Does charging metal negatively decrease the work function?

[Christofer Br]

Since positive charge on the photocatode increases work function of electrons, does charging metal photocatode negatively decrease work function? If not, why?

 

[mfb]

Since positive charge on the photocatode increases work function of electrons

It doesn't, at least not notably. It just makes the electrons fly back after they were released.

does charging metal photocatode negatively decrease work function?

In principle: Yes. In practice you won't see an effect for flat surfaces and realistic voltages. For very sharp outer corners you can see an effect.