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RamayyaIWCE09PaperFinal - Ultrascaled Silicon Nanowires as...

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Ultrascaled Silicon Nanowires as Efficient Thermoelectric Materials E. B. Ramayya and I. Knezevic Electrical and Computer Engineering, University of Wisconsin, Madison, Wisconsin 53706 Email: [email protected], [email protected] Abstract —The room-temperature thermoelectric figure of merit ( ZT ) of highly doped silicon nanowires (SiNWs) of square cross section was calculated by solving the electron and phonon Boltzmann transport equations with a proper account of the two dimensional confinement of both electrons and phonons. The ZT in SiNWs is almost two orders of magnitude larger than that of bulk silicon. The enhancement of ZT in SiNWs occurs primarily because of strong phonon-boundary scattering that degrades the lattice thermal conductivity by about two orders of magnitude from its value in bulk silicon. With decreasing wire cross section, the electrical conductivity ( σ ) and thermal conductivity ( κ ) decrease, whereas the Seebeck coefficient ( S ) increases. Therefore, the ZT variation with cross section is non- monotonic, with ZT maximal for a wire of cross section 4 × 4 nm 2 . Boundary roughness scattering indeed proves to have a significant effect on both electronic and thermal transport in SiNWs. I. I NTRODUCTION Thermoelectric phenomena include conversion of electricity to heat and heat to electricity using solid state devices. A thermoelectric (TE) generator converts a temperature differ- ence between two ends of a conductor into a bias voltage, whereas a TE refrigerator utilizes electrical current to create a temperature difference between two ends of a conductor (by pumping heat from cold end to hot end). Suitability of a material for thermoelectric applications at temperature T is judged from its figure of merit ZT = S 2 σT/κ , where S , σ , and κ are the Seebeck coefficient (thermopower), electrical conductivity, and thermal conductivity, respectively [1]. S 2 σ has to be as high as possible to ensure maximal conversion of electric power to heat and to minimize the Joule heating losses in the material, whereas thermal conductivity should be as small as possible to maintain the temperature gradient between the heat source and the heat sink (low κ will ensure that the heat is carried by the charge carriers from the source to the sink under the influence of the applied electric field rather than by the carriers diffusing in the opposite direction due to the presence of the thermal gradient). ZT > 3 . 0 (corresponds to about 20-30 % Carnot efficiency) is required to replace conventional chloroflurocarbon (CFC) based coolers by TE coolers, but increasing ZT of bulk semiconductors beyond 1.0 has been a big challenge due to the interdependence of σ and S e (the electronic contribution to the Seebeck coefficient). Unlike conventional refrigerators, which pollute the atmo- sphere because of CFC leaks, TE coolers are environmentally friendly. But TE devices are still not a commercially-viable alternative to conventional generators and coolers because of - e n p + h + Heat sink I Object being cooled T C T H x = 0 x = L n x = L
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