We consider the problem of identifying possibly discontinuous doping profiles in semiconductor devices from data obtained by\,stationary voltage-current maps. In particular, we focus on the so-called unipolar case, a system of PDE's derived directly from the drift diffusion equations. The related inverse problem corresponds to an inverse conductivity problem with partial data. The identification issue for this inverse problem is considered. In particular, for a discretized version of the problem, we derive a result connected to diffusion tomography theory. A numerical approach for the identification problem using level set methods is presented. Our method is compared with previous results in the literature, where Landweber-Kaczmarz type methods were used to solve a similar problem.

中文翻译：

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静态电压-电流图的反掺杂分布问题

我们考虑这样的问题，即从通过静态电压-电流图获得的数据中识别半导体器件中可能不连续的掺杂分布。特别是，我们专注于所谓的单极情况，这是直接从漂移扩散方程式导出的PDE系统。相关的反问题对应于具有部分数据的反电导率问题。考虑该逆问题的识别问题。特别是，对于该问题的离散版本，我们得出与扩散层析成像理论有关的结果。提出了一种使用水平集方法识别问题的数值方法。我们的方法与文献中以前的结果进行了比较，文献中使用Landweber-Kaczmarz类型的方法来解决类似的问题。