Technology CAD: Technology Modeling, Device Design and Simulation S. Saha and B. Gadepally

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Title: Technology CAD: Technology Modeling, Device Design and Simulation S. Saha and B. Gadepally

1
Technology CAD Technology Modeling Device
Design and SimulationS. Saha and B. Gadepally
2004 VLSI Design Tutorial January 5 2004
Mumbai India
2
Technology CAD Technology Modeling Device
Design and Simulation

Coordinator Prof. Bhaskar Gadepally
Adjunct Prof. Electrical Engineering IIT Bombay
Chairman Reliance Software Consulting Inc.
155 E. Campbell Ave. Campbell CA 95008 (USA)
bhaskar_at_relianceworld.com
2004 VLSI Design Tutorial January 5 2004
Mumbai India

3
Technology CAD Technology Modeling Device
Design and Simulation

Instructor Dr. Samar Saha
Silicon Storage Technology Inc.
1171 Sonora Court
Sunnyvale CA 94086 (USA)
samar_at_ieee.org
2004 VLSI Design Tutorial January 5 2004
Mumbai India

4
Tutorial Outline

Prof. B. Gadepally
Introduction and Tutorial Overview.
Dr. S. Saha
Front-end Process Technology CAD (TCAD) Models
and Process Simulations
Device TCAD Models and Device Simulations
Industrial Application of TCAD
Calibration of Process and Device Models
Industrial Application of TCAD in
Device Research
Compact / SPICE Modeling.

5
Technology CAD Technology Modeling Device
Design and Simulation Introduction and Tutorial
Overview
2004 VLSI Design Tutorial January 5 2004
Mumbai India
6
Overview of IC Technology

In the past three decades
device densities have grown exponentially
device and technology complexities have increased
significantly
design constraints are many-fold
ultra thin oxide
interconnect
power supply
technology development cost has increased
enormously.

7
Overview of IC Technology
8
Overview of IC Devices

New device and device physics are continuously
evolving
nano-scale devices
microscopic diffusion
quantum mechanical carrier transport
molecular dynamics
quantum chemistry
high-frequency interconnect behavior.

9
Technology CAD

With the increased complexities in IC process and
device physics
intuitive analysis is no longer possible to
design advanced IC processes and devices
TCAD tools are crucial for efficient technology
and device design
to quantify potential roadblocks
to indicate new solutions
for continuos scaling of devices.

10
Technology CAD

Scope of TCAD
front-end process modeling and simulation
implant diffusion oxidation etc.
numerical device modeling and simulation
I - V C - V etc. simulation
topography modeling and simulation
deposition lithography etching etc.
device modeling for circuit simulation
compact / SPICE modeling
interconnect simulation
capacitance inductance etc.

11
Tutorial Objective

Offer insight into the physical basis of TCAD
especially bulk-process and device TCAD.
Describe systematic methodologies for an
effective application of TCAD tools.
Describe systematic calibration methodology for
predictive usage of TCAD tools
process models
device models.
Offer users sufficient insight to leverage new
tools.

12
Session 1 Bulk-Process Simulation

Front-end process models implemented in process
TCAD tools
ion implantation models
analytical
Monte Carlo
microscopic diffusion models
point defects
oxidation
transient enhanced diffusion.

13
Session 2 Device Simulation

Device models implemented in device TCAD tools
fundamentals of carrier transport
drift-diffusion solution
hydrodynamic solution
carrier mobility models
device physics of nanoscale technology
inversion layer quantization
fundamental limits of MOSFETs.

14
Session 3 Industry Application

Introduction to process and device simulation
tools.
Mesh generation.
Model selection.
Predictive usage of TCAD
process model calibration
device model calibration.
Predictive simulation of CMOS technology.

15
Session 3 Industry Application - Calibration
16
Session 4 TCAD in Research Modeling

Simulation tools in device research
simulation structure
model selection
examples
sub-100 nm MOSFETs
DG-MOSFETs - FinFETs.
TCAD in device (compact) modeling
examples
substrate current model
flash memory cell macro-model.

17
Technology CAD Technology Modeling Device
Design and SimulationBulk-Process Simulation
2004 VLSI Design Tutorial January 5 2004
Mumbai India
18
Outline

Introduction.
Bulk-process Models
Ion Implantation
Diffusion
Oxidation.
Summary.

19
Introduction

Front-end IC fabrication processes include
implant S/D and halo (low energy) well (high
energy) etc.
diffusion Rapid thermal annealing (RTA) Þ
Transient Enhanced Diffusion (TED) and other
anomalous effects
oxidation gate oxide STI liner oxide etc.

20
Introduction

Objective of this session
understanding of physical models implemented in a
process TCAD tool
model hierarchy
model limitations
building new models
basic understanding of general purpose simulator
internals
TCAD models in general without considering any
particular tools.

21
Ion Implantation

Ion Implantation Mechanisms.
Ion Implant Models
Analytical
Monte Carlo (MC).
Implant-induced Damage Modeling.
Plus-one Approximation.
Summary.

22
Ion Implantation

Bombard wafers with energetic ions energy E 0.5
KeV - 1 MeV gt Ebinding.
Ions collide elastically with target atoms
creating
ion deflections energy loss
displaced target atoms (recoils).
Ions suffer inelastic drag force from target
electrons
ion energy loss
lattice heating.

23
Ion Implantation

Channeling is caused by ions traveling with few
collisions and little drag along certain crystal
directions.
Ions come to rest after losing all the energy on
elastic collisions (nuclear stopping)
inelastic drag (electronic stopping).

24
Ion Energy Loss Mechanisms

Nuclear stopping (Sn(E))

ion energy loss to target atom by interaction
with the electric field of the target atoms
nucleus

classical relationship of two colliding particles
the scattering potential with the exponential
screening function is given by
where
Z1 atomic number of incoming ion
Z2 atomic number of target atom.

25
Ion Energy Loss Mechanisms

Electronic stopping (Se(E)) is due to the viscous
drag force on moving ion in a dielectric medium.

ke is a model parameter.
Accurate model must account for the variation of
Se in space.
Stopping power S of an ion is given by

26
Ion Range Distribution

Ions come to rest over a distribution of
locations.
Peak depth and lateral spread of distribution
are determined by
ion mass energy dose and incident angle
target atom composition geometry structure
and temperature.
Implanted profile can be represented by
particles
distribution functions.

27
Ion Range Distribution
28
Ion Range Distribution

The as-implanted 1D distribution function is
described by a series of coefficients called
moments.
2D distribution of the implanted profile is
constructed from 1D distribution function taking
lateral spread vertical spread.

29
1D Analytical Ion Implantation Models

Gaussian distribution
amorphous targets
two coefficients
where
Q implant dose (/cm-2)
Rp projected range º normalized first moment
sp straggle/standard deviation º second moment.

30
1D Analytical Ion Implantation Models

Pearson-IV
crystalline targets without channeling
four coefficients (Rp sp skewness kurtosis)
crystalline targets with channeling tilt and
rotation.
six coefficients.
Dual Pearson-IV
crystalline targets with channeling tilt and
rotation
second profile to model the channeling
nine coefficients.
Legendre Polynomials - 19 coefficients.

31
1D Analytical Ion Implantation Models

Coefficients are fit to the measured doping
profiles.
Coefficient-set for each distribution is
tabulated for different
ion mass (As B In P Sb)
dose energy tilt and rotation
target type.
Multi-layer targets
each material is treated separately and scaled by
its Rp.
dose absorbed on the top layer is calculated and
is used as the dose matching thickness for the
layer below.

32
2D/3D Analytical Ion Implantation Models

Each 1D profile along a vertical line is
converted to 2D or 3D distribution by multiplying
it by a function of lateral coordinates
here lateral straggle sl sp
Multi-layer targets and sloped surfaces are
converted to 2D/3D by dose matching approach.
More complex models have sl(x).
Low energy profiles need non-separable
point-response functions.

33
Monte Carlo Modeling of Ion Implantation

The collision energy loss is modeled by binary
collision approximation (BCA) that is each ion
collides with one target atom at a time.
The energy loss (DE) is modeled in terms of
incident energy E0 and scattering angle q0 of
ion
separation between two particles
coulomb potential between two particles
impact parameter.
BCA requires special formulation for
ion channeling
low energies when lattice movements come into
play.

34
Monte Carlo Modeling of Ion Implantation

Ongoing development in MC modeling is to improve
speed of calculations
electronic stopping power Se model
detailed local model for Se
local and non-local split in energy loss due to
Se
where
fnl fraction of non-local energy split
a universal screening length
p impact parameter.
Overall accuracy of MC implant model is excellent.

35
Ion Channeling in Crystalline Silicon

Along certain angles in crystal ion may
encounter no target atoms.

Repeated small-angle collisions steer the ion
back into the channel.

Channeling was first discovered by MC simulation.
Channeling is
important at any energy
critical at low energy where lt110gt channels steer
Boron ions under MOS gate.
Analytic channeling model is complex.

36
Ion Channeling in Crystalline Silicon
37
Damage Creation Models

Each incoming ions generates damage seen by
subsequent ions
recoils target atoms knocked out of lattice
sites
amorphous pockets.
The effect of damage is significant on
as-implanted profile as well as during subsequent
diffusion.
Models based on Kinchin-Pease formulation is used
to estimate damage density n Er/2Ed
where
Er recoil energy
Ed target displacement energy ( 15 eV for
Silicon).

38
Plus-one Damage Model

Most recoiled interstitials (I) find a vacancy
(V) and recombine rapidly either during the
implantation or the first instants of annealing.
Distribution of remaining recoils shows
net excess of V near the surface
net excess of I toward bulk.
At low ion mass and/or moderate energy
population of net I and net V is less than the
population of I due to dopant atoms taking
substitutional sites
one extra-ion is created for each dopant atom
taking a substitutional site.

39
Deviation from Plus-one Model

Plus-one approximation often fails for
heavy ions
as the population of recoils can become quite
large relative to extra ion population
low energy
low dose.
An effective plus-n factor as a function of ion
species energy and dose is used. Typical
values
As n 3.5 _at_ E 5 KeV n 1.2 _at_ E 500 KeV
B n 1.2 _at_ E 5 KeV n 1.0 for E gt 20 KeV
P n 2.2 _at_ E 5 KeV n 1.0 _at_ E 500 KeV.

40
Ion Implantation Summary

Ion implantation with ion energy gt Ebinding of
target atoms is used to implant impurity atoms
into target.
Analytical ion implantation model
the impurity profile is represented by moments
for different species dose energy tilt and
rotation
the moments are extracted from the experimental
profile to create look-up table
simulation is performed using this look-up table.
MC ion implantation model is more accurate
particularly for low energy.
The implant damage is modeled by plus-n model.

41
Diffusion

Fundamentals of Dopant Diffusion
Ficks Laws
Oxidation Enhanced Diffusion (OED)
Oxidation Retarded Diffusion (ORD)
Transient Enhanced Diffusion (TED).
Point Defect Model.
Clusters and Precipitates.
Polysilicon Diffusion.
Impurity Profiling.
Summary.

42
Ficks Laws of Diffusion

Ficks first law
describes flux (F) through any surface
diffusion is downhill - high low concentration
- sign
Ficks second law law of conservation of
particles
Low concentration diffusion in
silicon is Fickian - each dopant
A satisfies

(D º diffusivity constant)
43
Concentration-Dependent Diffusion

Typically intrinsic carrier concentrations (ni)
at processing temperatures are high 1019 cm-3.
For high doping concentrations C gt ni dopant
diffusion shows enhancements of the form
Diffusion enhancement is due to the variation of
point defect population with Fermi level.
The effective extrinsic diffusivity is given by

44
Surface Effects on Bulk Diffusion OED/ORD

Experimental data show that processes which
modify the surface can affect diffusion in the
bulk.
Enhancement of diffusivity in one species while
retardation in another is the evidence of two
different diffusion mechanisms I and V.

45
Transient Enhanced Diffusion (TED)

Anomalous displacement of implanted dopants
during low temperature anneals.
Reverse temperature effect displacement larger
at lower temperatures - up to 0.3-0.4 mm.
Displacement increases with implant dose and
energy.
Corresponds to temporary increase in diffusivity
10000X.
Implant of one species can drive diffusion of
another.
Enhancement is transient.
Spatially non-uniform diffusion enhancements.
Reduced activation.

46
Transient Enhanced Diffusion (TED)

As implanted over a buried B layer.
As implant creates damage deep into the
substrate.
The implant damage causes a significant
enhancement in B diffusion deep into the
substrate during 20 sec. anneal at 850 C.
Simulation results Þ

47
Point Defect Model for Dopant Diffusion

Point defects (I and V) model explains
most of the observed trends in dopant diffusion
by relating them to the properties of I and V
action-at-a-distance effect of the surface on
bulk diffusion.

48
Defect Charge States

Defects which have states in the gap will have a
distribution of charge states.
The concentration of charged point defects
depends on Fermi level.
Dopants can diffuse with any of the defect charge
states some combinations have higher
probability.
In principle must solve a set of
PDEs one for each
combination.
Five-stream diffusion model solves equations
Three-stream model solves
equations.

49
Electric-field Effects

For high doping concentration gt ni at the
processing temperature the electric field set up
by ionized dopants affects diffusivity.
Example
As B co-diffusion at 900 C 15 min.
Þ B- pulled towards the N region due to e-field
effects.

50
Generation/Recombination of Defects

General flux model
where q
fraction of silicon atom injected
Vm silicon atom/cm3
assumed generation µ growth rate G.
recombination rate µ surface excess I - I and
increases under a growing surface.
Lateral diffusion of defects during OED is
governed by the ratio of DI/Kinert 10 mm.

51
Surface Generation/Recombination

During OED recombination/generation fluxes are
large and must balance
Fixed interstitial super-saturations also occur
under nitride silicide surfaces.
During TED recombination appears to be fast
even at inert surfaces recombination rate
Several models are available.
Optimize Kinert for TED and adjust q to fit OED
at the expense of lateral OED decay length.

52
Gradient Effects in Transient Diffusion

Dopant flux arises from diffusion of
defects-dopant pairs
boron flux DBIÑBI.
Number of pairs is proportional to the boron and
interstitial concentrations
boron flux DBIkpair(IÑB BÑI)
where
IÑB interstitials enhance boron diffusion
ÑI boron diffusion due to defect gradient
During TED ÑI is large near the surface causing
extra dopant flux to the surface
surface pile-up (and possible interface loss) of
dopant.

53
Interstitial Clustering Model

The growth and dissolution is given by
where
kd is the decay constant
kc is the growth constant
C concentration of clustered interstitials
I concentration of unclustered interstitials.
After implantation I is large dC/dt C(kcI) Þ
clusters grow exponentially until I kd/kc.
When I is small clusters decay exponentially
with time constant 1/kd.

54
311 Cluster Dissolution

311 defects
rod-shaped defect clusters condensed from 1
amount of damaged silicon-I at annealing T gt 400
C
precipitate on 311 planes and extend in the
lt110gt directions to form planar defects.
Time scale for 311 evaporation is similar to
the time scale for TED.
Simple reaction-based model offers first-order
account of evaporation curve.
Steady super saturation of dopant diffusion is
observed during TED.

55
Dopant Clustering/Precipitation

Dopants are only soluble up to a limit at any
temperature (solid solubility limit).
Dopants also show deactivation below the solid
solubility limit.
Due to the clusters of size
m dopant atoms such as
As with m 4
clustering reaction emits
interstitials to generate required V.
Can generate enhanced diffusion at the same level
as TED.

56
Chemical Pump Effects

Dopant atom A interacting with I form A I AI
interstitial-assisted mobile species.
When AI pairs diffuse out of a region of high I
to a region of low I pairs are out of
equilibrium and must dissociate AI A I.
A is deposited while I diffuses (pumped) away
from the surface enhancing diffusion in bulk.
Surface dopant layer may cause enhanced diffusion
in bulk - e.g. D/D 70 at 900 C.
Causes cooperative diffusion e.g. emitter push
effect in bipolar junction transistors.

57
Diffusion in Polysilicon

Point defects usually pinned near equilibrium in
poly due to grain boundaries.
Dopants diffuse in two streams via grain and in
boundary.
An effective model includes
two streams
dopant transfer from grain to grain boundary
grain growth with time
dopant transfer to grain boundary.
Segregation coefficient growth rate and
re-growth rate f(temperature grain size Fermi
level).

58
Metrology for Developing Diffusion Models

Spreading resistance profile (SRP)

1D carrier profiles
good sensitivity
modest depth resolution
carrier spilling
difficult to use for shallow junctions.

p
59
Metrology for Developing Diffusion Models

Secondary Ion Mass Spectroscopy (SIMS)
1D chemical profiles
good sensitivity to all dopants
excellent depth resolution
surface region troublesome.
2D carrier profiling with excellent space
resolution
scanning capacitance microscopy (SCM)
measurement affects sample
transmission electron holography (TEH)
measures electrostatic potential
difficult sample preparation.

60
Monte Carlo Diffusion Methods Algorithm
Monte Carlo diffusion program (MARLOWE
UT-Austin) offers accurate diffusion modeling.
61
Diffusion Summary

Diffusion is critical to activate the implanted
dopants in the semiconductor devices.
Dopants diffuse in silicon by interacting with
point defects through a number of possible
atomic-scale mechanisms.
For short times the diffusion is dominated by
TED because of high concentration of point
defects.
Point defect concentrations depend on
temperature Fermi level implant damage and
surface processes like oxidation.
1D/2D metrology is used to calibrate diffusion
model.

62
Oxidation

Fundamentals of Thermal Oxidation.
Oxide Growth Model
Deal-Grove Model
Thin Oxide Model.
Oxidation Chemistry.
Oxide Flow
Oxidation-induced Stress
Visco-elastic Model.
Summary.

63
Oxidation Diffusion Reaction Flow

Oxidation proceeds by three sequential processes
oxidant diffuses through existing oxide
oxidant reacts at silicon surface to create new
oxide
overlying oxide flows to accommodate new volume.

Process is at first limited by reaction but
diffusion through growing oxide becomes limiting.

64
Oxidation Deal-Grove Model

D diffusivity of oxidant
CL concentration at Si-SiO2 interface
C0 concentration at the SiO2 surface
L oxide thickness
k interface reaction rate constant

65
Oxidation Deal-Grove Model

At equilibrium Fdiff Freac \ CL C0 / 1
kL/D
Oxidation growth rate is given by
where
C equil. oxidant conc. Ns oxidant/cm3 in
oxide

66
Thin Oxide Models

Deal-Grove model does not fit the early part of
oxidation curve.
The data in thin regime can be fitted with an
addition to Deal-Grove model given by
where and
C0 3.6x108 mm/hr EA 2.35 eV and l 7 nm in
lt111gt or lt100gt oriented silicon substrates.
This model can be found in TCAD tools like
SUPREM4.

67
Oxidation - Planar Growth

Planar growth generates an intrinsic stress in
oxide during growth process
modest stress (3x109 dynes/cm2)
density increases (lt 3)
refractive index increases (1) relative to fully
relaxed oxides.

Two-step oxidation shows a significant difference
in oxide density.

DL grown in the second step varies depending on
the thermal history of oxide (not just on L).

68
Oxidation - Planar Growth

Intrinsic stress is an atomistic process.
Relaxes gradually with annealing at a rate which
steadily decreases.
Recent measurements show that relaxation rate is
independent of stress level.
History effects are not accounted for in most
process simulators.
Measured linear/parabolic coefficients describe
oxidation in a state of intrinsic stress.
1D stress already accounted for in one-step
oxidation.

69
Oxidation Chemistry

Oxidation rate coefficients are sensitive to
ambient additives
steam 20 - 50 times faster than O2
3 Cl2 increases growth rate by 20 - 30
100 ppm NF2 increases growth rate by 2 - 5
heavy substrate doping increases rate by 2 - 10
according to the relation
all easily accounted for by building table of B
B/A vs. additive or dopant concentration.
NO NO2 are not supported in most process TCAD
tools.

70
Oxide Flow

Oxide growing on a curved
surface must flow.
Resulting deformations (and stresses) can be
large! LOCOS top surface must stretch by 15 -
20.
Elastic limit of glass ltlt 1

71
Oxide Flow

Large deformations on a curved surface during
oxidation mean viscous flow must occur.
Viscous flow model used to model stress during
oxide growth includes
incompressible viscous flow
linear elasticity.
Visco-elastic flow model
allows oxide to be slightly compressible
eliminates pressure equation
offers a significant numerical benefit.

72
Visco-elastic Model Stress Simulation

Oxide stress after local oxidation.
Length of stress vector µ amount of stress.

73
Oxidation Summary

Basic growth mechanism of thermal oxide
oxidant transport through the SiO2 layer to
Si/SiO2 interface
chemical reaction at the interface to produce the
new layer of oxide.
The growth is linear parabolic law.
The basic Deal-Grove model is extended to
explain
thin oxide growth
mixed ambient oxidation.
Important effects of thermal oxidation include
OED ORD and impurity redistribution and
segregation.

74
Bulk-Process Simulation Summary

Accurate process models and TCAD tools are
extremely critical for continuous scaling of ICs
.
Workstation performance is continuously improving
for cost-effective computer experiments.
Existing models and TCAD tools treat different
aspects of process simulation quite well.
As new understanding develops new models are
incorporated in TCAD tools to improve
predictability.
Successful process TCAD will require a firm grasp
of the controlling process physics.

75
Technology CAD Technology Modeling Device
Design and SimulationDevice Simulation
2004 VLSI Design Tutorial January 5 2004
Mumbai India
76
Outline

Introduction.
Carrier Transport Models.
Inversion Layer Mobility.
Quantum Mechanical Confinement.
Discrete Dopant Effects.
Numerical Methods.
Summary.

77
Introduction

A device TCAD tool solves a set of equations to
deal with various physical phenomena in
semiconductor devices

78
Introduction

Objectives of this session is to
focus on the underlying physics and models for
practical application of device TCAD such as
identify device physics issues for simulation
discuss and compare simulation approaches
identify
limitations
uncertainties
challenges.

79
Carrier Transport Models

A device TCAD tool generates device
characteristics by solving
Poissons Ñ.D r(r) carrier transport
equations self-consistently.
Carrier transport models include
drift-diffusion (DD) - standard
Monte Carlo (MC)
molecular dynamics
hydrodynamic (HD)
Boltzmann equation
quantum balance equations.

80
Carrier Transport Models

The basic concept in transport theory is the
carrier distribution function f(rpxt).
f(rpxt) probability of a carrier at the
position r with momentum px at any instant t.

f(rpxt) is a Maxwellian distribution function
with
area carrier density n(rt)
the spread depends on carrier temperature

first moment is velocity
second moment is kinetic energy.

81
Carrier Transport Models

At equilibrium f(rpxt) is symmetric around px
0.
If an e-field is applied along the negative px
direction
electron distribution is distorted and displaced
from the origin
causes electron scattering.
Device TCAD challenge is to solve f(rpxt).

82
Carrier Transport Models

To solve for f(rpt) - Boltzmann Transport
Equation (BTE)
six dimensions
three in position space
three in momentum space
solution techniques
MC simulation
spherical harmonics
scattering matrix
and so on.

83
Carrier Transport Models

Solving f(rpt) we can find the quantities that
device engineers deal with directly such as
carrier density n(rt)
current density Jn(rt)
energy current JE(rt)
average kinetic energy un(rt)
electron temperature Tn(rt)
heat flux Qn(rt).
Six-dimensional equation is difficult to solve
and computationally demanding.
In TCAD we directly solve for the quantities of
interest.

84
Carrier Transport Balance Equations

Basic idea to solve for a quantity (nf) of
interest is to formulate a balance equation such
as
rate of increase in nf rate nf flows into the
volume net generation rate.

85
Carrier Transport Models

Assuming slowly varying time we can write the
current equation
where
t average time between collisions
m effective mass of electrons.
We need a balance equation for kinetic energy
uxx.
For simplicity of computation
approximate the effects of scattering in mn
close the balance equations by approximating uxx.

86
Carrier Transport Models Drift-Diffusion

The simplest solution of carrier transport
equation is local field or DD approach.
In DD m is determined by scattering scattering
is determined by uxx and uxx is determined by e.
For high fields in bulk silicon e(x) and uxx are
constants or slowly varying
here mn m0NTLe(x) Dn (kBTL/q)mn
Then the current equation is given by
Þ Local field transport model mn f(local
field)

87
Carrier Transport Models Drift-Diffusion

DD solution fails to predict device
characteristics for small geometry ( 0.1 mm)
MOSFETs.
We know
here lttgt is related to the average carrier
energy un(Tn) and Tn local electron
temperature.
Thus the DD-transport model can be improved by
assuming mn as a function of local energy.
Local energy transport model mn f(local
energy)
Alternatively mn m0NTLTn

88
Carrier Transport Models Local Energy

Solve for energy density nf W(xt) nu
where tE relaxation time.
nf JE(xt)
Unknowns e(x) n(x) p(x) un(x) and up(x)

89
Carrier Transport Models DD vs. HD

DD vs. HD model data deviate significantly for 40
nm devices.

90
Macroscopic Transport Models Summary

Models are derived directly from BTE.
Require numerous simplifying assumptions
closure scattering.
Difficult to assess the validity of assumptions.
Many flavors HD energy transport (ET).
Beyond DD adds significant numerical complexity.
HD/ET generally provide good estimates of
average carrier energy
current density.
Significant differences between various models.

91
Carrier Transport Models MC Simulation

MC is a rigorous transport model.
The essence of the model is

r1 free flight duration
r2 scattering event
r3 direction after scattering r4

92
MC Simulation Summary

Advantages
numerical method for solving the BTE with e-e
correlation
advanced physics is readily treated (e.g.
scattering and complete band structures)
most reliable transport method for treating hot
electron distributions and for assessing novel
devices.
Disadvantage
computationally demanding
under near-equilibrium conditions
for examining rare events.

93
Carrier Transport Models Quantum

Different techniques available include
(1) equilibrium or ballistic transport
simplest form is used for MOS capacitor
simulation
(2) wave propagation with phase randomizing
scattering
non equilibrium Greens function approach (Wigner
functions density matrix)
(3) density gradient/QM potential approach

94
Carrier Transport Models Summary

Drift-diffusion (local field model)
m f(local field)
Balance equations (mostly local energy)
m f(local energy)
Examples HD ET etc.
Boltzmann solvers
MC
Quantum transport
Schrodinger-Poisson
density gradient / quantum potential.

95
Inversion Layer Mobility

Choice of mobility model can significantly alter
the simulation results.
Inversion layer mobility versus effective normal
electric field show well-known characteristics
high fields universal behavior independent of
doping density.
low fields dependent on 1) doping density and 2)
interface charge.

96
Inversion Layer Mobility

Mobility versus effective normal electric field
curve is modeled using three components
coulomb scattering (due to ionized impurity)
phonon scattering - almost constant
surface roughness scattering (at Si/SiO2
interface).
At low normal fields
less inversion charge density
ionized impurity scattering dominates and meff
f(NA).
At high normal fields
higher inversion charge density close to the
interface
surface roughness scattering dominates.

97
Inversion Layer Mobility

For higher normal fields universal behavior as a
function of effective normal field
The effective field is a non-local quantity.
Local field mobility models preferred for device
TCAD should produce universal behavior in terms
of the computed effective field.
Example
Lombardi Surface Mobility Model.

98
Inversion Layer Mobility

For ultra-thin gate oxide thickness the inversion
layer carrier wave function can extend through
Si/SiO2 interface to SiO2/polysilicon interface.
Mobility may depend on the surface roughness of
SiO2/polysilicon interface remote interface
roughness scattering.

99
Choice of Surface Mobility Models
100
Inversion Layer Mobility Summary

Mobility is extremely critical for advanced
MOSFET device simulation.
Choice of mobility model can effect simulation
data.
Local field mobility models are being extended
for high normal fields and high doping densities.
New effects may begin to be felt in ultra-thin
oxide devices
Example
remote interface scattering.

101
Quantum Mechanical Confinement

The charges near the silicon surface are confined
to a potential well formed by
oxide barrier
bend Si-conduction
band due to applied
gate potential.
Due to QM confinement of
charges near the surface
energy levels are grouped in discrete energy
sub-bands
each sub-band corresponds to a quantized level
for carrier motion in the normal direction.

102
Quantum Mechanical Confinement

Due to QM confinement the inversion layer
concentration
peaks below the SiO2/Si interface
0 at the interface and is determined by the
boundary condition for the electron wave function.

Dz shift in the centroid of charge in silicon
away from the interface.
Equivalent oxide thickness for Dz is

103
Quantum Mechanical Confinement

Classical
CSi gtgt COX (accumulation / inversion)
Ctotal COX (accumulation / inversion)
Quantum
CSi eSi/Dz
Ctotal lt COX (accumulation / inversion)
Impact of QM confinement
Vth since more band bending is required to
populate the lowest sub-band
TOXeff since a higher VG over-drive is required
to produce a given level of inversion charge
density
Ctotal since TOXeff TOX (eOX/eSi)Dz.

104
QM Confinement Modeling Approach

van Dorts model amount of band-gap widening due
to splitting of energy levels is given by
where
B constant
y distance from Si/SiO2 interface
yref reference distance for the material
En normal electrical field
and

105
QM Confinement Modeling Approach

Modified local density approximation (MLDA)
robust and efficient formulation to compute
quantization of carrier concentration near
Si/SiO2 interface
offers a good compromise between the accuracy and
simulation time
the confined carrier density is given by FD
statistics

106
QM Confinement COX Reduction
Simulation data obtained by simulation program
TSUPREM4
107
QM Confinement TOX Measurement
DTOX º TOXeff - TOX
108
QM Confinement Effect on Vth

Vth increase due to QM effect depends on channel
doping Nch.
Maximum increase in Vth 100 mV for Nch 1x1018
cm-3.

109
QM Confinement Effect on ION

Ion decrease due to QM confinement depends on
Nch.
Maximum drop in Ion 20 for Nch 1x1018 cm-3.

110
QM Confinement Summary

Impact of QM confinement becomes significant for
TOX lt 4 nm.
QM confinement affects
TOX measurement
drive current
scaling limits.
Modeling approaches
semi-physical (e.g. van Dort)
quantum potentials - MLDA
1D self-consistent Schrodinger-Poisson.

111
Discrete Dopant Effects

The volume of active channel region for an
advanced MOSFET
V (W) x (L) x (Xj)
Typically
length L 40 nm
width W 100 nm
junction depth Xj 25 nm
Nchannel 1x1018 cm-3
Ntot 100 impurity atoms.

Þ The number of dopants in V is a statistical
quantity.

112
Discrete Dopant Effects

Effects of discrete dopants
significant threshold (Vth) variation sVth (10s
of mV)
lower average Vth (10s of mV)
asymmetry in drive current IDS.

3D transport leads to inhomogeneous conduction in
sub-100 nm devices.
Continuum diffusion models are inadequate to
model discrete dopant effects in sub-100 nm
MOSFETs.

113
Discrete Dopant Effects Summary

2D continuum models can predict spread in Vth.
Full 3D simulation is necessary to predict mean.
The role of continuum versus granular models will
become increasingly important as devices continue
to shrink.

114
Hot Electron Effects

Effect
hot electron injection.
Outcome
substrate current.
Trends
power supplies are decreasing
electric fields are increasing.

115
Hot-Carrier Effects

Channel electron traveling through high electric
field near the drain end can

become highly energetic i.e. hot
cause impact ionization and generate e- and holes
holes go into the substrate creating substrate
current Isub.
Some channel e- have enough energy to overcome
the SiO2-Si energy barrier generating gate
current Ig.
The maximum e-field Em near the drain has the
greatest control of hot carrier effects.

116
Hot Electron Effects Substrate Current

Local field model (DD)
ec critical electrical field 1.2 MV/cm
a impact ionization coefficient.
calibration of impact ionization model parameters
are required to match silicon data
tuned parameter values can be non-physical and
non-predictive for a new technology.

117
Hot Electron Effects Isub using DD Model

DD simulation results with default Isub model
parameters do not match the measurement data.

118
Hot Electron Effects Substrate Current

Local energy model (HD / ET model)
surface impact ionization
better predictive capability than DD approach
but still uses tuned parameters.
Non-local energy model.
Full band MC.

119
Hot Electron Effects Summary

Local field models are highly unphysical that
result in unphysical calibrated parameters.
Local energy models are more physical but still
require calibration of model parameters.
Physically sound models that provide accurate
results without calibration of model parameters
are
full band MC
non-local energy transport models.

120
Device TCAD Summary

As devices scale down to 0.1 mm and below new
physical effects are coming into play.
Existing tools treat different aspects of device
simulation fairly well.
No single tool treats all of the important
physics.
Successful device TCAD will require a firm grasp
of the controlling device physics.

121
Technology CAD Technology Modeling Device
Design and SimulationIndustry Application
Calibration of Process and Device Models
2004 VLSI Design Tutorial January 5 2004
Mumbai India
122
Outline

Objectives.
Technology and Industry Trends affecting TCAD.
TCAD Challenges.
TCAD Tool Set.
Calibration
Process Models
Device Models.
Mesh Generation.
TCAD in Technology Development.
Summary.

123
Objectives

Present issues and solutions for industrial TCAD
process simulation
calibration
device simulation
key physical models
mesh generation
optimal approach
calibration examples
submicron process
submicron device.

124
Industry Trends affecting TCAD

CMOS logic as technology driver
CMOS logic technology design-space much larger
than that of DRAM or BJT technologies
CMOS logic generation life-span is extremely
short
CMOS simulation is essentially 2D.
Logic technology offerings becoming broader
high-Vth devices
thick-oxide devices
low-Vth devices.

125
Industry Trends affecting TCAD

System-on-a-chip (SOC) and logic derivatives
integration issues driving increasing share of
TCAD cycles
integrating memory and logic (NVRAM DRAM)
BiCMOS
CMOS imaging
SiGe BJT and PFET.
Net result
Rapidly expanding opportunities for TCAD to
contribute.

126
Industry Trends affecting TCAD

Rapid thermal processing (RTP)
easy process addition Þ increases design space
many subtle electrical effects.
Larger wafer sizes
interaction of process variations on circuit
performance becoming increasingly important Þ new
TCAD arena.
New impurity species Þ increase design options
In
Ge
N.

127
Industry Trends affecting TCAD

New materials and methods
nitrided gate oxide
high-K gate dielectric
junction pre-amorphization
SOI
selective epitaxial growth
laser thermal annealing (LTA).
Net result
rapidly expanding design space for TCAD to cover
process TCAD challenges predominate.

128
Industrial TCAD Challenges

Challenge is to transform TCAD potential into
valuable results for process and device
engineers.
Key tasks
system perspective
connect process recipes to device
parametric/circuit performance (virtual fab)
organize TCAD process to make non-experts
productive TCAD users and maximize productivity
of experts
process and device simulations
process simulation reflect actual process results
accurate electrical results for compact model
extraction.

129
Industrial TCAD Challenges

Critical assumptions for success
calibrate/characterize complex physical models
for the present range of operation - global
calibration
timely development/implementation of required
physical models
timely calibration (local calibration) of process
and device models to contribute significantly for
the next generation
technology development
technology transfer.
TCAD usage can be significantly broadened.

130
TCAD Tool Set

Process simulation
2D capability with
extensive detailed physical model set for
implantation diffusion oxidation deposition
and etching
detailed knowledge of model formulation and
modification.
examples based on
vendor supported SUPREM4-process platform
generalized calibration procedure.

131
TCAD Tool Set

Device Simulation
general 2D capability based on moments of
Boltzmann equation
control-volume discretization of DD/HD equations
examples based on
vendor supported MEDICI-device platform
generalized calibration procedure
user environment
vendor supported TWB-framework platform.

132
Calibration - Role of TCAD

TCAD in research
evaluate advanced device options
understand device physics.
TCAD in technology development (TD)
perform tradeoffs for design options to reduce
experimental wafer starts
assess manufacturability and design options
diagnose device/layout problems.
TCAD in manufacturing
process simplification for production
technologies
problem diagnosis and fix.
Accuracy is crucial especially for TD and
manufacturing.

133
Need for Calibration

Deviation of simulation and measured data
technology dependent
different focus area and application
different physical models involved.
site/fab dependent
equipment
material
environment
measurement techniques
human interface.

134
Need for Calibration

Limitation of physical models
secondary mechanisms become important
model dependency on implementation details
model short-fall in describing the target
generation of process technology and devices.
Limitation of model characterization/range
may not cover all possible process conditions
may not cover all technologies
may not be able to measure directly.

135
Calibration Challenges

Experimental data
expensive to obtain especially SIMS profiles
insufficient processing information
statistical fluctuations.
Model complexity
some parameters can not be directly measured
more parameters than data points.
Simulation accuracy
grid dependency
practical limitation on CPU and memory.

136
Objective of Tool Calibration

Device specific calibration
operation region (optimization)
technology development
items of importance.
DOE and characterization.
Calibration of model parameters.
Supporting software utilities.

137
General Calibration Methodology

Use short flows to characterize process profiles
design process splits to cover design space.
Use full flows to characterize devices with
different dimensions (L and W dependencies).
Tool calibration
match SIMS profiles
use device data to correlate 2D effects
match device characteristics.
Two-phase process.

138
Process Simulation Overview

Model calibration for process simulation
overview of calibration process
Phase 1 1D impurity calibration
methodology
example - nMOSFET channel profile
Phase 2 2D calibration (process device)
methodology
example - reverse short channel effect (RSCE).
Summary.

139
Process Modeling Approach

Predictive capability for a wide range of logic
and memory technologies necessitates
new implant tables with new species like In Ge
etc.
3-stream TED model for dopant interstitials and
vacancies
plus-n damage model with accumulated damage
from multiple implants
amorphization due to implant damage
transient activation/deactivation of dopants
dislocation loops as source/sink for
interstitials
3-phase segregation model.

140
Process Simulation Calibration Overview

Model calibration (Phase 1)
implant models
diffusion models
oxidation models
etch/deposition models.
TEM/SEM cross-sections SIMS profiles key (1D)
electrical parameters.
Technology/2D calibration (Phase 2)
key process model parameters
selected set of 2D electrical parameters.

141
MOSFETs Process Model Calibration Flow
142
MOSFETs 1D Process Model Calibration

Cross-section for short loop experiments
A / D Þ NMOS / PMOS channel
B / E Þ NMOS / PMOS SDE
C / F Þ NMOS / PMOS S/D.

143
A Typical Short Loop Experiment for P-Well
144
Calibration Example Channel Profile

Use of detailed physical models to achieve 1D
SIMS profile fit
typical Phase-1 calibration activity
model updated over several technology
generations.
Channel profile after complete technology thermal
cycle.
Initial approach for implant and diffusion
MC implant
significant CPU burden
scaled solid solubility
physics-based implant moments / implant table
update.

145
Example NMOS Channel Profile
146
Technology Calibration - Phase 2

Coupled process and device simulations using
Phase 1 calibration data.
Target output (electrical) parameters
C - V curves
Vth
RSCE.
Input variables (5 - 8 process model parameters)
point-defect distributions from implants
plus-n model
key impurity segregation coefficients
parabolic oxidation rate.

147
2D Calibration Example RSCE
148
Process Modeling Summary

Systematic process model calibration methodology
is critical.
Observed success within a (CMOS) technology
process re-optimization offered a significant
improvement in device performance
process centering achieved at manufacturing
co-location with minimum development effort.
Observation
each successive technology generation requires a
significant calibration effort (model update).

149
Device TCAD

Role of device simulation in TCAD
Key physical models and examples
mobility models for deep sub-micron CMOS
quantum effects in scaled CMOS devices
DD model.
Device model calibration
impact ionization with DD model.
Summary.

150
Device Simulation Role in TCAD

Simulate device electrical behavior with
sufficient accuracy to calibrate process
simulation models
primarily 2D electrostatic simulation
Vth DIBL Ioff body effect capacitances
expect DD model is sufficient for most
requirements for MOSFETs with Leff ³ 0.1 mm.
Provide capability for the physical simulation of
wide range of device parameters
substrate current latch-up ESD and so on.
Support exploratory device simulation for
research.

151
Device Simulation CPU Burden