Electrical Resistance and Seebeck Coefficient in PbTe Nanowires SITANGSHU BHATTACHARYA 1 and RAMESH CHANDRA MALLIK 2,3.4 1.—Nanoscale Device Research Laboratory, Department of Electronic Systems Engineering, (formerly CEDT), Indian Institute of Science, Bangalore 560 012, India. 2.—Thermoelectric Materials and Device Laboratory, Department of Physics, Indian Institute of Science, Bangalore 560 012, India. 3.—e-mail: rcmallik@physics.iisc.ernet.in 4.—e-mail: rameshmallik@gmail.com We address a physics-based simplified analytical formulation of the diffusive electrical resistance (R X ) and Seebeck coefficient (S) in a PbTe nanowire dominated by acoustic phonon scattering under the presence of a low static longitudinal electric field. The use of a second-order nonparabolic electron energy band structure involving a geometry-dependent band gap has been selected in principle to demonstrate that the electron mean free path (MFP) in such a system can reach as low as about 8 nm at room temperature for a 10-nm-wide PbTe nanowire. This is followed by the formulation of the carrier back-scattering coefficient for determination of R X and S as functions of wire dimensions, temperature, and the field, respectively. The present analytical formulation agrees well with the available experimental data and may find extensive use in determination of various electrothermal transport phenom- ena in PbTe-based one-dimensional electron devices. Key words: Nanowires, phonon scattering, band nonparabolicity, electrical resistance, Seebeck coefficient INTRODUCTION As device dimensions are scaled down in an aggressive way, bottleneck issues related to elec- trothermal management are gaining importance. Methods, both experiments and theoretical optimi- zations, are in great demand and are currently being developed and deployed to counteract the heating effects and other hot-spot issues due to the extremely high current density in very narrow channels in ultra-small scaled integrated (ULSI) circuits. 1 One of the main challenges in electrical modeling of the current transport mechanism in ULSI devices is understanding how much electrical resistance R X the channel offers. Also, apart from electrical characterization, challenges in the quan- tification of various thermal parameters must also be faced, particularly for high-efficiency thermo- electric scaled materials where large thermoelectric figure of merit is absolutely necessary. 2 This is principally dependent on the magnitudes of three inherent and interdependent quantities, namely the Seebeck coefficient (S), the electrical conductivity, and the thermal conductivity of the material. Experimentally, these can be analyzed randomly for different materials and are under consideration. 2–5 However, to categorize the system there should also be a proper analytical method to predict the varia- tion of these parameters under different geometric scaling conditions. The present paper considers such a quantification and answers with a closed-form analytical method for R X and S under diffusive-mode electron transport in a thermoelectric nanowire. Lead chalcogenides such as PbTe are narrow- band-gap IV–VI compound semiconductors with large Bohr exciton radius, studies of which over several decades have been motivated by their importance as high-temperature thermoelectric materials, not only in bulk form but also as films, quantum wells, superlattices, nanowires, etc. 6–8 These studies have revealed some interesting fea- tures that have been observed in bulk PbTe; how- ever, the effect of energy band nonparabolicity on (Received July 16, 2011; accepted January 12, 2012; published online February 24, 2012) Journal of ELECTRONIC MATERIALS, Vol. 41, No. 6, 2012 DOI: 10.1007/s11664-012-1930-z Ó 2012 TMS 1421