slides (pdf)

Ab-initio Assisted Process and Device
Simulation for Nanoelectronic Devices
As impl.
SIMS
Model
800 o C
20 min
Wolfgang Windl
MSE, The Ohio State University, Columbus, OH, USA
Computational Materials Science and Engineering
I
V

Insulator
(SiO 2 )
+
+
Source
+
-
P +
N: e - , e.g. As
(Donor)
-
Semiconductor Devices – MOSFET
Metal Oxide Semiconductor Field Effect Transistor
+
+
+
-
-
-
0V G
Gate
(Me)
Channel
-
N
Doping:
-
-
-
+
+
+
+
+
Si
Spacer
P: holes, e.g. B
(Acceptor)
-
+
Drain
+ +
+ P +
+
-
– V D
Source
+ P +
Computational Materials Science and Engineering
+
+
+
+ +
-
Gate
N
+
Drain
+ +
+ P
+
+ + +
+
+
+
+
+
+
-
- -
+
+
+ +
+
+
+ +
-
-
- -
-
-
– V G
I D
-
Si
– V D
• Analog: Amplification
• Digital: Logic gates
-

1. Semiconductor Technology Scaling
– Improving Traditional TCAD
• Feature size shrinks on average by 12% p.a.; speed ∝ size
• Chip size increases on average by 2.3% p.a.
Overall performance: ↑ by ~55% p.a. or
~ doubling every 18 months (“Moore’s Law”)
Computational Materials Science and Engineering

Semiconductor Technology Scaling
– Gate Oxide
Gate oxide
(SiO 2 )
+
+
Source
+
-
P +
-
+
+
Gate
(Me)
Channel
+
Drain
+ +
+ P +
Computational Materials Science and Engineering
+
-
-
-
0V G
-
-
N
-
-
+
+
+
+
+
Si
-
+
-
– V D
C = ε A/d
+
+
+
+ +
-
Bacterium
Virus
Protein
molecule
Atom

Role of Ab-Initio Methods on Nanoscale
1. Improving traditional (continuum) process
modeling to include nanoscale effects
– Identify relevant equations & parameters (“physics”)
– Basis for atomistic process modeling
(Monte Carlo, MD)
2. Nanoscale characterization
= Combination of experiment & ab-initio calculations
3. Atomic-level process + transport modeling
= structure-property relationship (“ultimate goal”)
Computational Materials Science and Engineering

1. “Nanoscale” Problems – Traditional MOS
What you expect:
Intrinsic diffusion
dC
dt
( D ∇ )
B = ∇ C B B
What you get:
•fast diffusion
(TED)
•immobile peak
•segregation
800 °C
20 min
800 °C
20 min
Computational Materials Science and Engineering
800 °C
1 month
Active B¯

Bridging the Length Scales: Ab-Initio to Continuum
dC
dt
D
K
I
r
I
2
I
=
=
∝
D
∇
0
I
D
I I2
( D ∇C
)
I
exp
a
I
2
I
I
( − E / kT )
exp
C
( I
E / kT )
2
Computational Materials Science and Engineering
m
−
− 2K
b
f
I
2
2
I
+ 2K
Need to calculate: ? Diffusion prefactors (Uberuaga et al., phys. stat. sol. 02)
r
I
2
C
? Migration barriers (Windl et al., PRL 99)
? Capture radii (Beardmore et al., Proc. ICCN 02)
? Binding energies (Liu et al., APL 00)
I
2
+

2. The Nanoscale Characterization Problem
• Traditional characterization techniques, e.g.:
– SIMS (average dopant distribution)
– TEM (interface quality; atomic-column
information)
• Missing: “Single-atom” information
– Exact interface (contact) structure (previous; next)
– Atom-by-atom dopant distribution (strong V T shifts)
• New approach: atomic-scale characterization
(TEM) plus modeling
Computational Materials Science and Engineering

Buczko et al.
Abrupt vs. Diffuse Interface
Abrupt Graded
Si 0
Si 2+
Si 4+
Si 0
Si 1,2,3+
Si 4+
How do we know? What does it mean?
Computational Materials Science and Engineering

0.1 nm
Scanning
Probe
EELS
Spectrometer
Atomic Resolution Z-Contrast
GaAs
Imaging
Computational Materials Science and Engineering
Z=31 Z=33
Ga
As
1.4Å

intensity (a.u.)
70
60
50
40
30
20
10
0
0
ZERO
LOSS
Electron Energy-Loss Spectrum
x25
VALENCE
LOSS
x500 x5000
optical properties
and
electronic structure
Si-L
bonding and
oxidation state
CORE
LOSS
C-K
silicon with
surface oxide and
carbon contamination
concentration
100 200 300 400 500
energy loss (eV)
Computational Materials Science and Engineering
O-K
CB
VB
Core hole
⇒ Z+1

Theoretical Methods
ab initio Density Functional Theory
plus LDA or GGA
implemented within
pseudopotential
and
full-potential (all electron) methods
Computational Materials Science and Engineering

site and
momentum
resolved
DOS
Si-L 2,3 Ionization Edge in EELS
energy
ground state of Si atom
with total energy E 0
conduction band minimum
EF 2p 3/2
2p 1/2
2s 1/2
1s 1/2
Computational Materials Science and Engineering
excited Si atom
with total energy E 1
~ 90eV ~ 115eV
2p 6
2p 5
Transition energy E T 1 0 = E - E0 E
ET = ~100 eV

Calculated Si-L 2,3 Edges at Si/SiO 2
0.8
0.4
0
0.6
0.2
1.2
0.4
0
1
0.5
0
Si
Si 2+
Si 4+
Si 1+
Si 3+
100 104
Energy-loss, eV
108
Computational Materials Science and Engineering

0.5 nm nm
Si
Combining Theory and Experiment
Calculation of EELS Spectra from Band Structure
Intensity
Si - L 2,3
100 105 110
Energy-loss (eV)
Computational Materials Science and Engineering

0.5 nm nm
Si
Combining Theory and Experiment
Calculation of EELS Spectra from Band Structure
Intensity
Si - L 2,3
100 105 110
Energy-loss (eV)
Computational Materials Science and Engineering
4
3
2
1
Fractions
.74
Si 0 Si 1+ Si 2+ Si 3+ Si 4+
⇒ “Measure” atomic structure of amorphous materials.

Band Line-Up Si/SiO 2
Real-space band structure:
•Calculate electron DOS
projected on atoms
•Average layers
⇒ Abrupt would be better!
Is there an abrupt
interface?
Lopatin et al., submitted to PRL
Computational Materials Science and Engineering
n
=
N
0
exp
⎛ EC
− E
⎜ −
⎝ k T B
F
⎞
⎟
⎠

• Yes!
Interfaces with Different Abruptness:
• Ge-implanted sample
from ORNL (1989).
• Sample history:
Si/SiO 2 vs. Si:Ge/SiO 2
• Ge implanted into Si
(10 16 cm -2 , 100 keV)
• ~ 800 o C oxidation
Computational Materials Science and Engineering
Initial Ge distribution
~120 nm
~4%

Intensity
Z-Contrast Ge/SiO Interface
2
1 2 3 4 5 6 nm
Si Ge
SiO2 Computational Materials Science and Engineering
• Ge after
oxidation
packed into
compact layer,
~ 4-5 nm wide
• peak ~100% Ge

Kinetic Monte Carlo Ox. Modeling
Simulation Algorithm for oxidation of Si:Ge:
– Si lattice with O added between Si atoms
– Addition of O atoms and hopping of Ge positions
by KMC*
– First-principles calculation of simplified energy
expression as function of bonds:
E
[ ]
eV
=
− 2.
71
− 7.
07
SiSi
GeOGe
GeGe
SiOSi
Windl et al., J. Comput. Theor. Nanosci.
Computational Materials Science and Engineering
n
n
− 2.
23
n
− 8.
94
n
− 2.
47
n
−8.
05
SiGe
n
SiOGe
*Hopping rate Ge: McVay, PRB 9 (74); ox rate SiGe: Paine, JAP 70 (91).

Monte Carlo Results - Animation
• O
• Ge
Si not shown
2×4×22 nm 3
Concentration (cm -3 )
Computational Materials Science and Engineering
Depth (cm)
Ge conc.
O conc.

Monte Carlo Results - Profiles
Initial Ge distribution 25 min, 1000 o C
oxide
Computational Materials Science and Engineering

0.5 nm
Si
Intensity
Si/SiO vs. Ge/SiO 2 2
Atomic Resolution EELS
Si - L 2,3
100 105 110
Energy-loss (eV)
0.5 nm
S. Lopatin et al., Microscopy and Microanalysis, San Antonio, 2003.
Si - L 2,3
Ge
Ge
Intensity
SiGe
Computational Materials Science and Engineering
100 105 110
Energy-loss (eV)
oxide

Band Line-Up Si/SiO 2 & Ge/SiO 2
Lopatin et al., submitted to PRL
Computational Materials Science and Engineering

Conclusions 2
• Atomic-scale characterization is possible:
Ab-initio methods in conjunction with Z-contrast &
EELS can resolve interface structure.
• Atomically sharp Ge/SiO 2 interface observed
• Reliable structure-property relationship for well
characterized structure (band line-up)
• Abrupt is good
• Sharp interface from Ge-O repulsion (“snowplowing”)
Computational Materials Science and Engineering

3. Process and Device Simulation of
Molecular Devices
300 nm
Possibilities:
Wind et al., JVST B, 2002.
Computational Materials Science and Engineering
• Carbon nanotubes (CNTs) as
channels in field effect transistors
• Single molecules to function as
devices
• Molecular wires to connect device
molecules
• Single-molecule circuits where
devices and interconnects are
integrated into one large molecule

I
p
( ) ( )
2
V = ∫ T , ( ) ( ) = ∫ ( )
lr E V fl
E fr
E dE Tlr
E
Using
Concept of Ab-Initio Device Simulation
2
8π
e
h
device
• Landauer formula for I p (V)
Zhang, Fonseca, Demkov, Phys Stat Sol (b), 233, 70 (2002)
Computational Materials Science and Engineering
E
E
F
F
+ V
/ 2
−V
/ 2
• Lippmann-Schwinger equation, T lr (E) = 〈 l⏐V + VGV ⏐r 〉
• Rigid-band approximation T(E,V) = T(E + ηV) with η = 0.5
2
dE

H
⎛H
l
⎜
= ⎜Vdl
⎜
⎝ 0
Zhang, Fonseca, Demkov,
Phys Stat Sol (b), 233,
T lr from Local-Orbital Hamiltonian
T lr
=
V
H
V
l
ld
d
rd
Vˆ
+ Vˆ
Gˆ
Vˆ
V
0
H
dr
r
⎞
⎟
⎟
⎟
⎠
r
( ) 1 −
E − Hˆ
+ i
Gˆ
( E)
= ε
...
Hˆ = Hˆ
l + Hˆ
r + Hˆ
d + Vˆ
dl + Vˆ
dr
Vˆ
left elec.
(H l )
device
(H d )
Computational Materials Science and Engineering
right elec.
(H r )
T l T dl T dr T r
• T lr (E) can be constructed from matrix elements of DFT tightbinding
Hamiltonian H. Pseudo atomic orbitals: ψ(r > r c )=0.
• We use matrix-element output from SIESTA.
...

The Molecular Transport Problem
I Expt.
Strong discrepancy expt.-theory!
Suspected Problems:
• Contact formation molecule/lead
not understood
• Influence of contact structure on
electronic properties
Theor.
Computational Materials Science and Engineering

What is “Process Modeling” for
Molecular Devices?
• Contact formation: need to follow influence of temperature
etc. on evolution of contact.
• Molecular level:
atom by atom
⇒ Molecular Dynamics
• Problem:
MD may never get to
relevant time scales
* 1-week simulation of 1000-atom metal
system, EAM potential
Accessible simulated time*
Computational Materials Science and Engineering
s
ms
μ s
ns
Moore’ s law
1990 2000
Year
2010

Accelerated Molecular Dynamics
• Possible solution: accelerated dynamics methods.
• Principle: run for t run. Simulated time: t sim = n t run, n >> 1
• Possible methods:
• Hyperdynamics (1997)
Methods
• Parallel Replica Dynamics (1998)
• Temperature Accelerated Dynamics (2000)
Voter et al., Annu. Rev. Mater. Res. 32, 321 (2002).
Computational Materials Science and Engineering

Temperature Accelerated Dynamics (TAD)
Concept:
• Raise temperature of system to make events occur more
frequently. Run several (many) times.
• Pick randomly event that should have occurred first at the
lower temperature.
Basic assumption (among others):
• Harmonic transition state theory (Arrhenius behavior) w/
ΔE from Nudged Elastic Band Method (see above).
⎛ ΔE
⎞
⎡ ⎛
⎞⎤
⎢ ⎜
1 1
k = ν
⎟ ⇒ = Δ − ⎟
0 exp ⎜−
tlow
thigh
exp E
⎥
⎝ kT ⎠
⎢
⎜
⎟
⎣ ⎝
kT kT low high ⎠⎥⎦
Voter et al., Annu. Rev. Mater. Res.
32, 321 (2002). Computational Materials Science and Engineering

Carbon Nanotube on Pt
• From work function, Pt possible lead candidate.
• Structure relaxed with VASP.
• Very small relaxations of Pt suggest little wetting
between CNT and Pt (⇒ bad contact!?).
Computational Materials Science and Engineering

Movie: Carbon Nanotube on Pt
Temperature-Accelerated MD at 300 K
•Nordlund empirical potential
t sim = 200 μ s
•Not much interaction observed ⇒ study different system.
Computational Materials Science and Engineering

Carbon Nanotube on Ti
•Large relaxations of Ti suggest strong reaction
(wetting) between CNT and Ti.
•Run ab-initio TAD for CNT on Ti (no empirical
potential available).
•Very strong reconstruction of contacts observed.
Computational Materials Science and Engineering

TAD MD for CNT/Ti
600 K, 0.8 ps
t sim (300 K) = 0.25 μ s
CNT bonds break on
top of Ti, very different
contact structure.
New structure 10 eV
lower in energy.
Computational Materials Science and Engineering

Contact Dependence of
I-V Curve for CNT on Ti
Difference 15-20%
Computational Materials Science and Engineering

Relaxed CNT on Ti “Inline Structure”
Computational Materials Science and Engineering
• In real devices, CNT embedded into
contact. Maybe major conduction
through ends of CNT?

Contact Dependence of
I-V Curve for CNT on Ti
Inline structure has 10x conductivity of on-top structure
Computational Materials Science and Engineering

• Currently major challenge for molecular devices: contacts
• Contact formation: “Process” modeling on MD basis.
• Accelerated MD
Conclusions
• Empirical potentials instead of ab initio when possible
• Major pathways of current flow through ends of CNT
Computational Materials Science and Engineering

Funding
• Semiconductor Research Corporation
• NSF-Europe
• Ohio Supercomputer Center
Computational Materials Science and Engineering

Acknowledgments (order of appearance)
• Dr. Roland Stumpf (SNL; B diffusion)
• Dr. Marius Bunea and Prof. Scott Dunham (B diffusion)
• Dr. Xiang-Yang Liu (Motorola/RPI; BICs)
• Dr. Leonardo Fonseca (Freescale; CNT transport)
• Karthik Ravichandran (OSU; CNT/Ti)
• Dr. Blas Uberuaga (LANL; CNT/Pt-TAD)
• Prof. Gerd Duscher (NCSU; TEM)
• Tao Liang (OSU; Ge/SiO 2)
• Sergei Lopatin (NCSU; TEM)
Computational Materials Science and Engineering

Right:
• Ti below 10 a.u. and above 60
a.u.
• CNT (3,3), 19 C planes, in
contact with Ti between 15 a.u. and
30 a.u. and between 45 a.u. and
60 a.u.
Left:
• Ti below 25 a.u. and above 55
a.u.
• CNT (armchair (3,3), 12 C planes)
in the middle

Minimal basis set used (SZ); I did a separate calculation for an isolated CNT
(3,3) and obtained a band gap of 1.76 eV (SZ) and 1.49 eV (DZP). Armchair
CNTs are metallic; to close the gap we need kpts in the z-direction.

The main peak in the X structure is
located at ~5 V, which is close to
the value from the inline structure
(~5.5 V). This indicates that the
qualitative features in the
conductance derive from the CNT
while the magnitude of the
conductance is set by the contacts.
The extra peaks seen on the right
may be due to incomplete
Notice the difference in the yaxis.
The X structure (below)
carries a current which is about
one order of magnitude smaller
than the CNT inline with the
contacts (left)

The main peak in the X structure is
located at ~5 V, which is close to
the value from the inline structure
(~5.5 V). This indicates that the
qualitative features in the
conductance derive from the CNT
while the magnitude of the
conductance is set by the contacts.
The extra peaks seen on the right
may be due to incomplete
Notice the difference in the yaxis.
The X structure (below)
carries a current which is about
one order of magnitude smaller
than the CNT inline with the
contacts (left)

Current (A)

PDOS for the relaxed CNT in line with contacts. The two curves correspond
to projections on atoms far away from the two interfaces. A (3,3) CNT is
metallic, still there is a gap of about 4 eV. Does the gap above result from
interactions with the slabs or from lack of kpts along z? This question is not
so important since the Fermi level is deep into the CNT valence band.

Previous calculations and new ones. Black is unrelaxed but converged with
Siesta while blue is relaxed with Vasp and converged with Siesta. From your
results it looks like you started from an unrelaxed structure and is trying to
converge it.

Current (A)
Bias (V)
Previous calculations and new ones. Black is relaxed with Vasp and
converged with Siesta.

MD smoothes out most of
the conductance peaks
calculated without MD.
However, the overall effect
of MD does not seem to be
very important. That is an
important result because it
tells us that the Schottky
barrier is extremely
important for the device
characteristics but interface
defects are not. Transport
seems to average out the
defects generated with MD.
Notice in the lower plot that
there is no exponential
regime, indicating ohmic
behavior. Slide 7 shows
that for the aligned
structure the tunneling
regime is very clear up to
~6 V.

Physical Multiscale Process Modeling REED-MD
Ab Initio: Diffusion
parameters, stress
dependence, etc.
2
Relate atomistic
calculations to
macroscopic eqs.
Device modeling
compare modeled
results to specs.
Met ⇒ done,
otherwise goto 1.
Computational Materials Science and Engineering
3
5
Diffusion Solver
- read in implant
- solve diffusion
Implant:
“ab-initio”
modeling
(3D dopant
distribution
)
1
4

MOSFET Scaling: Ultrashallow Junctions
Shallower Implant
Better insulation (off)
Higher Doping
*P. Packan, MRS Bulletin
Computational Materials Science and Engineering
To get enough
current with shallow
source & drain

Gate
Channel
Source Drain
Implantation & Diffusion
• Dopants inserted by ion implantation
⇒ damage
• Damage healed by annealing
• During annealing, dopants diffuse fast
(assisted by defects)
⇒ important to optimize anneal
*Hoechbauer, Nastasi, Windl
Computational Materials Science and Engineering
*

Ab-Initio Calculations – Standard Codes
Input:
● Coordinates and types of group of atoms
(molecule, crystal, crystal + defect, etc.)
Output:
● Solve quantum mechanical Schrödinger equation,
Hψ = Eψ ⇒ total energy of system
● Calculate forces on atoms, update positions
⇒ equilibrium configuration
⇒ thermal motion (MD),
vibrational properties
Computational Materials Science and Engineering
H
H
H
O
O
H

“real”
Ab-Initio Calculations
DFT
Computational Materials Science and Engineering
effective potential
• Error from effective potential corrected by (exchange-)correlation term
• Local Density Approximation (LDA)
• Generalized-Gradient Approximations (GGAs)
• Others (“Exact exchange”, “hybrid functionals” etc.)
• “Correct one!?”
• “Everybody’s” choice:
Ab-initio code VASP (Technische Universität Wien), LDA and GGA

How To Find Migration Barriers I
• “Easy”: Can guess final state & diffusion path (e.g. vacancy diffusion)
“By hand”, “drag” method. Extensive use in the past.
Energy
ΔE ~ 0.4 eV ΔE
Fails even for exchange N-V in Si (“detour” lowers barrier by ~2 eV)
drag
real
Unreliable!
Computational Materials Science and Engineering

How To Find Migration Barriers II
New reliable search methods for diffusion paths exist like:
• Nudged elastic band method” (Jónsson et al.). Used in this work.
• Dimer method (Henkelman et al.)
• MD (usually too slow); but can do “accelerated” MD (Voter)
• All in VASP, easy to use.
a b c
Initial Saddle Final
Elastic band method:
Minimize energy of all snapshots plus
spring terms, E chain :
E
E
chain
spring
ab
=
=
all atoms
b c
spring
ab
1
k j j
2
Computational Materials Science and Engineering
E
a
+
∑
E
2
+ E
+ E
+
E
spring
bc
( a b
x − x ) ( Hooke' s Law )

Calculation of Diffusion Prefactors
• Vineyard theory
• From vibrational
frequencies
⇒
const.
Prefactor
×
N
∏
j=
1
N −1
∏
j=
1
ν
ν
A
j
S
j
given
,
ν
j
by
phonon
freqs.
Energy
Computational Materials Science and Engineering
ΔE
A S B
• Phonon calculation in VASP
• Download our scripts from Johnsson group website (UW)
A
S
B

Reason for TED: Implant Damage
NEBM-DFT: Interstitial assisted two-step mechanism:
Intrinsic diffusion:
Create interstitial, B captures interstitial, diffuse together
⇒ Diffusion barrier: E form (I) – E bind (BI) + E mig (BI)
4 eV 1 eV 0.6 eV ~ 3.6 eV
After implant:
Interstitials for “free” ⇒ transient enhanced diffusion
W. Windl, M.M. Bunea, R. Stumpf, S.T. Dunham, and M.P. Masquelier,
Proc. MSM99 (Cambridge, MA, 1999), p. 369; MRS Proc. 568, 91 (1999); Phys. Rev. Lett. 83, 4345 (1999).
Computational Materials Science and Engineering

T( o C)
Reason for Deactivation – Si-B Phase Diagram
2200
2000
1800
1600
1400
1200
1000
2092
2020
B
SiB 14
Si 10 B 60
1850
Si 1.8B 5.2
1385
1270
Computational Materials Science and Engineering
1414
800
0 10 20 30 40 50 60 70 80 90 100
B
Si
L
Si

Deactivation – Sub-Microscopic Clusters
Experimental findings:
• Structures too small to be seen in EM ⇒ only “few” atoms
• New phase nucleates, but decays quickly
• Clustering dependent on B concentration and
interstitial concentration
⇒ formation of B mI n clusters postulated;
experimental estimate: m / n ~ 1.5*
⇒ Approach:
• Calculate clustering energies from first principles up to
“max.” m, n
• Build continuum or atomistic kinetic-Monte Carlo model
*S. Solmi et al., JAP 88, 4547 (2000).
Computational Materials Science and Engineering

Cluster Formation – Reaction Barriers
*Uberuaga, Windl et al.
Computational Materials Science and Engineering
Dimer study of the
breakup of B 3 I 2 into B 2 I
and BI showed:*
•BIC reactions diffusion
limited
•Reaction barrier can be
well approximated by
difference in formation
energies plus migration
energy of mobile species.

B-I Cluster Structures from Ab Initio Calculations
B x I
B x I 2
B x I 3
I>3
BI +
LDA −0.5
GGA −0.4
BI 2 0
−2.5
−2.3
B 2 I 0
B 2 I 2 0
B 3 I -
B 3 I 2 0
+ 0
-
-
BI3 B2I3 B3I3 B4I3 −4.8
−4.5
B 4 I 4 -
−9.2
−7.8
−2.0
−1.2
−3.0
−2.4
−6.0
−5.3
−3.0
−2.2
−4.1
−2.6
−6.6
−5.6
X.-Y. Liu, W. Windl, and M. P. Masquelier,
APL 77, 2018 (2000).
Computational Materials Science and Engineering
B 4 I 2-
−5.5
−4.3
B 4 I 2 0
−5.5
−4.3
−7.0
−5.9
B 12 I 7 2-
−24.4
N/A

Activation and Clusters
30 min anneal, different T (equiv. constant T, varying times)
GGA
B 3 I 3 -
B 3 I -
Computational Materials Science and Engineering

Conc. (cm -3 )
Calibration with SIMS Measurements
• Sum of small errors in ab-initio exponents has big effect on
continuum model
∀⇒ refining of ab-initio numbers necessary
• Use Genetic Algorithm for recalibration
10 19
10 18
10 17
10 16
650 o C
20 min
As impl.
SIMS
Model
1025 o C
20 s
0 0.5 0 0.5 0 0.5
Depth (μm)
800 o C
20 min
Computational Materials Science and Engineering
30 min

*A. Asenov
Statistical Effects in Nanoelectronics:
Why KMC?
Computational Materials Science and Engineering
SIMS
Need to think about exact distribution ⇒ atomic scale!

Conclusion 1
• Atomistic, especially ab-initio, calculations
very useful to determine equation set and
parameters for physical process modeling.
• First applications of this “virtual fab” in
semiconductor field.
• In future, atomistic modeling needed (example:
oxidation model later).
Computational Materials Science and Engineering

Vacuum
level
E F
Lead CNT
VB
CNT-FET as Schottky Junction
CB
Φ L
Φ CNT
VB
CB
E F
Metal
lead
Computational Materials Science and Engineering
Vo
E o
CNT
Before contact After contact
E F
Φ B = Φ L – Φ CNT
Desirable: Φ B = 0 to minimize contact resistance.
Metals with “right” Φ B : Pt, Ti, Pd.

Computational Materials Science and Engineering

The main peak in the X structure is
located at ~5 V, which is close to
the value from the inline structure
(~5.5 V). This indicates that the
qualitative features in the
conductance derive from the CNT
while the magnitude of the
conductance is set by the contacts.
The extra peaks seen on the right
may be due to incomplete
Notice the difference in the yaxis.
The X structure (below)
carries a current which is about
one order of magnitude smaller
than the CNT inline with the
contacts (left)

Current (A)

PDOS for the relaxed CNT in line with contacts. The two curves correspond
to projections on atoms far away from the two interfaces. A (3,3) CNT is
metallic, still there is a gap of about 4 eV. Does the gap above result from
interactions with the slabs or from lack of kpts along z? This question is not
so important since the Fermi level is deep into the CNT valence band.