Task-5 Calculate the work function difference assuming a gold (Au) gate.

Work function is defined as the energy difference from the ‘fermi-level’ to the ‘vacuum level’. 

For a metal,  work function is a constant that can be measured. 

For a semiconductor

, where  Xs is electron affinity, and is 4.14eV for silicon.  Eg is the band gap energy and is 1.1eV for silicon, Finally,  the last term is the Fermi level relative to the middle of the band gap, and can be calculated using formula .

Therefore

The function difference is