FTO material model

1. Introduction

This page contains the OghmaNano material model for FTO (SnO2:F).

Fluorine-doped tin oxide (SnO2:F), transparent conducting 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 "FTO", enabled
end


function material.description()
	local enabled = true

	return "Fluorine-doped tin oxide (SnO2:F), transparent conducting oxide", enabled
end


function material.formula()
	local enabled = true

	return "SnO2:F", enabled
end


function material.Eg(state)
	-- Units: eV
	--
	-- Reference:
	-- M. Batzill, U. Diebold, "The surface and materials science of
	-- tin oxide", Prog. Surf. Sci. 79, 47-154, 2005.
	--
	-- Fundamental (direct) gap of SnO2 ~3.6 eV at 300 K.
	--
	-- Note: FTO is a DEGENERATE n-type semiconductor. Heavy doping
	-- fills the conduction band, so the *optical* (apparent) gap is
	-- widened by the Burstein-Moss shift to ~4.0-4.6 eV. This function
	-- returns the fundamental gap, not the optical gap.
	--
	-- Temperature dependence is weak and not well characterised for
	-- device films, so a constant value is used rather than a fitted
	-- Varshni expression.

	local enabled = true
	local value = 3.6

	return value, enabled
end


function material.Xi(state)
	-- Electron affinity
	-- Units: eV
	--
	-- Reference:
	-- M. Batzill, U. Diebold, Prog. Surf. Sci. 79, 47, 2005;
	-- and device-alignment literature.
	--
	-- SnO2 electron affinity ~4.5 eV. Because FTO is degenerate, the
	-- Fermi level sits in/near the conduction band and the effective
	-- work function (~4.4 eV, treatment-dependent, ~4.4-4.8 eV) nearly
	-- coincides with the affinity. The work function is the number
	-- that actually sets contact alignment when FTO is used as an
	-- electrode.

	local enabled = true
	local value = 4.5

	return value, enabled
end


function material.Nc(state)
	-- Effective conduction-band density of states
	-- Units: m^-3
	--
	-- Reference:
	-- Estimated from SnO2 conduction-band effective mass
	-- m_e* ~ 0.3 m0 (M. Batzill, U. Diebold, Prog. Surf. Sci. 79,
	-- 47-154, 2005): Nc(300 K) ~ 4e18 cm^-3 = 4e24 m^-3. Approximate.
	--
	-- Note: FTO is degenerate (free-electron density ~1e20-1e21
	-- cm^-3), so this parabolic-band Nc is a formal quantity only; the
	-- carrier density is set by doping, not by Nc*exp(...). The
	-- (T/300)^1.5 form is the simple non-degenerate model.

	local enabled = true
	local T = state.T
	local value = 4.0e24*(T/300.0)^1.5

	return value, enabled
end


function material.Nv(state)
	-- Effective valence-band density of states
	-- Units: m^-3
	--
	-- Reference:
	-- Estimated from a heavy valence-band mass (m_h* ~ 1 m0):
	-- Nv(300 K) ~ 2.5e19 cm^-3 = 2.5e25 m^-3.
	--
	-- Note: the SnO2 hole mass is poorly constrained (see M. Batzill,
	-- U. Diebold, Prog. Surf. Sci. 79, 47, 2005); treat as approximate.
	-- Rarely relevant for an n-type TCO.

	local enabled = true
	local T = state.T
	local value = 2.5e25*(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:
	-- Representative FTO thin-film Hall mobility from the
	-- transparent-conducting-oxide literature (~10-30 cm^2/V/s); a
	-- mid value of 15 cm^2/V/s = 0.0015 m^2/V/s is used. Approximate.
	--
	-- Note: transport is ionised-impurity limited in this degenerate
	-- material, NOT phonon limited, so no (300/T)^n phonon power law
	-- is applied. Temperature dependence is weak; a constant is used.

	local enabled = true
	local value = 0.0015

	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: FTO is an n-type electrode; hole transport is essentially
	-- irrelevant to device operation and is not experimentally
	-- constrained. A small placeholder is used. Enabled left true so
	-- the solver has a finite value, but do not rely on it.

	local enabled = true
	local value = 1.0e-4

	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:
	-- SnO2 (rutile) static permittivity, M. Batzill, U. Diebold,
	-- Prog. Surf. Sci. 79, 47, 2005.
	--
	-- Note: rutile SnO2 is anisotropic (~9 perpendicular to c, ~14
	-- parallel to c). A representative perpendicular value is used.

	local enabled = true
	local value = 9.0

	return value, enabled
end


function material.free_to_free_recombination(state)
	-- Radiative (band-to-band) recombination coefficient
	-- Units: m^3 s^-1
	--
	-- Note: SnO2 is an indirect/wide-gap oxide and, as a degenerate
	-- electrode, bulk radiative recombination is not the operative
	-- physics (contact recombination dominates). Poorly constrained
	-- placeholder.

	local enabled = true
	local value = 1.0e-21

	return value, enabled
end


function material.auger_Cn(state)
	-- Electron Auger recombination coefficient
	-- Units: m^6 s^-1
	--
	-- Note: not characterised for FTO. 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 for FTO. 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.

	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:
	-- Bulk rutile SnO2 ~55-98 W/m/K, anisotropic (CRC Handbook of
	-- Chemistry and Physics; thermal-transport literature).
	--
	-- Note: polycrystalline FTO device FILMS are much lower
	-- (~1-15 W/m/K) owing to grain-boundary and thickness-dependent
	-- scattering. A low film-appropriate value is used. Approximate /
	-- poorly constrained.

	local enabled = true
	local value = 5.0

	return value, enabled
end


function material.heat_capacity(state)
	-- Specific heat capacity
	-- Units: J kg^-1 K^-1
	--
	-- Reference:
	-- SnO2, c_p(300 K) ~ 350 J/kg/K (CRC Handbook of Chemistry and
	-- Physics; thermochemical data). Approximate.

	local enabled = true
	local value = 350.0

	return value, enabled
end


function material.density(state)
	-- Mass density
	-- Units: kg m^-3
	--
	-- Reference:
	-- SnO2 (rutile/cassiterite) rho = 6.95 g/cm^3 (CRC Handbook of
	-- Chemistry and Physics).

	local enabled = true
	local value = 6950.0

	return value, enabled
end


function material.lattice_constant(state)
	-- Cubic lattice constant
	-- Units: m
	--
	-- DISABLED: SnO2 is tetragonal (rutile), NOT cubic, so a single
	-- cubic lattice constant is not meaningful.
	--
	-- Reference (crystallography):
	-- R. W. G. Wyckoff, "Crystal Structures"; CRC Handbook.
	-- Rutile SnO2: a = b = 4.737 A, c = 3.186 A at 300 K.
	-- The a-axis value is returned for reference only.

	local enabled = false
	local value = 4.737e-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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