Absolute Value Determination of Vacancy Concentration in Silicon Crystals Using Low-Temperature Ultrasonic Measurements

For the samples taken from the void region of the CZ silicon crystal having various thermal histories, we performed the low-temperature ultrasonic measurements for the relative magnitude S of the elastic softening, which is proportional to the concentration of the single vacancies [Vs], i.e. [Vs] =g S. Here, g is the proportionality constant to be determined below. We also carried out void observation by means of the infrared light-scattering tomography, which gave us the information on the concentration and size of the voids (i.e., the size distribution of the voids), from which we calculated the concentration of the vacancies [Vc] consumed for the void formation. From the result of these two experiments, we have found that the formula [Vc]+ aS = U holds for the samples belonging to the same value of the crystal-growth parameter v/G. Here, a is the obtained numerical value, and U is the obtained function of the crystal-growth parameter. When we reasonably assume that, in the void region, the sum [Vc]+[Vs] is the function of the crystal-growth parameter: [Vc]+[Vs]= W(v/G) , then we find U= W(v/G), which further leads us to the present conclusion, g = a. Using this obtained value of g, we can determine the absolute value of [Vs] from [Vs] =g S. Some examples of determining the absolute values of [Vs] are demonstrated.

We will also represent briefly our completely new technique of measuring the vacancy concentration in the near surface region of the silicon wafers. In this technique, the elastic softening due to the near-surface vacancies is selectively observed by the surface acoustic wave, instead of the bulk sound wave used for the above-mentioned measurement.