Iue Annual Review 2005

Biography:
Viktor Sverdlov received his Master of Science and Ph.D. degrees in physics from the State University of St.Petersburg, Russia in 1985 and 1989, respectively. From 1989 to 1999 he worked as a staff research scientist at the V.A.Fock Institute of Physics, St.Petersburg State University. During this time he visited European research centers and universities: ICTP (Italy, 1993), University of Geneva (Switzerland, 1993-1994), University of Oulu (Finland,1995), Helsinki University of Technology (Finland, 1996-1998), Free University of Berlin (Germany, 1997), NORDITA (Denmark, 1998). In 1999 he became a Staff Research Scientist at the State University of New York at Stony Brook. He joined the Institute of Microelectronics, Technische Universität Wien in 2004. His scientific interests include device simulations, computational physics, solid-state physics and nanoelectronics.

The Wigner Monte Carlo Method for Semiconductor Device Simulation

Aggressive scaling of MOSFETs below a feature size of 50 nm makes the theoretical description and modeling of carrier transport in these devices challenging. Not only the degradation of electrostatic channel control, but also the carrier transport in the channel is determined by quantum mechanical effects. The two major quantum effects to be taken into account are size quantization in the channel and quantum mechanical tunneling along the channel. Both effects call into question the use of powerful and well developed simulation methods based on the semi-classical Boltzmann equation. Continued scaling of MOSFET feature sizes well below 50nm requires the development of new simulation techniques capable of incorporating the quantum effects properly. One of the promising approaches developed at the Institute is the Wigner function method. An advantage of the Wigner function approach is that it also includes all scattering mechanisms in a natural way via the Boltzmann scattering integrals, allowing a rigorous transport model to be developed which accounts for both quantum interference phenomena and the scattering mechanisms.
It is essential that the Wigner equation formalism treats the scattering and quantum mechanical effects equally through the corresponding scattering integrals. The collision-free propagation of the carriers is described by the Liouville operator acting on the Wigner function and is similar to that of the Boltzmann equation. Analogous to the solution of the Boltzmann equation, it prompts for a solution of the Wigner equation with a Monte Carlo algorithm. However, because the kernel of the quantum scattering operator is not positively defined, the numerical weight of a particle trajectory increases rapidly in absolute value, and the numerical stability of a trajectory-based Monte Carlo algorithm becomes a critical issue. A multiple trajectories method is being developed at the Institute in order to overcome this difficulty. In this algorithm the problem of the scattering operator with the non-positive kernel and growing statistical weights of a single trajectory is addressed by creating a number of trajectories with positive and negative finite weights. The latter algorithm allows the annihilation of trajectories with similar statistical properties, which introduces a possibility of controlling the number of trajectories and obtaining convergent results.

Carrier density in a double-gate MOSFET calculated for several gate length values using the semi-classical Boltzmann equation (red) and fully quantum Wigner Monte Carlo approach (blue). Quantum effects play an important role leading to an increase in carrier density for shorter gate lengths due to an additional contribution from electrons tunneling under the barrier.