I have the following two questions in the derivation of current in a diode.

1) In forward bias, an assumption "abrupt junction" is made and field is equal to 0 is also made. But then we still use built in potential. How is this okay?

2) In most semiconductor classes and also in Millman and Halkias they have left reverse bias case as similar. But can anyone help me out with the actual derivation? Because i don't see how the exponential decrease in hole concentration with distance occurs if the field is non zero in the continuity equation

Any help would be appreciated. Thanks

  • \$\begingroup\$ Could you clarify what you mean by "field is equal to 0"? I'm not familiar with that assumption for diode analysis. Basic diode analysis usually assumes an abrupt junction (a step function dopant profile) and that there are zero electrons and holes in the depletion region. I also don't understand what you mean about exponential decrease in hole concentration with distance. If you make the previous assumptions then your hole concentration will be a step function as well. 0 inside the depletion region and \$N_A\$ outside the depletion region. \$\endgroup\$ – Matt Aug 8 '18 at 13:29
  • \$\begingroup\$ The exponential is not from pside to n-side. But rather within the n-side from the junction taken as x=0. By the field I mean the field that causes drift current . \$\endgroup\$ – pranav Aug 8 '18 at 13:54
  • \$\begingroup\$ The field cant be equal to 0. A diode expierences both drift and diffusion currents and cant work if you just assume away the drift current part. You must misunderstand something. I'm still not following this exponential decrease in hole concentration. At the junction the hole concentration is zero, and since hole concentration cant be negative, I dont see what you mean. \$\endgroup\$ – Matt Aug 8 '18 at 14:02
  • \$\begingroup\$ Hmn... you didnt mention where you are assuming the field is equal to zero. Its equal to zero outside the depletion region. Is this what you mean? \$\endgroup\$ – Matt Aug 8 '18 at 14:05
  • \$\begingroup\$ For an abrupt junction we neglect the width of the junction and assume step function right? \$\endgroup\$ – pranav Aug 8 '18 at 14:06

See the diagram below which shows the three regions in a pn-junction: two neutral regions and a depletion region.

from wiki(fig taken from wikipedia)

  1. The fact that the junction is abrupt does not mean that there is no depletion region or voltage drop across the junction. The diagram above actually represents that of an abrupt junction.

    For simplicity, it is usually assumed that the entire voltage applied across the diode appears across the depletion region and hence the drop in the neutral region is zero. Which in turn means that the electric field is zero in neutral region. There exists a non-zero field in depletion region.

  2. The exponential decay of carriers actually happens outside depletion region, where the electric field is zero. And hence it can be assumed that the carrier concentration decay/grow exponentially with distance inside these quasi-neutral regions. This is true for both forward and reverse bias. The derivation of current equation for a diode found in textbook usually is done for some applied bias, can be forward or reverse.

  • \$\begingroup\$ @pranav you can mark the answer as accepted if you feel that it has answered your question properly. \$\endgroup\$ – nidhin Oct 27 '18 at 14:12

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