SnO2 material model

1. Introduction

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

Tin oxide (nominally undoped/lightly-doped SnO2), n-type wide-gap semiconductor / electron-transport layer

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 "SnO2", enabled
end


function material.description()
	local enabled = true

	return "Tin oxide (nominally undoped/lightly-doped SnO2), n-type wide-gap semiconductor / electron-transport layer", enabled
end


function material.formula()
	local enabled = true

	return "SnO2", 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 ~3.6 eV at 300 K.
	--
	-- Note: this is the undoped/lightly-doped semiconductor (e.g. an
	-- ETL in perovskite cells). Unlike degenerate FTO, there is no
	-- strong Burstein-Moss widening. T-dependence weak and not well
	-- characterised for films; a constant is used.

	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;
	-- perovskite-device-modelling literature.
	--
	-- SnO2 electron affinity ~4.5 eV. Device-modelling values for the
	-- SnO2 conduction band scatter over ~4.0-4.5 eV; this shallow CB
	-- and deep VB are what make SnO2 a good electron-transport /
	-- hole-blocking layer. Approximate.

	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:
	-- From SnO2 CB effective mass m_e* ~ 0.3 m0 (M. Batzill,
	-- U. Diebold, Prog. Surf. Sci. 79, 47, 2005):
	-- Nc(300 K) ~ 4e18 cm^-3 = 4e24 m^-3. Approximate.

	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:
	-- 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 (M. Batzill,
	-- U. Diebold, Prog. Surf. Sci. 79, 47, 2005); approximate.

	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:
	-- Single-crystal SnO2 electron mobility up to ~240 cm^2/V/s
	-- (M. Batzill, U. Diebold, Prog. Surf. Sci. 79, 47, 2005).
	--
	-- Note: polycrystalline SnO2 ETL device FILMS are far lower and
	-- strongly process-dependent (~0.1-25 cm^2/V/s). A representative
	-- 10 cm^2/V/s = 1e-3 m^2/V/s is used. Film transport is
	-- grain-boundary limited, not phonon limited, so no (300/T)^n law
	-- is applied. Approximate; tune to your film.

	local enabled = true
	local value = 1.0e-3

	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: in an SnO2 ETL holes are the blocked minority carrier;
	-- hole mobility is poorly constrained and rarely the limiting
	-- quantity. Low placeholder.

	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 a wide-gap oxide with weak intrinsic radiative
	-- recombination; not the operative loss channel in an ETL. Poorly
	-- constrained placeholder.

	local enabled = true
	local value = 1.0e-20

	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
	--
	-- Note: for an SnO2 ETL, interfacial/bulk SRH recombination is
	-- often the dominant loss and this is the key parameter. Strongly
	-- quality-dependent; placeholder to be 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:
	-- Bulk rutile SnO2 ~55-98 W/m/K, anisotropic (CRC Handbook of
	-- Chemistry and Physics).
	--
	-- Note: polycrystalline device films are much lower (~1-15 W/m/K).
	-- A bulk value is returned; reduce for thin films. Approximate.

	local enabled = true
	local value = 55.0

	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). 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".
	-- 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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