Highly Sensitive and Accurate Infrared Absorption Measurement of Carbon Concentration in Si Crystal
Authors: Inoue Naohisa , Watanabe Kaori , Seki Hirofumi , Uno Hiroyuki , Oyama Hidenori , Kawamura Yuichi 
Published: February 2020

Introduction

Infrared absorption measurement of (substitutional) carbon concentration [Cs] in Si crystal meets many problems. Its practical detection limit is around 5E+15 cm-3 and [Cs] estimated to be below that is inaccurate due primarily to that the concentration of nominally “carbon-free” reference crystal is around that and “unknown.” Thus it is impossible to measure the carbon concentration of modern commercial Si crystal, estimated to be between 5E+15 and 5E+14 cm-3. Moreover it is inconvenient that the standard measurement procedure requires 2 mm thick, double sides mirror polished samples [1]. It is hard to prepare such a sample, because the “as-cut” wafer in factory usually is thinner than that. To solve one of the problems, we have previously established to reduce [Cs] in a reference sample well below 1E+15 cm-3 by the electron irradiation [2]. Here we got the good result covering the above range, by improving the measurement of CiOi introduced by the electron irradiation, proposed about 30 years ago [3].

Experimental

The samples were prepared from CZ and FZ crystals. [C] in most samples was calibrated by using the samples with known [C] obtained by charged particle activation analysis. Electron was irradiated at RT for 1E+15 to 3E+17 cm-2. Most sample thickness was 2 mm and both sides were mirror polished. 1 mm thick samples were also prepared for some samples. Infrared absorption measurement was done using FTIR on the absorption line of CiOi at 862 cm-1 at RT. The detection limit was 2E-6 of peak absorbance at best [4]. The wavenumber resolution was 2cm-1. Samples were also prepared from high [C] crystals and poly-Si crystals.

Results and Discussion

Figure 1 shows the relation between [C] (cm-3) and the absorption coefficient by CiOi (cm-1). The results for [C]>1E+16 cm-3 were taken from the previous paper [3]. The absorption by CiOi increased, saturated and turned to reduce by the dose increase. The maxima were shown here. Those for [C]<1E+16 cm-3 were obtained in this work. Both results showed nearly same dependence. The dose for maxima was around 3E+16 cm-2 for estimated [C] below 1E+15 cm-3 and 1E+17 for [C] around 1E+15 cm-3. They were lower than those for higher [C] reported previously [3]. Thus it was confirmed that [C] could be estimated for down to 1E+15 cm-3 by measuring the absorption by CiOi. The open circle below 1E+15 cm-3 was plotted against the estimated [C]. Tentative calibration line was drawn in the figure.
It was confirmed that the reference with [C] well below 1E+15 cm-3 could be prepared by the electron irradiation.
Absorption from the 1mm thick samples was compared to that from 2mm thick samples, and it was confirmed that the equivalent result could be obtained. The results of high [C] and poly-Si samples were compared to those of the previous paper and the low [C] samples.

Summary

In summary, it was shown that [C] around and below 1E+15 cm-3 could be estimated by measuring the absorption by CiOi introduced by the electron irradiation. The detection limit of CiOi is about 2E+12 cm-3. The expected detection limit of [C] is better than 1E+13cm-3. We may use 1 mm thick samples instead of 2mm thick samples.
Fig. 1 The relation between carbon concentration [C] and absorption coefficient by CiOi.

References

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[2] N. Inoue, S. Shirafuji, H. Oyama, Y. Goto, T. Sugiyama and H. Ono, Si Forum, Niigata 2007.
[3] A. S. Oates and R. C. Newman, Appl. Phys. Lett., 49 (1986) 262.
[4] N. Inoue, Y. Goto, T. Sugiyama and Y. Kawamura, physica status solidi, (c)9 (2012) 1931.