Divya Tiwari,
Kirti Verma,
- Assistant Professor, Department of Engineering Mathematics, Gyan Ganga Institute of Technology & Sciences, Jabalpur, Madhya Pradesh, India
- Associate Professor, Department of Engineering Physics, Gyan Ganga Institute of Technology and Sciences Jabalpur, Madhya Pradesh, India
Abstract
Semiconductor device physics forms the foundation of modern electronic and optoelectronic technologies. Mathematical modelling provides a rigorous framework for understanding, predicting, and optimizing the behavior of semiconductor devices by linking physical principles with device-level performance. This work presents an analytical approach to the mathematical modelling of semiconductor devices, emphasizing the derivation and interpretation of governing equations that describe charge transport and electrostatic behavior. The model is based on fundamental physical laws, including Poisson’s equation for electrostatic potential and the carrier continuity equations for electrons and holes, coupled with appropriate transport models such as drift diffusion theory. Analytical solutions are explored under simplifying assumptions such as steady-state operation, low-level injection, and one-dimensional geometries to gain physical insight into carrier distribution, electric field profiles, and current–voltage characteristics. Classical devices, including the p–n junction diode and metal oxide semiconductor (MOS) structures, are used as representative examples to illustrate the modelling methodology. By focusing on analytical techniques, the study highlights the relationship between material properties, device geometry, and operating conditions, enabling clearer interpretation of device behavior compared to purely numerical approaches. Although analytical models involve approximations, they remain essential for initial device design, parameter extraction, and educational purposes, as well as for validating numerical simulations. The presented analytical framework demonstrates how mathematical modelling bridges semiconductor physics and practical device engineering. It provides a compact yet powerful tool for understanding fundamental mechanisms, guiding device optimization, and supporting the development of next-generation semiconductor technologies.
Keywords: Semiconductor devices, analytical modelling, device physics, poisson’s equation, drift–diffusion model
[This article belongs to Research & Reviews: Discrete Mathematical Structures ]
Divya Tiwari, Kirti Verma. Mathematical Modelling of Semiconductor Device Physics: An Analytical Approach. Research & Reviews: Discrete Mathematical Structures. 2026; 13(01):36-42.
Divya Tiwari, Kirti Verma. Mathematical Modelling of Semiconductor Device Physics: An Analytical Approach. Research & Reviews: Discrete Mathematical Structures. 2026; 13(01):36-42. Available from: https://journals.stmjournals.com/rrdms/article=2026/view=238984
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Research & Reviews: Discrete Mathematical Structures
| Volume | 13 |
| Issue | 01 |
| Received | 04/02/2026 |
| Accepted | 26/02/2026 |
| Published | 10/03/2026 |
| Publication Time | 34 Days |
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