Caesium lead bromide perovskite material model

1. Introduction

This page contains the OghmaNano material model for Caesium lead bromide perovskite (CsPbBr3).

Caesium lead bromide perovskite (CsPbBr3), cubic phase; eight-band k.p parameters from Gawarecki et al., Phys. Rev. Applied 22, 014058 (2024).

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: CsPbBr3
-- Caesium lead bromide perovskite
--
-- Phase: Cubic alpha-phase, Pm-3m (space group 221, Oh point group).
-- Phase: This is the phase used by the k.p model.
-- Phase: NOTE: cubic CsPbBr3 is the equilibrium phase only above ~403 K; at 300 K the equilibrium phase is orthorhombic.
-- Phase: The paper explicitly flags CsPbBr3 (and CsPbI3) as orthorhombic at room temperature.
-- Phase: Cubic-phase values are used throughout for phase consistency with the Hamiltonian.
--
-- The eight perovskite_* functions and material.Eg_qw
-- carry the eight-band k.p parameters from Table I of Gawarecki et al.,
-- Phys. Rev. Applied 22, 014058 (2024). Ordinary device properties
-- (Eg, Xi, mobilities, permittivity, recombination, thermal) come from
-- separate experimental sources cited inside each function. Numerical
-- k.p values were transcribed from the accepted manuscript
-- arXiv:2306.08643 v2; verify against the published APS PDF if possible.
--
-- Units are SI unless stated otherwise. P_parallel and Pz are kept in
-- eV*Angstrom exactly as published (they are NOT the Kane energy Ep).

local material = {}

function material.name()
	local enabled = true

	return "Caesium lead bromide perovskite", enabled
end

function material.description()
	local enabled = true

	return "Caesium lead bromide perovskite (CsPbBr3), cubic phase; eight-band k.p parameters from Gawarecki et al., Phys. Rev. Applied 22, 014058 (2024).", enabled
end

function material.formula()
	local enabled = true

	return "CsPbBr3", enabled
end

function material.Eg(state)
	-- Band gap (general device model)
	-- Units: eV
	--
	-- Cubic/RT single-crystal optical gap ~2.25-2.36 eV.
	-- Reference:
	-- G. Mannino et al., J. Phys. Chem. Lett. 11, 2490 (2020).
	-- DOI: 10.1021/acs.jpclett.0c00295
	-- Representative 2.30 eV. Differs from Gawarecki Table-I DFT gap
	-- (2.073 eV); see material.Eg_qw.

	local enabled = true
	local value = 2.3

	return value, enabled
end

function material.Xi(state)
	-- Electron affinity (absolute conduction-band minimum vs vacuum)
	-- Units: eV
	--
	-- Electron affinity. Representative ~3.6 eV (CBM ~ -3.6 eV;
	-- VBM ~ -5.9 eV). Reported CsPbBr3 band positions scatter by
	-- several tenths of an eV. Confidence: Low.

	local enabled = true
	local value = 3.6

	return value, enabled
end

function material.Nc(state)
	-- Effective conduction-band density of states
	-- Units: m^-3
	--
	-- Nc = 2*(2*pi*m_e*kB*T/h^2)^(3/2).
	-- The conduction band of these perovskites is p-like; a single
	-- Table-I electron mass is not tabulated, so the electron mass is
	-- taken comparable to the valence-band mass m_v = 0.158 m0 from
	-- Table I of Gawarecki et al. (electron and hole masses are of the
	-- same order in lead halides). Value basis: family approximation.
	-- Confidence: Low-Medium. Nc(300 K) = 1.576e+24 m^-3.

	local enabled = true
	local T = state.T
	local value = 1.576e+24*(T/300.0)^1.5

	return value, enabled
end

function material.Nv(state)
	-- Effective valence-band density of states
	-- Units: m^-3
	--
	-- Nv = 2*(2*pi*m_h*kB*T/h^2)^(3/2), with the hole mass taken as the
	-- s-like valence-band effective mass m_v = 0.158 m0 from Table I of
	-- Gawarecki et al., Phys. Rev. Applied 22, 014058 (2024).
	-- Nv(300 K) = 1.576e+24 m^-3. Confidence: Medium (mass is paper-sourced).

	local enabled = true
	local T = state.T
	local value = 1.576e+24*(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
	--
	-- CsPbBr3 single crystals show very high mobilities (up to
	-- ~1000 cm^2/V/s); polycrystalline films are far lower (~1-30).
	-- Representative device value 20 cm^2/V/s = 2.0e-3 m^2/V/s.
	-- Strongly processing dependent. Confidence: Low.
	-- (300/T)^1.5 phonon-limited form applied.
	-- Electron and hole mobilities taken equal (comparable in these
	-- materials).

	local enabled = true
	local T = state.T
	local value = 2.000e-03*(300.0/T)^1.5

	return value, enabled
end

function material.mue_x(state)
	return material.mu_e(state)
end

function material.mue_y(state)
	return material.mu_e(state)
end

function material.mue_z(state)
	return material.mu_e(state)
end

function material.mu_h(state)
	-- Low-field hole mobility
	-- Units: m^2 V^-1 s^-1
	--
	-- CsPbBr3 single crystals show very high mobilities (up to
	-- ~1000 cm^2/V/s); polycrystalline films are far lower (~1-30).
	-- Representative device value 20 cm^2/V/s = 2.0e-3 m^2/V/s.
	-- Strongly processing dependent. Confidence: Low.
	-- (300/T)^1.5 phonon-limited form applied.
	-- Set equal to the electron mobility (comparable in these materials).

	local enabled = true
	local T = state.T
	local value = 2.000e-03*(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
	--
	-- High-frequency eps_inf = 4.8
	-- [S. Becker et al., Nature 553, 189 (2018), arXiv:1707.03071].
	-- Low-frequency (LO-phonon) static value ~16-22; representative
	-- static 20 used for the electrostatic model. Slow ionic
	-- response excluded. Confidence: Low-Medium.

	local enabled = true
	local value = 20.0

	return value, enabled
end

function material.free_to_free_recombination(state)
	-- Radiative (band-to-band) recombination coefficient
	-- Units: m^3 s^-1
	--
	-- Radiative coefficient. Lead-halide k2 ~0.6e-10 to 14e-10 cm^3/s
	-- [L. M. Herz, Acc. Chem. Res. 49, 146 (2016)]. Representative
	-- 1.0e-10 cm^3/s = 1.0e-16 m^3/s. Confidence: Low.
	-- Conversion: cm^3/s * 1e-6 = m^3/s.

	local enabled = true
	local value = 1.000e-16

	return value, enabled
end

function material.auger_Cn(state)
	-- Electron Auger recombination coefficient
	-- Units: m^6 s^-1
	--
	-- Representative Auger coefficient ~1e-28 cm^6/s = 1.0e-40 m^6/s,
	-- anchored to MAPbI3 measurements and used across the family.
	-- Reference:
	-- L. M. Herz, Acc. Chem. Res. 49, 146 (2016).
	-- Conversion: cm^6/s * 1e-12 = m^6/s.
	-- Value basis: perovskite family estimate. Confidence: Low.

	local enabled = true
	local value = 1.0e-40

	return value, enabled
end

function material.auger_Cp(state)
	-- Hole Auger recombination coefficient
	-- Units: m^6 s^-1
	--
	-- Representative Auger coefficient ~1e-28 cm^6/s = 1.0e-40 m^6/s,
	-- anchored to MAPbI3 measurements and used across the family.
	-- Reference:
	-- L. M. Herz, Acc. Chem. Res. 49, 146 (2016).
	-- Conversion: cm^6/s * 1e-12 = m^6/s.
	-- Value basis: perovskite family estimate. Confidence: Low.

	local enabled = true
	local value = 1.0e-40

	return value, enabled
end

function material.ss_srh_trap_energy(state)
	-- SRH trap energy relative to mid-gap
	-- Units: eV
	--
	-- Positive = towards the conduction band, negative = towards the
	-- valence band. Representative mid-gap value; sample dependent.

	local enabled = true
	local value = 0.0

	return value, enabled
end

function material.ss_srh_Nt(state)
	-- SRH trap density
	-- Units: m^-3
	--
	-- Representative device-model value rather than an intrinsic material
	-- constant. Trap density is strongly processing dependent; set from a
	-- measured carrier lifetime for a given sample. Confidence: Low.

	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 device-model value; sample dependent.

	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 device-model value; sample dependent.

	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
	--
	-- Ultralow, ~0.4-0.45 W/m/K (soft anharmonic lattice).
	-- Representative 0.40 W/m/K.

	local enabled = true
	local value = 0.4

	return value, enabled
end

function material.heat_capacity(state)
	-- Specific heat capacity
	-- Units: J kg^-1 K^-1
	--
	-- Specific heat ~300-340 J/kg/K; representative 320. Confidence: Low.

	local enabled = true
	local value = 320.0

	return value, enabled
end

function material.density(state)
	-- Mass density
	-- Units: kg m^-3
	--
	-- Computed from the cubic/pseudo-cubic lattice constant and molar mass
	-- (Z = 1 formula unit per primitive cell), so it is phase-consistent
	-- with the k.p model:
	--   rho = M / (N_A * a^3)
	--   M     = 579.817 g/mol
	--   a     = 5.886 Angstrom (a_exp, Table I of Gawarecki et al. 2024)
	--   rho   = 4.7215 g/cm^3 = 4721.5 kg/m^3
	-- Confidence: Medium (crystallographic value for the idealised cell).

	local enabled = true
	local value = 4721.5

	return value, enabled
end

function material.lattice_constant(state)
	-- Cubic / pseudo-cubic lattice constant
	-- Units: m
	--
	-- 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.
	-- Source transcription: arXiv:2306.08643 v2 (accepted manuscript);
	-- spot-check against the paywalled APS PDF if a subscription is available.
	--
	-- a_exp = 5.886 Angstrom = 5.886e-10 m (experimental cubic/pseudo-cubic value
	-- listed in Table I). This is a genuine cubic/pseudo-cubic parameter,
	-- NOT an orthorhombic or tetragonal supercell dimension.

	local enabled = true
	local value = 5.886e-10

	return value, enabled
end

function material.thermal_tau_e(state)
	-- Electron energy relaxation time towards the lattice temperature
	-- Units: s
	--
	-- Value basis: Perovskite family estimate
	-- Confidence: Low
	--
	-- No robust carrier-specific hydrodynamic value was found for this
	-- material; use 1 ps and perform a sensitivity analysis.

	local enabled = true
	local value = 1.000000e-12

	return value, enabled
end

function material.thermal_tau_h(state)
	-- Hole energy relaxation time towards the lattice temperature
	-- Units: s
	--
	-- Value basis: Perovskite family estimate
	-- Confidence: Low
	--
	-- No robust carrier-specific hydrodynamic value was found for this
	-- material; use 1 ps and perform a sensitivity analysis.

	local enabled = true
	local value = 1.000000e-12

	return value, enabled
end

function material.Eg_qw(state)
	-- Band gap used by the eight-band k.p Hamiltonian (R point)
	-- Units: eV
	--
	-- 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.
	-- Source transcription: arXiv:2306.08643 v2 (accepted manuscript);
	-- spot-check against the paywalled APS PDF if a subscription is available.
	--
	-- This is the DFT gap the k.p parameters were fitted with. It differs
	-- from material.Eg() (an experimental room-temperature device value),
	-- so it is exposed separately to let the Hamiltonian exactly reproduce
	-- the parameterization in the paper. Table-I value: 2.073 eV.

	local enabled = true
	local value = 2.073

	return value, enabled
end

function material.perovskite_delta_c(state)
	-- Conduction-band spin-orbit splitting Delta_c
	-- Units: eV
	--
	-- 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.
	-- Source transcription: arXiv:2306.08643 v2 (accepted manuscript);
	-- spot-check against the paywalled APS PDF if a subscription is available.
	--
	-- This is a perovskite-specific conduction-band spin-orbit parameter
	-- (the CB is p-like). It is NOT interchangeable with a conventional
	-- III-V valence-band spin-orbit splitting delta_so.

	local enabled = true
	local value = 1.476

	return value, enabled
end

function material.perovskite_delta(state)
	-- Non-cubic splitting parameter delta
	-- Units: eV
	--
	-- 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.
	-- Source transcription: arXiv:2306.08643 v2 (accepted manuscript);
	-- spot-check against the paywalled APS PDF if a subscription is available.
	--
	-- Splits the heavy/light electron block in C4v. In the cubic limit
	-- (CsPbX3, Oh symmetry) delta = 0 exactly; this zero is physically
	-- meaningful (enabled), not a missing value.

	local enabled = true
	local value = 0.0

	return value, enabled
end

function material.perovskite_zeta(state)
	-- Non-cubic / asymmetry coupling zeta
	-- Units: eV
	--
	-- 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.
	-- Source transcription: arXiv:2306.08643 v2 (accepted manuscript);
	-- spot-check against the paywalled APS PDF if a subscription is available.
	--
	-- Symmetry-breaking coupling <S_v|H0|Z_c> = i*zeta; drives the linear
	-- (Rashba-like) conduction-band splitting. In the cubic limit
	-- (CsPbX3) zeta = 0 exactly (enabled, physically meaningful).

	local enabled = true
	local value = 0.0

	return value, enabled
end

function material.perovskite_P_parallel(state)
	-- Kane momentum coupling P_parallel
	-- Units: eV Angstrom
	--
	-- 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.
	-- Source transcription: arXiv:2306.08643 v2 (accepted manuscript);
	-- spot-check against the paywalled APS PDF if a subscription is available.
	--
	-- In-plane interband momentum matrix element
	-- P_parallel = (hbar/m0)<S_v|p_x|X_c> = (hbar/m0)<S_v|p_y|Y_c>.
	-- Kept in eV*Angstrom exactly as published; this is NOT the Kane
	-- energy Ep. For CsPbX3 (Oh) P_parallel = Pz.

	local enabled = true
	local value = 8.948

	return value, enabled
end

function material.perovskite_Pz(state)
	-- Kane momentum coupling P_z
	-- Units: eV Angstrom
	--
	-- 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.
	-- Source transcription: arXiv:2306.08643 v2 (accepted manuscript);
	-- spot-check against the paywalled APS PDF if a subscription is available.
	--
	-- Out-of-plane interband momentum matrix element
	-- P_z = (hbar/m0)<S_v|p_z|Z_c>. Kept in eV*Angstrom exactly as
	-- published; NOT the Kane energy Ep. For CsPbX3 (Oh) Pz = P_parallel.

	local enabled = true
	local value = 8.948

	return value, enabled
end

function material.perovskite_gamma1_prime(state)
	-- Modified Luttinger-like parameter gamma1' (primed)
	-- Units: dimensionless
	--
	-- 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.
	-- Source transcription: arXiv:2306.08643 v2 (accepted manuscript);
	-- spot-check against the paywalled APS PDF if a subscription is available.
	--
	-- PRIMED far-band parameter used directly in the Hamiltonian. Do NOT
	-- substitute the unprimed gamma1 (listed separately in Table I for
	-- reference only).

	local enabled = true
	local value = 2.183

	return value, enabled
end

function material.perovskite_gamma2_prime(state)
	-- Modified Luttinger-like parameter gamma2' (primed)
	-- Units: dimensionless
	--
	-- 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.
	-- Source transcription: arXiv:2306.08643 v2 (accepted manuscript);
	-- spot-check against the paywalled APS PDF if a subscription is available.
	--
	-- PRIMED far-band parameter used directly in the Hamiltonian. Do NOT
	-- substitute the unprimed gamma2.

	local enabled = true
	local value = 0.394

	return value, enabled
end

function material.perovskite_gamma3_prime(state)
	-- Modified Luttinger-like parameter gamma3' (primed)
	-- Units: dimensionless
	--
	-- 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.
	-- Source transcription: arXiv:2306.08643 v2 (accepted manuscript);
	-- spot-check against the paywalled APS PDF if a subscription is available.
	--
	-- PRIMED far-band parameter used directly in the Hamiltonian. Do NOT
	-- substitute the unprimed gamma3. Sign is negative for all six
	-- materials and is preserved exactly as published.

	local enabled = true
	local value = -1.081

	return value, enabled
end

function material.phonon_lo_energy(state)
	-- Effective longitudinal optical phonon energy
	-- Units: eV
	--
	-- Most strongly coupled LO phonon mode: 18 meV.
	--
	-- Reference:
	-- M. R. Filip, J. B. Haber, and J. B. Neaton,
	-- "Phonon Screening of Excitons in Semiconductors:
	-- Halide Perovskites and Beyond,"
	-- Phys. Rev. Lett. 127, 067401 (2021).
	-- DOI: 10.1103/PhysRevLett.127.067401

	local enabled = true
	local value = 0.018

	return value, enabled
end

function material.epsilon_static(state)
	-- Static dielectric constant used for polar optical phonon scattering
	-- Dimensionless
	--
	-- Calculated static dielectric constant: 18.6.
	--
	-- Reference:
	-- M. R. Filip, J. B. Haber, and J. B. Neaton,
	-- "Phonon Screening of Excitons in Semiconductors:
	-- Halide Perovskites and Beyond,"
	-- Phys. Rev. Lett. 127, 067401 (2021).
	-- DOI: 10.1103/PhysRevLett.127.067401

	local enabled = true
	local value = 18.6

	return value, enabled
end

function material.epsilon_inf(state)
	-- High-frequency dielectric constant used for polar optical phonon scattering
	-- Dimensionless
	--
	-- Calculated electronic dielectric constant: 4.5.
	--
	-- Reference:
	-- M. R. Filip, J. B. Haber, and J. B. Neaton,
	-- "Phonon Screening of Excitons in Semiconductors:
	-- Halide Perovskites and Beyond,"
	-- Phys. Rev. Lett. 127, 067401 (2021).
	-- DOI: 10.1103/PhysRevLett.127.067401

	local enabled = true
	local value = 4.5

	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:
    -- Songvilay et al. (2019) give only C44 and (C11-C12)/2 = 4.45 GPa for
    -- CsPbBr3, not C11 itself. No verified C11.

    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:
    -- Only (C11-C12)/2 = 4.45 GPa available (Songvilay et al. 2019); C12
    -- cannot be separated without C11.

    local enabled = false
    local value = 0.0

    return value, enabled
end

function material.C44(state)
    -- Elastic stiffness constant C44
    -- Units: Pa
    --
    -- Reference:
    -- M. Songvilay, N. Giles-Donovan, M. Bari, Z.-G. Ye, J. L. Minns,
    -- M. A. Green, G. Xu, P. M. Gehring, K. Schmalzl, W. D. Ratcliff,
    -- C. M. Brown, D. Chernyshov, W. van Beek, S. Cochran, C. Stock,
    -- "Common acoustic phonon lifetimes in inorganic and hybrid lead halide
    -- perovskites,"
    -- Phys. Rev. Materials 3, 093602 (2019), Table 1.
    -- DOI: 10.1103/PhysRevMaterials.3.093602
    --
    -- Notes:
    -- Neutron TA1 slope: C44 = 2.45(3) GPa. Measured in the cubic phase
    -- (420 K) and orthorhombic phase (300 K) with no clear change at the THz
    -- scale. Note: CsPbBr3 is orthorhombic below ~360 K.

    local enabled = true
    local value = 2.45e9

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