1. Technology CAD: Technology Modeling, Device Design and Simulation S
Technology CAD: Technology Modeling, Device Design and Simulation S. Saha and B. Gadepally
2004 VLSI Design Tutorial, January 5, 2004
Mumbai, India
S. Saha and B. Gadepally

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 (USA)
2004 VLSI Design Tutorial, January 5, 2004
Mumbai, India
S. Saha and B. Gadepally

3. Technology CAD: Technology Modeling, Device Design and Simulation
Instructor: Dr. Samar Saha
Silicon Storage Technology, Inc.
1171 Sonora Court
Sunnyvale, CA (USA)
2004 VLSI Design Tutorial, January 5, 2004
Mumbai, India
S. Saha and B. Gadepally

4. Tutorial Outline Prof. B. Gadepally: Dr. S. Saha:
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.
S. Saha and B. Gadepally

5. Technology CAD: Technology Modeling, Device Design and Simulation Introduction and Tutorial Overview
2004 VLSI Design Tutorial, January 5, 2004
Mumbai, India
Bhaskar Gadepally

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.
Bhaskar Gadepally

7. Overview of IC Technology
Channel Engineering
- non-uniform channel doping
- Quantum Mechanical effects
- low-diffusivity impurities
- threshold voltage control
Source-Drain Engineering
- ultra-shallow extensions
- low-energy implants
- RTA/LTA techniques
- halo optimization
p-substrate
p-well
n-well n+
PMOS p+
STI
Halo
P+ poly
Spacer
NMOS
(Shallow
Trench
Isolation)
Gate Engineering: Dielectric
- ultra-thin gate oxide
- direct tunneling
- high-k dielectrics
Gate Engineering: Stack
- dual-poly / poly depletion
- work function engineering
- interface properties
N+ poly
Bhaskar Gadepally

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.
Bhaskar Gadepally

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.
Bhaskar Gadepally

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.
Bhaskar Gadepally

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.
Bhaskar Gadepally

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.
Bhaskar Gadepally

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.
Bhaskar Gadepally

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.
Bhaskar Gadepally

15. Session 3: Industry Application - Calibration
Calibration Effort
TD Effectiveness
Low
Moderate
High
No or a limited
calibration only
provides some
physical trends
and is useful
for a first-order
process and
device analysis.
Global calibration
provides higher
accuracy and
predictability of
simulation data.
Local calibration
with the previous
generation of
technology will
provide physical
trends. Absolute
values may not
match real data.
Bhaskar Gadepally

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:
substrate current model
flash memory cell macro-model.
Bhaskar Gadepally

17. Technology CAD: Technology Modeling, Device Design and Simulation Bulk-Process Simulation
2004 VLSI Design Tutorial, January 5, 2004
Mumbai, India
Samar Saha

18. Outline Introduction. Bulk-process Models: Summary. Ion Implantation
Diffusion
Oxidation.
Summary.
Samar Saha

19. Introduction Front-end IC fabrication processes include: p-substrate
p-well
n-well n+
PMOS p+
STI
Gate oxide
Halo
P+ poly
Spacer
N+ poly
NMOS
(Shallow
Trench
Isolation)
Source
Drain
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.
Samar Saha

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.
Samar Saha

21. Ion Implantation Ion Implantation Mechanisms. Ion Implant Models:
Analytical
Monte Carlo (MC).
Implant-induced Damage Modeling.
“Plus-one” Approximation.
Summary.
Samar Saha

22. Ion Implantation
Bombard wafers with energetic ions energy, E 0.5 KeV - 1 MeV > 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.
Ion
Target
Recoil
channeling
Samar Saha

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).
Ion
Target
Recoil
channeling
Samar Saha

24. Ion Energy Loss Mechanisms
Nuclear stopping (Sn(E)):
Deflected
Ion
Target
Recoil q
ion energy loss to target atom by interaction with the electric field of the target atom’s 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.
Samar Saha

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:
Samar Saha

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.
Samar Saha

27. Ion Range Distribution
Samar Saha

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.
Samar Saha

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. x Rp N
Samar Saha

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.
Samar Saha

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.
Samar Saha

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.
Samar Saha

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.
Samar Saha

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.
Samar Saha

35. Ion Channeling in Crystalline Silicon
Along certain angles in crystal, ion may encounter no target atoms.
Ion
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 <110> channels steer Boron ions under MOS gate.
Analytic channeling model is complex.
Samar Saha

36. Ion Channeling in Crystalline Silicon
Samar Saha

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).
Samar Saha

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.
Samar Saha

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 » E » 5 KeV; n » E » 500 KeV
B: n » E » 5 KeV; n » 1.0 for E > 20 KeV
P: n » E » 5 KeV; n » E » 500 KeV.
Samar Saha

40. Ion Implantation: Summary
Ion implantation with ion energy > 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.
Samar Saha

41. Diffusion Fundamentals of Dopant Diffusion Point Defect Model.
Fick’s Laws
Oxidation Enhanced Diffusion (OED)
Oxidation Retarded Diffusion (ORD)
Transient Enhanced Diffusion (TED).
Point Defect Model.
Clusters and Precipitates.
Polysilicon Diffusion.
Impurity Profiling.
Summary.
Samar Saha

42. Fick’s Laws of Diffusion
Fick’s first law:
describes flux (F) through any surface
diffusion is downhill - high ® low concentration, “- sign”
Fick’s second law ® law of conservation of particles
Low concentration diffusion in
silicon is Fickian - each dopant
A satisfies:
(D º diffusivity = constant)
Fin
Fout Dx DC
Samar Saha

43. Concentration-Dependent Diffusion
Typically, intrinsic carrier concentrations (ni) at processing temperatures are high » 1019 cm-3.
For high doping concentrations, C > 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:
Samar Saha

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.
Samar Saha

45. Transient Enhanced Diffusion (TED)
Anomalous displacement of implanted dopants during low temperature anneals.
Reverse temperature effect: displacement larger at lower temperatures - up to mm.
Displacement increases with implant dose and energy.
Corresponds to temporary increase in diffusivity ~ 10,000X.
Implant of one species can drive diffusion of another.
Enhancement is transient.
Spatially non-uniform diffusion enhancements.
Reduced activation.
Samar Saha

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
Samar Saha

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.
Vacancy mechanism
As, Sb
Kick-out mechanism
B, P, In, As, Au, Zn, P
above 900 °C
Frank-Turnbull
mechanism
Zn, below 900 °C
Samar Saha

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.
Samar Saha

49. “Electric-field” Effects
For high doping concentration > 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.
Samar Saha

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.
Samar Saha

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.
Samar Saha

52. Gradient Effects in Transient Diffusion
Dopant flux arises from diffusion of defects-dopant pairs:
boron flux = DBIÑ[BI].
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.
Samar Saha

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.
Samar Saha

54. {311} Cluster Dissolution
{311} defects:
rod-shaped defect clusters condensed from “+1” amount of damaged silicon-I at annealing T > 400 °C
precipitate on {311} planes and extend in the <110> 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.
Samar Saha

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. As V
Samar Saha

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.
Samar Saha

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).
Samar Saha

58. Metrology for Developing Diffusion Models
Spreading resistance profile (SRP) n
1D carrier profiles
good sensitivity
modest depth resolution
carrier spilling
difficult to use for shallow junctions. p
Samar Saha

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.
Samar Saha

60. Monte Carlo Diffusion Methods: Algorithm
Monte Carlo diffusion program (MARLOWE, UT-Austin) offers
accurate diffusion modeling.
MARLOWE
Generates initial I, V positions
THEORETICAL
CALCULATIONS
Energy of interactions
and
diffusion barriers
EXPERIMENTS
MONTE CARLO DIFFUSION CODE
- Diffusion
- Clustering
- I - V recombination
- Surface annihilation
- I, V trapping
- Boron kick-out, kick-in
Samar Saha

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.
Samar Saha

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.
Samar Saha

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.
O2 or H2O ambient
Oxidant
Reaction
zone
Nitride
Silicon
Process is at first limited by reaction but diffusion through growing oxide becomes limiting.
Samar Saha

64. Oxidation: Deal-Grove ModelC0 CL
Silicon
SiO2
Freac = kCL
D = diffusivity of oxidant
CL = concentration at Si-SiO2 interface
C0 = concentration at the SiO2 surface
L = oxide thickness
k = interface reaction rate constant
Samar Saha

65. Oxidation: Deal-Grove ModelC0 CL
Silicon
SiO2
Freac = kCL
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
Samar Saha

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 <111> or <100> oriented silicon substrates.
This model can be found in TCAD tools like SUPREM4.
Samar Saha

67. Oxidation - Planar Growth
Planar growth generates an intrinsic stress in oxide during growth process:
modest stress (3x109 dynes/cm2)
density increases (< 3%)
refractive index increases (1%) relative to fully relaxed oxides.
First oxidation
Second oxidation
1100 °C
800 °C
900 °C
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).
Samar Saha

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.
Samar Saha

69. Oxidation Chemistry
Oxidation rate coefficients are sensitive to ambient additives:
steam times faster than O2
3% Cl2 increases growth rate by %
100 ppm NF2 increases growth rate by 2 - 5
heavy substrate doping increases rate by 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.
Samar Saha

70. Oxide Flow Oxide growing on a curved surface must flow.
Resulting deformations (and stresses) can be large! LOCOS top surface must stretch by %.
Elastic limit of glass << 1%
Silicon
Old Oxide
New Oxide
Si3N4
Silicon
Oxide
Samar Saha

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.
Samar Saha

72. Visco-elastic Model: Stress Simulation
Compression
Tension
SiO2
Si3N4
Oxide stress after local oxidation.
Length of stress vector µ amount of stress.
Samar Saha

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.
Samar Saha

74. Bulk-Process Simulation: Summary
Accurate process models and TCAD tools are extremely critical for continuous scaling of IC’s .
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.
Samar Saha

75. Technology CAD: Technology Modeling, Device Design and Simulation Device Simulation
2004 VLSI Design Tutorial, January 5, 2004
Mumbai, India
Samar Saha

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

77. Quasi-ballistic transport
Introduction
A device TCAD tool solves a set of equations to deal with various physical phenomena in semiconductor devices:
p-substrate
p-well n+
STI
Poly
hot carriers
Non-local transport
(velocity overshoot)
QM tunneling
Electrostatics:
- 2D/3D effects
- discrete charges
Atomic
scale
effects
QM confinement
Surface scattering
Quasi-ballistic transport
Samar Saha

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.
Samar Saha

79. Carrier Transport Models
A device TCAD tool generates device characteristics by solving:
Poisson’s [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.
Samar Saha

80. Carrier Transport Models
The basic concept in transport theory is the carrier distribution function = f(r,px,t).
f(r,px,t) = probability of a carrier at the position r with momentum px at any instant t.
f(r,px,t) is a Maxwellian distribution function with:
area = carrier density, n(r,t)
the spread depends on carrier temperature
f(r,px,t) px
Equilibrium
first moment is velocity
second moment is kinetic energy.
Samar Saha

81. Carrier Transport Models
f(r,px,t) px
Equilibrium
Non-equilibrium ex
At equilibrium, f(r,px,t) 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(r,px,t).
Samar Saha

82. Carrier Transport Models
To solve for f(r,p,t) - 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.
Samar Saha

83. Carrier Transport Models
Solving f(r,p,t), we can find the quantities that device engineers deal with directly such as:
carrier density, n(r,t)
current density, Jn(r,t)
energy current, JE(r,t)
average kinetic energy, un(r,t)
electron temperature, Tn(r,t)
heat flux, Qn(r,t).
Six-dimensional equation is difficult to solve and computationally demanding.
In TCAD, we directly solve for the quantities of interest.
Samar Saha

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.
Examples:
nf = n(x,t): Þ continuity equation.
nf = Jnx(x,t): Þ current equation.
Samar Saha

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.
Samar Saha

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 = m0[N,TL,e(x)]; Dn = (kBTL/q)mn
Then the current equation is given by:
Þ Local field transport model: [mn = f(local field)]
Samar Saha

87. Carrier Transport Models: Drift-Diffusion
DD solution fails to predict device characteristics for small geometry (£ 0.1 mm) MOSFETs.
We know:
here <t> 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 = m0[N,TL,Tn]
Samar Saha

88. Carrier Transport Models: Local Energy
Solve for energy density, nf = W(x,t) = nu:
where tE = relaxation time.
nf = JE(x,t):
Unknowns: e(x), n(x), p(x), un(x), and up(x)
increase in
energy flux
input e-field
rate of energy
dissipation
Samar Saha

89. Carrier Transport Models: DD vs. HD
DD vs. HD model data deviate significantly for 40 nm devices.
Samar Saha

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.
Samar Saha

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
electron r1 r2
r3, r4
Samar Saha

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.
Samar Saha

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 Green’s function approach (Wigner functions, density matrix)
(3) density gradient/QM potential approach
Samar Saha

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.
Samar Saha

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.
universal behavior
Samar Saha

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.
Samar Saha

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.
Samar Saha

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.
p-substrate
p-well n+
STI
NMOS
Poly
Gate Oxide
Electron
wave function
Samar Saha

99. Choice of Surface Mobility Models
Samar Saha

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.
Samar Saha

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.
EC(y)
Depth into Si (y) EF
Energy
Samar Saha

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.
Depth into Si (y)
n(y)
Classical
Quantum Dz
Dz = shift in the centroid of charge in silicon away from the interface.
Equivalent oxide thickness for Dz is:
Samar Saha

103. Quantum Mechanical Confinement
Classical:
CSi >> COX (accumulation / inversion)
Ctotal ~ COX (accumulation / inversion)
Quantum:
CSi ~ eSi/Dz
Ctotal < 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.
Cox
CSi
Vgate
Samar Saha

104. QM Confinement: Modeling Approach
van Dort’s 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,
Samar Saha

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
Samar Saha

106. QM Confinement: COX Reduction
Simulation data obtained by simulation program TSUPREM4
Samar Saha

107. QM Confinement: TOX Measurement
DTOX º TOXeff - TOX
Samar Saha

108. QM Confinement: Effect on Vth
uniform
1e17 GR AR ST
Nch (cm-3)
Transition
depth
1E18
1E17
GR-Graded
Retrograde
AR-Abrupt
Depth
Conventional
Step, ST
Vth increase due to QM effect depends on channel doping, Nch.
Maximum increase in Vth ~ 100 mV for Nch ~ 1x1018 cm-3.
Samar Saha

109. QM Confinement: Effect on IONGR AR ST
1e18
uniform
1e17
Ion decrease due to QM confinement depends on Nch.
Maximum drop in Ion~ 20% for Nch ~ 1x1018 cm-3.
Samar Saha

110. QM Confinement: Summary
Impact of QM confinement becomes significant for TOX < 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.
Samar Saha

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. V
P (NA cm-3)
Source
Drain Xj
Þ The number of dopants in V is a statistical quantity.
Samar Saha

112. Discrete Dopant Effects
Effects of discrete dopants:
significant threshold (Vth) variation, sVth (10’s of mV)
lower average Vth (10’s of mV)
asymmetry in drive current, IDS.
Source
Drain
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.
Samar Saha

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.
Samar Saha

114. Hot Electron Effects Effect: Outcome: Trends: hot electron injection.
substrate current.
Trends:
power supplies are decreasing
electric fields are increasing.
Samar Saha

115. Hot-Carrier Effects
Channel electron traveling through high electric field near the drain end can:
Gate Ig
n+ Drain
n+ Source
Isub m
hole
hot e- l
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.
Samar Saha

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.
Samar Saha

117. Hot Electron Effects: Isub using DD Model
DD simulation results with default Isub model parameters do not match the measurement data.
Samar Saha

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.
Samar Saha

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.
Samar Saha

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.
Samar Saha

121. Technology CAD: Technology Modeling, Device Design and Simulation Industry Application: Calibration of Process and Device Models
2004 VLSI Design Tutorial, January 5, 2004
Mumbai, India
Samar Saha

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.
Samar Saha

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.
Samar Saha

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.
Samar Saha

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.
Samar Saha

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.
Samar Saha

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.
Samar Saha

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.
Samar Saha

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.
Samar Saha

130. TCAD Tool Set Process simulation: 2D capability with examples based on
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.
Samar Saha

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.
Samar Saha

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.
Samar Saha

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.
Samar Saha

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.
Samar Saha

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.
Samar Saha

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.
Samar Saha

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.
Samar Saha

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)
example - reverse short channel effect (RSCE).
Summary.
Samar Saha

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.
Samar Saha

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.
Samar Saha

141. MOSFETs Process Model Calibration Flow
Match SIMS profiles
Adjust for dose loss
Match Vth
RSCE
Two-dimensional Calibration
DIBL
Surface recombination
Damage by S/D implant
One-dimensional Calibration
Implant moments/table
OED
Segregation (set by channel profile)
Diffusivity (in oxide for dose loss)
Tox (QM,Poly-depletion corrections)
Diffusivity of dopant-defect pair
Diffusivity of defects
Samar Saha

142. MOSFETs 1D Process Model Calibration
p-substrate
p-well
n-well n+
PMOS p+
STI
NMOS
A B C
F E D
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.
Samar Saha

143. A Typical Short Loop Experiment for P-Well
Samar Saha

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.
Samar Saha

145. Example: NMOS Channel Profile
P-Well B, 200 KeV
after spacer deposition/etch
Depth (mm)
log10 (Boron)
SIMS
Simulation
Samar Saha

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.
Samar Saha

147. 2D Calibration Example: RSCE
Samar Saha

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).
Samar Saha

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.
Samar Saha

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.
Samar Saha

151. Device Simulation: CPU Burden
Numerical issues associated with device simulation are well established:
core issue is repeated solution of large, sparse, ill-conditioned, non-symmetric sets of linear equations
typical industrial CMOS problem:
~ 10,000 mesh nodes
simultaneous solution for (y, n, p)
iterative solution methods often exhibit lack of convergence on problems of industrial interest.
Optimized direct solution methods along with optimal mesh generation techniques can reduce CPU burden significantly without sacrificing accuracy.
Samar Saha

152. Critical TCAD Models: Carrier Mobility
Device-design trends arising from CMOS scaling require consideration of:
coulombic scattering in the inversion layer
high substrate/channel doping levels
channel doping can vary significantly across the device
inversion- and accumulation-layer mobility.
Industrial use of a mobility model requires:
strictly local calculation of mobility
minor increase in program complexity
no restrictions on device geometries or device designs.
Samar Saha

153. Critical Device TCAD Models: QM Effects
CMOS scaling requires inclusion of inversion-layer QM effects in device simulation for:
thinner gate oxides
higher substrate doping.
Inversion-layer QM correction model must be:
strictly local calculation of required physical quantities
minor increase in program complexity
no restrictions on device geometries or device designs
acceptable CPU burden
no significant degradation in robustness.
Models: van Dort / MLDA.
Samar Saha

154. MOSFETs: Device Model Calibration Flow
Work function
QM model
Low field mobility
High field mobility
Band to band tunneling
Impact Ionization
IDS vs. VGS (Vth)
@ VBS = 0,VDS = 50 mV
Isub vs. VGS
@ VBS = 0,VGS = 0
IDS vs. VGS (IDS vs. VDS)
@ VBS = 0,VDS = VDD
IDS vs. VDS
Samar Saha

155. Example: Impact Ionization Model
DD-simulation over estimates Isub by more than an order.
Samar Saha

156. Example: Impact Ionization Model
Impact Ionization model calibration:
used calibrated process model (technology calibration)
used calibrated device models (device calibration)
calibrate impact ionization coefficients.
The electron impact ionization rate:
where
Ai and Bi are empirical constants
Eeff = effective electric field due to non-local effect.
Samar Saha

157. Example: Impact Ionization Model
For DD, transform the model in terms of local electric field, E. Assume, Eeff a E,
Eeff = k * Eh
where
k and h are constants depending on the spatial variation of E near the drain-end of the channel.
Substituting for Eeff and defining Bi º k * bih, the modified impact ionization coefficient is:
\Optimize bi and h to fit the measurement data.
Samar Saha

158. Example: Impact Ionization Model
Calibrate device TCAD models: comparison of I - V data.
Samar Saha

159. Example: Impact Ionization Model
Simulation with calibrated impact ionization coefficients.
Samar Saha

160. Example: Impact Ionization Model
Simulation with calibrated impact ionization coefficients.
Samar Saha

161. Device TCAD: Summary
Vendor supported device TCAD tools work very well with the present applications such as:
MOSFET I - V and C - V characteristics for technology development
logic
DRAM.
Model selection and calibration show good results for sub-0.25 mm technology development.
Device TCAD effectiveness depends on:
mobility model suitable for the target technology
inversion-layer QM effects.
Samar Saha

162. Mesh Generation for Simulation
Role and Requirements.
Methods:
structured
quadtree
unstructured
hybrid.
Example:
typical MOSFET mesh and gridding considerations.
Summary.
Samar Saha

163. Mesh Generation: Role and Requirements
Requirement is to support complete automation of process-to-device simulation transition:
highest barriers to expanded TCAD usage are
mesh generation
process simulation accuracy.
Consistent and specialized grid distribution is an important key to simulation of high-performance MOSET devices:
resolution of inversion layers and depletion regions
resolution of mobility-model physical effects.
Samar Saha

164. Mesh Generation: Role and Requirements
must accept device structures from detailed process simulation
no restrictions on device structures
mesh generation approach must minimize computational burden without compromising solution robustness and accuracy
key:
anisotropic grid-point distributions (the capability of supporting extreme differences in grid-point spacing in x- and y-directions).
Samar Saha

165. Mesh Generation Methods
Samar Saha

166. Hybrid Mesh Generation: Half-MOSFETx y
Gate
S/D
Channel
Source/Drain
Samar Saha

167. Mesh Generation
Dependence of device performance on vertical grid-spacing.
Samar Saha

168. Mesh Generation
Dependence of device performance on horizontal grid-spacing.
Samar Saha

169. Mesh Generation: Summary
Mesh generation is the critical component of an effective TCAD system.
Simulation results vary significantly on mesh and may result in:
unphysical calibration parameters
unpredictable/inconsistent results.
Robust mesh:
allows process simulators to be consistently and robustly linked to device simulators by non-experts
significantly reduces CPU burden for device simulation.
Samar Saha

170. Industry Application: Summary
Vendor supported TCAD tools offer most simulation capabilities for industrial usage.
Systematic calibration procedure is required to support efficient:
process technology optimization
future technology development.
Mesh generation is crucial for predictive technology simulation.
Well calibrated physical models provide efficient predictive TCAD capability.
Samar Saha

171. Technology CAD: Technology Modeling, Device Design and Simulation Industry Application: TCAD in Device Research and Compact Modeling
2004 VLSI Design Tutorial, January 5, 2004
Mumbai, India
Samar Saha

172. Research Application: Overview
Role of TCAD in device research:
how it differs from development/manufacturing.
examples
sub-100 nm MOSFET device design
design optimization of FinFETs.
TCAD for compact modeling:
TCAD-based compact model parameter extraction for substrate current modeling
flash memory cell macro model.
Summary.
Samar Saha

173. Role of TCAD in Research
Performance analysis of future device design options to guide development effort.
Understand device physics for new device concepts.
Typically, research TCAD is not the “virtual fab” paradigm:
process simulation is not used, since device cannot be made with current process technologies.
Circuit performance is directly evaluated from the output of device simulation using two different ways:
device simulation Þ model extraction Þ circuit simulation
mixed-mode device/circuit simulation.
Samar Saha

174. Example: Sub-100 nm MOSFET Design
Design issues in achieving MOSFET devices near the lower limit of channel length:
scaling requirements
material limitations of scaling
feasibility of continuous scaling.
Methodology to generate sub-100 nm MOSFET device characteristics vs. scaling parameters.
Results and discussions.
Summary.
Samar Saha

175. Scaling Requirements vs. Limitations
Samar Saha

176. Feasibility of Continuous TOX and Xj Scaling
Scaling Tox(eff) < 2 nm is feasible with a high-K dielectric gate material to maintain:
a thicker value of TOX(physical) for a tolerable value of Lg
a target value of gate capacitance (COX) equivalent to that of an ultra-thin SiO2 gate material.
Scaling Xj < 30 nm is essential to:
scale down Lg, gate area, and COX
improve ac device performance.
Samar Saha

177. Idealized Device Simulation Structure
Leff
Halo
Xjd Xj
DSD
SDE
Lext
TOX Lg
Body (B)
Poly-Si gate
Spacer
Channel doping profile: vertically and laterally non-uniform.
SDE: heavily-doped source-drain extension regions with junction depth Xj.
DSD: heavily-doped deep source-drain of junction depth Xjd.
Halo: channel-type doping around SDE regions.
Samar Saha

178. Design Simulation Experiment
Designed CMOS technologies for Leff = 25 nm with:
{Lg = 40 nm, 14 nm, Tox(eff) = {1,1.5, 2} nm}
{Lg = 50 nm, 20 nm, Tox(eff) = {1,1.5, 2} nm}
{Lg = 60 nm, 26 nm, Tox(eff) = {1,1.5, 2} nm}.
For each technology:
non-uniform vertical channel doping profile was optimized for the target long channel 0.23 V
two halo profiles (double halo architecture) were used to
reduce DIBL from both SDE and DSD regions
achieve non-uniform lateral channel doping profile with the target 10 |VDD| = 1 V.
Samar Saha

179. Simulation Strategy Optimized technology parameters:
SDE peak 2.5x1020 cm-3
DSD peak 3.7x1020 cm-3
peak halo 5x x1019 cm-3.
Channel concentration ® dependent on Lg.
Device characteristics were generated using MEDICI with:
hydrodynamic model for semiconductors
van Dort’s Quantum Mechanical model
calibrated device models (global calibration!!).
Samar Saha

180. Simulated Channel Doping ContoursLg
Samar Saha

181. Simulated Vth vs. Leff for different TOX(eff)
|Vth| increases with the increase in TOX(eff) for all devices.
Devices with Leff = 25 nm and TOX(eff) = 2 nm, |Vth| > 0.4 V is too high for high-performance |VDD| £ 1 V.
TOX(eff) < 2 nm offers lower |Vth| for low power operation.
Samar Saha

182. Simulated IDSAT vs. Ioff for different TOX(eff)
Devices with 10 nA/mm represents Leff = 25 nm.
At a constant |Ioff| ³ 2 nA/mm:
|IDSAT| increases as TOX(eff) decreases
TOX(eff) < 2 nm is essential to improve IDSAT for Leff = 25 nm devices.
Samar Saha

183. Simulated I - V Data for TOX(eff) = 1 nm
For a typical 50 nm technology with Leff = 25 nm and Tox(eff) = 1 nm:
80 mV/decade
60 mV
680 mA/mm, 275 |VGS| = 1 V = |VDS|.
Samar Saha

184. Simulated I - V Data for TOX(eff) = 1.5 nm
For 25 nm devices of a 50 nm CMOS technology, as Tox(eff) increases from 1 nm ® 1.5 nm:
S increases 8 mV/decade]
DIBL increases 30 mV]
|IDSAT| decreases 102 mA/mm; 42 mA/mm].
Samar Saha

185. Simulated I - V Data for TOX(eff) = 2 nm
For 25 nm devices of a 50 nm CMOS technology, as Tox(eff) increases from 1 nm ® 2 nm:
S increases 16 mV/decade]
DIBL increases 60 mV]
|IDSAT| decreases 214 mA/mm; 72 mA/mm].
Samar Saha

186. Simulated Vth vs. Xj for Different TOX(eff)
Samar Saha

187. Simulated IDSAT vs. Xj for Different TOX(eff)
Samar Saha

188. Simulated DIBL vs. Xj for Different TOX(eff)
Samar Saha

189. Simulated S vs. Xj for Different TOX(eff)
Samar Saha

190. Simulated Delay for Different Xj and Lg
Samar Saha

191. Sub-100 nm MOSFET Design: Summary
The simulation results show the feasibility of 25 nm MOSFETs with:
TOX(eff) < 2 nm to
maintain lower |Vth| for |VDD| £ 1 V operation
achieve higher |IDSAT| for a target value of |Ioff|
lower value of DIBL
lower value of 80 mV/decade
Xj < 30 nm to
scale Lg < 60 nm
improve device speed.
25 nm devices with 14 nm and 40 nm show a significant improvement in speed.
Samar Saha

192. Example: Double Gate MOSFET Design
Design FinFET (double-gate MOSFET) Simulation Structure.
Optimize Different Fin-dimensions.
Feasibility of 20 nm FinFET Device.
Comparison of 20 nm Device Performance using FinFET vs. Conventional MOSFET Architecture.
Summary.
Samar Saha

193. Idealized Double Gate MOSFET Structure
Tox
TSi
Source
Drain
Top Gate
Bottom Gate Lg
Tox = Top/bottom gate oxide thickness.
TSi = Un-doped/lightly-doped channel width.
Lg = Channel length.
Samar Saha

194. Simulated DG-MOSFET FinFET Structure
Hfin Lg
Samar Saha

195. Major Process Steps to Generate FinFETs
1. Define Si-Fin
2. Gate oxidation
3. Poly-Si gate
4. Nitride spacer
S/D implant
5. Half-structure
6. Full-structure
Oxide
Si-Fin
BOX
Nitride
Poly
Samar Saha

196. Critical Parameters for FinFET Simulation
Parameters used for simulation structure design:
Tfin = 10 to 30 nm
Hfin = 50 nm
Lg = 10 to 50 nm
Tox = 1.5 nm.
For device simulation, channel doping was optimized to obtain 0.1 V for Lg = 20 nm nFinFETs.
Device structures and the characteristics were generated using 3D-simulation tool Taurus (from Synopsys).
Samar Saha

197. Vth vs. Lg for Different Tfin; Hfin = 50 nm
Samar Saha

198. IDSAT vs. Lg for Different Tfin; Hfin = 50 nm
Samar Saha

199. S vs. Lg for Different Tfin; Hfin = 50 nm
Samar Saha

200. I - V Characteristics of 20 nm FinFETs
Samar Saha

201. FinFETs vs. Conventional MOSFETs
20 nm FinFETs show superior device performance compared to 20 nm conventional MOSFETs.
Samar Saha

202. FinFET Design: Summary
TCAD is used to design and study FinFET device characteristics.
The simulation data for nFinFETs with 10 nm < Lg < 50 nm and Hfin = 50 nm show:
higher Vth roll-off as Lg decreases for thicker Tfin devices
lower IDSAT in thinner Tfin devices due to higher s/d resistance
increase in S with decrease in Lg for Tfin < 50-nm
S ® 60 mV/decade for all Tfin with Lg >>40-nm.
20 nm FinFETs show superior device performance than 20 nm conventional bulk-MOSFETs.
Samar Saha

203. Example: Compact Model Extraction for Isub
Procedure for TCAD-based Compact Model Parameter Extraction.
Simplification of Isub Model for TCAD-based Compact Modeling.
Model Extraction.
Model Verification.
Summary.
Samar Saha

204. Substrate Current, Isub Model
Isub generated due to impact ionization is given by:
where
Ai and Bi are impact ionization parameters
lc = characteristic length of saturation region
Em = maximum lateral electric field near the drain
Ec = critical electric field for velocity saturation.
Samar Saha

205. Substrate Current, Isub Model
At strong inversion (VDS >> VDSAT) Em is given by:
where
Leff = effective channel length of device
Vth = threshold voltage of device.
Samar Saha

206. Substrate Current, Isub Model
The bias dependence of Ec is given by:
Ec = Ec0 + EcgVGS + EcbVBS
where Ec0, Ecg, and Ecb are model parameters given by:
Ec0 = VGS = VBS = 0
Ecg = slope of Ec vs. VGS VBS = constant
Ecb = slope of Ec vs. VBS VGS = constant
The bias dependence of lc is given by:
lc = (lc0 + lc1VDS)ÖTOX
here lc0 and lc1 are model parameters.
Samar Saha

207. Isub Model Parameters Empirical constants:
Ai = 1.65x106 (1/cm)
Bi = 1.66x106 (V/cm)
Technology dependent parameters:
Ec0 = bias independent constant (V/cm)
Ecg= gate bias dependent parameter (1/cm)
Ecb = back-gate bias dependent parameter (1/cm)
lc0 = bias independent constant (Öcm)
lc1 = bias dependent constant (Öcm/V).
We assume, lc = lc0 is a technology dependent constant for TCAD-based parameter extraction (i.e. ignore lc1).
Samar Saha

208. TCAD-based Isub Model Extraction
VDSAT extraction
Ec extraction
lc extraction
SPICE simulation
Format I - V data
Compute Isub/IDS
Device
Simulation
Device Model
Calibration
At each VGS, generate:
IDS - VDS and Isub - VDS
Process
Process Model
Generate:
Device Structure
Extraction of
{Ec0, Ecg, Ecb}
Samar Saha

209. Parameter Extraction: VDSAT
VDSAT is extracted by mapping constant Isub/IDS contours on IDS vs. VDS family of simulated curves.
Samar Saha

210. Parameter Extraction: Ec0, Ecg, and Ecb
Ec0 and Ecg extraction:
extract VDSAT for different values of VGS at VBS = 0.
compute Ec from:
plot Ec vs. VGS to extract:
Ec0 = VGS = 0
Ecg = slope.
Same procedure to extract Ecb with VBS ¹ 0.
Samar Saha

211. Parameter Extraction: lc and Components
The simplified from of the expression:
log(Y) = mX + C,
where
X = 1/(VDS - VDSAT)
Y = Isub/[IDS(VDS - VDSAT)]
Parameters are extracted from log(Y) vs. X plots:
slope, m = - Bi lc
intercept, C = ln(Ai/Bi).
Samar Saha

212. Parameter Extraction: lc and Components
Samar Saha

213. TCAD-based Isub Models
For nMOSFET devices of the target technology:
Ec0 = 5.50E+04 (V/cm)
Ecg = 3.50E+03 (1/cm)
lc = 1.38E-05 (cm)
Ai = 1.65E+06 (1/cm)
Bi = 1.66E+06 (V/cm)
Samar Saha

214. Model Verification
Measurement and simulation data using the extracted models.
Samar Saha

215. Model Verification
Measurement and simulation data using the extracted models.
Samar Saha

216. Model Extraction for Isub: Summary
The example shows the basic idea to use TCAD for compact model parameter extraction using:
calibrated process models for process TCAD
calibrated device models for device TCAD
simplified equations and extraction routines, as needed.
Process and device models were calibrated for the target technology.
Isub model is simplified to extract model parameters.
The simulation data using TCAD-based model agree very well with the measurement data.
Samar Saha

217. Example: Flash Memory Cell - Macro Model
Flash Memory Cell Compact Modeling
split gate cell
two-transistor macro model
necessity for TCAD-based macro model.
Model extraction.
procedure.
Samar Saha

218. Flash Memory Cell - Split Gate Structure
Cell consists of:
WL transistor
FG transistor.
FG may not have contact pad for measurement.
Typically, 1T-cell model is used.
2T-model provides more accurate cell characteristics.
TCAD-based.
Samar Saha

219. Flash Memory Cell: TCAD-based Model
Calibrated
Device Model
Process Model
Extract SPICE
Model for T1
Model for T2
Model Verification
Simulate
I - V for T1
Test Structures
SPICE/Circuit
Simulation
Generate
Macro Model
I - V for T2
Samar Saha

220. TCAD in Research & Modeling: Summary
Device TCAD can be successfully used in device research to:
study different device options
examine new device ideas
optimize device design range for technology development guideline.
Calibrated TCAD models can be used accurately to:
predict device performance
extract compact model
predict circuit performance.
Samar Saha

221. References
[1] J.D. Plummer et al., Silicon VLSI Technology - Fundamentals, Practice and Modeling. Prentice Hall, New Jersey, 2002.
[2] S. Tian, “Predictive Monte Carlo ion implantation simulator from sub-keV to above 10 MeV,” J. Appl. Phys., vol. 93, No. 10, p 5893, 2003.
[3] S. Furukawa et al., “Theoretical considerations on lateral spread of implanted ions,” Jap. J. Appl. Phys., vol. 11, p 134, 1992.
[4] S. Hobler and S. Selberherr, “Two-dimensional modeling of ion implantation induced point defects,” IEEE Trans. Computer-Aided Design, vol. 7, p 174, 1998.
[5] L. Pelaz et al., “Modeling of the ion mass effect on transient enhanced diffusion: deviation from ‘+1’ model,” Appl. Physics. Lett., vol. 73, p 1421, 1998.
[6] S. Chakravarthi and S.T. Dunham, “Influence of extended defect models on prediction of boron transient enhanced diffusion,” in Silicon Front End Technology - Materials Processing and Modeling, N. Cowern, P. Griffin, D. Jacobsen, P. Packan, and R. Webb, eds. (Mat. Res. Soc. Proc. vol. 532, Pittsburgh, PA, 1998).
Samar Saha

222. References
[7] P.M. Fahey et al., “Point Defects and Dopant Diffusion in Silicon,” Rev. Modern Physics, vol. 61, p. 289, 1989.
[8] A. S. Grove, Physics and Technology of Semiconductor Devices. John Wiley & Sons, New York, 1967.
[9] H.Z. Massoud et al., “Thermal Oxidation of Silicon in Dry Oxygen: Growth-Rate Enhancement in the Thin Regime I. Experimental Results, II Physical Mechanisms,” J. Electrochem. Soc., vol. 132, p and 2693, 1985.
[10] F. Nouri et al., “Optimized shallow trench isolation for sub-0.18 mm technology,” Proc. SPIE Conf. on Microelectronic Device Technology, vol. 3506, p. 156, 1998.
[11] TSUPREM4, Synopsys Corp., Mountain View, CA.
[12] H. Kosina et al., Device modeling for the 1990’s,” Microelectron. J., vol. 26, p. 217, 1995.
[13] S.E. Laux and M.V. Fischetti, “Transport models for advanced device simulation-truth or consequences?,” BCTM Tech. Dig., 1995.
Samar Saha

223. References
[14] M.K. Ieong and T.W. Tang, “Influence of hydrodynamic models on the prediction of semiconductor device characteristics,” IEEE-TED, vol. 44, p. 2242, 1997.
[15] M.S. Lundstrom, Fundamentals of carrier transport, 2nd edition Cambridge University Press, 2000.
[16] M.N. Darwish et al., “An improved electron and hole mobility model for general purpose device simulation,” IEEE-TED, vol. 44, p. 1529, 1998.
[17] D. Vasileska et al., “Scaled silicon MOSFETs: Degradation of the total gate capacitance,” IEEE-TED, vol. 44, p. 584, 1997.
[18] C. Rafferty et al., “Multi-dimensional quantum effect simulation using a density-gradient model and script-level programming techniques,” Simulation of Semiconductor Process and Devices, K.De Meyer and S Biesemans (eds.), p. 137, 1998, Springer-Verlag.
[19] M.J. van Dort et al., “A simple model for quantization effects in heavily-doped silicon MOSFETs at inversion conditions,” Solid-St. Electron., vol. 37, p. 411, 1994.
Samar Saha

224. References
[20] P. Vande Voorde et al., “Accurate doping profile determination using TED/QM models extendible to sub-quarter micron nMOSFETs,” IEDM Tech. Dig., p. 811, 1996.
[21] S. Selberherr, “MOS device modeling at 77K,” IEEE-TED, vol. 36, p.1464, 1989.
[22] S. Saha, “Effects of inversion layer quantization on channel profile engineering for nMOSFETs with 0.1 mm channel lengths,” Solid-State Electron., vol. 42, p. 1985, 1998.
[23] S. Saha et al., “Effects of inversion layer quantization and polysilicon gate depletion on tunneling current of ultra-thin SiO2 gate material,” Mater. Res. Soc. Symp. Proc., vol. 567, p. 275, 1999.
[24] P. Wong and Y. Taur, “Three-dimensional atomistic simulation of discrete random dopant distribution effects in sub-0.1 mm MOSFETs,” IEDM Tech. Dig., p. 705, 1993.
[25] P.A. Stolk et al., “Modeling statistical dopant fluctuations in MOS Transistors,” IEEE-TED, vol. 45, p. 1960, 1998.
Samar Saha

225. References
[26] S.E. Laux and M.V. Fischetti, “The physics of hot-electron degradation of Si MOSFETs: can we understand it?,” App. Surf. Sci., vol. 39, p. 578, 1989.
[27] C. Jungemann et al., “Is physically sound and predictive modeling of NMOS substrate currents possible?,” Solid-St. Electron., vol. 42, p. 647, 1998.
[28] S. Saha et al., “Impact ionization rate of electrons for accurate simulation of substrate current in submicron devices,” Solid-State Electron., vol. 36, p. 1429, 1993.
[29] R.W. Dutton and Z. Yu, Technology CAD: Computer simulation of IC processes and devices. Kluwer, 1993.
[30] S. Selberherr, Analysis and simulation of semiconductor devices. Springer-Verlag, 1984.
[31] N. Arora, MOSFET models for VLSI circuit simulation – theory and practice. Springer-Verlag, 1993.
[32] S. Saha, “Managing technology CAD for competitive advantage: An efficient approach for integrated circuit fabrication technology development,” IEEE Trans. Eng. Manage., vol. 46, p. 221, 1999.
Samar Saha

226. References
[33] S. Saha, “Improving the efficiency and effectiveness of IC manufacturing technology development,” in Technology and Innovation Management, D.F. Kocaoglu, T.R. Anderson, D.Z. Milosevic, K. Niwa, and H. Tschirky (eds.), Portland, OR: PICMET 1999, p. 540, 1999.
[34] S. Saha, “Technology CAD for integrated circuit fabrication technology development and technology transfer,” in Proc. SPIE Conf. on Design and Process Integration for Microelectronic Manufacturing II, vol. 5042, p. 63, 2003.
[35] C.V. Mouli, “Models and methods: Effective use of technology-computer aided design in the industry,” J. Vac. Sci. Tech. B., vol. 18, p. 354, 2000.
[36] C. Lombardi et al., “A physically based mobility model for numerical simulation of non-planar devices,” IEEE Trans. Computer-Aided Design., vol. 17, p. 1164, 1988.
[37] S. Saha, “MOSFET test structures for two-dimensional device simulation,” Solid-State Electron., vol. 38, p. 69, 1995.
[38] O.C. Zienkiewcz, The Finite Element Method, McGraw-Hill, 1977.
Samar Saha

227. References
[39] S. Saha, “Scaling considerations for high performance 25 nm metal-oxide-semiconductor field-effect transistors,” J. Vac. Sci. Tech.. B, vol. 19, p. 2240, 2001.
[40] S. Saha, “Design considerations for 25 nm MOSFET devices,” Solid-State Electron., vol. 45, p. 1851, 2001.
[41] C.C. Hu, “FinFET – a device for nanoscale IC (NSI),” in IEEE Silicon Nanoelectronics Workshop Digest, p. 1, 2002.
[42] S. Saha, “Device characteristics of sub-20 nm silicon nanotransistors,” in Proc. SPIE Conf. on Design and Process Integration for Microelectronic Manufacturing II, vol. 5042, p. 172, 2003.
[43] G. Pei et al., “FinFET design consideration based on 3-d simulation and analytical modeling,” IEEE Trans. Electron. Dev., vol. 49, p.1411, 2002.
[44] TAURUS, Synopsys Corp., Mountain View, CA.
[45] MEDICI, Synopsys Corp., Mountain View, CA.
[46] S. Saha, “Extraction of substrate current model parameters from device simulation,” Solid-State Electron., vol. 37, p. 1786, 1994.
Samar Saha