{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:10:50Z","timestamp":1760242250467,"version":"build-2065373602"},"reference-count":51,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2017,2,10]],"date-time":"2017-02-10T00:00:00Z","timestamp":1486684800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"NSF of China","doi-asserted-by":"publisher","award":["11374016"],"award-info":[{"award-number":["11374016"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"MOST of China","award":["2012CB932702"],"award-info":[{"award-number":["2012CB932702"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper, we report the results of slight changes in the thermopower of long W, Mo, Zn, Cu, brass, and Ti wires, that resulted from changes in the wire\u2019s diameter or cross-sectional area. The samples used in the tests had a round shape with a diameter that ranged from tens of micron to 2 mm, which was much larger than the corresponding mean free paths of these materials. Nevertheless, a small change in thermopower, at the order of 1\u201310 nV\/K, was repeatedly observed when the wire diameter was changed, or when the cross-sectional area of the wire was altered by mechanical methods, such as grinding or splitting. The results are consistent with previous observations showing that the thermopower in metallic thin film stripes changes with their width, from 100 \u03bcm to as little as 70 nm, implying a universal, geometric-boundary-related size effect of thermopower in metal materials, that occurs at the nanometer scale and continuously decreases all the way to the millimeter scale. This effect could be applied in the manufacturing of high-temperature sensors with simple structures.<\/jats:p>","DOI":"10.3390\/s17020331","type":"journal-article","created":{"date-parts":[[2017,2,10]],"date-time":"2017-02-10T05:27:09Z","timestamp":1486704429000},"page":"331","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Geometric Shape Induced Small Change of Seebeck Coefficient in Bulky Metallic Wires"],"prefix":"10.3390","volume":"17","author":[{"given":"Gang","family":"Li","sequence":"first","affiliation":[{"name":"Key Laboratory for the Physics & Chemistry of Nanodevices, and Department of Electronics, Peking University, Beijing 100871, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaohui","family":"Su","sequence":"additional","affiliation":[{"name":"Key Laboratory for the Physics & Chemistry of Nanodevices, and Department of Electronics, Peking University, Beijing 100871, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fan","family":"Yang","sequence":"additional","affiliation":[{"name":"Key Laboratory for the Physics & Chemistry of Nanodevices, and Department of Electronics, Peking University, Beijing 100871, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoye","family":"Huo","sequence":"additional","affiliation":[{"name":"Key Laboratory for the Physics & Chemistry of Nanodevices, and Department of Electronics, Peking University, Beijing 100871, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gengmin","family":"Zhang","sequence":"additional","affiliation":[{"name":"Key Laboratory for the Physics & Chemistry of Nanodevices, and Department of Electronics, Peking University, Beijing 100871, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9567-5980","authenticated-orcid":false,"given":"Shengyong","family":"Xu","sequence":"additional","affiliation":[{"name":"Key Laboratory for the Physics & Chemistry of Nanodevices, and Department of Electronics, Peking University, Beijing 100871, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,2,10]]},"reference":[{"key":"ref_1","unstructured":"International Roadmap Committee (2013). International Technology Roadmap for Semiconductors, Semiconductor Industry Association."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"066001","DOI":"10.1088\/1674-4926\/34\/6\/066001","article-title":"Interconnects for nanoscale MOSFET technology: A review","volume":"34","author":"Chaudhry","year":"2013","journal-title":"J. Semicond."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1039\/B917150A","article-title":"Electrochemical sensing in paper-based microfluidic devices","volume":"10","author":"Nie","year":"2010","journal-title":"Lab Chip"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"013001","DOI":"10.1088\/0960-1317\/26\/1\/013001","article-title":"Review of polymer MEMS micromachining","volume":"26","author":"Kim","year":"2016","journal-title":"J. Micromech. Microeng."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1038\/nnano.2012.40","article-title":"Nanoelectromechanical contact switches","volume":"7","author":"Loh","year":"2012","journal-title":"Nat. Nanotechnol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1038\/nphoton.2015.36","article-title":"High-efficiency light-emitting devices based on quantum dots with tailored nanostructures","volume":"9","author":"Yang","year":"2015","journal-title":"Nat. Photonics"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"703","DOI":"10.1038\/nnano.2010.173","article-title":"Hybrid superconductor\u2013quantum dot devices","volume":"5","author":"Kouwenhoven","year":"2010","journal-title":"Nat. Nanotechnol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"e234-1","DOI":"10.1038\/lsa.2015.7","article-title":"Integrated colloidal quantum dot photodetectors with color-tunable plasmonic nanofocusing lenses","volume":"4","author":"Diedenhofen","year":"2015","journal-title":"Light Sci. Appl."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1038\/nature14270","article-title":"State preservation by repetitive error detection in a superconducting quantum circuit","volume":"511","author":"Kelly","year":"2015","journal-title":"Nature"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1038\/nphoton.2013.70","article-title":"High-efficiency quantum-dot light-emitting devices with enhanced charge injection","volume":"7","author":"Mashford","year":"2013","journal-title":"Nat. Photonics"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"789","DOI":"10.1109\/4.222178","article-title":"A Programmable Artificial Retina","volume":"28","author":"Bernard","year":"1993","journal-title":"IEEE J. Solid-State Circuits"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1109\/MSPEC.2007.323430","article-title":"The murky ethics of implanted chips","volume":"44","author":"Foster","year":"2007","journal-title":"IEEE Spectr."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1016\/j.sna.2005.11.070","article-title":"Fabrication of pyramid shaped three-dimensional 8 \u00d7 8 electrodes for artificial retina","volume":"130","author":"Koo","year":"2006","journal-title":"Sens. Actuators A Phys."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"905","DOI":"10.4155\/bio-2015-0023","article-title":"Challenges and opportunities for translating medical microdevices: Insights from the programmable bio-nano-chip","volume":"8","author":"McRae","year":"2016","journal-title":"Bioanalysis"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/j.expthermflusci.2005.05.004","article-title":"A fast-response thin film thermocouple to measure rapid surface temperature changes","volume":"30","author":"Heichal","year":"2005","journal-title":"Exp. Therm. Fluid Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1016\/j.sna.2007.01.007","article-title":"Fabrication and application of micro thin film thermocouples for transient temperature measurement in nanosecond pulsed laser micromachining of nickel","volume":"136","author":"Choi","year":"2007","journal-title":"Sens. Actuators A Phys."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1016\/j.jmapro.2012.10.002","article-title":"Insertable thin film thermocouples for in situ transient temperature monitoring in ultrasonic metal welding of battery tabs","volume":"15","author":"Zhao","year":"2013","journal-title":"J. Manuf. Process."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1606","DOI":"10.1109\/LED.2011.2165522","article-title":"Thin-Film Thermocouple Array for Time-Resolved Local Temperature Mapping","volume":"32","author":"Liu","year":"2011","journal-title":"IEEE Electron. Device Lett."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"3275","DOI":"10.1002\/adma.201200644","article-title":"An Extremely Simple Thermocouple Made of a Single Layer of Metal","volume":"24","author":"Liu","year":"2012","journal-title":"Adv. Mater."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Li, G., Wang, Z., Mao, X., Zhang, Y., Huo, X., and Xu, S. (2016). Real-Time Two-Dimensional Mapping of Relative Local Surface Temperatures with a Thin-Film Sensor Array. Sensors, 16.","DOI":"10.3390\/s16070977"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1126\/science.aaa2433","article-title":"Nanoscale temperature mapping in operating microelectronic devices","volume":"347","author":"Meclenburg","year":"2015","journal-title":"Science"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"40185","DOI":"10.1039\/C6RA06353E","article-title":"A sub-200 nanometer wide 3D stacking thin-film temperature sensor","volume":"6","author":"Huo","year":"2016","journal-title":"RSC Adv."},{"key":"ref_23","unstructured":"Ziman, J.M. (1962). Electrons and Phonons, Clarendon."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"L125","DOI":"10.1088\/0022-3727\/14\/8\/003","article-title":"Thermoelectric effect in ytterbium and samarium films","volume":"14","author":"Angadi","year":"1981","journal-title":"J. Phys. D Appl. Phys."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1007\/BF00731027","article-title":"Thermoelectric power measurements in thin palladium films","volume":"1","author":"Angadi","year":"1982","journal-title":"J. Mater. Sci. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"L103","DOI":"10.1088\/0022-3727\/14\/7\/002","article-title":"Thermoelectric power measurements in thin tin films","volume":"14","author":"Angadi","year":"1981","journal-title":"J. Phys. D Appl. Phys."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"4022","DOI":"10.1063\/1.332583","article-title":"Thermoelectric power of aluminum films","volume":"54","author":"De","year":"1983","journal-title":"J. Appl. Phys."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"5990","DOI":"10.1103\/PhysRevB.35.5990","article-title":"Size and temperature effects on the Seebeck coefficient of thin bismuth films","volume":"35","author":"Das","year":"1987","journal-title":"Phys. Rev. B"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/0040-6090(94)90671-8","article-title":"Influence of deposition rates and thickness on the electrical resistivity and thermoelectric power of thin iron films","volume":"251","author":"Schepis","year":"1994","journal-title":"Thin Solid Films"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"133106","DOI":"10.1063\/1.2189192","article-title":"Thermoelectric effect in very thin film Pt\/Au thermocouples","volume":"88","author":"Salvadori","year":"2006","journal-title":"Appl. Phys. Lett."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"4777","DOI":"10.1063\/1.321503","article-title":"Electron transport properties of copper films. II. Thermoelectric power","volume":"46","author":"Thakoor","year":"1975","journal-title":"J. Appl. Phys."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1038\/508327a","article-title":"Thermoelectricity: The ugly duckling","volume":"508","author":"Heremans","year":"2014","journal-title":"Nature"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1017\/S0305004100019952","article-title":"The conductivity of thin metallic films according to the electron theory of metals","volume":"34","author":"Fuchs","year":"1938","journal-title":"Proc. Camb. Philos. Soc."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/00018735200101151","article-title":"The mean free path of electrons in metals","volume":"1","author":"Sondheimer","year":"1952","journal-title":"Adv. Phys."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"3634","DOI":"10.1063\/1.1660781","article-title":"Thermoelectric Power of Thin Gold Films","volume":"42","author":"Lin","year":"1971","journal-title":"J. Appl. Phys."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"5324","DOI":"10.1063\/1.1662151","article-title":"Thermoelectric power of thin silver films","volume":"44","author":"Yu","year":"1973","journal-title":"J. Appl. Phys."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"5320","DOI":"10.1063\/1.1662150","article-title":"Thermoelectric power of thin copper films","volume":"44","author":"Leonard","year":"1973","journal-title":"J. Appl. Phys."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1710","DOI":"10.1063\/1.1709746","article-title":"Statistical Model for the Size Effect in Electrical Conduction","volume":"38","author":"Soffer","year":"1967","journal-title":"J. Appl. Phys."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"532","DOI":"10.1039\/C4NR04184D","article-title":"Characterization of nanometer-thick polycrystalline silicon with phonon-boundary scattering enhanced thermoelectric properties and its application in infrared sensors","volume":"7","author":"Zhou","year":"2015","journal-title":"Nanoscale"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"83709-1","DOI":"10.1063\/1.3653824","article-title":"Unexpected size effect in the thermopower of thin-film stripes","volume":"110","author":"Sun","year":"2011","journal-title":"J. Appl. Phys."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"3869","DOI":"10.1002\/smll.201303942","article-title":"A Nano-Stripe Based Sensor for Temperature Measurement at the Submicrometer and Nano Scales","volume":"10","author":"Huo","year":"2014","journal-title":"Small"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1234","DOI":"10.1109\/TNANO.2014.2358532","article-title":"Single-Metal Nanoscale Thermocouples","volume":"13","author":"Szakmany","year":"2014","journal-title":"IEEE Trans. Nanotechnol."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"4236","DOI":"10.1109\/TMTT.2015.2496379","article-title":"High-Speed Antenna-Coupled Terahertz Thermocouple Detectors and Mixers","volume":"63","author":"Russer","year":"2015","journal-title":"IEEE Trans. Microw. Theory Tech."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"236101-1","DOI":"10.1063\/1.4884735","article-title":"Comment on \u201cUnexpected size effect in the thermopower of thin-film stripes\u201d [J. Appl. Phys. 110, 083709 (2013)]","volume":"115","author":"Szakmany","year":"2014","journal-title":"J. Appl. Phys."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"236102-1","DOI":"10.1063\/1.4884736","article-title":"Response to \u201cComment on \u2018Unexpected size effect in the thermopower of thin-film stripes\u2019\u201d [J. Appl. Phys. 115, 236101 (2014)]","volume":"115","author":"Huo","year":"2014","journal-title":"J. Appl. Phys."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"035422","DOI":"10.1103\/PhysRevB.77.035422","article-title":"Diameter-dependent thermopower of bismuth nanowires","volume":"77","author":"Nikolaeva","year":"2008","journal-title":"Phys. Rev. B"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"063102","DOI":"10.1063\/1.3204005","article-title":"Size dependent thermoelectric properties of silicon nanowires","volume":"95","author":"Shi","year":"2009","journal-title":"Appl. Phys. Lett."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"3037","DOI":"10.1021\/nl101505q","article-title":"Diameter Dependence of the Transport Properties of Antimony Telluride Nanowires","volume":"10","author":"Zuev","year":"2010","journal-title":"Nano Lett."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"1382","DOI":"10.1103\/PhysRevB.1.1382","article-title":"Electrical-Resistivity Model for Polycrystalline Films: The Case of Arbitrary Reflection at External Surfaces","volume":"1","author":"Mayadas","year":"1970","journal-title":"Phys. Rev. B"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1016\/0040-6090(78)90293-6","article-title":"A theoretical description of grain boundary electron scattering by an effective mean free path","volume":"51","author":"Tellier","year":"1978","journal-title":"Thin Solid Films"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"2009","DOI":"10.1088\/0305-4608\/10\/9\/016","article-title":"Thermoelectric power of thin polycrystalline metal films in an effective mean free path model","volume":"10","author":"Pichard","year":"1980","journal-title":"J. Phys. F Met. Phys."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/2\/331\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:27:54Z","timestamp":1760207274000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/2\/331"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,2,10]]},"references-count":51,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2017,2]]}},"alternative-id":["s17020331"],"URL":"https:\/\/doi.org\/10.3390\/s17020331","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2017,2,10]]}}}