Dielectric Properties of Solids

Dielectric Properties of Solids http://www.eetimes.com/document.asp?doc_id=1276895

(SDRAM = Syncronous dynamic RAM)

Prof.Shih-Ying Hsu, Department of Electrophysics, National Central University, Taiwan

Dielectric Properties of Solids

Introduction (concept)

macroscopically, i) When no dielectric,

ii) When a dielectric is inserted, iii) The calculation of is an important aim of any microscopic theory of dielectrics.

dAC oo

=

dAC ro=

?

Dielectric

appE

Charge can not flow freely in the direction of , but

affect the internal structure of such materials.

can penetrate into their interiors and appE

appE

For some materials (at RT) upon They are called insulators or dielectrics.

appE

0

Capacitor (condenser)

( )

iv) also, their response to the AC field reflected in

Ex: Ferroelectricity, piezoelectricity

v) In some ionic crystal, even when ,

there may be long-range electrostatic force between the

ions (in addition to the lattice potential)

E

=n

and as optical range

It leads to optical properties of dielectrics

0=appE

https://chemistry.osu.edu/~woodward/ch754/lect2003/dielectrics_lect28.ppt

+ +

+ -

+ +

E

Ionic polarization occurs in all ionic solids: NaCl, MgO

-

- -

-

+ -

-

+ +

E

Molecular polarization, occurs in all insulating molecules; oils, polymers,

H2O

Review of basic formulas

dipole moment ( - + )

Potential energy

Torque felt

Ep =

EpV =

In discussing dielectric materials

P

PN

Definition

dqp =

+

- E

Eq

Eq

+ - q+q d

Polarization = # of dipole moment / unit volume

=

In dielectrics, there are no free charges, but bound charges, i.e. electric dipoles are present.

the dipole moment density : units of C/m2

LV

E 00 =

Electric field inside the parallel plate :

Now, insert a slab of dielectric modify the field to a new value E

EEE0

=

due to polarization change E

EEE0

=

Now,

Electric displacement (just outside the dielectric) or 00ED

=

PED

+= 0

00

PEE

=

EEPED

r00 ==+=also,

0

here w =r

: new field inside the slab

All the dielectric and optical characteristics of

substances are contained in this constant.

(inside dielectric)

Dielectric constant

Ep =

Polarizability

Polarization ENpNP ==

and

EN

ENEPED

+=

+=+=

00

00

1

0

0

N

ED

r

r

+=

=

1

Previously,

The dielectric constant and polarizability : the local field

The polarization of a medium is produced by the field

Dipole moment

Define electrical susceptibility such that

EP

0=

then

0 N=

In fact,

localEP

=

ENP

= cf.

+= 1r

instead of MaxwellEP

=

If this microscopic field is averaged, one obtains the macroscopic or Maxwell field E .

Recap


*)Soda-lime glass, also called soda-lime-silica glass, is the most prevalent type of glass, used for windowpanes, an

d glass containers (bottles and jars) for beverages, food, and some commodity items. Source Wikipedia

Local effective field at an atom or an ion in a dielectric sample :

Eloc = Eo + E1 + E2 + E3

Eo : the field produced by fixed charges external to the body

E1 : depolarization field of induced surface charges on the boundary

E2 : the field produced at the center of an imaginary cavity by the polarization-induced surface charges over the cavity

E3 : the field produced at the center of the imaginary cavity due to the discrete dipoles distributed over all atomic sites.

3210local EEEEE

+++=

What is the local field ? localE

depolarization

Lorentz field

dipole field inside the cavity

01

PE

== depolarization field

0

2

0 20

2

2 3sin2

4cos

PdR

RPE

=

=

03 =E

for the symmetric structure such as cubic

PEPPEElocal

00

000 3

203 =++=

See Kittel

Eo

E3 from dipoles inside sphere

E2 from surface of spherical cavity

Lorentz cavity field E2 and field of dipoles inside cavity E3

+ + + + + + +

rd

Therefore, 00

0 3 PPEElocal

+

=

03PEE Maxwelllocal

+= localE : microscopic field which fluctuates within the medium

Now,

localENP

=03

PEE Maxwelllocal

+=

PNENPENP

00 33 +=

+=

ENNP

=

031 031

N

NP

=

By the way,

EENEPED rN

0

300

01

=

+=+=

( )EE

NrN

N

03

30

0

0

1

1=

+

0

0

3

32

1

1

N

N

r

+=

00 32131

NNr +=

( ) 123 0=+ rr

N

=

=+

31

321

0

N

r

rClausius-Mosotti relation

ex) dipolar(orientational), ionic, electronic polarizability

Upon , those dipoles align with

Probability of finding it along direction

Sources of polarizability (Mechanism) Different types of physical processes gives rise to polarizability

a) Dipolar (orientational) polarizability molecules with permanent dipole moment are present with random orientation.

E

E

potential cosPEEPV ==

kTPEkTV eef cos== 0 /2

1

f()

E= 0 E 0

Average value of P, now only considering Px ( )

( ) = df

dfPP xx

dedeP

kTPE

kTPE

sinsincos

cos

cos

22

0

0

=

( )uPL= ( ) ( ) kTPEuuuuL == ,coth

1where

Langevin function

Paraelectricity

For small E field,

Ethermal Enalorientatio

3 ~

3

2==

TkpE p E

TkpP

BBx p

Tkp

B3

2

0 =

Substitute this into the Clausius-Mosotti equation

+

=

+

TkpN

Bei

r

r

3321 2

0

or M

NN A

=

Thus, the dipolar (orientational) polarizability is

M: molecular weight

+

=

+

TkpNM

Bei

A

r

r

3321 2

0

Number of dipoles in unit volume

ei- induced polarizability

kTP

d22=

in solids

kTP

d 32

= applicable in solids ?

Probability of leftward orientation :

E

cf. jumping frequency kT

De =

kT

De

1cf. relax time

Probability of rightward orientation : 1

finally:

If we plot the TvsM

r

r 121

.

+

+=

+

TkPNM

Bei

A

r

r

3321 2

0

M. A. OMAR, ELEMENTARY SOLID STATE PHYSICS: Principles and Applications ADDISON-1993

https://s3-ap-southeast-1.amazonaws.com/erbuc/files/4155_16642919-af64-4cad-b717-e2cc45746249.pdf

The dipole moments for various molecules,

1 debye = 3.33 10-30 Cm


b) Dipolar dispersion (frequency dependence of orientational polar)

The equation to describe the motion of dipole polarization

For AC applied field

( ) ( )

tPPdt

tdP dd = 0

Since (equilibrium moment) ( ) tid AePEP == 00,

( ) ( ) ( ) tiddd Ae0tPdt

tdP

=+

Lets try a solution of the form

The polarization is no longer in phase with the field (This gives rise to energy absorption)

( ) ( ) ( ) ( ) tiddd AetEtP ==

( ) ( ) ( ) ( ) tidtidtid Ae0AeiAe

=+

( )( ) ( )

01 dd i =

( ) ( )( )

=i

dd 1

0: static polarizability

)(

=

=ti

ti

BePAeE

( )0d

To derive the expression for r()

where ionic concentration assumed negligible

Now, in microwave region, the electronic susceptibility is constant (e- light, respond to instantaneously)

Not follow the instantaneously

: the same complex form as d()

( ) ( ) ( ) der ++= 1

( )E

( ) ( ) dr n += 2Then, where en += 12

( ) ( ) 2nrd = a phase lag is expected.

( ) ( )

i

dd

= 10

( ) ( ) 200 nrd =

( )E

( ) ( )

i

nn rr

+= 1

0 22

( ) ( ) ( ) ( )

22

2

22

22

10

10

+

++

+=+=

ni

nni rrrr

( ) ( ) 222

21

0

+

+=n

n rr

( ) ( )

22

2

10

+

=nr

r

: Debye equations


d) Ionic polarizability It is related with the optical properties of lattice vibration. The frequency dependent dielectric constant is given by

( ) ( ) ( ) ( )21

0

+=

t

rrrr

Since ( ) 2nr =( ) ( ) 2

22

1

0

+=

t

rr

nn

Dielectric constant r() versus , showing dispersion in infrared region due to optical phonons in an ionic crystal. Dashed curve indicates removal of divergence due to collisions of ions

from


e) Electronic polarizability For the e- under AC field

tieeExmdtdxm

dtxdm =++ 0202

2

To be consistent with previous derivation

( ) tiextx = 0 (can be done with ) ( ) tiextx 0=

ti

ti

eeEtxim

eeExmtximtxim

=

=++

022

0

02

02

)(}){(

)()()()(

( ) ( ) mk

ieE

metx

ti

=

=

0220

0 ,

The polarization is

)()( 0** tNexeENP tiee ==

( ) ( ) ime

e

= 220

2

*

eP

( ) tire eEEP == 0*00* 1also

( )

ieE

meeE

titi

e =

220

02

0* )(

( ) tirtie eEeEN = 0*00* 1)(and

( )

imeN

Ner

+=

+=

)(11

1)(

220

2

0

0

*

( )( ) 222220

220

0

21

+

+= m

Ner

( )( ) 2222200

2

+= m

Ner

( )( ) 222220

220

0

21

+

+= m

Ner

( )( ) 2222200

2

+= m

Ner


Within a solid which contains permanent dipoles, all three of the above phenomena contribute to the polarizability at low frequencies through to high frequencies.

The dielectric constant at optical frequencies :

electronic polarizability.

The other two contributions are small at high frequencies due to the inertia of the molecules and ions.

(Ionic movements can no longer keep up with the alternations of the applied field.)


Microwave Ovens A microwave oven generates

electromagnetic radiation at about 2.5 GHz. This energy is pretty good at causing H2O molecules to oscillate their orientation (orientational dielectric constant changes greatly).

5 GHz - 100 GHz would be ideal, but then most of the energy would be absorbed by the outermost layer of the food, defeating the purpose.

Ice has a low dielectric constant, so not much energy is absorbed by it. Once there is a bit of melted ice, though, then you are really cooking. http://home.howstuffworks.com/framed.htm?parent=micriwave.htm&url=http://www.amasci.com/weird/microexp.html

Barium titanate BaTiO3

Below 408K, spontaneous polarization arises from coupling bet. ionic and electronic dipole moments. A displacement of Ti4+ creates an ionic dipole moment in the direction of the displacement and associated electric field. O2- become polarized in the opposite direction. Polarization does not increase infinitely because anharmonic elastic forces limit Ti displacement.

Simple cubic T > 408K

Ba2+ at cube corners

O2- at face centers

Ti4+ at body center

Paraelectric property


E=0 E0

E=0

(1) Perovskite-type lead zirconate titanate (PZT) unit cell in the symmetric cubic state above the Curie temperature.

(2) Tetragonally distorted unit cell below the Curie temperature

Ferroelectrics (digression)

A ferroelectric crystal exhibits an electric dipole

even in the absence of an external electric field.

In the ferroelectric state the center of positive

charge of the crystal does not coincide with the

center of negative charge.

A nave picture

A nave picture

The local alignment of dipoles can exist over any length scale.

Different regions may exist with different polarisation orientations: Call these domains in line

with magnetic materials. In contrast with magnetism,

domain walls are abrupt.

Polarization Switching by an Electric Field

E=0

E>0

EEC

http://www.arne-lueker.de/Objects/work/Pb-free%20ferroelectrics/pb_free_quest.html

Electrical (or 1800-domains) to minimize depolarization.

Polarization Switching by an Electric Field

from Kittel

Ferroelectricity Usually ionic susceptibility is not sensitive to variation in temperature. However, the so called ferroelectric materials have

: Curie-Weiss law (TC - Curie Temp.)

CC

r TTTTCB >

+= ,

Ferro- electric phase

Para- electric phase

Ferro-electric phase

No E applied

(Spontaneous polarization) Static Dielectric Constant

C- Curie constant

potassium dihydrogen phosphate

http://ckw.phys.ncku.edu.tw/public/pub/Notes/CondensedMatter/Powerpoint/

Rochelle salt

KDP

BaTiO3

from Kittel

Domain Wall Movement

http://slideplayer.com/slide/4829425/

Technical Ceramics Dr. Sabar D. Hutagalung

see Electroceramics: Materials, Properties, Applications By A. J. Moulson, J. M. Herbert

see Electroceramics: Materials, Properties, Applications, By A. J. Moulson, J. M. Herbert

T>TC cubic T

Pyroelectric Detectors/Sensors

DRAM SEM Micrograph

http://www.tf.uni-kiel.de/matwis/amat/elmat_en/kap_5/illustr/i5_1_1.html

The two deep "trenches" (they are really holes) contain the capacitors on their walls. The dielectric (with ~ 7 nm far too thin to be visible) is "ONO", a triple layer of Oxide (SiO2) Nitride (Si3N4) Oxide (SiO2). This is an early 64 MBit DRAM (1996).

Dynamic random access memory (DRAM)

Hynix Announces 512Mbit Mobile DRAM Hynix Semiconductor, a noted memory maker has said it has developed the world's fastest and smallest 512 MBit mobile DRAM. The new DRAM operates at 200 MHz and processes 1.6 GB of data per second. "The product will deliver the memory capacity and speed required for third generation mobile phones that provide new services, such as digital media broadcast (DMB), to subscribers," the chip maker has said. It is expected that Hynix will combine this 512Mb mobile DRAM and Nand Flash in a multi-chip package which will allow mobile manufacturers to make slimmer mobile phones.

http://www.tech2.com/india/news

Non-Volatile RAMs (memory)

Smart cards use ferroelectric memories. They can hold relatively large amounts of information and do not wear out from use, as magnetic strips do, because they use contactless radio frequency input/output. These cards are the size and shape of credit cards but contain ferroelectric memory that can carry substantial information, such as its bearer's medical history for use by doctors, pharmacists and even paramedics in an emergency. Current smart cards carry about 250 kilobytes of memory.

http://www.slideshare.net/researcher1234/ferroelectric-and-piezoelectric-materials

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Dielectric Properties of Solids - Babeș-Bolyai...

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