Physical Modeling of Deep-Submicron Devices

Abstract

This paper gives an overview of established methods to describe quantum effects in deep-submicron CMOS. Recent progress in the integration of quantum models in TCAD packages is illustrated by a number of applications.

Quantum-corrected drift-diffusion models for transport in semiconductor devices

“…Comparing QDD and SPDD predictions seems to indicate that the QDD model underestimates the peak shift effect while it overestimates the effect of charge penetration under the channel barrier. As a concluding modeling remark, we point out that all the results provided by the QDD simulations rely on a proper choice of the value of the quantum diffusion coefficient d 2 n , which is typically used as a fitting parameter depending on the semiconductor material [42]. The weight of quantum-mechanical effects along different spatial directions suggests that to fit the QDD results with the SPDD predictions one might choose to take d 2 n as a rank-two tensor instead of a scalar quantity.…”

“…Special attention must be paid to the treatment of the net recombination rate in the solution of the linearized electron and hole continuity equations. As a matter of fact, the expressions (42) and (43) have rigorous validity only if, as is the case for this paper, the recombination term is neglected, otherwise one should also linearize U with respect to u n and u p . A possible strategy could be to resort to the lagging procedure described in [15], although a more thorough investigation is needed about this issue (see [24] for some numerical results in the case of the QDD model).…”

“…During the execution of Step 1, the functions u n and u p are given and kept fixed, while in Steps 2 and 3, the functions u, G n and G p resulting from Step 1 are plugged into (42) and (43) and kept fixed, as in a standard Gauss-Seidel procedure (see [15] for a thorough discussion of this latter aspect). Special attention must be paid to the treatment of the net recombination rate in the solution of the linearized electron and hole continuity equations.…”

Multi-Subband Monte Carlo simulations of degradation due to fin thickness fluctuations in FinFETs

“…The purpose of this comparison with MSMC simulations is to assess their capability to handle T Si discontinuities. Note that the DG correction is a semi-empirical model to include quantization effects in both the directions perpendicular and parallel to the transport [33]. In [24] it is demonstrated that DG correction and potential smoothing are somehow equivalent, and a formula (Eq.…”

TCAD simulation in development and fabrication of deep-sub-/spl mu/m devices

“…for nitrided oxides. Quantum corrections are calculated by using the Density Gradient Method [6] where normally no adjustments are necessaly. Transfer characteristics (LI=ld(VJ) at low drain bias voltage allow to .verify the parameters determined using CV curve.…”