This paper contains a thorough investigation into plane-strain electroelastic surface instabilities of dielectric elastomers. We employ a systematic approach to our investigation, introducing three ways to actuate an elastomer device, namely, actuation by means of (1) attached compliant electrodes, (2) sprayed charges onto the opposite surfaces, and (3) fixed electrodes between which the device "floats" in vacuum and expands transversally. We examine electromechanical instability with particular attention to the third listed mode of actuation and the features of the specimen. We then tackle surface instability for the three modes, showing the relationship between applied pre-stress and the stability domain, as well as the characteristics of the obtained bifurcation fields. The effects of the stiffness of the electrode (relevant in the first listed mode of actuation) on surface instabilities are then investigated by adopting an elastic surface-substrate interaction model in which the properties of the coating enter the boundary conditions for the substrate. Various electrode materials are assumed, demonstrating that their implementation in the model increases the number of solutions at bifurcation and changes the overall stability domain. We present this new enriched bifurcation map, showing the dependence on the wavenumber, and characterise the solutions by examining the bifurcated fields.
