Dielectric properties of ceramics

Polarization mechanisms

Electronic polarization: deformation of the electronic shell.

Atomic or ionic polarization: displacement of negative and positive ions in relation to one another

Dipolar and orientation polarization•Alignement of dipolar molecules in a liquid•Spontaneous alignement of dipoles in a polar solid (ferroelectricity)•Ion jump polarization occurs when two or more lattice positions are available for a ion or lattice defect•Reorientation of dipolar defects

Space charge polarization occurs when charges accumulate at interfaces: composite materials, insulating surface skin, electrode polarization effects

After application of an electric field, the center of gravity of positive and negative charges does not correspond anymore

Electronic

Ionic

DipolarOrientation

Space charge or diffusional

f

Dipole moment

Polarization (dipole moment per unit volume)

Dielectric displacement (0 is the vacuum permittivity)

Surface charge density

For a linear dielectric

Capacitance

Permittivity

Relative permittivity (or dielectric constant)

dQ

NP

PET 0

EP e 0 EeT 01

PED 0

h

A

p

Dipoles and surface charges in a polarized dielectric

p

h

A

h

AC

h

A

Eh

A

U

A

U

QC re

TTT00 ;1

e 10 er 10

Polarization, capacitance and dielectric constant

(e is the electric susceptibility)

Polarizability () (induced dipole moment per unit field)

Clausius-Mosotti relationship

E

032

1

ii

r

rN

iii

iir N

N

1

10

is the local field constantMore generally

scdipione

Electronic polarizabilities are rather independent of crystal environment and high frequency dielectric constant can be predicted

1 iiiN rIf than

“Polarization catastroph” The local field produced by polarization can increase more rapidly than the restoring force thus stabilizing the polarization further possibility of spontaneous polarization (ferroelectric instability)

Polarization, capacitance and dielectric constant

00

1E

Pr for a linear dielectric

NP

Dielectric losses

tan2

1tan

2

1 2

00CUIUP cW Power dissipated per unit time

Dielectric or ac conductivity tan0 rac

Ideal capacitor: 90° phase difference between I and U, no dissipation

Voltage

Cu

rre

nt Angular frequency

=2f = 2/T

Real capacitor: <90° phase difference between I and U.Ic: charging current (capacitative component)Il: loss current, dissipative comp., power loss

Il: in phase with U

IC: 90° in advance of U

Dissipated power density tan2

10

2

0 rW EV

P

tan: “dissipation factor” or “loss tangent”rtan: “loss factor”

acW EV

P 202

1

By analogy with dc current 2EV

PW

Complex permittivity

The behaviour of ac circuits can be conveniently analysed using complex quantities

1sincos)exp( iii

Vacuum capacitor UCiCUQI o 0

Complex sinusoidal voltage

UitiUiUtiUU expexp 00

90° in advance

Capacitor with a lossy dielectric'''*rrr i

'

''

''0

'0

0''

0'

tanr

r

acrlrC

rr

EEIEiI

UCUCiI

Ic

Il

Real partImaginary part

Im

Re

By analogy with Ohm’s law:I =U/R or J = E

""tan''' factorlossrr

Resonance effects in dielectrics

Charged particle in a harmonic potential well

E )exp(020 tiEqEmxmxm Equation of motion

0: natural vibration frequency: damping factorQ: chargem: massE: local field

This behaviour is generally observed for the electronic and ionic polarization processes, where the charges/dipoles move around the equilibrium positions and final polarization is almost instantaneously achieved. Resonant frequencies are of the order of 1013 and 1015 s-

1, respectively, and fall in the optical range.

Dipolar and space charge polarization is generally accompanied by the diffusional movement of charge and dipoles over several atomic distances and surmounting energy barriers of different high. These polarization processes are relatively slow and strongly temperature dependent (thermally activated). If the transient polarization is described by a simple exponential function, the dipolar relaxation is described by the Debye equation.

Relaxation effects in dielectrics – migration & orientation polarization

Electrostatic potential in a glass or defective oxide

Debye relaxation

r

rsrac

rsrr

rsrrr

rsrrr i

11

1

1

1

22

',

',2

22

',

',''

22

',

','

,'

',

','

,*

Relaxation time

Reorientation of dipolar defects (defects pairs)

OTiOTiOOTiBaBaTiO

xKKKKKClK

KCl

VFeVFeVOFeBaBaOOFe

VCaVCaVClCaCaCl

'''32

'''2

5222

)(2

3

FeTi VO

PP

dt

dP f

’r

’’ r

’

’ r’r,s

’r,

½(’r,s- ’r,)

(’r,s- ’r,)/

=1

Frequency dispersion region

Debye relaxation

Tk

E

B

aexp0

Ea takes values typical of ionic conduction processes (0.7 eV), giving a loss peak in the range 103 – 106 Hz.

<< r: ions follow the field low losses

>> r: ions do not jump low losses

Maximum loss occurs when the field frequency is equal to the jump frequency , =1

Debye relaxation holds when the transient polarization is described by a simple exponential with a single relaxation time. In most materials, including single crystals, a distribution of relaxation times exists and permittivity dispersion is observed over a wider frequency range. This is related to variations of the ionic environment and thermal fluctuations with distance and existence of lattice defects. The extreme case is represented by glasses and amorphous materials.

Relaxation effects in dielectrics – migration polarization

Dielectric relaxation is better described by the equation (Cole&Cole)

which takes into account that the the motion of ions responsible for relaxation can be of cooperative type. = 0.2-0.3 for glasses. = 1: Debye

i

rsrrr

1

',

','

,*

Dielectric dispersion in silicate glasses

'r

100',

',

''

rsr

r

Relaxation effects in dielectrics – effect of temperature and frequency

Electronic and ionic polarization resonance occurs at f>1010 Hz which is above the limit of normal uses. The effect of temperature is small.Contribution from ion and defect migration as well as dc conductivity determine a sharp rise of permittivity with increasing temperature and decreasing frequency. Increasing concentration of charge carriers in turn leads to space charge effects.

Dielectric constant of single crystal Al2O3

Dielectric constant of soda-lime silica glass

Relaxation effects in dielectrics - Space charge polarization

Polycrystalline and polyphase ceramics exhibit interface or space charge polarization (also called Maxwell-Wagner polarization) arising from different conductivity of the various phases. The most important occurrence of this phenomenon is in semiconducting ceramic oxides with resistive (oxidized) grain boundaries (magnetic ferrites, titanates, niobates) , in which the low frequency permittivity can be several orders of magnitude higher than the high frequency dielectric constant and is dominated by the contribution of grain boundaries.

If x = d1/d2 << 1, 1 >> 2 and ’r,1= ’r,2

1102 x

221

22

21'

2'0

'2

'

x

xrrrr

21

21'20'

xr

d1

d2

(1)

(2)

Brick-wall model

Special relationships involving permittivity

At optical frequencies, electronic polarization is the main contribution to permittivity. If n is the index of refraction

2', nr

BaTiO3 single crystal

TC =120°C

UV-VisIRRF & MW

For ferroelectric materials in the paraelectric regime (T > TC)

0

'

TT

Cr

C: Curie constantT0: Curie-Weiss temperature

00

' 1E

Pr

0E

NP

Properties and applications of dielectric ceramics of commercial

interest

Dielectric losses

0'2

tan

r

ac

f For alumina ceramics, = 10-12 ohm cm, ’

r = 10, tan = 2x10-4 at 1 kHz

MW region

Properties of ceramics with low permittivity and low losses

Material Applications

Steatite Porcelain insulators

Cordierite Applications requiring good thermal shock resistance. Supports for high-power wire-wound resistors.

Alumina Best compromise of dielectric losses, high mechanical strength, high thermal conductivity. Reliable metal-ceramic joining technoloy (MolyMn) available.

Beryllia Good properties, very high thermal conductivity, expensive and difficult processing. Insulating parts in high-power electromagnetic energy generation (klynstrons and magnetotrons).

AlN High thermal conductivity and TEC close to that of silicon. Substrate for power electronic circuits and chips.

Glass & glass-ceramics Cheap material and easy processing. Low thermal conductivity

Typical properties of dielectric ceramics

Typical properties of alumina ceramics

Properties of ceramics with low permittivity and low losses

Spark plugs

Insulating parts in high-power electromagnetic generation. Windows for high-power microwave generators. Substrates for electronic circuits. Cheap packaging.

Tan of 99.9% alumina ceramics

99.9% Al2O3 96% Al2O3

Microstructure of alumina ceramics

Electronic substrates and chip packaging

Power electronic substrates

The role of the substrate in power electronics is to provide the interconnections to form an electric circuit (like a printed circuit board), and to cool the components. Compared to materials and techniques used in lower power microelectronics, these substrates must carry higher currents and provide a higher voltage isolation (up to several thousand volts). They also must operate over a wide temperature range (up to 150 or 200°C).

Direct bonded copper (DBC) substrates are commonly used in power modules, because of their very good thermal conductivity. They are composed of a ceramic tile (commonly alumina) with a sheet of copper bonded to one or both sides by a high-temperature oxidation process. The top copper layer can be preformed prior to firing or chemically etched using printed circuit board technology to form an electrical circuit, while the bottom copper layer is usually kept plain. The substrate is attached to a heat spreader by soldering the bottom copper layer to it. Ceramic materials used in DBC include Al2O3, AlN and BeO.

Dual in-line package (DIP)

Plastic Ceramic (Intel 8080)

Ceramic (EPROM)

Pin grid array packaging (PGA)

Celeron (top) Pentium (bottom)Socket PGA (AMD)