Semiconductors constitute the heart and soul of integrated electronic systems, thus of modern technology. The extraordinary progress in circuit integration, since Moore’s prediction from the early seventies, can certainly be majorly credited to the concurrent refinement of computer-aided design tools. Indeed, a higher scale of integration has punctually demanded a deeper understanding of semiconductor physics and more accurate mathematical models of devices to be numerically implemented and simulated. Charge transport is the starring phenomenon that needs to be predicted in order to build a mathematical model, based on higher-level quantities (e.g. electric current and voltage), that can be practically used for device simulation. A rigorous description demands statistics and quantum mechanics of electron/hole ensembles in crystal lattices, an approach that eventually leads to the Boltzmann transport equation, which solves for a state density function in the position-momentum space. The Boltzmann transport equation is extremely complex to deal with. In most applications, it is licit to call for simplifying assumptions to the degree where electron and hole ensembles are seen as gases of classical particles having an effective mass, which accounts for them being subjected to the electrostatic field produced by the atomic lattice. As a result, charge carrier transport is eventually described by a drift-diffusion model. This yields a system of partial differential equations (PDEs) which can be solved at two levels: (1) Quasistatic approximation - The external force applied to the crystal is electrostatic, and drift-diffusion equations are coupled to a Poisson equation for the electrostatic potential. The goal is to determine the spatial distribution of carrier concentrations and the electric field (deduced from the potential); (2) Fullwave model - The crystal is subject to an applied electromagnetic field, and Maxwell equations are coupled with transport equations for carrier dynamics. The goal is to determine the space-time evolution of carrier concentrations and the electromagnetic field. The quasistatic approximation is rigorous when the steady state of the semiconductor has to be calculated. The fullwave model is particularly relevant to electro-optics, i.e. when light-matter interaction is investigated. Indeed, such study is essential to understanding and accurately modeling the operation of photonic devices for light generation, modulation, absorption. In this latter context, we study the formulation, analysis and development of a DGTD method for solving the coupled system of Maxwell equatiosn and drift-diffusion equations in the fullwave setting. Tis work is conducted in collabortaion and with the support of the TCAD division of Silvaco Inc.