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Transverse Thermoelectric Effect University of New Orleans ScholarWorks@UNO University of New Orleans Theses and Dissertations Dissertations and Theses Summer 8-13-2014 Transverse Thermoelectric Effect Charles Crawford [email protected] Follow this and additional works at: https://scholarworks.uno.edu/td Recommended Citation Crawford, Charles, "Transverse Thermoelectric Effect" (2014). University of New Orleans Theses and Dissertations. 1866. https://scholarworks.uno.edu/td/1866 This Thesis-Restricted is protected by copyright and/or related rights. It has been brought to you by ScholarWorks@UNO with permission from the rights-holder(s). You are free to use this Thesis-Restricted in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s) directly, unless additional rights are indicated by a Creative Commons license in the record and/or on the work itself. This Thesis-Restricted has been accepted for inclusion in University of New Orleans Theses and Dissertations by an authorized administrator of ScholarWorks@UNO. For more information, please contact [email protected]. Transverse Thermoelectric Effect A Thesis Submitted to the Graduate Faculty of the University of New Orleans in partial fulfillment of the requirements for the degree of Master of Science in Applied Physics by Charles Crawford B.S. Louisiana State University in Shreveport, 2010 B.S. Louisiana State University in Shreveport, 2010 August, 2014 Contents List of Figures ix List of Tablesx Abstract xi 1 Introduction1 2 Background6 2.1 Transport Equations . .6 2.1.1 Low Field Boltzmann Transport Equation Solution . .6 2.1.2 Coupled Current Equations . 10 2.2 Using the Coupled Current Equations . 12 2.2.1 The General Equations . 12 2.2.2 Transverse Thermoelectric Geometry . 16 2.3 Open Circuit Eddy Currents . 18 2.4 Finite Element Method . 19 ii 3 Simulations 24 3.1 COMSOL Transverse Thermoelectric Package . 24 3.1.1 COMSOL Physics Builder . 24 3.1.2 Modifying the Thermoelectric Module . 25 3.2 Validation Simulations . 28 3.3 Transverse Seebeck Effect . 32 3.4 Transverse Peltier Effect . 35 4 Results 37 4.1 Transverse Seebeck Effect . 37 4.1.1 Aspect Ratio and Output Voltage . 37 4.1.2 Angle of Inclination and Aspect Ratio . 38 4.1.3 Seebeck Tensor and Potential . 41 4.1.4 Eddy Currents in the ASM and ILM . 44 4.1.5 Mathematical Difference in ILM and ASM . 47 4.2 Transverse Peltier Effect . 53 4.2.1 Peltier Aspect Ratio Comparison . 54 4.2.2 ASM and ILM Differences . 57 4.3 Device Engineering . 61 4.3.1 ILM . 61 4.3.2 ASM . 62 5 Conclusion 65 iii A Landauer Approach 68 A.1 Charge Current . 68 A.2 Heat Current . 72 B Computation Tables 74 B.1 Zahner et al. Validation Tables . 74 B.2 Kyarad et al. Validation Tables . 76 C List of Symbols 78 Bibliography 83 Vita 84 iv List of Figures 1.1 Schematic of a thermoelectric couple consisting of an n- and p-type semiconductor operating in power generation mode. A source of heat at the top drives charge carries to the cooler side, producing a current.2 1.2 Schematic of a thermoelectric couple consisting of an n- and p-type semiconductor operating in cooling mode. A source of current carries heat to the bottom heat sink, cooling the top plate. .2 1.3 Schematic of a longitudinal thermoelectric device in power generation mode. .3 1.4 Diagram of the transverse Seebeck effect simulation where a temper- ature difference is in z-direction, and the potential difference is calcu- lated in the x-direction. .5 1.5 Diagram of the transverse Peltier effect simulation where a current is injected in the z-direction, and heat flows in z-direction to cool off the top plate. .5 v 2.1 Geometry of a synthetically created anisotropic thermoelectric device with parallel and perpendicular components of material parameters shown. 16 3.1 CAD model of a device made using the isotropic layer model where the layers are apparent. 26 3.2 CAD model of a device made using the anisotropic slab model where the continuity of the geometry implies the purely mathematical nature of the model. 27 3.3 Experimental set up in Zahner et al. with constant heat flux applied to sample top and potential difference calculated from left to right. 28 3.4 Validation of the physics modules with the data in measured in Zahner et al. for both ILM and ASM. 29 3.5 Experimental set up in Kyarad et al. in which a current is injected into the left face, and Peltier cooling occurs across the top of the device with the bottom face kept at constant temperature. 30 3.6 Validation of the physics modules with the data in measured in Kyarad et al. for the ASM using the midpoint computation as well as the surface average. 31 3.7 Diagram of the transverse Seebeck effect simulation where a temper- ature difference is in z-direction, and the potential difference is calcu- lated in the x-direction. 32 vi 3.8 Diagram of the transverse Peltier effect simulation where a current is injected in the z-direction, and heat flows in z-direction to cool off the top plate. 35 4.1 Difference in voltage drop profile across z-axis for the ASM and ILM in a Seebeck effect simulation. 38 4.2 Seebeck effect model comparison of ILM and ASM for aspect ratios ∆x=∆z = (10; 5; 2;:5). 39 4.3 Magnitude of Seebeck components, Sxz and Szz for angles of inclina- tion 0◦-90◦................................. 42 4.4 Magnitude of voltage components contributing to x component of the thermoelectric field for angles of inclination 0◦-90◦........... 43 4.5 ASM (left) and ILM (right) shown with normalized eddy current den- sities for open circuit Seebeck potential at 45 degree angle of inclina- tion, aspect ratio of 1/2, and ten degree temperature difference top to bottom. 45 4.6 ASM (left) and ILM (right) shown with normalized eddy current den- sity for open circuit Seebeck potential at 45 degree angle of inclination, aspect ratio of 1/1, and ten degree temperature difference top to bottom. 45 4.7 ASM normalized eddy current density for open circuit Seebeck po- tential at 45 degree angle of inclination, aspect ratio of 2/1, and ten degree temperature difference top to bottom. 46 vii 4.8 ILM normalized eddy current density for open circuit Seebeck poten- tial at 45 degree angle of inclination, aspect ratio of 2/1, and ten degree temperature difference top to bottom. 46 4.9 Effect of width on the ASM for angles of inclination 0◦-90◦....... 52 4.10 Temperature distribution across thermoelectric device CAD model of Peltier effect for ILM and ASM. 53 4.11 Temperature difference created in z-direction for injected currents for ILM and ASM for aspect ratios ∆x=∆z =(5,2,1). 54 4.12 Temperature difference for aspect ratio ∆x=∆z = (10; 5) showing the divergence of models at high aspect ratio. 55 4.13 Convergence of ILM to ASM in the limit that layer thickness goes to zero tA ! 0 and tB ! 0.......................... 56 4.14 Difference in temperature distribution across x-direction for the ASM and ILM in a Peltier effect simulation. 58 4.15 Current density plots for ILM and ASM showing the extra component in the ILM. 59 4.16 Zoomed in current density plot for the Peltier ILM simulation showing extra surface perpendicular component. 60 4.17 Zoomed in current density plot of Peltier ASM simulation showing no surface perpendicular component. 60 4.18 Single transverse thermoelectric device geometry built in the ILM. 61 viii 4.19 ILM surface plot of the potential distribution over a transverse ther- moelectric device with heat flux applied of 137; 000(W=m2) to top, and 0V held at right side. 62 4.20 ASM model of a single transverse thermoelectric with heat flux applied of 137; 000(W=m2) to the top section, and 0V held at bottom right side copper plate. 63 4.21 Transverse thermoelectric device linked in series with heat flux applied of 137; 000(W=m2) to the top of each section, and 0V held at bottom right side copper plate. 64 A.1 A change in Fermi distribution due to an applied potential . 69 A.2 A change in Fermi distribution due to a change in temperature. 69 A.3 A change in Fermi distribution due to a change in temperature and an applied voltage. 71 ix List of Tables 2.1 Symbol Definitions . 21 B.1 Computations of ILM for the Zahner confirmation simulations to de- termine the validity of the custom physics modules. 74 B.2 Computations of ASM for the Zahner confirmation simulations to de- termine the validity of the custom physics modules. 75 B.3 Computations of ASM for the Kyarad confirmation simulations to determine the validity of the custom physics modules. 76 B.4 Computations of ILM for the Kyarad confirmation simulations to de- termine the validity of the custom physics modules. 77 C.1 Symbols used throughout the paper. 80 x Abstract Anisotropic thermoelectric effects can be measured in certain materials. Anisotropy can also be simulated using a repeated, layered structure of two materials cut at an angle. Various aspect ratios and angles of inclination are investigated in device geometry in order to maximize the thermopower. Eddy currents have been shown to occur in thermoelectric devices, and evidence of these currents are revealed in finite element analysis of the artificially synthesized anisotropic Peltier effect.
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