Exercises 12.4: Contact potential and work functions

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12.4.1 The figure shows the band diagram for a contact potential measurement (MIS-diode with vacuum for insulator) on a semiconductor with a donor concentration of 10^18 /cm^2. The applied voltage has been tuned to the Kelvin condition.

A) What is the the work function of the semiconductor surface, knowing that the reference-metal work function is 3 volts and that the applied voltage to obtain the Kelvin condition is 1.28 volts?

B) What is the sheet charge density associated with the surface states for this sample?

C) What would be the work function measured for this surface if the surface states were completely eliminated?