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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
https://chemistry.osu.edu/~woodward/ch754/lect2003/dielectrics_lect28.ppt
*)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
https://chemistry.osu.edu/~woodward/ch754/lect2003/dielectrics_lect28.ppt
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
https://s3-ap-southeast-1.amazonaws.com/erbuc/files/4155_16642919-af64-4cad-b717-e2cc45746249.pdf
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
https://s3-ap-southeast-1.amazonaws.com/erbuc/files/4155_16642919-af64-4cad-b717-e2cc45746249.pdf
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
https://s3-ap-southeast-1.amazonaws.com/erbuc/files/4155_16642919-af64-4cad-b717-e2cc45746249.pdf
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
https://s3-ap-southeast-1.amazonaws.com/erbuc/files/4155_16642919-af64-4cad-b717-e2cc45746249.pdf
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.)
Prof.Shih-Ying Hsu, Department of Electrophysics, National Central University, Taiwan
https://chemistry.osu.edu/~woodward/ch754/lect2003/dielectrics_lect28.ppt
https://chemistry.osu.edu/~woodward/ch754/lect2003/dielectrics_lect28.ppt
https://chemistry.osu.edu/~woodward/ch754/lect2003/dielectrics_lect28.ppt
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
Prof.Shih-Ying Hsu, Department of Electrophysics, National Central University, Taiwan
https://chemistry.osu.edu/~woodward/ch754/lect2003/dielectrics_lect28.ppt
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
https://chemistry.osu.edu/~woodward/ch754/lect2003/dielectrics_lect28.ppt
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
https://chemistry.osu.edu/~woodward/ch754/lect2003/dielectrics_lect28.ppt
https://chemistry.osu.edu/~woodward/ch754/lect2003/dielectrics_lect28.ppt
https://chemistry.osu.edu/~woodward/ch754/lect2003/dielectrics_lect28.ppt
https://chemistry.osu.edu/~woodward/ch754/lect2003/dielectrics_lect28.ppt
https://chemistry.osu.edu/~woodward/ch754/lect2003/dielectrics_lect28.ppt
https://chemistry.osu.edu/~woodward/ch754/lect2003/dielectrics_lect28.ppt
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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