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I'm sorry in advance for this post, because I know that homework type questions are not allowed here.

I have to calcualte the radial distribution of the tunnel current $j(r)$ from the surface of a metalic probe to the tip of a STM. Using the radial distribution, I'm asked to calculate the lateral resolution $\sigma$ of the STM. The geometry of the tip is given by the equation $$z(r)=\frac{r^2}{2R}$$ (I can approximate the transmissioncoefficient for big arguments of $sinh(x)$)

The problem is, that I've been going back and forth in my scriptum and also went through endless websites but I just can't find any useful resources which explain the topic without any "hardcore" math which are way over my study progress (third semester BSc).

I know how to derive the transmissioncoefficient $T$ for the tunnel effect and that it should be linked to the current $j(r)$. But I don't know how to get from there to the lateral resolution.

I would be really grateful if anyone, who knows a little bit more about this topic, could guide me to some useful resources which will give me a starting point for this problem. Thank you!

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