We study the nonlinear steady state structures created in a one-dimensional collisionless electron plasma by a transparent grid raised to a given potential. Moreover, natural structures, i.e., in the absence of a grid and consequently of any external charge, can also be obtained. For the electrons (here ions are supposed motionless and uniform), the structure must involve a hole in the trapped electron density distribution and is consequently attractive. A relationship between the depth of the potential and its possible length is obtained. These studies are preliminary to the problems of stability and waves propagating in strongly inhomogeneous plasma structures.