P3HT material model

1. Introduction

This page contains the OghmaNano material model for P3HT ((C10H14S)n).

Regioregular poly(3-hexylthiophene) conjugated 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 = {}

function material.name()
	local enabled = true

	return "P3HT", enabled
end


function material.description()
	local enabled = true

	return "Regioregular poly(3-hexylthiophene) conjugated polymer", enabled
end


function material.formula()
	local enabled = true

	return "(C10H14S)n", enabled
end


function material.Eg(state)
	-- Units: eV
	--
	-- Optical band gap of regioregular P3HT (absorption onset ~650 nm).
	-- The transport gap (HOMO-LUMO separation used in drift-diffusion) is
	-- slightly larger than the optical gap because of the exciton binding
	-- energy (~0.3 eV), so some device models use ~2.0-2.2 eV instead.
	--
	-- The Varshni model used for crystalline GaAs does NOT apply to a
	-- disordered polymer: the gap is only weakly temperature dependent and
	-- is treated here as constant. A representative value is returned.
	--
	-- Reference:
	-- Y. Kim et al., "A strong regioregularity effect in self-organizing
	-- conjugated polymer films and high-efficiency polythiophene:fullerene
	-- solar cells", Nature Materials, 5, 197-203, 2006.

	local enabled = true
	local value = 1.9

	return value, enabled
end


function material.Xi(state)
	-- Electron affinity (LUMO level below vacuum)
	-- Units: eV
	--
	-- Reported LUMO of P3HT is typically -3.0 to -3.2 eV and HOMO
	-- -5.0 to -5.2 eV (cyclic voltammetry / UPS). With Xi = 3.2 eV and
	-- Eg = 1.9 eV the implied HOMO is ~-5.1 eV, consistent with literature.
	-- Absolute values are method dependent; a representative value is used.
	--
	-- Reference:
	-- Y. Kim et al., Nature Materials, 5, 197-203, 2006.

	local enabled = true
	local value = 3.2

	return value, enabled
end


function material.Nc(state)
	-- Effective conduction-band (LUMO) density of states
	-- Units: m^-3
	--
	-- Organic semiconductors have a disordered (approximately Gaussian) DOS
	-- rather than a parabolic band, so the crystalline (T/300)^1.5 scaling
	-- used for GaAs does not apply and a constant effective DOS is used.
	-- The P3HT monomer site density is ~4e27 m^-3 (density 1100 kg/m^3,
	-- repeat-unit mass ~166 g/mol); the effective transport-level DOS used
	-- in drift-diffusion is normally set well below this, commonly
	-- 1e25-1e27 m^-3. A representative value is used.
	--
	-- Reference:
	-- Add the precise reference used for the effective density of states.

	local enabled = true
	local value = 1.0e26

	return value, enabled
end


function material.Nv(state)
	-- Effective valence-band (HOMO) density of states
	-- Units: m^-3
	--
	-- See the note in material.Nc. Constant effective DOS used; the
	-- crystalline temperature scaling does not apply to a disordered
	-- polymer. A representative value is used.
	--
	-- Reference:
	-- Add the precise reference used for the effective density of states.

	local enabled = true
	local value = 1.0e26

	return value, enabled
end


function material.mu_e(state)
	-- Low-field electron mobility
	-- Units: m^2 V^-1 s^-1
	--
	-- P3HT is a strongly hole-transporting (p-type) polymer; electron
	-- transport is deep-trap limited and poorly defined for the pristine
	-- material. Reported values scatter widely and are typically several
	-- orders of magnitude below the hole mobility. A representative value
	-- is used and should be adjusted for the specific film/blend.
	--
	-- Note: organic mobility is thermally activated (increases with T,
	-- opposite to the phonon-limited GaAs power law), field dependent
	-- (Poole-Frenkel) and carrier-density dependent. A single low-field
	-- value is returned here.
	--
	-- Reference:
	-- Add the precise reference used for this value.

	local enabled = true
	local value = 1.0e-11

	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
	--
	-- Space-charge-limited hole mobility of P3HT in the ~1e-8 m^2/V/s range
	-- for as-cast films, rising towards ~1e-7 m^2/V/s after thermal
	-- annealing (increased crystallinity). Field-effect (in-plane)
	-- mobilities are higher (~1e-6 to 1e-5 m^2/V/s) due to anisotropy.
	-- A representative vertical (SCLC) value is used.
	--
	-- Note: organic mobility is thermally activated (increases with T),
	-- field dependent (Poole-Frenkel) and carrier-density dependent; the
	-- crystalline (300/T)^n form is not used.
	--
	-- Reference:
	-- V. D. Mihailetchi, H. Xie, B. de Boer, L. J. A. Koster, P. W. M. Blom,
	-- "Charge Transport and Photocurrent Generation in
	-- Poly(3-hexylthiophene):Methanofullerene Bulk-Heterojunction Solar
	-- Cells", Adv. Funct. Mater., 16, 699-708, 2006.

	local enabled = true
	local value = 1.0e-8

	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
	--
	-- Low-frequency dielectric constant of P3HT is commonly taken as
	-- 3.0-3.5 in device modelling. A representative value is used.
	--
	-- Reference:
	-- Add the precise reference used for this value.

	local enabled = true
	local value = 3.4

	return value, enabled
end


function material.free_to_free_recombination(state)
	-- Bimolecular (band-to-band) recombination coefficient
	-- Units: m^3 s^-1
	--
	-- In organic semiconductors free-carrier recombination is dominated by
	-- non-radiative Langevin-type encounters, not radiative emission. The
	-- Langevin coefficient is beta = q*(mu_e + mu_h)/(eps0*eps_r), which for
	-- the mobilities and permittivity above gives ~5e-17 m^3/s. Experiment
	-- often shows reduced (sub-)Langevin behaviour with a prefactor of
	-- 0.01-0.1. A representative effective value is used.
	--
	-- Reference:
	-- Add the precise reference used for this value.

	local enabled = true
	local value = 1.0e-17

	return value, enabled
end


function material.auger_Cn(state)
	-- Electron Auger recombination coefficient
	-- Units: m^6 s^-1
	--
	-- Auger recombination is generally negligible in organic semiconductors
	-- at operational carrier densities and is not usually included in P3HT
	-- device models. A very small representative value is used so the
	-- channel is effectively inactive.
	--
	-- Reference:
	-- Not applicable / negligible for organic semiconductors.

	local enabled = true
	local value = 1.0e-45

	return value, enabled
end


function material.auger_Cp(state)
	-- Hole Auger recombination coefficient
	-- Units: m^6 s^-1
	--
	-- See material.auger_Cn: negligible for organics. A very small
	-- representative value is used.
	--
	-- Reference:
	-- Not applicable / negligible for organic semiconductors.

	local enabled = true
	local value = 1.0e-45

	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/LUMO band).
	-- Negative values are below mid-gap (towards the valence/HOMO band).
	--
	-- Placed at mid-gap as a representative single-level approximation; real
	-- P3HT trapping is better described by the exponential tail states
	-- (see Ntrape/Ntraph/Etrape/Etraph below).

	local enabled = true
	local value = 0.0

	return value, enabled
end


function material.ss_srh_Nt(state)
	-- SRH trap density
	-- Units: m^-3
	--
	-- Representative value; trap densities in P3HT films vary strongly with
	-- purity, morphology and processing.

	local enabled = true
	local value = 1.0e22

	return value, enabled
end


function material.ss_srh_sigma_n(state)
	-- Electron capture cross section
	-- Units: m^2
	--
	-- Representative value.

	local enabled = true
	local value = 1.0e-20

	return value, enabled
end


function material.ss_srh_sigma_p(state)
	-- Hole capture cross section
	-- Units: m^2
	--
	-- Representative value.

	local enabled = true
	local value = 1.0e-20

	return value, enabled
end


function material.thermal_conductivity(state)
	-- Thermal conductivity
	-- Units: W m^-1 K^-1
	--
	-- P3HT is a low-conductivity, semicrystalline polymer. Reported values
	-- are ~0.1-0.3 W/m/K and are anisotropic (higher along the chain/
	-- in-plane direction). The crystalline phonon (300/T)^n scaling used for
	-- GaAs does not apply; a constant representative value is used.
	--
	-- Reference:
	-- Add the precise reference used for this value (measurements report
	-- ~0.1-0.3 W/m/K depending on morphology and orientation).

	local enabled = true
	local value = 0.2

	return value, enabled
end


function material.heat_capacity(state)
	-- Specific heat capacity
	-- Units: J kg^-1 K^-1
	--
	-- Organic polymers typically fall in the ~1000-2000 J/kg/K range near
	-- room temperature. A representative value is used.
	--
	-- Reference:
	-- Add the precise reference used for this value.

	local enabled = true
	local value = 1200.0

	return value, enabled
end


function material.density(state)
	-- Mass density
	-- Units: kg m^-3
	--
	-- P3HT film density is ~1.1 g/cm^3. A representative value is used.
	--
	-- Reference:
	-- Add the precise reference used for this value.

	local enabled = true
	local value = 1100.0

	return value, enabled
end


function material.lattice_constant(state)
	-- Characteristic structural spacing
	-- Units: m
	--
	-- P3HT is a semicrystalline polymer, NOT a cubic crystal, so a single
	-- cubic lattice constant is not physically meaningful. The monoclinic
	-- unit cell has approximately a ~1.6e-9 m (lamellar / alkyl stacking,
	-- the (100) XRD peak), b ~0.78e-9 m (backbone repeat) and a pi-pi
	-- stacking distance of ~0.38e-9 m. The largest and most commonly
	-- reported spacing (the lamellar a-axis) is returned as a
	-- representative value. Thermal expansion is anisotropic and is not
	-- included.
	--
	-- Reference:
	-- N. Kayunkid, S. Uttiya, M. Brinkmann, "Structural Model of Regioregular
	-- Poly(3-hexylthiophene) Obtained by Electron Diffraction Analysis",
	-- Macromolecules, 43, 4961-4967, 2010.

	local enabled = true
	local value = 1.66e-9

	return value, enabled
end

function material.Ntrape(state)
	-- Electron tail (exponential band-tail) trap density
	-- Units: m^-3
	--
	-- Disordered organics have substantial exponential tail states. A
	-- representative magnitude is used; adjust for the specific film.

	local enabled = true
	local value = 1.0e26

	return value, enabled
end


function material.Ntraph(state)
	-- Hole tail (exponential band-tail) trap density
	-- Units: m^-3
	--
	-- See material.Ntrape. Representative value.

	local enabled = true
	local value = 1.0e26

	return value, enabled
end


function material.Etrape(state)
	-- Electron tail characteristic (Urbach) energy
	-- Units: eV
	--
	-- The Urbach energy of P3HT is typically ~50-70 meV. A representative
	-- value is used.

	local enabled = true
	local value = 0.06

	return value, enabled
end


function material.Etraph(state)
	-- Hole tail characteristic (Urbach) energy
	-- Units: eV
	--
	-- See material.Etrape. Representative value.

	local enabled = true
	local value = 0.06

	return value, enabled
end


function material.srhsigman_e(state)
	-- Electron-to-electron capture cross section
	-- Units: m^2
	--
	-- Representative value for the tail-state SRH model.

	local enabled = true
	local value = 1.0e-20

	return value, enabled
end


function material.srhsigmap_e(state)
	-- Hole-to-electron capture cross section
	-- Units: m^2
	--
	-- Representative value for the tail-state SRH model.

	local enabled = true
	local value = 1.0e-20

	return value, enabled
end


function material.srhsigman_h(state)
	-- Electron-to-hole capture cross section
	-- Units: m^2
	--
	-- Representative value for the tail-state SRH model.

	local enabled = true
	local value = 1.0e-20

	return value, enabled
end


function material.srhsigmap_h(state)
	-- Hole-to-hole capture cross section
	-- Units: m^2
	--
	-- Representative value for the tail-state SRH model.

	local enabled = true
	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

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-- All rights reserved.
--
-- This file is part of the OghmaNano Materials Model Library.
--
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-- https://www.oghma-nano.com
--
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-- https://www.oghma-nano.com/manual/material-scripts.html
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