Iue Annual Review 2013

Biography:
Markus Bina was born in St. Pölten, Austria, in 1985. He studied electrical engineering at the Technische Universität Wien, where he received the degree of Diplomingenieur in 2010. He joined the Institute for Microelectronics in May 2010, where he is currently working on his doctoral degree. In 2013 he completed his studies in Biomedical Engineering at the Technische Universität Wien. His current scientific interests include charge carrier transport, BTI, channel hot-carrier effects and variability in semiconductor devices.

Modeling of Hot-Carrier Degradation Using a Spherical Harmonics Expansion of the Bipolar Boltzmann Transport Equation

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.

Shown are the simulated electron (top) and hole (bottom) distribution function together with the corresponding acceleration integrals in an nMOSFET subjected to hot-carrier stress. Remarkable is the fact that the distribution function is properly resolved up to high energies by the SHE method. This is important since the acceleration integral strongly depends on the energy distribution function.