Boundary conditions for Density Gradient corrections in 3D Monte Carlo simulations

Abstract

Monte Carlo remains an effective simulations methodology for the study of MOSFET devices well into the decananometre regime as it captures non-equilibrium and quasi-ballistic transport. The inclusion of quantum corrections further extends the usefulness of this technique without adding significant computational cost. In this paper we examine the impact of boundary conditions at the Ohmic contacts when Density Gradient based quantum corrections are implemented in a 3D Monte Carlo simulator. We show that Neumann boundary conditions lead to more stable and physically correct simulation results compared to the traditional use of Dirichlet boundary conditions.

Simulation of statistical variability in nano-CMOS transistors using drift-diffusion, Monte Carlo and non-equilibrium Green’s function techniques

“…However, the inclusion of quantum corrections alters the confined carrier distribution, shifting the peak away from the semiconductor/oxide interface, and can complicate carrier injection when the contact is adjacent to a confined system. Therefore, Neumann BCs [43,44] have been implemented at the Ohmic contact regions similar to the techniques used in NEGF simulations [14], which help maintain stability in the simulation. The validity of the three self-consistency schemes introduced above is evaluated in comparison with DD simulations for the device with dimensions shown in Table 3.…”

Many-particle Monte Carlo Approach to Electron Transport

“…Other MC simulators do also consider Neumann boundary conditions (i.e. a fixed zero electric-field) (Riddet et al, 2008). The latter conditions fix also the scalar potential (up to an arbitrary constant) so that the injected charge can also be indirectly determined when a known electrochemical potential is assumed.…”

“…The latter conditions fix also the scalar potential (up to an arbitrary constant) so that the injected charge can also be indirectly determined when a known electrochemical potential is assumed. Although all these boundary conditions are successful for large simulation boxes, they are quite inaccurate for small simulation boxes that exclude the leads (Riddet et al, 2008). In principle, there are no much computational difficulties in applying a semi-classical MC technique in large simulation boxes when dealing with mean-field approaches.…”

Use of density gradient quantum corrections in the simulation of statistical variability in MOSFETs

“…The important elements to be captured are the V T shift and the quantum carrier distribution at the source end of the channel, which do not change significantly with the applied drain voltage. Additionally, the boundary conditions at the source and drain Ohmic contacts require careful treatment to maintain stability within the simulation [34,35] and Neumann boundary conditions are use as described previously. The validity of these approaches is evaluated in comparison with DD simulations for a double gate MOSFET with a 20 nm square channel, 3.3 nm thick silicon layer and 1 nm oxide.…”