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

Supporting definitions

-- 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_kl(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.thermal_tau_e(state)
	-- Electron energy relaxation time towards the lattice temperature
	-- Units: s
	--
	-- Value basis: Numerical fallback
	-- Confidence: Low
	--
	-- Reference:
	-- No specific reference supplied.
	--
	-- Comments:
	-- Passive insulator/optical layer. No mobile-carrier hydrodynamic equation
	-- should normally be solved; fast fallback only.

	local enabled = false
	local value = 1.000000e-14

	return value, enabled
end

function material.thermal_tau_h(state)
	-- Hole energy relaxation time towards the lattice temperature
	-- Units: s
	--
	-- Value basis: Numerical fallback
	-- Confidence: Low
	--
	-- Reference:
	-- No specific reference supplied.
	--
	-- Comments:
	-- Passive insulator/optical layer. No mobile-carrier hydrodynamic equation
	-- should normally be solved; fast fallback only.

	local enabled = false
	local value = 1.000000e-14

	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("Electron energy relax.:  %.6e s", material.thermal_tau_e(state)))
	print(string.format("Hole energy relax.:      %.6e s", material.thermal_tau_h(state)))

	print(string.format("Thermal conductivity:   %.6e W/m/K", material.thermal_kl(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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