绘制硅单晶电阻率等值线的Mapping技术(英文)

A Mapping Technique to Draw Resistivity Isocontours for Slice-of-Silicon Monocrystal

用斜置式四探针测定了硅单晶片(Ф75mm)上3mm间距测试点的电阻率分布.本文从电阻率的统计分布出发,确定了电阻率的分隔数和差值,采用指数函数作为模糊集的隶属度,并且选择合适的门槛值,利用模糊数学将电阻率数据归类于不同的模糊集.同一模糊集对应相同的电阻率,这样使电阻率能以一定的间隔分布,然后结合MATLAB软件画出电阻率等值线,以构成Mapping图.在同一等电阻率线条上各点具有较小的阻值偏差,且剩余未连接点少.连接质量好,可以应用于指导实际生产.

A resistivity distribution with a space of 3mm between test points was measured on a slice-of-silicon monocrystal （diameter 75mm） using an inclined four-point probe. This paper has determined the number of resistivity divisions and their separations by statistical methods and introduced fuzzy mathematics to place the data into different fuzzy sets, after choosing the exponent function as a membership function for fuzzy sets and suitable values of thresholds. One fuzzy set corresponds to one resistivity isocontour. Then,the resistivity isocontours can be drawn with a definite separation and fi- nally shown in a map with MATLAB. The deviation of resistivity data on an isocontour is small and there are few residual test points without connections. So, the connection of the isocontours are high-quality and useful in application for instructing practical production.