掃描式Seebeck係數微探針偵測系統主要是針對熱電材料研究所發展的一種量測方法，其功能是藉由所測得之Seebeck係數於空間之分布來判定材料性質的均勻程度，進而提供熱電材料合成之必要訊息。在真實的量測中，因為材料的非均勻相區域小於微探針偵測的解析度亦或量測系統的時間延遲過大，會將不必要的誤差一併考慮進來導致量測的準確度降低。在本研究中，我們結合ANSYS多重物理計算模型與訊號處理並藉由去捲積(deconvolution)的觀念，以數值模型尋求適當的轉換函數來驗證此方法對於提升掃描式Seebeck係數微探針偵測系統解析度之可行性。研究結果顯示以塊材熱電材料為量測樣品，運用正確的轉換函數可以修正被干擾的線量測訊號而成功地提升微探針系統之解析度。因為探針大小、系統時間延遲及掃描間距均是改變量測結果的重要因素，因此我們將詳細地討論這些系統參數對量測解析度變化的影響。此外，如果進一步以薄膜熱電材料為量測樣品，研究結果發現熱流穿透過基板會使所測得之Seebeck訊號嚴重失真而導致解析度降低。為此，我們根據微探針偵測系統的低通特性接著提出一個修正轉換函數的方法並成功地運用於提升系統量測解析度。
然而，數值模型中ANSYS必須計算整個物理區域的節點是一種不具效率的計算方式，所以本研究最後提出一種模型降階方法取代ANSYS內部的龐雜計算，將一個較大的模型轉為一個較小的計算模型，藉此可降低暫態三維計算所耗費的時間，最後將可以快速地提升掃描式Seebeck係數微探針偵測系統解析度，此系統是目前唯一可以偵測到這種非均勻性Seebeck係數分布的重要儀器。

A Potential Seebeck Microprobe apparatus is described that a profile of Seebeck coefficients can be detected on a material sample surface for thermopower investigations. Due to its spatially resolved limit on detecting small inhomogeneities of dopants or composition changes, we here propose a constructive combination of ANSYS coupled-field numerical simulation and digital signal processing in order to improve the spatial resolution by deconvolution algorithm. The relevant transfer function, obtained from numerical calculations, was validated and successfully applied to theoretical and experimental data. The improvement in detecting thermoelectric bulk material sample was demonstrated, in which the spatial resolution of Potential Seebeck Microprobe is increased by the inverse of measured Seebeck signal. Also, the systemic preconditions (tip size, signal capture time and scan period), which are the main factors to affect the captured thermovoltages, were discussed in detail. In addition, for detecting thermoelectric film material sample, we found that the heat flow penetrating into substrate causes an additional Seebeck distortion, leading to a low spatial resolution. Therefore, a correct transfer function, according to the characteristic of Potential Seebeck Microprobe as a low-pass filter, is next proposed for the successful spatial resolution improvement.
Finally, we provide an efficient route to use model order reduction, which reduces the transient three-dimensional analysis time, for searching the required transfer functions. Thus, we can fast perform significant improvements beyond the current measured resolution of Potential Seebeck Microprobe, which is the unique technique to detect the thermopower of thermoelectric inhomogeneities.

[1] L.E. Bell, "Cooling, heating, generating power, and recovering waste heat with thermoelectric systems," Science, vol. 321, pp. 1457-1461, 2008.
[2] G. Chen, A. Shakouri, "Heat transfer in nanostructures for solid-state energy conversion," Journal of Heat Transfer-Transactions of the Asme, vol. 124, pp. 242-252, 2002.
[3] I. Chowdhury, R. Prasher, K. Lofgreen, G. Chrysler, S. Narasimhan, R. Mahajan, D. Koester, R. Alley, R. Venkatasubramanian, "On-chip cooling by superlattice-based thin-film thermoelectrics," Nature Nanotechnology, vol. 4, pp. 235-238, 2009.
[4] R.E. Simons, M.J. Ellsworth, R.C. Chu, "An assessment of module cooling enhancement with thermoelectric coolers," Journal of Heat Transfer-Transactions of the Asme, vol. 127, pp. 76-84, 2005.
[5] Y. Zhang, A. Shakouri, G.H. Zeng, "High-power-density spot cooling using bulk thermoelectrics," Applied Physics Letters, vol. 85, pp. 2977-2979, 2004.
[6] D.M. Rowe, "Thermoelectrics, an environmentally-friendly source of electrical power," Renewable Energy, vol. 16, pp. 1251-1256, 1999.
[7] H.X. Xi, L.G. Luo, G. Fraisse, "Development and applications of solar-based thermoelectric technologies," Renewable & Sustainable Energy Reviews, vol. 11, pp. 923-936, 2007.
[8] B. Poudel, Q. Hao, Y. Ma, Y.C. Lan, A. Minnich, B. Yu, X. Yan, D.Z. Wang, A. Muto, D. Vashaee, X.Y. Chen, J.M. Liu, M.S. Dresselhaus, G. Chen, Z. Ren, "High-thermoelectric performance of nanostructured bismuth antimony telluride bulk alloys," Science, vol. 320, pp. 634-638, 2008.
[9] F.J. DiSalvo, "Thermoelectric cooling and power generation," Science, vol. 285, pp. 703-706, 1999.
[10]W.D. Shi, L. Zhou, S.Y. Song, J.H. Yang, H.J. Zhang, "Hydrothermal synthesis and thermoelectric transport properties of impurity-free antimony telluride hexagonal nanoplates," Advanced Materials, vol. 20, pp. 1892-1897, 2008.
[11]H.Y. Chen, X.B. Zhao, C. Stiewe, D. Platzek, E. Mueller, "Microstructures and thermoelectric properties of Co-doped iron disilicides prepared by rapid solidification and hot pressing," Journal of Alloys and Compounds, vol. 433, pp. 338-344, 2007.
[12]Z. Dashevsky, S. Shusterman, M.P. Dariel, I. Drabkin, "Thermoelectric efficiency in graded indium-doped PbTe crystals," Journal of Applied Physics, vol. 92, pp. 1425-1430, 2002.
[13]R.G. Yang, G. Chen, M.S. Dresselhaus, "Thermal conductivity of simple and tubular nanowire composites in the longitudinal direction," Physical Review B, vol. 72, pp. 125418, 2005.
[14]Z.M. He, C. Stiewe, D. Platzek, G. Karpinski, E. Mueller, S.H. Li, M. Toprak, M. Muhammed, "Nano ZrO2/CoSb3 composites with improved thermoelectric figure of merit," Nanotechnology, vol. 18, pp. 235602, 2007.
[15]M.S. Dresselhaus, G. Chen, M.Y. Tang, R.G. Yang, H. Lee, D.Z. Wang, Z.F. Ren, J.P. Fleurial, P. Gogna, "New directions for low-dimensional thermoelectric materials," Advanced Materials, vol. 19, pp. 1043-1053, 2007.
[16]A.J. Minnich, M.S. Dresselhaus, Z.F. Ren, G. Chen, "Bulk nanostructured thermoelectric materials: current research and future prospects," Energy & Environmental Science, vol. 2, pp. 466-479, 2009.
[17]X.B. Zhao, X.H. Ji, Y.H. Zhang, T.J. Zhu, J.P. Tu, X.B. Zhang, "Bismuth telluride nanotubes and the effects on the thermoelectric properties of nanotube-containing nanocomposites," Applied Physics Letters, vol. 86, pp. 062111, 2005.
[18]H.L. Ni, X.B. Zhao, T.J. Zhu, X.H. Ji, J.P. Tu, "Synthesis and thermoelectric properties of Bi2Te3 based nanocomposites," Journal of Alloys and Compounds, vol. 397, pp. 317-321, 2005.
[19]M. Takashiri, S. Tanaka, M. Takiishi, M. Kihara, K. Miyazaki, H. Tsukamoto, "Preparation and characterization of Bi0.4Te3.0Sb1.6 nanoparticles and their thin films," Journal of Alloys and Compounds, vol. 462, pp. 351-355, 2008.
[20]Y.Y. Wang, K.F. Cai, X. Yao, "Facile synthesis of PbTe nanoparticles and thin films in alkaline aqueous solution at room temperature," Journal of Solid State Chemistry, vol. 182, pp. 3383-3386, 2009.
[21]R. Venkatasubramanian, E. Siivola, T. Colpitts, B. O'Quinn, "Thin-film thermoelectric devices with high room-temperature figures of merit," Nature, vol. 413, pp. 597-602, 2001.
[22]X. Gao, K. Uehara, D.D. Klug, J.S. Tse, "Rational design of high-efficiency thermoelectric materials with low band gap conductive polymers," Computational Materials Science, vol. 36, pp. 49-53, 2006.
[23]J.P. Heremans, V. Jovovic, E.S. Toberer, A. Saramat, K. Kurosaki, A. Charoenphakdee, S. Yamanaka, G.J. Snyder, "Enhancement of thermoelectric efficiency in PbTe by distortion of the electronic density of states," Science, vol. 321, pp. 554-557, 2008.
[24]J.R. Sootsman, H. Kong, C. Uher, J.J. D'Angelo, C.I. Wu, T.P. Hogan, T. Caillat, M.G. Kanatzidis, "Large enhancements in the thermoelectric power factor of bulk PbTe at high temperature by synergistic nanostructuring," Angewandte Chemie-International Edition, vol. 47, pp. 8618-8622, 2008.
[25]B. Yang, J.L. Liu, K.L. Wang, G. Chen, "Simultaneous measurements of Seebeck coefficient and thermal conductivity across superlattice," Applied Physics Letters, vol. 80, pp. 1758-1760, 2002.
[26]Z.H. Zhou, C. Uher, "Apparatus for Seebeck coefficient and electrical resistivity measurements of bulk thermoelectric materials at high temperature," Review of Scientific Instruments, vol. 76, pp. 023901, 2005.
[27]L. Gravier, A. Fabian, A. Rudolf, A. Cachin, K. Hjort, J.P. Ansermet, "Thermopower measurement of single isolated metallic nanostructures," Measurement Science & Technology, vol. 15, pp. 420-424, 2004.
[28]N. Chen, F. Gascoin, G.J. Snyder, E. Mueller, G. Karpinski, C. Stiewe, "Macroscopic thermoelectric inhomogeneities in (AgSbTe2)x(PbTe)1-x," Applied Physics Letters, vol. 87, pp. 171903, 2005.
[29]D. Platzek, G. Karpinski, C. Stiewe, P. Ziolkowski, C. Drasar, E. Mueller, "Potential-Seebeck-Microprobe PSM: Measuring the spatial resolution of the Seebeck coefficient and the electric potential," Proceedings of the 24th International Conference on Thermoelectrics (ICT) pp. 13-16, 2005.
[30]H.L. Ni, X.B. Zhao, G. Karpinski, E. Mueller, "Mapping and analysis of microscopic Seebeck coefficient distribution," Journal of Materials Science, vol. 40, pp. 605-608, 2005.
[31]G.S. Nolas, J. Sharp, H.J. Goldsmid, Thermoelectrics - Basic Principles and New Materials Developments, Springer-Verlag, Berlin Heidelberg, 2001.
[32]L.S. Sharath Chandra, A. Lakhani, D. Jain, S. Pandya, P.N. Vishwakarma, M. Gangrade, V. Ganesan, "Simple and precise thermoelectric power measurement setup for different environments," Review of Scientific Instruments, vol. 79, pp. 103907, 2008.
[33]S.R.S. Kumar, S. Kasiviswanathan, "A hot probe setup for the measurement of Seebeck coefficient of thin wires and thin films using integral method," Review of Scientific Instruments, vol. 79, pp. 024302, 2008.
[34]J.W. Cai, G.D. Mahan, "Effective Seebeck coefficient for semiconductors," Physical Review B, vol. 74, pp. 075201, 2006.
[35]D. Platzek, G. Karpinski, C. Drasar, E. Mueller, "Seebeck scanning microprobe for thermoelectric FGM," Functionally Graded Materials VIII, vol. 492-493, pp. 587-592, 2005.
[36]K.H. Wu, C.I. Hung, P. Ziolkowski, D. Platzek, G. Karpinski, C. Stiewe, E. Mueller, "Improvement of spatial resolution for local Seebeck coefficient measurements by deconvolution algorithm," Review of Scientific Instruments, vol. 80, pp. 105104, 2009.
[37]M. Takashiri, K. Miyazaki, H. Tsukamoto, "Structural and thermoelectric properties of fine-grained Bi0.4Te3.0Sb1.6 thin films with preferred orientation deposited by flash evaporation method," Thin Solid Films, vol. 516, pp. 6336-6343, 2008.
[38]H. Obara, S. Higomo, M. Ohta, A. Yamamoto, K. Ueno, T. Iida, "Thermoelectric properties of Bi2Te3-based thin films with fine grains fabricated by pulsed laser deposition," Japanese Journal of Applied Physics, vol. 48, pp. 085506, 2009.
[39]A.I. Boukai, Y. Bunimovich, J. Tahir-Kheli, J.K. Yu, W.A. Goddard, J.R. Heath, "Silicon nanowires as efficient thermoelectric materials," Nature, vol. 451, pp. 168-171, 2008.
[40]M.S. Toprak, C. Stiewe, D. Platzek, S. Williams, L. Bertini, E.C. Muller, C. Gatti, Y. Zhang, M. Rowe, M. Muhammed, "The impact of nanostructuring on the thermal conductivity of thermoelectric CoSb3," Advanced Functional Materials, vol. 14, pp. 1189-1196, 2004.
[41]J. Zhou, S. Li, H.M.A. Soliman, M.S. Toprak, M. Muhammed, D. Platzek, E. Muller, "Seebeck coefficient of nanostructured phosphorus-alloyed bismuth telluride thick films," Journal of Alloys and Compounds, vol. 471, pp. 278-281, 2009.
[42]G. Nakamoto, M. Kurisu, "Spatial distribution of the Seebeck coefficient in Zn13Sb10 determined by a Seebeck microprobe measurement system," Journal of Electronic Materials, vol. 38, pp. 916-919, 2009.
[43]C. Dames, G. Chen, "Theoretical phonon thermal conductivity of Si/Ge superlattice nanowires," Journal of Applied Physics, vol. 95, pp. 682-693, 2004.
[44]H.K. Lyeo, A.A. Khajetoorians, L. Shi, K.P. Pipe, R.J. Ram, A. Shakouri, C.K. Shih, "Profiling the thermoelectric power of semiconductor junctions with nanometer resolution," Science, vol. 303, pp. 816-818, 2004.
[45]Z.X. Bian, A. Shakouri, L. Shi, H.K. Lyeo, C.K. Shih, "Three-dimensional modeling of nanoscale Seebeck measurements by scanning thermoelectric microscopy," Applied Physics Letters, vol. 87, pp. 053115, 2005.
[46]S.H. Li, H.M.A. Soliman, J. Zhou, M.S. Toprak, M. Muhammed, D. Platzek, P. Ziolkowski, E. Mueller, "Effects of annealing and doping on nanostructured bismuth telluride thick films," Chemistry of Materials, vol. 20, pp. 4403-4410, 2008.
[47]R.S. Makala, K. Jagannadham, B.C. Sales, "Pulsed laser deposition of Bi2Te3-based thermoelectric thin films," Journal of Applied Physics, vol. 94, pp. 3907-3918, 2003.
[48]D.H. Kim, E. Byon, G.H. Lee, S. Cho, "Effect of deposition temperature on the structural and thermoelectric properties of bismuth telluride thin films grown by co-sputtering," Thin Solid Films, vol. 510, pp. 148-153, 2006.
[49]D.H. Kim, S.H. Lee, J.K. Kim, G.H. Lee, "Structure and electrical transport properties of bismuth thin films prepared by RF magnetron sputtering," Applied Surface Science, vol. 252, pp. 3525-3531, 2006.
[50]L.M. Goncalves, P. Alpuim, G. Min, D.M. Rowe, C. Couto, J.H. Correia, "Optimization of Bi2Te3 and Sb2Te3 thin films deposited by co-evaporation on polyimide for thermoelectric applications," Vacuum, vol. 82, pp. 1499-1502, 2008.
[51]L.W. da Silva, M. Kaviany, C. Uher, "Thermoelectric performance of films in the bismuth-tellurium and antimony-tellurium systems," Journal of Applied Physics, vol. 97, pp. 114903, 2005.
[52]L.X. Bu, W. Wang, H. Wang, "Effect of the substrate on the electrodeposition of Bi2Te3-ySey thin films," Materials Research Bulletin, vol. 43, pp. 1808-1813, 2008.
[53]D. Platzek, G. Karpinski, C. Stiewe, P. Ziolkowski, M. Stordeur, B. Engers, E. Mueller, "Spatial resolution of the Seebeck coefficient measured on thermoelectric thin films," Proceedings of the 3rd European Conference on Thermoelectrics (ECT), pp. 119-122, 2005.
[54]L.M. Goncalves, C. Couto, P. Alpuim, A.G. Rolo, F. Voelklein, J.H. Correia, "Optimization of thermoelectric properties on Bi2Te3 thin films deposited by thermal co-evaporation," Thin Solid Films, vol. 518, pp. 2816-2821, 2010.
[55]R.S. Puri, D. Morrey, A.J. Bell, J.F. Durodola, E.B. Rudnyi, J.G. Korvink, "Reduced order fully coupled structural-acoustic analysis via implicit moment matching," Applied Mathematical Modelling, vol. 33, pp. 4097-4119, 2009.
[56]K.A. Smith, C.D. Rahn, C.Y. Wang, "Model order reduction of 1D diffusion systems via residue grouping," Journal of Dynamic Systems Measurement and Control-Transactions of the Asme, vol. 130, pp. 011012, 2008.
[57]W.Z. Lin, E.T. Ong, E.H. Ong, "Efficient simulation of hard disk drive operational shock response using model order reduction," Microsystem Technologies-Micro-and Nanosystems-Information Storage and Processing Systems, vol. 15, pp. 1521-1524, 2009.
[58]T. Bechtold, E.B. Rudnyi, J.G. Korvink, "Dynamic electro-thermal simulation of microsystems - a review," Journal of Micromechanics and Microengineering, vol. 15, pp. R17-R31, 2005.
[59]T. Bechtold, D. Hohlfeld, E.B. Rudnyi, M. Gunther, "Efficient extraction of thin-film thermal parameters from numerical models via parametric model order reduction," Journal of Micromechanics and Microengineering, vol. 20, pp. 045030, 2010.
[60]J.S. Han, E.B. Rudnyi, J.G. Korvink, "Efficient optimisation of transient dynamic problems in MEMS devices using model order reduction," Journal of Micromechanics and Microengineering, vol. 15, pp. 822-832, 2005.
[61]M. Genix, P. Vairac, B. Cretin, "Local temperature surface measurement with intrinsic thermocouple," International Journal of Thermal Sciences, vol. 48, pp. 1679-1682, 2009.
[62]E. Muller, C. Drasar, J. Schilz, W.A. Kaysser, "Functionally graded materials for sensor and energy applications," Materials Science and Engineering a-Structural Materials Properties Microstructure and Processing, vol. 362, pp. 17-39, 2003.
[63]Y.G. Gurevich, G.N. Logvinov, "Physics of thermoelectric cooling," Semiconductor Science and Technology, vol. 20, pp. R57-R64, 2005.
[64]E.E. Antonova, D.C. Looman, "Finite elements for thermoelectric device analysis in ANSYS," Proceedings of the 24th International Conference on Thermoelectrics (ICT), pp. 215-218, 2005.
[65]Y. Katznelson, An Introduction to Harmonic Analysis Cambridge University Press, Cambridge, U.K. , 2004.
[66]P. Ziolkowski, G. Karpinski, D. Platzek, C. Stiewe, E. Mueller, "Application overview of the potential Seebeck microscope," Proceedings of the 25th International Conference on Thermoelectrics (ICT), pp. 684-688, 2006.
[67]P.S.R. Diniz, E.A.B.d. Silva, S.L. Netto., Digital Signal Processing: System Analysis and Design, Cambridge University Press, Cambridge, U.K., 2002.
[68]R.S. Graves, T.G. Kollie, D.L. McElroy, K.E. Gilchrist, "The thermal-conductivity of AISI 304L stainless-steel," International Journal of Thermophysics, vol. 12, pp. 409-415, 1991.
[69]A. Schick, W. Wefelmeyer, "Root n consistent and optimal density estimators for moving average processes," Scandinavian Journal of Statistics, vol. 31, pp. 63-78, 2004.
[70]F. Wolk, H. Yamazaki, H. Li, R.G. Lueck, "Calibrating the spatial response of bio-optical sensors," Journal of Atmospheric and Oceanic Technology, vol. 23, pp. 511-516, 2006.
[71]T. Bechtold, E.B. Rudnyi, J.G. Korvink, M. Graf, A. Hierlemarm, "Connecting heat transfer macromodels for array MEMS structures," Journal of Micromechanics and Microengineering, vol. 15, pp. 1205-1214, 2005.
[72]P.P. Silvester, R.L. Ferrari, Finite Elements for Electrical Engineers, 3rd Edition, Cambridge University Press, New York, 1996.