The directional atom drift under direct electric current (DC) flowing through a sample is a unique tool for the surface morphology manipulation, which was previously studied in detail for Si surfaces. We show that electromigration can significantly influence the heterostructures growth process. Without electromigration, the surface morphology is formed under the action of two driving forces determined by a surface and strain energy minimization. DC shifts the balance between them in favor of one of them, depending on the DC direction, producing unusual surface nanostructures during the Ge deposition on Si(111) at 850-900 degrees C. When electromigration inhibits the surface energy minimization, the high atomic steps are formed. Their edges became wavy and unstable when the step edges reached the height larger than 15 nm. The instability induced disintegration of the step edges with the flat-shaped islands formation.