Diffusion current and carrier concentration equilibrium (unbiased)

In summary, the conversation discusses two scenarios involving non-uniformly doped semiconductors without an applied bias. In the first scenario, the equilibrium hole distribution is not uniform due to the exposed space charge from the dopants. In the second scenario, with a lot of injected electrons, the equilibrium carrier concentration becomes essentially uniform, leading to minimal diffusion and drift. The conversation also raises questions about the effects of injecting electrons in a p-type material and the potential for a depletion region near x=0 due to recombination.
  • #1
halleff
4
1
TL;DR Summary
Confused about the equilibrium conditions for carrier concentrations in semiconductors depending on how the semiconductor is doped, if at all
Suppose you have a non-uniformly doped piece of semiconductor (without an applied bias) such that the acceptor dopant concentration Na(x) decreases from left to right (as x increases). In this case, the equilibrium hole distribution p(x) will not be uniform since then there would be a net drift current due to the exposed space charge from the dopants. So instead equilibrium p(x) will vary such that diffusion is balanced by drift.

Now suppose you have an intrinsic piece of silicon without an applied bias. If you inject a lot of electrons at one end of it (without also injecting holes), at a time immediately after injection you have n(x=0) large and n(x) decreases as x increases. Say that it decreases exponentially as x increases, becoming zero at the opposite end of the semiconductor (x=L). In this case, what is the shape of the equilibrium carrier concentration? Does it become essentially uniform so that there is no diffusion current and very little drift, since there isn't a lot of recombination due to being intrinsic silicon?

Related to this, if this were a p-type material, then I think this would be similar to what happens at a p-n junction. I'm not sure it's necessarily identical because I'm not assuming that the electrons are being injected due to the presence of an n-type material adjacent to the p-type and so the holes in the p-type won't also be diffusing toward the left. So if this were an isolated (no adjacent n-type block) uniformly doped p-type block and somehow you had a bunch of electrons instantaneously injected at the x=0 end, for example at a concentration comparable to the acceptor doping level, is the equilibrium carrier distribution uniform, or do you still get a space charge region near x=0 due to recombination, so that you approximately have a depletion region around x=0 and then constant p(x) and n(x) to the right of it?

I hope these questions are clear. These aren't homework questions so I don't have given diagrams to accompany them, but if you need them I can make some to try to show what I'm asking. Thank you very much.
 
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  • #2
In both scenarios I’m not sure how uncovered charge gets permanently created which means there can’t be a persistent e-field which means eventually p(x) and charge will be uniformly distributed.
 

Related to Diffusion current and carrier concentration equilibrium (unbiased)

1. What is diffusion current?

Diffusion current is the flow of charge carriers (electrons or holes) due to their random movement from an area of high concentration to an area of low concentration.

2. How is diffusion current related to carrier concentration equilibrium?

In an unbiased state, the diffusion current is equal to the drift current, which is the flow of charge carriers due to an applied electric field. This equilibrium is maintained when the concentration of charge carriers is constant throughout the material.

3. What is meant by "unbiased" in the context of diffusion current and carrier concentration equilibrium?

Unbiased refers to the absence of any external electric field or voltage applied to the material. In this state, the diffusion and drift currents are equal, and the concentration of charge carriers remains constant.

4. How does temperature affect diffusion current and carrier concentration equilibrium?

As temperature increases, the diffusion current also increases due to the higher thermal energy of the charge carriers. This can disrupt the equilibrium of carrier concentration, leading to a higher concentration of carriers in one area and a lower concentration in another.

5. What are the practical applications of understanding diffusion current and carrier concentration equilibrium?

Understanding diffusion current and carrier concentration equilibrium is essential in the design and operation of electronic devices, such as transistors and diodes. It also plays a crucial role in the study of semiconductor materials and their properties.

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