GaAsP material model

1. Introduction

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

GaAs(1-x)P(x), x = P fraction ~ 0.40 (direct below x~0.45)

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 GaAsP (read before using):
--
-- GaAs(1-x)P(x) is a zinc-blende III-V, the classic red/orange/yellow LED alloy.
-- Here x is the PHOSPHORUS fraction (x=0 -> GaAs, x=1 -> GaP). It has a
-- DIRECT-to-INDIRECT crossover near x ~ 0.45-0.49:
--   * x < ~0.45: fundamental gap is direct (Gamma) - efficient emitter.
--   * x > ~0.45: fundamental gap is indirect (X) - poor emitter without
--     iso-electronic (N) doping.
-- Eg() below computes BOTH the Gamma and X gaps and returns the lower
-- (fundamental) one. Modelled at x = 0.40 (still direct, ~1.95 eV, ~635 nm red).
--
-- Eg and lattice constant are computed from x; other parameters are given at
-- x = 0.40 with GaAs/GaP end points noted. Near/above the crossover, electron
-- transport changes character (light Gamma -> heavy X), so revise Nc and the
-- mobilities if you move x past ~0.45.
--
-- REFERENCES
--
-- [1]  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). [end-point Gamma/X gaps, Varshni parameters, bowing]
-- [2]  S. Adachi, "Properties of Semiconductor Alloys", Wiley (2009).
--      [transport / dielectric / thermal]
-- [3]  O. Madelung, "Semiconductors: Data Handbook", Springer (2004).
-- ---------------------------------------------------------------------------

function material.name()
	local enabled = true

	return "GaAsP", enabled
end

function material.description()
	local enabled = true

	return "GaAs(1-x)P(x), x = P fraction ~ 0.40 (direct below x~0.45)", enabled
end

function material.formula()
	local enabled = true

	return "GaAsP", enabled
end

function material.Eg(state)
	-- Units: eV
	-- Refs: [1]
	--
	-- Fundamental gap = min(Gamma, X). End-point Varshni fits [1]:
	--   GaAs Gamma: 1.519 - 0.5405e-3*T^2/(T+204)
	--   GaP  Gamma: 2.886 - 0.1081e-3*T^2/(T+164)
	--   GaAs X:     1.981 - 0.460e-3 *T^2/(T+204)
	--   GaP  X:     2.350 - 0.5771e-3*T^2/(T+372)
	-- interpolated in P fraction x with bowing b_Gamma = 0.19, b_X = 0.24 eV:
	--   Eg_G(x,T) = (1-x)*GaAs_G + x*GaP_G - 0.19*x*(1-x)
	--   Eg_X(x,T) = (1-x)*GaAs_X + x*GaP_X - 0.24*x*(1-x)
	-- x = 0.40 -> Gamma ~1.95 eV < X ~1.99 eV, so still direct (~635 nm).
	-- Crossover to indirect near x ~ 0.45. Change p_fraction here and in the
	-- functions noted in the header.

	local enabled = true
	local p_fraction = 0.40
	local x = p_fraction
	local T = state.T
	local gaas_g = 1.519 - 0.5405e-3*T*T/(T + 204.0)
	local gap_g  = 2.886 - 0.1081e-3*T*T/(T + 164.0)
	local gaas_x = 1.981 - 0.460e-3 *T*T/(T + 204.0)
	local gap_x  = 2.350 - 0.5771e-3*T*T/(T + 372.0)
	local eg_gamma = (1.0 - x)*gaas_g + x*gap_g - 0.19*x*(1.0 - x)
	local eg_x     = (1.0 - x)*gaas_x + x*gap_x - 0.24*x*(1.0 - x)
	local value = math.min(eg_gamma, eg_x)

	return value, enabled
end

function material.Xi(state)
	-- Electron affinity
	-- Units: eV
	-- Refs: [2],[3]
	--
	-- ~3.96 eV at x = 0.40 (linear GaAs 4.07 -> GaP 3.80 eV).

	local enabled = true
	local value = 3.96

	return value, enabled
end

function material.me(state)
    local enabled = true
    local x = state.x     -- P fraction, GaAs1-xPx
    -- Gamma mass, GaAs 0.067 -> GaP 0.13. WARNING: X-indirect for x > ~0.45.
    local value = 0.067 + 0.063*x
    return value, enabled
end

function material.mh(state)
    local enabled = true
    local x = state.x
    -- HH[001]: GaAs 0.35 -> GaP 0.33
    local value = 0.35 - 0.02*x
    return value, enabled
end

function material.Nc(state)
	-- Effective conduction-band density of states
	-- Units: m^-3
	-- Refs: [2],[3]
	--
	-- ~1.0e24 m^-3 at 300 K for x = 0.40 (still Gamma-like, light mass).
	-- Endpoints: GaAs ~4.4e23 (Gamma), GaP ~1.8e25 m^-3 (X, multi-valley).
	-- ABOVE the crossover the band is X-like and Nc rises sharply toward
	-- the GaP value - revise for x > ~0.45.

	local enabled = true
	local T = state.T
	local value = 1.0e24*(T/300.0)^1.5

	return value, enabled
end

function material.Nv(state)
	-- Effective valence-band density of states
	-- Units: m^-3
	-- Refs: [2],[3]
	--
	-- ~1.2e25 m^-3 at 300 K for x = 0.40 (GaAs ~9e24, GaP ~1.8e25 m^-3).

	local enabled = true
	local T = state.T
	local value = 1.2e25*(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: [2]
	--
	-- ~0.15 m^2/V/s (1500 cm^2/V/s) at x = 0.40 - alloy-scattering-reduced
	-- from GaAs (~8500 cm^2/V/s). ABOVE the crossover it drops much
	-- further as the heavy indirect X valleys take over (GaP ~250
	-- cm^2/V/s). (300/T)^1.5 approximate lattice-limited.

	local enabled = true
	local T = state.T
	local value = 0.15*(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: [2]
	--
	-- ~0.015 m^2/V/s (150 cm^2/V/s) at x = 0.40 (GaAs ~400, GaP ~150
	-- cm^2/V/s). (300/T)^1.5 approximate.

	local enabled = true
	local T = state.T
	local value = 0.015*(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: [2],[3]
	--
	-- ~12.2 at x = 0.40 (linear GaAs 12.9 -> GaP 11.1).

	local enabled = true
	local value = 12.2

	return value, enabled
end

function material.free_to_free_recombination(state)
	-- Radiative recombination coefficient
	-- Units: m^3 s^-1
	-- Refs: representative (see note)
	--
	-- ~1e-10 cm^3/s = 1e-16 m^3/s while the alloy is DIRECT (x < ~0.45).
	-- Above the crossover the gap is indirect and effective radiative
	-- recombination falls by orders of magnitude - reduce this sharply for
	-- x > 0.45 (or model N iso-electronic traps separately).

	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; modest in this
	-- wide-ish gap and usually sub-dominant to radiative (direct) or SRH.

	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.

	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. Note that indirect GaAsP (x > 0.45) is often doped
	-- with iso-electronic N to create a radiative recombination centre
	-- ~0.1 eV below the conduction band - if modelling N-doped material,
	-- set this level accordingly. 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 = 1.0e21

	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]
	--
	-- Alloy-disorder model between GaAs (~45) and GaP (~77 W/m/K):
	--   1/kappa = (1-x)/45 + x/77 + 0.20*x*(1-x)   (W/m/K)^-1
	-- giving ~45 (GaAs), ~15 (x=0.4), ~77 (GaP). (300/T)^0.5 is a weak,
	-- alloy-appropriate dependence; near the pure endpoints ~T^-1.3 applies.

	local enabled = true
	local p_fraction = 0.40
	local x = p_fraction
	local T = state.T
	local inv_k = (1.0 - x)/45.0 + x/77.0 + 0.20*x*(1.0 - x)
	local value = (1.0/inv_k)*(300.0/T)^0.5

	return value, enabled
end

function material.heat_capacity(state)
	-- Specific heat capacity
	-- Units: J kg^-1 K^-1
	-- Refs: [3]
	--
	-- ~370 J/kg/K at x = 0.40 (GaAs ~330, GaP ~430 J/kg/K; interpolated).

	local enabled = true
	local value = 370.0

	return value, enabled
end

function material.density(state)
	-- Mass density
	-- Units: kg m^-3
	-- Refs: [3]
	--
	-- ~4850 kg/m^3 at x = 0.40 (GaAs 5320, GaP 4140 kg/m^3; interpolated).

	local enabled = true
	local value = 4850.0

	return value, enabled
end

function material.lattice_constant(state)
	-- Cubic lattice constant
	-- Units: m
	-- Refs: [1],[3]
	--
	-- Vegard: a(x) = 5.6533 - 0.2028*x (angstrom), GaAs 5.6533 A ->
	-- GaP 5.4505 A. x = 0.40 -> 5.572 A. Linear thermal expansion
	-- ~5.3e-6 /K at x = 0.40.

	local enabled = true
	local p_fraction = 0.40
	local x = p_fraction
	local T = state.T
	local a300 = (5.6533 - 0.2028*x)*1.0e-10
	local expansion = 5.3e-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: 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 GaAs, GaP from
	-- Vurgaftman, Meyer, Ram-Mohan, J. Appl. Phys. 89, 5815 (2001).
	--
	-- Note:
	-- Composition: GaAs(x)P(1-x); x = As mole fraction (group V).
	-- Linear interpolation of endpoints (no bowing applied).

	local enabled = true
	local x = state.x
	local value = (x)*0.341 + ((1.0-x))*0.08

	return value, enabled
end

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

	local enabled = true
	local x = state.x
	local value = (x)*28.8 + ((1.0-x))*31.4

	return value, enabled
end

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

	local enabled = true
	local x = state.x
	local value = (x)*6.98 + ((1.0-x))*4.05

	return value, enabled
end

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

	local enabled = true
	local x = state.x
	local value = (x)*2.06 + ((1.0-x))*0.49

	return value, enabled
end

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

	local enabled = true
	local x = state.x
	local value = (x)*2.93 + ((1.0-x))*1.25

	return value, enabled
end

function material.ac(state)
	-- Conduction-band hydrostatic deformation potential a_c
	-- Units: eV
	--
	-- Reference:
	-- Linear interpolation of binary endpoints GaAs, GaP from
	-- Vurgaftman, Meyer, Ram-Mohan, J. Appl. Phys. 89, 5815 (2001).
	--
	-- Note:
	-- Composition: GaAs(x)P(1-x); x = As mole fraction (group V).
	-- 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)*-7.17 + ((1.0-x))*-8.2

	return value, enabled
end

function material.av(state)
	-- Valence-band hydrostatic deformation potential a_v
	-- Units: eV
	--
	-- Reference:
	-- Linear interpolation of binary endpoints GaAs, GaP from
	-- Vurgaftman, Meyer, Ram-Mohan, J. Appl. Phys. 89, 5815 (2001).
	--
	-- Note:
	-- Composition: GaAs(x)P(1-x); x = As mole fraction (group V).
	-- 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)*1.16 + ((1.0-x))*1.7

	return value, enabled
end

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

	return value, enabled
end

function material.d(state)
	-- Valence-band shear (rhombohedral) deformation potential d
	-- Units: eV
	--
	-- Reference:
	-- Linear interpolation of binary endpoints GaAs, GaP from
	-- Vurgaftman, Meyer, Ram-Mohan, J. Appl. Phys. 89, 5815 (2001).
	--
	-- Note:
	-- Composition: GaAs(x)P(1-x); x = As mole fraction (group V).
	-- 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)*-4.8 + ((1.0-x))*-4.6

	return value, enabled
end

function material.lattice_a(state)
	-- Cubic (zincblende) lattice constant a
	-- Units: m
	--
	-- Reference:
	-- Vegard's law (linear) interpolation of GaAs, GaP endpoints,
	-- Vurgaftman, Meyer, Ram-Mohan, J. Appl. Phys. 89, 5815 (2001).
	--
	-- Note:
	-- Composition: GaAs(x)P(1-x); x = As mole fraction (group V).
	-- 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)*(5.65325 + 3.88e-05*(T-300.0)) + ((1.0-x))*(5.4505 + 2.92e-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 GaAs, GaP from
	-- Vurgaftman, Meyer, Ram-Mohan, J. Appl. Phys. 89, 5815 (2001).
	--
	-- Note:
	-- Composition: GaAs(x)P(1-x); x = As mole fraction (group V).
	-- Linear interpolation of endpoints (no bowing applied).

	local enabled = true
	local x = state.x
	local value = ((x)*122.1 + ((1.0-x))*140.5)*1e9

	return value, enabled
end

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

	local enabled = true
	local x = state.x
	local value = ((x)*56.6 + ((1.0-x))*62.03)*1e9

	return value, enabled
end

function material.C44(state)
    -- Elastic stiffness constant C44
    -- Units: Pa
    --
    -- Composition: GaAs_(1-x) P_x, x = state.x is the P fraction (standard GaAs_(1-x)P_x notation)
    --
    -- Endpoint GaAs: Vurgaftman et al. (2001) recommended 600 kbar (underlying ultrasonic data; Ioffe/Burenkov 1973 gives 59.6 GPa at 300 K) -> 60 GPa.
    -- Endpoint GaP: Vurgaftman et al. (2001) recommended 703.3 kbar (Yogurtcu et al. 1981 ultrasonic: 70.3 GPa) -> 70.33 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)*GaAs + x*GaP. No bowing applied
    -- (none verified for this quantity).

    local enabled = true
    local x = state.x

    local GaAs = 60e9
    local GaP = 70.33e9

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

    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: GaAs_(1-x) P_x, x = state.x is the P fraction (standard GaAs_(1-x)P_x notation)
    --
    -- Endpoint GaAs: 12.9
    -- Endpoint GaP: 11.1
    -- 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)*GaAs + x*GaP. No bowing applied
    -- (none verified for this quantity).

    local enabled = true
    local x = state.x

    local GaAs = 12.9
    local GaP = 11.1

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

    return value, enabled
end

function material.epsilon_inf(state)
    -- High-frequency (electronic) relative dielectric constant
    -- Dimensionless
    --
    -- Composition: GaAs_(1-x) P_x, x = state.x is the P fraction (standard GaAs_(1-x)P_x notation)
    --
    -- Endpoint GaAs: 10.89
    -- Endpoint GaP: 9.11
    -- 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)*GaAs + x*GaP. No bowing applied
    -- (none verified for this quantity).

    local enabled = true
    local x = state.x

    local GaAs = 10.89
    local GaP = 9.11

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

    return value, enabled
end

function material.e14(state)
    -- Zincblende piezoelectric stress coefficient e14
    -- Units: C m^-2
    --
    -- Composition: GaAs_(1-x) P_x, x = state.x is the P fraction (standard GaAs_(1-x)P_x notation)
    --
    -- Endpoint GaAs: -0.16
    -- Endpoint GaP: -0.1
    -- 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)*GaAs + x*GaP. 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 GaAs = -0.16
    local GaP = -0.1

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

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