标题： 用于单极半导体器件中掺杂分布识别的贝叶斯反演 显示英文标题

标题： Bayesian inversion for the identification of the doping profile in unipolar semiconductor devices

摘要： 一个严格的贝叶斯公式化方法，用于无限维的静态线性化单极漂移-扩散模型中半导体器件的反向掺杂分布问题。目标是估计掺杂分布的后验概率分布并计算其后验均值。这使得可以从电压-电流测量中重建掺杂分布。通过证明半导体模型相对于未知参数的有界性和连续性性质，展示了贝叶斯逆问题的适定性。提出了一种使用物理信息先验模型的预条件Crank-Nicolson马尔可夫链蒙特卡罗方法，用于掺杂分布的贝叶斯估计。二维二极管的数值结果说明了所提出方法的效率。 显示英文摘要

摘要： A rigorous Bayesian formulation of the inverse doping profile problem in infinite dimensions for a stationary linearized unipolar drift-diffusion model for semiconductor devices is given. The goal is to estimate the posterior probability distribution of the doping profile and to compute its posterior mean. This allows for the reconstruction of the doping profile from voltage-current measurements. The well-posedness of the Bayesian inverse problem is shown by proving boundedness and continuity properties of the semiconductor model with respect to the unknown parameter. A preconditioned Crank-Nicolson Markov chain Monte-Carlo method for the Bayesian estimation of the doping profile, using a physics-informed prior model, is proposed. The numerical results for a two-dimensional diode illustrate the efficiency of the proposed approach.