Two-dimensional crystals have emerged as a class of materials that may impact future electronic technologies. Experimentally identifying and characterizing new functional two-dimensional materials is challenging, but also potentially rewarding. Here, we fabricate field-effect transistors based on few-layer black phosphorus crystals with thickness down to a few nanometres. Reliable transistor performance is achieved at room temperature in samples thinner than 7.5 nm, with drain current modulation on the order of 10(5) and well-developed current saturation in the I-V characteristics. The charge-carrier mobility is found to be thickness-dependent, with the highest values up to ∼ 1,000 cm(2) V(-1) s(-1) obtained for a thickness of ∼ 10 nm. Our results demonstrate the potential of black phosphorus thin crystals as a new two-dimensional material for applications in nanoelectronic devices.

http://absimage.aps.org/image/MAR14/MWS_MAR14-2013-005031.pdf

Black Phosphorus Field-effect Transistors

In this paper, we propose an approximate solution to solve the two dimensional potential distribution in ultra-thin body junctionless double gate MOSFET (JL DG MOSFET) operating in the subthreshold regime. Basically, we solved the 2D-Poisson equation along the channel, while assuming a parabolic potential across the silicon thickness, which in turn leads to some explicit relationships of the subthreshold current, subthreshold slope (SS) and drain induced barrier lowering (DIBL). This approach has been assessed with Technology Computer Aided Design (TCAD) simulations, confirming that this represents an interesting solution for further implementation in generic JL DG MOSFETs compact models.

Analytical model for ultra-thin body junctionless symmetric double gate MOSFETs in subthreshold regime

A 2-D semianalytical solution for the electrostatic potential valid for junctionless symmetric double-gate field-effect transistors in subthreshold regime is proposed, which is based on the parabolic approximation for the potential and removes previous limitations. Based on such a solution, a semi-analytical expression for the current is derived. The potential and current models are validated through comparisons with TCAD simulations and are used to evaluate relevant short-channel effect parameters, such as threshold roll-off, drain-induced barrier lowering, and inverse subthreshold slope. The implications of different possible definitions of threshold voltage, either based on the potential in the channel or on a fixed current level, are discussed. Finally, a fully analytical simplification for the current is suggested, which can be used in compact models for circuit simulations.

Semianalytical Model of the Subthreshold Current in Short-Channel Junctionless Symmetric Double-Gate Field-Effect Transistors

A 2-D closed form, analytical compact model for long- and short-channel junctionless accumulation mode double gate MOSFETs is presented. The physics-based 2-D model for the potential is derived with the help of Poisson's equation and the conformal mapping technique by Schwarz-Christoffel. From this closed-form solution, we derive simple equations for the calculation of the threshold voltage VT and subthreshold slope S. Using Lambert's W-function and a smoothing function for the transition between the depletion and accumulation regions, a unified charge model valid for all operating regimes is developed. Dependencies between the physical device parameters and their impact on the device performance are worked out. A comparison of our 2-D physics-based compact model is done versus 2-D technology computer-aided design (TCAD) Sentaurus simulation data.

Compact Model for Short-Channel Junctionless Accumulation Mode Double Gate MOSFETs

With the exact solution of the 2-D Poisson's equation in cylindrical coordinates, analytical subthreshold behavior models for junctionless cylindrical surrounding-gate (JLCSG) MOSFETs are developed. Using these analytical models, subthreshold characteristics of JLCSG MOSFETs are investigated in terms of channel electrostatic potential distribution, subthreshold current, and subthreshold slope (SS). It is shown that the electrostatic potential distribution, subthreshold current, and SS predicted by the analytical models are in close agreement with 3-D numerical simulation results without the need of any fitting parameters. These analytical models not only provide useful physical insight into the subthreshold behaviors, but also offer basic design guideline for the nanoscale JLCSG MOSFETs.

Subthreshold Behavior Models for Nanoscale Short-Channel Junctionless Cylindrical Surrounding-Gate MOSFETs

This report focuses on the development of an analytical two-dimensional model to calculate the potential within ultra-scaled junctionless double-gate MOSFETs (DG MOSFETs), which is valid in the subthreshold regime. From that we derive an expression for calculating the threshold voltage of such devices, and present our first results. Compared to conventional MOSFETs, the proposed junctionless transistor has no pn-junctions. Its type of doping in the channel region is the same as in the source/drain regions. The device is turned on by creating a conducting channel in the center of the silicon film, and turned off by depleting it. To achieve good I on / I off ratios, and to ensure a safe switching behavior, the investigation of the subthreshold region is therefore important. The analytical model is compared with numerical simulation results from TCAD Sentaurus. Its validity is confirmed for long-channel, as well as for ultra-scaled devices having a channel length about 22 nm. Since the junctionless device is still in its infancy, an analytical model, especially for short-channel devices, can provide help to understand its electrostatic characteristics.

Threshold voltage, and 2D potential modeling within short-channel junctionless DG MOSFETs in subthreshold region

In this paper, we present a new compact drain-current model for double-gate or triple-gate silicon on insulator (SOI) metal-oxide-semiconductor field-effect transistors, which is based on a physics-based 3-D analysis. Explicit analytical model equations for the height of the potential barrier are derived in closed form from a 3-D model for the channel electrostatics without the need to introduce any fitting parameter. The device current is described by a superposition of a surface-channel current above threshold and a center current in the subthreshold region, accounting for the movement of the most leaky path in the device cross section. Comparison with Technology Computer Aided Design (TCAD) shows a good scalability of the model down to a gate length of 30 nm. Furthermore, the I-V characteristics are compared with measurements and obtain accurate results down to an effective channel length of 53 nm.

$\hbox{MOS}^{3}$ : A New Physics-Based Explicit Compact Model for Lightly Doped Short-Channel Triple-Gate SOI MOSFETs

We derived an analytical two-dimensional model to calculate the potential within ultra-scaled junctionless double-gate MOSFETs (DG MOSFETs) valid in subthreshold region. We propose an approach how to calculate the threshold voltage of such devices, and present our first results. Compared to conventional MOSFETs, the proposed junctionless transistor has no pn-junctions. Its type of doping in the channel region is the same as in the source/drain. The device is turned on by creating a conducting channel in the center of the silicon, and turned off by depleting it. To ensure a safe switching behavior, the investigation of the subthreshold region is therefore important. A Comparison of our model with numerical simulation results confirms its validity for ultra-scaled devices having a channel length about 22 nm.

2D analytical potential modeling of junctionless DG MOSFETs in subthreshold region including proposal for calculating the threshold voltage

An analytical closed-form model to calculate the electrostatics in undoped or lightly doped Double-Gate MOSFETs or Schottky barrier Double-Gate MOSFETs (SB-DG-MOSFETs) in subthreshold region is presented. The model does not introduce any kind of fitting parameters, all parameters depend on geometry and boundary conditions. 2D Poisson’s equation is solved in an analytical closed-form with the conformal mapping technique. The extended approach for the potential is compared with a previously presented approach of the same authors. Furthermore, a framework to apply the 2D analytical closed-form calculation of the electrostatic potential and a 2D analytical closed-form solution of the electric field from a previous work is presented. Solutions for constant and linear boundary conditions are used to model the potential and the electric field of these Double-Gate MOSFET structures step by step.

Analytical compact modeling framework for the 2D electrostatics in lightly doped double-gate MOSFETs

The physical influence of temperature down to the cryogenic regime is analyzed in a comprehensive study and the comparison of IV and III–V Schottky barrier (SB) double-gate MOSFETs. The exploration is done using the Synopsys TCAD Sentaurus device simulator and first benchmarked with experimental data. The important device physics of both SB-MOSFETs and conventional MOSFETs are reviewed. The impact of temperature on device performance down to the liquid-nitrogen regime is then explored. We find reduced drive currents in SB-MOSFETs fabricated on small effective mass materials and that SB lowering can significantly improve SB-MOSFETs, especially at low temperatures.

Mike Schwarz

Papers

Threshold voltage, and 2D potential modeling within short-channel junctionless DG MOSFETs in subthreshold region

$\hbox{MOS}^{3}$ : A New Physics-Based Explicit Compact Model for Lightly Doped Short-Channel Triple-Gate SOI MOSFETs

2D analytical potential modeling of junctionless DG MOSFETs in subthreshold region including proposal for calculating the threshold voltage

Analytical compact modeling framework for the 2D electrostatics in lightly doped double-gate MOSFETs

On the Physical Behavior of Cryogenic IV and III–V Schottky Barrier MOSFET Devices