ITO material model
1. Introduction
This page contains the OghmaNano material model for ITO (In2O3:Sn).
Indium tin oxide (In2O3:Sn), degenerate 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 "ITO", enabled
end
function material.description()
local enabled = true
return "Indium tin oxide (In2O3:Sn), degenerate transparent conducting oxide", enabled
end
function material.formula()
local enabled = true
return "In2O3:Sn", enabled
end
function material.Eg(state)
-- Units: eV
--
-- Reference:
-- A. Walsh et al., "Nature of the band gap of In2O3 revealed by
-- first-principles calculations and X-ray spectroscopy",
-- Phys. Rev. Lett. 100, 167402, 2008.
--
-- Subtlety: the true fundamental (direct) gap of In2O3 is ~2.9 eV,
-- but the onset transition is weak/dipole-forbidden, so the strong
-- optical absorption edge sits higher (~3.75 eV), and in degenerate
-- ITO the Burstein-Moss shift widens the apparent optical gap
-- further to ~3.75-4.3 eV.
--
-- A device-relevant value of 3.6 eV is used. Constant.
local enabled = true
local value = 3.6
return value, enabled
end
function material.Xi(state)
-- Electron affinity
-- Units: eV
--
-- Reference:
-- ITO electrode work-function literature.
--
-- ITO work function is treatment-dependent (~4.4-4.8 eV; ~4.7 eV
-- after oxygen-plasma / UV-ozone). Because ITO is DEGENERATE, the
-- Fermi level sits in the conduction band and the effective work
-- function nearly coincides with the electron affinity. The work
-- function is the number that sets contact alignment. Approximate.
local enabled = true
local value = 4.7
return value, enabled
end
function material.Nc(state)
-- Effective conduction-band density of states
-- Units: m^-3
--
-- Reference:
-- From In2O3 CB effective mass m_e* ~ 0.3 m0:
-- Nc(300 K) ~ 4e18 cm^-3 = 4e24 m^-3.
--
-- Note: ITO is degenerate (free-electron density ~1e21 cm^-3), so
-- this parabolic Nc is a formal quantity only; carrier density is
-- set by doping. 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 In2O3 hole mass is poorly constrained; 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 ITO thin-film Hall mobility ~15-50 cm^2/V/s; a
-- mid value of 35 cm^2/V/s = 0.0035 m^2/V/s is used.
--
-- Note: transport is ionised-impurity limited in this degenerate
-- material (not phonon limited), so no (300/T)^n law is applied.
-- Approximate.
local enabled = true
local value = 0.0035
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: ITO is an n-type electrode; hole transport is essentially
-- irrelevant to device operation and not experimentally
-- constrained. Small placeholder; 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:
-- In2O3 / ITO static permittivity ~8.9-9.5 (In2O3 optical and
-- dielectric literature).
--
-- A representative value of 9.0 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: 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 ITO. 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 ITO. 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:
-- ITO thin-film thermal conductivity ~3-11 W/m/K (thin-film
-- thermal-transport literature).
--
-- A representative 8 W/m/K is used. Poorly constrained /
-- thickness-dependent.
local enabled = true
local value = 8.0
return value, enabled
end
function material.heat_capacity(state)
-- Specific heat capacity
-- Units: J kg^-1 K^-1
--
-- Reference:
-- In2O3, c_p(300 K) ~ 360 J/kg/K (CRC Handbook of Chemistry and
-- Physics). Approximate.
local enabled = true
local value = 360.0
return value, enabled
end
function material.density(state)
-- Mass density
-- Units: kg m^-3
--
-- Reference:
-- In2O3 / ITO rho ~ 7.15 g/cm^3 (CRC Handbook of Chemistry and
-- Physics).
local enabled = true
local value = 7150.0
return value, enabled
end
function material.lattice_constant(state)
-- Cubic lattice constant
-- Units: m
--
-- ENABLED: unlike the other TCOs here, the parent oxide In2O3
-- crystallises in the CUBIC bixbyite structure, so a single cubic
-- lattice constant IS meaningful.
--
-- Reference (crystallography):
-- R. W. G. Wyckoff, "Crystal Structures".
-- Bixbyite In2O3: a = 10.117 A at 300 K (large 80-atom cell); Sn
-- substitutes on In sites in ITO. Linear thermal expansion
-- ~6.7e-6 /K near 300 K is applied (approximate).
local enabled = true
local T = state.T
local a300 = 10.117e-10
local expansion = 6.7e-6
local value = a300*(1.0 + expansion*(T - 300.0))
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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