Date post: | 08-Nov-2014 |
Category: |
Documents |
Upload: | udai-singh |
View: | 53 times |
Download: | 6 times |
IHPIm Technologiepark 2515236 Frankfurt (Oder)
Germany
IHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany www.ihp-microelectronics.com
Physics of Dielectricsand DRAMThomas Schroeder
IHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany www.ihp-microelectronics.com
Physics of Dielectrics and DRAM
Dielectrics
IHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany www.ihp-microelectronics.com
Dielectric behavior in a „nut shell“:
A dielectric material is a non-conducting substancewhose bound charges are polarized under the influence
of an externally applied electric field.
The figure of merrit to describe the degree of polarizationin a given material is the dielectric constant
It is clear that the degree of polarization is related to thestructure of the material. In consequence, dielectric
behavior in electrostatic and alternating electric fieldsdepends on static and dynamical properties of the
structure.
Dielectric behavior must be specified with respect to thetime or frequency domain
Description of a dielectric material
IHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany www.ihp-microelectronics.com
Electrostatics: Basic experiment to get the central idea
Plate capacitor with oppositely charged plates and no material inserted. According to the surface charge density, a certain electric
field E is created inside.
If dielectric material is inserted, polarized chargesneutralizes some of the charges on the plates.
In this way, one talks about free (unneutralized) and bound charges(neutralized) on the plates. As only free charges create electric field,
a current must raise the free charge density and keep E constant.
If dielectric material is inserted and current source disconnectedmthe polarized charges neutralize some of the free charges on theplates. In consequence, a constant D results in a decrease of the
electric field between the plates.
IHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany www.ihp-microelectronics.com
Electrostatics: Macroscopic description of dielectrics
freedivD ρ=
0D E Pε= +
0 eP Eε χ=
0 0(1 )e rD E Eε χ ε ε= + =
Poisson Equation
Dielectric Displacement D
electric field E
Polarisation
Polarisation
Electric Susceptibility
Putting things together:
dielectric displacement D is linearly related to the electric field and the dielectric constant is the linear coefficient of the relationship
DielectricConstant
Result:
IHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany www.ihp-microelectronics.com
a a locP N p N Eα= ⋅ =
loc a dipoleE E E= +∑
0
13 2
a r
r
N εαε ε
−=
+
Electrostatics: Microscopic Approach and the local field
Polarisation: applied electric
field
polarisability
Local electric field:
density of induced dipoles
The local electric field can be calculated according to the crystalstructure by the method of Clausius and Mosotti.
For example, for cubic structures the Clausius – Mosotti equationreads:
For example, to design a material with high dielectric constant:
- ions with high polarisability- material with high density of induced dipoles
IHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany www.ihp-microelectronics.com
Microscopic Mechanism of dielectricpolarisation and frequency dependence
Space charge polarisationmaterials with space charge inhomogeneities
(ceramics with conducting grainsand insulating boundaries)
Orientation polarizationalignment of permanent
dipoles in a material
Ionic polarizationmutual displacement of negative
and positive sublattice in ionic crystals
Electronic polarizationdisplacement of electron shell
against positive nucleus
Rel
axat
ion
Rel
axat
ion
Res
onan
ceR
eson
ance
Different mechanism show different dynamic behavior in time domain.
In consequence, adsorption occurs at differentwindows in frequency domain
IHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany www.ihp-microelectronics.com
' ''e e eiχ χ χ= +
uur
''
'tan : r
r
εδε
=
tan (tan ) (tan )dipole condδ δ δ= +
Dielectric Behaviour in alternating electric fields
In alternating electric fields, a frequency dependent phase shift occurs between applied electricfield and displacement of charges in the material
To express this mathematically, a complex extension of dielectric function and susceptibilty isintroduced:
Figure of merrit for a dielectric material: the quality factor Q
' ''r r riε ε ε= +ur
' ''r r riε ε ε= +ur
' ''r riε ε+
''
'tan : r
r
εδε
=
' ''r r riε ε ε= +ur
1:tan
Qδ
=
A low quality factor states that a material heavilydissipates energy from the alternating
electric field by adsorbing mechanisms
IHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany www.ihp-microelectronics.com
Description of ionic and electronic resonance phenomena
2* * * 2
0,2i i i i i i loc
d u dum m m u q Edt dt
γ ω+ + =
acting forceEquation of motion
friction
displacement from equilibrium
acting force
restoring forceresonancefrequency
Case 1: Acting force is a dc field and switched off at a given moment
Restoring force pulls charges back in equilibrium position
a) If friction force is negligible, we arrive at undamped oscillations
b) If friction force is not negligible, we arrive at damped oscillation. (behavior similar to relaxation process with certain time constant)
IHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany www.ihp-microelectronics.com
Description of ionic and electronic resonance phenomena
2* * * 2
0,2i i i i i i loc
d u dum m m u q Edt dt
γ ω+ + =
acting forceEquation of motion
friction
displacement from equilibrium
acting force
restoring forceresonancefrequency
Case 2: Acting force is an ac field
Result:
( ),0
i kr tloc locE E e ω−= ⋅
uuurElectric ac field:
( )0
i kr tu u e ω−= ⋅r ur
Ansatz:
*,0
0 2 20,
( / )i i loc
i i
q m Eu
iω ω γ ω⋅
=− +
urFrequency dependent amplitude u of oscillations and dipole field:
( ) ( )0 ,0
i kr t i kr ti i i ocp q u e E eω ωα− −= ⋅ = ⋅uur uur
IHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany www.ihp-microelectronics.com
Description of ionic and electronic resonance phenomena
2* * * 2
0,2i i i i i i loc
d u dum m m u q Edt dt
γ ω+ + =
acting forceEquation of motion
friction
displacement from equilibrium
acting force
restoring forceresonancefrequency
Case 2: Acting force is an ac fieldFrequency dependent complex polarisability forionic and electronic mechanisms (f > 1011 Hz):
2 *' ''
2 20,
/( ) ( ) ( )i ii i i
i i
q m ii
α ω α ω α ωω ω γ ω
= = +− +
uur
2 22' 0,
2 2 2 2 2 20,
( )( )
iii
i i i
qm
ω ωα ω
ω ω γ ω−
=− +
2''
2 2 2 2 2 20,
( )( )
i ii
i i i
qm
γ ωα ωω ω γ ω
=− +
2' ''
, 2 20,
: (0) (0) 0ii s i i
i i
q andm
α α αω
= = =Reduces in the static case to:
IHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany www.ihp-microelectronics.com
Description of ionic and electronic resonance phenomena
2* * * 2
0,2i i i i i i loc
d u dum m m u q Edt dt
γ ω+ + =
acting forceEquation of motion
friction
displacement from equilibrium
acting force
restoring forceresonancefrequency
Case 2: Acting force is an ac fieldWith the frequency dependent complex polarisability and the Clausius-Mosotti equation, we get
the frequency dependent complex dielectric function in the frequency range > 1011Hz :
In the case of an ideal insulator with negligible magnetisation, the optical refractive index is given by Maxwell`s law
' '' 0 0
0 2 20 0
( ) ( )( ) ( )1 ( / ) /
r rr r i
ε ω ε ωε ω ε ωω ω γω ω
− ++
−= +
− +
ur
( ) ( )rn ω ε ω=r ur
Optical properties of matters: ectric properties under the influence of alternating electric fields with f > 1011 Hz
IHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany www.ihp-microelectronics.com
Description of relaxation phenomena: orientation and space charge contributions
Debye Relaxation
Debye relaxation denotes a system with a single relaxation time t. Example: Medium with one type of oriented dipole which can be oriented by external field
' '' 0 0
0 2 20 0
( ) ( )( ) ( )1 ( / ) /
r rr r i
ε ω ε ωε ω ε ωω ω γω ω
− ++
−= +
− +
ur
' ' '' '0 0
0 020
( ) ( )( ) ( ) ( )1 / 1
r r rr r ri i
ε ω ε ω εε ω ε ω ε ωγω ω ωτ
− ++ +
− ∆= + = +
+ +
ur
Such a system can be directly described by the general expressionwhen the term of the restoring force is omitted:
' ' ' 20 0 0: ( ) ( ) : /r r r andε ε ω ε ω τ γ ω− +∆ = − =
We get:
The relaxation step describes the part of the permittivity due to a relaxation process:
IHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany www.ihp-microelectronics.com
Description of relaxation phenomena: orientation and space charge contributions
Debye Relaxation
The real and imaginary part of the dielectric function for Debye relaxation than read:
'' '
0 2 2( ) ( )
1r
r r
εε ω ε ωω τ+
∆= +
+'
''
2 2( )
1r
r
ωτ εε ωω τ∆
=+
The relaxation step describes the part of the permittivity due to a relaxation process:
' ' ' 20 0 0: ( ) ( ) : /r r r andε ε ω ε ω τ γ ω− +∆ = − =For microelectronics this means:
There is no high-k material without energy dissipating process. Find a material which is well behavinin the frequency range of interest !
IHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany www.ihp-microelectronics.com
Description of relaxation phenomena: orientation and space charge contributions
How to identify Debye relaxation ?
relaxation step
/00
W k TBeτ τ= ⋅
Certainly, this results in an exponential dependance of the relaxation frequency with temperature
1) Thermal behaviour
2) Cole – Cole diagram
In case of true Debye behavior(only one relaxation time)
plotting imaginary against real partforms a semi-circle
This example should make clear that dielectricmeasurements are often interesting alternatives to study
the structure and dynamics of materials.However, the microscopic origin is not easy to reveal !
IHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany www.ihp-microelectronics.com
Description of relaxation phenomena: orientation and space charge contributions
Space Charge Polarisation
The trapped space charge in the grain oscillates in the applied ac electric field like a dipole. Therefore, space charge and classical orientation polarisation behave similar
Space charge or Maxwell – Wagner polarisationoccurs in dielectrics with inhomogeneous regions of different conductivity.
For example:polycristalline materials with slightly conducting grains and highly insulting grain boundaries
With the help of equivalent circuits the behavior of dielectric systems can be simulated and comparison with experiments made
In microelectronics: electrical engineers and materials scientists are neededto describe such systems
conductinggrains
Ceramics Equivalent Circuit
insulatingboundaries
IHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany www.ihp-microelectronics.com
Description of relaxation phenomena: orientation and space charge contributions
Space Charge Polarisation
For example:with the help of the equivalent circuit, the current response of the ceramic to a step voltage can be
simulated
Equivalent Circuit
' ' /0 0 0( ) (1 )t
r rD E E e τε ε ω ε ε −
+= + ∆ −
' 1 /0
tR rj D Ee τε ε τ − −= = ∆
Current response to step voltage
Step voltage
Dielectricdisplacement
Relaxationcurrent
IHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany www.ihp-microelectronics.com
Physics of Dielectrics and DRAM
DRAM
IHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany www.ihp-microelectronics.com
Random Access Memories
Definition:digital information storage devices are commenly grouped
in random and sequential access devices
Random access devices:storage cells are organized in a matrix so that short access times are
realized independent of the physical location of the data cell.
Application: computer memory to store instructions and data for fast access
Sequential access devices:sequential cell architecture so that access time depends on physical
location of the storage cell with respect to read/write head.
Application: large and permanent mass storage devices like hard discs
IHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany www.ihp-microelectronics.com
Random Access Memories
History:first RAM were based on tiny, wire-threaded ferrite torroids arranged in a matrix set-up
Two states of the remanent magnetization present the binary „0“ and „1“
Write operation:current pulse are passed through
selected row and column. only at crossing point strong
enough toswitch magnetization
Read operation:a „1“ is written into the cell
in case of „0“ in the cell, change of magnetizationinduces current pulse in read line connected to a
sense amplifier. Appearance or absence of this pulse read as „0“ or „1“.
IHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany www.ihp-microelectronics.com
Random Access Memories
Three important insights:
Write operation:n passive matrix, all cells exhibit part of the signaldvantage: high demand on threshold behavior of cells.
n active matrix, each cell is adressed individuallyby a switch transistor
Disadvantage: higher complexity
Read operation:the read operation is destructive(destructive read out: DRO) and
requires a subsequent write back operation
Storage capacity:
Each cell has two states
In case of mRows and n columns:
2 n+m bits
Example:N + m = 20
1Mbit (M = 1024K and k=1024)
IHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany www.ihp-microelectronics.com
RAM families
randomrandom accessaccess memorymemory ((RAM):RAM):as discussed, used for data storage where quick access is needed
readread onlyonly memorymemory ((ROM):ROM):typically used for instruction storage
OnceOnce--programmableprogrammable ROM:ROM:used for instruction storage
Mask-based ROM(programmed by supplier)
PROM(once programmed by customere-.g. metal connects are fused )
ReRe--programmableprogrammable ROM:ROM:MOSFET`s with floating gate
layer in gate dielectric
EPROM(information deleted by UV light)
EEPROM(information deleted by enhacned voltage;
very succesfull is FLASH EEPROM with shortReprogramming times)
StaticStatic RAM (SRAM)RAM (SRAM)::interlocked state of logic gates
DynamicDynamic RAM (DRAM)RAM (DRAM)::stored charge level in capacitor
IHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany www.ihp-microelectronics.com
RAM families
randomrandom accessaccess memorymemory ((RAM):RAM):as discussed, used for data storage where quick access is needed
readread onlyonly memorymemory ((ROM):ROM):typically used for instruction storage
OnceOnce--programmableprogrammable ROM:ROM:used for instruction storage
Mask-based ROM(programmed by supplier)
PROM(once programmed by customere-.g. metal connects are fused )
ReRe--programmableprogrammable ROM:ROM:MOSFET`s with floating gate
layer in gate dielectric
EPROM(information deleted by UV light)
EEPROM(information deleted by enhacned voltage;
very succesfull is FLASH EEPROM with shortReprogramming times)
StaticStatic RAM (SRAM)RAM (SRAM)::interlocked state of logic gates
DynamicDynamic RAM (DRAM)RAM (DRAM)::stored charge level in capacitor
IHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany www.ihp-microelectronics.com
Scaling of Memory Cell
The DRAM success storyMoore`s law:
exponential increase ofMemory cells on chipOver the last 40 years
(doubles each eigtheenmonths)
Made possible by:
1) Reduction in feature size
comparable simple matrix set-upmakes DRAM the technology driver for
dry etching and lithography
2) Cost effectiveness:
tremendous improvement offabrication productivity
IHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany www.ihp-microelectronics.com
Basic Operation of DRAM Cell
DRAM is a 1Tr – 1 C Cell (active matrix array):
1) Transistor (Tr)Switch adressed by wordline (WL)
2) Capacitor (C)Charge storage element connected to Bitline (BL)
Write Operation:
switch is closed and voltage levels+ VCC or 0 applied to capacitor
via BL
Read Operation:
switch is closed and capacitor connected to BL which is on + VCC/2
capacitor charge QS redistributes over BL
absence or presence of voltage change is sensedby sense amplifier and enhanced
IHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany www.ihp-microelectronics.com
Circuit Cleverness to ease reliability issues
The sense amplifier needs to see a certain chargelevel QSto read out the stored information:
Case 1: imagine Vp is at VCC:By the read operation, capacitor is in one state completely discharged („1“)
and in the other state („0“) extremely chargedDisadvantage:
Dielectric breakdown by high electric field
Case 2: imagine Vp is at VCC//2:By the read operation, capacitor is in
one state at +VCC/2 („1“) and in theother state at -VCC/2 („0“)
Advantage:Dielectric experiences lower electric field
IHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany www.ihp-microelectronics.com
Challenges in Gb DRAM capacitors
Miniaturization reduces first of all area but thesense amplifier needs to „see“ certain charge
level QS for reliable read out
Approaches to keep CS high:
1) Thin out the SiO2 capacitor dielectric :⇒leakage current limits this approach
(leakage is very tough criterion for 1 GB DRAM capacitors)
2) Integrate high-k dielectric : => Teq tells how much thicker you can make it for same CS
so that leakage is reduced
3) 3D - integration : => increase capacitor area again
2
2 2
,0 0 , , 3.9.r SiOS S
s r r SiO eq phys r SiOphys eq r
A AC with t t andt t
εε ε ε ε ε
ε= = = =
IHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany www.ihp-microelectronics.com
3D Device Architectures
Trench Technology
very successful approach but one big disadvantage:
Trench capacitor is prepared before switch transistor. As transistor needs RTO step (1000°C / 10 to 30 sec), future high-k capacitor
dielectrics needs to survive this cruel treatment=> very tough materials selection criterion
IHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany www.ihp-microelectronics.com
3D Device Architectures
Stack Technology
The advantage is that the capacitor is formed after the transistor:=> Easier materials selection for high-k dielectrics
The disadvantage is the geometry of the disk technology: => Homogeneous coverage required to avoid dielectric breakdown
IHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany www.ihp-microelectronics.com
Materials science aspects
Voltage dependence of dielectric constant
The charge difference between level „0“ and „1“ is the result of an integrateddielectric.
"1"
"0"
/ 20
/ 2
( ) ( )DD
DD
V VS
S rV V
AQ C V dV V dVtε ε
+
−
∆ = =∫ ∫
BaTiO3 has a high dielectric constantBut is strongly bias dependent
IHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany www.ihp-microelectronics.com
Materials science aspects
Interface effects limit dielectric constant
If interfaces have lower dielectric constant, these „dead layers“ limit theachievable capacitance density. The materials system can be viewed as a seriesconnection of three capacitors whose effective capacitance density is certainly
Determined by the lower – k value materials.
A systematic electric study allows to deducethickness of interfaces and their k values
( )1
, , , ,0 0 0 0
0 ,
1,
BI TIBI TI
r eff r BI r BST r TI
BI TIBI TIr BST
t t tt tC tA
A Afor t t t tC C
ε ε ε ε ε ε ε ε
ε ε
− − +⎛ ⎞ = = + +⎜ ⎟⎝ ⎠
⎛ ⎞ ⎛ ⎞>> ≈ + +⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠