1. Introduction crystal site that can be essential at precision measurements of its parameters .
Locating at interstitial positions, the atoms of oxygen Carbon and oxygen impurities are permanently present form a Si-O-Si quasi-molecule with the environment which in silicon single crystals manufactured both by Czochraloriginates an IR active local vibrational mode (LVM) with ski (Cz) (the manufacturing process itself is the main the maximum of the most intensive antisymmetric stretching source of impurities), and float-zone (FZ) method as well band 3 at 1106 cm-1 at room temperature. The most as by deposition from the vapor phase. The atoms of intensive LVM absorption band of Si-C at 605 cm-1 at the oxygen are located at interstitial positions of silicon crystal same temperature is characteristic of carbon substitutionally lattice at the concentration lower than that of solubility incorporated into the silicon lattice. Both these bands (2 · 1018 cm-3 at the melting temperature) and the atoms of overlap in different extent with the bands of intrinsic the dissolved carbon (solubility at the melting temperature is phonon absorption of Si. Special features of these and 3.5 · 1017 cm-3) are located at the lattice sites. Despite the other less intensive absorption bands of oxygen and carbon fact that both impurities are not electrically active, the strucat different temperatures and impurity concentrations are ture of the impurity in the lattice and concentration are of being in detail discussed in literature for many years importance both to provide a controllable growth of silicon (e.g., the reviews [5,6]). On the basis of these data the crystals and to apply Si in manufacture of semiconductor standard measurement procedures have been developed structures. It is known, as an example, that heat treatment for IR spectroscopic determination of the impurities of of Cz-Si leads to formation of oxygen-containing thermal oxygen and carbon [7,8].
donors — electrically active centers affecting the main The above-mentioned statements refer to the silicon electrical parameters of this material  and playing a role samples of natural isotopic composition containing of initial stage of formation of the second-phase inclusions 28 29 Si 92.21%, Si 4.70% and Si 3.09%. It might be (precipitates) . The precipitates themselves become the expected that in going to the samples of isotopically pure Si source of a great amount of structural defects (e.g., of the noticeable changes in spectral parameters of absorption dislocations). The latter can also be the intrinsic getters“ of bands of oxygen and carbon will be observed due to ” the undesirable impurities in the process of manufacturing changes in the lattice parameters and phonon spectrum.
of semiconductor devices. It is also known  that carbon Earlier it was evidently demonstrated for the oxygen band noticeably effects the precipitation processes of oxygen and at 862 cm-1 in isotopically enriched germanium (98% enits gettering functions. Besides, the impurities of oxygen and richment) . Similar studies for mono-isotopic samples carbon present at the level of 3 · 1015 cm-3 even in high- of Si are evidently of scientific and applied interest, first of purity silicon crystals, also lead to a certain distortion in all from the point of view of quantitative determination of Spectroscopic parameters of LVM absorption bands of carbon and oxygen impurities in isotopic... Table 1. Concentration (cm-3) of oxygen and carbon impurities in reference silicon samples with natural isotopic composition according to IR inter-laboratory determination Oxygen Carbon Number of samples (thickness, mm) IChHPS (17 K) PTB (5.2 K) Passport data IChHPS (17 K) PTB (5.2 K) Passport data 1 (2.21) 3 · 1014 3 · 1014 (3.0 ± 0.1) · 1014 3 · 1015 (1.8 ± 0.9) · 1015 3 · 2 (4.02) (4.4 ± 0.3) · 1015 (4.3 ± 0.2) · 1015 - 3 · 1015 (2.0 ± 0.3) · 1015 3 (2.96) (2 ± 01) · 1015 (1.9 ± 0.2) · 1015 (1.8 ± 0.1) · 1015 3 · 1015 (3.0 ± 0.2) · 1015 3 · 4 (1.95) (3.1 ± 0.1) · 1015 - 3.1 · 1015 (1.5 ± 0.2) · 1016 - (1.0 ± 0.1) · 5 (0.37) (7.0 ± 0.1) · 1017 - (6.9 ± 0.1) · 1017 < 1 · 1016 (300 K) - PTB — Physicalish-Technische Bundesanstalt these important impurities. However, it was impossible to The commercial samples of Si of natural isotopic comdo it up to the latest time due to a lack of bulk samples position with the impurity content and structural perfection, 28 29 of Si, Si and Si with sufficient degree of purity, close to the samples of mono-isotopic Si (Table 1), were crystalline perfection and high enrichment. Experiments, used as reference samples.
including the investigation of IR spectra, with different The samples investigated were in the form of planesilicon isotopes can now be realized due to the development parallel discs with diameter of 8-12 mm and thickness of the technique [10,11] for production of high-purity mono- of 0.37-2.2 mm. During preparation of the samples for IR 28 29 isotopic Si as well as Si and Si . measurements they were grinded and mechanically polished with diamond powder of 1 µm dispersion.
The goal of the present work is to investigate IR absorpThe absorption spectra were recorded by IFS-113v tion spectra of the carbon and oxygen impurities in single 28 29 (IChHPS) and IFS-66 (PTB) IR spectrometers with speccrystal samples of Si, Si and Si of the record high tral resolution of 1 cm-1 (T = 300 K); 0.5 cm-1 (5K);
isotopic enrichment (see below) at room temperature an at 0.5, 0.3 and 0.1 cm-1 (T = 17 K) in the spectral range T = 17 and 5 K. One of the aims of this work was to find 500-1400 cm-1 and Happ Genzel apodization function.
out the possibility to apply the above-mentioned standard The sample were cooled down to the temperature techniques [7,8], developed for material with natural isotopic of 16 K using RGD 210 (IChHPS) refrigerator-cryostat composition, for quantitative determination of the impurities and down to 5 K using Optistat CF helium flow-through of carbon and oxygen in mono-isotopic Si. It should be cryostat (PTB).
noted that then this study was in progress the paper of Kato et al.  has been published, there the high-resolution IR absorption study together with theoretical calculations of 28 3. Results and discussion the LVM’s of oxygen in isotopically enriched Si (99.86%), 29 (97.10%) and Si (98.74%) were reported.
3.1. IR absorption spectra of C and O in Si of natural isotopic composition (natSi) 2. Experimental Due to the fact that the measurement of spectra was carried out in two different groups on various equipment The bulk single crystal samples of mono-isotopic Si, with goal to determine the reproducibility of results, an 29 Si and Si were investigated. The starting polycrystals inter-laboratory experiment was carried out on investigation were obtained by the technique  at the Institute of of impurity spectra of carbon and oxygen in five samples Chemistry of High-Purity Substances (IChHPS) (Nizhny of single crystal silicon with natural isotopic composition.
Novgorod) from silicon tetrafluoride enriched in ScienceIn four samples for oxygen and three samples for carbon Technical Centre Elechtrochemical Plant (CENTROTEKH, the content of impurities was determined independently St. Petersburg). The single crystals were grown at the (Table 1). The necessity of these measurements was also Institute of Crystal Growth (Berlin) by combination of due to the fact that the known calibration coefficients, Cz-method and the crucibleless FZ-method (28Si) or only by used in standard analytical techniques for determination of Cz-method (29Si and Si). According to the laser ionization the impurities of C and O in silicon [7,8], refer to room mass spectrometry the enrichment of the studied Si temperature. At the same time a sufficiently low level of the samples was on the average equal to 99.91%. The mentioned impurities in mono-isotopic samples necessitated 29 enrichment for Si was 99.86%, Si — 99.74%. The the measurements at low (below 20 K) temperatures. The samples were of n-(29Si, Si) and p-(28Si) type conductivity literature data on calibration coefficients at these conditions and contained (by the data of IR spectroscopy) electrically are rather contradictory, at least with respect to the impurity active impurities (B, P) at the level of 1014-1015 cm-3. of oxygen [5,14].
3 Физика и техника полупроводников, 2005, том 39, вып. 322 P.G. Sennikov, T.V. Kotereva, A.G. Kurganov, B.A. Andreev, H. Niemann, D. Schiel, V.V. Emtsev...
nat temperature (Table 2). The content of oxygen in Si Table 2. Spectral positions (max, cm-1) of phonon modes in IR spectrum of silicon with natural isotopic composition (natSi) and is determined by a relation similar to (1) including of mono-isotopic Si at T = 300 K the calibration coefficient KO for oxygen which amounts 3.14 · 1017 at/cm2 according to  (in  a close value max(natSi) of 3.07 · 1017 at/cm2 is given). The oxygen band shows Phonons max(natSi) max(28Si) max(29Si) max(30Si)  a complex temperature behavior. At low temperatures near 5 K the broad room temperature band at 1107 cm-LO + TA 566 566.4 569.1 559 548.is removed by a relatively narrow band at 1136 cm-1 and TO + TA 610 610.8 612 601.6 591.two smaller band components at 1134, 1132 cm-1 (Fig. 2).
LO + LA 739 739.1 741 728.3 715.These three band components correspond to the isotopic TO + LA 819 819 817.8 804.3 28 TO + LO 886 888 890 873.5 859 LVM of the Si-O groups Si-16O-28Si, Si-16O-29Si and TO + TO 960 959 962 944 Si-16O-30Si.
2TO + TA 1118 1119 1122.4 () () For measurements at low temperatures the influence of 2TO + LO 1299 1299.5 1302 1278.3 1253.the lattice (phonon) absorption in this region is not signifi3TO 1448 1448.8 1450 1425.1 1398.cant since, as it can be seen fromFig. 2, a narrowband of asymmetric stretching vibrations of quasi-molecule Si-O-Si () Not determined because of high concentration of oxygen in sample.
is located in the range of maximum of much less intensive Error in the determination of phonon peak does not exceed 0.3 cm-1.
combination 2TO + TA band (absorption coefficient is equal to 0.345 cm-1 T = 7K ).
3.1.1. IR spectrum of carbon. The band of optical In general the calibration coefficient KO of the absorption at 605 cm-1 (300 K), and 607 cm-1 (16 K) is band centered at 1136.4 cm-1 in temperature range of nat due to LVM of Si-Cs group with participation of the atoms 17 < T < 50 K depends upon temperature, spectral resoluof Si of natural isotopic composition having a full width at half maximum (FWHM) 6cm-1 at 300 K and 3cm-below 80 K [6,8]. Thus, for its measurement a spectral resolution of 0.5 cm-1 is sufficient. However a real problem is the fact that the Si-C band is just situated at the top of the strongest intrinsic absorption of Si which is a combined absorption band of transverse optical (TO) and acoustic (TA) phonon at 610 cm-1 (Table 2).
Fig.1 gives the absorption spectrum of carbon impurities in sample 4 (Table 1), obtained after subtraction of the spectrum of a sample with an ultimately low content of carbon. The carbon content NC (cm-3) is found from a known relation:
NC = CKC, (1) nat Figure 1. Absorption spectra of Si at 607 cm-1 (T = 17 K):
where C is the experimentally determinable absorption 1 — sample 1, 2 — sample 4, 3 — absorption band of Si-12C coefficient, KC is the calibration coefficient. According to complex in sample 4. Numeration of samples corresponds to the standard  the values for calibration coefficients in Table 1.
case of carbon are equal to 8.2 · 1016 and 3.7 · 1016 at/cmat T = 300 K and at T < 80 K, respectively.
The results for the determination of carbon impurities in the investigated samples of poly-isotopic Si are given in Table 1. The correlation between the data of both laboratories as well as with passport data ( certified values“) ” is given.
3.1.2. IR spectra of oxygen. As it was already pointed out, the most intensive band, corresponding to the impurity of oxygen in Si of natural isotopic composition, is close to 1107 cm-1 at room temperature and has a FWHM of about 32 cm-1. It refers to an asymmetrical nat stretching vibration of the Si-16O-natSi quasi-molecule nat and overlaps with the intrinsic absorption band of silicon Figure 2. Absorption spectra of the Si at 1136 cm-lattice comprising a combination of a transverse optical (T = 17 K): 1 — sample 1, 2 — sample 4, 3 — absorption band of Si-16O-Si quasi-molecule in sample 4. Numeration of samples phonon and a transverse acoustic phonon with the center corresponds to Table 1.
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