硅中的辐照缺陷建模及双峰电场成因解释

在高辐照剂量作用下，硅探测器的材料块体中会产生均匀分布的缺陷，可以用能级（往往是深能级）、引入率和电子/空穴捕获截面四个参数描述之。 深能级中的载流子具有两条重要的特殊性质： 其一在于它们在被捕获之后等效于正/负电中心，会改变有效掺杂率； 其二在于它们通过隧穿的方式具有导电能力。 因此，原则上可以从各种掺杂的捕获率与释放率（来自热力学）计算平衡时深能级电流的连续性方程，从而得到有效掺杂分布。 （实际上由于团块缺陷难以建模等原因，通常用主要的五种缺陷拟合各种缺陷带来的总效果，该模型称之为HPTM。） 这样的分布中，空穴向正电中心密集区汇集，反之亦然，使掺杂分布与探测器厚度方向坐标近似于成递减关系，自然使电场成下凸关系。

延伸阅读：

J. Schwandt, E. Fretwurst, E. Garutti, R. Klanner, C. Scharf and G. Steinbrueck, “A new model for the TCAD simulation of the silicon damage by high fluence proton irradiation,” 2018 IEEE Nuclear Science Symposium and Medical Imaging Conference Proceedings (NSS/MIC), 2018, pp. 1-3, doi: 10.1109/NSSMIC.2018.8824412;

V Eremin, E Verbitskaya, Z Li, “The origin of double peak electric field distribution in heavily irradiated silicon detectors,” Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment (NIM A), 2002, pp. 556-564, doi: 10.1016/S0168-9002(01)01642-4.

Modeling of Radiation-Induced Defects inside Si Material & Explaination of the Double-Peak Electric Field

Under high-flux radiation, uniformly attributed defects will emerge inside the bulk of a Si particle detector. Those defects could be described by four parameters: the energy level(usually deep), the introduction rate, and the capture cross section of electrons and holes. Carriers on deep levels are equipped with two major properties: First, they are equivalent to charge centers and change the effective doping level; Second, they are conductive as they could tunnel between different defects. Thus, theoretically we could deduce a balanced effective doping distribution with the capture rates and emission rates. (In practice, with difficulties like cluster defects are hard to model, usually we fit the overall radiation effect with five major defects, known as HPTM.) In such distribution, holes tend to gather at high-density positive charge area and vise versa, which makes the effective doping level decrease with the depth inside the bulk and the intensity-depth function be convex downward.

Further reading:

J. Schwandt, E. Fretwurst, E. Garutti, R. Klanner, C. Scharf and G. Steinbrueck, “A new model for the TCAD simulation of the silicon damage by high fluence proton irradiation,” 2018 IEEE Nuclear Science Symposium and Medical Imaging Conference Proceedings (NSS/MIC), 2018, pp. 1-3, doi: 10.1109/NSSMIC.2018.8824412;

V Eremin, E Verbitskaya, Z Li, “The origin of double peak electric field distribution in heavily irradiated silicon detectors,” Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment (NIM A), 2002, pp. 556-564, doi: 10.1016/S0168-9002(01)01642-4.