ZnS material model

1. Introduction

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

Bulk zinc-blende (cubic) zinc sulfide

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 = {}

-- ---------------------------------------------------------------------------
-- NOTES ON ZnS (read before using):
--
-- ZnS is the widest-gap common II-VI (~3.7 eV, direct), modelled here in the
-- cubic zinc-blende (sphalerite) phase; the wurtzite polytype has a slightly
-- larger gap (~3.8-3.9 eV) and different constants. Like ZnSe/ZnTe it is NOT
-- in the Ioffe NSM archive, so values are from Madelung's Data Handbook and
-- Adachi plus specific papers, with more scatter than the III-Vs. ZnS is
-- naturally n-type and very hard to dope p-type (strong self-compensation);
-- hole transport is correspondingly poorly characterised.
--
-- REFERENCES
--
-- [1]  O. Madelung (ed.), "Semiconductors: Data Handbook", 3rd ed.,
--      Springer (2004). [primary II-VI data compilation]
-- [2]  S. Adachi, "Properties of Group-IV, III-V and II-VI Semiconductors",
--      Wiley (2005).
-- [3]  R. Passler et al., "Temperature dependence of exciton peak energies in
--      ZnS, ZnSe, and ZnTe epitaxial films", J. Appl. Phys. (1999).
--      [Eg(T) / Varshni analysis]
--
-- Nc and Nv are COMPUTED from density-of-states effective masses via
-- N = 2.509e25 * (m*/m0)^1.5 * (T/300)^1.5  m^-3, not directly tabulated;
-- the hole mass (hence Nv) is the least certain input. Zinc-blende values.
-- ---------------------------------------------------------------------------

function material.name()
	local enabled = true

	return "ZnS", enabled
end

function material.description()
	local enabled = true

	return "Bulk zinc-blende (cubic) zinc sulfide", enabled
end

function material.formula()
	local enabled = true

	return "ZnS", enabled
end

function material.Eg(state)
	-- Units: eV
	-- Refs: [1],[3]; Varshni form [3]
	--
	-- Varshni form (cubic ZnS): Eg(0) = 3.84 eV, alpha = 6.5e-4 eV/K,
	-- beta = 200 K, giving Eg(300 K) = 3.72 eV. Reported cubic-ZnS 300 K
	-- gaps span ~3.66-3.78 eV; wurtzite is ~0.1-0.2 eV wider. II-VI
	-- Varshni parameters vary between sources - these reproduce the
	-- accepted zinc-blende 300 K value.

	local enabled = true
	local T = state.T
	local value = 3.84 - 6.5e-4*T*T/(T + 200.0)

	return value, enabled
end

function material.Xi(state)
	-- Electron affinity
	-- Units: eV
	-- Refs: [1],[2]
	--
	-- ~3.9 eV. Reported ZnS electron affinities scatter widely
	-- (~3.9-4.5 eV); sets the heterojunction band offset.

	local enabled = true
	local value = 3.9

	return value, enabled
end

function material.me(state)
    local enabled = true
    local value = 0.28    -- zincblende Gamma electron mass (Adachi 2005)
    -- NOTE: ZnS also has a wurtzite polytype with different, anisotropic masses.
    return value, enabled
end

function material.mh(state)
    local enabled = true
    local value = 1.3     -- heavy HH; large literature spread 1.3-1.8 (Adachi 2005)
    return value, enabled
end

function material.Nc(state)
	-- Effective conduction-band density of states
	-- Units: m^-3
	-- Refs: computed from m_e* = 0.34 m0 (zinc blende) [1],[2]
	--
	-- Nc = 2.509e25*(0.34)^1.5*(T/300)^1.5 = 5.0e24 m^-3 at 300 K
	-- (5.0e18 cm^-3).

	local enabled = true
	local T = state.T
	local value = 5.0e24*(T/300.0)^1.5

	return value, enabled
end

function material.Nv(state)
	-- Effective valence-band density of states
	-- Units: m^-3
	-- Refs: computed from m_h(DOS) ~ 0.8 m0 [1],[2]
	--
	-- Nv = 2.509e25*(0.8)^1.5*(T/300)^1.5 = 1.8e25 m^-3 at 300 K
	-- (1.8e19 cm^-3). DOS hole mass uncertain; Nv is the softer input.

	local enabled = true
	local T = state.T
	local value = 1.8e25*(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
	-- Refs: [1],[2]
	--
	-- ~165 cm^2/V/s = 0.0165 m^2/V/s at 300 K (single crystal). The
	-- (300/T)^1.5 factor is an approximate lattice-limited dependence;
	-- polar-optical-phonon scattering dominates near 300 K and real
	-- (especially thin-film) material is lower.

	local enabled = true
	local T = state.T
	local value = 0.0165*(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
	-- Refs: [1],[2]
	--
	-- ~40 cm^2/V/s = 0.004 m^2/V/s at 300 K - low and poorly
	-- constrained (ZnS is hard to make p-type). (300/T)^1.5 approximate.

	local enabled = true
	local T = state.T
	local value = 0.004*(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
	-- Refs: [1],[2]
	--
	-- Static 8.3 (high-frequency 5.1), zinc blende.

	local enabled = true
	local value = 8.3

	return value, enabled
end

function material.free_to_free_recombination(state)
	-- Radiative recombination coefficient
	-- Units: m^3 s^-1
	-- Refs: representative (see note)
	--
	-- Representative direct-gap value ~1e-10 cm^3/s = 1e-16 m^3/s.
	-- Not well tabulated for ZnS; placeholder, refine against measured
	-- lifetimes.

	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
	-- Refs: representative (see note)
	--
	-- Small representative ~1e-30 cm^6/s = 1e-42 m^6/s. Auger is
	-- negligible in this very wide-gap material under normal conditions.

	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
	-- Refs: representative (see note)
	--
	-- As auger_Cn: representative 1e-30 cm^6/s = 1e-42 m^6/s, negligible
	-- in wide-gap ZnS.

	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).
	--
	-- Defect-dependent, not an intrinsic constant. ZnS luminescence and
	-- transport are dominated by native defects and self-compensation;
	-- set from your own data. Mid-gap is a neutral default.

	local enabled = true
	local value = 0.0

	return value, enabled
end

function material.ss_srh_Nt(state)
	-- SRH trap density
	-- Units: m^-3
	--
	-- Defect-dependent placeholder; set from the intended material
	-- quality.

	local enabled = true
	local value = 1.0e22

	return value, enabled
end

function material.ss_srh_sigma_n(state)
	-- Electron capture cross section
	-- Units: m^2
	--
	-- Defect-dependent placeholder; set from measurement.

	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
	--
	-- Defect-dependent placeholder; set from measurement.

	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
	-- Refs: [2]
	--
	-- ~27 W/m/K (0.27 W/cm/K) at 300 K [2]. The (300/T)^1.0 factor is
	-- the usual phonon-Umklapp scaling; polycrystalline films are lower.

	local enabled = true
	local T = state.T
	local value = 27.0*(300.0/T)^1.0

	return value, enabled
end

function material.heat_capacity(state)
	-- Specific heat capacity
	-- Units: J kg^-1 K^-1
	-- Refs: [1],[2]
	--
	-- ~470 J/kg/K near 300 K (0.47 J/g/K), consistent with the
	-- Dulong-Petit limit for ZnS (M = 97.44 g/mol).

	local enabled = true
	local value = 470.0

	return value, enabled
end

function material.density(state)
	-- Mass density
	-- Units: kg m^-3
	-- Refs: [1]
	--
	-- 4.09 g/cm^3 (crystallographic: Z = 4, M = 97.44 g/mol,
	-- a = 5.41 A), zinc blende.

	local enabled = true
	local value = 4090.0

	return value, enabled
end

function material.lattice_constant(state)
	-- Cubic lattice constant
	-- Units: m
	-- Refs: [1],[2]
	--
	-- a(300 K) = 5.41 A (zinc blende) [1]. Linear thermal expansion
	-- ~6.5e-6 /K.

	local enabled = true
	local T = state.T
	local a300 = 5.41e-10
	local expansion = 6.5e-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


-- ZnS (wurtzite). The stable phase is zinc-blende; wurtzite ZnS is the
-- metastable 2H polytype. No complete 8-band Chuang-Chang/RSP wurtzite
-- k.p parameter set (A1..A6, Ep, S, deformation) exists for it in the
-- accessible literature, and even the crystal-field/spin-orbit values
-- are not authoritatively established in the wurtzite k.p context.
-- Everything is therefore disabled and returns 0.0. (The wurtzite
-- valence-band review, Solid State Commun. 1996, treats ZnS only at the
-- gamma1,gamma2 level - not a full A1..A6 set.)

function material.qw_delta1(state)
-- Crystal-field splitting delta1. Units: eV.
-- enabled=false: not reliably established for wurtzite ZnS.
--
-- 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_delta2(state)
-- Spin-orbit delta2 = Dso/3. Units: eV.
-- enabled=false: see qw_delta1 (ZnS).
	local enabled = false
	local value = 0.0
	return value, enabled
end

function material.qw_delta3(state)
-- Spin-orbit delta3 = Dso/3. Units: eV.
-- enabled=false: see qw_delta1 (ZnS).
	local enabled = false
	local value = 0.0
	return value, enabled
end

function material.qw_A1(state)
-- Wurtzite valence-band k.p parameter A1. Units: dimensionless (hbar^2/2m0).
-- enabled=false: see qw_delta1 (ZnS).
	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 (hbar^2/2m0).
-- enabled=false: see qw_delta1 (ZnS).
	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 (hbar^2/2m0).
-- enabled=false: see qw_delta1 (ZnS).
	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 (hbar^2/2m0).
-- enabled=false: see qw_delta1 (ZnS).
	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 (hbar^2/2m0).
-- enabled=false: see qw_delta1 (ZnS).
	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 (hbar^2/2m0).
-- enabled=false: see qw_delta1 (ZnS).
	local enabled = false
	local value = 0.0
	return value, enabled
end

function material.qw_Ep1(state)
-- Kane energy || c. Units: eV.
-- enabled=false: see qw_delta1 (ZnS).
	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_delta1 (ZnS).
	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: see qw_delta1 (ZnS).
	local enabled = false
	local value = 0.0
	return value, enabled
end

function material.qw_S2(state)
-- Conduction remote+free-electron parameter perp c. Units: dimensionless (hbar^2/2m0).
-- enabled=false: see qw_delta1 (ZnS).
	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: see qw_delta1 (ZnS).
	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_delta1 (ZnS).
	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: see qw_delta1 (ZnS).
	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_delta1 (ZnS).
	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_delta1 (ZnS).
	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_delta1 (ZnS).
	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_delta1 (ZnS).
	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_delta1 (ZnS).
	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:
	-- Cubic zinc-blende ZnS (sphalerite, space group F-43m), the stable
	-- bulk phase at room temperature. Cubic cell edge a = 5.4102 Angstrom
	-- at ~300 K (for a cubic crystal the a-axis is the cell edge).
	-- If your ZnS model is instead wurtzite, use a = 3.8226 Angstrom
	-- (3.8226e-10 m) for the a-axis (c = 6.2605 Angstrom).
	-- Room-temperature value.

	local enabled = true
	local value = 5.4102e-10

	return value, enabled
end

function material.qw_C11(state)
    -- Elastic stiffness constant C11
    -- Units: Pa
    --
    -- Crystal phase: wurtzite (hexagonal) ZnS.
    --
    -- Reference:
    -- M. Grunwald, A. Zayak, J. B. Neaton, P. L. Geissler, E. Rabani,
    -- "Transferable pair potentials for CdS and ZnS crystals,"
    -- J. Chem. Phys. 136, 234111 (2012), Table 2 (experimental comparison
    -- column; the table attributes its experimental values collectively to
    -- Berlincourt et al. 1963, Corll 1967 and others without per-entry
    -- labels).
    --
    -- Notes:
    -- Experimental comparison values for wurtzite ZnS from the cited table
    -- (primary sources attributed collectively; individual entries not
    -- traced to a single measurement). Values in GPa -> x 1e9 Pa.
    -- Full set: C11 131.2, C12 66.3, C13 50.9, C33 140.8, C44 28.6 GPa.

    local enabled = true
    local value = 131.2e9

    return value, enabled
end

function material.qw_C12(state)
    -- Elastic stiffness constant C12
    -- Units: Pa
    --
    -- Crystal phase: wurtzite (hexagonal) ZnS.
    --
    -- Reference:
    -- M. Grunwald, A. Zayak, J. B. Neaton, P. L. Geissler, E. Rabani,
    -- "Transferable pair potentials for CdS and ZnS crystals,"
    -- J. Chem. Phys. 136, 234111 (2012), Table 2 (experimental comparison
    -- column; the table attributes its experimental values collectively to
    -- Berlincourt et al. 1963, Corll 1967 and others without per-entry
    -- labels).
    --
    -- Notes:
    -- Experimental comparison values for wurtzite ZnS from the cited table
    -- (primary sources attributed collectively; individual entries not
    -- traced to a single measurement). Values in GPa -> x 1e9 Pa.
    -- Full set: C11 131.2, C12 66.3, C13 50.9, C33 140.8, C44 28.6 GPa.

    local enabled = true
    local value = 66.3e9

    return value, enabled
end

function material.qw_C13(state)
    -- Elastic stiffness constant C13
    -- Units: Pa
    --
    -- Crystal phase: wurtzite (hexagonal) ZnS.
    --
    -- Reference:
    -- M. Grunwald, A. Zayak, J. B. Neaton, P. L. Geissler, E. Rabani,
    -- "Transferable pair potentials for CdS and ZnS crystals,"
    -- J. Chem. Phys. 136, 234111 (2012), Table 2 (experimental comparison
    -- column; the table attributes its experimental values collectively to
    -- Berlincourt et al. 1963, Corll 1967 and others without per-entry
    -- labels).
    --
    -- Notes:
    -- Experimental comparison values for wurtzite ZnS from the cited table
    -- (primary sources attributed collectively; individual entries not
    -- traced to a single measurement). Values in GPa -> x 1e9 Pa.
    -- Full set: C11 131.2, C12 66.3, C13 50.9, C33 140.8, C44 28.6 GPa.

    local enabled = true
    local value = 50.9e9

    return value, enabled
end

function material.qw_C33(state)
    -- Elastic stiffness constant C33
    -- Units: Pa
    --
    -- Crystal phase: wurtzite (hexagonal) ZnS.
    --
    -- Reference:
    -- M. Grunwald, A. Zayak, J. B. Neaton, P. L. Geissler, E. Rabani,
    -- "Transferable pair potentials for CdS and ZnS crystals,"
    -- J. Chem. Phys. 136, 234111 (2012), Table 2 (experimental comparison
    -- column; the table attributes its experimental values collectively to
    -- Berlincourt et al. 1963, Corll 1967 and others without per-entry
    -- labels).
    --
    -- Notes:
    -- Experimental comparison values for wurtzite ZnS from the cited table
    -- (primary sources attributed collectively; individual entries not
    -- traced to a single measurement). Values in GPa -> x 1e9 Pa.
    -- Full set: C11 131.2, C12 66.3, C13 50.9, C33 140.8, C44 28.6 GPa.

    local enabled = true
    local value = 140.8e9

    return value, enabled
end

function material.qw_C44(state)
    -- Elastic stiffness constant C44
    -- Units: Pa
    --
    -- Crystal phase: wurtzite (hexagonal) ZnS.
    --
    -- Reference:
    -- M. Grunwald, A. Zayak, J. B. Neaton, P. L. Geissler, E. Rabani,
    -- "Transferable pair potentials for CdS and ZnS crystals,"
    -- J. Chem. Phys. 136, 234111 (2012), Table 2 (experimental comparison
    -- column; the table attributes its experimental values collectively to
    -- Berlincourt et al. 1963, Corll 1967 and others without per-entry
    -- labels).
    --
    -- Notes:
    -- Experimental comparison values for wurtzite ZnS from the cited table
    -- (primary sources attributed collectively; individual entries not
    -- traced to a single measurement). Values in GPa -> x 1e9 Pa.
    -- Full set: C11 131.2, C12 66.3, C13 50.9, C33 140.8, C44 28.6 GPa.

    local enabled = true
    local value = 28.6e9

    return value, enabled
end

function material.phonon_lo_energy(state)
    -- Representative LO phonon energy for polar optical (Frohlich) scattering
    -- Units: eV
    --
    -- No sufficiently reliable value/reference identified.
    -- Disabled rather than estimated.
    --
    -- Notes:
    -- Audit marks ZnS as wurtzite. Optical-phonon and dielectric data
    -- verified in this pass (Berlincourt 1963; neutron/IR in Gopal et al.)
    -- refer to cubic (sphalerite) ZnS and must not be reused for the
    -- hexagonal phase. No verified wurtzite-ZnS value identified.

    local enabled = false
    local value = 0.0

    return value, enabled
end

function material.epsilon_static(state)
    -- Static relative dielectric constant (lattice + electronic)
    -- Dimensionless
    --
    -- No sufficiently reliable value/reference identified.
    -- Disabled rather than estimated.
    --
    -- Notes:
    -- Audit marks ZnS as wurtzite. Optical-phonon and dielectric data
    -- verified in this pass (Berlincourt 1963; neutron/IR in Gopal et al.)
    -- refer to cubic (sphalerite) ZnS and must not be reused for the
    -- hexagonal phase. No verified wurtzite-ZnS value identified.

    local enabled = false
    local value = 0.0

    return value, enabled
end

function material.epsilon_inf(state)
    -- High-frequency (electronic) relative dielectric constant
    -- Dimensionless
    --
    -- No sufficiently reliable value/reference identified.
    -- Disabled rather than estimated.
    --
    -- Notes:
    -- Audit marks ZnS as wurtzite. Optical-phonon and dielectric data
    -- verified in this pass (Berlincourt 1963; neutron/IR in Gopal et al.)
    -- refer to cubic (sphalerite) ZnS and must not be reused for the
    -- hexagonal phase. No verified wurtzite-ZnS value identified.

    local enabled = false
    local value = 0.0

    return value, enabled
end

function material.qw_e15(state)
    -- Wurtzite piezoelectric stress coefficient e15
    -- Units: C m^-2
    --
    -- No sufficiently reliable value/reference identified.
    -- Disabled rather than estimated.
    --
    -- Notes:
    -- Wurtzite ZnS piezoelectric constants are scarce (bulk wurtzite ZnS
    -- crystals are usually polytype-mixed); no e15/e31/e33 set with a
    -- verified primary source and sign convention was found.

    local enabled = false
    local value = 0.0

    return value, enabled
end

function material.e31(state)
    -- Wurtzite piezoelectric stress coefficient e31
    -- Units: C m^-2
    --
    -- No sufficiently reliable value/reference identified.
    -- Disabled rather than estimated.
    --
    -- Notes:
    -- Wurtzite ZnS piezoelectric constants are scarce (bulk wurtzite ZnS
    -- crystals are usually polytype-mixed); no e15/e31/e33 set with a
    -- verified primary source and sign convention was found.

    local enabled = false
    local value = 0.0

    return value, enabled
end

function material.e33(state)
    -- Wurtzite piezoelectric stress coefficient e33
    -- Units: C m^-2
    --
    -- No sufficiently reliable value/reference identified.
    -- Disabled rather than estimated.
    --
    -- Notes:
    -- Wurtzite ZnS piezoelectric constants are scarce (bulk wurtzite ZnS
    -- crystals are usually polytype-mixed); no e15/e31/e33 set with a
    -- verified primary source and sign convention was found.

    local enabled = false
    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

-- ============================================================================
-- 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.
-- ============================================================================