Modeling of hot carrier degradation using a spherical harmonics expansion of the bipolar Boltzmann transport equation

Recent studies have clearly demonstrated that the degradation of MOS transistors due to hot carriers is highly sensitive to the energy distribution of the carriers. These distributions can only be obtained in sufficient detail by the simultaneous solution of the Boltzmann transport equation (BTE) for both carrier types. For predictive simulations, the energy distributions have to be thoroughly resolved by including the fullband structure, impact ionization (II), electron electron scattering (EE), as well as the interaction of minority carriers with the majority carriers. We demonstrate that this challenging problem can be efficiently tackled using a deterministic approach based on the spherical harmonics expansion (SHE) of the BTE.