While the first Hot-Carrier Degradation (HCD) models used
the channel electric field as the driving force, it has long been
realized that the phenomenon is energy- rather than field-driven.
In order to obtain the energy distribution of the carriers, the Boltzmann Transport Equation (BTE) has to be solved,
which is challenging in its own right. In addition, as HCD is highly sensitive to
the high-energy tail of the distribution, modeling of
the scattering operator requires special attention.
In particular, impact ionization as well as electron-electron interactions have to be taken into account.
For example, it has been shown that the adequacy of the BTE solution
ignoring electron-electron scattering can be seriously hampered.
Furthermore, it has been shown that the majority carriers can significantly
contribute to the damage, requiring a coupled solution of the BTE for
electrons and holes. Finally, since an accurate resolution of the
energy distribution at high energies is required, information about
the full band structure has to be included into the model.
Traditionally, this complicated problem has been approached by using the
Monte Carlo method, which is computationally- and time-intensive, particularly when the
high-energy tails of the distribution function have to be resolved in detail.
We demonstrated a Spherical Harmonics Expansion (SHE) solution of the bipolar
BTE, which has been applied to the investigation of HCD in n-channel MOSFETs (cf. figure) and does not
show the noise present in data from Monte Carlo simulations.