Schottky barrier !! ?

eusername

hi all

something i cant understand in the schottky barrier diode
i know that when electrons move from semiconductor(n type) to metal a depletion region appears in the n side so potentail difference is created
so for electrons to move from S.c to metal they need to overcome this potential

the question is:
why the electrons to move from metal to sc ther have to overcome the barrier not the potential

i really have a problem to understand the meaning of barrier