Mod\'elisation des performances des structures lasers \`a base des chalcog\'enures de m\'etaux de transition: MoS$_2$/WSe$_2$

Two-dimensional semiconductors, known as Transition Metal Dichalcogenides (TMDCs), are of great interest among many materials due to their unique 2D characteristics, including exceptional electronic and optical properties. These compounds belong to the family of lamellar materials having a general formula of type $MX_2$, where M represents a transition metal belonging to one of groups IV, V, or VI of Mendeleev's periodic table, and X is a chalcogenide. These materials exhibit fundamental properties that are qualitatively different from their three-dimensional (3D) counterparts, often relating to their electronic and phononic band structure. The in-depth study of these materials has revealed remarkable phenomena, such as two-dimensional quantum phase transitions and optoelectronic phenomena related to electronic "valleys", which exploit the wavevector selectivity of the emission and the absorption of photons. Unlike graphene, materials such as MoS$_2$, MoSe$_2$, WS$_2$, and WSe$_2$ are semiconductors that have a bandgap varying from 1.2 to 1.9 electron volts (eV), depending on the number of layers. This characteristic makes them suitable for use as active elements in optoelectronic devices. Additionally, their two-dimensional nature and mechanical strength enable the realization of quantum phase transitions and electronic components on flexible substrates. It is also possible to create quantum wells based on MoS$_2$, with materials such as MoSe$_2$, WS$_2$, and WSe$_2$, depending on the band shift between the components of the quantum well. This work aims to propose a theoretical and numerical model for these materials, which will make it possible to determine the electronic band structure as well as the optical gain in an active zone composed of two-dimensional semiconductors. This research is of great importance for evaluating the performance of active zones in laser devices based on these materials.