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I am currently reading through a semiconductor physics book and I am currently in a section discussing the I-V characteristics of an abrupt P-N junction. A few things have come to my attention that I am having a difficult time understanding (that the book does not seem to elaborate on):

  1. When finding the diffusion current density of the minority holes in the N region, the diffusion current density exponentially decreases as a function of x away from the end of the depletion region xn (with a similar analogue for the minority electrons in the P region). However, the diode current equation is then written by using the sum of the diffusion current densities at the boundaries of the depletion region and multiplying that expression by the area of the junction. If the current density decreases exponentially away from the depletion region, why can the total current through the diode be represented by the current density through the edges of the depletion region?

  2. What of the drift current density? I assume that it's negligible, but what justification do we have for saying that it's negligible?

  3. Why is the current governed by the minority charge carriers rather than the majority charge carriers?

Any help would be appreciated! Thanks!

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My answers:

(1) You are obviously speaking of the Shockley model of the pn-junction, which is one-dimensional. From the current continuity in one dimension along the diode, it follows that the total current (sum of electron and hole current) at each cross section along the pn-juction must me constant and equal to the current through the diode. The Shockley model assumes that there is no recombination in the depletion zone. Therefore both the electron and the hole current along the depletion zone are constant. To obtain the total pn-junction current, you have to know the electron and hole current only at one cross section. If you consider the electron diffusion current at the boundary of the depletion zone with the quasi-neutral p-region, you have the total electron current, which is a minority diffusion current, at this boundary. To obtain the hole current at this boundary, which is a majority carrier current there, due to the constancy of the hole current along the depletion zone, you know that this must be the hole diffusion current at the depletion zone boundary with the n-region, which is also a simple minority diffusion current. This is why you can express the total pn-junction current as the sum of the minority carrier diffusion currents at the depletion zone boundaries.

(2) Under the low injection condition of the Shockley model, the electric fields in the quasi-neutral p- and n-regions are so small that the minority carrier drift currents are negligible compared to the diffusion currents. There are, however, majority carrier drift currents due to the high carrier concentrations. You should also keep in mind, that the minority diffusion currents decrease exponentially due to the recombination and that the decreasing minority currents continue to flow as majority drift currents so that the total current density is constant.

(3) This is already explained in point (3).

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