We use 3D real-space self-consistent field calculations to study the solvent-response of diblock copolymers A-B grafted to a flat surface all by the A-ends. We focus on the effects of block lengths, chain-grafting density and A-B incompatibility on the surface-layer composition and lateral inhomogeneity of the brush treated by different solvents. In the cases where one of the blocks is charged, we further investigate the use of other external stimuli including ionic strength, solution pH and applied electric field to enhance the surface switchability and to overcome the lateral inhomogeneity. Our calculation results agree with available experiments.