InGaP material model

1. Introduction

This page contains the OghmaNano material model for InGaP (In(1-x)Ga(x)P).

In(1-x)Ga(x)P 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 = {}

-- =====================================================================
-- In(1-x)Ga(x)P ternary alloy.
--
-- Composition convention:
--   x = Ga fraction   (In fraction = 1 - x)
--   (This is a ternary: state.y is not used.)
--
-- Binary corners:
--   (x=0) -> InP
--   (x=1) -> GaP
--
-- Most properties are linear (Vegard-style) interpolation between the
-- InP and GaP corner values, each evaluated at state.T:
--
--   Q(x) = (1-x) Q_InP + x Q_GaP
--
-- Two properties are treated more carefully:
--   * Eg          -- direct/indirect (Gamma/X) crossover near x~0.74.
--   * thermal cond -- strong alloy-disorder dip mid-composition.
--
-- The central composition is Ga(0.51)In(0.49)P (x = 0.51), which is
-- lattice-matched to GaAs and has Eg ~ 1.9 eV (direct). It is the top
-- cell of GaAs-based multi-junction solar cells and the active layer
-- of AlGaInP visible LEDs / HBT emitters.
--
-- FIRST-PASS LIMITATIONS:
--   * Electron MOBILITY is interpolated linearly and is OPTIMISTIC:
--     alloy-disorder scattering (and, above the crossover, transfer to
--     the heavy X valleys) reduce the real mobility below this value.
--   * CuPt-B ordering (see Eg) shifts the gap and is not modelled.
-- =====================================================================

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

local function lerp(x, v_InP, v_GaP)
	return (1.0 - x)*v_InP + x*v_GaP
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 "InGaP", enabled
end

function material.description()
	local enabled = true

	return "In(1-x)Ga(x)P ternary alloy", enabled
end

function material.formula()
	local enabled = true

	return "In(1-x)Ga(x)P", enabled
end

function material.Eg(state)
	-- Units: eV
	--
	-- Fundamental band gap of In(1-x)Ga(x)P, taken as the minimum of
	-- the Gamma-valley (direct) and X-valley (indirect) gaps. InGaP is
	-- direct for x below ~0.74 and indirect above it.
	--
	-- Method:
	--  1. Interpolate the Gamma gap between InP and GaP (Varshni
	--     endpoints, temperature dependent) with Gamma bowing.
	--  2. Interpolate the X gap similarly with X bowing.
	--  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.
	--   InP Gamma: Eg0=1.4236, a=3.63e-4, b=162
	--   GaP Gamma: Eg0=2.886,  a=1.081e-3, b=164
	--   InP X:     Eg0=2.384,  a=3.70e-4, b=147
	--   GaP X:     Eg0=2.35,   a=5.771e-4, b=372
	--   Gamma bowing 0.65 eV, X bowing 0.20 eV.
	--
	-- Gives Eg(300 K) = 1.35 eV (x=0, InP), ~1.87 eV at x=0.51
	-- (lattice-matched to GaAs, direct), crossover near x=0.74, and
	-- 2.27 eV (x=1, indirect GaP).
	--
	-- Note: real Ga(0.51)In(0.49)P shows spontaneous CuPt-B atomic
	-- ordering during growth, which lowers the gap by up to ~100 meV
	-- (disordered ~1.90 eV, strongly ordered ~1.85 eV). This
	-- growth-dependent shift is NOT modelled here; adjust if you need
	-- to match a specific ordered material.

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

	local EgG_InP = varshni(T, 1.4236, 3.63e-4, 162.0)
	local EgG_GaP = varshni(T, 2.886, 1.081e-3, 164.0)
	local Eg_Gamma = lerp(x, EgG_InP, EgG_GaP) - 0.65*x*(1.0 - x)

	local EgX_InP = varshni(T, 2.384, 3.70e-4, 147.0)
	local EgX_GaP = varshni(T, 2.35, 5.771e-4, 372.0)
	local Eg_X = lerp(x, EgX_InP, EgX_GaP) - 0.20*x*(1.0 - x)

	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:
	-- InP 4.38, GaP 3.8 eV.
	--
	-- Note: corner affinities are uncertain and affinity differencing
	-- is unreliable for heterojunction offsets (e.g. the
	-- Ga(0.51)In(0.49)P/GaAs offset is better taken from a measured
	-- value). Treat as approximate.

	local enabled = true
	local x = state.x

	local value = lerp(x, 4.38, 3.8)

	return value, enabled
end

function material.me(state)
    local enabled = true
    local x = state.x     -- x=0 InP, x=1 GaP (VERIFY convention)
    -- Gamma mass, InP 0.079 -> GaP 0.13. WARNING: X-indirect for Ga-rich beyond LM.
    local value = 0.079 + 0.051*x
    return value, enabled
end

function material.mh(state)
    local enabled = true
    local x = state.x
    -- HH[001]: InP 0.53 -> GaP 0.33
    local value = 0.53 - 0.20*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): InP 5.7e23, GaP 1.8e25 m^-3.
	--
	-- Note: Nc rises with x partly because the heavier, multi-valley X
	-- minima take over above the crossover; the linear form smooths
	-- this transition.

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

	local value = lerp(x, 5.7e23, 1.8e25)*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): InP 1.1e25, GaP 1.9e25 m^-3.

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

	local value = lerp(x, 1.1e25, 1.9e25)*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:
	--   InP 0.54  * (300/T)^2.0
	--   GaP 0.025 * (300/T)^1.8
	--
	-- WARNING: this linear interpolation is OPTIMISTIC. Alloy-disorder
	-- scattering suppresses the real electron mobility below the
	-- interpolated value, and above the crossover (x > ~0.74) transfer
	-- to the heavy X valleys reduces it further. For example the
	-- linear form gives ~0.28 m^2/V/s (2800 cm^2/V/s) at x=0.51,
	-- whereas measured Ga(0.51)In(0.49)P is ~0.1-0.2 m^2/V/s
	-- (1000-2000 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_InP = 0.54 *(300.0/T)^2.0
	local m_GaP = 0.025*(300.0/T)^1.8

	local value = lerp(x, m_InP, m_GaP)

	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:
	--   InP 0.02  * (300/T)^2.0
	--   GaP 0.015 * (300/T)^1.8
	--
	-- 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_InP = 0.02 *(300.0/T)^2.0
	local m_GaP = 0.015*(300.0/T)^1.8

	local value = lerp(x, m_InP, m_GaP)

	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:
	-- InP 12.5, GaP 11.1.

	local enabled = true
	local x = state.x

	local value = lerp(x, 12.5, 11.1)

	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:
	-- InP 1.2e-16, GaP 5.0e-20.
	--
	-- Note: physically B should fall sharply once the alloy becomes
	-- indirect (x > ~0.74); in the direct region (used for solar cells
	-- and LEDs) the interpolation is reasonable. Adjust by hand.

	local enabled = true
	local x = state.x

	local value = lerp(x, 1.2e-16, 5.0e-20)

	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:
	-- InP 9.0e-43, GaP 1.0e-43.
	--
	-- Note: representative values; adjust by hand for quantitative
	-- work.

	local enabled = true
	local x = state.x

	local value = lerp(x, 9.0e-43, 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:
	-- InP 9.0e-43, GaP 1.0e-43.

	local enabled = true
	local x = state.x

	local value = lerp(x, 9.0e-43, 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_InP(T) + x W_GaP(T) + C_alloy * x(1-x)
	--   kappa  = 1 / W
	--
	-- with C_alloy = 0.70 m*K/W (fitted to reproduce the measured
	-- Ga(0.51)In(0.49)P value of ~5 W/m/K), and endpoint
	-- conductivities kappa_InP = 68*(300/T)^1.4 and
	-- kappa_GaP = 110*(300/T)^1.4 W/m/K.
	--
	-- This reproduces the strong InGaP conductivity dip: kappa falls to
	-- ~5 W/m/K near the lattice-matched composition, an order of
	-- magnitude below the binaries. A linear interpolation would badly
	-- overestimate mid-composition conductivity and under-predict
	-- self-heating.

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

	local W_InP = 1.0/(68.0 *(300.0/T)^1.4)
	local W_GaP = 1.0/(110.0*(300.0/T)^1.4)
	local C_alloy = 0.70

	local W = (1.0 - x)*W_InP + x*W_GaP + 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: InP 310, GaP 430.

	local enabled = true
	local x = state.x

	local value = lerp(x, 310.0, 430.0)

	return value, enabled
end

function material.density(state)
	-- Mass density
	-- Units: kg m^-3
	--
	-- Linear interpolation of the binary corner values:
	-- InP 4810, GaP 4138.

	local enabled = true
	local x = state.x

	local value = lerp(x, 4810.0, 4138.0)

	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:
	--   InP a=5.8697 A, exp 4.6e-6 /K
	--   GaP a=5.4505 A, exp 5.3e-6 /K
	-- (Vurgaftman et al., 2001.)
	--
	-- Lattice matching to GaAs (a = 5.65325 A) occurs at x ~ 0.51, i.e.
	-- Ga(0.51)In(0.49)P -- the standard composition for GaAs-based
	-- multi-junction solar cells and AlGaInP LEDs.

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

	local a_InP = 5.8697e-10*(1.0 + 4.6e-6*(T - 300.0))
	local a_GaP = 5.4505e-10*(1.0 + 5.3e-6*(T - 300.0))

	local value = lerp(x, a_InP, a_GaP)

	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 GaP, InP from
	-- Vurgaftman, Meyer, Ram-Mohan, J. Appl. Phys. 89, 5815 (2001).
	--
	-- Note:
	-- Composition: Ga(x)In(1-x)P; x = Ga mole fraction.
	-- Linear interpolation of endpoints (no bowing applied).

	local enabled = true
	local x = state.x
	local value = (x)*0.08 + ((1.0-x))*0.108

	return value, enabled
end

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

	local enabled = true
	local x = state.x
	local value = (x)*31.4 + ((1.0-x))*20.7

	return value, enabled
end

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

	local enabled = true
	local x = state.x
	local value = (x)*4.05 + ((1.0-x))*5.08

	return value, enabled
end

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

	local enabled = true
	local x = state.x
	local value = (x)*0.49 + ((1.0-x))*1.6

	return value, enabled
end

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

	local enabled = true
	local x = state.x
	local value = (x)*1.25 + ((1.0-x))*2.1

	return value, enabled
end

function material.ac(state)
	-- Conduction-band hydrostatic deformation potential a_c
	-- Units: eV
	--
	-- Reference:
	-- Linear interpolation of binary endpoints GaP, InP from
	-- Vurgaftman, Meyer, Ram-Mohan, J. Appl. Phys. 89, 5815 (2001).
	--
	-- Note:
	-- Composition: Ga(x)In(1-x)P; x = Ga 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)*-8.2 + ((1.0-x))*-6

	return value, enabled
end

function material.av(state)
	-- Valence-band hydrostatic deformation potential a_v
	-- Units: eV
	--
	-- Reference:
	-- Linear interpolation of binary endpoints GaP, InP from
	-- Vurgaftman, Meyer, Ram-Mohan, J. Appl. Phys. 89, 5815 (2001).
	--
	-- Note:
	-- Composition: Ga(x)In(1-x)P; x = Ga 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)*1.7 + ((1.0-x))*1.27

	return value, enabled
end

function material.b(state)
	-- Valence-band shear (tetragonal) deformation potential b
	-- Units: eV
	--
	-- Reference:
	-- Linear interpolation of binary endpoints GaP, InP from
	-- Vurgaftman, Meyer, Ram-Mohan, J. Appl. Phys. 89, 5815 (2001).
	--
	-- Note:
	-- Composition: Ga(x)In(1-x)P; x = Ga 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)*-1.6 + ((1.0-x))*-2

	return value, enabled
end

function material.d(state)
	-- Valence-band shear (rhombohedral) deformation potential d
	-- Units: eV
	--
	-- Reference:
	-- Linear interpolation of binary endpoints GaP, InP from
	-- Vurgaftman, Meyer, Ram-Mohan, J. Appl. Phys. 89, 5815 (2001).
	--
	-- Note:
	-- Composition: Ga(x)In(1-x)P; x = Ga 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)*-4.6 + ((1.0-x))*-5

	return value, enabled
end

function material.lattice_a(state)
	-- Cubic (zincblende) lattice constant a
	-- Units: m
	--
	-- Reference:
	-- Vegard's law (linear) interpolation of GaP, InP endpoints,
	-- Vurgaftman, Meyer, Ram-Mohan, J. Appl. Phys. 89, 5815 (2001).
	--
	-- Note:
	-- Composition: Ga(x)In(1-x)P; x = Ga 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)*(5.4505 + 2.92e-05*(T-300.0)) + ((1.0-x))*(5.8697 + 2.79e-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 GaP, InP from
	-- Vurgaftman, Meyer, Ram-Mohan, J. Appl. Phys. 89, 5815 (2001).
	--
	-- Note:
	-- Composition: Ga(x)In(1-x)P; x = Ga mole fraction.
	-- Linear interpolation of endpoints (no bowing applied).

	local enabled = true
	local x = state.x
	local value = ((x)*140.5 + ((1.0-x))*101.1)*1e9

	return value, enabled
end

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

	local enabled = true
	local x = state.x
	local value = ((x)*62.03 + ((1.0-x))*56.1)*1e9

	return value, enabled
end

function material.C44(state)
    -- Elastic stiffness constant C44
    -- Units: Pa
    --
    -- Composition: In_x Ga_(1-x) P, x = state.x is the In fraction (In_x Ga_(1-x) P)
    --
    -- Endpoint GaP: Vurgaftman et al. (2001) recommended 703.3 kbar (Yogurtcu et al. 1981 ultrasonic: 70.3 GPa) -> 70.33 GPa.
    -- Endpoint InP: Vurgaftman et al. (2001) recommended 456 kbar (Nichols et al. 1980 ultrasonic: 45.6 GPa) -> 45.6 GPa.
    -- Both endpoints 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 (2001), recommended binary parameter tables
    -- (Tables I-VI checked for GaAs, AlAs, InAs, GaP, AlP, InP).
    -- DOI: 10.1063/1.1368156
    -- (1 kbar = 1e8 Pa)
    --
    -- Interpolation:
    -- Linear in state.x: value = (1-x)*GaP + x*InP. No bowing applied
    -- (none verified for this quantity).

    local enabled = true
    local x = state.x

    local GaP = 70.33e9
    local InP = 45.6e9

    local value = (1.0-x)*GaP + x*InP

    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:
    -- Two-mode (or multi-mode) LO phonon behaviour in this alloy. A targeted
    -- search of transport-model and parameter-compilation literature found
    -- only composition-specific effective polar-optical energies (e.g. about
    -- 34 meV quoted for lattice-matched Ga0.47In0.53As), not a general
    -- composition-dependent one-mode representation with a primary
    -- reference (unlike AlGaAs, for which Adachi 1985 gives one). Averaging
    -- the endpoint LO energies is not a recognised representation, so the
    -- parameter is left disabled.

    local enabled = false
    local value = 0.0

    return value, enabled
end

function material.epsilon_static(state)
    -- Static relative dielectric constant (lattice + electronic)
    -- Dimensionless
    --
    -- Composition: In_x Ga_(1-x) P, x = state.x is the In fraction (In_x Ga_(1-x) P)
    --
    -- Endpoint GaP: 11.1
    -- Endpoint InP: 12.5
    -- Both endpoints 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/).
    --
    -- Interpolation:
    -- Linear in state.x: value = (1-x)*GaP + x*InP. No bowing applied
    -- (none verified for this quantity).

    local enabled = true
    local x = state.x

    local GaP = 11.1
    local InP = 12.5

    local value = (1.0-x)*GaP + x*InP

    return value, enabled
end

function material.epsilon_inf(state)
    -- High-frequency (electronic) relative dielectric constant
    -- Dimensionless
    --
    -- Composition: In_x Ga_(1-x) P, x = state.x is the In fraction (In_x Ga_(1-x) P)
    --
    -- Endpoint GaP: 9.11
    -- Endpoint InP: 9.61
    -- Both endpoints 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/).
    --
    -- Interpolation:
    -- Linear in state.x: value = (1-x)*GaP + x*InP. No bowing applied
    -- (none verified for this quantity).

    local enabled = true
    local x = state.x

    local GaP = 9.11
    local InP = 9.61

    local value = (1.0-x)*GaP + x*InP

    return value, enabled
end

function material.e14(state)
    -- Zincblende piezoelectric stress coefficient e14
    -- Units: C m^-2
    --
    -- Composition: In_x Ga_(1-x) P, x = state.x is the In fraction (In_x Ga_(1-x) P)
    --
    -- Endpoint GaP: -0.1
    -- Endpoint InP: -0.035
    -- Both endpoints 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/).
    --
    -- Interpolation:
    -- Linear in state.x: value = (1-x)*GaP + x*InP. No bowing applied
    -- (none verified for this quantity).
    -- Sign as tabulated in the compilation (negative for III-V in that
    -- convention). e14 sign conventions differ between sources (orientation of
    -- [111] relative to the cation->anion bond); piezoelectric scattering
    -- depends only on e14^2.

    local enabled = true
    local x = state.x

    local GaP = -0.1
    local InP = -0.035

    local value = (1.0-x)*GaP + x*InP

    return value, enabled
end

function material.print()
	-- Representative composition: Ga(0.51)In(0.49)P, lattice-matched
	-- to GaAs (x = Ga fraction = 0.51).
	local state = {
		T = 300.0,
		x = 0.51,
		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 (Ga):     %.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

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-- 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.
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