Investigation of nanoscale heat transport in sub-10 nm carbon nanotube field-effect transistors based on the finite element method

https://doi.org/10.1016/j.tsep.2021.100938Get rights and content

Highlights

  • Thermal mapping technique is a promising for the analysis of nanoscale heat transport.

  • Accurate phonon hydrodynamic equation is used to investigate the nanoscale thermal management in sub 10-nm CNTFETs.

  • Enhancing the thermal conductivity of CNTs is a feasible way to improve the heat dissipation ability of nanodevices.

  • Lower thermal boundary resistance can optimize the thermal stability of carbon nanotube field-effect transistors.

Abstract

During the past few years, computational approaches and engineering thermal optimizations have been investigated due to its essential role in heat conduction problems related to the next-generation transistors. This paper probes the significance of thermal management applications in carbon nanotube field-effect transistors (CNTFETs). In this work, we refer to the phonon hydrodynamic model for thermal modeling of sub-10nm CNTFETs. Here, we report the nanoscale heat transport within CNTFETs based on the finite-element method (FEM). The excellent agreement between the phonon Boltzmann transport equation (BTE) and our model prediction provides the validity of the present methodology. Our computation techniques suggest that limiting the heat propagation can be ensured by increasing specular phonon reflection inside the channel region. In addition, enhancing the thermal conductivity of CNTs with a small thermal boundary resistance is a feasible way to improve the heat dissipation ability.

Introduction

Considerable investigations have been focused on the rapid development of technology nodes and emerging research on advanced nanoelectronics. In recent years, thermal management becomes highly important for enhancing the heat transport in nanostructured materials and relevant nanoelectronics [1], [2], [3], [4]. The Moore’s law has been made in descriptions of the size of the metal-oxide semiconductor field-effect transistors (MOSFETs) and complimentary MOS (CMOS) devices. The smaller channel FETs was assumed less than 10 nanometers for the 2020 version [5], [6], [7]. While, the state-of-the art 10nm CNTFETs technology suffered from the self-heating process due to the reduced thermal conductivity [8], [9]. In general, thermal heating in nanoscale regime is caused by the miniaturization and phonon scattering mechanism inside the channel region of nanotransistors. Therefore, studying the heat conduction in nanoelectronics play a key feature in the characterization of the thermal stability within nanodevices [10], [11], [12].

In fact, the conventional Fourier’s law has typically utilized to predict the diffusive heat conduction at room temperature. The conventional heat conduction based on local equilibrium lead to the linear equationq=-κT, where q is the heat flux, Tis the temperature gradient and κis the bulk thermal conductivity. Certainly, energy carrier transport in solids and mainly in semiconductors can be studied via phonon distributions. To the best of our knowledge, phonon Boltzmann transport equation (BTE) simulations are performed for solving heat conduction problems within surface and interface scattering [14], [15], [16], [17], [18]. In addition, the phonon BTE is an efficient method to study the temperature discontinuities and non-Fourier heat conduction in nanosystems. Many transport models derived from the BTE are used to investigate the thermal transport in solid–solid interfaces [13], [14], nanotransistors [19], [20], [21], [22], carbon nanotube (CNTs) and nanostructured materials [23], [24], [25], [26].

Usually, nanoscale heat transport includes both non-local effects and phonon scattering mechanisms. The phonon hydrodynamic model [27], [28], [29], [30], Guyer-Krumhansl equation (GKE) [31], [32], [33], ballistic-diffusive equation (BDE) [14], [21] and dual-phase-lag (DPL) [19], [20] model have been applied to simulate thermal transport behavior in nanostructures. Under phonon hydrodynamic model, Guo and Wang [29] studied the non-local effects to examine the heat transport in diffusive and ballistic regime. They found that the effective thermal conductivity (ETC) depends on the Knudsen number (Kn). Sellitto et al. [28], developed the G-K equation, in which they introduced both of normal (N) and resistive (R) processes to address the phonon transport analysis in nanosystems. Beardo and co-workers [34], used the finite-element method (FEM) under multi-scale phonon hydrodynamic model to evaluate the nanoscale heat conduction in silicon thin films. The FEM is an accurate technique to solve two-dimensional 2D heat transfer problems and overall computational treatment of phonon BTE. In addition, this method facilitates the inclusion of boundary conditions and reduce the computing time. Today, computational methods have gathered considerable demand for modeling of nanoscale heat transport [34], [35], [36]. Several new advanced algorithms and recent numerical schemes are involved in thermal management applications such as phononics materials [37], carbon-based nanoelectronics [38] and resolving thermoelectric cooling challenges [39].

In the present work, we explain the nature of nanoscale heat transport in CNTFETs using the phonon hydrodynamic model. Besides, we analyze the evolution of the thermal heating and the origin of heat dissipation along ultra-short channel CNTFETs. The objective of this study is to address suitable and practical way to enhance the nanoscale thermal transport inside nanodevices. This manuscript is organized as follow: The derivation of phonon hydrodynamic model and size-dependent ETC are developed in Sec. Ⅱ. Boundary conduction and the structure of the suggested CNTFETs architecture are clarified in Sec.III. In Sec. Ⅳ, we validate our model prediction with data related to 2D classical Si MOSFETs. Thereafter, further theoretical discussions based on nanoscale thermal analysis (NTA) are addressed by thermal mapping of local heat source along the channel transistor. Finally, concluding remarks and perspectives are treated in Sec. Ⅴ.

Section snippets

Phonon hydrodynamics at room temperature

Based on extended irreversible thermodynamics (EIT), the phonon hydrodynamic model is developed to treat non-local phonon transport, which originates in nanoscale regime [27], [28], [29], [40], [41]. This model is aimed for modeling of non-Fourier heat conduction problems. The useful phonon hydrodynamic equation is given by the following expression [29], [30], [31], [32]:q+τRqt=-κT+l25(13.q+Δq)where τRis the relaxation time related to resistive (R) collision, lis phonon mean-free path

Classical 2D Si MOSFETs

In this section, we validate our model prediction with different methods and data involving to this study. The FEM is an accurate procedure to compute the thermal behavior with good precision and easy manipulation of slip boundary condition for interfacial phonon transport [14], [35], [47]. We develop a consistent framework based on the phonon hydrodynamic model for probing nanoscale heat transport. The validity of the present new methodology is considered with additional comparison of the ETC

Conclusions and perspectives

In summary, we have investigated the nanoscale thermal transport in CNTFETs based on phonon hydrodynamic equation. We also apply the FEM to report the interfacial heat conduction between layered nanostructures. We find that the proposed model is able to handle both the thermal heating and localized hot-spot temperature inside the nanodevice. In general, the maximum surface temperature is detected in the interface related the CNT to the dioxide layer. We also succeed to capture the nanoscale

CRediT authorship contribution statement

Houssem Rezgui: Conceptualization, Methodology, Formal analysis, Investigation, Data curation, Writing - original draft, Writing - review & editing. Faouzi Nasri: Investigation, Formal analysis, Writing - review & editing. Mohamed Fadhel Ben Aissa: Formal analysis, Writing - review & editing. Amen Allah Guizani: Supervision, Writing - review & editing.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

References (54)

  • Y.C. Hua et al.

    The effective thermal conductivity of ballistic-diffusive heat conduction in nanostructures with internal heat source

    Int. J. of Heat and Mass Trans.

    (2016)
  • O. Zobiri et al.

    Study of robin condition influence on phonon nano-heat conduction using mesoscale method in MOSFET and SOI-MOSFET devices

    Mat. Comm.

    (2021)
  • D.S. Schulman et al.

    Contact engineering for 2D materials and devices

    Chem. Soc. Rev.

    (2018)
  • A. Malhotra et al.

    Enhancing thermal transport in layered nanomaterials

    Sci. Rep.

    (2018)
  • J.S. Kang et al.

    Experimental observation of high thermal conductivity in boron arsenide

    Science

    (2018)
  • L.M. Peng, Z. Zhang, S. Wang, Carbon nanotube electronics: recent advances, materials today 17 (9) (2014)...
  • F. VanGessel et al.

    A review of computational phononics: the bulk, interfaces, and surfaces

    J. Mater. Sci.

    (2018)
  • H. Rezgui, F. Nasri, A. Ben Haj Ali, A.A. Guizani, Analysis of the ultrafast transient heat transport in sub 7-nm SOI...
  • J. Yang et al.

    Sub 10 nm bilayer Bi2O2Se transistors

    Adv. Electron. Mater.

    (2019)
  • A. Shakouri

    Nanoscale thermal transport and microrefrigeration on a chip

    Proc. Of the IEEE

    (2006)
  • V.P. Pham et al.

    Direct growth of graphene on rigid and flexible substrates: progress, applications and challenges

    Chem. Soc. Rev.

    (2017)
  • F. Gao, H. Yang, P. Hu, Interfacial engineering for fabricating high-performance filed-effect transistors based on 2D...
  • H. Zhang et al.

    Multi-Scale modeling of heat dissipation in 2D transistors based on phosphorene and silicene

    J. Phys. Chem. C

    (2018)
  • Y. Hu et al.

    Spectral mapping of thermal conductivity through nanoscale ballistic transport

    Nature Comm.

    (2015)
  • H. Belmabrouk et al.

    Interfacial heat transport across multilayer nanofilms in ballistic-diffusive regime

    The Eur. Phys. Jour. Plus

    (2020)
  • J. Ordonez-Miranda et al.

    Steady state and modulated heat conduction in layered systems predicted by the analytical solution of the phonon Boltzmann transport equation

    J. Appl. Phys.

    (2015)
  • M.F. Ben Aissa et al.

    Multidimensional nano heat conduction in cylindrical transistors

    IEEE Trans. Electron Devices

    (2017)
  • Cited by (0)

    View full text