The homotopy perturbation method (HPM) has been applied for the solving nonlinear differential equations of quantum dots (QDs). However, the HPM just gives the QDs behavior inside thick dielectric barriers as well as islands with deep quantum wells. In this paper, we apply a new approach which is based on modified homotopy perturbation method (MHPM) with self limiting model (SLM) to investigate the QDs behavior inside islands between clusters of sample surface. The MHPM and SLM are very effective, convenient and quite accurate to systems of partial differential equations and deal with nonlinearities distribution of the nonlinear differential equation. By using this method, we can find the exact solution of the QDs problem inside the islands.
