DEPARTMENT CODE: PH-500

Quantum & Semiconductor Physics Simulators Hub

P-N junction energy band bending, carrier drift-diffusion, quantum potential well tunneling, and wave-particle dispersion.

            Governing Formulation: i\hbar \frac{\partial}{\partial t} \Psi(\mathbf{r},t) = \left[ -\frac{\hbar^2}{2m}\nabla^2 + V(\mathbf{r}) \right] \Psi(\mathbf{r},t)
          

Interactive Workbenches in Quantum & Semiconductor Physics

Poisson-Boltzmann / Shockley Intermediate

P-N Junction Diode Band Bending & Carrier Transport

Solve the 1D Poisson-Boltzmann equation across an abrupt metallurgical junction. Watch the electrostatic potential barrier collapse under forward bias and widen under reverse bias, driving exponential minority carrier injection.

Equation: W = \sqrt{\frac{2\epsilon_s}{q}\left(\frac{1}{N_A} + \frac{1}{N_D}\right)(V_{bi} - V_a)}, \quad I = I_s\left(e^{qV_a / k_B T} - 1\right)

Standard: IEEE Trans. Electron Devices / Sze Physics of Semiconductor Devices

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