Supposed we have a metal sandwitched between two thin dielectrics. If i contact an electrical voltage on the dielectric, there will be tunneling current due to electron tunneling from the metal across the dielectric. i could attempt to calculate this current from a semiclassical approach using *Current=N x Freq x Prob* (where N is number density of electrons. Freq is the impact frequency of an electron on the dielectric wall. Prob is the probability it will penetrate the dielectric, taken to be the probability it can be found in the dielectric.)(adsbygoogle = window.adsbygoogle || []).push({});

Now, the Prob can be calculate very accurately using numerical approach for any arbitrary dielectric potential barrier. But how does one account for Freq "quantum mechanically" ???

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# Exact calculation of tunneling current?

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