K-M花样分析法测定薄晶体厚度和消光距离的不确定度评定  

Evaluation of uncertainty in measuring thin crystal thickness and extinction distance by Kossel-Mollenstedt pattern analysis

作　　者：娄艳芝 李玉武[2] Lou Yan-Zhi;Li Yu-Wu(AECC Beijing Institute of Aeronautical Materials,Beijing 100095,China;National Research Center for Environmental Analysis and Measurement,Beijing 100029,China)

机构地区：[1]中国航发北京航空材料研究院,北京100095 [2]国家环境分析测试中心,北京100029

出　　处：《物理学报》2022年第14期210-219,共10页Acta Physica Sinica

摘　　要：本文通过分析200 kV加速电压条件下,单晶Si薄膜样品的透射电子显微镜(TEM)双束会聚束衍射(CBED)Kossel-Mollenstedt(K-M)花样,测定了单晶Si薄膜样品的局部厚度和Si晶体(400)晶面的消光距离ζ400.分析了影响测量不确定度的因素,并运用一阶偏导的方法讨论了各个因素对测量不确定度的影响系数,依据GB/T 27418-2017《测量不确定度评定与表示》对实验估计值进行了不确定度评定.结论如下:被测Si晶体局部厚度的实验估计值为239 nm,其合成标准不确定度为5 nm,相对标准不确定度为2.2%;包含概率为0.95时,包含因子为2.07,扩展不确定度为11 nm;加速电压为200 kV时,Si晶体(400)晶面的消光距离ζ400的实验估计值为194 nm,合成标准不确定度为20 nm;包含概率为0.85时,包含因子为1.49,扩展不确定度为30 nm.影响试样厚度合成标准不确定度的主要因素是相机常数、加速电压和试样厚度;影响消光距离合成标准不确定度的主要因素是相机常数、加速电压和消光距离.双束K-M花样测量数据的测量不确定度u(Δθi)对消光距离不确定度的影响约是对试样厚度不确定度影响的ni(ζ/t^(3))(ni为正整数,ni≥1)倍,对拟合直线斜率的不确定度的影响是对截距不确定度影响的倍.如果试样有一定厚度,即ni>1,则用TEM双束会聚束衍射K-M花样分析薄晶体厚度的不确定度较小,而用此方法分析消光距离的不确定度较大.In this paper,the local thickness of single crystal Si film sample and the extinction distance of the(400)plane of Si crystal are obtained by analyzing the double-beam converging beam diffraction(CBED)pattern of single crystal Si film sample under the 200 kV of accelerated voltage.The factors affecting the measurement uncertainty are analyzed,and the influence coefficients of each factor on the measurement uncertainty are discussed by using the concept of first-order partial derivative.The measurement uncertainty of thin crystal thickness and extinction distance are evaluated and expressed according to national standards GB/T 27418-2017.The conclusions are as follows.The local thickness of the measured Si crystal is estimated at 239 nm,the combined standard uncertainty is 5 nm,and the relative standard uncertainty is 2.2%.With the inclusion probability being 0.95,the coverage factor is 2.07 and the expanded uncertainty is 11 nm.With the accelerated voltage being 200 kV,the extinction distance ζ400 of Si crystal(400)plane is estimated at 194 nm,the combined standard uncertainty of the extinction distance is 20 nm,and the relative standard uncertainty of the extinction distance is 10%.With the inclusion probability being 0.85,the coverage factor is 1.49 and the expanded uncertainty is 30 nm.The main factors that can affect the combined standard uncertainty of sample thickness t 0 are camera constant,accelerating voltage and sample thickness,while the factors that influence the combined standard uncertainty of extinction distance are camera constant,accelerating voltage and extinction distance.The influence of the uncertainties of the measurement data of the Kossel-Mollenstedt pattern on the uncertainty of the extinction distance is ni(ζ/t)^(3)times that on the sample thickness,and their influence on the slope of the fitting line is about ni times that on the intercept of the line,where ni is a positive integer and greater than or equal to 1.If the sample is not too thin,that is,ni is greater than 1,then the uncer

关 键 词：会聚束电子衍射 厚度测定 消光距离 不确定度 

分 类 号：O785[理学—晶体学]