Fundamentals of Electron Escape Energy

In any stable material, electrons are retained within the substance by electrostatic forces which bind electrons to the positively charged nuclei. An ionization energy (renamed the work function in a solid and defined below) quantifies 

We define this ionization energy to be at the reference level of zero electron volts. The energy E of any bound electron is then measured with respect to this zero or vacuum-level energy, E =0. Since electron escape requires E E, we now consider electron energy values in various materials. 

Within a solid there exist a definite number of discrete energy levels in which an electron can reside all other energy values are forbidden [5.32-35] although the number of allowed energy states is always many times greater than the total number of bound electrons actually in the solid. 

The energy at the middle of this smeared electron distribution is the Fermi energy, at = Ep the probability of occupancy is 1/2 (for a nondegenerate state). The occupancy probability falls exponentially with higher energy as exp[( p — )//c7 at energy above p and rises accordingly for below p. Here k is the Boltzmann constant and T is temperature in Kelvin. 

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