We have calculated the coulomb drag cause the electron-electron interaction in bilayer quantum wells of nonhomogeneous dielectric background at finite temperatures, in Ballistic and at low temperatures limit. We may consider a set of two sheets two-dimensional electron gas (2DEG) separated by a barrier with the effect of dielectric background of the system is not homogeneous. The effective interaction cause of scattering between electron-electron is measured, by using the mean field approximation (or RPA) and Generalized-RPA (G-RPA) methods. The GRPA coupling takes into account exchange processes also which is stronger than the RPA, and gives better results. The interaction form factor is drawn from the Poisson equation solution of a three-layer dielectric medium at the interfaces, separating the distinct materials. We used the analytical formulas to measure the drag resistivity ρD at large interlayer separation (d) limit kFd » 1. We have done the calculation for finding the behavior of temperature and density with respect to drag resistivity and compared the results to InAs/GaAs and InAs/GaSb coupled-layer structures. We measure the contribution of the density (n), interlayer separation (d) and temperature (T) dependency at non-finite and finite width (L=0, 5, and 10 nm). [ABSTRACT FROM AUTHOR]