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Using STM equipment, we can get the LDOS(local density of states) on the surface of a sample. I want to know whether the LDOS within the sample(not surface) can be detected by STM. what is the limitation of the depth?

On the other hand, a thin film is grown on a substrate, and one want to use STM to detect the DOS of the film. How thick should the film be to make the DOS of substrate be negligible for STM studies?

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    $\begingroup$ Welcome to Physics Stack Exchange. Many SE users will have no idea what the STM/LDOS/DOS acronyms mean; it would be helpful to spell them out in your questions. $\endgroup$ – Daniel Griscom Nov 18 '15 at 3:22
  • $\begingroup$ I have added those full names. Thank you for your advise. $\endgroup$ – user41568 Nov 18 '15 at 9:47
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In STM, you tunnel from states of your tip into states of the sample. Electrons can tunnel into states within the whole bulk and the matter beneath. However, their spectral weight decays rather quickly. As a rule of thumb in STM, your current increases by one order of magnitude per Angstroem that you reduced the tip-sample distance. So, the DOS of matter 1 Angstroem below the surface plane will contribute to your $dI/dV$ signal only 10 % of those directly from the surface.

I would say, that everything below 2 or 3 monolayers will never be observable in your experiment. When you have an insulating layer however, you will tunnel through the layer into the metal beneath. You can look at the papers from the 60's and 70's (e.g. the famous superconductor tunnel experiments by Giaever) for such experiments.

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