Investigation of Electro-thermal and Thermoelectric Properties of Carbon Nanomaterials
Due to the aggressive downscaling of the CMOS technology, power and current densities are increasing inside the chip. The limiting current conduction capacity(106 Acm−2)and thermal conductivity(201Wm−1K−1 for Al and 400 Wm−1K−1 for Cu) of the existing interconnects materials has given rise to different electro-thermal issues such a shot-spot formation, electromigration, etc. Exploration of new materials with high thermal conductivity and current conduction has thus attracted much attention for future integrated circuit technology. Among all the elemental materials, carbon nanomaterials (graphene and carbon nanotube) possess exceptionally high thermal (600-7000 Wm−1K−1) and current( ~108 -109 Acm−2)conduction properties at room temperature, which makes them potential candidate for interconnect materials. At the same time development of efficient energy harvesting techniques are also becoming important for future wireless autonomous devices. The excess heat generated at the hot-spot location could be used to drive an electronic circuit through a suitable thermoelectric generator. As the See beck coefficient of graphene is reported to be the highest among all elementary semiconductors, exploration of thermoelectric properties of graphene is very important. This thesis investigates the electrothermal and thermoelectric properties of metallic single walled carbon nanotube (SWCNT) and single layer graphene (SLG) for their possible applications in thermal management in next generation integrated circuits. A closed form analytical solution of Joule-heating equation in metallic SWCNTs is thus proposed by considering a temperature dependent lattice thermal conductivity (κ) on the basis of three-phonon Umklapp, mass-diﬀerence and boundary scattering phenomena. The solution of which gives the temperature profile over the SWCNT length and hence the location of hot-spot(created due to the self-heating inside the chip) can be predicted. This self-heating phenomenon is further extended to estimate the electromigration performance and mean-time-to-failure of metallic SWCNTs. It is shown that metallic SWCNTs are less prone to electromigration. To analyze the electro-thermal effects in a suspended SLG, a physics-based flexural phonon dominated thermal conductivity model is developed, which shows that κ follows a T1.5 and T−2 law at lower(<300 K) and higher temperature respectively in the absence of isotopes(C13 atoms). However in the presence of isotopic impurity, the behavior of κ sharply deviates from T−2 at higher temperatures. The proposed model of κ is found to be in excellent match with the available experimental data over a wide range of temperatures and can be utilized for an efficient electro-thermal analysis of encased/supported graphene. By considering the interaction of electron with in-plane and flexural phonons in a doped SLG sheet, a physics-based electrical conductance(σ) model of SLG under self-heating effect is also discussed that particularly exhibits the variation of electrical resistance with temperature at different current levels and matches well with the available experimental data. To investigate the thermoelectric performance of a SLG sheet, analytical models for See beck effect coefficient (SB) and specific heat (Cph) are developed, which are found to be in good agreement with the experimental data. Using those analytical models, it is predicted that one can achieve a thermoelectric figure of merit(ZT) of ~ 0.62 at room temperature by adding isotopic impurities(C13 atoms) in a degenerate SLG. Such prediction shows the immense potential of graphene in waste-heat recovery applications. Those models for σ, κ, SB and Cph are further used to determine the time evolution of temperature distribution along suspended SLG sheet through a transient analysis of Joule-heating equation under the Thomson effect. The proposed methodology can be extended to analyze the graphene heat-spreader theory and interconnects and graphene based thermoelectrics.
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