AlInAs material model

1. Introduction

This page contains the OghmaNano material model for AlInAs (Al(x)In(1-x)As).

Al(x)In(1-x)As ternary alloy

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 = {}

-- =====================================================================
-- Al(x)In(1-x)As ternary alloy.
--
-- Composition convention:
--   x = Al fraction   (In fraction = 1 - x)
--   (This is a ternary: state.y is not used.)
--
-- Binary corners:
--   (x=0) -> InAs
--   (x=1) -> AlAs
--
-- Most properties are linear (Vegard-style) interpolation between the
-- InAs and AlAs corner values, each evaluated at state.T:
--
--   Q(x) = (1-x) Q_InAs + x Q_AlAs
--
-- Two properties are treated more carefully:
--   * Eg          -- direct/indirect (Gamma/X) crossover near x~0.63.
--   * thermal cond -- strong alloy-disorder dip mid-composition.
--
-- The central composition is Al(0.48)In(0.52)As (x = 0.48), which is
-- lattice-matched to InP and has Eg ~ 1.46 eV (direct). It is the
-- standard barrier/buffer for InP-based HEMTs, paired with
-- lattice-matched In(0.53)Ga(0.47)As channels.
--
-- FIRST-PASS LIMITATION:
--   * Electron MOBILITY is interpolated linearly and is badly
--     OPTIMISTIC: In and Al differ strongly, so alloy-disorder
--     scattering is severe and the real mobility is far below the
--     interpolation at intermediate x (see mu_e).
-- =====================================================================

-- Two-corner linear interpolation helper (v0 at x=0 = InAs).

local function lerp(x, v_InAs, v_AlAs)
	return (1.0 - x)*v_InAs + x*v_AlAs
end

-- Varshni helper (eV).

local function varshni(T, Eg0, a, b)
	return Eg0 - a*T*T/(T + b)
end

function material.name()
	local enabled = true

	return "AlInAs", enabled
end

function material.description()
	local enabled = true

	return "Al(x)In(1-x)As ternary alloy", enabled
end

function material.formula()
	local enabled = true

	return "Al(x)In(1-x)As", enabled
end

function material.Eg(state)
	-- Units: eV
	--
	-- Fundamental band gap of Al(x)In(1-x)As, taken as the minimum of
	-- the Gamma-valley (direct) and X-valley (indirect) gaps. AlInAs is
	-- direct for x below ~0.63 and indirect above it.
	--
	-- Method:
	--  1. Interpolate the Gamma gap between InAs and AlAs (Varshni
	--     endpoints, temperature dependent) with Gamma bowing.
	--  2. Interpolate the X gap similarly.
	--  3. Return min(Eg_Gamma, Eg_X).
	--
	-- Parameters 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.
	--   InAs Gamma: Eg0=0.417, a=2.76e-4, b=93
	--   AlAs Gamma: Eg0=3.099, a=8.85e-4, b=530
	--   InAs X:     Eg0=1.433, a=2.76e-4, b=93
	--   AlAs X:     Eg0=2.24,  a=7.0e-4,  b=530
	--   Gamma bowing 0.70 eV, X bowing ~0.
	--
	-- Gives Eg(300 K) = 0.354 eV (x=0, InAs), ~1.46 eV at x=0.48
	-- (lattice-matched to InP, direct), crossover near x=0.63, and
	-- 2.16 eV (x=1, indirect AlAs).

	local enabled = true
	local T = state.T
	local x = state.x

	local EgG_InAs = varshni(T, 0.417, 2.76e-4, 93.0)
	local EgG_AlAs = varshni(T, 3.099, 8.85e-4, 530.0)
	local Eg_Gamma = lerp(x, EgG_InAs, EgG_AlAs) - 0.70*x*(1.0 - x)

	local EgX_InAs = varshni(T, 1.433, 2.76e-4, 93.0)
	local EgX_AlAs = varshni(T, 2.24, 7.0e-4, 530.0)
	local Eg_X = lerp(x, EgX_InAs, EgX_AlAs)

	local value = Eg_Gamma
	if Eg_X < value then
		value = Eg_X
	end

	return value, enabled
end

function material.Xi(state)
	-- Electron affinity
	-- Units: eV
	--
	-- Linear interpolation of the binary corner affinities:
	-- InAs 4.9, AlAs 3.5 eV.
	--
	-- Note: for the AlInAs/InGaAs system the conduction-band offset is
	-- best set from a measured band alignment rather than from affinity
	-- differencing. Treat as approximate.

	local enabled = true
	local x = state.x

	local value = lerp(x, 4.9, 3.5)

	return value, enabled
end

function material.me(state)
    local enabled = true
    local x = state.x     -- Al fraction, AlxIn1-xAs (LM-to-InP is x~0.48; direct)
    -- Gamma mass, InAs 0.026 -> AlAs 0.15; slight bowing (LM x=0.48 ~0.075)
    local value = 0.026 + 0.124*x
    return value, enabled
end

function material.mh(state)
    local enabled = true
    local x = state.x
    -- HH[001]: InAs 0.333 -> AlAs 0.472
    local value = 0.333 + 0.139*x
    return value, enabled
end

function material.Nc(state)
	-- Effective conduction-band density of states
	-- Units: m^-3
	--
	-- Linear interpolation of the binary corner values, each with the
	-- (T/300)^1.5 parabolic-band temperature dependence.
	-- Nc(300 K): InAs 8.7e22, AlAs 1.5e25 m^-3.
	--
	-- Note: Nc rises steeply with x partly because the heavier,
	-- multi-valley X minima take over above the crossover; the linear
	-- form smooths this transition. Near the In-rich corner, the light
	-- InAs mass also makes the parabolic-band form approximate.

	local enabled = true
	local T = state.T
	local x = state.x
	local f = (T/300.0)^1.5

	local value = lerp(x, 8.7e22, 1.5e25)*f

	return value, enabled
end

function material.Nv(state)
	-- Effective valence-band density of states
	-- Units: m^-3
	--
	-- Linear interpolation of the binary corner values, each with the
	-- (T/300)^1.5 temperature dependence.
	-- Nv(300 K): InAs 6.6e24, AlAs 1.7e25 m^-3.

	local enabled = true
	local T = state.T
	local x = state.x
	local f = (T/300.0)^1.5

	local value = lerp(x, 6.6e24, 1.7e25)*f

	return value, enabled
end

function material.mu_e(state)
	-- Low-field electron mobility
	-- Units: m^2 V^-1 s^-1
	--
	-- Linear interpolation of the binary corner mobilities, each with
	-- its own phonon-limited temperature dependence:
	--   InAs 3.3   * (300/T)^1.7
	--   AlAs 0.028 * (300/T)^2.1
	--
	-- WARNING: this linear interpolation is badly OPTIMISTIC. Because
	-- In and Al are very dissimilar, alloy-disorder scattering is
	-- strong, and above the crossover (x > ~0.63) electrons also
	-- transfer to the heavy X valleys. The linear form gives ~1.7
	-- m^2/V/s (17000 cm^2/V/s) at x=0.48, whereas measured bulk
	-- Al(0.48)In(0.52)As is only ~0.4-0.5 m^2/V/s (4000-5000
	-- cm^2/V/s). Override with a measured mobility for quantitative
	-- work.

	local enabled = true
	local T = state.T
	local x = state.x

	local m_InAs = 3.3  *(300.0/T)^1.7
	local m_AlAs = 0.028*(300.0/T)^2.1

	local value = lerp(x, m_InAs, m_AlAs)

	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
	--
	-- Linear interpolation of the binary corner mobilities:
	--   InAs 0.05  * (300/T)^2.3
	--   AlAs 0.010 * (300/T)^2.1
	--
	-- Note: as for mu_e, alloy-disorder scattering reduces the real
	-- hole mobility below this interpolation at intermediate x.

	local enabled = true
	local T = state.T
	local x = state.x

	local m_InAs = 0.05*(300.0/T)^2.3
	local m_AlAs = 0.010*(300.0/T)^2.1

	local value = lerp(x, m_InAs, m_AlAs)

	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
	--
	-- Linear interpolation of the binary corner values:
	-- InAs 15.15, AlAs 10.06.
	-- (Gives ~12.7 at the Al(0.48)In(0.52)As composition.)

	local enabled = true
	local x = state.x

	local value = lerp(x, 15.15, 10.06)

	return value, enabled
end

function material.free_to_free_recombination(state)
	-- Radiative (band-to-band) recombination coefficient
	-- Units: m^3 s^-1
	--
	-- Linear interpolation of the binary corner values:
	-- InAs 1.1e-16, AlAs 1.0e-19.
	--
	-- Note: B should fall once the alloy becomes indirect (x > ~0.63).
	-- In the direct region the interpolation is reasonable. Adjust by
	-- hand.

	local enabled = true
	local x = state.x

	local value = lerp(x, 1.1e-16, 1.0e-19)

	return value, enabled
end

function material.auger_Cn(state)
	-- Electron Auger recombination coefficient
	-- Units: m^6 s^-1
	--
	-- Linear interpolation of the binary corner values:
	-- InAs 1.0e-39, AlAs 1.0e-43.
	--
	-- Note: the InAs corner is large (narrow gap), so the interpolated
	-- coefficient rises steeply toward the In-rich corner. Corner
	-- values are representative; adjust by hand.

	local enabled = true
	local x = state.x

	local value = lerp(x, 1.0e-39, 1.0e-43)

	return value, enabled
end

function material.auger_Cp(state)
	-- Hole Auger recombination coefficient
	-- Units: m^6 s^-1
	--
	-- Linear interpolation of the binary corner values:
	-- InAs 1.0e-39, AlAs 1.0e-43.
	--
	-- Note: see auger_Cn. Adjust by hand.

	local enabled = true
	local x = state.x

	local value = lerp(x, 1.0e-39, 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
	--
	-- 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
	--
	-- Alloy thermal conductivity via a thermal-resistivity model
	-- (after S. Adachi): the resistivity W = 1/kappa interpolates
	-- linearly between the binaries PLUS a bimodal alloy-disorder term
	-- that peaks mid-composition:
	--
	--   W(x,T) = (1-x) W_InAs(T) + x W_AlAs(T) + C_alloy * x(1-x)
	--   kappa  = 1 / W
	--
	-- with C_alloy = 0.70 m*K/W (fitted to reproduce the measured
	-- Al(0.48)In(0.52)As value of ~5 W/m/K), and endpoint
	-- conductivities kappa_InAs = 27*(300/T)^1.4 and
	-- kappa_AlAs = 91*(300/T)^1.4 W/m/K.
	--
	-- This reproduces the strong AlInAs conductivity dip: kappa falls
	-- to ~5 W/m/K near the lattice-matched composition, well below the
	-- binaries. A linear interpolation would badly overestimate
	-- mid-composition conductivity and under-predict self-heating
	-- (important for InP HEMT thermal modelling).

	local enabled = true
	local T = state.T
	local x = state.x

	local W_InAs = 1.0/(27.0*(300.0/T)^1.4)
	local W_AlAs = 1.0/(91.0*(300.0/T)^1.4)
	local C_alloy = 0.70

	local W = (1.0 - x)*W_InAs + x*W_AlAs + C_alloy*x*(1.0 - x)
	local value = 1.0/W

	return value, enabled
end

function material.heat_capacity(state)
	-- Specific heat capacity
	-- Units: J kg^-1 K^-1
	--
	-- Linear interpolation (approximately Neumann-Kopp) of the binary
	-- corner values: InAs 250, AlAs 450.

	local enabled = true
	local x = state.x

	local value = lerp(x, 250.0, 450.0)

	return value, enabled
end

function material.density(state)
	-- Mass density
	-- Units: kg m^-3
	--
	-- Linear interpolation of the binary corner values:
	-- InAs 5670, AlAs 3760.

	local enabled = true
	local x = state.x

	local value = lerp(x, 5670.0, 3760.0)

	return value, enabled
end

function material.lattice_constant(state)
	-- Cubic lattice constant
	-- Units: m
	--
	-- Vegard's law between the binary corners, each with its own
	-- linear thermal expansion:
	--   InAs a=6.0583 A, exp 4.5e-6 /K
	--   AlAs a=5.6611 A, exp 5.2e-6 /K
	-- (Vurgaftman et al., 2001.)
	--
	-- Lattice matching to InP (a = 5.8697 A) occurs at x ~ 0.48, i.e.
	-- Al(0.48)In(0.52)As -- the standard InP-based HEMT barrier, and
	-- the wide-gap partner to lattice-matched In(0.53)Ga(0.47)As.

	local enabled = true
	local T = state.T
	local x = state.x

	local a_InAs = 6.0583e-10*(1.0 + 4.5e-6*(T - 300.0))
	local a_AlAs = 5.6611e-10*(1.0 + 5.2e-6*(T - 300.0))

	local value = lerp(x, a_InAs, a_AlAs)

	return value, enabled
end

function material.thermal_tau_e(state)
	-- Electron energy relaxation time towards the lattice temperature
	-- Units: s
	--
	-- Value basis: III-V family estimate
	-- Confidence: Medium
	--
	-- Reference:
	-- https://www.mdpi.com/2673-3978/3/2/16
	--
	-- Comments:
	-- Representative III-V carrier-to-lattice relaxation time. GaAs-like values
	-- are typically sub-ps to ps and field dependent.

	local enabled = true
	local value = 5.000000e-13

	return value, enabled
end

function material.thermal_tau_h(state)
	-- Hole energy relaxation time towards the lattice temperature
	-- Units: s
	--
	-- Value basis: III-V family estimate
	-- Confidence: Medium
	--
	-- Reference:
	-- https://www.mdpi.com/2673-3978/3/2/16
	--
	-- Comments:
	-- Representative III-V carrier-to-lattice relaxation time. GaAs-like values
	-- are typically sub-ps to ps and field dependent.

	local enabled = true
	local value = 5.000000e-13

	return value, enabled
end

function material.delta_so(state)
	-- Spin-orbit splitting energy (Delta_SO)
	-- Units: eV
	--
	-- Reference:
	-- Linear interpolation of binary endpoints AlAs, InAs from
	-- Vurgaftman, Meyer, Ram-Mohan, J. Appl. Phys. 89, 5815 (2001).
	--
	-- Note:
	-- Composition: Al(x)In(1-x)As; x = Al mole fraction.
	-- Linear interpolation of endpoints (no bowing applied).

	local enabled = true
	local x = state.x
	local value = (x)*0.28 + ((1.0-x))*0.39

	return value, enabled
end

function material.Ep(state)
	-- Kane energy E_P (optical matrix element parameter)
	-- Units: eV
	--
	-- Reference:
	-- Linear interpolation of binary endpoints AlAs, InAs from
	-- Vurgaftman, Meyer, Ram-Mohan, J. Appl. Phys. 89, 5815 (2001).
	--
	-- Note:
	-- Composition: Al(x)In(1-x)As; x = Al mole fraction.
	-- Linear interpolation of endpoints (no bowing applied).

	local enabled = true
	local x = state.x
	local value = (x)*21.1 + ((1.0-x))*21.5

	return value, enabled
end

function material.gamma1(state)
	-- Luttinger parameter gamma1
	-- Units: dimensionless
	--
	-- Reference:
	-- Linear interpolation of binary endpoints AlAs, InAs from
	-- Vurgaftman, Meyer, Ram-Mohan, J. Appl. Phys. 89, 5815 (2001).
	--
	-- Note:
	-- Composition: Al(x)In(1-x)As; x = Al mole fraction.
	-- Linear interpolation of endpoints (no bowing applied).

	local enabled = true
	local x = state.x
	local value = (x)*3.76 + ((1.0-x))*20

	return value, enabled
end

function material.gamma2(state)
	-- Luttinger parameter gamma2
	-- Units: dimensionless
	--
	-- Reference:
	-- Linear interpolation of binary endpoints AlAs, InAs from
	-- Vurgaftman, Meyer, Ram-Mohan, J. Appl. Phys. 89, 5815 (2001).
	--
	-- Note:
	-- Composition: Al(x)In(1-x)As; x = Al mole fraction.
	-- Linear interpolation of endpoints (no bowing applied).

	local enabled = true
	local x = state.x
	local value = (x)*0.82 + ((1.0-x))*8.5

	return value, enabled
end

function material.gamma3(state)
	-- Luttinger parameter gamma3
	-- Units: dimensionless
	--
	-- Reference:
	-- Linear interpolation of binary endpoints AlAs, InAs from
	-- Vurgaftman, Meyer, Ram-Mohan, J. Appl. Phys. 89, 5815 (2001).
	--
	-- Note:
	-- Composition: Al(x)In(1-x)As; x = Al mole fraction.
	-- Linear interpolation of endpoints (no bowing applied).

	local enabled = true
	local x = state.x
	local value = (x)*1.42 + ((1.0-x))*9.2

	return value, enabled
end

function material.ac(state)
	-- Conduction-band hydrostatic deformation potential a_c
	-- Units: eV
	--
	-- Reference:
	-- Linear interpolation of binary endpoints AlAs, InAs from
	-- Vurgaftman, Meyer, Ram-Mohan, J. Appl. Phys. 89, 5815 (2001).
	--
	-- Note:
	-- Composition: Al(x)In(1-x)As; x = Al mole fraction.
	-- VMR sign convention: interband hydrostatic deformation potential
	-- a_gap = a_c - a_v, with a_c negative and a_v tabulated positive.
	-- Sign preserved from source; no sign flip applied.
	-- Linear interpolation of endpoints (no bowing applied).

	local enabled = true
	local x = state.x
	local value = (x)*-5.64 + ((1.0-x))*-5.08

	return value, enabled
end

function material.av(state)
	-- Valence-band hydrostatic deformation potential a_v
	-- Units: eV
	--
	-- Reference:
	-- Linear interpolation of binary endpoints AlAs, InAs from
	-- Vurgaftman, Meyer, Ram-Mohan, J. Appl. Phys. 89, 5815 (2001).
	--
	-- Note:
	-- Composition: Al(x)In(1-x)As; x = Al mole fraction.
	-- VMR sign convention: a_v tabulated as a POSITIVE number; the
	-- interband hydrostatic deformation potential is a_gap = a_c - a_v.
	-- Sign preserved from source; no sign flip applied.
	-- Linear interpolation of endpoints (no bowing applied).

	local enabled = true
	local x = state.x
	local value = (x)*2.47 + ((1.0-x))*1

	return value, enabled
end

function material.b(state)
	-- Valence-band shear (tetragonal) deformation potential b
	-- Units: eV
	--
	-- Reference:
	-- Linear interpolation of binary endpoints AlAs, InAs from
	-- Vurgaftman, Meyer, Ram-Mohan, J. Appl. Phys. 89, 5815 (2001).
	--
	-- Note:
	-- Composition: Al(x)In(1-x)As; x = Al mole fraction.
	-- Sign convention as in VMR (b negative). Sign preserved; not flipped.
	-- Linear interpolation of endpoints (no bowing applied).

	local enabled = true
	local x = state.x
	local value = (x)*-2.3 + ((1.0-x))*-1.8

	return value, enabled
end

function material.d(state)
	-- Valence-band shear (rhombohedral) deformation potential d
	-- Units: eV
	--
	-- Reference:
	-- Linear interpolation of binary endpoints AlAs, InAs from
	-- Vurgaftman, Meyer, Ram-Mohan, J. Appl. Phys. 89, 5815 (2001).
	--
	-- Note:
	-- Composition: Al(x)In(1-x)As; x = Al mole fraction.
	-- Sign convention as in VMR (d negative). Sign preserved; not flipped.
	-- Linear interpolation of endpoints (no bowing applied).

	local enabled = true
	local x = state.x
	local value = (x)*-3.4 + ((1.0-x))*-3.6

	return value, enabled
end

function material.lattice_a(state)
	-- Cubic (zincblende) lattice constant a
	-- Units: m
	--
	-- Reference:
	-- Vegard's law (linear) interpolation of AlAs, InAs endpoints,
	-- Vurgaftman, Meyer, Ram-Mohan, J. Appl. Phys. 89, 5815 (2001).
	--
	-- Note:
	-- Composition: Al(x)In(1-x)As; x = Al mole fraction.
	-- Endpoint a(T)=a300+da/dT*(T-300); linear (Vegard) mixing.

	local enabled = true
	local x = state.x
	local T = state.T
	local value = ((x)*(5.6611 + 2.90e-05*(T-300.0)) + ((1.0-x))*(6.0583 + 2.74e-05*(T-300.0)))*1e-10

	return value, enabled
end

function material.C11(state)
	-- Elastic stiffness constant C11
	-- Units: Pa
	--
	-- Reference:
	-- Linear interpolation of binary endpoints AlAs, InAs from
	-- Vurgaftman, Meyer, Ram-Mohan, J. Appl. Phys. 89, 5815 (2001).
	--
	-- Note:
	-- Composition: Al(x)In(1-x)As; x = Al mole fraction.
	-- Linear interpolation of endpoints (no bowing applied).

	local enabled = true
	local x = state.x
	local value = ((x)*125 + ((1.0-x))*83.29)*1e9

	return value, enabled
end

function material.C12(state)
	-- Elastic stiffness constant C12
	-- Units: Pa
	--
	-- Reference:
	-- Linear interpolation of binary endpoints AlAs, InAs from
	-- Vurgaftman, Meyer, Ram-Mohan, J. Appl. Phys. 89, 5815 (2001).
	--
	-- Note:
	-- Composition: Al(x)In(1-x)As; x = Al mole fraction.
	-- Linear interpolation of endpoints (no bowing applied).

	local enabled = true
	local x = state.x
	local value = ((x)*53.4 + ((1.0-x))*45.26)*1e9

	return value, enabled
end

function material.C44(state)
    -- Elastic stiffness constant C44
    -- Units: Pa
    --
    -- Composition: Al_x In_(1-x) As, x = state.x (first-listed cation carries
    -- x, as for AlGaAs; check against the existing file's convention).
    --
    -- Reference (both endpoints):
    -- I. Vurgaftman, J. R. Meyer, L. R. Ram-Mohan,
    -- "Band parameters for III-V compound semiconductors and their alloys,"
    -- J. Appl. Phys. 89, 5815 (2001), recommended binary parameter tables
    -- (Tables I-VI checked for GaAs, AlAs, InAs, GaP, AlP, InP).
    -- DOI: 10.1063/1.1368156
    --
    -- Notes:
    -- Recommended binary values: AlAs C44 = 542 kbar = 54.2 GPa,
    -- InAs C44 = 395.9 kbar = 39.59 GPa (1 kbar = 1e8 Pa).
    -- Both endpoints are taken from one compilation for consistency.
    -- Alternative AlAs value from the Adachi (1985) AlGaAs relation:
    -- 58.9 GPa (see AlAs.lua); bulk AlAs data are sparse.
    --
    -- Interpolation:
    -- Linear in state.x: C44(x) = (1-x)*C44_InAs + x*C44_AlAs. No bowing
    -- applied (none given by the compilation for elastic constants).

    local enabled = true
    local x = state.x

    local InAs = 39.59e9
    local AlAs = 54.2e9

    local value = (1.0-x)*InAs + x*AlAs

    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:
    -- AlInAs has two-mode (InAs-like / AlAs-like) LO phonons. A targeted
    -- search of transport and parameter-compilation literature found only
    -- single-composition effective values (mostly for lattice-matched
    -- Al0.48In0.52As on InP), not a composition-dependent one-mode Frohlich
    -- energy with a primary reference. Linear averaging of the binary LO
    -- energies is not a recognised representation, so none is implemented.

    local enabled = false
    local value = 0.0

    return value, enabled
end

function material.epsilon_static(state)
    -- Static relative dielectric constant (lattice + electronic)
    -- Dimensionless
    --
    -- Composition: Al_x In_(1-x) As, x = state.x
    --
    -- Endpoints (both from):
    -- 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/).
    -- AlAs: AlGaAs relation 12.90 - 2.84x at x = 1 -> 10.06.
    -- InAs: 15.15 (300 K). Consistent with LST using Hass & Henvis (1962)
    -- InAs TO/LO = 218.9/243.3 cm^-1: 12.3*(243.3/218.9)^2 = 15.2.
    --
    -- Interpolation:
    -- Linear in state.x (first-order approximation; no bowing applied).

    local enabled = true
    local x = state.x

    local InAs = 15.15
    local AlAs = 10.06

    local value = (1.0-x)*InAs + x*AlAs

    return value, enabled
end

function material.epsilon_inf(state)
    -- High-frequency (electronic) relative dielectric constant
    -- Dimensionless
    --
    -- Composition: Al_x In_(1-x) As, x = state.x
    --
    -- Endpoints (both from):
    -- 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/).
    -- AlAs: AlGaAs relation 10.89 - 2.73x at x = 1 -> 8.16.
    -- InAs: 12.3 (300 K).
    --
    -- Interpolation:
    -- Linear in state.x; no bowing applied.

    local enabled = true
    local x = state.x

    local InAs = 12.3
    local AlAs = 8.16

    local value = (1.0-x)*InAs + x*AlAs

    return value, enabled
end

function material.e14(state)
    -- Zincblende piezoelectric stress coefficient e14
    -- Units: C m^-2
    --
    -- Composition: Al_x In_(1-x) As, x = state.x
    --
    -- Endpoint AlAs: Adachi (1985) relation -0.16 - 0.065x at x = 1 -> -0.225.
    -- S. Adachi,
    -- "GaAs, AlAs, and AlxGa1-xAs: Material parameters for use in research
    -- and device applications,"
    -- J. Appl. Phys. 58, R1 (1985).
    -- DOI: 10.1063/1.336070
    -- Endpoint InAs: -0.045 C/m^2,
    -- 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/).
    --
    -- Interpolation:
    -- Linear in state.x.
    --
    -- Notes:
    -- Sign as tabulated in both sources (same convention); e14 sign
    -- conventions differ in the wider literature.

    local enabled = true
    local x = state.x

    local InAs = -0.045
    local AlAs = -0.225

    local value = (1.0-x)*InAs + x*AlAs

    return value, enabled
end

function material.print()
	-- Representative composition: Al(0.48)In(0.52)As, lattice-matched
	-- to InP (x = Al fraction = 0.48).
	local state = {
		T = 300.0,
		x = 0.48,
		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("Composition x (Al):     %.4f", state.x))
	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.
-- ============================================================================