Model of transport properties of thermoelectric nanocomposite materials A. Popescu, L. M. Woods, J. Martin, and G. S. Nolas Department of Physics, University of South Florida, Tampa, Florida 33620, USA Received 17 September 2008; revised manuscript received 6 January 2009; published 5 May 2009 We present a model describing the carrier conductivity and Seebeck coefficient of thermoelectric nanocom- posite materials consisting of granular regions. The model is successfully applied to explain relevant experi- mental data for PbTe nanocomposites. A key factor is the grain potential boundary scattering mechanism. Other mechanisms, such as carrier-acoustic phonon, carrier-nonpolar optical phonon, and carrier-ionized impurities scattering are also included. Our calculations reveal that by changing the physical characteristics of the grains, such as potential barrier height, width, and distance between the grains, one can increase the mean energy per carrier in order to obtain an optimum power factor for improved thermoelectric performance. The model can be applied to other nanocomposites by incorporating the appropriate electronic structure parameters. DOI: 10.1103/PhysRevB.79.205302 PACS numbers: 73.63.Bd, 72.20.Pa, 72.20.Dp I. INTRODUCTION The efficiency of thermoelectric TE devices is charac- terized by the thermoelectric figure of merit, defined as the dimensionless quantity ZT = S 2 T / , where S is the Seebeck coefficient,  is the carrier conductivity,  is the thermal conductivity, and T is the absolute temperature. Materials with larger values of ZT warrant better thermoelectric de- vices, thus researchers have devoted much effort in finding ways to increase ZT. Since the transport properties that de- fine ZT are interrelated, it is difficult to control them inde- pendently for a three-dimensional crystal. Therefore, nano- structured materials have become of great interest because they offer the opportunity of independently varying those properties. 1,2 The reduction in the thermal conductivity in nanostruc- tured materials has been viewed as the primary way to in- crease ZT. The particular mechanism is the effective scatter- ing of phonons due to the presence of interfaces. However, recent experimental studies involving bulk thermoelectric materials with nanostructure inclusions or granular nano- composites have suggested that the thermoelectric properties can be enhanced by increasing the power factor, S 2 . For example, it has been demonstrated that PbTe/PbTeSe quan- tum dot superlattices can have a twofold increase in room temperature ZT as compared to the bulk. 3,4 Also, materials containing PbTe nanogranular formations 5,6 or Si and Ge nanoparticles 7 have also been shown to exhibit an increase in ZT. These experimental studies indicate that the carrier scat- tering at the interfaces may be an important factor in the overall increase in ZT. In particular, it is speculated that for polycrystalline materials the grains appear as traps for low energy carriers, while the higher energy carriers diffuse trough the specimen. 8 In fact, the enhancement of the TE properties in nanocomposites has been attributed to the pres- ence of carrier-interface potential barrier scattering mecha- nism, which is not typical for bulk materials. The grain boundaries therefore appear to filter out the lower energy carriers. Since the mean energy per carrier is increased, S increases while  is not degraded significantly. Filtering by energy barriers has been theoretically predicted and experi- mentally observed in thin films and heterostructure systems. 9–11 In this work, we propose a phenomenological model to describe the diffusion transport of carriers through a material composed of nanogranular regions. The material is viewed as containing interface potential barriers due to the grains, and the transport includes quantum transmission through and re- flection from those barriers. Additional scattering mecha- nisms, such as carriers-acoustic phonons, carriers-nonpolar optical phonons, and carriers-ionized impurities, which are relevant for thermoelectric materials, are also taken into ac- count. The model involves a set of physical parameters which can be measured independently or taken from the lit- erature to calculate or make predictions for the transport characteristics for relevant thermoelectrics. The model is tested by comparing the calculated carrier conductivity and thermopower to experimental data for PbTe nanocomposites. We also use this theory to understand the importance of the grain barrier characteristics, such as height, width, and dis- tance between them, and see to what extent they influence the thermoelectric transport. The paper is organized as follows. The model is presented in Sec. II. In Sec. III experimental results and theoretical calculations for PbTe nanocomposite specimens are given, and  and S are analyzed in terms of the carrier concentra- tion and barrier characteristics. The summary and conclu- sions are given in Sec. IV . II. MODEL We consider a thermoelectric material for which the mo- tion of the carriers is in quasiequilibrium and diffusive. Then one can describe the charge transport with the following expressions 12 for  and S:  = 2e 2 3m   0  EgEE -  f E  E  dE , 1 PHYSICAL REVIEW B 79, 205302 2009 1098-0121/2009/7920/2053027 ©2009 The American Physical Society 205302-1