Modelling and numerical simulation of semiconductors is necessary for the development of new industrial devices to increase their efficiency and reduce their manufacturing cost and time. In this project,the viscous-quantum-hydrodynamic model of the semiconductor devices is analyzed. In this model, the governing equations for electron and current densities are the Euler equations together with a viscous and quantum correction terms and the electrostatic potential is given by the Poisson equation. The model equations are highly nonlinear in nature which require efficient and accurate numerical methods to get physically realistic solutions. Several state-of-the-art numerical methods such as kinetic approaches, finite volume schemes (FVS) and finite element methods (FEMs) have been used to investigate the model. For validation of the obtained numerical results, different test problems have been performed.