We present a theoretical model and experimental data describing the response of a thin liquid polymer film to a heterogeneous electric field. The theory predicts two different regimes separated by a distinct boundary: in one regime the film is characterized by steady-state low amplitude surface modulations following the periodicity of the electric field, in the other regime the film breaks up into pillars centered around the region of highest field strength. The theoretical analysis describes the film destabilization in terms of two dimensionless variables, which fully describe the low amplitude limit. The corresponding experimental system was realized with a photo-structured epoxy resin covering the top electrode and thin polystyrene films that were destabilized by the applied electric field and characterized by AFM after quenching. Theoretical and experimental results allow us to determine the destabilization conditions and to identify the experimental variables that characterize film destabilization. The theoretical framework provides a tool for the experimentalist to predict in detail the structures generated by film destabilization, thereby enabling a new way of 'soft-lithography'.