Diffusion at a concentration step

[Otterhoofd]

Homework Statement

You have a solar cell with a constant electron density n, and known dimensions. I am looking for the change in density due to diffusion, so basically the diffusion current. All other relevant parameters are also known (temperature, D diffusion constant, etc.)

To summarize the problem: I have a cube with electron density n, outside electron density 0. Question: what is [itex] \frac{dn}{dt} [/itex] due to diffusion?

Homework Equations

Fick's Law: [itex] J = - D \times \frac{dn}{dx} [/itex]
Or root mean square distance traveled by brownian motion:
[itex] \Delta x_{rms} = \sqrt{2\times D \times t} [/itex]

The Attempt at a Solution

Using Fick's law, you get a infinite current since there is a concentration step from n inside to 0 outside the device. However, i think that Ficks law does not hold for this steep concentration gradients. Maybe one could solve this using equipartition of energy? But then again, the exercise hints at the use of the diffusion parameter and says the question should be simple to answer.

Any help would be greatly appreciated. Thank you.

 

[Gokul43201]

Hint: There's a more useful equation than Fick's first law.