Numerical Modeling of Electrothermal Effects in Silicon Nanowires
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Numerical Modeling of Electrothermal Effects in Silicon Nanowires Cicek Boztug, Gokhan Bakan, Mustafa Akbulut, Ali Gokirmak, and Helena Silva Department of Electrical and Computer Engineering, University of Connecticut, Storrs, CT, 06269 Abstract Asymmetric melting was observed in electrically pulsed n-type (phosphorus) nanocrystalline silicon (nc-Si) wires fabricated lithographically. Scanning electron microscope (SEM) images taken from the pulsed wires showed that melting initiates from the ground terminal end of the wires instead of the center as initially expected. Asymmetry in the temperature profile is caused by heat exchanged between charge carriers and phonons when an electrical current is passed along a temperature gradient. This effect is known as Thomson effect, a thermoelectric heat transfer mechanism. One dimensional (1D) time dependent heat diffusion equation including Thomson heat term was solved to model the temperature profile on our structures. The modeling results show that Thomson effect introduces significant shifts in the temperature distribution. The effect of Thomson heat is modeled for various electrical pulse conditions and wires dimensions. Our results indicate that Thomson effect is significant in small scale electronic devices operating under high current densities. Introduction Heat transfer is a critical mechanism in devices that utilize coupled electrical and thermal effects such as thermoelectric devices and phase change memory devices, as well as in conventional electronics. In thermoelectric coolers an electrical current is passed through the junction between two dissimilar materials. Although the cooling occurs at the junction due to the Peltier effect [1], hotspots originated by the applied current appear on both materials. In these devices the location of the hotspot affects the cooling efficiency of the junction and the Thomson effect can be utilized to improve performance [2]. Programming of phase change memory cells is based on Joule heating due to a short current pulse applied through the cell. Thermal transport during the pulse has to be modeled accurately since it directly affects the programming characteristics of the cell [3]. Furthermore, investigation of heat transport at small scales is crucial to understand hotspots formed in electronic devices and integrated circuits which lead to reliability and performance issues [4]. Thomson effect has been observed before in larger scale silicon structures under high current densities [5, 6]. In order to study the Thomson effect on the temperature distribution of electrically pulsed n-type nc-Si sub-μm wires the 1D time dependent heat diffusion equation is solved numerically including heat conduction along the wires and to the substrate, Joule heat and Thomson heat. Fabrication and SEM characterization of pulsed nanocrystalline Si wires Wires with various lengths (L ~ 1-5.5 μm) and widths (W ~ 200 - 450 nm) with large contact pads were defined on a 75 nm thick n-type (phosphorus) nc-Si film on SiO2, and etched using
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