CH3NH3PbBr3 material model

1. Introduction

This page contains the OghmaNano material model for CH3NH3PbBr3 (CH3NH3PbBr3).

Methylammonium lead tribromide (MAPbBr3), 3D hybrid perovskite (wide-gap absorber)

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

-- See end of file for copyright, licensing and documentation links.

local material = {}

function material.name()
	local enabled = true

	return "CH3NH3PbBr3", enabled
end


function material.description()
	local enabled = true

	return "Methylammonium lead tribromide (MAPbBr3), 3D hybrid perovskite (wide-gap absorber)", enabled
end


function material.formula()
	local enabled = true

	return "CH3NH3PbBr3", enabled
end


function material.Eg(state)
	-- Units: eV
	--
	-- Reference:
	-- M. A. Green, A. Ho-Baillie, H. J. Snaith, Nat. Photonics 8, 506,
	-- 2014; halide-perovskite optical literature.
	--
	-- Direct gap ~2.30 eV at 300 K (reported ~2.2-2.3 eV).
	--
	-- Note: like MAPbI3, MAPbBr3 has an ANOMALOUS POSITIVE dEg/dT
	-- (~+0.3 meV/K, opposite to Varshni). The linear term below is
	-- approximate. MAPbBr3 is cubic at room temperature (see
	-- lattice_constant).

	local enabled = true
	local T = state.T
	local value = 2.30 + 3.0e-4*(T - 300.0)

	return value, enabled
end


function material.Xi(state)
	-- Electron affinity
	-- Units: eV
	--
	-- Reference:
	-- Photoemission / device band-alignment literature for MAPbBr3.
	--
	-- Conduction-band minimum ~ -3.6 eV vs vacuum (electron affinity
	-- ~3.6 eV); with Eg ~2.3 eV the valence band is at ~ -5.9 eV. Both
	-- bands are shallower/deeper than MAPbI3 respectively. Reported
	-- values scatter ~0.2 eV. Approximate.

	local enabled = true
	local value = 3.6

	return value, enabled
end


function material.Nc(state)
	-- Effective conduction-band density of states
	-- Units: m^-3
	--
	-- Reference:
	-- From CB effective mass m_e* ~ 0.23 m0 (slightly heavier than the
	-- iodide): Nc(300 K) ~ 2.5e18 cm^-3 = 2.5e24 m^-3. Approximate.

	local enabled = true
	local T = state.T
	local value = 2.5e24*(T/300.0)^1.5

	return value, enabled
end


function material.Nv(state)
	-- Effective valence-band density of states
	-- Units: m^-3
	--
	-- Reference:
	-- From VB effective mass m_h* ~ 0.26 m0:
	-- Nv(300 K) ~ 3.0e18 cm^-3 = 3.0e24 m^-3. Approximate.

	local enabled = true
	local T = state.T
	local value = 3.0e24*(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
	--
	-- Reference:
	-- L. M. Herz, "Charge-Carrier Mobilities in Metal Halide
	-- Perovskites", Annu. Rev. Phys. Chem. 67, 65, 2016.
	--
	-- Single-crystal MAPbBr3 ~20-115 cm^2/V/s; device films lower. A
	-- representative 10 cm^2/V/s = 1e-3 m^2/V/s is used with a
	-- (300/T)^1.5 phonon form. Approximate; tune to film.

	local enabled = true
	local T = state.T
	local value = 1.0e-3*(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
	--
	-- Reference:
	-- L. M. Herz, Annu. Rev. Phys. Chem. 67, 65, 2016.
	--
	-- Comparable to the electron value (fairly ambipolar); 10
	-- cm^2/V/s = 1e-3 m^2/V/s with (300/T)^1.5. Approximate.

	local enabled = true
	local T = state.T
	local value = 1.0e-3*(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
	--
	-- Reference:
	-- Dielectric studies of MAPbBr3.
	--
	-- Frequency-dependent: high-frequency epsilon_inf ~4.7-5; the
	-- low-frequency value (ionic + MA dipole) rises to ~25-30. A
	-- low-frequency value ~25 is used for drift-diffusion; choose to
	-- match your timescale. Approximate.

	local enabled = true
	local value = 25.0

	return value, enabled
end


function material.free_to_free_recombination(state)
	-- Radiative (band-to-band) recombination coefficient
	-- Units: m^3 s^-1
	--
	-- Reference:
	-- L. M. Herz, Annu. Rev. Phys. Chem. 67, 65, 2016.
	--
	-- Bimolecular coefficient ~1e-10 cm^3/s = 1e-16 m^3/s. Direct-gap
	-- emitter (MAPbBr3 is a good green emitter). Approximate.

	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
	--
	-- Reference:
	-- L. M. Herz, Annu. Rev. Phys. Chem. 67, 65, 2016.
	-- ~1e-28 cm^6/s = 1e-40 m^6/s. Approximate.

	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
	--
	-- Reference:
	-- L. M. Herz, Annu. Rev. Phys. Chem. 67, 65, 2016.
	-- ~1e-28 cm^6/s = 1e-40 m^6/s. Approximate.

	local enabled = true
	local value = 1.0e-40

	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
	--
	-- Note: quality-dependent placeholder (~1e15 cm^-3 for good
	-- films); interfaces dominate real devices. Set from measurement.

	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

	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

	local enabled = true
	local value = 1.0e-19

	return value, enabled
end


function material.thermal_conductivity(state)
	-- Thermal conductivity
	-- Units: W m^-1 K^-1
	--
	-- Reference:
	-- Ultralow lattice thermal conductivity of MAPbBr3, ~0.4-0.5
	-- W/m/K (strong anharmonicity, MA disorder).
	--
	-- A value of 0.5 W/m/K is used. Approximate.

	local enabled = true
	local value = 0.5

	return value, enabled
end


function material.heat_capacity(state)
	-- Specific heat capacity
	-- Units: J kg^-1 K^-1
	--
	-- Reference:
	-- Calorimetry of MAPbBr3, c_p(300 K) ~ 330 J/kg/K. Approximate.

	local enabled = true
	local value = 330.0

	return value, enabled
end


function material.density(state)
	-- Mass density
	-- Units: kg m^-3
	--
	-- Reference:
	-- C. C. Stoumpos, C. D. Malliakas, M. G. Kanatzidis, Inorg. Chem.
	-- 52, 9019, 2013. Cubic MAPbBr3 rho ~ 3.58 g/cm^3.

	local enabled = true
	local value = 3580.0

	return value, enabled
end


function material.lattice_constant(state)
	-- Cubic lattice constant
	-- Units: m
	--
	-- Reference:
	-- C. C. Stoumpos, C. D. Malliakas, M. G. Kanatzidis, Inorg. Chem.
	-- 52, 9019, 2013.
	--
	-- MAPbBr3 IS cubic (Pm-3m) at room temperature, so this is a
	-- genuine cubic lattice constant: a = 5.93 A at 300 K. (It
	-- transitions to tetragonal/orthorhombic only below ~236 K.)

	local enabled = true
	local value = 5.93e-10

	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("Thermal conductivity:   %.6e W/m/K", material.thermal_conductivity(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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