Electron-Phonon Interaction Model and Thermal Transport Simulation During ESD Event in NMOS Transistor

An electron-phonon interaction model is proposed and applied to the transient thermal transport simulation during electrostatic discharge (ESD) event in the NMOS transistor. The high electron energy induced by the ESD in the transistor is transferred to the lattice phonons through electron-phonon interaction in the local region of the transistor. Due to this fact, a hot spot turns up, the size of which is much smaller than the phonon mean free path in the silicon layer. The full phonon dispersion model based on the Boltzmann transport equation (BTE) with the relaxation time approximation is applied to describe the interactions among different phonon branches and different phonon frequencies. The Joule heating by the electronphonon scattering is modeled through the intervalley and intravalley processes by introducing the average electron energy. In the simulation, the electron-phonon interaction model is used in the hot spot region, and then after a quasi-equilibrium state is achieved there, the temperature of lattice phonons in the silicon is calculated by using the phonon-phonon interaction model. The revolution of peak temperature in the hot spot during the ESD event is simulated and compared to that obtained by the previous full phonon dispersion model which treats the electron-phonon scattering as a volumetric heat source. The results show that the lower group velocity phonon modes (i.e. higher frequency) and optical mode of negligible group velocity obtain the highest energy density from electrons during the ESD event, which induces the devices melting phenomenon. The thermal response of phonon is also investigated, and it is found that the ratio of the phonon group velocity to the phonon specific heat can account for the phonon thermal response. If the ratio is higher than 2, the phonon have a good response to the heat input changes.