Thermoelectric properties of phosphorene at the nanoscale

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Phosphorene is a new-emerging two-dimensional material with many fascinating electronic and thermal properties. Using nonequilibrium Green’s function technique, we investigate the thermoelectric transport properties of phosphorene in the ballistic transport regime. We find that while the electronic conductance and thermal conductance of phosphorene are highly anisotropic, the Seebeck coefficient is isotropic. The maximum predicted thermopower reaches 2500 lV/K. We also find that the Wiedemann–Franz law is valid only when the chemical potential is inside valence band or conduction band. When the chemical potential is near the valence band maximum or conduction band minimum; however, the Wiedemann–Franz law becomes invalid, and interestingly, the figure of merit ZT reaches its maximum value. We also find that figure of merit ZT increases with the increase of temperature, and ZT in the armchair direction is much higher than that in the zigzag direction. By analyzing the various effects on ZT, we discuss the possible routines to enhance figure of merit ZT. I. INTRODUCTION

High-performance thermoelectric devices are highly desirable in clean energy applications, such as thermoelectric generators and refrigerators.1–3 However, the bottleneck of such applications is the energy conversion efficiency, which is closely related to the thermoelectric properties of the material used. In general, the thermoelectric efficiency of a material is characterized by a dimensionless positive quantity called  figure of merit, ZT, which is defined as ZT ¼ Ge S2 T re þ rph , where Ge is electronic conductance, S is the Seebeck coefficient, T is temperature, re is the electronic thermal conductance, and rph is the phonon thermal conductance. A larger ZT corresponds to a higher efficiency of energy conversion. For traditional metal materials, ZT is constrained by the Wiedemann–Franz (WF) law,4 which states that the ratio of electronic thermal conductance and electronic conductance is fixed upon to temperature, re/Ge 5 LT where L 5 2.44  108 WXK2 is the Lorenz number. Unfortunately, the Lorenz number is too large, which caps the upper limit of ZT, and thus limits the practical applications of metals as thermoelectric materials. Interestingly, semiconductors, in particular, semiconducting nanostructures allow the breakdown of the WF law.5 In recent years, two-dimensional (2D) materials were found to have many fascinating physical and chemical properties, and thus they have received a great deal of

Contributing Editor: Terry M. Tritt a) Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/jmr.2016.333

attention in material science. Studies have shown that 2D materials present many novel properties that are not observed in their bulk counterparts.6,7 However, highly conducting 2D materials such as graphene are of an ultrahigh thermal conduction, thus limiting their application in thermoelectric devices. Since some of 2D materials are semiconducting, it is expected that these semiconducting 2D materials are promisi

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