本项目拟采用解析求解和数值模拟计算相结合的方法，探讨反映掺杂随机波动 影响的纳米绝缘体上硅（SOI）MOSFETs 统计模型，以应用于纳米尺寸SOI 集成电路的工艺指导与电路设计。首先考虑由实际工艺因素引起的掺杂非均匀分布，对非均匀分布采用统计近似，提出基于该近似的沟道有效势分布函数，有效求解泊松方程，通过器件的电荷和电流方程的耦合求取载流子浓度或电荷分布，建立反映非均匀掺杂的解析模型；然后将掺杂波动分为数目波动和位置波动进行考虑，通过数值求解得到所需器件参数的各阶随机统计量的数字特征，采用均方根耦合的方式将两者影响计入模型。数值求解中，采用随机有限元法研究改进基于非平衡格林函数的泊松-薛定谔方程自洽求解的计算效率。本项目的研究将推动我国具有自主知识产权的，面向市场、面向企业、面向核心竞争力的纳米级SOI 器件新模型和电路模拟工具的新发展。

The statistical model of Nanoscale SOI MOSFETs accouting for the random dopant fluctuation is studied in this project based on the combination method of analytical derivation and numerical simulation. Firstly，the nonuniform doping distribution caused by practical process factors is considered using a statistical distribution approximation. A novle effective potential distribution function is presented to derive the carrier distribution and the charge distribution through the coupling of Poisson's equation, the charge and the current equations. And thus an analytical model accounting for the nonunifrom profile is derived. Then the required device parameters various order of random statistics digital features are obtained by numerical simulation. The random dopant fluctuation is divided into the impurity ions number fluctuation and the position fluctuations. The affection of the two is coupling to the final model using Root-Mean-Square way. In view of the devices with different sizes during the numerical calculation, the stochastic finite element analysis method based on self-consistent solving of Poisson-Schrodinger equation using Non-Equilibrium Green's Functions (NEGF), are presented. This simulation strategy can effectively improve the calculation efficiency. The project will promote researches of the novel nanoscale SOI model and circuit device simulation tools facing the market, the enterprise, and the core competitiveness with independent intellectual property rights.