When a voltage is applied across two surfaces of metals or semiconductors the associated electric field is able to penetrate the surface of the semiconductor. Because the semiconductor material contains little charge carriers the electric field will cause an accumulation of charges on the semiconductor surface. When V>0, a forward bias, the band bends downwards. A reverse bias (V<0) would cause an accumulation of holes on the surface which would bend the band upwards. This follows again from Poisson's equation.
