ZnO material model

1. Introduction

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

Zinc oxide (wurtzite), n-type wide-gap semiconductor / window / 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 "ZnO", enabled
end


function material.description()
	local enabled = true

	return "Zinc oxide (wurtzite), n-type wide-gap semiconductor / window / electron-transport layer", enabled
end


function material.formula()
	local enabled = true

	return "ZnO", enabled
end


function material.Eg(state)
	-- Units: eV
	--
	-- Reference:
	-- U. Ozgur et al., "A comprehensive review of ZnO materials and
	-- devices", J. Appl. Phys. 98, 041301, 2005.
	--
	-- Direct gap ~3.37 eV at 300 K. Note the large free-exciton
	-- binding energy (~60 meV), so near-band-edge optics is strongly
	-- excitonic. T-dependence exists but is not a clean Varshni fit;
	-- a constant value is used here rather than fitted coefficients.

	local enabled = true
	local value = 3.37

	return value, enabled
end


function material.Xi(state)
	-- Electron affinity
	-- Units: eV
	--
	-- Reference:
	-- ZnO electron affinity ~4.1-4.35 eV (U. Ozgur et al.,
	-- J. Appl. Phys. 98, 041301, 2005; device-alignment literature).
	--
	-- A representative 4.2 eV is used. Shallow CB makes ZnO a good
	-- electron-transport / window layer. Approximate.

	local enabled = true
	local value = 4.2

	return value, enabled
end


function material.Nc(state)
	-- Effective conduction-band density of states
	-- Units: m^-3
	--
	-- Reference:
	-- From ZnO CB effective mass m_e* ~ 0.26 m0 (U. Ozgur et al.,
	-- J. Appl. Phys. 98, 041301, 2005):
	-- Nc(300 K) ~ 3.7e18 cm^-3 = 3.7e24 m^-3. Approximate.

	local enabled = true
	local T = state.T
	local value = 3.7e24*(T/300.0)^1.5

	return value, enabled
end


function material.Nv(state)
	-- Effective valence-band density of states
	-- Units: m^-3
	--
	-- Reference:
	-- From ZnO valence-band mass m_h* ~ 0.6 m0 (U. Ozgur et al.,
	-- J. Appl. Phys. 98, 041301, 2005):
	-- Nv(300 K) ~ 1.1e19 cm^-3 = 1.1e25 m^-3. Approximate.

	local enabled = true
	local T = state.T
	local value = 1.1e25*(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:
	-- Bulk single-crystal ZnO ~200-440 cm^2/V/s (U. Ozgur et al.,
	-- J. Appl. Phys. 98, 041301, 2005).
	--
	-- Note: a bulk value of 200 cm^2/V/s = 0.02 m^2/V/s is returned.
	-- Sol-gel / nanoparticle ZnO device films are ORDERS of magnitude
	-- lower and grain-boundary limited; reduce accordingly. No phonon
	-- (300/T)^n law applied (film transport is not phonon limited).
	-- Approximate.

	local enabled = true
	local value = 0.02

	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: ZnO hole mobility is poorly constrained (stable p-type ZnO
	-- is notoriously hard to achieve). Reported ~5-50 cm^2/V/s. As a
	-- window/ETL, holes are the blocked minority carrier. Low
	-- placeholder (~5 cm^2/V/s).

	local enabled = true
	local value = 5.0e-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:
	-- ZnO static permittivity ~8.5 (U. Ozgur et al., J. Appl. Phys.
	-- 98, 041301, 2005). High-frequency epsilon_inf ~3.7.
	--
	-- Note: slightly anisotropic (wurtzite); a representative value is
	-- used.

	local enabled = true
	local value = 8.5

	return value, enabled
end


function material.free_to_free_recombination(state)
	-- Radiative (band-to-band) recombination coefficient
	-- Units: m^3 s^-1
	--
	-- Reference:
	-- Representative bimolecular coefficient for direct-gap ZnO,
	-- ~1e-10 cm^3/s = 1e-16 m^3/s.
	--
	-- Note: ZnO is a DIRECT-gap UV emitter, so unlike the indirect
	-- oxides radiative recombination can matter; but near-edge
	-- emission is excitonic and B is not tightly constrained. Treat as
	-- approximate.

	local enabled = true
	local value = 1.0e-16

	return value, enabled
end


function material.auger_Cn(state)
	-- Electron Auger recombination coefficient
	-- Units: m^6 s^-1
	--
	-- Note: weak in wide-gap ZnO and poorly constrained.
	-- 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: as for Cn, poorly constrained 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. ZnO commonly carries
	-- native point defects (O vacancies, Zn interstitials) that act as
	-- recombination/doping centres; 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 single-crystal ZnO ~50-100 W/m/K, anisotropic (CRC
	-- Handbook; U. Ozgur et al., J. Appl. Phys. 98, 041301, 2005).
	--
	-- Note: thin/nanostructured films are much lower. A conservative
	-- bulk value is returned. Approximate.

	local enabled = true
	local value = 50.0

	return value, enabled
end


function material.heat_capacity(state)
	-- Specific heat capacity
	-- Units: J kg^-1 K^-1
	--
	-- Reference:
	-- ZnO, c_p(300 K) ~ 495 J/kg/K (CRC Handbook of Chemistry and
	-- Physics).

	local enabled = true
	local value = 495.0

	return value, enabled
end


function material.density(state)
	-- Mass density
	-- Units: kg m^-3
	--
	-- Reference:
	-- ZnO (wurtzite) rho = 5.61 g/cm^3 (CRC Handbook of Chemistry and
	-- Physics).

	local enabled = true
	local value = 5610.0

	return value, enabled
end


function material.lattice_constant(state)
	-- Cubic lattice constant
	-- Units: m
	--
	-- DISABLED: ZnO is hexagonal (wurtzite), NOT cubic, so a single
	-- cubic lattice constant is not meaningful.
	--
	-- Reference (crystallography):
	-- R. W. G. Wyckoff, "Crystal Structures".
	-- Wurtzite ZnO: a = 3.2495 A, c = 5.2069 A at 300 K.
	-- The a-axis value is returned for reference only.

	local enabled = false
	local value = 3.2495e-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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-- https://www.oghma-nano.com
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