at 1118 cm-1 and a FWHM of about 50 cm-1 at room Физика и техника полупроводников, 2005, том 39, вып. Spectroscopic parameters of LVM absorption bands of carbon and oxygen impurities in isotopic... tion, and the selected apodization function. However, as it was shown in [16,17], at T < 17 K the value of KO actually does not depend upon temperature but only upon resolution and apodization function . Thus, at 8 K and at resolution of 0.3 cm-1, it is equal to 1.05 · 1016 at/cm2 . While determining the impurity of oxygen in natural and mono-isotopic (see below) Si we used the value of KO = 1.23 · 1016 at/cmestimated for the series of silicon samples with various content of oxygen and registered with spectral resolution of 0.5 cm-1 at T = 17 K (IChHPS) and T = 5K (PTB).
The coefficient KO = 1.23 · 1016 at/cm2 has been derived by means of measurements of the same material at low and at room temperature and the use of the generally accepted value of KO = 3.14 · 1016 at/cm2 for the calculation of the oxygen content from the room temperature spectrum. The Figure 4. LO + LA phonon frequencies as function of average used sample thickness were 3 cm for the 393 K and 0.3 cm nuclear mass in samples of various isotopic composition of Si nat for the 5 K measurement.
including Si (T = 300 K).
3.2. IR absorption spectra of C and O in samples of mono-isotopic silicon 28 3.2.1. Phonon spectra of samples Si, Si and Si. It follows from the previous section that in order to provide an edaquate description of the absorption bands of the carbon and oxygen impurities in silicon with natural composition the data are required on lattice vibrations, i. e. on spectral position and on intensity of different phonon modes observed in the absorption range of the stated impurities. At going to isotopically enriched samples alongside with the averaged lattice mass change both the phonon spectrum of the matrix, and position of Si-16O-Si and Si-12C quasi-molecule bands, comprising the silicon atoms of the given isotops should be changed.
Fig. 3 gives the experimental phonon spectra for monoFigure 5. Absorption spectrum of TO + TA phonons and 28 29 30 nat isotopic Si, Si, Si and for Si at room temperature Si-C complex in silicon samples of various isotopic composiin the range 1200 and 600 cm-1. It can be seen that tion (T = 17 K): 1 — sample Si30-2-Pr8-part2, 2 — sample the absorption bands of Si, lattice are shifted to higher Si29-2-Pr8-part2, 3 — sample Si28-4-Pr10, 4 — sample 4, nat frequencies with respect to the phonon spectrum of Si 5 — sample 1. Numeration of samples corresponds to Table and Table 1.
30 and the corresponding bands of isotopic Si and Si are shifted to the opposite frequency direction according to the well-known relation between the frequency of phonon (k) and the atomic mass m [18,19]:
(k) m-1/2. (2) Table 2 gives the maxima of phonons absorpiton for Si with different isotopic contents in the stated spectral range at room temperature. The dependence of phonon frequency (k) (with LO + LA phonon as an example) upon the average isotopic atomic mass of Si for the samples with different isotopic composition is given in Fig. 4.
3.2.2. IR spectra of carbon in mono-isotopic sili28 29 con. As it was stated above, the absorption band of Si-C Figure 3. Phonon spectra of monoisotopic Si, Si, Si and nat nat Si composition in the range 1200-500 cm-1 at T = 300 K. groups in the spectrum of Si is situated at the top of 3 Физика и техника полупроводников, 2005, том 39, вып. 324 P.G. Sennikov, T.V. Kotereva, A.G. Kurganov, B.A. Andreev, H. Niemann, D. Schiel, V.V. Emtsev...
Table 3. Spectral position max (cm-1) and full width at half-maximum (FWHM) 1/2 (cm-1) of absorption bands of Si-12C quasinat molecule in IR spectra of silicon with natural isotopic composition Si and of mono-isotopic Si nat 28 29 Si-12C Si-12C Si-12C Si-12C T, K max 1/2 max 1/2 max 1/2 max 1/ 300 605 5.3 ± 0.1 605 603.1 600.17 607.4 2.57 ± 0.03 607.7 2.44 ± 0.04 605.6 2.67 ± 0.06 603.8 2.89 ± 0. 605.0 cm-1, 1/2 = 6cm-1 at T = 300 K ; 607.5 cm-1, 1/2 = 3cm-1 at T < 80 K .
Not determined because of great error of bands separation.
Table 4. Concentration (cm-3) of oxygen and carbon impurities in mono-isotopic silicon according to IR inter-laboratory determination Oxygen Carbon Designation of sample according to SIC (thickness, mm) IChHPS, T = 300 K PTB, T = 5K IChHPS, T = 300 K PTB, T = 5K Si28-4-Pr10 (1.66) (3.2 ± 0.5) · 1016 (4 ± 0.4) · 1016 (2.8 ± 1.4) · 1016 (1.4 ± 0.1) · Si28-3-Pr10 (2.18) 8 · 1015 (3.3 ± 0.1) · 1014 5 · 1015 (1.6 ± 1.0) · Si28-6.1-Pr10-part4 (2.18) (2.3 ± 0.4) · 1017 (2.0 ± 0.2) · 1017 (3.7 ± 0.2) · 1016 (3.3 ± 0.4) · Si29-2-Pr8-part2 (2.33) (3.1 ± 0.8) · 1017 (5 ± 1) · Si30-2-Pr8-part2 (1.78) (5.6 ± 0.6) · 1017 (4 ± 1.5) · 1016 (4.6 ± 0.1) · Sample Identification Code (SIC): isotop-number of charge-number of product (10 — FZ single crystal, 8 — Cz single crystal) —number of studied part of the crystal according to cutting scheme. For samples in the 1 and 2 lines of the Table 4 the number of studied part of crystal is not determined.
Not determined because of high concentration of oxygen and carbon in the sample (full absorption).
the strongest phonon absorption of Si. The same situation exchange (though it takes additional experimental testing in is also observed in case of enriched Si, as it is seen from future), the phonon band of the sample of natural isotopic Fig. 5 where the composite band near 610 cm-1 shifts with composition with carbon content less than 3 · 1015 cm-nat respect to the same band in Si according to (2). Due to on Fig. 1 could be taken for the baseline substraction. The 28 the fact that the samples with different isotopic composition obtained absorption bands of quasi-molecules Si-C, Si-C and with the content of carbon lower than the limit of and Si-C are given on Fig. 6 and their spectral parameters detection of IR spectroscopic method were not available at 17 K are presented in Table 3. For the determination of ( 5 · 1014 cm-3) , it was, strictly speaking, impossible to carbon in the investigated mono-isotopic samples we used isolate the absorption band of carbon from composite bands the above-given values for calibration coefficients from  shown in Fig. 5. Assuming that the band shape of TO + TA at room temperature and below 80 K for the band centered phonon band do not change significantly due to the isotop at 607 cm-1. The data obtained are diven in Table 4.
Table 5. Dependence of position max, full width at the half maximum (FWHM) 1/2 and intensity of absorption band of Si-16O-28Si quasi-molecule in IR spectrum of monoisotopic silicon Si (sample Si28-4-Pr10) on spectral resolution at T = 17 K (Happ-Genzel apodization function) Resolution, cm-1 max, cm-1 1/2, cm-1 Intensity, r.u.
0.5 1136.3 0.81 ± 0.02 0.0.3 -”- 0.68 ± 0.01 0.0.2 -”- 0.63 ± 0.01 0.0.1 -”- 0.59 ± 0.01 0. FWHM was determined by approximation of band shape with Lorenz function.
Figure 6. Absorption spectra of Si-12C complex at 600 cm-(T = 17 K) in samples of monoisotopic Si and of silicon with 3.2.3. IR spectrum of oxygen in mono-isotopic natural isotopic composition: Si — sample Si30-2-Pr8-part2, 29 28 silicon. Table 6 gives the spectral positions and FWHMs Si — sample Si29-2-Pr8-part2, Si — sample Si28-4-Pr10, nat at room temperature of the absorption bands of quasiSi — sample 4. Numeration of samples corresponds to Table 28 29 molecules Si-16O-28Si, Si-16O-29Si and Si-16O-30Si for and Table 1.
Физика и техника полупроводников, 2005, том 39, вып. Spectroscopic parameters of LVM absorption bands of carbon and oxygen impurities in isotopic... corresponding samples of mono-isotopic silicon. The small Table 6. Position (max, cm-1) and full width at half maximum low-frequency shift at practically unchanged half-width is (FWHM) 1/2 (cm-1) of absorption bands of Si-16O-Si quasimolecules in IR spectra of silicon with natural isotopic composiobserved.
nat tion Si and mono-isotopic silicon at two temperatures The oxygen spectra for the samples of mono-isotopic silicon at low temperatures, i. e. below 20 K, are of the 28 29 nat Si-16O-28Si Si-16O-29Si Si-16O-30Si greatest interest since, as it is seen from Fig. 2, for the Si T, K an isotopic splitting of the band centered at 1136 cm-1 takes max 1/2 max 1/2 max 1/place.
300 1107 32 ± 1 1103.1 36 ± 1 1099.3 33 ± 0.Determination of principal spectral parameters (position 17 1136.31) 0.60 ± 0.01 1132.52) () 1128.93) () and FWHM) of the Si-16O-Si band at low temperatures in spectra of mono-isotopic silicon calls for their registration at () Not determined because of great concentration of oxygen in the spectral resolution 0.3cm-1 . Fig. 7 demonstrates the sample.
1) 2) Si-16O-28Si band at 1136.4 cm-1 for sample Si28-4-Pr10 max = 1136.4cm-1 ; max = 1131.0cm-1 according to theoretical data  and max = 1132.5cm-1 according to experimental data ;
3) max = 1125.3cm-1 according to theoretical data , max = 1129.2cm-1  and max = 1129.1cm-1 to experimental data .
from Table 4 recorded with four values of spectral resolution. The obtained values of FWHM of this band are given in Table 6. It can be seen that in going from resolution 0.5 cm-1 to 0.1 cm-1 the FWHM slightly decreases and at further increase of resolution becomes constant and equal to (0.59 ± 0.01) cm-1. It is evidence for registration of true shape of this band. This value agrees with FWHM of the same band in spectrum of nat the Si [5,16,17].
Unfortunately, the registration of true band shapes of 29 Si-16O-29Si and Si-16O-30Si quasi-molecules in spectra 29 of Si and Si was impossible due to high concentration Figure 7. Dependencies of the full width at half maximum of oxygen in the sample. Even for its minimal thick(FWHM) of the absorbtion band of Si-16O-28Si quasi-molecule ness (0.9 mm) the total absorption of corresponding bands in mono-isotopic Si (sample Si28-4-Pr10 from Table 4) on was observed. That is why Table 6 summarizes only spectral resolution (T = 17 K): 1 — 0.1 cm-1, 2 — 0.2 cm-1, spectral positions of absorption bands of quasi-molecules 3 — 0.3 cm-1, 4 — 0.5 cm-1.
Si-16O-Si. It should be noted that, as it was expected, the 28 position of the Si-16O-28Si band for Si coincides with the position of the same band in the spectrum of natural silicon but it does not have low-frequency components correspon28 ding to vibrations of Si-16O-29Si and Si-16O-30Si. The obtained earlier theoretically in [20,21] and experimentally determined in  spectral position of the Si-16O-29Si band agrees satisfactorily with the experimental value for Si obtained in this study (Table 6). The spectral position of Si-16O-30Si band was determined earlier in  nat from spectrum of Si but containing 3 · 1017 cm-3 of oxygen, as well as in isotopically enriched Si . It can be seen from Table 6 that these values are very close to the experimental one obtained here for Si and is by 3.6 cm-higher as compared with the predicted value . The 28 isotopic shift of oxygen bands of Si and of Si amounts 3.8 cm-1 just as the shift of the oxygen bands of Si and of Si. The isotopic shift, theoretically predicted in [20,21], was slightly greater and equal to 5.3 cm-1 that Figure 8. Normalized to thickness spectra of Si-16O-Si quasican be probably explained by theoretical model fallibility molecule at 1130 cm-1 (T = 17 K) in mono-isotopic samples that does not consider influence of nearest and extended Si30-2-Pr8-part2, Si28-6.1-Pr10-part4, Si29-2-Pr8-part2 (Table 4) nat silicon atoms. It should be noted that the vibrational and in Si, sample 5 (Table 1). 1 — Si-16O-28Si (1136.4 cm-1), 28 frequencies of the Si-O-Si molecule (for all isotopic species) 2 — Si-16O-29Si (1134.5 cm-1), 3 — Si-16O-30Si (1132.2 cm-1), 29 predicted recently according to improved multy-atom model 4 — Si-16O-29Si (1132.5 cm-1), 5 — Si-16O-30Si (1129.2 cm-1).
The last spectrum is twice reduced along ordinate axis. in  are very close to experimental values.
Физика и техника полупроводников, 2005, том 39, вып. 326 P.G. Sennikov, T.V. Kotereva, A.G. Kurganov, B.A. Andreev, H. Niemann, D. Schiel, V.V. Emtsev...
Fig. 8 presents spectra of quasi-molecules Si-16O-Si resolution has been studied. Its full width at half maximum at 1130 cm-1 (T = 17 K) for samples Si30-2-Pr8-part2, height equal to 0.6 cm-1 agrees with the value for the Si28-6.1-Pr10-part4, Si29-2-Pr8-part2 and natural silicon natural silicon.
4. The perspectives of generalization of IR spectroscopy sample 5 from Table 1, normalized to thickness, and method for determination of carbon and oxygen impurities evidently demonstrates the isotopic shift of antisymmetric in silicon of natural isotopic composition to mono-isotopic stretching vibration band of quasi-molecule Si-16O-Si while silicon have been discussed. The content of C and O going from silicon of natural isotopic composition to mono28 29 impurities in Si, Si and Si single crystals has been isotopic samples.
estimated. It was shown that the content of carbon and Actually there is no difference between the quantitative 28 oxygen in the studied samples of Si and of carbon in Si determination of oxygen content in Si and in natural and Si is 1016 cm-3 on average. The content of oxygen silicon.
29 in Si is by an order of magnitude greater.
As for Si and Si isotopes, due to absence for known reasons of calibration coefficients for Si-16O-29Si and This work was supported in part by ISTC (grant N 1354) Si-16O-30Si bands and assuming that their band shape and INTAS (01-0468).
does not differ strongly from the shape of Si-16O-28Si band in natural silicon we also used the calibration 28 References coefficient of Si-16O-28Si band in natural silicon equal to 1.23 · 1016 cm-2 for determination of oxygen in Si  P. Wagner, J. Hage. Appl. Phys. A, 49, 123 (1989).
and Si (for resolution 0.5 cm-1, T = 17 K and 5.2 K). The  S. Kashino, Y. Matsushita, M. Kanamori, T. Iisaka. Jap. J.
results found for oxygen concentration in all studied samples Appl. Phys., 21 (1), (1982).
are given in Table 4.
 H. Foll, B.O. Kolbesen. The Electrochemical Society Softbond As it can be seen from above presented results, generaProceedings Series (Princeton, N. J., 1977) p. 565.
lization of IR spectroscopy methods for determination of  P. Becker, H. Bettin, L. Kolnders, A. Martin, A. Nicolaus, S. Kffer. PTB-Mitteilungen, 106, 321 (1996).
carbon and oxygen to mono-isotopic silicon, elaborated for  B. Pajot. Analusis, 5 (7), 293 (1977).
natural silicon, can be done at the moment only by taking  B.O. Kolbesen, T. Kladenovi. Kristall und Tecknic, 15 (1), into account some limitations and assumptions. The possible K1–K3 (1980).
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