PHYSICAL REVIEW B 86, 115328 (2012) Thermoelectric properties of ultrathin silicon nanowires E. B. Ramayya, * L. N. Maurer, A. H. Davoody, and I. Knezevic † Department of Electrical and Computer Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA (Received 20 October 2011; revised manuscript received 23 July 2012; published 24 September 2012) We calculate the room-temperature thermoelectric properties of highly doped ultrathin silicon nanowires (SiNW) of square cross section (3 × 3 to 8 × 8 nm 2 ) by solving the Boltzmann transport equations for electrons and phonons on an equal footing, using the ensemble Monte Carlo technique for each. We account for the two-dimensional confinement of both electrons and phonons and all the relevant scattering mechanisms, and present data for the dependence of electrical conductivity, the electronic and phononic thermal conductivities, the electronic and phonon-drag Seebeck coefficients, as well as the thermoelectric figure of merit (ZT ) on the SiNW rms roughness and thickness. ZT in ultrascaled SiNWs does not increase as drastically with decreasing wire cross section as suggested by earlier studies. The reason is surface roughness, which (beneficially) degrades thermal conductivity, but also (adversely) degrades electrical conductivity and offsets the Seebeck coefficient enhancement that comes from confinement. Overall, room-temperature ZT of ultrathin SiNWs varies slowly with thickness, having a soft maximum of about 0.4 at the nanowire thickness of 4 nm. DOI: 10.1103/PhysRevB.86.115328 PACS number(s): 72.20.Pa, 84.60.Rb, 73.63.Nm, 65.80.−g I. INTRODUCTION Thermoelectric (TE) phenomena include conversion of electricity to heat and heat to electricity using solid-state devices. 1–3 Suitability of a material for thermoelectric ap- plications 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. Highly doped semiconductors make the best thermoelectric materials 4,5 because heat is carried pre- dominantly by the lattice, so thermal conductivity κ is largely decoupled from the power factor S 2 σ . ZT > 3.0 is required to replace conventional chlorofluorocarbon (CFC) coolers by TE coolers, but increasing ZT of bulk semiconductors beyond 1.0 has been a challenge. 4 Ideally, we want to improve the power factor S 2 σ while simultaneously reducing thermal conductivity κ . 6 Nanostruc- turing could, in principle, bring about both of these benefits. 7,8 On the one hand, inclusion of various size nanostructured obstacles can scatter phonons of different wavelengths and quench conduction of heat. Indeed, high figures of merit due to low thermal conductivity have been demonstrated on materials incorporating nanoscale inclusions. 9–11 On the other hand, Hicks and Dresselhaus 12,13 pioneered the concept that nanostructuring, through the modification of the density of states for electrons and holes, could significantly enhance the Seebeck coefficient and consequently the power factor. Nanowires are particularly interesting in this regard because of their sharp density of states. Recent experimental work on rough silicon nanowires 14,15 demonstrated room temperature ZT ∼ 0.6, nearly two orders of magnitude above the bulk- silicon value of ZT = 0.01. These are exciting results as they brought silicon, a cheap and abundant semiconductor, into the realm of plausibility for thermoelectric applications. It is now fairly certain that the enhanced ZT in these experiments came primarily from a drastic thermal conductivity degradation because the wires were very rough (rms roughness even in the nanometer range) 16 and most of them were too thick (20–50 nm) for the quantum confinement effects to be really significant. However, Boukai et al. 14 also proposed that the phonon-drag component in very thin nanowires, especially at lower temperatures, may be responsible in part for the ZT enhancement. In ultrathin wires, thermal conductivity is expected to be very low, based on theoretical work using molecu- lar dynamics, 17–20 nonequilibrium Green’s functions in the harmonic approximation, 21–23 and the Boltzmann transport equation addressing phonon transport. 24–28 Theoretical work focusing on the electronic part of the picture 29–34 indicates that confinement benefits to the power factor should be realizable in ultrathin wires; however, they have not been reported experimentally. 8 Therefore, whether strong confinement in nanowires can indeed bring about both low thermal conduc- tivity and enhanced thermoelectic power factor and whether unusual features such as enhanced phonon drag emerge due to nanostructuring are presently open questions. In this paper, we present a simulation of electronic and thermal transport in ultrathin square silicon nanowires (cross sections ranging from 3 × 3 to 8 × 8 nm 2 ), highly doped and surrounded by a native oxide. Transport of charge and heat is described by solving the Boltzmann transport equations (BTEs) for both electrons and acoustic phonons on an equal footing by using the ensemble Monte Carlo 35,36 (EMC) technique for each. Electronic states are calculated based on a self-consistent Schr¨ odinger-Poisson solver within the effective mass framework, 37,38 appropriate for ultrathin wires. 39,40 Acoustic phonon intravalley, intervalley, ionized impurity, and surface-roughness scattering (according to gen- eralized Ando’s model 38,41–43 ) have been accounted for in the electronic transport simulation. In the phonon simulation, we work with bulk instead of confined phonons, as the one-dimensional to three-dimensional (1D to 3D) crossover for wires of thicknesses such as ours happens at temperatures considerably lower than 300 K. 44 The phonons undergo three-phonon normal and umpklapp scattering, impurity, and surface-roughness scattering. In the phonon simulation, the random rough surface of a SiNW is numerically generated based on an autocorrelation length and rms height, and is directly included in the phonon EMC kernel. The wires in this 115328-1 1098-0121/2012/86(11)/115328(11) ©2012 American Physical Society