8 Contact potential

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Here we have used a heavily doped n-type semiconductor, and chosen the insulator to be vacuum by the choice of 1 for its dielectric constant. The parameter A_metal = 3 V is the work function of the metal and A_semi = 1 V is very nearly the work function for the semiconductor. We will ignore the difference. Compare the two conditions:

Which corresponds to the sophomore physics statement for a configuration of conductors that the potential at the metal and at the semiconductor are the same? (The answer depends on what chapter of the sophomore text you're reading)

With materials with different work functions, the contact potential is the difference in work functions of the two materials. As you have seen, it may be evidenced in different ways. If there is no voltage applied to the device, how is the potential just outside one material related to the value just outside the other? What happens to the charge on the gate if the thickness of the vacuum layer Dins is changed, keeping Vapplied constant?

Why is the condition of no screening charge on either material equivalent to the statement that there is no electric field between the two materials? What is the difference in chemical potentials when this condition is established? Will there be any charge flow in an external circuit if the vacuum thickness is changed? This is the basis of the Kelvin method for determining contact potentials, and hence work functions, of materials.