Linearized Boltzmann transport calculator for thermoelectric materials

By Je-Hyeong Bahk1, Robert Benjamin Post2, Kevin Margatan1, Zhixi Bian, Ali Shakouri1

1. Purdue University 2. University of Texas at El Paso

Simulation tool to calculate thermoelectric transport properties of bulk materials based on their multiple nonparabolic band structure information using the linearized Boltzmann transport equation

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Version 1.1 - published on 14 Aug 2014

doi:10.4231/D37M04151 cite this

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    PbTe band structure Mg2SnSi band structure Band parameter input Scattering input Simulation condition input Output plot of seebeck and electrical conductivity Differential conductivity analysis Differential conductivity analysis summary Output plot of power factor and ZT Output plot of mobilities



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This simulation tool allows users to calculate various thermoelectric properties such as Seebeck coefficient, electrical conductivity, and electronic thermal conductivity for any semiconductor materials with band structures modeled using the nonparabolic dispersion relation. The linearized Boltzmann transport equation under the relaxation time approximation is used for the calculations. Maximum two conduction bands and two valence bands can be included in the band structure, and temperature- and composition- dependent band parameters can be taken into account. Various scattering mechanism such as the acoustic phonon deformation scattering, ionized impurity scattering, polar optical phonon scatterings and others can be included for the calculation of realistic energy-dependent scattering time. Simpler scattering models with constant scattering time or constant mean free path are also possible as a scattering option. We offer users to plot the differential conductivity and the density of states as a function of electron energy for a given band structure, Fermi level, and temperature. Using this differential conductivity analysis, users would be able to study why there is a trade-off between the Seebeck coefficient and the electrical conductivity, and how these properties can be modified or enhanced using different band structures and parameters. The resulting thermoelectric transport properties can be plotted as a function of temperature for a fixed carrier concentration, or as a function of carrier concentration at a fixed temperature for versatile material optimization with doping density over a temperature range of interest. Realistic estimation of thermoelectric properties for conventional thermoelectric materials such as PbTe, Mg2SnSi and InGaAlAs can be performed using this simulation tools. The band structure and scattering information about these materials are already stored in the material library in this simulation tool, so users can just select the material in the material selection menu, and are ready to go for the simulations. Users can create their own material using the easy and convenient graphical user interfaces and simulate. Additional feature with a cut-off energy for simulation of the perfect electron energy filtering is also included. Please feel free to ask questions/comments/suggestions or send bug reports to Dr Je-Hyeong Bahk (


1. J.-H. Bahk and A. Shakouri, “Electron transport engineering by nanostructures for efficient thermoelectrics,” to be published in Thermoelectrics at Nanoscale, Ed. Z. Wang, a book series of Lecture Notes on Nanoscale Science and Technology (Springer, 2013). 2. J.-H. Bahk, Z. Bian, M. Zebarjadi, J. M. O. Zide, H. Lu, D. Xu, J. P. Feser, G. Zeng, A. Majumdar, A. C. Gossard, A. Shakouri, and J. E. Bowers, “Thermoelectric figure of merit of (In0.53Ga0.47As)0.8(In0.52Al0.48As)0.2 III-V semiconductor alloys” Phys. Rev. B 81, 235209 (2010). 3. J.-H. Bahk, Z. Bian, and A. Shakouri, “Electron energy filtering by a non-planar barrier to enhance the thermoelectric power factor in bulk materials,” Phys. Rev. B 87, 075204 (2013). 4. J.-H. Bahk, Z. Bian, and A. Shakouri “Electron transport modeling and energy filtering effect for efficient thermoelectric Mg2Si1-xSnx solid solutions,” submitted to Phys. Rev. B (2013).

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Researchers should cite this work as follows:

  • Je-Hyeong Bahk, Robert Benjamin Post, Kevin Margatan, Zhixi Bian, Ali Shakouri (2014), "Linearized Boltzmann transport calculator for thermoelectric materials," (DOI: 10.4231/D37M04151).

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