Mani Vaidyanathan

Self-consistent ac quantum transport using nonequilibrium Green functions

We develop an approach for self-consistent ac quantum transport in the presence of time-dependent potentials at nontransport terminals. We apply the approach to calculate the high-frequency characteristics of a nanotube transistor with the ac signal applied at the gate terminal. We show that the self-consistent feedback between the ac charge and potential is essential to properly capture the transport properties of the system. In the on-state, this feedback leads to the excitation of plasmons, which appear as pronounced divergent peaks in the dynamic conductance at terahertz frequencies. In the off-state, these collective features vanish, and the conductance exhibits smooth oscillations, a signature of single-particle excitations. The proposed approach is general and will allow the study of the high-frequency characteristics of many other low-dimensional nanoscale materials such as nanowires and graphene-based systems, which are attractive for terahertz devices, including those that exploit plasmonic excitations.

RF Performance Potential of Array-Based Carbon-Nanotube Transistors—Part II: Extrinsic Results

A comprehensive study, which is presented in two parts, is performed to assess the radio-frequency (RF) performance potential of array-based carbon-nanotube field-effect transistors. In Part II, which is presented in this paper, the infrastructure from Part I is utilized to examine more advanced aspects of the RF characteristics. The subversive effects of the extrinsic (parasitic) resistances and capacitances are added to an array-based structure, and the behaviors of key RF figures of merit, such as the extrinsic unity-current-gain frequency fT, the attainable power gain, and the unity-power-gain frequency fmax, are examined versus tube pitch and gate-finger layout. The results are compared with those of state-of-the-art high-frequency transistors and to the benchmark determined by the next generation of RF CMOS-as defined by the International Technology Roadmap for Semiconductors for the year 2015-and they provide an indication of the potential advantages and disadvantages of array-based nanotube transistors.

Understanding the Frequency- and Time-Dependent Behavior of Ballistic Carbon-Nanotube Transistors

The high-frequency and time-dependent behavior of carbon-nanotube (CN) transistors is examined by numerically solving the time-dependent Boltzmann transport equation self-consistently with the Poisson equation. The two-port admittance matrix, containing the transistors y-parameters, is extracted. At frequencies below the transistors unity-current-gain frequency fT, the y-parameters are shown to agree with those predicted from a quasi-static description of transistor operation, provided that the partitioning factor for the device charge is extracted through application of an appropriate time-dependent ramp voltage to the gate. The physics of time-dependent transport is described, and by examining the positive- and negative-going components of electron charge in the nanotube, it is shown for an nin device structure that the n regions can add a time delay to the device response, even though these regions do not affect the transistors extrapolated fT. For very high frequencies, or for very fast transients, it is pointed out that the conventional ldquofloating boundary conditionrdquo approach, which was originally suggested for dc simulations of ballistic Mosfets, becomes questionable when applied to time-dependent simulations of nanotubes. While this paper omits collisions and focuses on an intrinsic transistor structure that excludes external parasitics, it provides a first useful step toward the full frequency- and time-dependent characterization of CN transistors.

RF Performance Limits and Operating Physics Arising From the Lack of a Bandgap in Graphene Transistors

With the aid of self-consistent quantum-mechanical simulations and simple expressions for the radio-frequency (RF) metrics, we examine the impact of a lack of a bandgap on limiting the RF potential of graphene transistors. We consider the transconductance, gate-input capacitance, output conductance, unity-current-gain frequency, and unity-power-gain frequency. We show that the lack of a bandgap leads to all RF metrics being optimal when the bias point is chosen such that the drain Fermi level aligns with the Dirac point at the midpoint of the channel. We are also able to quantify the precise extent to which the lack of a bandgap limits the transistors cutoff frequencies, an issue that has been flagged as requiring crucial attention to make graphene transistors competitive. For an 18-nm channel length, we show that the extrinsic unity-current-gain frequency could be improved by 300 GHz and the unity-power-gain frequency could be doubled if a bandgap could be introduced to reduce the output conductance to zero.

RF Linearity Potential of Carbon-Nanotube Transistors Versus MOSFETs

Carbon-nanotube, field-effect transistors (CNFETs) are among the candidates for emerging radio-frequency applications, and improved linearity has recently been identified as one of the performance advantages they might offer. In this paper, the potential for improved linearity has been investigated by considering an array-based device structure under the best-case scenario of ballistic transport. A nonlinear equivalent circuit for ballistic field-effect transistors is used to compare the linearity of CNFETs to conventional MOSFETs. We show that nanotube devices working at high frequencies are not inherently linear, as recently suggested in the literature, and that CNFETs exhibit overall linearity that is comparable to their MOSFET counterparts. The nonlinear quantum capacitance is identified to be a major source of high-frequency nonlinearity in CNFETs. The impacts of device parameters such as oxide capacitance, channel width, and tube pitch are also investigated.

Switching-Speed Limitations of Ferroelectric Negative-Capacitance FETs

Recently, negative-capacitance FETs (NCFETs) have been proposed to reduce subthreshold slope and help continue supply-voltage scaling alongside channel-length scaling. We investigate the high-frequency switching behavior of NCFETs using the Landau-Khalatnikov equation to model ferroelectric materials. Multidomain interactions in the ferroelectric are considered, resulting in strong agreement with experimental measurements. Operation of NCFETs at gigahertz frequencies is investigated with this experimentally validated multidomain model. We find that the effectiveness of the voltage amplification in NCFETs is strongly dependent on the viscosity coefficient ρ of the ferroelectric, and that a low ρ (<;0.1 Ω · m) is required for the operation at the high gigahertz frequencies.

RF Linearity Performance Potential of Short-Channel Graphene Field-Effect Transistors

The radio-frequency (RF) linearity performance potential of short-channel graphene field-effect transistors (GFETs) is assessed by using a nonlinear small-signal circuit model under the first approximation of ballistic transport. An intrinsic GFET is examined to reveal the key features of GFET linearity, and extrinsic parasitics are then included to assess the overall RF linearity. It is shown that short-channel GFETs can be expected to have a signature behavior versus gate bias that includes a constant-linearity region at low gate bias, sweet spots of high linearity before and after the gate bias for peak cutoff frequency, and poor linearity at the gate bias corresponding to the peak cutoff frequency. It is otherwise found that a GFET offers overall linearity that is comparable to a MOSFET and a CNFET, with the exception that the amount of intermodulation distortion in a GFET is dominated by the drain-injected carriers, a unique outcome of graphenes lack of a bandgap. Qualitative agreement with experiment in the signature behavior of GFET linearity supports the approach and conclusions.

Electronics From the Bottom Up: Strategies for Teaching Nanoelectronics at the Undergraduate Level

Nanoelectronics is an emerging area of electrical and computer engineering that deals with the current-voltage behavior of atomic-scale electronic devices. As the trend toward ever smaller devices continues, there is a need to update traditional undergraduate curricula to introduce electrical engineers to the fundamentals of the field. These fundamentals encompass topics from quantum mechanics and condensed-matter physics, and they pose new teaching challenges in electronics education; specifically, unconventional ideas must be presented in a rapid and yet complete way so that engineering undergraduates can quickly yet satisfyingly absorb the key concepts, and then apply these concepts to emerging devices. This paper describes the strategies employed by the author in teaching the subject to large undergraduate classes at his institution. These strategies include the use of computer visualization, a careful introduction of quantum mechanics, and a constant demonstration of the relevance of theory by practical examples and calculations. The effectiveness of the approach is illustrated through survey results of the Universal Student Ratings of Instruction at the authors institution and by way of typical assignment and exam questions that demonstrate the level of sophistication that students can attain in what might otherwise be viewed as a purely mathematical and esoteric subject.

Nonquasi-Static Effects and the Role of Kinetic Inductance in Ballistic Carbon-Nanotube Transistors

Nonquasi-static effects in ballistic carbon-nanotube (CN) FETs (CNFETs) are examined by solving the Boltzmann transport equation self-consistently with the Poisson equation. We begin by specifying the proper boundary conditions that should be employed in time-dependent simulations at high speeds; these are the proper boundary conditions for a characterization of the so-called intrinsic transistor, i.e., the internal portion of the device that is unaffected by the source and drain contacts. A transmission-line model that includes both the kinetic inductance (LK) and quantum capacitance (CQ) is then analytically developed from the Boltzmann and Poisson equations, and it is shown to represent the intrinsic transistors behavior at high frequencies, including a correct prediction of resonances in the transistors y-parameters. Finally, we show how to represent LK using lumped elements in the transistors traditional quasi-static equivalent circuit, and we demonstrate that the resulting circuit is capable of modeling the intrinsic behavior of a ballistic CNFET, including the observed resonances, to frequencies beyond the unity-current-gain frequency fT. External parasitics can be easily added for an overall compact model of ballistic CNFET operation.

Self-consistent simulation of array-based CNFETs: Impact of tube pitch on RF performance

The quantum-mechanical Schrodinger equation, implemented in an NEGF (non-equilibrium Greens function) framework, is solved self-consistently with the Poisson equation to study the impact of the distance between the tubes (pitch) on the high-frequency (RF) performance of array-based, carbon nanotube, field-effect transistors.