Physics of Dielectrics and DRAM

IHPIm Technologiepark 2515236 Frankfurt (Oder)

Germany

IHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany www.ihp-microelectronics.com

Physics of Dielectricsand DRAMThomas Schroeder


Physics of Dielectrics and DRAM

Dielectrics


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


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.


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:


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


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


' ''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 riε ε+

''

'tan : r

r

εδε

=


1:tan

Qδ

=

A low quality factor states that a material heavilydissipates energy from the alternating

electric field by adsorbing mechanisms


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)



2* * * 2

0,2i i i i i i loc


γ ω+ + =


friction


acting force


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



2* * * 2

0,2i i i i i i loc


γ ω+ + =


friction


acting force


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:



2* * * 2

0,2i i i i i i loc


γ ω+ + =


friction


acting force


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


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:



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 !



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 !



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



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


Physics of Dielectrics and DRAM

DRAM


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



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“.



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)


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


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


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


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


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


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= = = =


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


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


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


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

− − +⎛ ⎞ = = + +⎜ ⎟⎝ ⎠

⎛ ⎞ ⎛ ⎞>> ≈ + +⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

Documents

Physics of Dielectrics and DRAM