1.For the first case, the situation is too uncertain. You have to know the substrate material, the thickness and type of the resist energy electrons.

2. What resist will be used? From this choice dose varies.

Considering the first question about the position of the Cr layer, the best case in terms of resolution if resolution matters, is having the metallic thin layer on the top of the resist. Underneath, electrons will be more scattered. As for the dose, the difference may be negligible.

Considering the second question which needs to be clarified ... if you intend to expose directly the PMMA on top of a Si02 layer itself on silicon charging will occur...

Generally speaking, the thin metallic layer on top of the resist is a rather versatile process that can be used for almost any substrate. Al may be preferred due to lower Z higher conductivity and in addition it can easily be removed in diluted KOH.

I may recommend you the following book chapter with a rather large section about electron beam lithography on non conductive substrate:

http://link.springer.com/chapter/10.1007%2F978-3-642-28079-5_9?LI=true

The question is underdetermined. The general answer for large patterns is that a layer on top will stop and backscatter a part of the electrons, resulting in a lower radiation dose in the resist so that the design dose must be increased whereas a layer below can backscatter electrons resulting in the electron passing through the resist twice.

The point is that the backscatter probability of the layer below must be compared with the backscatter probability of the substrate. If the layer below has a higher backscatter probability (high Z material) the resist will receive more dose resulting in a need to lower the design dose.

In your question you do not specify the non-conducting substrate material, therefore the question does not have a unique answer.

The scattering probabilities are energy dependent and EBL is clearly a multiple (many) scattering process. Therefore with arbitrary materials/thicknesses such problems are quite messy, requiring monte carlo simulations to give an answer.

There are free programs that can do that. Performing a dose test is usually faster and certainly more precise.

Why do you offer PMMA? There are many other electron resistors, and their choice depends on the purpose ..

Thank you all for your comments and answers and sorry if it seemed a bit vague. I wasn't looking to simulate or get precise values, just a general rule of thumb as I consider switching substrates. PMMA is actually the resist I am using.

Thanks again.

As the above stated comments say, its hard to make predictions without knowing the materials, since the resist exposure depends alot on scattered electrons.

However, making the assumption that you are using an acceleration voltage of 20kV or more and that by non conductive substrate you mean glass the clearing dose will be about the same in both cases.

As for the top layer, I generally recommend our lab users to use a conductive polymer instead of metal layers, there are conductive polymers sold for this specific purpose and they are typically easily removed by water after exposure.

If you dont want to get that, use aluminum instead of chrome as it causes less scattering and has less influence on the dose. Al is easily removed, typically by TMAH, which you probably already have in your lab if you do uv lithography as well.