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

Abstract

We extended the density-gradient (DG) model to include a second-order quantum correction (SOQC) term. The DG model has been widely used as a device simulation model capable of simulating quantum effects in efficient way. However, when only the first order quantum correction term is considered in the DG model, it is difficult to accurately describe device characteristics such as carrier density or potential fluctuation in the narrow region due to discrete charges such as dopants and interface traps. Thus, we extended the DG model to the SOQC, implemented it as a three-dimensional (3D) simulator, and compared the simulation results for sub-10-nm devices, which have a single point charge, in the DG model and the 3D Schrödinger-Poisson (SP) solver. Through this, we identified that the DG extended to SOQC well reproduces the SP simulation results in terms of both capacitance-voltage (C-V) and local fluctuation in electron density.

Parallel approach of Schrödinger-based quantum corrections for ultrascaled semiconductor devices

“…After the device geometry and properties have been defined, in the beginning of every simulation, an initial solution is calculated using only the Poisson equation at equilibrium at V G = 0.0 V and V D = 0.0 V. The output of this initial routine is a purely classical electrostatic potential. However, a solution that seeks a compromise between sound results and short simulation times has been to include quantum corrections [18,31,32]. Some of the most commonly used quantum corrections are the DG corrections that require calibration against a quantum mechanical simulation as explained in [12] or the SCH corrections, based on solving the FE 2D SCH equation that does not demand any fitting parameters.…”

A Simulation Study of Gate-All-Around Nanowire Transistor With a Core-Substrate

“…Since pure drift-diffusion model is not accurate enough beyond nanometers [19], and ballistic transport effects must be considered, we also incorporated ballistic mobility models [20], [21]. Because the oxide thickness and channel width have reached quantum-mechanical length scales, the wave nature of electrons and holes can no longer be neglected, thus Density-Gradient [22] is used to simulate quantization effects. In the high channel doping region, IAL mobility (Inversion and accumulation layer mobility) model is used to model 2D Coulomb scattering [23].…”