Introduction to electrets: Principles, equations, experimental techniques

Transcription

1 Introduction to electrets: Principles, equations, experimental techniques Gerhard M. Sessler Darmstadt University of Technology Institute for Telecommunications Merckstrasse 25, Darmstadt, Germany

2 Principles Charges Materials Electret classes Equations Fields Forces Currents Charge transport Overview Experimental techniques Charging Surface potential Thermally-stimulated discharge Dielectric measurements Charge distribution (surface) Charge distribution (volume)

3 Electret charges

4 Energy diagram and density of states for a polymer

5 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 polymers Cellular PP Porous PTFE Anorganic materials Silicon oxide (SiO 2 ) Silicon nitride (Si 3 N 4 ) Aluminum oxide (Al 2 O 3 ) Glas (SiO 2 + Na, S, Se, B,...) Photorefractive materials

6 Charged or polarized dielectrics Category Materials Charge or polarization Properties Density Geometry [mc/m 2 ] Applications Real-charge electrets FEP, SiO External electric field and force NLO materials /, Electrooptic and NLO effects Ferroelectric materials, Piezo- and pyroelectricity

7 Principles Charges Materials Electret classes Equations Fields Forces Currents Charge transport Overview Experimental techniques Charging Surface potential Thermally-stimulated discharge Charge distribution (surface) Charge distribution (volume)

8 Equations 1: Fields of an electret Surface charges only: d 2 d 1 E 2 E 1 σ = σ r + P P σ ρ (x) x Volume charges only: ρ (x) = ρ r (x) + ρ P (x) ˆ σ = 1 d 1 d 1 0 xρ( x) dx E E 1 2 σ d2 = ε ( ε d + d1) = σ d1 ε ( ε d + d1) (1) (2) External field E2 from Eq. (2) with σ = ˆ σ

9 Equations 2: Force of an electret on an electrode E 2 E 1 F = 1 2 ε E 0 2 2

10 Equations 3: Currents in an electret E(x,t) P p (x,t) i c (x,t) Current density ( ε0 ε E + Pp ) i ( t) = + i t i c = µ ρ µ ρ ) E ( c

11 Equations 4: Charge transport equations Current Equation: E( x, t) ε + µρ t f ( x, t) E( x, t) + I( x) Poisson Equation: E( x, t) ε = ρf ( x, t) + ρt( x, t) t (2) = I 0 (1) e - I 0 I(x) Poisson Equation: ρ ( x, t) t = 1 t ρf ( x, t) ρt( x, t) τ Parameters of Model: I(x) : current τ : free-carrier lifetime ρ m µ : free-carrier mobility ρ m : trap density (3) ρ f /τ CB Trap level ρ f ρ t

12 Measured and calculated location of charge peak in electron-beam charged FEP (Sessler 2004) 12 Peak Location (µm) Injected Charge Density ( nc/cm 2 )

13 Principles Charges Materials Electret classes Equations Fields Forces Currents Charge transport Overview Experimental techniques Charging Surface potential Thermally-stimulated discharge Dielectric measurements Charge distribution (surface) Charge distribution (volume)

14 Charging methods CORONA ELECTRON BEAM (Vacuum) THERMAL ~10kV e- (2-40 kev) Heating chamber ~200V surface charge (and polarization) volume or surface charges and polarization surface and volume charges and/or polarization

15 Surface potential measurement Electret film Electrostatic voltmeter Movable sample holder Surface potential [V] Surface potential of PP P1 P2 P3 P4 P5 P6 90 C Annealing time [min] Determination of charge stability of different electret materials by isothermal discharging at elevated temperatures

16 Thermally-stimulated discharge (TSD) Heating chamber I I Linear temperature increase T, t Separation of surface and volume traps Activation energies Trap densities

17 Measurement of activation energy A: Initial-rise-method current i ln i temperature T 1/T d(ln i) d(1/ T ) = A k

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

19 Principles Charges Materials Electret classes Equations Fields Forces Currents Charge transport Overview Experimental techniques Charging Surface potential Thermally stimulated discharge Charge distribution (surface) Charge distribution (volume)

20 Kelvin probe force microscope (KFM) (Jacobs et al 1997) Measures lateral potential distribution

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

22 Thermal pulse method (Collins 1975) r = d V ( t V ( t 2 1 ) ) V V(t 2 ) V(t) V(t 1 ) t 1 t 2 t

23 Thermal wave method (Bauer 1996) Measures charge distribution close to surface

24 Laser-Induced Pressure Pulse (LIPP) method hν ρ( x) P( x) e( x) I( t) electrode charges t,x I( t) charges in dielectric ρ- dp dx I( t) ( γ+ 1) ( ) - de, dx x=ct

25 Charge distribution in e-beam irradiated FEP (Sessler et al 1983) 20 kev 5 ns/div ( 6.5 µm/div = 30 kev 5 ns/div ( 6.5 µm/div =

26 Evolution of charge distribution in LDPE measured with Pulsed ElectroAcoustic (PEA) method (Hozumi et al 1998) LDPE

27 CV-method for measuring charge centroid location Measures location of charge centroid and total charge

28 Charge drift in double layers of SiO 2 (300 nm) and Si 3 N 4 (150 nm) (Zhang et al 2002) normalized units 1 0,8 0,6 0,4 0, annealing time [min] 400 C surface potential mean charge depth integrated charge density

29 Scanning Electron Microscope (SEM) method

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

31 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.