Secondary Electron Dose, relation to primary dose?

I have been wondering if I specify an electron beam dose of 100 uC/cm^2, what is the actual secondary electron dose?

Wouldn't this vary for each different trial? Building the dose model seems futile.

It should correlate to secondary electron yield.

It's a random, variable number rather than a fundamental, predicted constant.

It was recently pointed out to me that electron ionization is itself a statistically noisy process. The most common manifestation is the avalanche photodiode. I think you might be able to work with a mean number of electrons expected, but you cannot pin down the actual number, which is the number that holds real meaning (which is why APD noise is meaningful).

In fact your original 100 uC of electrons probably go straight through. Some electrons also escape the surface and some may come from beneath the layer.

By this same argument, how do we even trust secondary electron yield measurements?

This is a nice paper...

Monte Carlo modeling in the low-energy domain of the secondary electron emission of polymethylmethacrylate for critical-dimension scanning electron microscopy
J. Micro/Nanolith. MEMS MOEMS, Vol. 9, 023001 (2010); Published 2 April 2010

It addresses secondary electron yield as well as energy loss mechanisms and finally the electron range relevant to lithography. I wouldnt waste so much time to consider any next generation lithography that ultimately is affected by these secondary electrons.

I think what really matters is the energy deposited per area, right?

Besides electrons, even photon energy deposition becomes uncertain, for example, under dim illumination conditions, where only few photons incident. A photon passing through an absorbing film, may be sometimes absorbed at the top, sometimes at the bottom, sometimes in the middle.

Like 10 photons in a square nm is probably too few to define anything on the order of 10 nm.

Yes the randomness of the photon absorption must be added to the randomness of the re-distribution of the energy.

For high energy beams, the primary electrons almost certainly go through the resist to the substrate. So it's only the secondary electrons defining the feature size.

Increasing the dose, normally you wouldn't expect the feature size to change, if you have fixed beam width, or assume fixed secondary electron range.

But since electron path distance is stochastic, increasing dose increases the likelihood of large electron range, or increasing the opportunity of random events of larger distance impact.

In NOR flash memory programming, the secondary electron tail distribution from hot holes is well known. The secondary electrons are desired to move in sufficient numbers well over ~10 nm at least to charge the floating gate. It might be a lithography issue but it is definitely a feature in key charge injection devices.

There have been reports of EUV dose calibration errors at Berkeley's Advanced Light Source. Almost a factor of two. I think it is related to sometimes you have two secondary electrons instead of one, for example.