https://doi.org/10.1140/epjb/s10051-023-00591-2
Regular Article - Solid State and Materials
The space–time-fractional derivatives order effect of Caputo–Fabrizio on the doping profiles for formation a p-n junction
1
Department of Exact Sciences, Ecole Normale Supérieure de Ouargla, 30000, Ouargla, Algeria
2
Department of Physics, Kasdi Merbah University, 30000, Ouargla, Algeria
Received:
12
July
2023
Accepted:
29
August
2023
Published online:
22
September
2023
In this study, we treated the space–time-fractional diffusion equation in a semi-infinite medium using a recently developed fractional derivative introduced by Caputo and Fabrizio. Our main focus was on simulating the diffusion profiles during the creation of a p-n junction according to the obtained solution. We made an interesting observation regarding the influence of the fractional-order derivatives on the depth estimation of the p-n junction. Increasing the order of the time-fractional derivative, denoted as 
, resulted in faster diffusion and deeper p-n junctions. On the other hand, increasing the order of the space fractional derivative, denoted as 
, led to slower diffusion and shallower p-n junctions. These findings demonstrate the significant impact of the fractional derivative orders on the diffusion behavior and depth characteristics of the p-n junction in the studied system.
Abdelkader Souigat, Zineb Korichi, Dris Slimani, Yamina Benkrima, and Mohammed Tayeb Meftah have contributed equally to this work.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
