Transcript Scattering - Lehigh University

Silicon-Interface Scattering in Carbon
Nanotube Transistors
Slava V. Rotkin
Physics Department &
Center for Advanced Materials
and Nanotechnology
Lehigh University
NCN Seminar, UIUC Mar 4 2009
Slava V Rotkin, Lehigh University
Acknowledgements
Dr. A.G. Petrov (Ioffe)
Prof. J.A. Rogers (UIUC)
Dr. V. Perebeinos and Dr. Ph. Avouris (IBM)
Prof. K. Hess (UIUC) and Prof. P. Vogl (UVienna)
NCN Seminar, UIUC Mar 4 2009
Slava V Rotkin, Lehigh University
OUTLINE
Introduction:
- NT Transistors with "non-monolithic" channel
The old "new" Surface Scattering
- Remote Coulomb Impurity scattering
- Remote Polariton Scattering
Physics of Surface Phonon Polariton (SPP)
SPP and heat dissipation in NT devices
Conclusions
NCN Seminar, UIUC Mar 4 2009
Slava V Rotkin, Lehigh University
NT Transistors
NCN Seminar, UIUC Mar 4 2009
Slava V Rotkin, Lehigh University
Quantum physics of TFT capacitance
Fabrication of NT-Array
TFTs revealed new "old"
physics.
• very large gate coupling –
too strong if not taking into
account intertube coupling
• non-uniformity of the
channel – self-screening
and "defect healing"
Most of the tubes are parallel, but the
distance between neighbor tubes may vary.
• multi-layer dielectrics and
surface E/M modes
• interface scattering
For TFT applications only semiconductor tubes
are needed. Thus one needs to destroy (burn out)
metallic tubes. Which randomizes the channel.
self-consistent modeling (Poisson+Schroedinger eqs) including e/m response
NCN Seminar, UIUC Mar 4 2009
Slava V Rotkin, Lehigh University
Physics of NT Devices on SiO2
• weak interaction
• electr. transport
• thermal coupling
• alignment
Weak van der Waals
interactions...
For a polar substrate
-- such as quartz,
sapphire, calcite -new physics due to
evanescent ElectroMagnetic (EM) modes,
aka Surface Phononintegrated
Polariton
modes
NCN Seminar, UIUC Mar 4 2009
empty space
Slava V Rotkin, Lehigh University
Charge Scattering:
Short Introduction
NCN Seminar, UIUC Mar 4 2009
Slava V Rotkin, Lehigh University
Transport Theory: What to Forget and
What to Remember
Equilibrium distribution function is Fermi-Dirac function:
e.d.f. is symmetric and thus j = 0
The asymmetric non-e.d.f. provides j > 0 (both in ballistic and diffusive model)
Quantum-mechanical calculation
of the conductivity may be
reduced to the Drude formula
electron velocity which enters the formula
can be related to m.f.p.
NCN Seminar, UIUC Mar 4 2009
vttr=L
Slava V Rotkin, Lehigh University
Conductivity: van Hove singularities
Scattering rate is proportional to
electron velocity which diverges at the
subband edge. Thus, the Drude
conductivity has "zeroes" at vHs.
Which holds for both metallic and
semiconductor tubes.
after Prof. T. Ando
NCN Seminar, UIUC Mar 4 2009
Slava V Rotkin, Lehigh University
Remote impurity
Scattering
NCN Seminar, UIUC Mar 4 2009
Slava V Rotkin, Lehigh University
Coulomb Center Scattering
Scattering in 1D systems is weak due to restricted phase space available for
electron: k -> -k
the Coulomb impurities are
on the substrate, not within
the NT lattice – the remote
impurity scattering
on average the Coulomb
potential
where e* and nS are the
charge and density of
impurities
NCN Seminar, UIUC Mar 4 2009
Slava V Rotkin, Lehigh University
Coulomb scattering: Results
Scattering in 1D systems is weak due to restricted phase space available for
electron: k -> -k
Within this model
a universal expression for
conductance was found
Modeling uses the nonequilibrium solution
of the Boltzmann transport equation
where a quantum mechanical scattering rate
is calculated in the Born Approximation and parameterized by the strength of the
Coulomb centers' potential
and DoS
NCN Seminar, UIUC Mar 4 2009
Slava V Rotkin, Lehigh University
RIS Details: Statistical averaging
Statistical averaging over a random impurity distribution of
starting with the
Coulomb potential
on average is
proportional to
strength of
potential
DoS
scattering
form-factor
then, the scattering rate is
here we used notations:
and
NCN Seminar, UIUC Mar 4 2009
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Surface Phonon Polariton
NCN Seminar, UIUC Mar 4 2009
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Digression:
A tutorial on SPP
NCN Seminar, UIUC Mar 4 2009
Slava V Rotkin, Lehigh University
Surface Polariton in SiO2
Surface phonons exist
in polar dielectrics:
Specifics of surface polaritons:
• electric field is not normal to the surface (at 45o)
• due to the dielectric
function difference
between the substrate
and the air, a surface
EM wave could exist
• electric field decays exponentially from the surface
(not a uniform solution of Maxwell equations)
• dielectric function of
the polar insulator has
a zero at wLO , at the
LO phonon frequency
• surface wave can be
obtained by solving
Maxwell equations with
proper boundary
conditions
E
q
H
• existence of a surface mode essentially depends
on existence of the anomalous dispersion region e<0
NCN Seminar, UIUC Mar 4 2009
Slava V Rotkin, Lehigh University
Remote Polariton
Scattering
NCN Seminar, UIUC Mar 4 2009
Slava V Rotkin, Lehigh University
Physics of SPP scattering in SiO2
Estimates for SiO2-quartz:
• electric field in the air is
proportional to decay
constant, determined from
Mxw.Eq+B.C., and F-factor
• relevant l is proportional
to the wavelength of hot
electron
for vF~108 cm/s
and wSO~150meV :
e ~ 10
5 V/
cm
• electric field ~107 V/m
• finally the scattering time
NCN Seminar, UIUC Mar 4 2009
Slava V Rotkin, Lehigh University
Conductivity: van Hove singularities
Scattering rate is
proportional to the velocity
which diverges at the
subband edge. Thus, the
Drude conductivity has
peculiarities at vHs.
Prof. T. Ando
NCN Seminar, UIUC Mar 4 2009
Slava V Rotkin, Lehigh University
Surface Polariton Scattering
• RPS rate varies for intra-subband and inter-subband scattering
• RPS has maximum at the van Hove singularities (for semiconductor-SWNT)
inter-subband transitions are negligible due to
non-zero angular momentum transfer
JETP Letters, 2006
NCN Seminar, UIUC Mar 4 2009
At vHs our Born approximation fails which
manifests itself as diverging
scattering
rate
Slava V Rotkin,
Lehigh University
Surface Polariton Scattering (2)
Correct many-body
picture includes phonon
renormalization of the
electron spectrum.
Within iterative
Quantum Mechanical
calculation (aka SCBA)
new scattering rate
obtained:
- averaged near the vHs
- still faster than other
channels
JETP Letters, 2006
Forward scattering dominates:
q~1/l : forward scattering
q~2ki : backward scattering
NCN Seminar, UIUC Mar 4 2009
for vF~108 cm/s and wSO~140meV : l~40 nm
2ki ~ 2p/a ~ 1/nm
Slava V Rotkin, Lehigh University
Remote SPP Scattering Rate
lattice T
T=77;
150;
210;
300;
370;
450 K
• scattering rate increases with the electric field strength because of stronger
warming of the electron distribution function
• similarly it increases with the temperature
• concentration dependence is weak and can be attributed to the tails of
distribution function
NCN Seminar, UIUC Mar 4 2009
Slava V Rotkin, Lehigh University
SPP Scattering Rate and Mobility
• for the SiO2 substrate the SPP
channel is likely prevailing over
inelastic scattering, such as due
to NT (own) optical phonons for
the small distance to the polar
substrate < ~ 4 nm;
JETP Letters, 2006 (3V,300K)
Nano Letters, 2009
• low-field mobility at 100+K is
totally dominated by SPP
SPP
• the effect is even stronger
for high-k dielectrics due to
increase of the Froehlich
constant : x20 and more;
NT
NCN Seminar, UIUC Mar 4 2009
• RPS has a weak dependence
on the NT radius, thus for
narrow NTs it will dominate
over the other 1/R mechanisms
Slava V Rotkin, Lehigh University
SPP Scattering Rate and Mobility
• for the SiO2 substrate the SPP
channel is likely prevailing over
inelastic scattering, such as due
to NT (own) optical phonons for
the small distance to the polar
substrate < l ~ 4 nm;
JETP Letters, 2006
lattice T
Nano Letters, 2009
• SPP low-field mobility for a
large number of various
chirality NTs allows to infer
empirical scaling on the NT
radius
• comparison with other
mechanisms: R2 for NT
acoustic phonons
• lattice temperature is taken
as given
NCN Seminar, UIUC Mar 4 2009
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Saturation Regime
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Saturation Regime: Optical Phonons
Scattering in 1D systems is weak due to restricted phase space available for
the electron: k -> -k.
However, the strong scattering at high drift electric field is inevitable:
saturation regime. The scattering mechanism is an optical phonon emission
which results in fast relaxation rates for the hot electrons and holes.
Inelastic scattering rates have been calculated for SWNTs earlier:
NCN Seminar, UIUC Mar 4 2009
Slava V Rotkin, Lehigh University
Saturation Regime: Heat Generation
What was known so far?
Inelastic optical phonon relaxation scattering is
likely a factor determining the saturation current in SWNTs :
The hot electron energy is transferred to the SWNT phonon subsystem.
The energy dissipation depends on the environment (thermal coupling).
NCN Seminar, UIUC Mar 4 2009
Slava V Rotkin, Lehigh University
SPP and Saturation Regime
Kane, PRL, 2000
Deviation from
Ohm's law: first
nonvanishing
term in R(Vd)=Ro
+Vd/Io
Inverse drain
current vs.
inverse applied
electric field
[17,0] NT at the
doping level 0.1 e/nm
NCN Seminar, UIUC Mar 4 2009
low-F and high-F
Is are essentially
different, being
determined by
different
scattering
mechanisms
Slava V Rotkin, Lehigh University
SPP and Saturation Regime
Kane, PRL, 2000
Deviation from
Ohm's law: first
nonvanishing
term in R(Vd)=Ro
+Vd/Io
Inverse drain
current vs.
inverse applied
electric field
low-F scattering is
due to all phonons
(including NT
intrinsic phonon
modes) and high-F
scattering is due to
SPP mechanism
NCN Seminar, UIUC Mar 4 2009
low-F and high-F
Is are essentially
different, being
determined by
different
scattering
mechanisms
Slava V Rotkin, Lehigh University
NCN Seminar, UIUC Mar 4 2009
Slava V Rotkin, Lehigh University
Modern Electronics and
Heat Dissipation Problem
NCN Seminar, UIUC Mar 4 2009
Slava V Rotkin, Lehigh University
ITRS Grand Challenges: The Heat
?
"Energy in Nature and Society: General Energetics of
Complex Systems" by V. Smil (2008)
S. Borkar, “Design challenges of
technology scaling,” IEEE Micro,
vol. 19 (4), 23–29, Jul.–Aug. 1999.
Among main evaluation parameters for novel semiconductor electronics
technologies the power consumption, and in particular the power dissipation
become more and more important
NCN Seminar, UIUC Mar 4 2009
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SPP Heat Dissipation
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Joule Heat Generation
q
j
j
q
Vd
q~area~nm2
channel heating due to Joule losses and low thermal coupling to leads
It exists, however, a relaxation mechanism which transfers the energy directly to
the substrate without intermediate exchange with the SWNT lattice (phonons)
which is an inelastic remote optical phonon scattering
Pioneering work by K. Hess and P. Vogl – back to 1972 – RIP scattering in Si.
The mechanism appeared to be
ineffective for Si MOS-FETs and was almost forgotten for decades...
NCN Seminar, UIUC Mar 4 2009
Slava V Rotkin, Lehigh University
SPP and Overheating
j
overheating of the channel : we neglect the thermal
sink in the leads (area~nm2), then only
substrate contributes
via thermal coupling:
qC
qph
where
QSPP
• two scattering (NT and SPP) and two coupling
(SPP and Kapitsa) mechanisms :
• NT phonons warm the NT lattice but
the Kapitsa
resistance is high
NCN Seminar, UIUC Mar 4 2009
Material
g=1/k, W/(m·K)
Silica Aerogel
0.004 - 0.04
Air
0.025
Wood / wool
0.04 - 0.4
Water (liquid)
0.6
Thermal epoxy
1-7
Glass
1.1
Concrete, stone
1.7 – 2.4
Stainless steel
12.11 ~ 45.0
Aluminium
200
Copper
380
Silver
429
Diamond
900 - 2320
Slava V Rotkin, Lehigh University
SPP and Overheating
overheating of the channel : we neglect the thermal
sink in the leads (area~nm2), then only
substrate contributes
via thermal coupling:
j
qph
where
• two scattering (NT and SPP) and two coupling
(SPP and Kapitsa) mechanisms :
• NT phonons warm the NT lattice but
the Kapitsa
resistance is high
QSPP
• assume for a moment that SPP
channel is absent
• Joule losses are NOT the same as
the total dissipation: NT phonons
take only a small fraction of IdF
NCN Seminar, UIUC Mar 4 2009
Slava V Rotkin, Lehigh University
SPP and Overheating
j
overheating of the channel : we neglect the thermal
sink in the leads (area~nm2), then only
substrate contributes
via thermal coupling:
qph
where
• two scattering (NT and SPP) and two coupling
(SPP and Kapitsa) mechanisms :
PSPP/PNT
• NT phonons warm the NT lattice but
200
the Kapitsa
100
resistance is high
50
• assume for a moment that SPP
20
channel is absent
10
• Joule losses are NOT the same as
the total dissipation: NT phonons
take only a small fraction of IdF
NCN Seminar, UIUC Mar 4 2009
QSPP
substrate T
5
2
1
2
4
6
8
10
F
(V/mm)
Slava V Rotkin, Lehigh University
12
SPP and Overheating (2)
• ratio of "real"-to-expected
losses for two tubes (R~0.5 and
1.0 nm) at two to= 77 and 300K
• inset: data collapse for (linear)
dependence on the electron
concentration (0.1 and 0.2 e/nm)
• SPP scattering is higher in smaller
diameter tubes: simply the SPP field
is stronger
• opposite R-dependence for two
scattering mechanisms
NCN Seminar, UIUC Mar 4 2009
Slava V Rotkin, Lehigh University
SPP and Overheating (2)
• even in case of no other
thermal coupling to substrate,
SPP channel releases the heat
(R~0.5 nm, T=300K)
• inset: same data vs. Joule loss
• NT transport in saturation regime is
determined by both channels
• different temperature dependence
for two scattering mechanisms
NCN Seminar, UIUC Mar 4 2009
Slava V Rotkin, Lehigh University
Conclusions
• Theory of NT scattering after 10 years still has new
uncovered physics
• Physics of interactions in NTs at the hetero-interface with
Si/SiO2 is rich for fundamental research
• Hot electron scattering due to SPP modes is by orders of
magnitude faster channel for non-suspended NT
• Remote SPP scattering provides a new and very effective
thermo-conductivity mechanism
NCN Seminar, UIUC Mar 4 2009
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NCN Seminar, UIUC Mar 4 2009
Slava V Rotkin, Lehigh University
NCN Seminar, UIUC Mar 4 2009
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Nanotube Quantum
Capacitance
NCN Seminar, UIUC Mar 4 2009
Slava V Rotkin, Lehigh University
Classical Capacitance: 1D case
Classical 1D capacitance: line charge has f = r 2 log r + const
therefore: Cg-1 = 2 log z/R
L
R
where z = min(d, L, lg)
Distance to metal leads around/nearby
1D channel defines the charge density
d
r(z) is different for different screening
of 1D, 2D and 3D electrodes.
NCN Seminar, UIUC Mar 4 2009
Slava V Rotkin, Lehigh University
Atomistic Capacitance of 1D FET
The transverse size a of nanowires and nanotubes is less than the
Debye screening length and other microscopic lengths of the material.
Classic view: Linear connection between electric potential and charge
Q=C V ,
in a 1D device:
r ~ - C jext
which is to be compared with 3D and 2D:
r ~ - d2j/dx2
r ~ - dj/dx
Quantum Mechanical view:
Selfconsistent calculation of
the charge density
NCN Seminar, UIUC Mar 4 2009
Rotkin
et.al.Lehigh
JETP-Letters,
2002
Slava
V Rotkin,
University
Atomistic Capacitance of 1D FET
The transverse size a of nanowires and nanotubes is less than the
Debye screening length and other microscopic lengths of the material.
Classic view: Linear connection between electric potential and charge
Q=C V ,
in a 1D device:
r ~ - C jext
which is to be compared with 3D and 2D:
r ~ - d2j/dx2
r ~ - dj/dx
Quantum Mechanical view:
Selfconsistent calculation of
the charge density
NCN Seminar, UIUC Mar 4 2009
Rotkin
et.al.Lehigh
JETP-Letters,
2002
Slava
V Rotkin,
University
Capacitance of the NT Array
Method of potential coefficients (or
EE circuit analysis): Screening by
neighbor NTs in the array – total
capacitance is of a bridge circuit
1 mm
1 mm
2d/L
Fig. : Gate coupling in array-TFT as
a function of the screening by
neighbor NTs (top to bottom):
same SiO2 thickness = 1.5 um,
NT densities = 0.2, 0.4 and 2 NT/um
1 mm
Screening depends on single parameter: 2d/Lo which has a physical meaning
of the number of NTs electrostatically coupled in the array. The tubes that are
further apart do not "know" about each other
NCN Seminar, UIUC Mar 4 2009
Slava V Rotkin, Lehigh University
Random Array Coupling: Self-healing
Current nonuniformity is a deficiency for device production.
Consider Dr due to non-uniform screening.
DC/C
-0.15
-0.25
-0.35
d=40 nm
d=600 nm
Three sample distributions of the tubes in the
random-tube array (d=160 nm, 80% variance).
One may expect a severe variance in device
characteristics because of non-uniform Cg
NCN Seminar, UIUC Mar 4 2009
Slava V Rotkin, Lehigh University
Correlation vs. Randomness
The capacitance of a random TFT
array (a single given realization)
as a function of the external
screening (insulator thickness).
DC, %
3.4
3.2
3.0
2.8
2.6
2.4
d, nm
25 50 75 100 125 150
The low density TFT array is
within a single tube limit...
...in the high density TFT array
the inter-NT coupling is very
strong and stabilizes the
overall device response.
NCN Seminar, UIUC Mar 4 2009
Slava V Rotkin, Lehigh University
Quantum Capacitance in NT-Array TFT
In a single tube FET total
capacitance has 2 terms:
geometric capacitance
and quantum capacitance
for NT array geometrical capacitance
further decreases:
1
C/Cclass0.9
0.8
L
0.7
0.6
d, nm
0.5
10
NCN Seminar, UIUC Mar 4 2009
20
50
100
200
Slava V Rotkin, Lehigh University
500
NCN Seminar, UIUC Mar 4 2009
Slava V Rotkin, Lehigh University
NCN Seminar, UIUC Mar 4 2009
Slava V Rotkin, Lehigh University
NCN Seminar, UIUC Mar 4 2009
Slava V Rotkin, Lehigh University
NCN Seminar, UIUC Mar 4 2009
Slava V Rotkin, Lehigh University
NCN Seminar, UIUC Mar 4 2009
Slava V Rotkin, Lehigh University
Charge Trapping
NCN Seminar, UIUC Mar 4 2009
Slava V Rotkin, Lehigh University
List of publications used in this presentation:
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Stacy E. Snyder, and Slava V. Rotkin, “Optical Identification of a DNA-Wrapped Carbon Nanotube: Signs of Helically Broken Symmetry", Small, accepted, 2008.
Seong Jun Kang, Coskun Kocabas, Taner Ozel, Moonsub Shim, Ninad Pimparkar, Muhammad A. Alam, Slava V. Rotkin, and John A. Rogers, “High performance electronics using
dense, perfectly aligned arrays of single walled carbon nanotubes”, Nature Nanotechnology, vol. 2 (no.4) 230-236 (2007).
Vadim Puller, and Slava V. Rotkin, "Helicity and Broken Symmetry in DNA-Nanotube Hybrids", Europhysics Letters 77 (2), 27006--1-6 (Jan 2007).
Qing Cao, Ming-Gang Xia, Coskun Kocabas, Moonsub Shim, John A. Rogers, and Slava V. Rotkin, “Gate Capacitance Coupling of Single-walled Nanotube Thin-film Transistors”,
Applied Physics Letters, vol. 90 (2), 023516 (2007).
Slava V. Rotkin, Narayan R. Aluru, and Karl Hess, ”Multiscale Theory and Modeling of Carbon Nanotube Nano-Electromechanical Systems”, in "Handbook of Nanoscience,
Engineering and Technology (2nd Edition)", Eds.: W. Goddard, D. Brenner, S. Lyshevski, G.J. Iafrate; Taylor and Francis-CRC Press, Chapter 13, pp. 13.20-13.32 (2007).
Slava V. Rotkin, Alexander Shik, “Electrostatics of nanowires and nanotubes: Application for field-effect devices”, in the Special Issue Nanowires and Nanotubes, Editor: Peter
Burke, Publ.: World Scientific, Singapore. International Journal of High Speed Electronics and Systems, vol. 16 (no.4), 937-958, (2006).
Stacy E. Snyder, and Slava V. Rotkin, “Polarization component of the cohesion energy in the complexes of a single-wall carbon nanotube and a DNA", JETP Lett 84, 348, (2006).
Alexey G. Petrov, Slava V. Rotkin, “Hot carrier energy relaxation in single-wall carbon nanotubes via surface optical phonons of the substrate” JETP Lett 84 (3), 156-160 (2006).
Yan Li, Umberto Ravaioli, and SV. Rotkin, "Metal-Semiconductor Transition and Fermi Velocity Renormalization in Metallic Carbon Nanotubes", Phys. Rev. B 73, 035415 (2006).
L. Rotkina, S. Oh, J.N. Eckstein, S.V. Rotkin, “Logarithmic behavior of the conductivity of electron-beam deposited granular Pt/C nanowires”, Phys. Rev. B 72, 233407 (2005).
Salvador Barraza-Lopez, Slava V. Rotkin, Yan Li, and Karl Hess, "Conductance Modulation of Metallic Nanotubes by Remote Charged Rings", Europhysics Lett 69, 1003 (2005).
Slava V. Rotkin, “From Quantum Models to Novel Effects to New Applications: Theory of Nanotube Devices”, in “Applied Physics of Nanotubes: Fundamentals of Theory, Optics
and Transport Devices”, Nanoscience and Nanotechnology Series, Ser.Ed.: Ph. Avouris, Springer Verlag GmbH & Co. KG (2005).
Yan Li, Deyu Lu, Klaus Schulten, Umberto Ravaioli, and Slava V. Rotkin, “Screening of Water Dipoles Inside Finite-Length Armchair Carbon Nanotubes”, Journal of
Computational Electronics, vol. 4, 161-165 (2005).
Arnaud Robert-Peillard, Slava V. Rotkin, “Modeling Hysteresis Phenomena in Nanotube Field-Effect Transistors”, IEEE Transactions on Nanotechnology, 4 (2), 284-288 (2005).
Deyu Lu, Yan Li, Slava V. Rotkin, Umberto Ravaioli, and Klaus Schulten, “Finite-Size Effect and Wall Polarization in a Carbon Nanotube Channel”, Nano Lett 4, 2383-2387 (2004).
Yan Li, Slava V. Rotkin, and Umberto Ravaioli, "Metal-Semiconductor Transition in Armchair Carbon Nanotubes by Symmetry Breaking", Applied Physics Lett 85, 4178 (2004).
Alexey G. Petrov, Slava V. Rotkin, "Transport in Nanotubes: Effect of Remote Impurity Scattering", Phys. Rev. B vol. 70 (3), 035408-1-10, 15 Jul 2004.
Slava V. Rotkin, and Karl Hess, "Possibility of a Metallic Field-Effect Transistor", Applied Physics Letters vol. 84 (16), p.3139-3141, 19 April 2004.
Slava V. Rotkin, Harry Ruda, Alexander Shik, "Field-effect transistor structures with a quasi-1D channel", International Journal of Nanoscience vol. 3 (1/2), 161-170, Feb 2004.
Kirill A. Bulashevich, Slava V. Rotkin, Robert A. Suris, "Excitons in Single Wall Carbon Nanotubes", International Journal of Nanoscience vol. 2 (6), pp. 521-526, Dec 2003.
Slava V. Rotkin, Harry Ruda, Alexander Shik, "Universal Description of Channel Conductivity for Nanotube and Nanowire Transistors", Applied Physics Letters 83, 1623, 2003.
Alexey G. Petrov, Slava V. Rotkin, "Breaking of Nanotube Symmetry by Substrate Polarization", Nano Letters vol. 3, No.6, 701-705, 2003.
Yan Li, Slava V. Rotkin, Umberto Ravaioli, "Electronic response and bandstructure modulation of carbon nanotubes in a transverse electrical field", Nano Letters 3, 183, 2003.
Slava V. Rotkin, "Theory of Nanotube Nanodevices", in Nanostructured Materials and Coatings for Biomedical and Sensor Applications. Editors: Y.G. Gogotsi and Irina V.
Uvarova. Kluwer, pp. 257-277, 2003.
Slava V. Rotkin, Vaishali Shrivastava, Kirill A. Bulashevich, and Narayan R. Aluru, "Atomistic Capacitance of a Nanotube Electromechanical Device", International Journal of
Nanoscience vol. 1, No. 3/4, 337-346, 2002.
Slava V. Rotkin, Ilya Zharov, "Nanotube Light-Controlled Electronic Switch", International Journal of Nanoscience vol. 1, No. 3/4, 347-355, 2002.
Kirill A. Bulashevich, Slava V. Rotkin, "Nanotube Devices: Microscopic Model", JETP Letters vol. 75 (4), 205-209, 2002.
Slava V. Rotkin, Yuri Gogotsi, "Analysis of non-planar graphitic structures: from arched edge planes of graphite crystals to nanotubes", Materi. Res. Innovations, 5, 191, 2002.
Marc Dequesnes, Slava V. Rotkin, Narayan R. Aluru, "Parameterization of continuum theories for single wall carbon nanotube switches by molecular dynamics simulations",
Journal of Computational Electronics 1 (3), 313-316, 2002.
Slava V. Rotkin, Karl Hess, "Many-body terms in van der Waals cohesion energy of nanotubes", Journal of Computational Electronics 1 (3), 323-326, 2002.
Marc Dequesnes, Slava V. Rotkin, Narayan R. Aluru, "Calculation of pull-in voltages for carbon nanotube-based nanoelectromechanical switches", Nanotechnology 13, 120, 2002.
downloadable from http://theory.physics.lehigh.edu/rotkin/text/pub-list.html
NCN Seminar, UIUC Mar 4 2009
Slava V Rotkin, Lehigh University