AlN material model

1. Introduction

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

Bulk crystalline aluminium nitride (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 "AlN", enabled
end

function material.description()
	local enabled = true

	return "Bulk crystalline aluminium nitride (wurtzite)", enabled
end

function material.formula()
	local enabled = true

	return "AlN", 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 AlN parameter set (Eg(0) = 6.25 eV,
	-- alpha = 1.799e-3 eV/K, beta = 1462 K) from
	-- I. Vurgaftman, J. R. Meyer, L. R. Ram-Mohan,
	-- "Band parameters for III-V compound semiconductors and their
	-- alloys", J. Appl. Phys. 89, 5815-5875, 2001.
	-- Gives Eg(300 K) = 6.16 eV. Direct, deep-UV gap.

	local enabled = true
	local T = state.T
	local value = 6.25 - 1.799e-3*T*T/(T + 1462.0)

	return value, enabled
end

function material.Xi(state)
	-- Electron affinity
	-- Units: eV
	--
	-- Reference:
	-- Device literature (values scatter strongly).
	--
	-- IMPORTANT: AlN electron affinity is very low and poorly defined;
	-- reported values range from near zero (negative electron affinity
	-- has been observed on some surfaces) to ~2 eV, depending on
	-- surface polarity and termination. 0.6 eV is a representative
	-- value. For AlGaN band engineering, set offsets from measured
	-- band offsets rather than from this number.

	local enabled = true
	local value = 0.6

	return value, enabled
end

function material.me(state)
    local enabled = true
    local value = 0.32    -- along c; me_perp ~0.30 (Vurgaftman 2003)
    return value, enabled
end

function material.mh(state)
    local enabled = true
    -- HH along c: -1/(A1+A3), A1=-3.86 A3=3.58 (Vurgaftman 2003)
    -- WARNING: very heavy, approximate; multiband VB.
    local value = 3.6
    return value, enabled
end

function material.Nc(state)
	-- Effective conduction-band density of states
	-- Units: m^-3
	--
	-- Reference:
	-- From electron effective mass m_e* ~ 0.4 m0 (wurtzite AlN).
	-- Nc(300 K) ~ 6.3e18 cm^-3 = 6.3e24 m^-3.
	--
	-- Note: the (T/300)^1.5 form is the simple parabolic-band model.

	local enabled = true
	local T = state.T
	local value = 6.3e24*(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 (large) wurtzite AlN hole density-of-states mass.
	-- Nv(300 K) ~ 1.8e20 cm^-3 = 1.8e26 m^-3.
	--
	-- Note: AlN has a heavy, strongly warped valence band; Nv is
	-- sensitive to the assumed hole DOS mass and is uncertain at the
	-- factor-of-two level.

	local enabled = true
	local T = state.T
	local value = 1.8e26*(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:
	-- Theoretical / best-case experimental AlN.
	-- mu_n(300 K) ~ 300 cm^2/V/s = 0.03 m^2/V/s, phonon-limited
	-- temperature dependence approximately (300/T)^1.5.
	--
	-- IMPORTANT: this is an intrinsic / best-case value. Real
	-- conductive n-AlN is very hard to achieve (Si donors are
	-- relatively deep and compensation is severe), so measured
	-- mobilities are typically much lower.

	local enabled = true
	local T = state.T
	local value = 0.03*(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:
	-- Estimated; AlN hole transport is essentially unmeasured in bulk.
	-- mu_p(300 K) ~ 10 cm^2/V/s = 0.001 m^2/V/s (order of magnitude),
	-- temperature dependence approximately (300/T)^2.0.
	--
	-- IMPORTANT: p-type AlN is not practically achievable by
	-- conventional doping (the Mg acceptor is extremely deep,
	-- ~0.5-0.6 eV). Treat this value as a placeholder only.

	local enabled = true
	local T = state.T
	local value = 0.001*(300.0/T)^2.0

	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:
	-- Ioffe NSM database (AlN).
	-- Static value ~8.5 (high-frequency value ~4.6).
	--
	-- Note: wurtzite AlN is anisotropic about the c-axis; a
	-- representative value is used.

	local enabled = true
	local value = 8.5

	return value, enabled
end

function material.free_to_free_recombination(state)
	-- Radiative (band-to-band) recombination coefficient
	-- Units: m^3 s^-1
	--
	-- Reference:
	-- Representative value for a direct-gap nitride,
	-- ~1e-11 cm^3/s = 1e-17 m^3/s.
	--
	-- AlN is direct-gap, but its band-to-band radiative coefficient
	-- is poorly characterised. Adjust by hand to match your material /
	-- device.

	local enabled = true
	local value = 1.0e-17

	return value, enabled
end

function material.auger_Cn(state)
	-- Electron Auger recombination coefficient
	-- Units: m^6 s^-1
	--
	-- Reference:
	-- Representative placeholder, ~1e-31 cm^6/s = 1e-43 m^6/s.
	--
	-- Note: AlN Auger coefficients are essentially unmeasured. Being
	-- very wide gap, Auger is expected to be weak. Treat as an
	-- order-of-magnitude placeholder and adjust by hand.

	local enabled = true
	local value = 1.0e-43

	return value, enabled
end

function material.auger_Cp(state)
	-- Hole Auger recombination coefficient
	-- Units: m^6 s^-1
	--
	-- Reference:
	-- Representative placeholder, ~1e-31 cm^6/s = 1e-43 m^6/s.
	--
	-- Note: as for Cn, essentially unmeasured. Placeholder only.

	local enabled = true
	local value = 1.0e-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 material.
	--
	-- Note: as with GaN, dislocations and point defects dominate the
	-- effective SRH lifetime in real AlN; set from your 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:
	-- Ioffe NSM database (AlN) / single-crystal measurements.
	-- kappa(300 K) ~ 285 W/m/K; near room temperature kappa decreases
	-- with T with an effective exponent of about -1.4.
	--
	-- Note: AlN is prized as a high-thermal-conductivity insulator.
	-- The value is strongly quality dependent; polycrystalline
	-- ceramic and thin-film AlN are well below the single-crystal
	-- value.

	local enabled = true
	local T = state.T
	local value = 285.0*(300.0/T)^1.4

	return value, enabled
end

function material.heat_capacity(state)
	-- Specific heat capacity
	-- Units: J kg^-1 K^-1
	--
	-- Reference:
	-- Ioffe NSM database (AlN). c_p(300 K) ~ 600 J/kg/K.

	local enabled = true
	local value = 600.0

	return value, enabled
end

function material.density(state)
	-- Mass density
	-- Units: kg m^-3
	--
	-- Reference:
	-- Ioffe NSM database (AlN). rho = 3.23 g/cm^3.

	local enabled = true
	local value = 3230.0

	return value, enabled
end

function material.lattice_constant(state)
	-- Lattice constant (hexagonal a-axis)
	-- Units: m
	--
	-- Reference:
	-- I. Vurgaftman, J. R. Meyer, L. R. Ram-Mohan,
	-- "Band parameters for III-V compound semiconductors and their
	-- alloys", J. Appl. Phys. 89, 5815-5875, 2001; Ioffe NSM database.
	-- a(300 K) = 3.112 A; linear expansion ~4.2e-6 /K near 300 K.
	--
	-- IMPORTANT: wurtzite AlN is hexagonal, with two lattice
	-- constants a = 3.112 A and c = 4.982 A. This single scalar field
	-- holds the a-axis constant only; the c-axis constant is not
	-- representable here.
	--
	-- Note: like GaN, wurtzite AlN has large spontaneous and
	-- piezoelectric polarization (larger than GaN). The resulting
	-- internal fields are important in AlGaN/GaN devices but are not
	-- captured by any scalar in this material file.

	local enabled = true
	local T = state.T
	local a300 = 3.112e-10
	local expansion = 4.2e-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: Hydrodynamic literature/family value
	-- Confidence: Medium
	--
	-- Reference:
	-- https://doi.org/10.1063/1.1383260
	--
	-- Comments:
	-- 0.2 ps is a commonly used GaN/AlGaN hydrodynamic energy-relaxation value;
	-- extended to related nitrides.

	local enabled = true
	local value = 2.000000e-13

	return value, enabled
end

function material.thermal_tau_h(state)
	-- Hole energy relaxation time towards the lattice temperature
	-- Units: s
	--
	-- Value basis: Hydrodynamic literature/family value
	-- Confidence: Medium
	--
	-- Reference:
	-- https://doi.org/10.1063/1.1383260
	--
	-- Comments:
	-- 0.2 ps is a commonly used GaN/AlGaN hydrodynamic energy-relaxation value;
	-- extended to related nitrides.

	local enabled = true
	local value = 2.000000e-13

	return value, enabled
end

function material.qw_delta1(state)
-- Crystal-field splitting delta1 (= Delta_CR). Units: eV.
-- Value: Rinke 2008 OEPx+G0W0, used for BOTH the band ordering
-- and the S1/S2 conduction denominators so the set stays self-
-- consistent. (Vurgaftman-Meyer 2003 give a different Delta_CR;
-- see notes.) VM2003 value for cross-check: -0.169 eV.
--
-- P. Rinke, M. Winkelnkemper, A. Qteish, D. Bimberg, J. Neugebauer,
-- and M. Scheffler, "Consistent set of band parameters for the
--  group-III nitrides AlN, GaN, and InN," Physical Review B 77,
--  075202 (2008). DOI: 10.1103/PhysRevB.77.075202
	local enabled = true
	local value = -0.295
	return value, enabled
end

function material.qw_delta2(state)
-- Spin-orbit parameter delta2 = Dso/3 (quasi-cubic). Units: eV.
-- Dso(AlN) = 0.019 eV -> delta2 = 0.0063 eV.
--
-- I. Vurgaftman and J. R. Meyer, "Band parameters for nitrogen-
--  containing semiconductors," Journal of Applied Physics 94,
--  3675-3696 (2003). DOI: 10.1063/1.1600519
	local enabled = true
	local Dso = 0.019
	local value = Dso/3.0
	return value, enabled
end

function material.qw_delta3(state)
-- Spin-orbit parameter delta3 = Dso/3 (quasi-cubic; = delta2 in this
-- limit). Units: eV.
--
-- I. Vurgaftman and J. R. Meyer, "Band parameters for nitrogen-
--  containing semiconductors," Journal of Applied Physics 94,
--  3675-3696 (2003). DOI: 10.1063/1.1600519
	local enabled = true
	local Dso = 0.019
	local value = Dso/3.0
	return value, enabled
end

function material.qw_A1(state)
-- Wurtzite valence-band k.p parameter A1.
-- Dimensionless (units hbar^2/2m0).
--
-- P. Rinke, M. Winkelnkemper, A. Qteish, D. Bimberg, J. Neugebauer,
-- and M. Scheffler, "Consistent set of band parameters for the
--  group-III nitrides AlN, GaN, and InN," Physical Review B 77,
--  075202 (2008). DOI: 10.1103/PhysRevB.77.075202
	local enabled = true
	local value = -3.991
	return value, enabled
end

function material.qw_A2(state)
-- Wurtzite valence-band k.p parameter A2.
-- Dimensionless (units hbar^2/2m0).
--
-- P. Rinke, M. Winkelnkemper, A. Qteish, D. Bimberg, J. Neugebauer,
-- and M. Scheffler, "Consistent set of band parameters for the
--  group-III nitrides AlN, GaN, and InN," Physical Review B 77,
--  075202 (2008). DOI: 10.1103/PhysRevB.77.075202
	local enabled = true
	local value = -0.311
	return value, enabled
end

function material.qw_A3(state)
-- Wurtzite valence-band k.p parameter A3.
-- Dimensionless (units hbar^2/2m0).
--
-- P. Rinke, M. Winkelnkemper, A. Qteish, D. Bimberg, J. Neugebauer,
-- and M. Scheffler, "Consistent set of band parameters for the
--  group-III nitrides AlN, GaN, and InN," Physical Review B 77,
--  075202 (2008). DOI: 10.1103/PhysRevB.77.075202
	local enabled = true
	local value = 3.671
	return value, enabled
end

function material.qw_A4(state)
-- Wurtzite valence-band k.p parameter A4.
-- Dimensionless (units hbar^2/2m0).
--
-- P. Rinke, M. Winkelnkemper, A. Qteish, D. Bimberg, J. Neugebauer,
-- and M. Scheffler, "Consistent set of band parameters for the
--  group-III nitrides AlN, GaN, and InN," Physical Review B 77,
--  075202 (2008). DOI: 10.1103/PhysRevB.77.075202
	local enabled = true
	local value = -1.147
	return value, enabled
end

function material.qw_A5(state)
-- Wurtzite valence-band k.p parameter A5.
-- Dimensionless (units hbar^2/2m0).
--
-- Sign is physical: enters N1=2 A5 and M1 (-A5) directly
-- (Chuang-Chang/Rinke convention). Do not use |A5|.
--
-- P. Rinke, M. Winkelnkemper, A. Qteish, D. Bimberg, J. Neugebauer,
-- and M. Scheffler, "Consistent set of band parameters for the
--  group-III nitrides AlN, GaN, and InN," Physical Review B 77,
--  075202 (2008). DOI: 10.1103/PhysRevB.77.075202
	local enabled = true
	local value = -1.329
	return value, enabled
end

function material.qw_A6(state)
-- Wurtzite valence-band k.p parameter A6.
-- Dimensionless (units hbar^2/2m0).
--
-- Sign is physical: enters N2=sqrt(2) A6 directly
-- (Chuang-Chang/Rinke convention). Do not use |A6|.
--
-- P. Rinke, M. Winkelnkemper, A. Qteish, D. Bimberg, J. Neugebauer,
-- and M. Scheffler, "Consistent set of band parameters for the
--  group-III nitrides AlN, GaN, and InN," Physical Review B 77,
--  075202 (2008). DOI: 10.1103/PhysRevB.77.075202
	local enabled = true
	local value = -1.952
	return value, enabled
end

function material.qw_Ep1(state)
-- Kane energy Ep parallel to c (|| c). Units: eV.
-- Ep1 = (2 m0/hbar^2) P1^2 ; Rinke tabulate Ep directly.
--
-- P. Rinke, M. Winkelnkemper, A. Qteish, D. Bimberg, J. Neugebauer,
-- and M. Scheffler, "Consistent set of band parameters for the
--  group-III nitrides AlN, GaN, and InN," Physical Review B 77,
--  075202 (2008). DOI: 10.1103/PhysRevB.77.075202
	local enabled = true
	local value = 16.972
	return value, enabled
end

function material.qw_Ep2(state)
-- Kane energy Ep perpendicular to c (perp c). Units: eV.
--
-- P. Rinke, M. Winkelnkemper, A. Qteish, D. Bimberg, J. Neugebauer,
-- and M. Scheffler, "Consistent set of band parameters for the
--  group-III nitrides AlN, GaN, and InN," Physical Review B 77,
--  075202 (2008). DOI: 10.1103/PhysRevB.77.075202
	local enabled = true
	local value = 18.165
	return value, enabled
end

function material.qw_S1(state)
-- Conduction remote+free-electron parameter || c (multiplies kz^2).
-- Dimensionless (units hbar^2/2m0).
-- The OghmaNano conduction diagonal carries NO separate free-electron
-- term, so S folds in the free-electron 1 and the remote bands, while
-- the Kane coupling is explicit. Setting the total kz^2 (kx^2) curvature
-- equal to hbar^2/(2 m_par) (hbar^2/(2 m_perp)) gives, to 2nd order:
--   S1 = m0/m_par  - Ep1/(Egtilde + delta1)
--   S2 = m0/m_perp - Ep2/(Egtilde)
-- with Egtilde = Eg (delta1>0) or Eg+|delta1| (delta1<0). The
-- denominators are the exact conduction<->Z and conduction<->X,Y
-- separations of the Kane block (Rinke 2008 Eq. A2), so by construction
-- the full 8-band Hamiltonian reproduces the source electron masses.
-- AlN: m_par=0.322, Ep1=16.972, Eg=6.47, delta1=-0.295 => Egtilde=6.765,
--   denominator Egtilde+delta1 = 6.47 (= Eg here, since delta1<0).
--   S1 = 1/0.322 - 16.972/6.47 = 0.4824 .
--
-- P. Rinke et al., Physical Review B 77, 075202 (2008).
-- DOI: 10.1103/PhysRevB.77.075202
	local m   = 0.322
	local Eg  = 6.47
	local d1  = -0.295
	local Ep1 = 16.972
	local Egt = Eg
	if d1 < 0.0 then Egt = Eg - d1 end   -- Egtilde = Eg + |d1|
	local enabled = true
	local value = 1.0/m - Ep1/(Egt + d1)
	return value, enabled
end

function material.qw_S2(state)
-- Conduction remote+free-electron parameter perp c (multiplies
-- kx^2+ky^2). Dimensionless (units hbar^2/2m0). See qw_S1 for method.
-- AlN: m_perp=0.329, Ep2=18.165, Egtilde=6.765 => 
--   S2 = 1/0.329 - 18.165/6.765 = 0.3544 .
--
-- P. Rinke et al., Physical Review B 77, 075202 (2008).
-- DOI: 10.1103/PhysRevB.77.075202
	local m   = 0.329
	local Eg  = 6.47
	local d1  = -0.295
	local Ep2 = 18.165
	local Egt = Eg
	if d1 < 0.0 then Egt = Eg - d1 end   -- Egtilde = Eg + |d1|
	local enabled = true
	local value = 1.0/m - Ep2/Egt
	return value, enabled
end

function material.qw_a1(state)
-- Conduction-band deformation potential || c. Units: eV.
-- This is the gap-related (acz - D1) combination in VM2003's
-- convention; OghmaNano reconstructs acz via az = a1 + D1.
-- Yan 2009 (HSE) give acz-D1 = -4.31 eV for AlN as an alternative.
--
-- I. Vurgaftman and J. R. Meyer, "Band parameters for nitrogen-
--  containing semiconductors," Journal of Applied Physics 94,
--  3675-3696 (2003). DOI: 10.1063/1.1600519
--
-- Original source cited therein:
-- J. Wagner and F. Bechstedt, "Properties of strained wurtzite GaN
--  and AlN: Ab initio studies," Physical Review B 66, 115202 (2002).
--  DOI: 10.1103/PhysRevB.66.115202
	local enabled = true
	local value = -3.4
	return value, enabled
end

function material.qw_a2(state)
-- Conduction-band deformation potential perp c. Units: eV.
-- = (act - D2) in VM2003's convention; axy = a2 + D2.
-- NOTE: VM2003 PRINTS this as "-11.8 meV"; that is a typo in the
-- paper for -11.8 eV (Yan 2009 HSE give act-D2 = -12.11 eV, close).
--
-- I. Vurgaftman and J. R. Meyer, "Band parameters for nitrogen-
--  containing semiconductors," Journal of Applied Physics 94,
--  3675-3696 (2003). DOI: 10.1063/1.1600519
--
-- Original source cited therein:
-- J. Wagner and F. Bechstedt, "Properties of strained wurtzite GaN
--  and AlN: Ab initio studies," Physical Review B 66, 115202 (2002).
--  DOI: 10.1103/PhysRevB.66.115202
	local enabled = true
	local value = -11.8
	return value, enabled
end

function material.qw_D1(state)
-- Valence-band deformation potential D1. Units: eV.
--
-- I. Vurgaftman and J. R. Meyer, "Band parameters for nitrogen-
--  containing semiconductors," Journal of Applied Physics 94,
--  3675-3696 (2003). DOI: 10.1063/1.1600519
--
-- Original parameter source cited therein:
-- K. Shimada, T. Sota, and K. Suzuki, "First-principles study on
--  electronic and elastic properties of BN, AlN, and GaN,"
--  Journal of Applied Physics 84, 4951-4958 (1998).
--  DOI: 10.1063/1.368739
	local enabled = true
	local value = -17.1
	return value, enabled
end

function material.qw_D2(state)
-- Valence-band deformation potential D2. Units: eV.
--
-- I. Vurgaftman and J. R. Meyer, "Band parameters for nitrogen-
--  containing semiconductors," Journal of Applied Physics 94,
--  3675-3696 (2003). DOI: 10.1063/1.1600519
--
-- Original parameter source cited therein:
-- K. Shimada, T. Sota, and K. Suzuki, "First-principles study on
--  electronic and elastic properties of BN, AlN, and GaN,"
--  Journal of Applied Physics 84, 4951-4958 (1998).
--  DOI: 10.1063/1.368739
	local enabled = true
	local value = 7.9
	return value, enabled
end

function material.qw_D3(state)
-- Valence-band deformation potential D3. Units: eV.
--
-- I. Vurgaftman and J. R. Meyer, "Band parameters for nitrogen-
--  containing semiconductors," Journal of Applied Physics 94,
--  3675-3696 (2003). DOI: 10.1063/1.1600519
--
-- Original parameter source cited therein:
-- K. Shimada, T. Sota, and K. Suzuki, "First-principles study on
--  electronic and elastic properties of BN, AlN, and GaN,"
--  Journal of Applied Physics 84, 4951-4958 (1998).
--  DOI: 10.1063/1.368739
	local enabled = true
	local value = 8.8
	return value, enabled
end

function material.qw_D4(state)
-- Valence-band deformation potential D4. Units: eV.
--
-- I. Vurgaftman and J. R. Meyer, "Band parameters for nitrogen-
--  containing semiconductors," Journal of Applied Physics 94,
--  3675-3696 (2003). DOI: 10.1063/1.1600519
--
-- Original parameter source cited therein:
-- K. Shimada, T. Sota, and K. Suzuki, "First-principles study on
--  electronic and elastic properties of BN, AlN, and GaN,"
--  Journal of Applied Physics 84, 4951-4958 (1998).
--  DOI: 10.1063/1.368739
	local enabled = true
	local value = -3.9
	return value, enabled
end

function material.qw_D5(state)
-- Valence-band deformation potential D5. Units: eV.
--
-- I. Vurgaftman and J. R. Meyer, "Band parameters for nitrogen-
--  containing semiconductors," Journal of Applied Physics 94,
--  3675-3696 (2003). DOI: 10.1063/1.1600519
--
-- Original parameter source cited therein:
-- K. Shimada, T. Sota, and K. Suzuki, "First-principles study on
--  electronic and elastic properties of BN, AlN, and GaN,"
--  Journal of Applied Physics 84, 4951-4958 (1998).
--  DOI: 10.1063/1.368739
	local enabled = true
	local value = -3.4
	return value, enabled
end

function material.qw_D6(state)
-- Valence-band deformation potential D6. Units: eV.
--
-- D6: VM2003 RECOMMENDED value, obtained from the quasi-cubic
-- approximation (D5 = D6 in that limit). It is NOT sqrt(2)*D3.
--
-- I. Vurgaftman and J. R. Meyer, "Band parameters for nitrogen-
--  containing semiconductors," Journal of Applied Physics 94,
--  3675-3696 (2003). DOI: 10.1063/1.1600519
--
-- Original parameter source cited therein:
-- K. Shimada, T. Sota, and K. Suzuki, "First-principles study on
--  electronic and elastic properties of BN, AlN, and GaN,"
--  Journal of Applied Physics 84, 4951-4958 (1998).
--  DOI: 10.1063/1.368739
	local enabled = true
	local value = -3.4
	return value, enabled
end

function material.qw_C13(state)
-- Elastic stiffness constant C13. Units: GPa.
--
-- Reference:
-- A. F. Wright, "Elastic properties of zinc-blende and wurtzite
--  AlN, GaN, and InN," Journal of Applied Physics 82, 2833-2839
--  (1997). DOI: 10.1063/1.366114
-- Adopted as recommended value in:
-- I. Vurgaftman and J. R. Meyer, Journal of Applied Physics 94,
--  3675-3696 (2003). DOI: 10.1063/1.1600519
	local value = 108.0e9
	local enabled = true
	return value, enabled
end

function material.qw_C33(state)
-- Elastic stiffness constant C33. Units: GPa.
--
-- Reference:
-- A. F. Wright, "Elastic properties of zinc-blende and wurtzite
--  AlN, GaN, and InN," Journal of Applied Physics 82, 2833-2839
--  (1997). DOI: 10.1063/1.366114
-- Adopted as recommended value in:
-- I. Vurgaftman and J. R. Meyer, Journal of Applied Physics 94,
--  3675-3696 (2003). DOI: 10.1063/1.1600519
	local value = 373.0e9
	local enabled = true
	return value, enabled
end

function material.qw_Psp(state)
-- Spontaneous polarization Psp. Units: C/m^2.
--
-- Reference:
-- F. Bernardini, V. Fiorentini, and D. Vanderbilt, "Spontaneous
--  polarization and piezoelectric constants of III-V nitrides,"
--  Physical Review B 56, R10024-R10027 (1997).
--  DOI: 10.1103/PhysRevB.56.R10024
-- Convention: effective Psp with zinc-blende reference, c-axis
--  wurtzite formulation Ptotal = Psp + 2*e31*exx + e33*ezz.
	local value = -0.081
	local enabled = true
	return value, enabled
end

function material.e31(state)
-- Piezoelectric coefficient e31. Units: C/m^2.
--
-- Reference:
-- F. Bernardini, V. Fiorentini, and D. Vanderbilt, "Spontaneous
--  polarization and piezoelectric constants of III-V nitrides,"
--  Physical Review B 56, R10024-R10027 (1997).
--  DOI: 10.1103/PhysRevB.56.R10024
	local value = -0.60
	local enabled = true
	return value, enabled
end

function material.e33(state)
-- Piezoelectric coefficient e33. Units: C/m^2.
--
-- Reference:
-- F. Bernardini, V. Fiorentini, and D. Vanderbilt, "Spontaneous
--  polarization and piezoelectric constants of III-V nitrides,"
--  Physical Review B 56, R10024-R10027 (1997).
--  DOI: 10.1103/PhysRevB.56.R10024
	local value = 1.46
	local enabled = true
	return value, enabled
end

function material.lattice_a(state)
	-- Lattice constant, a-axis
	-- Units: m
	--
	-- Reference:
	-- I. Vurgaftman and J. R. Meyer,
	-- "Band parameters for nitrogen-containing semiconductors,"
	-- J. Appl. Phys. 94, 3675 (2003).
	-- DOI: 10.1063/1.1600519
	--
	-- Notes:
	-- Wurtzite AlN (space group P6_3mc). In-plane a-axis
	-- a = 3.112 Angstrom at ~300 K; the c-axis (c = 4.982 Angstrom) is
	-- NOT returned here. Room-temperature value.

	local enabled = true
	local value = 3.112e-10

	return value, enabled
end

function material.qw_C11(state)
    -- Elastic stiffness constant C11
    -- Units: Pa
    --
    -- Reference:
    -- A. F. Wright,
    -- "Elastic properties of zinc-blende and wurtzite AlN, GaN, and InN,"
    -- J. Appl. Phys. 82, 2833 (1997). (first-principles)
    -- Set adopted by:
    -- I. Vurgaftman and J. R. Meyer,
    -- "Band parameters for nitrogen-containing semiconductors,"
    -- J. Appl. Phys. 94, 3675 (2003).
    -- DOI: 10.1063/1.1600519
    --
    -- Notes:
    -- Chosen for consistency with the Vurgaftman/Wright
    -- C13/C33 set commonly used alongside it.
    -- Experimental Brillouin alternative:
    -- L. E. McNeil, M. Grimsditch, R. H. French,
    -- "Vibrational spectroscopy of aluminum nitride,"
    -- J. Am. Ceram. Soc. 76, 1132 (1993).
    -- DOI: 10.1111/j.1151-2916.1993.tb03730.x
    -- C11 = 410 GPa.

    local enabled = true
    local value = 396e9

    return value, enabled
end

function material.qw_C12(state)
    -- Elastic stiffness constant C12
    -- Units: Pa
    --
    -- Reference:
    -- A. F. Wright,
    -- "Elastic properties of zinc-blende and wurtzite AlN, GaN, and InN,"
    -- J. Appl. Phys. 82, 2833 (1997). (first-principles)
    -- (adopted by Vurgaftman & Meyer 2003, DOI: 10.1063/1.1600519)
    --
    -- Notes:
    -- 137 GPa -> 137e9 Pa. McNeil et al. (1993) Brillouin: 149 GPa.

    local enabled = true
    local value = 137e9

    return value, enabled
end

function material.qw_C44(state)
    -- Elastic stiffness constant C44
    -- Units: Pa
    --
    -- Reference:
    -- A. F. Wright,
    -- "Elastic properties of zinc-blende and wurtzite AlN, GaN, and InN,"
    -- J. Appl. Phys. 82, 2833 (1997). (first-principles)
    -- (adopted by Vurgaftman & Meyer 2003, DOI: 10.1063/1.1600519)
    --
    -- Notes:
    -- 116 GPa -> 116e9 Pa. McNeil et al. (1993) Brillouin: 125 GPa.

    local enabled = true
    local value = 116e9

    return value, enabled
end

function material.phonon_lo_energy(state)
    -- Representative LO phonon energy for polar optical (Frohlich) scattering
    -- Units: eV
    --
    -- Reference:
    -- A. T. Collins, E. C. Lightowlers, P. J. Dean,
    -- "Lattice vibration spectra of aluminum nitride,"
    -- Phys. Rev. 158, 833 (1967).
    --
    -- Notes:
    -- Dispersion-theory fit to IR reflectivity: LO = 113.6 meV (916.3 cm^-1),
    -- TO = 82.7 meV (666.7 cm^-1). Same source as the dielectric constants
    -- below -> self-consistent Frohlich set. Raman: E1(LO) ~910-912 cm^-1,
    -- A1(LO) ~890 cm^-1 (McNeil et al. 1993). 0.1136 eV.

    local enabled = true
    local value = 0.1136

    return value, enabled
end

function material.epsilon_static(state)
    -- Static relative dielectric constant (lattice + electronic)
    -- Dimensionless
    --
    -- Reference:
    -- A. T. Collins, E. C. Lightowlers, P. J. Dean,
    -- "Lattice vibration spectra of aluminum nitride,"
    -- Phys. Rev. 158, 833 (1967).
    --
    -- Notes:
    -- eps_0 = 9.14 (IR reflectivity, ~300 K).
    -- LST check: 4.84*(916.3/666.7)^2 = 9.14.

    local enabled = true
    local value = 9.14

    return value, enabled
end

function material.epsilon_inf(state)
    -- High-frequency (electronic) relative dielectric constant
    -- Dimensionless
    --
    -- Reference:
    -- A. T. Collins, E. C. Lightowlers, P. J. Dean,
    -- "Lattice vibration spectra of aluminum nitride,"
    -- Phys. Rev. 158, 833 (1967).
    --
    -- Notes:
    -- eps_inf = 4.84 (IR reflectivity, ~300 K).

    local enabled = true
    local value = 4.84

    return value, enabled
end

function material.qw_e15(state)
    -- Wurtzite piezoelectric stress coefficient e15
    -- Units: C m^-2
    --
    -- Reference:
    -- K. Tsubouchi and N. Mikoshiba,
    -- IEEE Trans. Sonics Ultrason. SU-32, 634 (1985) (AlN acoustic-wave
    -- measurements), as quoted in the nextnano material database; the
    -- original paper was not independently accessed.
    --
    -- Notes:
    -- e15 = -0.48 C/m^2 (experiment). Convention: e33 > 0 for metal-polar +c.
    -- First-principles values differ in magnitude and sign depending on
    -- method/convention; the experimental value is preferred.

    local enabled = true
    local value = -0.48

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