AI 中文总结
该研究开发了用于椭圆界面问题的二阶非拟合幽灵有限元方法，将其应用于石墨烯场效应晶体管的静电模拟，验证了方法的精度并重现了器件的转移特性，支持采用完整二维静电描述。
AI 中文摘要
我们开发了一种针对具有不连续扩散系数的椭圆界面问题的非拟合幽灵有限元方法（unfitted ghost finite element method），并将其应用于低维半导体器件的静电模拟。该方法基于固定笛卡尔网格，通过水平集函数（level-set functions）表示几何结构，即使存在界面也无需网格生成与重新网格化。采用网格回弹策略（snapping-back-to-grid strategy）控制小切割单元（small-cut-cell）问题，同时通过对称Nitsche公式弱施界面条件。该方法首先在具有不同几何形状和系数跃变的基准椭圆界面问题上进行验证，结果显示解的精度达到二阶，梯度的精度达到一阶。作为应用，我们考虑由自洽漂移-扩散-泊松模型描述的石墨烯场效应晶体管（graphene field-effect transistor），在二维氧化物/石墨烯/氧化物结构中计算静电势，其中石墨烯层的电荷传输在简并情况下采用一维双极漂移-扩散方程建模，并纳入与场相关的迁移率模型。耦合非线性系统通过阻尼定点迭代（damped fixed-point iteration）结合三层几何的域分解处理求解。数值模拟重现了从关态（OFF state）到开态（ON state）的清晰转移特性，并展示了栅极电压对二维静电势的影响。结果还表明，石墨烯层的有效厚度和离散化会影响横向势分布，支持采用带有显式氧化物/石墨烯界面条件的完整二维静电描述。
英文摘要
We develop an unfitted ghost finite element method for elliptic interface problems with discontinuous diffusion coefficients and apply it to the electrostatic simulation of low-dimensional semiconductor devices. The proposed approach is based on a fixed Cartesian grid and represents the geometry by level-set functions, avoiding mesh generation and remeshing even in the presence of interfaces. A snapping-back-to-grid strategy is used to control the small-cut-cell issue, while interface conditions are weakly enforced by a symmetric Nitsche formulation. The method is first validated on benchmark elliptic interface problems with different geometries and coefficient jumps, showing second-order accuracy for the solution and first-order accuracy for its gradient. As an application, we consider a graphene field-effect transistor described by a self-consistent drift-diffusion-Poisson model. The electrostatic potential is computed in a two-dimensional oxide/graphene/oxide structure, while charge transport in the graphene layer is modeled by one-dimensional bipolar drift-diffusion equations in the degenerate case and by including a field-dependent mobility model. The coupled nonlinear system is solved by a damped fixed-point iteration combined with a domain-decomposition treatment of the three-layer geometry. Numerical simulations reproduce transfer characteristics with a clear transition from an OFF state to an ON state and show the influence of the gate voltage on the two-dimensional electrostatic potential. The results also indicate that the effective thickness and discretization of the graphene layer affect the transverse potential profile, supporting the use of a full two-dimensional electrostatic description with explicit oxide/graphene interface conditions.
Comments25 pages, 12 figures, 2 tables
