Integration of the Density Gradient Model into a General Purpose Device Simulator

Abstract

A generalized Density Gradient model has been implemented into the device simulator Dessis [DESSIS 7.0 reference manual (2001). ISE Integrated Systems Engineering AG, Balgriststrasse 102, CH-8008 Zürich].We describe the multidimensional discretization scheme used and discuss our modifications to the standard Density Gradient model. The evaluation of the model shows good agreement to results obtained by the Schro¨dinger equation.

Physical Modeling of Deep-Submicron Devices

“…Fig. 9 illustrates the potential and density profiles across an NMOSFET with 3 nm oxide thickness at 2 V gate voltage [21,4]. It is striking that the density decays into the barrier from both sides, although the tunnel current flows from channel to gate.…”

“…NMOSFETs with a gate length of 300 nm, a gate width of 1 µm and oxide thicknesses of 2 nm and 3 nm, respectively, were simulated with both the self-consistent Schrödinger method and the DG model. To fit the latter to the former, the mobility in the oxide was adjusted to µ n = 0.05 cm 2 /Vs using the case t ox =2 nm [21,4]. The agreement is within one order of magnitude.…”

Density-gradient theory: a macroscopic approach to quantum confinement and tunneling in semiconductor devices

“…Tools for device analysis using the DGC equations as described above are readily available. All of the major commercial device simulators offer a DGC capability, e.g., it comes as an option in Silvaco's ATLAS simulator, 10 in Synopsys's SENTAURUS simulator, 11 and in Xilinx's ISE Simulator [29]. 12 The author has also found Comsol's generalpurpose finite element simulator 13 to be quite effective at solving these equations, although at present this tool is incapable of implementing the Scharfetter-Gummel discretization.…”

Extension of the DG Model to the Second-Order Quantum Correction for Analysis of the Single-Charge Effect in Sub-10-nm MOS Devices

“…The DG model is similar to classical drift-diffusion models; hence, it is used as a tool for analyzing complicated structures of multidimensional devices [7]- [9]. Moreover, the DG model is widely accepted in academia and industry because it not only accurately predict the C-V of very thin SiO 2 like SP models [10], [11], but is also much more computationally efficient. With these advantages, the model has been extended to the modeling of electrostatic effects of discrete dopants [12], [13] and the quantum transport of carriers by including the concept of the quantum field [14]- [16].…”