Al2O3 material model
1. Introduction
This page contains the OghmaNano material model for Al2O3 (Al2O3).
Aluminium oxide (amorphous ALD alumina / sapphire), insulator / passivation & tunnelling dielectric
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 "Al2O3", enabled
end
function material.description()
local enabled = true
return "Aluminium oxide (amorphous ALD alumina / sapphire), insulator / passivation & tunnelling dielectric", enabled
end
function material.formula()
local enabled = true
return "Al2O3", enabled
end
function material.Eg(state)
-- Units: eV
--
-- Reference:
-- J. Robertson, "High dielectric constant oxides",
-- Eur. Phys. J. Appl. Phys. 28, 265-291, 2004 (crystalline);
-- ALD-Al2O3 spectroscopy literature (amorphous films).
--
-- Amorphous ALD Al2O3 band gap ~6.4-6.7 eV; a value of 6.7 eV is
-- used. Crystalline sapphire (alpha-Al2O3) is wider, ~8.8 eV.
-- Wide-gap insulator either way.
local enabled = true
local value = 6.7
return value, enabled
end
function material.Xi(state)
-- Electron affinity
-- Units: eV
--
-- Reference:
-- J. Robertson, Eur. Phys. J. Appl. Phys. 28, 265, 2004.
--
-- Al2O3 electron affinity ~1.0-1.4 eV; ~1.35 eV is used. The small
-- affinity together with the wide gap gives large barriers for
-- both electrons and holes, which is why Al2O3 is used for
-- passivation and as a tunnelling dielectric. Device-relevant.
local enabled = true
local value = 1.35
return value, enabled
end
function material.Nc(state)
-- Effective conduction-band density of states
-- Units: m^-3
--
-- Note: Al2O3 is an insulator with essentially no thermally
-- generated free carriers, so Nc is a purely FORMAL quantity. A
-- nominal value (m* ~ 0.4 m0) is provided; the (T/300)^1.5 form is
-- retained for interface consistency only.
local enabled = true
local T = state.T
local value = 6.4e24*(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 = 6.4e24*(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: Al2O3 is used as an insulating barrier / tunnelling
-- dielectric. There is no band-like free-carrier drift transport;
-- any leakage is tunnelling / trap-assisted, which a drift
-- mobility does not represent. Tiny placeholder 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:
-- J. Robertson, Eur. Phys. J. Appl. Phys. 28, 265, 2004;
-- ALD-Al2O3 literature.
--
-- A value of 9.0 is used. ALD amorphous Al2O3 films are typically
-- ~7-9; crystalline sapphire is ~9.3-11.5 and anisotropic. This is
-- the primary device-relevant property of the layer.
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
--
-- DISABLED: no free carriers in an insulating barrier, so
-- band-to-band recombination is not meaningful.
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.
-- Fixed charge and border traps in Al2O3 matter for passivation
-- (field-effect and chemical) 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:
-- Amorphous ALD Al2O3 ~1.5-2 W/m/K; crystalline sapphire is far
-- higher (~30-40 W/m/K) (CRC Handbook; thin-film literature).
--
-- A film-appropriate value of 1.7 W/m/K is used. Approximate.
local enabled = true
local value = 1.7
return value, enabled
end
function material.heat_capacity(state)
-- Specific heat capacity
-- Units: J kg^-1 K^-1
--
-- Reference:
-- Al2O3, c_p(300 K) ~ 880 J/kg/K (CRC Handbook of Chemistry and
-- Physics).
local enabled = true
local value = 880.0
return value, enabled
end
function material.density(state)
-- Mass density
-- Units: kg m^-3
--
-- Reference:
-- Amorphous ALD Al2O3 rho ~3.0 g/cm^3; crystalline sapphire is
-- 3.98 g/cm^3 (CRC Handbook of Chemistry and Physics).
--
-- A film-appropriate value is used. Approximate.
local enabled = true
local value = 3000.0
return value, enabled
end
function material.lattice_constant(state)
-- Cubic lattice constant
-- Units: m
--
-- DISABLED: device Al2O3 is usually AMORPHOUS (ALD), and
-- crystalline sapphire (alpha-Al2O3, corundum) is trigonal, NOT
-- cubic, so a single cubic lattice constant is not meaningful.
--
-- Reference (crystallography):
-- R. W. G. Wyckoff, "Crystal Structures".
-- Sapphire (alpha-Al2O3): a = 4.759 A, c = 12.991 A.
-- The a-axis value is returned only so the field is finite.
local enabled = false
local value = 4.759e-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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