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按照著名的二分之三次方定律,热电子阴极工作在空间电荷限制区,共1gU_a-1gI_a 直线的斜率应该为1.5。但是,在实际测量中,特别是工作温度比较高的阴极(如钡钨阴极),该斜率往往在1.35到1.45之间。那么,这种阴极是不是工作在空间电荷限制区?能不能正常使用?偏离1.5的原因是什么?针对这些问题,我们作了一些计算和实验,试图找到一个明确的答案。从理论上分析,影响斜率的原因,包括电子初速的接触电位差、电场强度的均匀性和阴极面发射的均匀性等因素。我们分两种情况来考虑这些因素对实际测量曲线的影响。首先分析一下收集极—阴极间距离比较小的情况。这时,考虑到电子初速和接触电位差这两个必然存在的因素,在空间电荷限制区的阳极电流应按下式计算:
According to the well-known law of dichotomy, thermionic cathodes work in the space-charge-limited area with a slope of 1.5g for a total of 1gU_a-1gI_a. However, in actual measurements, especially in cathodes that operate at higher temperatures (such as barium tungsten cathodes), the slope tends to be between 1.35 and 1.45. So, this cathode is not working in the space charge-limited area? Can not normally use? What is the reason for the deviation of 1.5? In response to these problems, we made some calculations and experiments in an attempt to find a clear answer. From the theoretical analysis, the reasons that affect the slope, including the initial velocity of the electron potential difference, the uniformity of the electric field intensity and uniformity of cathode surface emission and other factors. We consider the impact of these factors on the actual measurement curve in two cases. First analyze the collector - cathode distance is relatively small. At this time, taking into account the two factors of electron velocity and contact potential difference, the anode current in the space charge limited region should be calculated as follows: