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can electron emission happen from insulators? I mean can the electrons in an insulator jump into the vacuum around them when sufficiently large electric fields are applied like in conductors?

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Yes it can. In an insulator, electrons are bound on Atoms, but do not form an electron gas as in metals. With electromagnetic Radiation of high intensity, electrons can be emitted from the Atom. A photon with frequency $\nu$ carries an energy $E=h \nu$. An electron of the exterior Atom hull will be emitted if the photon energy is greater than the electrostatic energy $E_s = |- \frac{Ze^2}{4 \pi \epsilon r} + \sum_{j \in E} \frac{e^2}{4 \pi \epsilon r_j}|$ with the set of all other electrons $E$, the electron-nucleus distance $r$ and electron-nucleus distances $r_j$ for all other electrons.

This formula is classical; for Quantum Treatment you must know the Quantum numbers of the electron to compute energy $E'$

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  • $\begingroup$ but can the electrons leave the conductor only because of electric fields, and how to compute the electron escape probability?... $\endgroup$
    – Chandrahas
    Dec 19, 2016 at 11:39
  • $\begingroup$ The escape probability per unit time can be computed by Fermi's Golden rule $P= \frac{2 \pi}{\hbar} \delta(E_{after}-E_{before}) |<e_{after}|V|e_{before}>|^2$ with electric potential $V$ and the electron state $<e_{before}|$ that is given by eigenfunction in bond state / electron state $<e_{after}|$ that is given by the eigenfunction of free electron $\endgroup$
    – kryomaxim
    Dec 19, 2016 at 11:43

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