-42

	return value, enabled
end

function material.auger_Cp(state)
	-- Hole Auger recombination coefficient
	-- Units: m^6 s^-1
	--
	-- Reference:
	-- Representative placeholder, ~1e-30 cm^6/s = 1e-42 m^6/s.
	--
	-- Note: as for Cn, poorly characterised. Placeholder only.

	local enabled = true
	local value = 1.0e-42

	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
	--
	-- Material-quality dependent; set from the intended bulk lifetime.
	-- Representative placeholder for device-grade material.

	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:
	-- CdSe compilation.
	-- kappa(300 K) ~ 6 W/m/K; near room temperature kappa decreases
	-- with T with an effective exponent of about -1.4.
	--
	-- Note: CdSe has a notably low thermal conductivity (reported
	-- ~4-9 W/m/K); thin-film values are lower still.

	local enabled = true
	local T = state.T
	local value = 6.0*(300.0/T)^1.4

	return value, enabled
end

function material.heat_capacity(state)
	-- Specific heat capacity
	-- Units: J kg^-1 K^-1
	--
	-- Reference:
	-- CdSe compilation. c_p(300 K) ~ 270 J/kg/K.

	local enabled = true
	local value = 270.0

	return value, enabled
end

function material.density(state)
	-- Mass density
	-- Units: kg m^-3
	--
	-- Reference:
	-- CdSe compilation. rho = 5.81 g/cm^3 (wurtzite).

	local enabled = true
	local value = 5810.0

	return value, enabled
end

function material.lattice_constant(state)
	-- Lattice constant (hexagonal a-axis)
	-- Units: m
	--
	-- Reference:
	-- CdSe compilation (Landolt-Boernstein).
	-- a(300 K) = 4.299 A; linear expansion ~4.9e-6 /K near 300 K.
	--
	-- IMPORTANT: wurtzite CdSe is hexagonal, with two lattice constants
	-- a = 4.299 A and c = 7.010 A. This single scalar field holds the
	-- a-axis constant only; the c-axis constant is not representable
	-- here.
	--
	-- Note: CdSe also has a metastable zinc-blende (cubic) form with
	-- a = 6.077 A. This file describes the wurtzite phase.

	local enabled = true
	local T = state.T
	local a300 = 4.299e-10
	local expansion = 4.9e-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: II-VI family estimate
	-- Confidence: Low
	--
	-- Reference:
	-- https://doi.org/10.1109/16.381985
	--
	-- Comments:
	-- II-VI family default. Direct carrier-specific hydrodynamic parameters are
	-- scarce; use sensitivity analysis.

	local enabled = true
	local value = 1.000000e-12

	return value, enabled
end

function material.thermal_tau_h(state)
	-- Hole energy relaxation time towards the lattice temperature
	-- Units: s
	--
	-- Value basis: II-VI family estimate
	-- Confidence: Low
	--
	-- Reference:
	-- https://doi.org/10.1109/16.381985
	--
	-- Comments:
	-- II-VI family default. Direct carrier-specific hydrodynamic parameters are
	-- scarce; use sensitivity analysis.

	local enabled = true
	local value = 1.000000e-12

	return value, enabled
end


-- CdSe (wurtzite, II-VI). Only crystal-field and spin-orbit splittings
-- are established. A serious search (incl. the wurtzite valence-band
-- review, Solid State Commun. 1996) confirms there is NO complete
-- A1..A6/Ep/deformation set for wurtzite CdSe in the Chuang-Chang/RSP
-- convention: that review reduces the description to gamma1,gamma2 and
-- states explicitly that even the spherical-cubic reduction FAILS for
-- CdSe. So the dispersion, conduction and deformation parameters are
-- disabled (return 0.0) rather than invented.

function material.qw_delta1(state)
-- Crystal-field splitting delta1. Units: eV (positive; Gamma9 top).
-- Bulk wurtzite CdSe crystal-field ~ 0.025-0.041 eV; 0.040 used.
--
-- Al. L. Efros et al., exciton/crystal-field data for wurtzite CdSe,
--  arXiv:cond-mat/0106108 (2001).
--
-- O. Madelung, "Semiconductors: Data Handbook," 3rd ed.,
--  Springer (2004), CdSe entry.
	local enabled = true
	local value = 0.040
	return value, enabled
end

function material.qw_delta2(state)
-- Spin-orbit delta2 = Dso/3 (quasi-cubic). Units: eV.
-- Dso(CdSe) ~ 0.42 eV -> delta2 ~ 0.14 eV.
-- FLAG: Dso is LARGE here, so delta2=delta3=Dso/3 is a real
-- approximation (unlike the nitrides); a measured delta3 is preferable
-- if available.
--
-- O. Madelung, "Semiconductors: Data Handbook," 3rd ed.,
--  Springer (2004), CdSe entry.
	local enabled = true
	local Dso = 0.42
	local value = Dso/3.0
	return value, enabled
end

function material.qw_delta3(state)
-- Spin-orbit delta3 = Dso/3 (quasi-cubic). Units: eV. See qw_delta2
-- for the large-Dso caveat.
--
-- O. Madelung, "Semiconductors: Data Handbook," 3rd ed.,
--  Springer (2004), CdSe entry.
	local enabled = true
	local Dso = 0.42
	local value = Dso/3.0
	return value, enabled
end

function material.qw_A1(state)
-- Wurtzite valence-band k.p parameter A1. Units: dimensionless (hbar^2/2m0).
-- enabled=false: no reliable A1..A6 set for wurtzite CdSe in the
-- Chuang-Chang/RSP convention. The wurtzite valence-band review
-- (below) reduces CdSe to gamma1,gamma2 and notes the spherical-
-- cubic reduction FAILS for CdSe, so A1..A6 cannot be reconstructed
-- unambiguously. Returns 0.0.
--
-- V. A. Fonoberov, E. P. Pokatilov, and A. A. Balandin (and related
--  work), "Valence band parameters of wurtzite materials," Solid
--  State Communications (1996), PII S0038-1098(96)00282-7.
	local enabled = false
	local value = 0.0
	return value, enabled
end

function material.qw_A2(state)
-- Wurtzite valence-band k.p parameter A2. Units: dimensionless.
-- enabled=false: see qw_A1 (CdSe).
	local enabled = false
	local value = 0.0
	return value, enabled
end

function material.qw_A3(state)
-- Wurtzite valence-band k.p parameter A3. Units: dimensionless.
-- enabled=false: see qw_A1 (CdSe).
	local enabled = false
	local value = 0.0
	return value, enabled
end

function material.qw_A4(state)
-- Wurtzite valence-band k.p parameter A4. Units: dimensionless.
-- enabled=false: see qw_A1 (CdSe).
	local enabled = false
	local value = 0.0
	return value, enabled
end

function material.qw_A5(state)
-- Wurtzite valence-band k.p parameter A5. Units: dimensionless.
-- enabled=false: see qw_A1 (CdSe).
	local enabled = false
	local value = 0.0
	return value, enabled
end

function material.qw_A6(state)
-- Wurtzite valence-band k.p parameter A6. Units: dimensionless.
-- enabled=false: see qw_A1 (CdSe).
	local enabled = false
	local value = 0.0
	return value, enabled
end

function material.qw_Ep1(state)
-- Kane energy || c. Units: eV.
-- enabled=false: no anisotropic Kane energy (Ep1/Ep2) for wurtzite
-- CdSe is established (bulk Ep ~ 17-20 eV is quoted but not split).
	local enabled = false
	local value = 0.0
	return value, enabled
end

function material.qw_Ep2(state)
-- Kane energy perp c. Units: eV.
-- enabled=false: see qw_Ep1 (CdSe).
	local enabled = false
	local value = 0.0
	return value, enabled
end

function material.qw_S1(state)
-- Conduction remote+free-electron parameter || c. Units: dimensionless (hbar^2/2m0).
-- enabled=false: cannot be derived (needs Ep1 and anisotropic mass,
-- neither established for wurtzite CdSe).
	local enabled = false
	local value = 0.0
	return value, enabled
end

function material.qw_S2(state)
-- Conduction remote+free-electron parameter perp c.
-- enabled=false: see qw_S1 (CdSe).
	local enabled = false
	local value = 0.0
	return value, enabled
end

function material.qw_a1(state)
-- Conduction-band deformation potential || c. Units: eV.
-- enabled=false: no wurtzite CdSe deformation potential set in this
-- convention was found.
	local enabled = false
	local value = 0.0
	return value, enabled
end

function material.qw_a2(state)
-- Conduction-band deformation potential perp c. Units: eV.
-- enabled=false: see qw_a1 (CdSe).
	local enabled = false
	local value = 0.0
	return value, enabled
end

function material.qw_D1(state)
-- Valence-band deformation potential D1. Units: eV.
-- enabled=false: no complete D1..D6 set for wurtzite CdSe in this
-- convention was found.
	local enabled = false
	local value = 0.0
	return value, enabled
end

function material.qw_D2(state)
-- Valence-band deformation potential D2. Units: eV.
-- enabled=false: see qw_D1 (CdSe).
	local enabled = false
	local value = 0.0
	return value, enabled
end

function material.qw_D3(state)
-- Valence-band deformation potential D3. Units: eV.
-- enabled=false: see qw_D1 (CdSe).
	local enabled = false
	local value = 0.0
	return value, enabled
end

function material.qw_D4(state)
-- Valence-band deformation potential D4. Units: eV.
-- enabled=false: see qw_D1 (CdSe).
	local enabled = false
	local value = 0.0
	return value, enabled
end

function material.qw_D5(state)
-- Valence-band deformation potential D5. Units: eV.
-- enabled=false: see qw_D1 (CdSe).
	local enabled = false
	local value = 0.0
	return value, enabled
end

function material.qw_D6(state)
-- Valence-band deformation potential D6. Units: eV.
-- enabled=false: see qw_D1 (CdSe).
	local enabled = false
	local value = 0.0
	return value, enabled
end

function material.lattice_a(state)
	-- Lattice constant, a-axis
	-- Units: m
	--
	-- Reference:
	-- O. Madelung, "Semiconductors: Data Handbook," 3rd ed.,
	-- Springer (2004), DOI: 10.1007/978-3-642-18865-7.
	--
	-- Notes:
	-- Wurtzite CdSe (space group P6_3mc), the stable bulk phase at room
	-- temperature. In-plane a-axis a = 4.2999 Angstrom at ~300 K; the
	-- c-axis (c = 7.0109 Angstrom) is NOT returned here.
	-- If your CdSe model is instead cubic zinc-blende, use
	-- a = 6.052 Angstrom (6.052e-10 m).
	-- Room-temperature value.

	local enabled = true
	local value = 4.2999e-10

	return value, enabled
end

function material.qw_C11(state)
    -- Elastic stiffness constant C11
    -- Units: Pa
    --
    -- Crystal phase: wurtzite CdSe.
    --
    -- Reference:
    -- S. Adachi, Handbook on Physical Properties of Semiconductors
    -- (Kluwer Academic, 2004), as tabulated in Planelles et al.,
    -- arXiv:1611.00973, Supporting Information Table S1.
    --
    -- Notes:
    -- 74.1 GPa -> 74.1e9 Pa.
    -- Cross-check: experimental column of Grunwald et al., J. Chem. Phys.
    -- 136, 234111 (2012): 74.6 GPa.

    local enabled = true
    local value = 74.1e9

    return value, enabled
end

function material.qw_C12(state)
    -- Elastic stiffness constant C12
    -- Units: Pa
    --
    -- Reference:
    -- S. Adachi, Handbook on Physical Properties of Semiconductors
    -- (Kluwer Academic, 2004), as tabulated in Planelles et al.,
    -- arXiv:1611.00973, Supporting Information Table S1.
    --
    -- Notes:
    -- 45.2 GPa -> 45.2e9 Pa.

    local enabled = true
    local value = 45.2e9

    return value, enabled
end

function material.qw_C13(state)
    -- Elastic stiffness constant C13
    -- Units: Pa
    --
    -- Reference:
    -- S. Adachi, Handbook on Physical Properties of Semiconductors
    -- (Kluwer Academic, 2004), as tabulated in Planelles et al.,
    -- arXiv:1611.00973, Supporting Information Table S1.
    --
    -- Notes:
    -- 38.9 GPa -> 38.9e9 Pa.

    local enabled = true
    local value = 38.9e9

    return value, enabled
end

function material.qw_C33(state)
    -- Elastic stiffness constant C33
    -- Units: Pa
    --
    -- Reference:
    -- S. Adachi, Handbook on Physical Properties of Semiconductors
    -- (Kluwer Academic, 2004), as tabulated in Planelles et al.,
    -- arXiv:1611.00973, Supporting Information Table S1.
    --
    -- Notes:
    -- 84.3 GPa -> 84.3e9 Pa.

    local enabled = true
    local value = 84.3e9

    return value, enabled
end

function material.qw_C44(state)
    -- Elastic stiffness constant C44
    -- Units: Pa
    --
    -- Reference:
    -- S. Adachi, Handbook on Physical Properties of Semiconductors
    -- (Kluwer Academic, 2004), as tabulated in Planelles et al.,
    -- arXiv:1611.00973, Supporting Information Table S1.
    --
    -- Notes:
    -- 13.4 GPa -> 13.4e9 Pa.

    local enabled = true
    local value = 13.4e9

    return value, enabled
end

function material.phonon_lo_energy(state)
    -- Representative LO phonon energy for polar optical (Frohlich) scattering
    -- Units: eV
    --
    -- Crystal phase: wurtzite CdSe.
    --
    -- Reference:
    -- S. S. Mitra, "Optically-active multiphonon processes in II-VI
    -- semiconductors," J. Phys. Soc. Jpn. 21, Supplement, 61 (1966)
    -- (wurtzite CdSe reststrahlen analysis, 80 K).
    -- (same group as Geick, Perry & Mitra 1966, the eps_static source)
    --
    -- Notes:
    -- Reststrahlen analysis, 80 K: omega_TO(E perp c) = 175 cm^-1,
    -- omega_TO(E par c) = 166 cm^-1; LO ~ 210 cm^-1.
    -- 210 x 1.239842e-4 eV/cm^-1 = 0.02604 eV. Room-temperature Raman LO of
    -- bulk CdSe is commonly reported near 210 cm^-1, so the 80 K value is
    -- used without temperature correction.

    local enabled = true
    local value = 0.02604

    return value, enabled
end

function material.epsilon_static(state)
    -- Static relative dielectric constant (lattice + electronic)
    -- Dimensionless
    --
    -- Crystal phase: wurtzite CdSe, E perp c.
    --
    -- Reference:
    -- J. Planelles, F. Rajadell, J. I. Climente,
    -- "Electronic origin of linearly polarized emission in CdSe/CdS
    -- dot-in-rod heterostructures," arXiv:1611.00973,
    -- Supporting Information Table S1.
    -- citing R. Geick, C. H. Perry, S. S. Mitra, "Lattice vibrational
    -- properties of hexagonal CdSe," J. Appl. Phys. 37, 1994 (1966).
    --
    -- Notes:
    -- eps_perp = 9.29 (eps_par = 10.16). Ordinary component used.

    local enabled = true
    local value = 9.29

    return value, enabled
end

function material.epsilon_inf(state)
    -- High-frequency (electronic) relative dielectric constant
    -- Dimensionless
    --
    -- Crystal phase: wurtzite CdSe, E perp c.
    --
    -- Reference:
    -- S. S. Mitra, "Optically-active multiphonon processes in II-VI
    -- semiconductors," J. Phys. Soc. Jpn. 21, Supplement, 61 (1966)
    -- (wurtzite CdSe reststrahlen analysis, 80 K).
    --
    -- Notes:
    -- eps_inf(perp) = 6.20 (eps_inf(par) = 6.30), 80 K reststrahlen fit.
    -- The same analysis gives eps_0(perp) = 9.15, vs 9.29 used for
    -- epsilon_static (Geick et al. 1966, room temperature); the ~1.5%
    -- difference is within the spread of measurements. LST check with these
    -- values: 6.20*(210/175)^2 = 8.93, i.e. the set is self-consistent to
    -- within ~4%.

    local enabled = true
    local value = 6.20

    return value, enabled
end

function material.qw_e15(state)
    -- Wurtzite piezoelectric stress coefficient e15
    -- Units: C m^-2
    --
    -- Reference:
    -- D. Berlincourt, H. Jaffe, L. R. Shiozawa,
    -- "Electroelastic properties of the sulfides, selenides, and tellurides
    -- of zinc and cadmium,"
    -- Phys. Rev. 129, 1009 (1963).
    -- DOI: 10.1103/PhysRev.129.1009
    -- as tabulated in Planelles et al., arXiv:1611.00973, SI Table S1.
    --
    -- Notes:
    -- e15 = -0.138 C/m^2 (Berlincourt convention, e33 > 0).

    local enabled = true
    local value = -0.138

    return value, enabled
end

function material.e31(state)
    -- Wurtzite piezoelectric stress coefficient e31
    -- Units: C m^-2
    --
    -- Reference:
    -- D. Berlincourt, H. Jaffe, L. R. Shiozawa,
    -- "Electroelastic properties of the sulfides, selenides, and tellurides
    -- of zinc and cadmium,"
    -- Phys. Rev. 129, 1009 (1963).
    -- DOI: 10.1103/PhysRev.129.1009
    -- as tabulated in Planelles et al., arXiv:1611.00973, SI Table S1.
    --
    -- Notes:
    -- e31 = -0.160 C/m^2 (Berlincourt convention, e33 > 0).

    local enabled = true
    local value = -0.160

    return value, enabled
end

function material.e33(state)
    -- Wurtzite piezoelectric stress coefficient e33
    -- Units: C m^-2
    --
    -- Reference:
    -- D. Berlincourt, H. Jaffe, L. R. Shiozawa,
    -- "Electroelastic properties of the sulfides, selenides, and tellurides
    -- of zinc and cadmium,"
    -- Phys. Rev. 129, 1009 (1963).
    -- DOI: 10.1103/PhysRev.129.1009
    -- as tabulated in Planelles et al., arXiv:1611.00973, SI Table S1.
    --
    -- Notes:
    -- e33 = +0.347 C/m^2.

    local enabled = true
    local value = 0.347

    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

-- ============================================================================
-- Copyright (C) 2026 The OghmaNano Project
-- 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.
-- ============================================================================