Recently, the fabrication resolution in electron beam-induced deposition (EBID) has improved significantly. Dots with an average diameter of 1 nm have been made. These results were all obtained in transmission electron microscopes on thin samples. As one may think that such resolution can be achieved on thin samples only, it is the objective of this paper to show that this should also be possible on thick samples. For that purpose we use Monte Carlo simulations of the electron-sample interaction and determine the surface area where secondary electrons are emitted. Assuming that these electrons cause the deposition in EBID, a comparison can be made between deposition on a thin and a thick sample. The Monte Carlo code we developed will be described and applied to the deposition induced by a 200 keV primary electron beam on an ultra-thin (10 nm) and a bulk-like (1,000 nm) Cu sample. Near the point of incidence of the primary beam, the deposit size is independent of the substrate thickness, such that a 1-nm resolution should be possible to achieve on a thick substrate as well. Thicker substrates only affect the tails of the deposit distribution which contain more mass than thin substrate deposit tails.