Introduction to Electrets: Principles, Equations, Experimental Techniques

Introduction to electrets: Principles, equations, experimental techniques

Gerhard M. Sessler

Darmstadt University of Technology Institute for Telecommunications Merckstrasse 25, 64283 Darmstadt, Germany

Darmstadt University of Technology • Institute for Telecommunications Overview Principles Charges Materials Electret classes Equations Fields Forces Currents Charge transport Experimental techniques Charging Surface potential Thermally-stimulated discharge Dielectric measurements Charge distribution (surface) Charge distribution (volume)

Darmstadt University of Technology • Institute for Telecommunications Electret charges

Darmstadt University of Technology • Institute for Telecommunications Energy diagram and density of states for a polymer

Darmstadt University of Technology • Institute for Telecommunications Electret materials

Polymers Anorganic materials

Fluoropolymers (PTFE, FEP) Silicon oxide (SiO 2) Polyethylene (HDPE, LDPE, XLPE) Silicon nitride (Si 3N4) Polypropylene (PP) Aluminum oxide (Al 2O3) Polyethylene terephtalate (PET) Glas (SiO 2 + Na, S, Se, B, ...) Polyimid (PI) Photorefractive materials Polymethylmethacrylate (PMMA) • Polyvinylidenefluoride (PVDF) • Ethylene vinyl acetate (EVA) • • • Cellular and porous polymers Cellular PP Porous PTFE

Darmstadt University of Technology • Institute for Telecommunications Charged or polarized dielectrics

Category Materials Charge or polarization Properties Applications Density Geometry [mC/m2 ]

Real-charge External electric FEP, SiO electrets 2 0.1 - 1 field and force

NLO Electrooptic / , - - - + + + 0.1 - 10 materials - and NLO effects - + +

Ferroelectric Piezo- and , 10 - 100 materials pyroelectricity

Darmstadt University of Technology • Institute for Telecommunications Overview Principles Charges Materials Electret classes Equations Fields Forces Currents Charge transport Experimental techniques Charging Surface potential Thermally-stimulated discharge Charge distribution (surface) Charge distribution (volume)

Darmstadt University of Technology • Institute for Telecommunications Equations 1: Fields of an electret

Surface charges only: Volume charges only: σ σ ∆ ρ ρ ρ = r + PP (x) = r (x) + P (x) x

σ d1 d2 E2 1 σˆ = xρ(x)dx ρ ∫ d1 E1 (x) d1 0

External field E2 from σ d σ = σ E = − 2 (1) Eq. (2) with ˆ 1 ε ε + 0 ( d2 d1) σ d E = 1 (2) 2 ε ε + 0 ( d2 d1)

Darmstadt University of Technology • Institute for Telecommunications Equations 2: Force of an electret on an electrode

1 F = ε E 2 2 0 2

Darmstadt University of Technology • Institute for Telecommunications Equations 3: Currents in an electret

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

Current density ∂(ε ε E + P ) (ti ) = 0 p + i ∂t c = µ ρ + µ ρ ic ( + + − − ) E

Darmstadt University of Technology • Institute for Telecommunications Equations 4: Charge transport equations e- Current Equation: I0 ∂E(x,t) ε + µρ (x,t) ⋅ E(x,t) + I(x) = I (1) ∂t f 0 I(x) Poisson Equation: ∂E(x,t) ε = ρ (x,t) + ρ (x,t) ∂t f t (2)

Poisson Equation: CB ρ f ∂ρ (x,t) ρ (x,t)  ρ (x,t) ρ τ t = f ⋅ − t (3) f / 1  ρ ∂t τ  ρ  t m Trap level Parameters of Model: I(x) : current µ : free-carrier mobility τ ρ : free-carrier lifetime m : trap density

Darmstadt University of Technology • Institute for Telecommunications Measured and calculated location of charge peak in electron-beam charged FEP (Sessler 2004) 12 m) µ 10

8 Peak Location ( PeakLocation 6 1 10 100 1000 Injected Charge Density ( nC/cm 2 )

Darmstadt University of Technology • Institute for Telecommunications Charging methods

CORONA ELECTRON THERMAL BEAM (Vacuum)

~10kV e- (2-40 keV) Heating chamber

~200V +++ ++++ + +++++++ ------+ + + + - + - + - + ------+++ + +++ + ------

surface charge volume or surface and (and polarization) surface charges volume charges and polarization and/or polarization

Darmstadt University of Technology • Institute for Telecommunications Surface potential measurement

Surface potential of PP 500 Electrostatic voltmeter Electret film 400 90°C

300

200 P1 P2 P3 100 P4 Surface [V] Surface potential P5 Movable sample holder P6 0 0 400 800 1200 1600 Annealing time [min]

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

Darmstadt University of Technology • Institute for Telecommunications Thermally-stimulated discharge (TSD)

HeatingHeizkammer chamber I + + +

------I

+ + + + + T, t Linear temperature increase

Separation of surface and volume traps Activation energies Trap densities

Darmstadt University of Technology • Institute for Telecommunications Measurement of activation energy A: Initial-rise-method

ln i currenti

temperature T 1/T

d(ln i) = − A d /1( T ) k

Darmstadt University of Technology • Institute for Telecommunications TSD for electron beam charged FEP (v. Seggern 1981)

Darmstadt University of Technology • Institute for Telecommunications Overview Principles Charges Materials Electret classes Equations Fields Forces Currents Charge transport Experimental techniques Charging Surface potential Thermally stimulated discharge Charge distribution (surface) Charge distribution (volume)

Darmstadt University of Technology • Institute for Telecommunications Kelvin probe force microscope (KFM) (Jacobs et al 1997)

Measures lateral potential distribution

Darmstadt University of Technology • Institute for Telecommunications KFM images of charge distribution on PMMA (Jacobs et al 2001)

Darmstadt University of Technology • Institute for Telecommunications Thermal pulse method (Collins 1975)

r = V (t2 ) d V (t1)

V(t2) V(t) V(t1) t t1 t2

Darmstadt University of Technology • Institute for Telecommunications Thermal wave method (Bauer 1996)

Measures charge distribution close to surface

Darmstadt University of Technology • Institute for Telecommunications Laser-Induced Pressure Pulse (LIPP) method

electrode + charges + I( t ) + + ρ(x ) + hν + + P( x ) + e( x ) ++ + + + t,x I( t ) charges in dielectric

I( t ) (γ+ 1 ) (ρ dP ) - de , x=ct - dx dx

Darmstadt University of Technology • Institute for Telecommunications Charge distribution in e-beam irradiated FEP (Sessler et al 1983)

20 keV 5 ns/DIV 30 keV 5 ns/DIV ( = 6.5 µm/DIV ( = 6.5 µm/DIV

Darmstadt University of Technology • Institute for Telecommunications Evolution of charge distribution in LDPE measured with Pulsed ElectroAcoustic (PEA) method (Hozumi et al 1998)

LDPE

Darmstadt University of Technology • Institute for Telecommunications CV-method for measuring charge centroid location

Measures location of charge centroid and total charge

Darmstadt University of Technology • Institute for Telecommunications Charge drift in double layers of SiO 2 (300 nm) and Si 3N4 (150 nm) (Zhang et al 2002)

1 400°C 0,8

0,6

0,4

normalized units surface potential 0,2 mean charge depth integrated charge density 0 0 200 400 600 annealing time [min]

Darmstadt University of Technology • Institute for Telecommunications Scanning Electron Microscope (SEM) method

Darmstadt University of Technology • Institute for Telecommunications SEM pictures of cross section of charged cellular PP (Hillenbrand et al 2000)

Darmstadt University of Technology • Institute for Telecommunications Summary: New aspects of electret research Electret materials NLO materials Cellular polymers Tailored polymers Silicon materials Theoretical approaches Charge transport models with dispersive transport generation-recombination models radiation effects Experimental methods Pressure pulse and thermal methods Atomic force microscopy Scanning electron microscopy CV-method Dielectric method Better understanding of Charging and charge transport in irradiated polymers, cellular polymers, etc.

Darmstadt University of Technology • Institute for Telecommunications