The Poisson equation in a p-Al_yGa_1−yAs/p-Al_0.45Ga_0.55As/n-GaAs structures structure under reverse bias is solved analytically subject to ohmic contact boundary conditions. The solution takes into account the linear variation of the dielectric constant in the compositionally graded region. It is shown that the dielectric constant in the graded region can be approximated by an average dielectric constant with good accuracy in solving for the electrostatic field distribution and potential.