{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:23:14Z","timestamp":1760242994134,"version":"build-2065373602"},"reference-count":10,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2015,1,29]],"date-time":"2015-01-29T00:00:00Z","timestamp":1422489600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In the theory of energy and momentum relaxation in semiconductor devices, the introduction of two temperatures and two mean velocities for electron and phonons is required. A new model, based on an asymptotic procedure for solving the kinetic equations of electrons and phonons is proposed, which naturally gives the displaced Maxwellian at the leading order. After that, balance equations for the electron number, energy densities and momentum densities are constructed, which constitute now a system of five equations for the chemical potential of electrons, the temperatures and the drift velocities. Moreover, Poisson\u2019s equation is coupled, in order to calculate the self-consistent electric field. In Bloch\u2019s approximation, we derive a telegrapher\u2019s-Poisson system for the electron number density and the electric potential, which could allow simple semiconductor calculations, but still including wave propagation effects.<\/jats:p>","DOI":"10.3390\/e17020528","type":"journal-article","created":{"date-parts":[[2015,1,29]],"date-time":"2015-01-29T10:10:02Z","timestamp":1422526202000},"page":"528-538","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A New Telegrapher\u2019s-Poisson System in Semiconductor Theory: A Singular Perturbation Approach"],"prefix":"10.3390","volume":"17","author":[{"given":"Alberto","family":"Rossani","sequence":"first","affiliation":[{"name":"Dipartimento di Scienza Applicata e Tecnologia, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,1,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Zakari, M. (1998). Stochastic model of plasma waves for a simple band structure in semiconductors. Phys. Rev. B, 57.","DOI":"10.1103\/PhysRevB.57.12145"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Allen, P.B. (1987). Theory of thermal relaxation of electrons in metals. Phys. Rev. Lett, 59.","DOI":"10.1103\/PhysRevLett.59.1460"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Rossani, A. (2010). Generalized balance equations for an electron-phonon system. J. Phys. A, 43.","DOI":"10.1088\/1751-8113\/43\/16\/165002"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"13186","DOI":"10.1103\/PhysRevB.46.13186","article-title":"Thermodynamic derivation of the hydrodynamical model for charge transport in semiconductors","volume":"46","author":"Anile","year":"1992","journal-title":"Phys. Rev. B"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/0165-2125(96)00012-1","article-title":"Asymptotic waves for the hydrodynamical model of semiconductors","volume":"24","author":"Romano","year":"1996","journal-title":"Wave Motion"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3329","DOI":"10.1016\/j.physa.2011.04.021","article-title":"Modeling of the non-equilibrium effects by hight electric fields in small semiconductor devices","volume":"390","author":"Rossani","year":"2011","journal-title":"Physica A"},{"key":"ref_7","unstructured":"Lifshitz, E.M., and Pitaevskii, L.P. (1981). Physical Kinetics, Pergamon Press."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1016\/S0378-4371(01)00682-3","article-title":"Generalized kinetic theory of electrons and phonons","volume":"305","author":"Rossani","year":"2002","journal-title":"Physica A"},{"key":"ref_9","unstructured":"Ziman, J.M. (2007). Electrons and Phonons, Claredon Press."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Lundstrom, M. (2000). Fundamentals of Carrier Transport, Cambridge University Press.","DOI":"10.1017\/CBO9780511618611"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/2\/528\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:42:09Z","timestamp":1760215329000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/2\/528"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,1,29]]},"references-count":10,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2015,2]]}},"alternative-id":["e17020528"],"URL":"https:\/\/doi.org\/10.3390\/e17020528","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2015,1,29]]}}}