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

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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 \(\alpha \), resulted in faster diffusion and deeper p-n junctions. On the other hand, increasing the order of the space fractional derivative, denoted as \(\beta \), 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.

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Data Availability Statement

The authors declare that no data supporting the findings of this study are used in the preparation of the paper. No external data are used, because the work is purely theoretical.

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Author notes

  1. Abdelkader Souigat, Zineb Korichi, Dris Slimani, Yamina Benkrima, and Mohammed Tayeb Meftah have contributed equally to this work.

Authors and Affiliations

  1. Department of Exact Sciences, Ecole Normale Supérieure de Ouargla, 30000, Ouargla, Algeria

    Abdelkader Souigat, Zineb Korichi, Dris Slimani & Yamina Benkrima

  2. Department of Physics, Kasdi Merbah University, 30000, Ouargla, Algeria

    Mohammed Tayeb Meftah

Authors
  1. Abdelkader Souigat
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  2. Zineb Korichi
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  3. Dris Slimani
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  4. Yamina Benkrima
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  5. Mohammed Tayeb Meftah
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The authors have contributed equally to the paper.

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Correspondence to Zineb Korichi.

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Souigat, A., Korichi, Z., Slimani, D. et al. The space–time-fractional derivatives order effect of Caputo–Fabrizio on the doping profiles for formation a p-n junction. Eur. Phys. J. B 96, 124 (2023). https://doi.org/10.1140/epjb/s10051-023-00591-2

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