V2O5 material model

1. Introduction

This page contains the OghmaNano material model for V2O5 (V2O5).

Vanadium pentoxide (alpha-V2O5), 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 "V2O5", enabled
end


function material.description()
	local enabled = true

	return "Vanadium pentoxide (alpha-V2O5), high-work-function hole-injection/extraction oxide", enabled
end


function material.formula()
	local enabled = true

	return "V2O5", enabled
end


function material.Eg(state)
	-- Units: eV
	--
	-- Reference:
	-- J. Meyer et al., "Transition Metal Oxides for Organic
	-- Electronics", Adv. Mater. 24, 5408-5427, 2012.
	--
	-- Optical gap of alpha-V2O5 ~2.3 eV (reported ~2.2-2.3 eV).
	-- Constant value; T-dependence weak/uncharacterised for films.

	local enabled = true
	local value = 2.3

	return value, enabled
end


function material.Xi(state)
	-- Electron affinity
	-- Units: eV
	--
	-- Reference:
	-- J. Meyer et al., Adv. Mater. 24, 5408, 2012;
	-- M. T. Greiner et al., Nat. Mater. 11, 76-81, 2012.
	--
	-- V2O5 electron affinity ~4.7 eV, ionisation potential ~7.0 eV
	-- (consistent with Eg ~2.3 eV). Like MoO3, V2O5 has a deep-lying
	-- conduction band and a very high effective work function
	-- (~5.3 eV typical, up to ~7 eV for clean surfaces), which is what
	-- makes it a hole-extraction / anode-buffer oxide via charge
	-- transfer from the adjacent organic HOMO. The high work function
	-- is the key device parameter; it degrades on air exposure.

	local enabled = true
	local value = 4.7

	return value, enabled
end


function material.Nc(state)
	-- Effective conduction-band density of states
	-- Units: m^-3
	--
	-- Note: not well established; carriers are electrons in a
	-- defect/vacancy-derived band rather than a clean parabolic CB.
	-- Order-of-magnitude placeholder.

	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:
	-- V2O5 single-crystal transport anisotropy from the
	-- vanadium-oxide literature; device-film behaviour discussed in
	-- J. Meyer et al., Adv. Mater. 24, 5408, 2012.
	--
	-- Note: V2O5 is a layered orthorhombic crystal with strongly
	-- anisotropic transport (higher along the b-axis chains).
	-- Single-crystal electron mobility ~0.1-0.5 cm^2/V/s; evaporated /
	-- amorphous device films are much lower (~1e-4 to 1e-2 cm^2/V/s).
	-- A representative 1e-3 cm^2/V/s = 1e-7 m^2/V/s is used
	-- (approximate). Transport in the disordered film is trap/hopping
	-- limited, so no phonon (300/T)^n law is applied.

	local enabled = true
	local value = 1.0e-7

	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: as with MoO3, V2O5 extracts holes from the adjacent
	-- organic by electron transfer into its deep CB, not by hole
	-- conduction within V2O5, so intrinsic hole mobility is not the
	-- operative 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-V2O5 optical constants / anisotropy from the
	-- vanadium-oxide optical (ellipsometry) literature.
	--
	-- Note: alpha-V2O5 is a layered orthorhombic crystal with
	-- anisotropic, not-well-constrained permittivity. High-frequency
	-- epsilon_inf ~4 (n ~2); the static value is somewhat larger and
	-- axis-dependent. A representative (approximate) value is used;
	-- verify if the field in this layer is important.

	local enabled = true
	local value = 4.0

	return value, enabled
end


function material.free_to_free_recombination(state)
	-- Radiative (band-to-band) recombination coefficient
	-- Units: m^3 s^-1
	--
	-- Note: 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. V2O5 films carry a high
	-- O-vacancy gap-state density; set from measurement if it matters.

	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 V2O5 thermal-transport
	-- literature (CRC Handbook; layered-oxide studies).
	--
	-- Note: alpha-V2O5 is a layered crystal with low, anisotropic
	-- thermal conductivity (order 0.5-4 W/m/K); 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 ~127 J/mol/K and M = 181.88 g/mol,
	-- c_p ~ 700 J/kg/K (CRC Handbook of Chemistry and Physics;
	-- thermochemical data). Approximate.

	local enabled = true
	local value = 700.0

	return value, enabled
end


function material.density(state)
	-- Mass density
	-- Units: kg m^-3
	--
	-- Reference:
	-- alpha-V2O5 rho = 3.36 g/cm^3 (CRC Handbook of Chemistry and
	-- Physics).

	local enabled = true
	local value = 3360.0

	return value, enabled
end


function material.lattice_constant(state)
	-- Cubic lattice constant
	-- Units: m
	--
	-- DISABLED: alpha-V2O5 is orthorhombic and layered, NOT cubic, so
	-- a single cubic lattice constant is not meaningful.
	--
	-- Reference (crystallography):
	-- R. W. G. Wyckoff, "Crystal Structures".
	-- alpha-V2O5: a = 11.512 A, b = 3.564 A, c = 4.368 A.
	-- The b-axis (chain direction) value is returned for reference
	-- only.

	local enabled = false
	local value = 3.564e-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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-- This file is part of the OghmaNano Materials Model Library.
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