This paper surveys, reviews, and critiques analytic models of MOSFET short-channel effects (SCEs) in subthreshold published over the past four decades. In the first half of this paper, the published models on SCEs are categorized into the following four main groups based on their approach: 1) charging sharing models; 2) empirical expressions; 3) polynomial potential models; and 4) analytic solutions to 2-D Poisson's equation. The strength and weakness of each approach are elaborated in terms of its physical soundness and predictive ability. A key development was the exponential dependence of SCE on channel length (L) , SCE ~ exp(-L/l0), leading to the introduction of scale length (l0). In the second half of this paper, the predictions of each analytic SCE model are examined by generic 2-D numerical simulations. In particular, the merit of each model is judged by its prediction on the scale length (l0) as a function of the thickness and dielectric constant (κ) of the gate insulator. Only one model, i.e., the generalized scale length model that treated the silicon and insulator regions as two distinct dielectric regions with shared boundary conditions, correctly predicted the MOSFET scale length under all dielectric constant and thickness conditions. A variation of the generalized scale length model applies to recent multiple-gate MOSFETs near the limit of scaling.

Review and Critique of Analytic Models of MOSFET Short-Channel Effects in Subthreshold

Compact-modeling principles and solutions for nanoscale double-gate and gate-all-around MOSFETs are explained The main challenges of compact modeling for these devices are addressed, and different approaches for describing the electrostatics, the transport mechanisms, and the high-frequency behavior are explained Several approximations used to derive analytical solutions of Poisson's equation for doped and undoped devices are discussed, and the need for self-consistency with Schrodinger's equation and with the current continuity equation resulting from the transport models is addressed Several techniques to extend the compact modeling to the high-frequency regime and to study the RF performance, including noise, are presented and discussed

Compact-Modeling Solutions For Nanoscale Double-Gate and Gate-All-Around MOSFETs

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

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

A precise modeling framework for short-channel nanoscale double-gate (DG) and gate-all-around (GAA) MOSFETs is presented. For the DG MOSFET, the modeling is based on a conformal mapping analysis of the potential distribution in the device body arising from the interelectrode capacitive coupling, combined with a self-consistent procedure to include the effects of the inversion charge. The DG interelectrode coupling, which dominates the subthreshold behavior of the device, can also be applied with a high degree of precision to the cylindrical GAA MOSFET by performing a simple geometric scaling transformation to account for the difference in gate control in the two devices. Near threshold, self-consistent procedures invoking Poisson's equation in combination with boundary conditions and suitable modeling expressions for the potential are applied to the two devices. In strong inversion, these solutions converge to those of the respective long-channel devices. The drain current is calculated as part of the self-consistent treatment. The results for both the electrostatics and the current are in excellent agreement with numerical simulations.

Precise Modeling Framework for Short-Channel Double-Gate and Gate-All-Around MOSFETs

In this paper we present a new theoretical approach in MOS modeling to derive analytical, physics-based model equations for the geometry and voltage dependence of threshold voltage and for the subthreshold behavior of short-channel MOSFETs. Our approach uses conformal mapping techniques to analytically solve the two-dimensional Poisson equation, whereby inhomogeneous substrate doping is taken into account. The presented model consists of analytical equations in closed form and uses only physically meaningful parameters. Therefore, the results are not only useful in circuit simulators but also in calculations of scaling behavior, where planned processes can be investigated. Comparison with numerical device simulation results and measurements confirm the high accuracy of the presented model.

A Kostka

Papers

A new analytical method of solving 2D Poisson's equation in MOS devices applied to threshold voltage and subthreshold modeling