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Sensitivity of Carbon Nanotube Transistors to a Charged Dielectric Coating Gary Pennington, Matthew H. Ervin, and Alma E. Wickenden

Abstract—This paper investigates the electronic properties of single-walled carbon nanotube field-effect transistors (SWCNT-FETs) in which the SWCNT element is coated with a charged dielectric. The presence of remote charge on the surface of the dielectric is considered to effect carrier transport in the nanotube as a result of both carrier-scattering and gate screening. Nanotube device characteristics are simulated using the multisubband Boltzmann transport method incorporating scattering from both phonons and remote charges. This allows assessment of the sensitivity of a nanotube FET to the presence of a charged dielectric coating during room temperature operation. Results show remote charge scattering affects the diameter ( ) dependence of the peak conductance and peak field-effect mobility of carbon nanotube devices. Under phonon-limited transport conditions, 2 , respectively. When these peak values increase as and remote charge scattering is significant, peak values cease to vary with diameter once a critical diameter reached. Charge scattering is found to particularly degrade device current at gate voltages that allow carriers scattering into or out of a subband minimum. Furthermore, simulations show that intersubband scattering resulting from asymmetry in the circumferential remote charge density becomes increasingly important as the nanotube length decreases. The authors propose that remote charge scattering effects may be applicable in sensing devices allowing for the identification of the charge on a functionalized CNT coating. Index Terms—Carbon nanotubes, phonon scattering, remote charge scattering, sensor devices.

I. INTRODUCTION HE DEVELOPMENT of nanoscale materials in recent years is leading to many exciting possibilities for novel chemical and biological electronic sensors [1]–[6]. These devices have the potential to far exceed the sensitivity and detection speed of conventional sensors, and allow for low-power identification of very small concentrations of targeted molecules or microbes/viruses. Among enabling nano-materials of interest, single-walled carbon nanotubes (SWCNTs) offer a very large carrier mobility [7], [8] and, thus, the potential for high sensitivity and fast detection. When compared with other nanowire materials, nanotubes are expected to be very sensitive to the surrounding environment since the charge carrier states exist on the tube surface. As expected, excellent sensitivity

T

Manuscript received August 6, 2007; revised December 4, 2007; accepted December 18, 2007. The associate editor coordinating the review of this paper and approving it for publication was Dr. Dwight Woolard. The authors are with the Army Research Laboratory, Adelphi, MD 20783 USA (e-mail: [email protected]; [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JSEN.2008.923218

to adsorbed chemicals has been demonstrated in experiments [9], [10]. The advantages of using carbon nanotubes in sensing devices are numerous. The nanoscale SWCNT diameter allows ultra-fast sensing to occur in a small volume. Arrays of nanotubes can be employed allowing for very large effective sensing areas [11]. Carbon nanotubes can be functionalized with sensing polymers or antigens which are immobilized on the nanotube surface with nanoscale spatial resolution [12], [13]. The large SWCNT aspect ratio and high mobility allow for low-power lightweight sensors. Although interest in the scientific and engineering communities is high, the physical mechanisms involved in nanotube-based electronic sensing are still largely undetermined. Chemical sensing may alter the transistor current by a number of mechanisms including variations in: charge transfer/doping, carrier scattering, screening and polarization, mechanical strain, and contact resistance/work function. In this work, we focus on an investigation of the importance of remote charges, which likely affect all of the above sensing modalities. Theoretical studies have indicated that ions located nearby the nanotube surface alter the electronic and mechanical properties of carbon nanotubes [14]–[20]. These effects have found applications in high-performance actuators [14], [21], [22], pH sensors [23], [24], and chemical sensors. Remote ionic charge may change CNT device characteristics through classical electrostatic/mechanical strain effects and through quantum effects including band structure variations, scattering, and bond weakening mechanisms. In this work, we focus on an investigation of SWCNT carrier scattering with remote charges. Also considered in simulations is the SWCNT device threshold voltage shift due to the presence of remote charge. Since it is often desirable to desensitize or to selectively functionalize a nanotube device with respect to the environment, we investigate the sensitivity of a single-walled carbon nanotube field-effect transistor (SWCNT-FET) to an exterior coating of nonconducting charge separated from the SWCNT surface by a thin polymer or dielectric coating. We envision that the coating is functionalized so that the surface charge can be switched on and off by adsorbing bio(chemical) molecules or by environmental changes (e.g., pH). To study the effect of remote charge on the device properties of SWCNT-FETs, we employ Boltzmann transport methods which have been successfully used to model phonon-scattering limited transport [8], [25]–[32], [51]. This allows investigation of charging affects alongside phonon scattering, the physical mechanisms that typically sets the intrinsic device behavior. Remote charges are assumed to be immobile, isolated from the CNT-FET by a thin encapsulating polymer or dielectric, as

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Fig. 2. Band structure of a semiconducting SWCNT showing three conduction subbands and three valance subbands (each doubly degenerate). Subbands are defined by a unique transverse wavevectors. For the lowest (highest) three con= d, 4/3d, 8/3d, where d is the tube diameter. duction (valence) subbands: Also shown is the hyperbolic band shape formula and group velocity both depending on the group velocity of a graphene sheet  . The band structure allows both slow states  < and fast states  > leading to switching device applications.

=2 3

(

Fig. 1. A back-gated single-wall nantotube device as modeled in this work. Also shown is a cross-section view of a dielectric coated nanotube. The outer shell of the dielectric is charged.

shown in Fig. 1. In this work, such charges are considered to alter device characteristics by varying the SWCNT Fermi level and by enhancing carrier scattering. Variations in the thickness and surface charge density (NC) of the dielectric coating are investigated. Results will show that the electronic properties of SWCNT-FETs depend on the nanotube length and diameter. The electronic properties of SWCNT-FETs are found to be sensitive to the transverse distribution of remote charge only . As the SWCNT when the tube length is small diameter increases, phonon scattering is reduced allowing charge scattering effects to become increasingly prominent. Results of this investigation are expected to lead to important insights into the sensitivity of SWCNT transistors to remote charges in the environment. Although only individual electrical charges are considered, results give a qualitative description of carrier scattering via higher electronic moments such as remote dipoles. The sensing of remote charge may be employed in sensing bio(chemical) molecules and environmental properties such as the pH. This will allow identification of device designs that successfully take advantage of the electronic and material properties of carbon nanotubes-polymer\dielectric device architectures. II. PHYSICAL DEVICE MODELS A. Phonon Scattering If environmental influences are removed, the characteristics of a long defect-free CNT-FET should be determined by carrier transport through the pristine quasi-1D nantoube band structure

)

(

)

under the influence of phonon scattering [8], [25]. Carrier subbands and phonon subbranches in a nanotube can be specified , 4/3 , and by a circumferential wavevector , with 8/3 for the first three subbands [33], [34]. The carrier subband structure of a SWCNT is shown in Fig. 2. Wavevectors and along the tube axis further define the carrier and phonon eigenstates, respectively. Using Fermi’s golden rule, the phonon meto final cardiated scattering rate from initial carrier state is given by rier state

(1) , and are the deformation potential per unit latHere, , tice displacement, phonon energy, and phonon number, respecis determined by the Bose–Einstein equilibrium distively. tribution. Phonon energies, shown in Fig. 2, are determined by continuum modeling [35]. The mass density of the nanotube is , where . The density of carrier states is , where [33], [34] and is the Fermi velocity of graphene is equal to 1/4 of the total den[26]. Here, due to conservation of both sity of final carrier states at spin and circumferential momentum in the interaction. and off-diagonal elements of the The diagonal deformation potential are [25], [35], [36]

(2) Here, the longitudinal and transverse sound velocities in graphene are and . Coupling is the chiral angle, and is the constants are and , energy of the breathing phonon mode [35], [37]. For intersubband scattering and intrasubband scattering by the breathing . phonon mode, the carrier-phonon interaction is given by

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Fig. 3. Continuum model for low energy phonon subbranch spectrum. A diagram of the intrasubband carrier scattering modes including the twisting (T), stretching (S), and breathing (B) phonon is shown. A plot of the phonon energy dispersion shows both intrasubband (1 = 0) and intersubband (1 6= 0) scattering phonons, where 1 is the perpendicular carrier wavevector transfer.

When the Fermi level is sufficiently close to the Fermi point of graphene in metallic carbon nanotubes, carriers couple with stretching ( ) and twisting ( ) phonons via the off-diagonal components and , respectively. Otherwise, the deformation potential for the mode is , whereas the deformation potential vanishes for the mode. In this work, we consider only semiconducting carbon nanotubes and, hence, use only the deformation potential and do not consider the suppression and of backscattering expected in armchair nanotubes [35], where small bandgap nanotubes n,m are fundamental nanotube indices. We investigate carrier transport in single-walled semiconducting carbon nanotubes by solving the spatially homogenous multisubband Boltzmann equation [25]

(3) directed along the subject to a small external field is solved for a given tube axis. The distribution function Fermi energy through specification of the 1-D SWCNT charge density . Considering a CNT-FET as in Fig. 1, application of a gate voltage is used to vary . The multisubband conductance , where the sum rule is then is used to sum over each subband (defined by unique ). The is found from the drift velocity and field acmobility cording to

(4) Previous simulations of phonon-limited transport [8], [20], [25] based on the above formulism, compare well with experimental measurements in semiconducting SWCNTs [7], [38], where micron scale tube lengths allowed diffusive transport. As expected, only the zone center low-energy phonons in Fig. 3

contribute significantly to scattering under the experimental conditions: low source-drain bias when the finite temperature Fermi level lies within the nanotube bands (degenerate). Since nanowires have also found application as sensors [39], a comparison of phonon-limited transport is of interest. The large phonon-limited mobility of a carbon nanotube ( for a 4 nm diameter tube) [7], [8], [25], [38] is larger than theoretical predictions for a corresponding width silicon nanowire ) [40]. This is likely a result of well defined (430 transverse quantization of carriers and phonons in the nanotube when compared with a nanowire. Carrier scattering is typically increased in the nanowire as more final carrier states are available due to enhanced wavefunction overlap [40]. Material properties such as the effective mass, phonon spectrum, and deformation potential would also play a role. Experimental measurements on FETs where the channel material employs silicon nanowires with widths of 10–20 nm, have shown mo[41] and 1000 [42]. bilities as large as 1350 Enhanced mobility was found by device annealing/passivation [41] and by the introduction of strain [42]. Semiconducting carbon nanotubes of similar diameter are not expected to form, yet such large mobilites in silicon nanowires should enable enhanced device performance. B. Remote Charge Scattering To investigate the effects of remote charge scattering, the appropriate rate must be included in (3). For long nanotubes, appropriate in sensing applications, the remote charge scattering rate is developed from methods used to model scattering at extended heterostructure interfaces [43]. However, for the present system charge is distributed on the surface of a concentric cylindrical dielectric shell encapsulating the SWCNT. This is shown in Fig. 1. Previous studies by Petrov and Rotkin [18] considered scattering arising from charged impurities located on the surface of a planar substrate underlying a carbon nanotube. Results showed enhanced scattering for small momentum transfer as is typical of coulombic scattering, and conductance degradation via the onset of intersubband scattering. Our treatment

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PENNINGTON et al.: SENSITIVITY OF CARBON NANOTUBE TRANSISTORS TO A CHARGED DIELECTRIC COATING

of remote charge scattering in semiconducting SWCNTs is distinguished from these previous studies since we: 1) include a multisubband nonequilibrium transport study applicable to devices; 2) investigate charge scattering in the presence of phonon scattering; and 3) develop a theory for remote charge correlation effects using methods that have found success in 2-D systems. Screening theory will be based on the self-consistent method of Petrov and Rotkin [18], [19]. In the present work, the unscreened carrier scattering rate due to a linear remote charge is density

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and the distribution of charges the momentum transfer . However, as the SWCNT along the azimuthal direction length decreases these effects begin to influence the density function, particularly when the charge density is large. Since the second term in (7) vanishes for intrasubband scattering , azimuthal remote charge distributions will enhance intersubband scattering events. Note that even in the limit of infinite , the scattering rate will still depend on through the term in (5) and (6). Screening of the remote charge by the SWCNT and the surrounding medium must be considered in the scattering rate [(5)]. Following the theory in [18] and [19], for a long SWCNT the charge fluctuation is screened according to

(5) The bracketed term is the density correlation function of the remote charge shell [20], [43], is the vacuum static dielectric constant, while is the length of both the nanotube and the surrounding charge shell. Also

(6) is the zero order modified Bessel function and is where the radius of the dielectric shell. The density correlation function is calculated assuming a finite length SWCNT

(7) where (8) Here, we have considered a random distribution of uncorrelated remote charges. The azimuthal charge distribution enters through the term (9) where is the charge pair probability distribution function. The formulation for the remote charge density function is appropriate for SWCNT carrier scattering in this work as we consider semiclassical homogeneous transport along the tube axis ( ). Scattering is formulated in terms of the average fluctuation in the remote charge distribution. This treatment is analogous to previous work in 2-D and 3-D systems [43]. A distinct cirmay be considcumferential distribution of remote charge ered and incorporated into the probability distribution function distributions will be presented in the through (9). Specific and the 2-D next section. Note that the specification of charge density on the surface of the coating dielectric , allows calculation of the linear remote charge density. In the case . of a uniform distribution along , In the limit of an infinitely long SWCNT/dielectric shell, the , independent of both density correlation function in (7) is

(10) The first term multiplying the charge fluctuation on the right side of (8) accounts for screening by the SWCNT mobile carriers, the back gate, and the dielectric shell. The nanotube is assumed to be long enough so that screening by the contact region may be ignored [18], [19]. Capacitances per unit length , appearing in (10) are the SWCNT quantum capacitance , and the the geometric capacitance of the SWCNT/gate . geometric capacitance of the SWCNT/dielectric coating The geometrical capacitances are and , for the dielectric geometry in Fig. 1. The quantum capacitance of the SWCNT is , the density of states at the SWCNT Fermi level (chemical potential). The second term multiplying the charge fluctuation in (10) accounts for image charge effects at the local interface region, where the remote charge resides [18]–[20]. As shown in Fig. 1, and are the static dielectric constants of the SWCNT coating material and the external surrounding material, respec, the image tively. If the device is in aqueous solution, charge screening term would then be a method to account for hydration of the remote charge surface. It is the fluctuation from the average remote charge distribution that scatters carriers in the encapsulated nanotube. The average charge density is expected to cause a shift in of the SWCNT. The the finite temperature Fermi level corresponding threshold voltage shift can be approximated as . Considering a p-type CNT-FET covered with a negative average charge density the turn-on gate voltage experiences a positive shift of . It is important to discuss the range of validity for using 1st order perturbation theory to develop the carrier/remote charge scattering rate. This approximation requires that the interaction energy is small compared with the carrier band energy which [18]. may be taken as the finite temperature Fermi energy in (6) and the density correlation function is Assuming in (7), the perturbation scheme is then valid when

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(11)

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Fig. 4. Distributions of remote charge covering the surface of a dielectric coated SWCNT. Shown are three distributions around the nanotube circumference (F  , 2, 3), corresponding to charge isolated to  ,  , and = of the circumference, respectively.

=1

2

2

Here, the right side of the equation is screened as in (10). Using , , and [35] for parameters graphitic materials, we find (11) is satisfied ( more than 10 larger) as long as . As we consider much smaller charge densities in this work, the first-order perturbation approximation in (5) should be valid. III. SIMULATION RESULTS To include the effects of remote charges on the device properties of a CNT-FET, we consider the charge distributions shown in Fig. 4. Three distributions around the circumferential direcare investigated and are designated as , 2, and tion distribution is the most asymmetric whereas 3. The distribution is completely symmetrical in . In all the cases remote charge extends along the entire SWCNT axis . As mentioned in the previous section, a random fluctuation of the remote charge density is considered. Analysis of carrier scattering and the effects on device characteristics will be studied as a function of the properties of the nanotube and the dielectric coating material. In Fig. 5, results are shown indicating SWCNT-FET device conductance variations predicted to occur when a 2-nm-thick charged dielectric covers the SWCNT channel. The SWCNT length is set at a micron, while both the gate and SWCNT . For the medium coating dielectrics are silica , surrounding the device, results are shown for vacuum , and salty water . The density of silica charges on the dielectric surface is set at and is uniform along . As we might expect, the density of surface oxygen atoms to occur at a density of 1 in silica, corresponds to the case when about 1% per of the surface oxygen atoms are charged. In the absence of remote charge, variations in the CNT-FET conductance with nanotube diameter, carrier density, and tube length have been shown to follow from phonon-limited transport [8], [25], [32]. These results showed that the conductance increased with increasing SWCNT tube diameter due to a reduction in phonon scattering and a decrease in carrier effective mass. Simulation results in Fig. 5 show that the effects of remote charge scattering are enhanced in larger diameter tubes. The SWCNT-FET is found to be more sensitive to charge scattering near the conductivity peaks which identify the onset of an additionally occupied subband. This agrees with experiments that report plateaus

Fig. 5. Simulated SWCNT conductance as a function of applied gate voltage. Two one micron length tubes with diameters of 2 and 4 nm are shown. Results are given for two cases: 1) without remote charge and 2) with a remote charge = of distribution F  located on the density of dielectric coating the nanotube. For case 2), the surface of a 2 nm thick dielectric constant of the surrounding medium is varied between " and for vacuum and salty water, respectively. "

Nc = 01 2 10 1 m SiO

= 80

=1

=1

Fig. 6. SWCNT valence band diagram showing cases when the Fermi level is at two levels E and E . Since the carrier-remote charge Coulombic rate decreases sharply with momentum transfer, scattering is stronger when the Fermi level is near a subband minima.

in the source to drain current of highly doped nanotubes [45], [46]. These results were attributed to interband scattering [45]. As shown in Fig. 6, when the Fermi level is close to a subband minima, Coulombic scattering via remote charge is enhanced since carriers can undergo transitions incurring a small momentum transfer. Reported current plateaus [45], [46] at gate voltages corresponding to the onset of a new transport subband mode may well result from columbic scattering of carriers with impurity charge. The effect of the medium surrounding the SWCNT-FET is found to be significant. For the simulated parameters in Fig. 5, we see significant conductance degradation in vacuum, yet minimal effects when the remote charges are in a salty water environment. The sensitivity of the SWCNT-FET to the circumferential symmetry of surrounding remote charges is found to depend on the length of the nanotube. As seen in Fig. 7, for a 500 nm length SWCNT the ON conductance is reduced by a factor of 2 to . as the charge distribution varies from

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Fig. 7. Simulated conductance of a single-walled nanotube backgated device as a function of applied gate voltage. Parameters are the same as those for the d nanotube simulation in Fig. 5 except for a variation in the device –3 (as shown length (L) and the distribution of remote charge density F  in Fig. 4). Furthermore, the two-dimensional charge density on the dielectric = multiplied by F  , so that the linear surface ( N ) is set at charge density is the same for each F  distribution considered.

= 4 nm

=1

Fig. 8. Simulated conductance of a single-walled nanotube back-gated device as a function of applied gate voltage. Parameters are the same as those for the " nanotube device simulation in Fig. 5 except for a variation d in the thickness of the dielectric coating the nanotube t .

= 4 nm = 1

05 2 10 m

When the tube length is increased to a micron, the conductance varies. Note that we have scaled the density varies little as when ) in Fig. 7 of charges ( is the same for all simso that the linear charge density ulated charge distributions. The gate voltage shift is, therefore, dependence of the conthe same in each case 2 V. The ductance is a result of variations in the remote charge scattering is strongly reduced as the tube rate. As seen in (7) and (8), -dependent length increases leading to a reduction in the terms in (7). As mentioned in the previous section, variations in the remote charge density will lead to enhanced intersubband scattering. This effect explains why the ON conductance, which occurs when multiple subbands are occupied, is reduced variations, whereas little degradation is seen in the by TURN-ON region when only one subband is typically occupied. -thick dielecSo far, simulations have been for a tric material coating the SWCNT. In Fig. 8, the device conductance is shown as a function of varying . Parameters are set to those in Fig. 5 for the case of a 4-nm diameter nanotube with vacuum as the surrounding medium. Results show that the device conductance is quite sensitive to the thickness of the dielectric coating. Note that there is more remote charge present when the dielectric is thicker since a fixed 2-D remote charge density is considered. For weak scattering, the conductance curves in Fig. 8 would rigidly shift due to variations in the threshold voltage. However, results show that there is a large increase in scattering as a function of , particularly when the dielectric the shape of thickness drops below 2 nm. When the conductance profile is distorted due to enhanced scattering. Simulations for the peak values of the field-effect mobility and are shown in Fig. 9. Rethe conductance as a function of , with silica used sults are for as the dielectric material. When only phonon scattering is considered, the mobility and conductance peaks are expected to in-

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( )

Fig. 9. Simulated peak values for the field-effect mobility and the conductance as a function of single-walled nanotube diameter. Results are shown for variations in the thickness of the charged dielectric coating the nanotube.

crease with SWCNT diameter as and , respectively (for degenerate transport) [25]. When remote charge scattering is included, the peak values are found to saturate at large diameters. This concurs with experiments where upon heavy doping a reduction in; 1) the sharpness of the nanotube turn-on current and 2) the current saturation level were both observed. [45] Here, theory predicts that the diameter for conductance (current) saturation onset increases with increasing thickness of the . The onset diameter is typically smaller dielectric coating for the peak mobility as compared with the peak conductance. In Fig. 9, the onset diameter is 2–2.5 for the mobility and 3–3.5 for the conductance. Variations with SWCNT diameter are found since: 1) phonon scattering dominates when d is small, and 2) small momentum transferring intersubband scattering is enhanced as increases. Note that the saturation onset diameter

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may be shifted by a variation in the dielectric coating or a variation in the density of remote charges. IV. CONCLUSION Simulations of the characteristics of carbon nanotube devices have been preformed incorporating scattering due to both phonons and remote charges within the nanotube environment. This study is based on the semiclassical Boltzmann treatment, and is applicable to long nanotubes typically desired in sensing applications. For transport in short nanotubes where coherent effects are needed, the reader is directed to references [47]–[50]. Our results show that CNT device properties are sensitive to the density and proximity of external charges. Such devices are typically sensitive to variations in the circumferential symmetry of the remote charge density distribution only when the for remote charge densities nanotube length is small ( ). Contrary to the effects of phonons whereby scattering weakens with increasing tube diameter, remote charge scattering is enhanced as the tube diameter increases. The Coulombic nature of the interactions provides increased device sensitivity when the gate voltage is set to a level which allows small momentum transfer scattering. This effect may be intrasuband in nature at low carrier densities, reducing the peak field-effect mobility, or an intersubband effect at higher CNT carrier densities. Both the peak field-effect mobility and the peak conductance are found to be strongly degraded by remote charge scattering for larger diameter tubes. Such an effect may be applicable in sensing devices allowing for the identification of the charge on a functionalized CNT coating. ACKNOWLEDGMENT The first author thanks the Army Research Laboratory and the Oak Ridge Associated Universities for support and thanks A. N. Akturk and N. Goldsman for useful discussions. REFERENCES [1] Y. Cui et al., “Nanowire nanosensors for highly sensitive and selective detection of biological and chemical species,” Science, vol. 293, pp. 1289–1292, Aug. 17, 2001. [2] T. Vo-Dinh, B. M. Cullum, and D. L. Stokes, “Nanosensors and biochips: Frontiers in biomolecular diagnosis,” Sens. Actuators B, vol. 74, pp. 2–11, 2001. [3] A. Modi et al., “Miniaturized gas ionization sensors using carbon nanotubes,” Nature, vol. 424, pp. 171–174, Jul. 10, 2003. [4] J. R. Stetter and G. J. Maclay, “Carbon nanotube sensors: A review,” in Advanced Micro and Nanosystems, H. Baltes, O. Brand, G. K. Fedder, C. Hierold, J. Korvink, and O. Tabata, Eds. Weinheim: Wiley, vol. 1, p. 358. [5] N. Sinha, J. Ma, and J. T. Yeow, “Carbon nanotube-based sensors,” J. Nanosci. Nanotechnol., vol. 6, pp. 573–590, 2006. [6] B. Mahar, C. Laslau, R. Yip, and Y. Sun, “Development of carbon nanotube-based sensors—A review,” IEEE Sensors J., vol. 7, no. 2, pp. 266–284, 2007. [7] T. Dürkop, S. A. Getty, E. Cobas, and M. S. Fuhrer, “Extraordinary mobility in semiconducting carbon nanotubes,” Nano Lett., vol. 4, pp. 35–39, 2004. [8] G. Pennington and N. Goldsman, “Semiclassical transport and phonon scattering of electrons in semiconducting carbon nanotubes,” Phys. Rev. B, vol. 68, pp. 45426–45437, 2003. [9] J. Kong, N. R. Franklin, C. Zhou, M. G. Chapline, S. Peng, K. Cho, and H. Dai, “Nanotube molecular wires as chemical sensors,” Science, vol. 287, pp. 622–625, 2000. [10] E. S. Snow, F. K. Perkins, E. J. Houser, S. C. Badescu, and T. L. Reinecke, “Chemical detection with a single-walled carbon nanotube capacitor,” Science, vol. 307, p. 1942, 2005.

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PENNINGTON et al.: SENSITIVITY OF CARBON NANOTUBE TRANSISTORS TO A CHARGED DIELECTRIC COATING

[38] X. Zhou, J. Y. Park, S. Huang, J. Liu, and P. L. McEuen, “Band structure, phonon scattering, and the performance limit of single-walled carbon nanotube transistors,” Phys. Rev. Lett., vol. 95, p. 146805, 2005. [39] W. Lu and C. M. Lieber, “Semiconductor nanowires,” J. Phys. D: Appl. Phys., vol. 39, pp. R387–R406, 2006. [40] R. Kotlyar, B. Obradovic, P. Matagne, M. Stettler, and M. D. Giles, “Assessment of room-temperature phonon-limited mobility in gated silicon nanowires,” Appl. Phys. Lett., vol. 84, pp. 5270–5272, 2004. [41] Y. Cui, Z. Zhong, D. Wang, W. Wang, and C. M. Lieber, “High performance silicon nanowire field effect transistors,” Nano Lett., vol. 3, no. 2, pp. 149–152, 2003. [42] S. Koo, A. Fujiwara, J. Han, E. M. Vogel, C. A. Richter, and J. E. Bonevich, “High inversion current in silicon nanowire field effect transistors,” Nano Lett., vol. 4, no. 11, pp. 2197–2201, 2004. [43] T. H. Ning and C. T. Sah, “Theory of scattering of electrons in a nondegenerate-semiconductor-surface inversion layer by surface-oxide charges,” Phys. Rev. B, vol. 6, no. 12, pp. 4605–4613, 1972. [44] L. X. Benedict, S. G. Louie, and M. L. Cohen, “Static polarizabilities of single-wall carbon nanotubes,” Phys. Rev. B, vol. 52, p. 8541, 1995. [45] J. Appenzeller, J. Knoch, M. Radosavljevic, and P. Avouris, “Multimode transport in Schottky-barrier carbon-nanotube field-effect transistors,” Phys. Rev. Lett., vol. 92, pp. 226802–226805, 2004. [46] R. D. Antonov and A. T. Johnson, “Subband population in a single-wall carbon nanotube diode,” Phys. Rev. Lett., vol. 83, pp. 3274–3276, 1999. [47] A. Svizhenko and M. P. Anantram, “Effect of scattering and contacts on current and electrostatics in carbon nanotubes,” Phys. Rev. B, vol. 72, p. 085430, 2005. [48] S. O. Koswatta, S. Hasan, and M. S. Lundstrom, “Ballisticity of nanotube field-effect transistors: Role of phonon energy and gate bias,” Appl. Phys. Lett., vol. 89, p. 023125, 2006. [49] S. O. Koswatta, S. Hasan, M. S. Lundstrom, M. P. Anantram, and D. E. Nikonov, “Nonequilibrium Green’s function treatment of phonon scattering in carbon-nanotube transistors,” IEEE Trans. Elec. Dev., vol. 54, p. 2339, 2007. [50] “The NEGF approach to nano-device simulation.” [Online]. Available: http://www.nanohub.org/topics/negf/ [51] A. Akturk, G. Pennington, and N. Goldsman, “Quantum modeling and proposed, designs of CNT-embedded nanoscale MOSFETs,” IEEE Trans. Elec. Dev., vol. 52, pp. 577–584, 2005.

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Gary Pennington is an Oak Ridge Associated Universities Postdoctoral Research Associate at the Army Research Laboratory, Adelphi, MD, working in the area of nanoelectronics. His previous research has involved both carbon nanotubes and wide bandgap semiconductors.

Matthew H. Ervin received the B.A. degree in chemistry from Lafayette College, Easton, PA, in 1986 and the Ph.D. degree in analytical chemistry from The Pennsylvania State University, University Park, in 1992. He has been a Research Chemist at the U.S. Army Research Laboratory. Adelphi, MD, since 1994. Current research interests include developing carbon nanotube-based high frequency FET, developing nanowire/carbon nanotubebased sensors, nanowire device assembly using nanomanipulation, and beam written contacts. Secondary interest include electron microscopic, focused ion beam, and energy dispersive X-ray characterization of materials and devices.

Alma E. Wickenden received the B.S. degree in physical science and the M.S. and Ph.D. degrees in materials science and engineering from The Johns Hopkins University, Baltimore, MD, in 1985, 1989, and 1993, respectively. She is a Senior Researcher with the Army Research Laboratory’s Sensors Electron Devices Directorate, Adelphi, MD. She established ARL’s Nanoelectronics Team, which focuses on the development of ultra-low-power amperometric nanoscale sensors and nanoscale electromagnetic devices for ultra-high-frequency (GHz-THz) communications. Her current research interests include the investigation of CNT-based field effect transistor devices for sensor applications and novel nanoscale oscillators for ultra-high (10 GHz–10 Thz) frequency communications. She has published over 70 publications in the field of wide bandgap III-nitride semiconductor materials. Dr. Wickenden is a member of the American Vacuum Society.

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Sensitivity of Carbon Nanotube Transistors to a Charged Dielectric ...

Abstract—This paper investigates the electronic proper- ties of single-walled carbon nanotube field-effect transistors. (SWCNT-FETs) in which the SWCNT element is coated with a charged dielectric. The presence of remote charge on the surface of the dielectric is considered to effect carrier transport in the nanotube as a ...

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