Sub-10 nm nanostructures have received broad interest for their intriguing nano-optical phenomena, such as extreme field localization and enhancement, quantum tunneling effect, and strong coupling. The range of cutting-edge applications based on single-digit-nanometer scale structures has expanded with the development of nanofabrication technologies. However, challenges still remain in overcoming fabrication limits, such as scalability, controllability, and reproducibility for further practical applications of the sub-10 nm nanostructures. In this review, we discuss the recent advances in top-down nanofabrication methods towards single-digit-nanometer-sized structures. The well-known examples include electron beam lithography (EBL), focused ion beam (FIB) milling or lithography, atomic layer deposition (ALD), and other unconventional techniques to obtain sub-10 nm nanostructures or nanogaps. We discuss state-of-the-art applications for sub-10 nm nanophotonics such as optical trapping or sensing devices, imaging devices, and electronic devices.

Top-down nanofabrication approaches toward single-digit-nanometer scale structures

A novel channel mobility model with two-dimensional (2D) aspect is presented covering the effects of source/drain voltage (VDS) and gate voltage (VGS), and incorporating the drift and diffusion current on the surface channel at the nano-node level, at the 28-nm node. The effect of the diffusion current is satisfactory to describe the behavior of the drive current in nano-node MOSFETs under the operations of two-dimensional electrical fields. This breakthrough in the model’s establishment opens up the integrity of long-and-short channel devices. By introducing the variables VDS and VGS, the mixed drift and diffusion current model effectively and meaningfully demonstrates the drive current of MOSFETs under the operation of horizontal, vertical, or 2D electrical fields. When comparing the simulated and experimental consequences, the electrical performance is impressive. The error between the simulation and experiment is less than 0.3%, better than the empirical adjustment required to issue a set of drive current models.

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Channel Mobility Model of Nano-Node MOSFETs Incorporating Drain-and-Gate Electric Fields

Performance metrics of current transport in pristine graphene nanoribbon field-effect transistors using recursive non-equilibrium Green's function approach

In this paper, a charge-based analytical model is proposed for double-gate MOSFETs working in the quasi-ballistic regime. The model includes both Lundstrom backscattering theory and conventional drift–diffusion theory. Both the theories are used to model the charge density along channel length, which are used to solve Poisson's equation to get the variation of the channel potential. To compute the ballistic segments and diffusive segments of the current, the calculated charge density and surface potential are used. The model is validated with reported numerical data of different channel length and found to be accurate.

Analytical model for quasi-ballistic transport in MOSFET including carrier backscattering

Molybdenum disulfide (MoS2) has distinctive electronic and mechanical properties which make it a highly prospective material for use as a channel in upcoming nanoelectronic devices. An analytical modeling framework was used to investigate the I–V characteristics of field-effect transistors based on MoS2. The study begins by developing a ballistic current equation using a circuit model with two contacts. The transmission probability, which considers both the acoustic and optical mean free path, is then derived. Next, the effect of phonon scattering on the device was examined by including transmission probabilities into the ballistic current equation. According to the findings, the presence of phonon scattering caused a decrease of 43.7% in the ballistic current of the device at room temperature when L = 10 nm. The influence of phonon scattering became more prominent as the temperature increased. In addition, this study also considers the impact of strain on the device. It is reported that applying compressive strain could increase the phonon scattering current by 13.3% at L = 10 nm at room temperature, as evaluated in terms of the electrons’ effective masses. However, the phonon scattering current decreased by 13.3% under the same condition due to the existence of tensile strain. Moreover, incorporating a high-k dielectric to mitigate the impact of scattering resulted in an even greater improvement in device performance. Specifically, at L = 6 nm, the ballistic current was surpassed by 58.4%. Furthermore, the study achieved SS = 68.2 mV/dec using Al2O3 and an on–off ratio of 7.75 × 104 using HfO2. Finally, the analytical results were validated with previous works, showing comparable agreement with the existing literature.

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Modeling the Impact of Phonon Scattering with Strain Effects on the Electrical Properties of MoS2 Field-Effect Transistors

This paper presents a physically valid quasi-ballistic drain current model applicable for nanoscale symmetric Double Gate (SDG) MOSFETs. The proposed drain current model includes both diffusive and ballistic transport phenomena. The model considers the important positional carrier scattering dependency effect near the source region described in terms of transmission and reflection co-efficients related to the scattering theory. The significance of carrier transport near the bottleneck source region is illustrated where the carriers diffuse into the channel at a relatively lower velocity before accelerating ballistically. The results obtained demonstrate carrier scattering dependency at the critical layer defined near the low field source region on the drain current characteristics. The proposed model partly evolves from Natori’s ballistic bulk MOSFET model that is modified accordingly to be valid for a symmetric Double Gate MOSFET in the nanoscale regime. Carrier degeneracy and Fermi–Dirac statistics are included in the work so as to justify the complete physicality of the model. The model is further extended and is shown to be continuous in terms of terminal charges and capacitances in all regions of operation. A comparative analysis is also done between the proposed quasi-ballistic model and a hypothetical complete ballistic device.

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A quasi-ballistic drain current, charge and capacitance model with positional carrier scattering dependency valid for symmetric DG MOSFETs in nanoscale regime.

This work presents a simple physics based quasi-ballistic drain current model applicable for nanoscale Double Gate (DG) MOSFETs. The proposed model is physical and includes both drift-diffusion and ballistic transport phenomena. The model considers scattering effects that occur in real nanoscale devices, in terms of transmission and reflection co-efficients related to scattering theory. The results obtained in the proposed work provide an intuitive analysis and signify the positional scattering dependency at the critical layer near the low field source region on the drain current characteristics. An insightful and comparative analysis is done for the proposed quasi-ballistic model, with a hypothetical complete ballistic device and a velocity saturated short channel DG MOSFET model.

A Quasi-Ballistic Drain current model with Positional Scattering Dependency applicable for Nanoscale DG MOSFETs

This paper presents a velocity saturated and channel length modulated drain current, charge and capacitance model for a symmetric Double Gate (SDG) short channel MOSFET. The proposed drain current model partially evolves from an existing and well established analytical potential long channel DG MOSFET model and is further modified to be applicable for short channel devices. The projected model includes velocity saturation effect and short channel effects (SCEs) like channel length modulation (CLM) and threshold voltage shift. These effects are incorporated by considering pseudo-two-dimensional electrostatics at the drain end. The proposed work is derived from Pao-Sah integral without using charge sheet approximation. The drain current model captures the essential physics and signature of a modern velocity saturated short channel device and provides continuity in all regions of MOSFET operation. Solutions for charges and capacitances in the presence of velocity saturation and short channel effects are given explicitly. The results obtained in this work are as per the scale length theory applicable for a Double Gate (DG) MOSFET and hence may be used in compact modeling of nanoscale transistors.

An Analytic Potential Based Velocity Saturated Drain Current, Charge and Capacitance Model for Short Channel Symmetric Double Gate MOSFETs

ABSTRACT The work proposes a physically accurate quasi-ballistic drain current model valid for Double Gate (DG) MOSFETs in the nanoscale regime. The proposed quasi-ballistic model considers the carrier scattering physics and includes both ballistic and diffusive transport. Based on the concepts of scattering theory, a semi-empirical approach is used to determine the diffusive carrier scattering at the critical channel length as a function of drain bias. A generalised three region scale length model is applied to the proposed device structure with arbitrary dielectric constants and oxide thicknesses to examine the device channel length scaling limits. The significance of Eigen values and the scale length equations applicable for the proposed device structure is discussed. The drain current model essentially captures the key signature effect observed in rigorously scaled short channel devices. Further, the proposed quasi-ballistic model demonstrates its physical aptness and optimal accuracy when compared with other similar recent works. The model results obtained are verified using numerical simulations and are found to exhibit excellent continuity in all regions of the device operation.

Vyas R. Murnal

Papers

A quasi-ballistic drain current, charge and capacitance model with positional carrier scattering dependency valid for symmetric DG MOSFETs in nanoscale regime.

A Quasi-Ballistic Drain current model with Positional Scattering Dependency applicable for Nanoscale DG MOSFETs

An Analytic Potential Based Velocity Saturated Drain Current, Charge and Capacitance Model for Short Channel Symmetric Double Gate MOSFETs

An optimized nanoscale Quasi-Ballistic DG MOSFET model with diffusive carrier scattering dependency