Calculating Seebeck Coefficients for Arbitrary Temperature Gradients
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Calculating Seebeck Coefficients for Arbitrary Temperature Gradients Peter P. F. Radkowski III1 and Timothy D. Sands2 1 Applied Science and Technology Graduate Group, University of California, Berkeley, CA 2 School of Materials Engineering and School of Electrical and Computer Engineering, Purdue University, Lafayette, IN ABSTRACT A novel computational scheme has been used to predict the electric potentials generated by arbitrary temperature gradients in semiconductor materials. Written in object-oriented code, the Discrete State Simulation (DSS) is a coupled cellular automata simulator that builds upon the objects and rules of quantum mechanics. The DSS represents global non-equilibrium processes as patterns that emerge through an ensemble of scattering events that are localized at vibronic nodes. By tracking the energymomentum-position coordinates of the individual particles that define the vibronic state at a node, the DSS undercuts equilibrium concepts such as temperature. Consequently, the DSS can represent physical systems that are described by more than one temperature or that contain physical features that defy definitions of temperature. Using modified bootstrap sampling algorithms, the DSS depicted (1) shifts in distribution functions induced by external fields and temperature gradients, (2) field-dependent transitions from linear mobility to non-linear mobility, (3) saturation velocities, (4) non-exponential decay functions generated by multiple phonon scattering modes, and (5) charge separations and electric potentials generated by temperature gradients. Ensemble averages were sensitive to the structure of dispersion relations, to the energy of the system, and to quantum coupling strengths. Seebeck coefficients were sensitive to the features of the electronic and the vibrational band structures, and their associated coupling coefficients. INTRODUCTION The initial development of the Discrete State Simulation [1, 2] focused on the charge and heat currents of thermoelectric devices. [3, 4] Whether used as power generators or solid state refrigerators, thermoelectric devices are inherently coupled: when bridging a heat source and a heat sink, heat fluxes in an open semiconductor circuit will generate an electromotive potential; driven by an externally applied electric potential, closed semiconductor circuits pump heat from cold to hot regions as charge currents carry thermal energies faster than the heat can be returned by diffusive lattice vibrations. Bulk implementations of thermoelectric technologies are widespread, generating power on satellites, heating seats in sport sedans, and cooling microprocessors in personal computers. Remarkably, although thermoelectricity was discovered nearly two centuries ago, thermoelectric research currently rides at the forefront of nanoscience and nanoengineering. Two-dimensional superlattices, one-dimensional nanowires, and zerodimensional quantum dots are predicted to exhibit enhanced thermoelectric transport
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properties.[5-7] Interstitial doping is pro
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