PMMA material model

1. Introduction

This page contains the OghmaNano material model for PMMA ((C5H8O2)n).

Poly(methyl methacrylate), amorphous insulating dielectric polymer

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 = {}

-- ============================================================================
-- IMPORTANT MODELLING NOTE
-- ----------------------------------------------------------------------------
-- PMMA is an amorphous INSULATING dielectric polymer, not a semiconductor.
-- It is used as a gate/interlayer dielectric, encapsulant/spacer, or a
-- transparent optical layer (refractive index n ~ 1.49, handled in the
-- optical n/k database rather than here).
--
-- The semiconductor-specific quantities (free-carrier DOS, mobility,
-- recombination, Auger, SRH traps, band tails) are not physical for an
-- insulator, so they are DISABLED here by returning enabled = false. The
-- format is preserved (every function is still present) so the interface is
-- unchanged; only the meaningful parameters are active:
--   Eg, Xi, epsilonr, thermal_conductivity, heat_capacity, density.
-- ============================================================================

function material.name()
	local enabled = true

	return "PMMA", enabled
end


function material.description()
	local enabled = true

	return "Poly(methyl methacrylate), amorphous insulating dielectric polymer", enabled
end


function material.formula()
	local enabled = true

	return "(C5H8O2)n", enabled
end


function material.Eg(state)
	-- Units: eV
	--
	-- PMMA is a wide-gap insulator. Reported optical band gaps span roughly
	-- 4.5-5.6 eV depending on the film and extraction method (e.g. Tauc);
	-- the fundamental/transport gap is larger. The Varshni model does not
	-- apply; a constant representative value is returned.
	--
	-- Reference:
	-- The PMMA optical gap is strongly method-dependent; UV-absorption
	-- (Tauc) analyses of PMMA films report values across ~4.5-5.6 eV. As a
	-- dielectric, PMMA's exact electronic gap is rarely used in device
	-- models (the permittivity is the relevant parameter), so a
	-- representative value is given rather than a single citation.

	local enabled = true
	local value = 5.6

	return value, enabled
end


function material.Xi(state)
	-- Electron affinity (LUMO level below vacuum)
	-- Units: eV
	--
	-- Only relevant for band-alignment / injection-barrier estimates when
	-- PMMA is used as a thin dielectric; it plays no transport role. The
	-- value is approximate and method dependent (reported ~2-2.5 eV). With
	-- Eg ~5.6 eV this implies an ionisation energy of ~8 eV, consistent with
	-- PMMA's large hole-injection barriers.
	--
	-- Reference:
	-- PMMA's electron affinity is not well defined and is rarely needed for
	-- a dielectric; the ~2.5 eV figure is an approximate value used only for
	-- band-alignment estimates, not a precisely measured level.

	local enabled = true
	local value = 2.5

	return value, enabled
end


function material.Nc(state)
	-- Effective conduction-band density of states
	-- Units: m^-3
	--
	-- Not applicable to an insulating dielectric (no free-carrier transport);
	-- disabled (enabled = false). Nominal value retained only to keep the
	-- return type valid.

	local enabled = false
	local value = 1.0e24

	return value, enabled
end


function material.Nv(state)
	-- Effective valence-band density of states
	-- Units: m^-3
	--
	-- Not applicable to an insulating dielectric; disabled (enabled = false).

	local enabled = false
	local value = 1.0e24

	return value, enabled
end


function material.mu_e(state)
	-- Low-field electron mobility
	-- Units: m^2 V^-1 s^-1
	--
	-- PMMA is an insulator; carrier mobility is not a meaningful device
	-- parameter. Disabled (enabled = false); a negligible nominal value is
	-- returned.

	local enabled = false
	local value = 1.0e-16

	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
	--
	-- PMMA is an insulator; disabled (enabled = false); negligible nominal
	-- value returned.

	local enabled = false
	local value = 1.0e-16

	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
	--
	-- Frequency dependent: ~3.3-3.9 at low frequency (relevant for
	-- electrostatics / gate-dielectric use), falling to ~2.6 near 1 MHz and
	-- ~2.2 optically (n ~ 1.49, eps_opt = n^2 ~ 2.22). The low-frequency
	-- value is returned.
	--
	-- Reference:
	-- J. Brandrup, E. H. Immergut, E. A. Grulke (Eds.), "Polymer Handbook",
	-- 4th ed., Wiley, 1999.

	local enabled = true
	local value = 3.6

	return value, enabled
end


function material.free_to_free_recombination(state)
	-- Bimolecular (band-to-band) recombination coefficient
	-- Units: m^3 s^-1
	--
	-- Not applicable to an insulator; disabled (enabled = false).

	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
	--
	-- Not applicable to an insulator; disabled (enabled = false).

	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
	--
	-- Not applicable to an insulator; disabled (enabled = false).

	local enabled = false
	local value = 0.0

	return value, enabled
end


function material.ss_srh_trap_energy(state)
	-- SRH trap energy relative to mid-gap
	-- Units: eV
	--
	-- Not applicable to an insulator; disabled (enabled = false).

	local enabled = false
	local value = 0.0

	return value, enabled
end


function material.ss_srh_Nt(state)
	-- SRH trap density
	-- Units: m^-3
	--
	-- Not applicable to an insulator; disabled (enabled = false).

	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
	--
	-- Not applicable to an insulator; disabled (enabled = false).

	local enabled = false
	local value = 1.0e-20

	return value, enabled
end


function material.ss_srh_sigma_p(state)
	-- Hole capture cross section
	-- Units: m^2
	--
	-- Not applicable to an insulator; disabled (enabled = false).

	local enabled = false
	local value = 1.0e-20

	return value, enabled
end


function material.thermal_conductivity(state)
	-- Thermal conductivity
	-- Units: W m^-1 K^-1
	--
	-- Well-established low value for bulk amorphous PMMA (~0.17-0.19 W/m/K),
	-- nearly temperature independent near room temperature. Constant value
	-- returned.
	--
	-- Reference:
	-- J. Brandrup, E. H. Immergut, E. A. Grulke (Eds.), "Polymer Handbook",
	-- 4th ed., Wiley, 1999.

	local enabled = true
	local value = 0.19

	return value, enabled
end


function material.heat_capacity(state)
	-- Specific heat capacity
	-- Units: J kg^-1 K^-1
	--
	-- Room-temperature specific heat of PMMA is ~1400-1500 J/kg/K. A
	-- representative value is returned.
	--
	-- Reference:
	-- J. Brandrup, E. H. Immergut, E. A. Grulke (Eds.), "Polymer Handbook",
	-- 4th ed., Wiley, 1999.

	local enabled = true
	local value = 1450.0

	return value, enabled
end


function material.density(state)
	-- Mass density
	-- Units: kg m^-3
	--
	-- Bulk amorphous PMMA density is ~1.18 g/cm^3.
	--
	-- Reference:
	-- J. Brandrup, E. H. Immergut, E. A. Grulke (Eds.), "Polymer Handbook",
	-- 4th ed., Wiley, 1999.

	local enabled = true
	local value = 1180.0

	return value, enabled
end


function material.lattice_constant(state)
	-- Characteristic structural spacing
	-- Units: m
	--
	-- PMMA is atactic and fully amorphous: it has no crystalline lattice, so
	-- this parameter is not applicable and is disabled (enabled = false). The
	-- nominal value (~1 nm) reflects only the amorphous inter-chain scattering
	-- halo and should not be treated as a lattice constant.

	local enabled = false
	local value = 1.0e-9

	return value, enabled
end

function material.Ntrape(state)
	-- Electron tail (band-tail) trap density
	-- Units: m^-3
	--
	-- Not applicable to an insulator; disabled (enabled = false).

	local enabled = false
	local value = 0.0

	return value, enabled
end


function material.Ntraph(state)
	-- Hole tail (band-tail) trap density
	-- Units: m^-3
	--
	-- Not applicable to an insulator; disabled (enabled = false).

	local enabled = false
	local value = 0.0

	return value, enabled
end


function material.Etrape(state)
	-- Electron tail characteristic energy
	-- Units: eV
	--
	-- Not applicable to an insulator; disabled (enabled = false).

	local enabled = false
	local value = 0.06

	return value, enabled
end


function material.Etraph(state)
	-- Hole tail characteristic energy
	-- Units: eV
	--
	-- Not applicable to an insulator; disabled (enabled = false).

	local enabled = false
	local value = 0.06

	return value, enabled
end


function material.srhsigman_e(state)
	-- Electron-to-electron capture cross section
	-- Units: m^2
	--
	-- Not applicable to an insulator; disabled (enabled = false).

	local enabled = false
	local value = 1.0e-20

	return value, enabled
end


function material.srhsigmap_e(state)
	-- Hole-to-electron capture cross section
	-- Units: m^2
	--
	-- Not applicable to an insulator; disabled (enabled = false).

	local enabled = false
	local value = 1.0e-20

	return value, enabled
end


function material.srhsigman_h(state)
	-- Electron-to-hole capture cross section
	-- Units: m^2
	--
	-- Not applicable to an insulator; disabled (enabled = false).

	local enabled = false
	local value = 1.0e-20

	return value, enabled
end


function material.srhsigmap_h(state)
	-- Hole-to-hole capture cross section
	-- Units: m^2
	--
	-- Not applicable to an insulator; disabled (enabled = false).

	local enabled = false
	local value = 1.0e-20

	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)))

	print(string.format("Electron trap density:  %.6e m^-3", material.Ntrape(state)))
	print(string.format("Hole trap density:      %.6e m^-3", material.Ntraph(state)))
	print(string.format("Electron trap energy:   %.6f eV", material.Etrape(state)))
	print(string.format("Hole trap energy:       %.6f eV", material.Etraph(state)))

	print(string.format("SRH sigma n->e:         %.6e m^2", material.srhsigman_e(state)))
	print(string.format("SRH sigma p->e:         %.6e m^2", material.srhsigmap_e(state)))
	print(string.format("SRH sigma n->h:         %.6e m^2", material.srhsigman_h(state)))
	print(string.format("SRH sigma p->h:         %.6e m^2", material.srhsigmap_h(state)))
end

return material

-- ============================================================================
-- Copyright (C) 2026 The OghmaNano Project
-- All rights reserved.
--
-- This file is part of the OghmaNano Materials Model Library.
--
-- Website:
-- https://www.oghma-nano.com
--
-- Documentation and accuracy statement:
-- https://www.oghma-nano.com/manual/material-scripts.html
--
-- These material models are provided to support scientific research and
-- semiconductor device simulation. If you find them useful, please cite
-- OghmaNano where appropriate. Please do not redistribute these files or
-- incorporate them into other software or databases without permission.
-- ============================================================================