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Dielectric Properties
of Ceramics
EBB 443
Dr. Sabar D. Hutagalung
School of Materials & Mineral Resources
Engineering, Universiti Sains Malaysia
Introduction
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Dielectric materials: high electrical resistivities,
but an efficient supporter of electrostatic fields.
Can store energy/charge.
Able to support an electrostatic field while
dissipating minimal energy in the form of heat.
The lower the dielectric loss (proportion of
energy lost as heat), the more effective is a
dielectric material.
Another consideration is the dielectric constant,
the extent to which a substance concentrates
the electrostatic lines of flux.
Dielectric Constant
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The capacitance, C, of a capacitor formed by two parallel
plates of area A spaced d apart with the area between the
plates filled with dielectric material with a relative
dielectric constant of ε is:
Dielectric Loss
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For a lossy (imperfect) dielectric the dielectric
constant can be represented by a complex
relative dielectric constant:
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The imaginary part of this complex dielectric
constant, ε at a frequency, ω is equivalent to a
frequency-dependent conductivity, σ(ω), given
by:
Dielectric Loss
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ε" is also known as the loss factor.
The small difference in phase from ideal behaviour is
defined by an angle δ, defined through the equation
tan δ is known as the loss tangent or dissipation factor.
A quality factor, Q, for the dielectric is given by the
reciprocal of tan δ.
Dielectric Loss
Equivalent circuit diagrams: (a) capacitive cell, (b)
charging and loss current, (c) loss tangent for a typical
dielectric
Dielectric Loss
Q =  oAV/d = CV
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From
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If V being sinusoidal, total charge Q may be written as
Q  C Vo eit
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Current flow on discharge of the capacitive cell in time, t:
dQ
I
 iCV
dt
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For a real dielectric the current I has vector components IC and IR:
I = IC + IR
Dielectric Loss
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From magnitude of these currents, also we can define a
dissipation factor, tan , as
IR
tan  
IC
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Quality factor Q is:
1
average energy stored
Q

tan  energy dissipated per cycle
Alternating Current Theory
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Impedance of a resistance = R
Impedance of a capacitance = 1/iωC
Mean power, P, dissipated over a cycle in a lossy
capacitor with plates of area A separated by a distance
d:
Dielectric Strength
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Dielectric materials are insulators (conduction cannot
generally occur).
However, under certain conditions, dielectric materials
can break down and conduct a significant current.
Generally, the lattice of a dielectric has sufficient strength
to absorb the energy from impacting electrons that are
accelerated by the applied electric field.
However, under a sufficiently large electric field, some
electrons present in the dielectric will have sufficient
kinetic energy to ionize the lattice atoms causing an
avalanching effect.
As a result, the dielectric will begin to conduct a
significant amount of current.
Dielectric Strength
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This phenomenon is called dielectric breakdown and the
corresponding field intensity is referred to as the
dielectric breakdown strength.
Dielectric strength may be defined as the maximum
potential gradient to which a material can be subjected
without insulating breakdown, that is
VB
 dV 
DS  


d
 dx  max
where DS is the dielectric strength in kV/mm,
VB the breakdown voltage, and d the thickness.
Current-voltage characteristic up to breakdown for
a typical dielectric materials
Dielectric Strength
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Dielectric strength depends on
 material homogeneity,
 specimen geometry,
 electrode shape and disposition,
 stress mode (ac, dc or pulsed) and
 ambient condition.
Capacitors
Tantalum capacitor
Capacitors
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The basic formula for the capacitance of a parallel-plate
capacitor is:
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To increase C, one either increases , increases A, or
decreases d.
Early capacitors consisted of metal foils separated by
wax ( ~ 2.5), mica ( ~ 3 - 6), steatite ( ~ 5.5 - 7.5), or
glass ( ~ 5 - 10).
The use of titania provided a significant increase ( ~
170), was followed by perovskite-based, such as BaTiO3
( ~ 1000).
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Capacitors
C = "capacitance"
= q /DV
Units: Coulomb/Volt
= Farad (F)
----------------------------The capacitance of a
capacitor is constant;
if q increases, DV
increases proportionately.
Michael Faraday
(1791-1867)
Capacitors
Capacitors
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DRAM chips currently utilize capacitors with Si3N4 or SiO2
as dielectric materials.
The electrodes are made of doped Si or poly-Si.
Capacitors can be fabricated onto IC chips.
They are commonly used in conjunction with transistors in
DRAM.
The capacitors help maintain the contents of memory.
Because of their tiny physical size, these components have
low capacitance.
They must be recharged thousands of times per second or
the DRAM will lose its data.
A
C   r o
d
AV
Q   r o
d
Q = CV
Q: charge (Coulomb)
C: capacitance (Farad)
V: potential difference (Volt)
d: separation/thickness (meter)
o: permitivity of vacuum =
8.854x10-12 C2/m2 or F/m
r: dielectric constant
Multilayer Ceramic Capacitor
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The multilayer ceramic capacitor (MLCC):
A( N  1)
C   r o
d
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where N is the number of stacked plates.
Ideally, the dielectric should have a low electrical
conductivity so that the leakage current is not too large.
Multilayer Ceramic Capacitor
Ceramic surface-mount
capacitors.
Cut-away view of multilayer
ceramic capacitor.
High-K Dielectric
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The bit count of MOS DRAM devices is
continuously increasing. However, as bit count
goes up, capacitor cell area goes down.
The capacitance per cell must remain in the 2530 fF range, which means the capacitance
density must increase.
One approach for DRAM manufacturing is to
replace the traditional silicon nitride + silicon
oxide with a higher dielectric constant (k) such
as tantalum pentoxide (Ta2O5), Hf-oxide (HfO2)
and Zr-oxide (ZrO2).
The roadmap of capacitor with DRAM technology.
D.-S. Yoon et al. / Progress in Materials Science 48 (2003) 275–371
High-K Dielectric
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High-k dielectric films are anticipated to be
required for certain applications with low power
and leakage current specifications.
High-k materials should be compatible with
conventional industry standard MOSFET
process flows using a poly-Si gate electrode.
HfO2, ZrO2, and Ta2O5 as high-k gatedielectrics.
HfO2/Poly-Si high-k transistor
ZrO2/Poly-Si high-k transistors
Typical material stack used in aTa2O5
DRAM capacitor
A Review of High High-k Dielectrics
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Gate dielectric materials having high dielectric
constant, large band gap with a favorable band
alignment, low interface state density and good
thermal stability are needed for future gate
dielectric applications.
Ultra high-k materials such as STO (SrTiO3) or
BST (BaSrTiO3) may cause fringing field
induced barrier lowering effect.
A Review of High High-k Dielectrics
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High-k gate dielectrics have a number of
difficulties:
(1) crystallization upon heating,
(2) dopant penetration,
(3) fixed charge,
(4) low channel mobility and
(5) uncontrolled oxide formation at the Si/high-k
interface.
High-K Problems
High-K and PolySi are Incompatible
Phonon Scattering in High-K
The Gate Stack
Schematic illustration of
important regions in a CMOS
FET gate stack
Expected performance trends for complementary
metal oxidesemiconductor (CMOS) transistor
technologies. The unrelenting reduction in transistor
size and the associated decrease in gate delay for (a)
an NMOS transistor and (b) a PMOS FET are
evident.
EOT- equivalent oxide
thickness
Schematic image of MOS transistors in the year 2003 and 2013.
Physical and electrical thickness of high-k gate dielectric (ideal).
SiO2 equivalent thickness EOT is smaller than high-k physical
thickness.
The depletion region of thickness Wd forms adjacent to the
poly-Si/oxide interface.
For example, if the capacitor dielectric is
SiO2, teq = 3.90o (A/C), o  8.85x10-3
fF/mm, thus a capacitance density of
C/A=34.5 fF/mm2 corresponds to teq =10 Å.
 A dielectric with a relative permittivity of 16
results in a physical thickness of ~40 Å, to
obtain teq =10 Å.
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Comparison of (a) stacked and (b) single-layer gate dielectrics in a
hypothetical transistor gate stack.
Either structure results in the same overall gate stack capacitance or
equivalent oxide thickness, teq =10 Å.