Michael Loong Peng Tan

The Ultimate Ballistic Drift Velocity in Carbon Nanotubes

The carriers in a carbon nanotube (CNT), like in any quasi-1-dimensional (Q1D) nanostructure, have analog energy spectrum only in the quasifree direction; while the other two Cartesian directions are quantum-confined leading to a digital (quantized) energy spectrum. We report the salient features of the mobility and saturation velocity controlling the charge transport in a semiconducting single-walled CNT (SWCNT) channel. The ultimate drift velocity in SWCNT due to the high-electric-field streaming is based on the asymmetrical distribution function that converts randomness in zero-field to a stream-lined one in a very high electric field. Specifically, we show that a higher mobility in an SWCNT does not necessarily lead to a higher saturation velocity that is limited by the mean intrinsic velocity depending upon the band parameters. The intrinsic velocity is found to be appropriate thermal velocity in the nondegenerate regime, increasing with the temperature, but independent of carrier concentration. However, this intrinsic velocity is the Fermi velocity that is independent of temperature, but depends strongly on carrier concentration. The velocity that saturates in a high electric field can be lower than the intrinsic velocity due to onset of a quantum emission. In an SWCNT, the mobility may also become ballistic if the length of the channel is comparable or less than the mean free path.

Ballistic quantum transport in a nanoscale metal-oxide-semiconductor field effect transistor

The ballistic saturation velocity in a nanoscale metal-oxide-semiconductor field effect transistor (MOSFET) is revealed to be limited to the Fermi velocity in a degenerately induced channel appropriate for the quasi-two-dimensional nature of the inverted channel. The saturation point drain velocity is shown to rise with the increasing drain voltage approaching the intrinsic Fermi velocity, giving the equivalent of channel-length modulation. Quantum confinement effect degrades the channel mobility to the confining gate electric field as well as increases the effective thickness of the gate oxide. When the theory developed is applied to an 80nm MOSFET, excellent agreement to the experimental data is obtained.

The drain velocity overshoot in an 80 nm metal-oxide-semiconductor field-effect transistor

The current at the onset of saturation in a metal-oxide-semiconductor field-effect transistor (MOSFET) is shown to be limited by the drain velocity that increases toward its saturation value with the increase in the drain voltage. The saturation of velocity crops up as randomly oriented velocity vectors in equilibrium realign themselves to become unidirectional in the presence of an extremely high electric field. The intrinsic velocity, the ultimate saturation velocity, is the function of carrier concentration and temperature, consistent with the predictions of the ballistic transport. The presence of a quantum emission either by emission of a phonon or photon lowers the saturation velocity below its intrinsic value. Channel conduction beyond the quasisaturation point enhances due to the drain velocity overshoot as a result of enhanced drain electric field as drain voltage is increased. The excellent agreement with experimental data on an 80 nm channel, without using any artificial parameters, confirms th...

Ballistic mobility and saturation velocity in low-dimensional nanostructures

Ohms law, a linear drift velocity response to the applied electric field, has been and continues to be the basis for characterizing, evaluating performance, and designing integrated circuits, but is shown not to hold its supremacy as channel lengths are being scaled down. In the high electric field, the collision-free ballistic transport is predicted, while in low electric field the transport remains predominantly scattering-limited in a long-channel. In a micro/nano-circuit, even a low logic voltage of 1V gives an electric field that is above its critical value ec (e>>ec) triggering non-ohmic behavior that results in ballistic velocity saturation. The saturation velocity is an appropriate thermal velocity for a non-degenerate and Fermi velocity for a degenerate system with given dimensionality. A quantum emission may lower this ballistic velocity. The collision-free ballistic mobility in the ohmic domain arises when the channel length is smaller than the mean free path. The results presented will have a profound influence in interpreting the data on a variety of low-dimensional nanostructures.

The high-field drift velocity in degenerately-doped silicon nanowires

The charge transport in nanowires suitable for high-speed applications depends on charge carriers mobility and saturation velocity in the conducting channel. It is shown that the high mobility does not always lead to higher carrier drift velocity. The ultimate drift velocity (the intrinsic velocity) due to the high-electric-field streaming is based on the asymmetrical distribution function that converts randomness in zero-field to a streamlined one in a very high electric field. The saturation velocity limited to the intrinsic velocity is an appropriate thermal velocity for a non-degenerately doped nanowire, increasing with the temperature, but independent of carrier concentration. However, this saturation velocity is the appropriate Fermi velocity for a degenerately doped silicon nanowire, increasing with carrier concentration but independent of temperature. The results obtained are applied to the modelling of a silicon nanowire transistor.

Analytical modeling of glucose biosensors based on carbon nanotubes

In recent years, carbon nanotubes have received widespread attention as promising carbon-based nanoelectronic devices. Due to their exceptional physical, chemical, and electrical properties, namely a high surface-to-volume ratio, their enhanced electron transfer properties, and their high thermal conductivity, carbon nanotubes can be used effectively as electrochemical sensors. The integration of carbon nanotubes with a functional group provides a good and solid support for the immobilization of enzymes. The determination of glucose levels using biosensors, particularly in the medical diagnostics and food industries, is gaining mass appeal. Glucose biosensors detect the glucose molecule by catalyzing glucose to gluconic acid and hydrogen peroxide in the presence of oxygen. This action provides high accuracy and a quick detection rate. In this paper, a single-wall carbon nanotube field-effect transistor biosensor for glucose detection is analytically modeled. In the proposed model, the glucose concentration is presented as a function of gate voltage. Subsequently, the proposed model is compared with existing experimental data. A good consensus between the model and the experimental data is reported. The simulated data demonstrate that the analytical model can be employed with an electrochemical glucose sensor to predict the behavior of the sensing mechanism in biosensors.

Transition of equilibrium stochastic to unidirectional velocity vectors in a nanowire subjected to a towering electric field

The equilibrium Fermi–Dirac distribution is revealed to transform to an asymmetric distribution in a very high electric field where the energy gained (or lost) in a mean free path is of paramount importance. The equilibrium stochastic velocity vectors randomly oriented in and opposite to the quasifree direction of a nanowire are shown to streamline in the presence of an extremely high electric field. The complete velocity-field characteristics are acquired. The ultimate directed drift velocity in a towering field is shown to be limited to the appropriately averaged Fermi velocity in the strongly degenerate limit where only half of the quantum states are accessible to electrons. This unidirectional velocity does not sensitively depend on the low-field Ohmic mobility. The emission of a quantum in the form of a phonon or photon lowers the saturation velocity from its ultimate unidirectional limit.

Enhanced Device and Circuit-Level Performance Benchmarking of Graphene Nanoribbon Field-Effect Transistor against a Nano-MOSFET with Interconnects

Comparative benchmarking of a graphene nanoribbon field-effect transistor (GNRFET) and a nanoscale metal-oxide-semiconductor field-effect transistor (nano-MOSFET) for applications in ultralarge-scale integration (ULSI) is reported. GNRFET is found to be distinctly superior in the circuit-level architecture. The remarkable transport properties of GNR propel it into an alternative technology to circumvent the limitations imposed by the silicon-based electronics. Budding GNRFET, using the circuit-level modeling software SPICE, exhibits enriched performance for digital logic gates in 16 nm process technology. The assessment of these performance metrics includes energy-delay product (EDP) and power-delay product (PDP) of inverter and NOR and NAND gates, forming the building blocks for ULSI. The evaluation of EDP and PDP is carried out for an interconnect length that ranges up to 100 μm. An analysis, based on the drain and gate current-voltage (- and -), for subthreshold swing (SS), drain-induced barrier lowering (DIBL), and current on/off ratio for circuit implementation is given. GNRFET can overcome the short-channel effects that are prevalent in sub-100 nm Si MOSFET. GNRFET provides reduced EDP and PDP one order of magnitude that is lower than that of a MOSFET. Even though the GNRFET is energy efficient, the circuit performance of the device is limited by the interconnect capacitances.

Device and circuit-level performance of carbon nanotube field-effect transistor with benchmarking against a nano-MOSFET

The performance of a semiconducting carbon nanotube (CNT) is assessed and tabulated for parameters against those of a metal-oxide-semiconductor field-effect transistor (MOSFET). Both CNT and MOSFET models considered agree well with the trends in the available experimental data. The results obtained show that nanotubes can significantly reduce the drain-induced barrier lowering effect and subthreshold swing in silicon channel replacement while sustaining smaller channel area at higher current density. Performance metrics of both devices such as current drive strength, current on-off ratio (Ion/Ioff), energy-delay product, and power-delay product for logic gates, namely NAND and NOR, are presented. Design rules used for carbon nanotube field-effect transistors (CNTFETs) are compatible with the 45-nm MOSFET technology. The parasitics associated with interconnects are also incorporated in the model. Interconnects can affect the propagation delay in a CNTFET. Smaller length interconnects result in higher cutoff frequency.

High-field transport in a graphene nanolayer

High-field electron transport properties in a two-dimensional nanolayer are studied by an application of the anisotropic nonequilibrium distribution function, a natural extension of the Fermi-Dirac distribution by inclusion of energy gained/absorbed in a mean free path (mfp). The drift velocity for conical band structure of graphene is shown to rise linearly with the electric field in a low electric field that is below the critical electric field. The critical electric field, equal to thermal voltage divided by the mfp, marks the transition from ohmic linear transport to saturated behavior in a high electric field. As field rises beyond its critical value, the drift velocity is sublinear resulting in ultimate saturation; the ultimate saturation velocity is comparable to the Fermi velocity in graphene. The quantum emission is found not to affect the mobility, but is efficient in lowering the saturation velocity. Excellent agreement is obtained with the experimental data for graphene on silicon dioxide substrate.