Introduction to electrets: Principles, equations, experimental

Transcription

Introduction to electrets:
Principles, equations, experimental techniques
Gerhard M. Sessler
Darmstadt University of Technology
Institute for Telecommunications
Merckstrasse 25, 64283 Darmstadt, Germany
[email protected]
Darmstadt University of Technology • Institute for Telecommunications
Principles
Overview
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)
Electret charges
Energy diagram and density of
states for a polymer
Electret materials
Polymers
Anorganic materials
Fluoropolymers (PTFE, FEP)
Polyethylene (HDPE, LDPE, XLPE)
Polypropylene (PP)
Polyethylene terephtalate (PET)
Polyimid (PI)
Polymethylmethacrylate (PMMA)
Polyvinylidenefluoride (PVDF)
Ethylene vinyl acetate (EVA)
•
•
Silicon oxide (SiO2)
Silicon nitride (Si3N4)
Aluminum oxide (Al2O3)
Glas (SiO2 + Na, S, Se, B, ...)
Photorefractive materials
•
•
•
Cellular and porous polymers
Cellular PP
Porous PTFE
Charged or polarized dielectrics
Category
Materials
Charge or polarization
electrets
External electric
FEP, SiO 2
NLO
/
materials
,
0.1 - 1
+
+
+
+
+
materials
field and force
Electrooptic
0.1 - 10
Ferroelectric
,
Applications
Density
[mC/m2 ]
Geometry
Real-charge
Properties
10 - 100
and NLO effects
Piezo- and
pyroelectricity
Overview
Principles
Charges
Materials
Electret classes
Equations
Fields
Forces
Currents
Charge transport
Charging
Surface potential
Equations 1:
Fields of an electret
Surface charges only:
Volume charges only:
σ = σr + ∆PP
ρ (x) = ρr (x) + ρP (x)
x
d2
E2
σ
d1
E1
ρ (x)
E1 = −
E2 =
σ d2
ε 0 (ε d 2 + d1 )
σ d1
ε 0 (ε d 2 + d1 )
d
1 1
σˆ = ∫ xρ ( x )dx
d1 0
(1)
External field E2 from
Eq. (2) with σ = σˆ
(2)
Equations 2:
Force of an electret on an electrode
E2
E1
1
2
F = ε 0 E2
2
Equations 3:
Currents in an electret
E(x,t)
Pp(x,t) ic(x,t)
Current density
i (t ) =
∂ (ε 0ε E + Pp )
∂t
+ ic
ic = ( µ+ ρ + + µ− ρ − ) E
Equations 4: Charge transport equations
e-
Current Equation:
∂E ( x, t )
ε
+ µρf ( x, t ) ⋅ E ( x, t ) + I ( x ) = I 0 (1)
∂t
Poisson Equation:
∂E ( x, t )
ε
= ρf ( x, t ) + ρ t ( x, t )
∂t
I0
I(x)
(2)
CB
Poisson Equation:
∂ρ t ( x, t ) ρ f ( x, t )  ρ t ( x, t ) 
=
⋅ 1 −

∂t
τ
ρ
m


(3)
ρf / τ
ρf
ρt
Trap level
Parameters of Model:
I(x) : current
τ : free-carrier lifetime
µ : free-carrier mobility
ρm : trap density
Measured and calculated location of charge
peak in electron-beam charged FEP
(Sessler 2004)
Peak Location (µm)
12
10
8
6
1
10
100
1000
2
Injected Charge Density ( nC/cm )
Overview
Principles
Charges
Materials
Electret classes
Equations
Fields
Forces
Currents
Charge transport
Charging
Surface potential
Dielectric measurements
Charging methods
ELECTRON
BEAM
CORONA
THERMAL
(Vacuum)
~10kV
e- (2-40 keV)
Heating
chamber
~200V
+++++++
++++++++
--------
+
++++ ++++
- - - --------
volume or
surface charges
and polarization
surface and
volume charges
and/or polarization
+
+
-------surface charge
(and polarization)
+
+
+
+
Surface potential measurement
Surface potential of PP
500
Movable sample holder
400
Surface potential [V]
Electret film
Electrostatic
voltmeter
90°C
300
200
P1
P2
P3
P4
P5
P6
100
0
0
400
800
1200
Annealing time [min]
• Determination of charge stability of different electret materials by
isothermal discharging at elevated temperatures
1600
Thermally-stimulated discharge (TSD)
Heating
chamber
Heizkammer
I
+ + +
--------
I
+++++
T, t
Linear temperature increase
Separation of surface and volume traps
Activation energies
Trap densities
current i
Measurement of activation energy A:
Initial-rise-method
ln i
temperature T
1/T
d (ln i )
A
=−
d (1 / T )
k
TSD for electron beam charged FEP
(v. Seggern 1981)
Overview
Principles
Charges
Materials
Electret classes
Equations
Fields
Forces
Currents
Charge transport
Charging
Surface potential
Thermally stimulated discharge
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)
r V ( t2 )
=
d V (t1 )
V
V(t2)
V(t)
V(t1)
t1
t2 t
Thermal wave method
(Bauer 1996)
Measures charge distribution close to surface
Laser-Induced Pressure Pulse
(LIPP) method
hν
+
+
+
+
+
+
+
ρ(x) +
P(x) +
e(x) + +
+
+
I(t)
electrode
charges
t,x
I(t)
charges in dielectric
I(t)
- de , x=ct
(γ+1) (ρ- dP
)
dx
dx
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
Evolution of charge distribution in LDPE
measured 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)
1
normalized units
400°C
0,8
0,6
0,4
surface potential
mean charge depth
integrated charge density
0,2
0
0
200
400
600
annealing time [min]
Scanning Electron Microscope (SEM) method
SEM pictures of cross section of
charged cellular PP
(Hillenbrand et al 2000)
-
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.

Introduction to electrets: Principles, equations, experimental

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