We present a computational investigation of the morphological changes of a growing thin film during condensation, driven by electromigration effects. Our findings reveal that while isotropic systems typically form separated circular adsorbate islands, the application of an electric field elongates these islands along the field direction. We analyze how the critical strength of the applied electric field, which governs the formation of percolating adsorbate islands, depends on key control parameters. Using a phase-field approach, we examine the dynamics of multilayer surface structures during epitaxial growth. Specifically, we establish how the anisotropic diffusion coefficient, proportional to the applied electric field strength, influences the dynamics of film thickness growth, surface structure height, surface morphology, statistical properties of multilayer adsorbate structures, and the distribution of surface height values.