Caesium lead iodide-bromide-chloride perovskite material model

1. Introduction

This page contains the OghmaNano material model for Caesium lead iodide-bromide-chloride perovskite (CsPb(I1-x-y Brx Cly)3).

Caesium lead mixed-halide perovskite CsPb(I1-x-y Brx Cly)3 (x = Br fraction, y = Cl fraction), cubic phase; ternary linear interpolation of CsPbI3, CsPbBr3 and CsPbCl3.

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.
--
-- OghmaNano material file: CsPb(I1-x-y Brx Cly)3
-- Caesium lead iodide-bromide-chloride perovskite
--
-- Composition: x = bromide fraction, y = chloride fraction,
-- iodide fraction = 1 - x - y (x >= 0, y >= 0, x + y <= 1),
-- taken from state.x and state.y.
--
-- Phase: Cubic alpha-phase, Pm-3m (space group 221, Oh point group),
-- Phase: as in all three endpoint files; the phase used by the k.p model.
--
-- Every numerical parameter is a ternary linear interpolation of the
-- endpoint files CsPbI3.lua, CsPbBr3.lua and CsPbCl3.lua:
--   p(x,y) = (1-x-y)*p_I + x*p_Br + y*p_Cl
-- Where an endpoint function has a temperature law, the law is kept
-- and its coefficient is interpolated.
-- Generated: 29 September 2026
--
-- The eight perovskite_* functions and material.Eg_qw carry the
-- eight-band k.p parameters of the endpoint files (Table I of
-- Gawarecki et al., Phys. Rev. Applied 22, 014058 (2024)).
--
-- Units are SI unless stated otherwise. P_parallel and Pz are kept in
-- eV*Angstrom exactly as in the endpoint files (they are NOT the Kane
-- energy Ep).

local material = {}

function material.name()
	local enabled = true

	return "Caesium lead iodide-bromide-chloride perovskite", enabled
end

function material.description()
	local enabled = true

	return "Caesium lead mixed-halide perovskite CsPb(I1-x-y Brx Cly)3 (x = Br fraction, y = Cl fraction), cubic phase; ternary linear interpolation of CsPbI3, CsPbBr3 and CsPbCl3.", enabled
end

function material.formula()
	local enabled = true

	return "CsPb(I1-x-y Brx Cly)3", enabled
end

function material.Eg(state)
	-- Band gap (general device model)
	-- Units: eV
	--
	-- Endpoint values:
	--   CsPbI3.lua   p_I  = 1.73
	--   CsPbBr3.lua  p_Br = 2.3
	--   CsPbCl3.lua  p_Cl = 3.0
	-- Interpolation: ternary linear interpolation
	-- p(x,y) = (1-x-y)*p_I + x*p_Br + y*p_Cl
	-- Generated: 29 September 2026
	--
	-- Endpoint references:
	-- CsPbI3:
	--   G. E. Eperon et al., J. Mater. Chem. A 3, 19688 (2015).
	--   DOI: 10.1039/C5TA06398A
	-- CsPbBr3:
	--   G. Mannino et al., J. Phys. Chem. Lett. 11, 2490 (2020).
	--   DOI: 10.1021/acs.jpclett.0c00295
	-- CsPbCl3:
	--   G. Murtaza and I. Ahmad, Physica B 406, 3222 (2011);
	--   L.-y. Huang, W. R. L. Lambrecht, Phys. Rev. B 88, 165203 (2013).

	local enabled = true
	local x = state.x
	local y = state.y
	local p_I = 1.73
	local p_Br = 2.3
	local p_Cl = 3.0
	local value = (1.0-x-y)*p_I + x*p_Br + y*p_Cl

	return value, enabled
end

function material.Xi(state)
	-- Electron affinity (absolute conduction-band minimum vs vacuum)
	-- Units: eV
	--
	-- Endpoint values:
	--   CsPbI3.lua   p_I  = 3.95
	--   CsPbBr3.lua  p_Br = 3.6
	--   CsPbCl3.lua  p_Cl = 3.0
	-- Interpolation: ternary linear interpolation
	-- p(x,y) = (1-x-y)*p_I + x*p_Br + y*p_Cl
	-- Generated: 29 September 2026

	local enabled = true
	local x = state.x
	local y = state.y
	local p_I = 3.95
	local p_Br = 3.6
	local p_Cl = 3.0
	local value = (1.0-x-y)*p_I + x*p_Br + y*p_Cl

	return value, enabled
end

function material.Nc(state)
	-- Effective conduction-band density of states
	-- Units: m^-3
	--
	-- Endpoint values:
	--   CsPbI3.lua   A_I  = 1.109e+24
	--   CsPbBr3.lua  A_Br = 1.576e+24
	--   CsPbCl3.lua  A_Cl = 2.062e+24
	-- Interpolation: ternary linear interpolation
	-- A(x,y) = (1-x-y)*A_I + x*A_Br + y*A_Cl
	-- value = A*(T/300)^1.5 (temperature law of the endpoint files)
	-- Generated: 29 September 2026
	--
	-- Endpoint reference:
	-- Gawarecki et al., Phys. Rev. Applied 22, 014058 (2024), Table I
	-- (valence-band masses m_v used for the endpoint values).

	local enabled = true
	local T = state.T
	local x = state.x
	local y = state.y
	local A_I = 1.109e+24
	local A_Br = 1.576e+24
	local A_Cl = 2.062e+24
	local A = (1.0-x-y)*A_I + x*A_Br + y*A_Cl
	local value = A*(T/300.0)^1.5

	return value, enabled
end

function material.Nv(state)
	-- Effective valence-band density of states
	-- Units: m^-3
	--
	-- Endpoint values:
	--   CsPbI3.lua   A_I  = 1.109e+24
	--   CsPbBr3.lua  A_Br = 1.576e+24
	--   CsPbCl3.lua  A_Cl = 2.062e+24
	-- Interpolation: ternary linear interpolation
	-- A(x,y) = (1-x-y)*A_I + x*A_Br + y*A_Cl
	-- value = A*(T/300)^1.5 (temperature law of the endpoint files)
	-- Generated: 29 September 2026
	--
	-- Endpoint reference:
	-- Gawarecki et al., Phys. Rev. Applied 22, 014058 (2024), Table I
	-- (valence-band masses m_v used for the endpoint values).

	local enabled = true
	local T = state.T
	local x = state.x
	local y = state.y
	local A_I = 1.109e+24
	local A_Br = 1.576e+24
	local A_Cl = 2.062e+24
	local A = (1.0-x-y)*A_I + x*A_Br + y*A_Cl
	local value = A*(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
	--
	-- Endpoint values:
	--   CsPbI3.lua   A_I  = 1.500e-03
	--   CsPbBr3.lua  A_Br = 2.000e-03
	--   CsPbCl3.lua  A_Cl = 5.000e-04
	-- Interpolation: ternary linear interpolation
	-- A(x,y) = (1-x-y)*A_I + x*A_Br + y*A_Cl
	-- value = A*(300/T)^1.5 (temperature law of the endpoint files)
	-- Generated: 29 September 2026

	local enabled = true
	local T = state.T
	local x = state.x
	local y = state.y
	local A_I = 1.500e-03
	local A_Br = 2.000e-03
	local A_Cl = 5.000e-04
	local A = (1.0-x-y)*A_I + x*A_Br + y*A_Cl
	local value = A*(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
	--
	-- Endpoint values:
	--   CsPbI3.lua   A_I  = 1.500e-03
	--   CsPbBr3.lua  A_Br = 2.000e-03
	--   CsPbCl3.lua  A_Cl = 5.000e-04
	-- Interpolation: ternary linear interpolation
	-- A(x,y) = (1-x-y)*A_I + x*A_Br + y*A_Cl
	-- value = A*(300/T)^1.5 (temperature law of the endpoint files)
	-- Generated: 29 September 2026

	local enabled = true
	local T = state.T
	local x = state.x
	local y = state.y
	local A_I = 1.500e-03
	local A_Br = 2.000e-03
	local A_Cl = 5.000e-04
	local A = (1.0-x-y)*A_I + x*A_Br + y*A_Cl
	local value = A*(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 permittivity for the electrostatic (drift-diffusion) model
	-- Dimensionless
	--
	-- Endpoint values:
	--   CsPbI3.lua   p_I  = 20.0
	--   CsPbBr3.lua  p_Br = 20.0
	--   CsPbCl3.lua  p_Cl = 20.0
	-- Interpolation: ternary linear interpolation
	-- p(x,y) = (1-x-y)*p_I + x*p_Br + y*p_Cl
	-- Generated: 29 September 2026
	--
	-- Endpoint reference:
	-- S. Becker et al., Nature 553, 189 (2018), arXiv:1707.03071.

	local enabled = true
	local x = state.x
	local y = state.y
	local p_I = 20.0
	local p_Br = 20.0
	local p_Cl = 20.0
	local value = (1.0-x-y)*p_I + x*p_Br + y*p_Cl

	return value, enabled
end

function material.free_to_free_recombination(state)
	-- Radiative (band-to-band) recombination coefficient
	-- Units: m^3 s^-1
	--
	-- Endpoint values:
	--   CsPbI3.lua   p_I  = 1.000e-16
	--   CsPbBr3.lua  p_Br = 1.000e-16
	--   CsPbCl3.lua  p_Cl = 1.000e-16
	-- Interpolation: ternary linear interpolation
	-- p(x,y) = (1-x-y)*p_I + x*p_Br + y*p_Cl
	-- Generated: 29 September 2026
	--
	-- Endpoint reference:
	-- L. M. Herz, Acc. Chem. Res. 49, 146 (2016).

	local enabled = true
	local x = state.x
	local y = state.y
	local p_I = 1.000e-16
	local p_Br = 1.000e-16
	local p_Cl = 1.000e-16
	local value = (1.0-x-y)*p_I + x*p_Br + y*p_Cl

	return value, enabled
end

function material.auger_Cn(state)
	-- Electron Auger recombination coefficient
	-- Units: m^6 s^-1
	--
	-- Endpoint values:
	--   CsPbI3.lua   p_I  = 1.0e-40
	--   CsPbBr3.lua  p_Br = 1.0e-40
	--   CsPbCl3.lua  p_Cl = 1.0e-40
	-- Interpolation: ternary linear interpolation
	-- p(x,y) = (1-x-y)*p_I + x*p_Br + y*p_Cl
	-- Generated: 29 September 2026
	--
	-- Endpoint reference:
	-- L. M. Herz, Acc. Chem. Res. 49, 146 (2016).

	local enabled = true
	local x = state.x
	local y = state.y
	local p_I = 1.0e-40
	local p_Br = 1.0e-40
	local p_Cl = 1.0e-40
	local value = (1.0-x-y)*p_I + x*p_Br + y*p_Cl

	return value, enabled
end

function material.auger_Cp(state)
	-- Hole Auger recombination coefficient
	-- Units: m^6 s^-1
	--
	-- Endpoint values:
	--   CsPbI3.lua   p_I  = 1.0e-40
	--   CsPbBr3.lua  p_Br = 1.0e-40
	--   CsPbCl3.lua  p_Cl = 1.0e-40
	-- Interpolation: ternary linear interpolation
	-- p(x,y) = (1-x-y)*p_I + x*p_Br + y*p_Cl
	-- Generated: 29 September 2026
	--
	-- Endpoint reference:
	-- L. M. Herz, Acc. Chem. Res. 49, 146 (2016).

	local enabled = true
	local x = state.x
	local y = state.y
	local p_I = 1.0e-40
	local p_Br = 1.0e-40
	local p_Cl = 1.0e-40
	local value = (1.0-x-y)*p_I + x*p_Br + y*p_Cl

	return value, enabled
end

function material.ss_srh_trap_energy(state)
	-- SRH trap energy relative to mid-gap
	-- Units: eV
	--
	-- Endpoint values:
	--   CsPbI3.lua   p_I  = 0.0
	--   CsPbBr3.lua  p_Br = 0.0
	--   CsPbCl3.lua  p_Cl = 0.0
	-- Interpolation: ternary linear interpolation
	-- p(x,y) = (1-x-y)*p_I + x*p_Br + y*p_Cl
	-- Generated: 29 September 2026

	local enabled = true
	local x = state.x
	local y = state.y
	local p_I = 0.0
	local p_Br = 0.0
	local p_Cl = 0.0
	local value = (1.0-x-y)*p_I + x*p_Br + y*p_Cl

	return value, enabled
end

function material.ss_srh_Nt(state)
	-- SRH trap density
	-- Units: m^-3
	--
	-- Endpoint values:
	--   CsPbI3.lua   p_I  = 1.0e21
	--   CsPbBr3.lua  p_Br = 1.0e21
	--   CsPbCl3.lua  p_Cl = 1.0e21
	-- Interpolation: ternary linear interpolation
	-- p(x,y) = (1-x-y)*p_I + x*p_Br + y*p_Cl
	-- Generated: 29 September 2026

	local enabled = true
	local x = state.x
	local y = state.y
	local p_I = 1.0e21
	local p_Br = 1.0e21
	local p_Cl = 1.0e21
	local value = (1.0-x-y)*p_I + x*p_Br + y*p_Cl

	return value, enabled
end

function material.ss_srh_sigma_n(state)
	-- Electron capture cross section
	-- Units: m^2
	--
	-- Endpoint values:
	--   CsPbI3.lua   p_I  = 1.0e-19
	--   CsPbBr3.lua  p_Br = 1.0e-19
	--   CsPbCl3.lua  p_Cl = 1.0e-19
	-- Interpolation: ternary linear interpolation
	-- p(x,y) = (1-x-y)*p_I + x*p_Br + y*p_Cl
	-- Generated: 29 September 2026

	local enabled = true
	local x = state.x
	local y = state.y
	local p_I = 1.0e-19
	local p_Br = 1.0e-19
	local p_Cl = 1.0e-19
	local value = (1.0-x-y)*p_I + x*p_Br + y*p_Cl

	return value, enabled
end

function material.ss_srh_sigma_p(state)
	-- Hole capture cross section
	-- Units: m^2
	--
	-- Endpoint values:
	--   CsPbI3.lua   p_I  = 1.0e-19
	--   CsPbBr3.lua  p_Br = 1.0e-19
	--   CsPbCl3.lua  p_Cl = 1.0e-19
	-- Interpolation: ternary linear interpolation
	-- p(x,y) = (1-x-y)*p_I + x*p_Br + y*p_Cl
	-- Generated: 29 September 2026

	local enabled = true
	local x = state.x
	local y = state.y
	local p_I = 1.0e-19
	local p_Br = 1.0e-19
	local p_Cl = 1.0e-19
	local value = (1.0-x-y)*p_I + x*p_Br + y*p_Cl

	return value, enabled
end

function material.thermal_kl(state)
	-- Thermal conductivity
	-- Units: W m^-1 K^-1
	--
	-- Endpoint values:
	--   CsPbI3.lua   p_I  = 0.4
	--   CsPbBr3.lua  p_Br = 0.4
	--   CsPbCl3.lua  p_Cl = 0.4
	-- Interpolation: ternary linear interpolation
	-- p(x,y) = (1-x-y)*p_I + x*p_Br + y*p_Cl
	-- Generated: 29 September 2026

	local enabled = true
	local x = state.x
	local y = state.y
	local p_I = 0.4
	local p_Br = 0.4
	local p_Cl = 0.4
	local value = (1.0-x-y)*p_I + x*p_Br + y*p_Cl

	return value, enabled
end

function material.heat_capacity(state)
	-- Specific heat capacity
	-- Units: J kg^-1 K^-1
	--
	-- Endpoint values:
	--   CsPbI3.lua   p_I  = 320.0
	--   CsPbBr3.lua  p_Br = 320.0
	--   CsPbCl3.lua  p_Cl = 320.0
	-- Interpolation: ternary linear interpolation
	-- p(x,y) = (1-x-y)*p_I + x*p_Br + y*p_Cl
	-- Generated: 29 September 2026

	local enabled = true
	local x = state.x
	local y = state.y
	local p_I = 320.0
	local p_Br = 320.0
	local p_Cl = 320.0
	local value = (1.0-x-y)*p_I + x*p_Br + y*p_Cl

	return value, enabled
end

function material.density(state)
	-- Mass density
	-- Units: kg m^-3
	--
	-- Endpoint values:
	--   CsPbI3.lua   p_I  = 4800.6
	--   CsPbBr3.lua  p_Br = 4721.5
	--   CsPbCl3.lua  p_Cl = 4210.2
	-- Interpolation: ternary linear interpolation
	-- p(x,y) = (1-x-y)*p_I + x*p_Br + y*p_Cl
	-- Generated: 29 September 2026

	local enabled = true
	local x = state.x
	local y = state.y
	local p_I = 4800.6
	local p_Br = 4721.5
	local p_Cl = 4210.2
	local value = (1.0-x-y)*p_I + x*p_Br + y*p_Cl

	return value, enabled
end

function material.lattice_constant(state)
	-- Cubic / pseudo-cubic lattice constant
	-- Units: m
	--
	-- Endpoint values:
	--   CsPbI3.lua   p_I  = 6.294e-10
	--   CsPbBr3.lua  p_Br = 5.886e-10
	--   CsPbCl3.lua  p_Cl = 5.605e-10
	-- Interpolation: ternary linear interpolation
	-- p(x,y) = (1-x-y)*p_I + x*p_Br + y*p_Cl
	-- Generated: 29 September 2026
	--
	-- Endpoint reference:
	-- K. Gawarecki, M. Wisniewski, M. Polak, R. Kudrawiec,
	-- and M. Gladysiewicz,
	-- "Eight-band k.p description and material gain for selected
	-- cubic and pseudocubic perovskites,"
	-- Physical Review Applied 22, 014058 (2024).
	-- DOI: 10.1103/PhysRevApplied.22.014058
	-- Table I.

	local enabled = true
	local x = state.x
	local y = state.y
	local p_I = 6.294e-10
	local p_Br = 5.886e-10
	local p_Cl = 5.605e-10
	local value = (1.0-x-y)*p_I + x*p_Br + y*p_Cl

	return value, enabled
end

function material.thermal_tau_e(state)
	-- Electron energy relaxation time towards the lattice temperature
	-- Units: s
	--
	-- Endpoint values:
	--   CsPbI3.lua   p_I  = 1.000000e-12
	--   CsPbBr3.lua  p_Br = 1.000000e-12
	--   CsPbCl3.lua  p_Cl = 1.000000e-12
	-- Interpolation: ternary linear interpolation
	-- p(x,y) = (1-x-y)*p_I + x*p_Br + y*p_Cl
	-- Generated: 29 September 2026

	local enabled = true
	local x = state.x
	local y = state.y
	local p_I = 1.000000e-12
	local p_Br = 1.000000e-12
	local p_Cl = 1.000000e-12
	local value = (1.0-x-y)*p_I + x*p_Br + y*p_Cl

	return value, enabled
end

function material.thermal_tau_h(state)
	-- Hole energy relaxation time towards the lattice temperature
	-- Units: s
	--
	-- Endpoint values:
	--   CsPbI3.lua   p_I  = 1.000000e-12
	--   CsPbBr3.lua  p_Br = 1.000000e-12
	--   CsPbCl3.lua  p_Cl = 1.000000e-12
	-- Interpolation: ternary linear interpolation
	-- p(x,y) = (1-x-y)*p_I + x*p_Br + y*p_Cl
	-- Generated: 29 September 2026

	local enabled = true
	local x = state.x
	local y = state.y
	local p_I = 1.000000e-12
	local p_Br = 1.000000e-12
	local p_Cl = 1.000000e-12
	local value = (1.0-x-y)*p_I + x*p_Br + y*p_Cl

	return value, enabled
end

function material.Eg_qw(state)
	-- Band gap used by the eight-band k.p Hamiltonian (R point)
	-- Units: eV
	--
	-- Endpoint values:
	--   CsPbI3.lua   p_I  = 1.416
	--   CsPbBr3.lua  p_Br = 2.073
	--   CsPbCl3.lua  p_Cl = 2.744
	-- Interpolation: ternary linear interpolation
	-- p(x,y) = (1-x-y)*p_I + x*p_Br + y*p_Cl
	-- Generated: 29 September 2026
	--
	-- DFT gap used by the eight-band k.p Hamiltonian; distinct from
	-- material.Eg() (the device-model gap).
	--
	-- Endpoint reference:
	-- K. Gawarecki, M. Wisniewski, M. Polak, R. Kudrawiec,
	-- and M. Gladysiewicz,
	-- "Eight-band k.p description and material gain for selected
	-- cubic and pseudocubic perovskites,"
	-- Physical Review Applied 22, 014058 (2024).
	-- DOI: 10.1103/PhysRevApplied.22.014058
	-- Table I.

	local enabled = true
	local x = state.x
	local y = state.y
	local p_I = 1.416
	local p_Br = 2.073
	local p_Cl = 2.744
	local value = (1.0-x-y)*p_I + x*p_Br + y*p_Cl

	return value, enabled
end

function material.perovskite_delta_c(state)
	-- Conduction-band spin-orbit splitting Delta_c
	-- Units: eV
	--
	-- Endpoint values:
	--   CsPbI3.lua   p_I  = 1.494
	--   CsPbBr3.lua  p_Br = 1.476
	--   CsPbCl3.lua  p_Cl = 1.444
	-- Interpolation: ternary linear interpolation
	-- p(x,y) = (1-x-y)*p_I + x*p_Br + y*p_Cl
	-- Generated: 29 September 2026
	--
	-- Perovskite-specific conduction-band spin-orbit parameter (the CB
	-- is p-like). NOT a III-V valence-band delta_so.
	--
	-- Endpoint reference:
	-- K. Gawarecki, M. Wisniewski, M. Polak, R. Kudrawiec,
	-- and M. Gladysiewicz,
	-- "Eight-band k.p description and material gain for selected
	-- cubic and pseudocubic perovskites,"
	-- Physical Review Applied 22, 014058 (2024).
	-- DOI: 10.1103/PhysRevApplied.22.014058
	-- Table I.

	local enabled = true
	local x = state.x
	local y = state.y
	local p_I = 1.494
	local p_Br = 1.476
	local p_Cl = 1.444
	local value = (1.0-x-y)*p_I + x*p_Br + y*p_Cl

	return value, enabled
end

function material.perovskite_delta(state)
	-- Non-cubic splitting parameter delta
	-- Units: eV
	--
	-- Endpoint values:
	--   CsPbI3.lua   p_I  = 0.0
	--   CsPbBr3.lua  p_Br = 0.0
	--   CsPbCl3.lua  p_Cl = 0.0
	-- Interpolation: ternary linear interpolation
	-- p(x,y) = (1-x-y)*p_I + x*p_Br + y*p_Cl
	-- Generated: 29 September 2026
	--
	-- delta = 0 exactly at all three cubic (Oh) endpoints, so the
	-- interpolated value is exactly 0 for all x, y.
	--
	-- Endpoint reference:
	-- K. Gawarecki, M. Wisniewski, M. Polak, R. Kudrawiec,
	-- and M. Gladysiewicz,
	-- "Eight-band k.p description and material gain for selected
	-- cubic and pseudocubic perovskites,"
	-- Physical Review Applied 22, 014058 (2024).
	-- DOI: 10.1103/PhysRevApplied.22.014058
	-- Table I.

	local enabled = true
	local x = state.x
	local y = state.y
	local p_I = 0.0
	local p_Br = 0.0
	local p_Cl = 0.0
	local value = (1.0-x-y)*p_I + x*p_Br + y*p_Cl

	return value, enabled
end

function material.perovskite_zeta(state)
	-- Non-cubic / asymmetry coupling zeta
	-- Units: eV
	--
	-- Endpoint values:
	--   CsPbI3.lua   p_I  = 0.0
	--   CsPbBr3.lua  p_Br = 0.0
	--   CsPbCl3.lua  p_Cl = 0.0
	-- Interpolation: ternary linear interpolation
	-- p(x,y) = (1-x-y)*p_I + x*p_Br + y*p_Cl
	-- Generated: 29 September 2026
	--
	-- zeta = 0 exactly at all three cubic (Oh) endpoints, so the
	-- interpolated value is exactly 0 for all x, y.
	--
	-- Endpoint reference:
	-- K. Gawarecki, M. Wisniewski, M. Polak, R. Kudrawiec,
	-- and M. Gladysiewicz,
	-- "Eight-band k.p description and material gain for selected
	-- cubic and pseudocubic perovskites,"
	-- Physical Review Applied 22, 014058 (2024).
	-- DOI: 10.1103/PhysRevApplied.22.014058
	-- Table I.

	local enabled = true
	local x = state.x
	local y = state.y
	local p_I = 0.0
	local p_Br = 0.0
	local p_Cl = 0.0
	local value = (1.0-x-y)*p_I + x*p_Br + y*p_Cl

	return value, enabled
end

function material.perovskite_P_parallel(state)
	-- Kane momentum coupling P_parallel
	-- Units: eV Angstrom
	--
	-- Endpoint values:
	--   CsPbI3.lua   p_I  = 8.601
	--   CsPbBr3.lua  p_Br = 8.948
	--   CsPbCl3.lua  p_Cl = 9.233
	-- Interpolation: ternary linear interpolation
	-- p(x,y) = (1-x-y)*p_I + x*p_Br + y*p_Cl
	-- Generated: 29 September 2026
	--
	-- Kept in eV*Angstrom as in the endpoint files; NOT the Kane energy Ep.
	-- P_parallel = Pz at all three endpoints, so P_parallel = Pz for all x, y.
	--
	-- Endpoint reference:
	-- K. Gawarecki, M. Wisniewski, M. Polak, R. Kudrawiec,
	-- and M. Gladysiewicz,
	-- "Eight-band k.p description and material gain for selected
	-- cubic and pseudocubic perovskites,"
	-- Physical Review Applied 22, 014058 (2024).
	-- DOI: 10.1103/PhysRevApplied.22.014058
	-- Table I.

	local enabled = true
	local x = state.x
	local y = state.y
	local p_I = 8.601
	local p_Br = 8.948
	local p_Cl = 9.233
	local value = (1.0-x-y)*p_I + x*p_Br + y*p_Cl

	return value, enabled
end

function material.perovskite_Pz(state)
	-- Kane momentum coupling P_z
	-- Units: eV Angstrom
	--
	-- Endpoint values:
	--   CsPbI3.lua   p_I  = 8.601
	--   CsPbBr3.lua  p_Br = 8.948
	--   CsPbCl3.lua  p_Cl = 9.233
	-- Interpolation: ternary linear interpolation
	-- p(x,y) = (1-x-y)*p_I + x*p_Br + y*p_Cl
	-- Generated: 29 September 2026
	--
	-- Kept in eV*Angstrom as in the endpoint files; NOT the Kane energy Ep.
	-- Pz = P_parallel at all three endpoints, so Pz = P_parallel for all x, y.
	--
	-- Endpoint reference:
	-- K. Gawarecki, M. Wisniewski, M. Polak, R. Kudrawiec,
	-- and M. Gladysiewicz,
	-- "Eight-band k.p description and material gain for selected
	-- cubic and pseudocubic perovskites,"
	-- Physical Review Applied 22, 014058 (2024).
	-- DOI: 10.1103/PhysRevApplied.22.014058
	-- Table I.

	local enabled = true
	local x = state.x
	local y = state.y
	local p_I = 8.601
	local p_Br = 8.948
	local p_Cl = 9.233
	local value = (1.0-x-y)*p_I + x*p_Br + y*p_Cl

	return value, enabled
end

function material.perovskite_gamma1_prime(state)
	-- Modified Luttinger-like parameter gamma1' (primed)
	-- Units: dimensionless
	--
	-- Endpoint values:
	--   CsPbI3.lua   p_I  = 2.997
	--   CsPbBr3.lua  p_Br = 2.183
	--   CsPbCl3.lua  p_Cl = 1.643
	-- Interpolation: ternary linear interpolation
	-- p(x,y) = (1-x-y)*p_I + x*p_Br + y*p_Cl
	-- Generated: 29 September 2026
	--
	-- PRIMED far-band parameter used directly in the Hamiltonian.
	-- Do NOT substitute the unprimed gamma1.
	--
	-- Endpoint reference:
	-- K. Gawarecki, M. Wisniewski, M. Polak, R. Kudrawiec,
	-- and M. Gladysiewicz,
	-- "Eight-band k.p description and material gain for selected
	-- cubic and pseudocubic perovskites,"
	-- Physical Review Applied 22, 014058 (2024).
	-- DOI: 10.1103/PhysRevApplied.22.014058
	-- Table I.

	local enabled = true
	local x = state.x
	local y = state.y
	local p_I = 2.997
	local p_Br = 2.183
	local p_Cl = 1.643
	local value = (1.0-x-y)*p_I + x*p_Br + y*p_Cl

	return value, enabled
end

function material.perovskite_gamma2_prime(state)
	-- Modified Luttinger-like parameter gamma2' (primed)
	-- Units: dimensionless
	--
	-- Endpoint values:
	--   CsPbI3.lua   p_I  = 0.683
	--   CsPbBr3.lua  p_Br = 0.394
	--   CsPbCl3.lua  p_Cl = 0.19
	-- Interpolation: ternary linear interpolation
	-- p(x,y) = (1-x-y)*p_I + x*p_Br + y*p_Cl
	-- Generated: 29 September 2026
	--
	-- PRIMED far-band parameter used directly in the Hamiltonian.
	-- Do NOT substitute the unprimed gamma2.
	--
	-- Endpoint reference:
	-- K. Gawarecki, M. Wisniewski, M. Polak, R. Kudrawiec,
	-- and M. Gladysiewicz,
	-- "Eight-band k.p description and material gain for selected
	-- cubic and pseudocubic perovskites,"
	-- Physical Review Applied 22, 014058 (2024).
	-- DOI: 10.1103/PhysRevApplied.22.014058
	-- Table I.

	local enabled = true
	local x = state.x
	local y = state.y
	local p_I = 0.683
	local p_Br = 0.394
	local p_Cl = 0.19
	local value = (1.0-x-y)*p_I + x*p_Br + y*p_Cl

	return value, enabled
end

function material.perovskite_gamma3_prime(state)
	-- Modified Luttinger-like parameter gamma3' (primed)
	-- Units: dimensionless
	--
	-- Endpoint values:
	--   CsPbI3.lua   p_I  = -1.169
	--   CsPbBr3.lua  p_Br = -1.081
	--   CsPbCl3.lua  p_Cl = -0.691
	-- Interpolation: ternary linear interpolation
	-- p(x,y) = (1-x-y)*p_I + x*p_Br + y*p_Cl
	-- Generated: 29 September 2026
	--
	-- PRIMED far-band parameter used directly in the Hamiltonian.
	-- Do NOT substitute the unprimed gamma3.
	--
	-- Endpoint reference:
	-- K. Gawarecki, M. Wisniewski, M. Polak, R. Kudrawiec,
	-- and M. Gladysiewicz,
	-- "Eight-band k.p description and material gain for selected
	-- cubic and pseudocubic perovskites,"
	-- Physical Review Applied 22, 014058 (2024).
	-- DOI: 10.1103/PhysRevApplied.22.014058
	-- Table I.

	local enabled = true
	local x = state.x
	local y = state.y
	local p_I = -1.169
	local p_Br = -1.081
	local p_Cl = -0.691
	local value = (1.0-x-y)*p_I + x*p_Br + y*p_Cl

	return value, enabled
end

function material.phonon_lo_energy(state)
	-- Effective longitudinal optical phonon energy
	-- Units: eV
	--
	-- Endpoint values:
	--   CsPbI3.lua   p_I  = 0.014
	--   CsPbBr3.lua  p_Br = 0.018
	--   CsPbCl3.lua  p_Cl = 0.026
	-- Interpolation: ternary linear interpolation
	-- p(x,y) = (1-x-y)*p_I + x*p_Br + y*p_Cl
	-- Generated: 29 September 2026
	--
	-- Endpoint references:
	-- CsPbI3:
	--   M. R. Filip, J. B. Haber, and J. B. Neaton, Phys. Rev. Lett. 127, 067401 (2021).
	-- CsPbBr3:
	--   M. R. Filip, J. B. Haber, and J. B. Neaton, Phys. Rev. Lett. 127, 067401 (2021).

	local enabled = true
	local x = state.x
	local y = state.y
	local p_I = 0.014
	local p_Br = 0.018
	local p_Cl = 0.026
	local value = (1.0-x-y)*p_I + x*p_Br + y*p_Cl

	return value, enabled
end

function material.epsilon_static(state)
	-- Static dielectric constant used for polar optical phonon scattering
	-- Dimensionless
	--
	-- Endpoint values:
	--   CsPbI3.lua   p_I  = 22.5
	--   CsPbBr3.lua  p_Br = 18.6
	--   CsPbCl3.lua  p_Cl = 17.5
	-- Interpolation: ternary linear interpolation
	-- p(x,y) = (1-x-y)*p_I + x*p_Br + y*p_Cl
	-- Generated: 29 September 2026
	--
	-- Endpoint references:
	-- CsPbI3:
	--   M. R. Filip, J. B. Haber, and J. B. Neaton, Phys. Rev. Lett. 127, 067401 (2021).
	-- CsPbBr3:
	--   M. R. Filip, J. B. Haber, and J. B. Neaton, Phys. Rev. Lett. 127, 067401 (2021).

	local enabled = true
	local x = state.x
	local y = state.y
	local p_I = 22.5
	local p_Br = 18.6
	local p_Cl = 17.5
	local value = (1.0-x-y)*p_I + x*p_Br + y*p_Cl

	return value, enabled
end

function material.epsilon_inf(state)
	-- High-frequency dielectric constant used for polar optical phonon scattering
	-- Dimensionless
	--
	-- Endpoint values:
	--   CsPbI3.lua   p_I  = 5.5
	--   CsPbBr3.lua  p_Br = 4.5
	--   CsPbCl3.lua  p_Cl = 3.7
	-- Interpolation: ternary linear interpolation
	-- p(x,y) = (1-x-y)*p_I + x*p_Br + y*p_Cl
	-- Generated: 29 September 2026
	--
	-- Endpoint references:
	-- CsPbI3:
	--   M. R. Filip, J. B. Haber, and J. B. Neaton, Phys. Rev. Lett. 127, 067401 (2021).
	-- CsPbBr3:
	--   M. R. Filip, J. B. Haber, and J. B. Neaton, Phys. Rev. Lett. 127, 067401 (2021).

	local enabled = true
	local x = state.x
	local y = state.y
	local p_I = 5.5
	local p_Br = 4.5
	local p_Cl = 3.7
	local value = (1.0-x-y)*p_I + x*p_Br + y*p_Cl

	return value, enabled
end

function material.C11(state)
    -- Elastic stiffness constant C11
    -- Units: Pa
    --
    -- No sufficiently reliable value/reference identified.
    -- Disabled rather than estimated.
    --
    -- Notes:
    -- The CsPbI3 endpoint has no verified cubic-phase elastic constants and
    -- CsPbBr3/CsPbCl3 lack C11/C12, so no interpolation over
    -- CsPb(I_(1-x-y) Br_x Cl_y)3 is possible.

    local enabled = false
    local value = 0.0

    return value, enabled
end

function material.C12(state)
    -- Elastic stiffness constant C12
    -- Units: Pa
    --
    -- No sufficiently reliable value/reference identified.
    -- Disabled rather than estimated.
    --
    -- Notes:
    -- The CsPbI3 endpoint has no verified cubic-phase elastic constants and
    -- CsPbBr3/CsPbCl3 lack C11/C12, so no interpolation over
    -- CsPb(I_(1-x-y) Br_x Cl_y)3 is possible.

    local enabled = false
    local value = 0.0

    return value, enabled
end

function material.C44(state)
    -- Elastic stiffness constant C44
    -- Units: Pa
    --
    -- No sufficiently reliable value/reference identified.
    -- Disabled rather than estimated.
    --
    -- Notes:
    -- The CsPbI3 endpoint has no verified cubic-phase elastic constants and
    -- CsPbBr3/CsPbCl3 lack C11/C12, so no interpolation over
    -- CsPb(I_(1-x-y) Br_x Cl_y)3 is possible.

    local enabled = false
    local value = 0.0

    return value, enabled
end

function material.D_ac_e(state)
    -- Effective scalar acoustic deformation potential for electrons
    -- Units: eV
    --
    -- No sufficiently reliable value/reference identified.
    -- Disabled rather than estimated.
    --
    -- Notes:
    -- Targeted search (coherent-acoustic-phonon / picosecond-ultrasonics
    -- experiments, temperature-dependent mobility fits, first-principles
    -- deformation-potential and electron-phonon studies, band-edge strain
    -- studies) found no defensible, separately-resolved scalar acoustic
    -- deformation potential for electrons and holes in this compound.
    -- Mobility-fit analyses of halide perovskites (e.g. the review by
    -- L. M. Herz, ACS Energy Lett. 2, 1539 (2017), DOI 10.1021/
    -- acsenergylett.7b00276) conclude that acoustic deformation-potential
    -- scattering is weak compared with Frohlich scattering but give no
    -- compound-specific D_ac. Band-gap deformation potentials (dEg/dlnV) and
    -- optical/Frohlich coupling constants are not substitutes. The only
    -- experimental separation of electron and hole values found is for
    -- MAPbI3 (Mante et al., Nat. Commun. 8, 14398 (2017)); transferring it to
    -- other halides or cations is not justified.

    local enabled = false
    local value = 0.0

    return value, enabled
end

function material.D_ac_h(state)
    -- Effective scalar acoustic deformation potential for holes
    -- Units: eV
    --
    -- No sufficiently reliable value/reference identified.
    -- Disabled rather than estimated.
    --
    -- Notes:
    -- Targeted search (coherent-acoustic-phonon / picosecond-ultrasonics
    -- experiments, temperature-dependent mobility fits, first-principles
    -- deformation-potential and electron-phonon studies, band-edge strain
    -- studies) found no defensible, separately-resolved scalar acoustic
    -- deformation potential for electrons and holes in this compound.
    -- Mobility-fit analyses of halide perovskites (e.g. the review by
    -- L. M. Herz, ACS Energy Lett. 2, 1539 (2017), DOI 10.1021/
    -- acsenergylett.7b00276) conclude that acoustic deformation-potential
    -- scattering is weak compared with Frohlich scattering but give no
    -- compound-specific D_ac. Band-gap deformation potentials (dEg/dlnV) and
    -- optical/Frohlich coupling constants are not substitutes. The only
    -- experimental separation of electron and hole values found is for
    -- MAPbI3 (Mante et al., Nat. Commun. 8, 14398 (2017)); transferring it to
    -- other halides or cations is not justified.

    local enabled = false
    local value = 0.0

    return value, enabled
end

function material.print()
	local state = {
		T = 300.0,
		x = 0.0,
		y = 0.0,
		z = 0.0,
		photon_density = 0.0,
	}

	print(string.format("Material:               %s", material.name()))
	print(string.format("Description:            %s", material.description()))
	print(string.format("Formula:                %s", material.formula()))
	print(string.format("Temperature:            %.2f K", state.T))
	print(string.format("Position:               %.6e, %.6e, %.6e m", state.x, state.y, state.z))
	print(string.format("Photon density:         %.6e m^-3", state.photon_density))

	print(string.format("Band gap:               %.6f eV", material.Eg(state)))
	print(string.format("Electron affinity:      %.6f eV", material.Xi(state)))
	print(string.format("Electron mobility:      %.6e m^2/V/s", material.mu_e(state)))
	print(string.format("Hole mobility:          %.6e m^2/V/s", material.mu_h(state)))
	print(string.format("Nc:                     %.6e m^-3", material.Nc(state)))
	print(string.format("Nv:                     %.6e m^-3", material.Nv(state)))
	print(string.format("Relative permittivity:  %.6f", material.epsilonr(state)))

	print(string.format("Radiative coeff.:       %.6e m^3/s", material.free_to_free_recombination(state)))
	print(string.format("Electron Auger coeff.:  %.6e m^6/s", material.auger_Cn(state)))
	print(string.format("Hole Auger coeff.:      %.6e m^6/s", material.auger_Cp(state)))

	print(string.format("SRH trap energy:        %.6f eV", material.ss_srh_trap_energy(state)))
	print(string.format("SRH trap density:       %.6e m^-3", material.ss_srh_Nt(state)))
	print(string.format("SRH sigma n:            %.6e m^2", material.ss_srh_sigma_n(state)))
	print(string.format("SRH sigma p:            %.6e m^2", material.ss_srh_sigma_p(state)))

	print(string.format("Electron energy relax.:  %.6e s", material.thermal_tau_e(state)))
	print(string.format("Hole energy relax.:      %.6e s", material.thermal_tau_h(state)))

	print(string.format("Thermal conductivity:   %.6e W/m/K", material.thermal_kl(state)))
	print(string.format("Heat capacity:          %.6e J/kg/K", material.heat_capacity(state)))
	print(string.format("Mass density:           %.6e kg/m^3", material.density(state)))
	print(string.format("Lattice constant:       %.6e m", material.lattice_constant(state)))

	print(string.format("kp Eg (Hamiltonian):    %.6f eV", material.Eg_qw(state)))
	print(string.format("kp Delta_c:             %.6f eV", material.perovskite_delta_c(state)))
	print(string.format("kp delta:               %.6f eV", material.perovskite_delta(state)))
	print(string.format("kp zeta:                %.6f eV", material.perovskite_zeta(state)))
	print(string.format("kp P_parallel:           %.6f eV A", material.perovskite_P_parallel(state)))
	print(string.format("kp Pz:                   %.6f eV A", material.perovskite_Pz(state)))
	print(string.format("kp gamma1 prime:         %.6f", material.perovskite_gamma1_prime(state)))
	print(string.format("kp gamma2 prime:         %.6f", material.perovskite_gamma2_prime(state)))
	print(string.format("kp gamma3 prime:         %.6f", material.perovskite_gamma3_prime(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.
-- ============================================================================