I want to know that is wearing face piece I mean covering half face (i.e except eyes and eyebrows) allowed?
Is there any criteria for it?

Permanent Niqab or face veil is not an Islamic requirement; it is a personal choice since Niqab is forbidden during Ihram according to most contemporary scholars based on traditions.
According to some rulings, it is better to cover if there is fear of being watched and attracted by Na Mahram.
Islam is a religion that is as easy as possible to follow. Thus when there is fear of such situations, maybe you can cover half your face and when there is no fear of on lookers, you can wear the normal Hijab without any extra attractions eg makeup, jewelry etc.