Investigation of nanoscale heat transport in sub-10 nm carbon nanotube field-effect transistors based on the finite element method
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 nanometers for the version [5], [6], [7]. While, the state-of-the art 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 equation, where is the heat flux, is the temperature gradient and is 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 and resistive 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 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 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]:where is the relaxation time related to resistive () collision, is 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)
- et al.
The thermal, electrical and thermoelectric properties of graphene nanomaterials
Nanomaterials
(2019) - et al.
Investigation of heat transport across Ge/Si interface using an enhanced ballistic-diffusive model
Superlattices and Microst.
(2018) - et al.
Heat conduction across 1D nano film: local thermal conductivity and extrapolation length
Int. J. Therm. Sci.
(2021) - et al.
An implicit kinetic scheme for multiscale heat transfer problem accounting for phonon dispersion and polarization
Int. J. of Heat and Mass Trans.
(2019) - et al.
Molecular dynamics simulations of thermal conductivity of carbon nanotubes: resolving the effects of computational parameters
Int. J. of Heat and Mass Trans.
(2014) - et al.
Thermal conductivity of carbon nanotubes and assemblies
Adv. Heat Trans.
(2018) - et al.
Phonon hydrodynamics and its applications in nanoscale heat transport
Phys. Rep.
(2015) - et al.
The worm-LBM, an algorithm for a high number of propagation directions on a lattice Boltzmann grid: The case of phonon transport
Int. J. of Heat and Mass Trans.
(2021) - et al.
A slip-based model for the size-dependent effective thermal conductivity of nanowires
Int. Comm. Int. J. Heat Mass Trans.
(2018) - et al.
Lattice Boltzmann numerical analysis of heat transfer in nano-scale silicon films induced by ultra-fast laser heating
Int. J. Therm. Sci.
(2015)