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.**