The space–time-fractional derivatives order effect of Caputo–Fabrizio on the doping profiles for formation a p-n junction

Abdelkader Souigat (), Zineb Korichi (), Dris Slimani (), Yamina Benkrima () and Mohammed Tayeb Meftah ()
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Abdelkader Souigat: Ecole Normale Supérieure de Ouargla
Zineb Korichi: Ecole Normale Supérieure de Ouargla
Dris Slimani: Ecole Normale Supérieure de Ouargla
Yamina Benkrima: Ecole Normale Supérieure de Ouargla
Mohammed Tayeb Meftah: Kasdi Merbah University

The European Physical Journal B: Condensed Matter and Complex Systems, 2023, vol. 96, issue 9, 1-7

Abstract: Abstract 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 $$\alpha $$ α , resulted in faster diffusion and deeper p-n junctions. On the other hand, increasing the order of the space fractional derivative, denoted as $$\beta $$ β , 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. Graphical abstract

Date: 2023
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DOI: 10.1140/epjb/s10051-023-00591-2

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