# Equation for photocurrent dep. wavelength, diffusion length,

• A
Hey,

I’m currently stuck at my research and I’d like to ask for some help.
First I’ll try to introduce the measurement and the setup and then I’ll get straight to the problem.
The goal is determining the diffusion length of charge carriers quantitatively in different materials.

For this project we use the AFM, specifically the photoconductive AFM (pc-AFM), to measure the photo current that is created due to an external light (laser) source.
As reference samples we use p-doped Silicon (with different Fe implantations, but that’s not important for the issue at hand; let’s assume a pure p-doped Si substrate) that is glued to a metal plate with conductive glue.

The plate is brought into contact with the AFM chuck through a magnet, thus ensuring good conductivity.
The tip used to measure conductive AFM (cAFM) is in our case a silicon tip coated with highly doped diamond. Thus we create a Schottky contact.

We now apply a small voltage to the setup (we apply the voltage to the chuck and the tip is grounded, thus we need to apply a negative bias) and also shine on the contact point of AFM and sample with our external lasers (we turn the AFM laser off to not influence the measurement).
The lasers are guided via fibers and have a power of approx. 50µW when hitting the surface of the sample.
Our laser source can provide different wavelengths to include this variation in our analysis.
The lasers we use are 660m, 905nm, 940nm and 980nm, with approx. penetration depths of 3µm up to 100µm.

It’s obvious that the external lasers now create charge carriers due to the photo effect and that the minority carriers (electrons) are pulled towards the AFM tip due to the applied bias.
We can now measure the photocurrent in dependency of a few variables, e.g. the laser wavelength (and thus the penetration depth / absorption coefficient), the laser power, etc.).

And now my big question. Is there a possible equation that can determine the photo current in dependency of the laser wavelength, laser power and most importantly Diffusion length / carrier lifetime.
Because as I’ve said we want to determine the Diffusion length by measuring the photo current as the other values can be controlled by us.

I’m running the entire problem also in Synopsys Sentaurus to get a feeling of the distribution of fields and the e- -density and currents and what we ultimatively have to expect.
But on the one hand I’m not 100% sure that I can trust all the settings I’ve set in the simulation and secondly the slope of the simulated curves to those in the experiment are not entirely the same and I just want to have an equation to get a better feeling about this entire problem….

In photovoltaics often the term of short circuit current is used in combination with photo current, but I have to apply the external bias, as I don’t use a p-n diode for my issues and then I’m not really looking at a short circuit current problem?
So I don’t think the short circuit current is actually the solution to my problem.

TL;DR:

I'm looking for an equation that gives me a correlation of the photo current to the wavelength of the incoming laser (absorption coefficient, penetration depth), the laser power (amount of incoming photons, for our lasers it’s fair to assume that one photon equals one charge carrier pair) and most importantly the diffusion length (or lifetime) of the material).
We do not have a p-n diode as in PV and thus I don’t think I can simply fall back to short circuit current equations?

Help would really really be appreciated!

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ZapperZ
Staff Emeritus
You might want to look up papers by Kevin Jensen at NRL. He has a series of papers on the painful details of photoemission process that might include the parameters that you are interested in.

As an example, this was the presentation he gave several years ago at the workshop that I attended:

http://psec.uchicago.edu/workshops/photocathodeConference/talks/2-Kevin_Jensen_PhotoWkspKLJ.pdf

If you do a reference search on his name, you'll come up with a bunch of stuff by him.

Zz.

thanks for the response (sry for my long delay, I was travelling)

I've now looked for papers from Kevin Jensen for quite some time, but I cannot find the solution to my problem.
Either I've skipped it, overread it or it is not exisiting :(