Elsevier

Solid-State Electronics

Volume 143, May 2018, Pages 49-55
Solid-State Electronics

Multi-Subband Ensemble Monte Carlo simulations of scaled GAA MOSFETs

https://doi.org/10.1016/j.sse.2018.02.004Get rights and content

Highlights

  • We developed a Multi-Subband Ensemble Monte Carlo simulator for 3D devices.

  • It considers quantum confinement effects in Si nanowire-based MOSFTEs.

  • Device performance is analyzed in terms of charge distribution and mobility.

  • Scaling analysis of the devices down to 8 nm channel lenght is performed.

Abstract

We developed a Multi-Subband Ensemble Monte Carlo simulator for non-planar devices, taking into account two-dimensional quantum confinement. It couples self-consistently the solution of the 3D Poisson equation, the 2D Schrödinger equation, and the 1D Boltzmann transport equation with the Ensemble Monte Carlo method. This simulator was employed to study MOS devices based on ultra-scaled Gate-All-Around Si nanowires with diameters in the range from 4 nm to 8 nm with gate length from 8 nm to 14 nm. We studied the output and transfer characteristics, interpreting the behavior in the sub-threshold region and in the ON state in terms of the spatial charge distribution and the mobility computed with the same simulator. We analyzed the results, highlighting the contribution of different valleys and subbands and the effect of the gate bias on the energy and velocity profiles. Finally the scaling behavior was studied, showing that only the devices with D=4nm maintain a good control of the short channel effects down to the gate length of 8nm.

Introduction

Non-planar MOS transistors with multiple gates represent the most promising solution to the ultimate scaling of CMOS technology [1] because of their superior immunity to short channel effects. Indeed, they are not only a possible future option under scrutiny, but they have already entered mass production [2], [3]. When the size of a device reaches the nanometric scale, quantum effects play an important role; quantum confinement is relevant for reduced lateral size (i. e. in the direction perpendicular to transport) and even more so in non-planar structures where confinement is two-dimensional. An approximately correct electron distribution taking into account quantum confinement can be obtained with corrections to the classical potential, employing algorithms which, however, need proper calibration for each considered structure and crystal orientation (see for example [4], [5]). As a consequence, to properly take into account quantum confinement effects in the cross section of the device it is necessary to solve the Schrödinger Equation (SE). The Multi-Subband Ensemble Monte Carlo (MS-EMC) approach employs the semi-classical Monte Carlo (MC) method to solve the Boltzmann transport equation, coupled with the solution of the SE in the perpendicular direction. The MC method, compared to common transport framework such as Drift–Diffusion, takes directly into account non-equilibrium carrier transport. On the other hand, compared to full quantum approaches, MC allows a simpler implementation of scattering mechanisms and relatively reduced computational requirements. For the same reason, in an effort to improve the classical Monte Carlo and Drift–Diffusion tools without an excessive computational demand, carrier band structure is described analytically employing the (anisotropic) effective mass approximation. Clearly, for severely reduced device dimensions in the transverse direction, this description is not as accurate as the one that could be obtained employing atomistic models such as those based on the Density Functional Theory or Tight Binding approach. However, it has been shown [6], [7] that reliable results can be obtained employing the effective mass model with bulk values of the effective mass for Si nanowires down to a diameter of 5nm and even below, if the value of the effective mass is correctly adjusted [7]. For all these reason, the chosen approach can be the optimal middle ground for devices whose transverse dimensions are small enough to make quantum confinement important, yet larger than a few nanometers where atomistic effects become essential.

In this work, we describe an MS-EMC simulator for 3D devices developed by our group, and show the possibilities it offers by studying the scaling properties of ultimate Gate-All-Around (GAA) MOS transistors with ultra-thin Si nanowires. Section 2 is devoted to the description of the simulator, while in the following one (Section 3) we define devices under study and report the obtained results and insights into the device behavior. Finally, conclusions are drawn in Section 4.

Section snippets

Simulator description

To model a non-planar device, such as GAA MOSFETs, we employ a simulator based on the MS-EMC approach. This method has been widely and successfully employed for the simulation of planar semiconductor devices [8], [9], [10], [11], and only recently it has been applied to 3D devices [12], [13]. The simulator is based on the space-mode approach [14], where the SE is solved in several cross sections perpendicular to the transport direction z, for each considered conduction band valley. Each SE

Results

We simulate GAA field-effect transistors based on cylindrical Si nanowires with channel along the 100 direction, with diameter D ranging from 4nm to 8nm. The choice of the channel orientation is motivated by the better performance predicted for 100 Si nanowires as n-MOSFET with respect to the 110 orientation, given by larger electron mobility [22] and higher ballistic conductance [23]. The coordinate reference system is chosen so that the x and y axes are in the cross section plane and

Conclusion

This paper describes a numerical simulator that solves in a self-consistent way the 3D Poisson equation, the 2D Schrödinger equation, and the 1D Boltzmann transport equation through the Ensemble Monte Carlo method. This software can be used to study the static characteristics of ultra-scaled MOSFET devices, also in the sub-threshold region thanks to the implementation of a variance reduction technique based on variable super-particle weights. It also allows us to inspect the carrier

Acknowledgment

The authors would like to thank the financial support of Spanish Government under project TEC2014-59730-R and EU H2020 program under projects REMINDER (Grant Agreement No. 687931) and WAYTOGO FAST (ECSEL-2014-2-662175).

Luca Donetti received the M.Sc. degree in physics from the University of Parma, Parma, Italy, in 1998 and the Ph.D. degree in physics from the Università degli Studi di Milano, Milano, Italy, in 2002. Since 2005, he has been with the Department of Electronics, Faculty of Sciences, University of Granada, Granada, Spain. His current research interests include the simulation of electron and hole transport properties in nanoscale electronic devices, including SOI and multi-gate devices. In

References (23)

  • E. Gnani et al.

    Band-structure effects in ultrascaled silicon nanowires

    IEEE Transa Electron Dev

    (2007)
  • Cited by (6)

    Luca Donetti received the M.Sc. degree in physics from the University of Parma, Parma, Italy, in 1998 and the Ph.D. degree in physics from the Università degli Studi di Milano, Milano, Italy, in 2002. Since 2005, he has been with the Department of Electronics, Faculty of Sciences, University of Granada, Granada, Spain. His current research interests include the simulation of electron and hole transport properties in nanoscale electronic devices, including SOI and multi-gate devices. In particular, the focus has been on carrier band-structure effects including simple non-parabolicity models, k·p Hamiltonians up to ab initio calculations, and on quantum effects.

    View full text