{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:33:45Z","timestamp":1787337225520,"version":"build-2736575974"},"reference-count":36,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2000,1]]},"abstract":"<jats:p>The energy-transport models describe the flow of electrons through a semiconductor crystal, influenced by diffusive, electrical, and thermal effects. They consist of the continuity equations for the mass and the energy, coupled with Poisson's equation for the electric potential. These models can be derived from the semiconductor Boltzmann equation.<\/jats:p>\n                  <jats:p>This paper consists of two parts. The first part concerns the modeling of the energy-transport system. The diffusion coefficients and the energy relaxation term are computed in terms of the electron density and temperature, under the assumptions of nondegenerate statistics and nonparabolic band diagrams. The equations can be rewritten in a drift-diffusion formulation which is used for the numerical discretization.<\/jats:p>\n                  <jats:p>In the second part, the stationary energy-transport equations are discretized using the exponential fitting mixed finite element method in one space dimension. Numerical simulations of a ballistic diode are performed.<\/jats:p>","DOI":"10.1137\/s1064827599360972","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"986-1007","source":"Crossref","is-referenced-by-count":46,"title":["Numerical Discretization of Energy-Transport Models for Semiconductors with Nonparabolic Band Structure"],"prefix":"10.1137","volume":"22","author":[{"given":"Pierre","family":"Degond","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ansgar","family":"J\u00fcngel","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Paola","family":"Pietra","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,25]]},"reference":[{"key":"R1","unstructured":"W. Allegretto, H. Xie, Nonisothermal semiconductor systems, Lecture Notes in Pure and Appl. Math., Vol. 162, Dekker, New York, 1994, 17\u20132495i:35298"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1109\/16.381985"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/1985190100071"},{"key":"R4","unstructured":"N. Ben Abdallah, P. Degond, P. Markowich, and C. Schmeiser,\n                      High field approximations of the spherical harmonics expansion model for semiconductors\n                      , Z. Angew. Math. Phys., to appear."},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1063\/1.531567"},{"key":"R6","first-page":"599","volume":"305","author":"Brezzi Franco","year":"1987","journal-title":"C. R. Acad. Sci. Paris S\u00e9r. I Math."},{"key":"R7","doi-asserted-by":"crossref","unstructured":"Franco Brezzi, Luisa Marini, Paola Pietra, Numerical simulation of semiconductor devices, Proceedings of the Eighth International Conference on Computing Methods in Applied Sciences and Engineering (Versailles, 1987), Vol. 75, 1989, 493\u201351491b:78023","DOI":"10.1016\/0045-7825(89)90044-3"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1137\/0726078"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1109\/55.144940"},{"key":"R10","unstructured":"D. Chen, E. Sangiorgi, M. Pinto, E. Kan, U. Ravaioli, and R. Dutton,\n                      Analysis of spurious velocity overshoot in hydrodynamic simulations\n                      , NUPAD IV, 1992, pp. 109\u2013114."},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1016\/S0764-4442(97)86960-1"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-7824(97)89980-1"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1099-1476(199810)21:15<1399::AID-MMA1>3.0.CO;2-#"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1002\/ett.4460010312"},{"key":"R15","unstructured":"J. Jerome,\n                      Analysis of Charge Transport. A Mathematical Study of Semiconductor Devices\n                      , Springer, Berlin, 1996."},{"key":"R16","doi-asserted-by":"crossref","unstructured":"Joseph Jerome, Chi\u2010Wang Shu, Energy transport systems for semiconductors: analysis and simulation, de Gruyter, Berlin, 1996, 3835\u201338461389337","DOI":"10.1515\/9783110883237.3835"},{"key":"R17","unstructured":"A. J\u00fcngel,\n                      The energy\u2010transport model for semiconductors: Some analytical and numerical results\n                      , in Proceedings of the International Workshop on \u201cRecent Progress in the Mathematical Theory on Vlasov\u2010Maxwell Equations,\u201d Paris, 1997, pp. 140\u2013158."},{"key":"R18","unstructured":"A. J\u00fcngel,\n                      Regularity and uniqueness of solutions to a system of parabolic equations in nonequilibrium thermodynamics\n                      , Nonlinear Anal., to appear."},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1142\/S0218202597000475"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1016\/0022-3697(57)90013-6"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1007\/BF01385735"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1108\/eb010094"},{"key":"R23","first-page":"219","volume":"8","author":"Marini L.","year":"1989","journal-title":"Mat. Apl. Comput."},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1108\/eb010080"},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/1994280201231"},{"key":"R26","doi-asserted-by":"crossref","unstructured":"P. A. Markowich, C. A. Ringhofer, and C. Schmeiser,\n                      Semiconductor Equations\n                      , Springer, Berlin, 1990.","DOI":"10.1007\/978-3-7091-6961-2"},{"key":"R27","unstructured":"A. Marrocco, P. Montarnal, and B. Perthame,\n                      Simulation of the energy\u2010transport and simplified hydrodynamic models for semiconductor devices using mixed finite elements\n                      , in Proceedings ECCOMAS 96, John Wiley, London, 1996."},{"key":"R28","doi-asserted-by":"publisher","DOI":"10.1108\/eb010032"},{"key":"R29","doi-asserted-by":"publisher","DOI":"10.1108\/eb010024"},{"key":"R30","doi-asserted-by":"crossref","unstructured":"P. Raviart and J. Thomas,\n                      A mixed finite element method for second order elliptic equations\n                      , in Mathematical Aspects of the Finite Element Method, Lecture Notes in Math. 606, Springer, Berlin, 1977, pp. 292\u2013315.","DOI":"10.1007\/BFb0064470"},{"key":"R31","doi-asserted-by":"publisher","DOI":"10.1109\/T-ED.1969.16566"},{"key":"R32","doi-asserted-by":"publisher","DOI":"10.1142\/S0218202598000032"},{"key":"R33","doi-asserted-by":"publisher","DOI":"10.1108\/eb051722"},{"key":"R34","doi-asserted-by":"publisher","DOI":"10.1108\/eb010127"},{"key":"R35","unstructured":"P. Visocky,\n                      A method for transient semiconductor device simulation using hot\u2010electron transport equations\n                      , Proceedings of the Nasecode X Conference., J. Miller, ed., Boole Press, Dublin, 1994, pp. 101\u2013104."},{"key":"R36","doi-asserted-by":"crossref","unstructured":"D. Woolard, M. Stroscio, M. Littlejohn, R. Trew, and H. Grubin,\n                      A new nonparabolic hydrodynamic model with quantum corrections\n                      , in Computational Electronics: Semiconductor Transport and Device Simulation, K. Hess, ed., Kluwer Academic Press, Boston, 1991, pp. 59\u201362.","DOI":"10.1007\/978-1-4757-2124-9_11"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S1064827599360972","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:50:51Z","timestamp":1787334651000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S1064827599360972"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,1]]},"references-count":36,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2000,1]]}},"alternative-id":["10.1137\/S1064827599360972"],"URL":"https:\/\/doi.org\/10.1137\/s1064827599360972","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,1]]}}}