48 Derivation of Electric Field & Potential in PN Junction | Poisson's Equation

How to calculate the Electric Field and Potential in a Step Graded PN Junction? 🧮

In this video, we perform the complete mathematical derivation starting from Poisson's Equation:
1. *Charge Density Profile:* Defining the acceptor (Na) and donor (Nd) ion distribution.
2. *Calculating Electric Field:* Integrating charge density to find the E-field equation.
3. *Finding Maximum Electric Field (Emax):* Why it occurs at the junction (x=0).
4. *Calculating Potential (V):* Integrating the E-field to derive the Potential Barrier equation.



We also derive the relationship between Depletion Width (W) and the Built-in Potential (Vbi). Essential for Engineering Physics and EDC exams.

#Derivation #Semiconductors #PoissonEquation #GATE2025 #EDC #Engineering

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