1.

Estimate the probability of cold electron emission from a metal, if there is a uniform field of strength E close to the surface of the metal.

Answer»


Solution :In the absence of an external electric field the electron in a metal is shielded by an infinitely wide potential barrier of height `U_(0)`. In the presence of a strong electric field of intensity E the potential barrier assumes a TRIANGULAR shape with height `U_(0)` and WIDTH `L=Phi//E=A_(0)//eE`, where `A_(0)` is the work function. Neglect the shape of the barrier and assume it to be rectangular. SINCE the energy of the electrons in the metal is `epsi_(F)`, and their work function is `A_(0)=U_(0)-epsi_(F)`, the PARAMETER a which determines the probability of the electron tunnelling through the potential barrier assumes the form
`a=(2L)/hsqrt(2m(U_(0)-epsilon_(F)))=(2A_(0))/(eEh)sqrt(2mA_(0))`


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