A New Approach for Approximate Solution of ADE: Physical-Based Modeling of Carriers in Doping Region

Leobardo Hernandez-Gonzalez, Jazmin Ramirez-Hernandez, Oswaldo Ulises Juarez-Sandoval, Miguel Angel Olivares-Robles, Ramon Blanco Sanchez and Rosario del Pilar Gibert Delgado
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Leobardo Hernandez-Gonzalez: Instituto Politecnico Nacional, Escuela Superior de Ingenieria Mecanica y Electrica, Unidad Culhuacan, Av. Santa Ana No. 1000, Col. San Francisco Culhuacan, Mexico City C.P. 04430, Mexico
Jazmin Ramirez-Hernandez: Instituto Politecnico Nacional, Escuela Superior de Ingenieria Mecanica y Electrica, Unidad Culhuacan, Av. Santa Ana No. 1000, Col. San Francisco Culhuacan, Mexico City C.P. 04430, Mexico
Oswaldo Ulises Juarez-Sandoval: Instituto Politecnico Nacional, Escuela Superior de Ingenieria Mecanica y Electrica, Unidad Culhuacan, Av. Santa Ana No. 1000, Col. San Francisco Culhuacan, Mexico City C.P. 04430, Mexico
Miguel Angel Olivares-Robles: Instituto Politecnico Nacional, Escuela Superior de Ingenieria Mecanica y Electrica, Unidad Culhuacan, Av. Santa Ana No. 1000, Col. San Francisco Culhuacan, Mexico City C.P. 04430, Mexico
Ramon Blanco Sanchez: Departamento de Matemática, Universidad de Camaguey Ignacio Agramonte Loynaz, Camagüey C.P. 70100, Cuba
Rosario del Pilar Gibert Delgado: Instituto Politecnico Nacional, Escuela Superior de Ingenieria Mecanica y Electrica, Unidad Culhuacan, Av. Santa Ana No. 1000, Col. San Francisco Culhuacan, Mexico City C.P. 04430, Mexico

Mathematics, 2021, vol. 9, issue 5, 1-18

Abstract: The electric behavior in semiconductor devices is the result of the electric carriers’ injection and evacuation in the low doping region, N-. The carrier’s dynamic is determined by the ambipolar diffusion equation (ADE), which involves the main physical phenomena in the low doping region. The ADE does not have a direct analytic solution since it is a spatio-temporal second-order differential equation. The numerical solution is the most used, but is inadequate to be integrated into commercial electric circuit simulators. In this paper, an empiric approximation is proposed as the solution of the ADE. The proposed solution was validated using the final equations that were implemented in a simulator; the results were compared with the experimental results in each phase, obtaining a similarity in the current waveforms. Finally, an advantage of the proposed methodology is that the final expressions obtained can be easily implemented in commercial simulators.

Keywords: physical modeling; silicon carbide; simulation semiconductor (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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