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EESM5200 (L1) Part I: Topic 5 - Derivation of Ideal PN Junction Diode Equation

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You are given the band diagram of a PN junction with doping NAย and NDย under forward bias of VFย below. Which of the following expression correctly describe the electron concentration as described below: (a) ๐‘ ๐ด ;ย  (b) ๐‘ ๐ท ;ย  (c) ๐‘› ๐‘– 2 ๐‘ ๐ด ;ย  (d) ๐‘› ๐‘– 2 ๐‘ ๐ท ;ย  (e) ๐‘ ๐ด ๐‘’ ๐‘ž ๐‘‰ ๐น ๐‘˜ ๐‘‡ ;ย  (f) ๐‘ ๐ท ๐‘’ ๐‘ž ๐‘‰ ๐น ๐‘˜ ๐‘‡ ;ย  (g) ๐‘› ๐‘– 2 ๐‘ ๐ด ๐‘’ ๐‘ž ๐‘‰ ๐น ๐‘˜ ๐‘‡ ; (h) ๐‘› ๐‘– 2 ๐‘ ๐ท ๐‘’ ๐‘ž ๐‘‰ ๐น ๐‘˜ ๐‘‡ At point A above ECp (g) At point A above ECn (b) At point B above ECp (g)

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The question asks us to identify expressions for the electron concentration under forward bias in a PN junction, referencing specific points A and B in the band diagram. We should first separate the ideas into two regions: the p-side (p-type, doped with NA) and the n-side (n-type, doped with ND). In a forward-biased PN junction, the electron concentration on the p-side (where electrons are minority carriers) is typically proportional to the intrinsic carrier concentration n_i squared divided by the acceptor concentration, and it gains a factor e^{qV/kT} due to the applied forward voltage. Conversely, on the n-side (where electrons are majority carriers), the minority electron concentration (near the depletion edge) similarly scales with n_i^2 divided by the donor concentration, with the same e^{qV/kT} factor for forward bias. With that in mind, we evaluate each general form: Option (a): N_A. This simply states that the electron concentration equals ......Login to view full explanation

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