{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T17:32:58Z","timestamp":1791307978664,"version":"4.3.1"},"reference-count":30,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2015,6,15]],"date-time":"2015-06-15T00:00:00Z","timestamp":1434326400000},"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>The main goal of this work is to determine a statistical non-equilibrium distribution function for the electron and holes in semiconductor heterostructures in steady-state conditions. Based on the postulates of local equilibrium, as well as on the integral form of the weighted Gyarmati\u2019s variational principle in the force representation, using an alternative method, we have derived general expressions, which have the form of the Fermi\u2013Dirac distribution function with four additional components. The physical interpretation of these components has been carried out in this paper. Some numerical results of a non-equilibrium distribution function for an electron in HgCdTe structures are also presented.<\/jats:p>","DOI":"10.3390\/e17064110","type":"journal-article","created":{"date-parts":[[2015,6,15]],"date-time":"2015-06-15T10:57:58Z","timestamp":1434365878000},"page":"4110-4133","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["The Non-Equilibrium Statistical Distribution Function for Electrons and Holes in Semiconductor Heterostructures in Steady-State Conditions"],"prefix":"10.3390","volume":"17","author":[{"given":"Krzysztof","family":"J\u1f79zwikowska","sequence":"first","affiliation":[{"name":"Institute of Applied Physics, Military University of Technology, 2 Kaliskiego St., 00-908 Warsaw, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alina","family":"J\u1f79zwikowska","sequence":"additional","affiliation":[{"name":"Faculty of Applied Informatics and Mathematics, Warsaw University of Life Science SGGW, Nowoursynowska 166 St., 02-787 Warsaw, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Micha\u0142","family":"Nietopiel","sequence":"additional","affiliation":[{"name":"Institute of Applied Physics, Military University of Technology, 2 Kaliskiego St., 00-908 Warsaw, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2015,6,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1002\/pssb.2220780209","article-title":"Conduction current and generalized einstein relation for degenerate semiconductors and metals","volume":"78","author":"Marshak","year":"1976","journal-title":"Phys. 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