SiO2 material model

1. Introduction

This page contains the OghmaNano material model for SiO2 (SiO2).

Amorphous silicon dioxide (thermal/dielectric oxide), insulator

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 "SiO2", enabled
end


function material.description()
	local enabled = true

	return "Amorphous silicon dioxide (thermal/dielectric oxide), insulator", enabled
end


function material.formula()
	local enabled = true

	return "SiO2", enabled
end


function material.Eg(state)
	-- Units: eV
	--
	-- Reference:
	-- J. Robertson, "High dielectric constant oxides",
	-- Eur. Phys. J. Appl. Phys. 28, 265-291, 2004.
	--
	-- Amorphous SiO2 band gap ~9.0 eV. Wide-gap insulator.
	-- Constant value; T-dependence negligible for device purposes.

	local enabled = true
	local value = 9.0

	return value, enabled
end


function material.Xi(state)
	-- Electron affinity
	-- Units: eV
	--
	-- Reference:
	-- J. Robertson, Eur. Phys. J. Appl. Phys. 28, 265, 2004.
	--
	-- SiO2 electron affinity ~0.9 eV. This small affinity (deep CB)
	-- and the wide gap are exactly what make SiO2 a good electron and
	-- hole barrier. This IS a meaningful, device-relevant parameter
	-- even though transport through the layer is negligible.

	local enabled = true
	local value = 0.9

	return value, enabled
end


function material.Nc(state)
	-- Effective conduction-band density of states
	-- Units: m^-3
	--
	-- Reference:
	-- Nominal m* ~ 0.5 m0 (SiO2 tunnelling/band-structure literature,
	-- e.g. S. M. Sze, "Physics of Semiconductor Devices").
	--
	-- Note: SiO2 is an insulator with essentially no thermally
	-- generated free carriers, so Nc is a purely FORMAL quantity here.
	-- The parabolic (T/300)^1.5 form is retained for interface
	-- consistency only.

	local enabled = true
	local T = state.T
	local value = 8.9e24*(T/300.0)^1.5

	return value, enabled
end


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

	local enabled = true
	local T = state.T
	local value = 8.9e24*(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
	--
	-- DISABLED: SiO2 is used as an insulating barrier/dielectric.
	-- There is no band-like free-carrier drift transport; any leakage
	-- is tunnelling / Fowler-Nordheim / Poole-Frenkel, which a
	-- drift-mobility does not represent. Tiny placeholder returned to
	-- keep the value finite.

	local enabled = false
	local value = 1.0e-15

	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
	--
	-- DISABLED: insulating barrier, no drift transport. See mu_e note.

	local enabled = false
	local value = 1.0e-15

	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:
	-- Standard value for thermal/fused SiO2: static epsilon_r = 3.9
	-- (S. M. Sze, "Physics of Semiconductor Devices"; J. Robertson,
	-- Eur. Phys. J. Appl. Phys. 28, 265, 2004).
	-- High-frequency epsilon_inf ~2.13 (refractive index n ~1.46).
	--
	-- This is the primary, well-established, device-relevant property
	-- of the layer.

	local enabled = true
	local value = 3.9

	return value, enabled
end


function material.free_to_free_recombination(state)
	-- Radiative (band-to-band) recombination coefficient
	-- Units: m^3 s^-1
	--
	-- DISABLED: no free carriers in an insulating barrier, so
	-- band-to-band recombination is not meaningful. Placeholder value.

	local enabled = false
	local value = 0.0

	return value, enabled
end


function material.auger_Cn(state)
	-- Electron Auger recombination coefficient
	-- Units: m^6 s^-1
	--
	-- DISABLED: no free carriers; not meaningful for an insulator.

	local enabled = false
	local value = 0.0

	return value, enabled
end


function material.auger_Cp(state)
	-- Hole Auger recombination coefficient
	-- Units: m^6 s^-1
	--
	-- DISABLED: no free carriers; not meaningful for an insulator.

	local enabled = false
	local value = 0.0

	return value, enabled
end


function material.ss_srh_trap_energy(state)
	-- SRH trap energy relative to the middle of the band gap.
	-- Units: eV
	--
	-- DISABLED: SRH recombination requires free carriers to capture.
	-- Oxide/border traps in SiO2 matter for reliability but not as a
	-- drift-diffusion recombination centre, so this channel is off.

	local enabled = false
	local value = 0.0

	return value, enabled
end


function material.ss_srh_Nt(state)
	-- SRH trap density
	-- Units: m^-3
	--
	-- DISABLED: see ss_srh_trap_energy note.

	local enabled = false
	local value = 0.0

	return value, enabled
end


function material.ss_srh_sigma_n(state)
	-- Electron capture cross section
	-- Units: m^2
	--
	-- DISABLED: see ss_srh_trap_energy note.

	local enabled = false
	local value = 1.0e-19

	return value, enabled
end


function material.ss_srh_sigma_p(state)
	-- Hole capture cross section
	-- Units: m^2
	--
	-- DISABLED: see ss_srh_trap_energy note.

	local enabled = false
	local value = 1.0e-19

	return value, enabled
end


function material.thermal_conductivity(state)
	-- Thermal conductivity
	-- Units: W m^-1 K^-1
	--
	-- Reference:
	-- Fused/thermal amorphous SiO2, kappa(300 K) ~ 1.4 W/m/K
	-- (CRC Handbook of Chemistry and Physics; fused-silica data).
	--
	-- Note: very thin films can appear lower owing to thermal
	-- boundary (Kapitza) resistance.

	local enabled = true
	local value = 1.4

	return value, enabled
end


function material.heat_capacity(state)
	-- Specific heat capacity
	-- Units: J kg^-1 K^-1
	--
	-- Reference:
	-- Fused silica, c_p(300 K) ~ 740 J/kg/K (CRC Handbook of
	-- Chemistry and Physics).

	local enabled = true
	local value = 740.0

	return value, enabled
end


function material.density(state)
	-- Mass density
	-- Units: kg m^-3
	--
	-- Reference:
	-- Fused silica / thermal oxide rho ~ 2.20 g/cm^3 (CRC Handbook of
	-- Chemistry and Physics).

	local enabled = true
	local value = 2200.0

	return value, enabled
end


function material.lattice_constant(state)
	-- Cubic lattice constant
	-- Units: m
	--
	-- DISABLED: device SiO2 is AMORPHOUS and has no long-range
	-- crystalline order, so a lattice constant is undefined. For
	-- reference, crystalline alpha-quartz is trigonal with
	-- a = 4.913 A, c = 5.405 A (R. W. G. Wyckoff, "Crystal
	-- Structures"); that a-axis value is returned only so the field is
	-- finite.

	local enabled = false
	local value = 4.913e-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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