Introduction to electrets: Principles, equations ... · Darmstadt University of Technology •...

Darmstadt University of Technology • Institute for Telecommunications

Introduction to electrets:Principles, equations, experimental techniques

Gerhard M. Sessler

Darmstadt University of Technology Institute for Telecommunications

Merckstrasse 25, 64283 Darmstadt, Germany

[email protected]


OverviewPrinciplesChargesMaterialsElectret classes

EquationsFieldsForcesCurrentsCharge transport

Experimental techniquesChargingSurface potentialThermally-stimulated dischargeDielectric measurementsCharge distribution (surface)Charge distribution (volume)


Electret charges


Energy diagram and density of states for a polymer


Electret materials

Polymers

Fluoropolymers (PTFE, FEP)Polyethylene (HDPE, LDPE, XLPE)Polypropylene (PP)Polyethylene terephtalate (PET)Polyimid (PI)Polymethylmethacrylate (PMMA)Polyvinylidenefluoride (PVDF)Ethylene vinyl acetate (EVA)••

Cellular and porous polymersCellular PPPorous PTFE

Anorganic materials

Silicon oxide (SiO2)Silicon nitride (Si3N4)Aluminum oxide (Al2O3)Glas (SiO2 + Na, S, Se, B, ...)Photorefractive materials•••


Charged or polarized dielectrics

Category Materials Charge or polarization Properties

GeometryDensity

Real-charge

electretsFEP, SiO 2

NLO

Ferroelectric

materials

/

,

External electric

field and force

Electrooptic

and NLO effects

Piezo- and

pyroelectricity

0.1 - 1

[mC/m ]2

0.1 - 10

10 - 100

-

+

+-

+

-

+

-

+-,

materials

Applications




Experimental techniquesChargingSurface potentialThermally-stimulated dischargeCharge distribution (surface)Charge distribution (volume)


Equations 1:Fields of an electret

Surface charges only: Volume charges only:σ = σr + ∆PP

d1

E2

E1 ρ (x)

d2 σx

)( 120

12 dd

dE

+=

εεσ

)( 120

21 dd

dE

+−=

εεσ

(1)

(2)

ρ (x) = ρr (x) + ρP (x)

∫=1

01

)(1

ˆd

dxxxd

ρσ

σσ ˆ with(2) Eq.

from field External 2

=E


Equations 2:Force of an electret on an electrode

E2

E1

2202

1EF ε=


Equations 3:Currents in an electret

E(x,t) Pp(x,t) ic(x,t)

cp0 )(

)( it

PEti +

∂+∂

=εε

Current density

Eic )( −−++ += ρµρµ


Equations 4: Charge transport equations

0f )(),(),(),(

IxItxEtxt

txE =+⋅+∂

∂ µρε

Current Equation:

Poisson Equation:

),(),(),(

tf txtxt

txE ρρε +=∂

∂

Poisson Equation:

−⋅=

∂∂

m

tft ),(1

),(),(

ρρ

τρρ txtx

t

tx

Parameters of Model:I(x) : current µ : free-carrier mobilityτ : free-carrier lifetime ρm : trap density

e-

I0

I(x)

ρf /τρf

ρt

CB

Trap level

(1)

(2)

(3)


Measured and calculated location of charge peak in electron-beam charged FEP

(Sessler 2004)

1 10 100 10006

8

10

12

Pea

k Lo

catio

n (µ

m)

Injected Charge Density ( nC/cm2 )




Experimental techniquesChargingSurface potentialThermally-stimulated dischargeDielectric measurements Charge distribution (surface)Charge distribution (volume)


Charging methods

+++++++

- - - - - - - -

- - - - - - - -

++++ ++++ - - --- - -- - - - -

++++++++

Heatingchamber

THERMALELECTRONBEAM

(Vacuum)

CORONA

e- (2-40 keV)

surface charge(and polarization)

volume orsurface charges

surface and volume charges

and/or polarization

~10kV

~200V

++ ++ +++

and polarization


Surface potential measurement

Electrostatic voltmeterElectret film

Movable sample holder

• Determination of charge stability of different electret materials by isothermal discharging at elevated temperatures

Surface potential of PP

0 400 800 1200 16000

100

200

300

400

500

90°C

Sur

face

pot

entia

l [V

]

Annealing time [min]

P1 P2 P3 P4 P5 P6


Thermally-stimulated discharge (TSD)

+ +

- - - - - - - -

+

+ + + + +

I

T, t

Heizkammer

I

Heating chamber

Linear temperature increase

Separation of surface and volume trapsActivation energies

Trap densities


Measurement of activation energy A:Initial-rise-method

k

A

Td

id −=)/1(

)(ln

curr

ent i

temperature T

ln i

1/T


TSD for electron beam charged FEP (v. Seggern 1981)




Experimental techniquesChargingSurface potentialThermally stimulated dischargeCharge distribution (surface)Charge distribution (volume)


Kelvin probe force microscope (KFM)(Jacobs et al 1997)

Measures lateral potential distribution


KFM images of charge distribution on PMMA(Jacobs et al 2001)


Thermal pulse method(Collins 1975)

V(t)

)(

)(

1

2

tV

tV

d

r =

t2t1tV(t1)

V(t2)

V


Thermal wave method (Bauer 1996)

Measures charge distribution close to surface


Laser-Induced Pressure Pulse (LIPP) method

++++

++++++

++

+

hν

x=ct

t,x

electrodecharges

charges in dielectric

ρ( )x

P x( )e x( )

I t( )

I t( )

I t 1( ) ( )γ+ ( )ρ- dPdx

dedx

- ,


Charge distribution in e-beam irradiated FEP(Sessler et al 1983)

20 keV 5 ns/DIV( 6.5 µm/DIV=

5 ns/DIV( 6.5 µm/DIV=

30 keV


Evolution of charge distribution in LDPEmeasured with Pulsed ElectroAcoustic (PEA) method

(Hozumi et al 1998)

LDPE


CV-method for measuring charge centroid location

Measures location of charge centroid and total charge


Charge drift in double layers of SiO2 (300 nm) and Si3N4 (150 nm)

(Zhang et al 2002)

0

0,2

0,4

0,6

0,8

1

0 200 400 600

annealing time [min]

norm

aliz

ed u

nits

surface potentialmean charge depthintegrated charge density

400°C


Scanning Electron Microscope (SEM) method


SEM pictures of cross section of charged cellular PP(Hillenbrand et al 2000)

-


Summary: New aspects of electret researchElectret materials

NLO materialsCellular polymersTailored polymersSilicon materials

Theoretical approachesCharge transport models with

dispersive transport generation-recombination modelsradiation effects

Experimental methodsPressure pulse and thermal methodsAtomic force microscopyScanning electron microscopyCV-methodDielectric method

Better understanding ofCharging and charge transport in irradiated polymers, cellular polymers, etc.

Introduction to electrets: Principles, equations ... · Darmstadt University of Technology •...

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