PN Junction Depletion Width & Electric Field | Built-in Potential and Asymmetric Diodes скачать в хорошем качестве

PN Junction Depletion Width & Electric Field | Built-in Potential and Asymmetric Diodes

n this semiconductor devices lecture, we go deeper into the physics of the PN junction, focusing on the potential profile, depletion width, and electric field inside the junction diode. We start from Poisson’s equation and the depletion approximation to derive the voltage and electric field as functions of position inside a step PN junction. Along the way, we connect the math back to the band diagram and the built-in potential Vbi that we previously derived from energy band bending. What’s covered in this video: – Writing Poisson’s equation for a step PN junction – Charge density profile in the depletion region (−Q·Na on p side, +Q·Nd on n side) – Why electric field E(x) is linear and potential V(x) is quadratic in x – Deriving V(x) in the n region and in the p region – Applying charge neutrality: Na·Xp = Nd·Xn – Expressing the built-in potential Vbi in terms of Xn and Xp – Solving for depletion widths Xn, Xp, and total width W = Xn + Xp – Relating Vbi to the area under the electric field triangle (Vbi = (1/2)·Emax·W) – Extracting Emax in terms of Vbi and W – Special case: asymmetric junctions (p+ n or n+ p) and where the depletion region primarily lies – Using 1/Na + 1/Nd to remember the depletion width expression – Rewriting Vbi in terms of majority/minority carrier concentrations (pp, pn, nn, np) – Physical intuition: higher doping, narrower depletion region; lighter doping, wider depletion region In the second part of the lecture, we move to biased PN junctions: – Qualitative band diagrams for forward and reverse bias – How applying a positive voltage to the p side lowers the barrier (Vbi − Va) – How applying reverse bias raises the barrier and widens the depletion region – Why current is large in forward bias and small (almost constant) in reverse bias – Interpreting forward and reverse I–V curves from the energy band perspective – Distinguishing equilibrium Fermi level from quasi-Fermi levels under bias This video is aimed at undergraduate students in electronics, electrical engineering, and related fields who want an intuitive but mathematically grounded understanding of PN junctions. If you’re comfortable with basic semiconductor concepts (ni, Na, Nd, band diagrams) and calculus (integration, differentiation), this lecture will help solidify how depletion width, electric field, and built-in potential all fit together. Use this as a revision resource before exams, or as a companion to your semiconductor devices course.