介绍了改进的范德堡法和鲁美采夫斯基法，即此时用方形四探针分别替代边缘的触点和直线四探针，在大直径硅片上进行微区电阻率的测量。我们采用灰度法和模糊数学分类测得数据，并将它们分别在硅片上绘制出电阻率分布图。所得大型硅片上电阻率分布图已用于指导工程技术人员的集成电路生产和单晶锭生长，取得了较好的效果。

The improved Van der Pauw method and Rymazewski method, i.e., the contacts at the edge and the linear four-point probe in the original methods are replaced by square four-point probes, are introduced to measure the resis- tivity in micro-areas of silicon slices with large diameters. The charts for resistivity distribution on the silicon slices are plotted by classifying the measured data with the grey-level method and fuzzy mathematics. The plotted charts have been used to give engineers an instruction to make IC and to grow mono-crystal ingots with good achievements.