The non-destructive estimation of doping concentrations in semiconductor devices is of paramount importance for many applications ranging from crystal growth, the recent redefinition of the 1kg to defect and inhomogeneity detection. A number of technologies (such as LBIC, EBIC and LPS) have been developed which allow the detection of doping variations via photovoltaic effects. The idea is to illuminate the sample at several positions, and detect the resulting voltage drop or current at the contacts. We model a general class of such photovoltaic technologies by ill-posed global and local inverse problems based on a drift-diffusion system which describes charge transport in a self-consistent electrical field. The doping profile is included as a parametric field. To numerically solve a physically relevant local inverse problem, we present three different data-driven approaches, based on least squares, multilayer perceptrons, and residual neural networks. Our data-driven methods reconstruct the doping profile for a given spatially varying voltage signal induced by a laser scan along the sample's surface. The methods are trained on synthetic data sets (pairs of discrete doping profiles and corresponding photovoltage signals at different illumination positions) which are generated by efficient physics-preserving finite volume solutions of the forward problem. While the linear least square method yields an average absolute error around 10%, the nonlinear networks roughly halve this error to 5%, respectively. Finally, we optimize the relevant hyperparameters and test the robustness of our approach with respect to noise.
翻译:对半导体装置中剂量浓度的非破坏性估计对于从晶体增长、最近重新定义1千克到缺陷和不相容性检测等许多应用而言,至关重要。已经开发出一些技术(如LBIC、EBIC和LPS),通过光伏效应检测剂量变异。设想是在若干位置点点点点亮样本,并检测由此产生的电压下降或当电时的电压流。我们以漂浮系统为基础,以描述自惯电场电流传输的漂移系统为基础,用全球和地方反差问题来模拟这类光伏伏技术的一般类别。剂量剖面图包含一个参数字段。为了从数字角度解决一个与物理相关的本地反差问题,我们提出了三种不同的数据驱动方法,其基础是最小方位、多层透视器和剩余神经网络。我们的数据驱动方法通过抽样表面的激光扫描扫描,对一个空间上差异的电流全球和地方的电压信号进行了一般分类。在合成数据中,对准的精确性数据结构进行了不精确性测试,而精确的直径直径的直径直径直径定位图则以10的直径的直径直径的直径直径分辨率分辨率图为我们生成的直径直径直径测测测测测测测测测测测测测测测测测测测测测测测测测的10的轨道。