electron in the metal has total energy that is higher than semicon

I am reading one chaper called metal semiconductor contacts.

Somewhere it gives a chart about energe level for metal and silicon.
And by comparing work function between metal and silicon, it says, if
the work function (the difference between E0 and fermi level) of metal
is less than semicon, electron of metal has total engery that is higher
than the average total engergy of an electron in semicon.


Not sure of this. if the work function of metal is less than silicon,
does that mean the electron of metal could flee to E0, and hence
further away from nuclei, compared with silicon, and therefore, have
more energy?

( forgive me, there are lots of charts, I can't past over, if you don't
know what this is talking about, please ignore...)