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.

中文翻译：

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将 DG 模型扩展到二阶量子校正，用于分析亚 10 nm MOS 器件中的单电荷效应


我们扩展了密度梯度 (DG) 模型以包含二阶量子校正 (SOQC) 项。 DG模型作为能够有效模拟量子效应的器件模拟模型已得到广泛应用。然而，当DG模型中仅考虑一阶量子校正项时，由于掺杂剂和界面陷阱等离散电荷，难以准确描述窄区域内的载流子密度或电势波动等器件特性。因此，我们将 DG 模型扩展到 SOQC，将其实现为三维 (3D) 模拟器，并比较了具有单点电荷的亚 10 纳米器件在 DG 模型和 3D 中的模拟结果。薛定谔-泊松 (SP) 求解器。通过这一点，我们发现扩展到 SOQC 的 DG 在电容电压 (C-V) 和电子密度局部波动方面很好地再现了 SP 模拟结果。