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So yes, if you compute the Poynting vector (energy flux density), $\vec E \times \vec H$, for an exponentially decaying evanescent wave, you indeed find zero time-averaged energy flux perpendicular to the reflecting plane. Ask you say, this leads to a conundrum --- how do evanescent waves transfer energy across barriers? For sure, we know they can transfer ...

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The electron does not deposit energy in the oxide layer. The oxide layer provides for a potential barrier, the electron moves though it despite the fact that in a classical picture the electron should have a negative kinetic energy there. You can consider a process where the electron is going to do some damage to the oxide layer, but such a process is only ...

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