Reviewer # 1:
Comment 1:
Transistor performance may be greatly limited and degraded by the Si/carbon
nanotube contacts. Thus Si/carbon nanotube contacts need to be explicitly treated...
Response 1:
We made major revisions in the paper to address this issue raised by the reviewer.
We treat Si/carbon barrier explicitly by taking into account different built-in potentials
and electron affinities of both materials. Thus we solve for the Schottky-type barrier both
for electrons and holes. We also solve for the quantum effects using density gradient
formalism, which further resolves quantum related effects at the Si/carbon barrier.
However an intermediate material structure has not been considered at the barrier. To our
knowledge, researchers treat Si/carbon barrier (equivalently the Shottky barrier formed at
the junction) similarly but with less detail [1,2].
Comment 2:
A. Electrostatic treatment of such transistor geometry requires solving a threedimensional Poisson equation, because the invariance in the Si MOSFET width direction
is broken after the tube is implanted…
B. Using a field-dependent mobility extracted from bulk simulation may not be
adequate to address the microscopic scattering mechanism in a carbon nanotube
transistor. Thus a field-dependent mobility may not be adequate to model this
transistor…
Response 2:
A. In device modeling in general, there is always a tradeoff between physical
detail and geometrical complexity. For this investigation, we felt that an accurate physical
representation would require self-consistent solutions the Poisson as well as the quantum
transport equations. This system forms a very complex highly nonlinear set of equations.
While a 3D solution would obviously be preferred, computational constraints make a 3D
solution to this system almost prohibitive at this point. As an initial investigation, we
therefore use a 2D approximation. We help justify this 2D approximation with the
following arguments. We embed a planar sheet of CNTs in the channel of a MOSFET
parallel to the interface. We here simulate a planar sheet of CNTs. In reference [3], the
potential distribution under a gate, which has a plane of only three tubes, is shown. The
field distribution around the middle tube mimics our case, where fringe effects are
observed for the other two. Even for this extreme case, where we have a plane of only
three metallic tubes, the field lines around the middle tube looks like that they are lined
straight in top to bottom fashion and the curvature of the field lines ending on the tube is
not too high. We also check the debye length for the space around the tubes. In figures 6
and 8, our calculated electron concentrations are plotted. We observe that the electron
concentration outside the tube is low, with the medium size tube having the sharpest
drop. We then calculate the debye lengths for these concentrations. Even if we assume
that the dielectric constant of the surrounding is equal to the vacuum level, debye lengths
are 10nm and 1nm for concentration values of 1016 and 1018, respectively. These values
are either much bigger than or on the order of the tube size. We also know that due to
confinement around the tube, electron concentration can not vary much and have sharp
field lines. Thus we concluded that this two-dimensional approach provides a reasonable
approach to the problem at this stage..
B. Again, we have a trade-off between geometrical-numerical complexity, and
physical details. While an energy dependent mobility term would may be more accurate.
There is also the danger that introducing an energy dependent model could lead to
erroneous results. For example, energy transport and hydrodynamic simulations for other
semiconductors often lead to spurious velocity overshoots, which overpredict terminal
current magnitudes. As a result, the associated margins of error can be much larger that
those associated with the quantum density gradient models we used here. This is
especially the case when one adds quantum effects to the hydrodynamic models. In fact,
in silicon device modeling, the quantum corrected drift-diffusion model is usually
employed for device analysis. Thus, until a well established energy-dependent model is
available, we choose to employ the more traditional drift-diffusion density gradient
approach.
Reviewer # 2:
Comment 1:
It has been shown that by various groups that transport in a semiconductor carbon
nanotube for not too large drain voltages is ballistic over a couple of hundred nanometers
at room-temperature…..
Response 1:
To our knowledge those carbon nanotubes investigated by various groups are big
diameter tubes (bigger than our biggest diameter tube). For our investigations we used
tubes with diameters ranging from 0.8nm to 1.7nm. For these tubes, (especially the
smaller diameter ones) the our MC calculations indicate that the mean free path is usually
less than 10nm for the horizontal field strengths that we find. In effort to be even more
conservative, we increased our length scale by fifty percent to 0.15micron. Furthermore,
our tubes with diameter 0.8nm have a narrow peak mfp of approximately 30nm, and the
1.7nm tubes have a narrow peak mfp of approximately100nm. Thus use of a mobility
model appears reasonable for these cases. We have revised the paper to include this
behavior.
Comment 2:
…”Schottky barriers”…The authors completely neglect the impact of contacts
between a semiconducting nanotube and a source/drain electrode…
Response 2:
We made major revisions in the paper to address this issue raised by the reviewer.
We treat Si/carbon barrier explicitly by taking into account different built-in potentials
and electron affinities of both materials. Thus we solve for the Schottky-type barrier both
for electrons and holes. We also solve for the quantum effects using density gradient
formalism, which further resolves quantum related effects at the Si/carbon barrier.
However an intermediate material structure has not been considered at the barrier. To our
knowledge, researchers treat Si/carbon barrier (equivalently the Shottky barrier formed at
the junction) similarly but with less detail [1,2].
Comment 3:
Fringing fields from the source and drain electrode to the nanotube channel are
crucial to be included in a model to explain basic characteristics of nanotube FETs.
Response 3:
Fringing fields are automatically accounted for in two of the dimensions by the
self-consistent simulations. For the third dimension, we take our devices to be of infinite
extent. In device modeling in general, there is always a tradeoff between physical detail
and geometrical complexity. For this investigation, we felt that an accurate physical
representation would require self-consistent solutions the Poisson as well as the quantum
transport equations. This system forms a very complex highly nonlinear set of equations.
While a 3D solution would obviously be preferred, computational constraints make a 3D
solution to this system almost prohibitive at this point. As an initial investigation, we
therefore use a 2D approximation. We help justify this 2D approximation with the
following arguments. We embed a planar sheet of CNTs in the channel of a MOSFET
parallel to the interface. We here simulate a planar sheet of CNTs. In reference [3], the
potential distribution under a gate, which has a plane of only three tubes, is shown. The
field distribution around the middle tube mimics our case, where fringe effects are
observed for the other two. Even for this extreme case, where we have a plane of only
three metallic tubes, the field lines around the middle tube looks like that they are lined
straight in top to bottom fashion and the curvature of the field lines ending on the tube is
not too high. We also check the debye length for the space around the tubes. In figures 6
and 8, our calculated electron concentrations are plotted. We observe that the electron
concentration outside the tube is low, with the medium size tube having the sharpest
drop. We then calculate the debye lengths for these concentrations. Even if we assume
that the dielectric constant of the surrounding is equal to the vacuum level, debye lengths
are 10nm and 1nm for concentration values of 1016 and 1018, respectively. These values
are either much bigger than or on the order of the tube size. We also know that due to
confinement around the tube, electron concentration can not vary much and have sharp
field lines. Thus we concluded that this two-dimensional approach provides a reasonable
approach to the problem at this stage.
Comment 4:
(A) It was not completely clear how many tubes are included in the channel.
(B)Why not exclusively use a nanotube array-without the silicon layer. What is the
potential benefit of this approach?
Response 4:
(A))We describe in the paper that we use a planar array of tubes. We revised the
paper to try and make this more clear. We also then expanded our work to include the
effects of putting several layers of tubes. These results are described in the revised
papers.
(B)We thought that integration of a well established device design with CNTs
would facilitate fabrication paradigms that are cost effective and would not necessitate
too much modification to the current fabrication flow. Including Si may give another
degree of freedom for charging and discharging tube. Our future works include
investigations of the more typical SOI-type CNT-FETs.
Comment 5:
The authors do not comment on how the proposed device could be fabricated.
Response 5:
We here concentrate more on the modeling aspect of these novel MOSFETs.
However, we also give some references, where fabrication techniques are investigated to
dope and modify the nanotubes. We agree that more discussion on the fabrication
techniques would be interesting. However, we believe that even if the mass fabrication
of these devices is not currently available, huge interest on the tube research would
facilitate new methods for the solution.
Comment 6:
Authors neglect vast amount of papers from other groups.
Response 6:
We here increase our references. However, there is very little, if any, selfconsistent modeling of CNT-FET charge and quantum transport equations.
Reviewer # 3:
Comment :
`It needs more on explanation how the two-D carriers are treated in the paper as
three-D carriers’.
Response 1:
The quantum density gradient model we employed takes into account the
confinement of carriers and the quasi-2dimensional/3dimensional system.
We here employ density gradient formalism instead of the Schrodinger equation
to come up with an approximate quantum solution both along and in the vertical direction
of the channel. We therefore try to overcome the limitations of the Schrodinger equation
and deal with a more generalized solution.
[1] J. Appenzeller, J. Knoch, and Ph. Avouris, “Carbon Nanotube Field-Effect
Transistors – An Example of an Ultra-Thin Body Schottky Barrier Devices,” Device
Research Conf., pp. 167-70, 2003.
[2] J. Appenzeller, J. Knoch, R. Martel, V. Derycke, S. Wind, and Ph. Avouris, “ShortChannel like Effects in Schottky Barrier Carbon Nanotube Field-Effect Transistors,”
IEDM 2002, pp. 285-8, 2002.
[3] X. Wang, H-S. P. Wong, P. Oldiges, and R. J. Miller, “Electrostatic Analysis of
Carbon Nanotube Arrays,” Sispad 2003, pp. 163-6, 2003.