This is the energy band diagram explaining work function.
For a metal, 
is a constant that can be measured; =5.1 eV for gold (Au).
is a constant that can be measured; =5.1 eV for gold (Au).
for a semiconductor, the work function depends on the doping level and is given by
as denoted in the figure.
where ni(Si)=1*10^16 m^-3 and Vt=kT/q=25mV at temperature of 300K
as denoted in the figure. where ni(Si)=1*10^16 m^-3 and Vt=kT/q=25mV at temperature of 300K
So that
Metal: 
Semiconductor:
Difference:
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