MoO3 material model

1. Introduction

This page contains the OghmaNano material model for MoO3 (MoO3).

Molybdenum trioxide (alpha-MoO3), high-work-function hole-injection/extraction oxide

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 "MoO3", enabled
end


function material.description()
	local enabled = true

	return "Molybdenum trioxide (alpha-MoO3), high-work-function hole-injection/extraction oxide", enabled
end


function material.formula()
	local enabled = true

	return "MoO3", enabled
end


function material.Eg(state)
	-- Units: eV
	--
	-- Reference:
	-- J. Meyer, A. Hamwi, M. Kroeger, W. Kowalsky, T. Riedl, A. Kahn,
	-- "Transition Metal Oxides for Organic Electronics: Energetics,
	-- Device Physics and Applications", Adv. Mater. 24, 5408-5427,
	-- 2012.
	--
	-- Optical gap of alpha-MoO3 ~3.0 eV (reported ~2.9-3.1 eV).
	--
	-- Temperature dependence not well characterised for evaporated
	-- films; a constant value is used.

	local enabled = true
	local value = 3.0

	return value, enabled
end


function material.Xi(state)
	-- Electron affinity
	-- Units: eV
	--
	-- Reference:
	-- M. Kroeger et al., Appl. Phys. Lett. 95, 123301, 2009;
	-- J. Meyer et al., Adv. Mater. 24, 5408, 2012.
	--
	-- This is the KEY device parameter for MoO3. Pristine alpha-MoO3
	-- has an exceptionally large electron affinity / work function
	-- ~6.7 eV, with a very deep-lying conduction band. This deep CB is
	-- what enables electron extraction from the HOMO of adjacent
	-- organics (charge-transfer / "n-type" hole-injection mechanism).
	--
	-- IMPORTANT: the effective work function degrades strongly on air
	-- exposure and mild reduction, commonly falling to ~5.3-5.7 eV in
	-- real devices. Choose the value to match your processing.

	local enabled = true
	local value = 6.7

	return value, enabled
end


function material.Nc(state)
	-- Effective conduction-band density of states
	-- Units: m^-3
	--
	-- Note: not well established for MoO3. The functioning carriers
	-- are electrons in an O-vacancy-derived gap/defect band rather
	-- than a clean parabolic conduction band, so this parabolic Nc is
	-- an order-of-magnitude placeholder only.

	local enabled = true
	local T = state.T
	local value = 1.0e25*(T/300.0)^1.5

	return value, enabled
end


function material.Nv(state)
	-- Effective valence-band density of states
	-- Units: m^-3
	--
	-- Note: order-of-magnitude placeholder; see Nc note.

	local enabled = true
	local T = state.T
	local value = 1.0e25*(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:
	-- Evaporated/amorphous MoO3 transport is discussed in
	-- J. Meyer et al., Adv. Mater. 24, 5408, 2012.
	--
	-- Note: electron mobility is very low and extremely
	-- process-dependent, reported anywhere from ~1e-6 to ~1e-1
	-- cm^2/V/s. An effective 1e-4 cm^2/V/s = 1e-8 m^2/V/s is used as a
	-- representative (approximate) device value. Transport is
	-- trap/hopping limited (disordered film), so no phonon (300/T)^n
	-- power law is applied. Tune to match your layer.

	local enabled = true
	local value = 1.0e-8

	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
	--
	-- Note: MoO3 extracts holes from adjacent organics via electron
	-- transfer into its deep CB, NOT by hole conduction within MoO3
	-- itself, so intrinsic hole mobility is not the operative
	-- transport channel and is poorly constrained. Low placeholder.

	local enabled = true
	local value = 1.0e-9

	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:
	-- alpha-MoO3 optical constants / anisotropy discussed in
	-- J. Meyer et al., Adv. Mater. 24, 5408, 2012, and optical
	-- (ellipsometry) studies of MoO3.
	--
	-- Note: alpha-MoO3 is a layered orthorhombic crystal and its
	-- permittivity is strongly anisotropic and poorly constrained for
	-- device films. High-frequency epsilon_inf ~5.5 (n ~2.2); the
	-- static value is larger and axis-dependent. A representative
	-- (approximate) value is used; verify against your own data if the
	-- field distribution in this layer matters.

	local enabled = true
	local value = 5.5

	return value, enabled
end


function material.free_to_free_recombination(state)
	-- Radiative (band-to-band) recombination coefficient
	-- Units: m^3 s^-1
	--
	-- Note: MoO3 acts as a thin charge-selective buffer, not an
	-- absorber; bulk radiative recombination is not the operative
	-- physics. Poorly constrained placeholder.

	local enabled = true
	local value = 1.0e-19

	return value, enabled
end


function material.auger_Cn(state)
	-- Electron Auger recombination coefficient
	-- Units: m^6 s^-1
	--
	-- Note: not characterised. Order-of-magnitude placeholder.

	local enabled = true
	local value = 1.0e-43

	return value, enabled
end


function material.auger_Cp(state)
	-- Hole Auger recombination coefficient
	-- Units: m^6 s^-1
	--
	-- Note: not characterised. Order-of-magnitude placeholder.

	local enabled = true
	local value = 1.0e-43

	return value, enabled
end


function material.ss_srh_trap_energy(state)
	-- SRH trap energy relative to the middle of the band gap.
	-- Units: eV
	--
	-- Positive values are above mid-gap (towards the conduction band).
	-- Negative values are below mid-gap (towards the valence band).

	local enabled = true
	local value = 0.0

	return value, enabled
end


function material.ss_srh_Nt(state)
	-- SRH trap density
	-- Units: m^-3
	--
	-- Material-quality dependent placeholder. Note that O vacancies
	-- give MoO3 a high gap-state density; the relevant value is very
	-- process-dependent.

	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:
	-- Low, anisotropic values from the MoO3 thermal-transport
	-- literature (CRC Handbook; layered-oxide studies).
	--
	-- Note: alpha-MoO3 is a van der Waals layered crystal with low,
	-- strongly anisotropic thermal conductivity (cross-plane much
	-- lower than in-plane). Evaporated device films are lower still. A
	-- low representative value is used; approximate / poorly
	-- constrained.

	local enabled = true
	local value = 1.0

	return value, enabled
end


function material.heat_capacity(state)
	-- Specific heat capacity
	-- Units: J kg^-1 K^-1
	--
	-- Reference:
	-- From molar heat capacity ~75 J/mol/K and M = 143.94 g/mol,
	-- c_p ~ 520 J/kg/K (CRC Handbook of Chemistry and Physics;
	-- thermochemical data). Approximate.

	local enabled = true
	local value = 520.0

	return value, enabled
end


function material.density(state)
	-- Mass density
	-- Units: kg m^-3
	--
	-- Reference:
	-- alpha-MoO3 rho = 4.69 g/cm^3 (CRC Handbook of Chemistry and
	-- Physics).

	local enabled = true
	local value = 4690.0

	return value, enabled
end


function material.lattice_constant(state)
	-- Cubic lattice constant
	-- Units: m
	--
	-- DISABLED: alpha-MoO3 is orthorhombic and layered (van der Waals
	-- stacking along b), NOT cubic, so a single cubic lattice constant
	-- is not meaningful.
	--
	-- Reference (crystallography):
	-- R. W. G. Wyckoff, "Crystal Structures".
	-- alpha-MoO3: a = 3.963 A, b = 13.855 A, c = 3.696 A.
	-- The a-axis value is returned for reference only.

	local enabled = false
	local value = 3.963e-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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