Infrared spectrophotometry for carbon in silicon as calibrated by

Infrared Spectrophotometry for Carbon in Silicon as Calibrated by Charged Particle Activation Yoshiyuki Endo, Yoshifumi Yatsurugi, and Nobuyuki Akiyama

Komatsu Electronic Metals Co., Hiratsuka, Japan Tadashi Nozaki

Institute of Ph ysical and Chemical Research, Wako-shi, Saitama, Japan The calibration curve for the infrared spectrophotometry of carbon in semiconductor silicon is presented based on data obtained for single crystal silicon already analyzed for carbon by charged particle activation. The curve thus obtained gives carbon contents lower by a factor of about 0.75 than the previously used curve. When silicon carefully analyzed by activation is used as the reference of the spectrophotometry, carbon as low as 50 wt ppb can be detected at room temperature. For concentrations over 500 wt ppb, the relative error can be regarded as usually less than 10%. Attention should be paid, however, to the existence of carbon insensitive to the present spectrophotometry. Usefulness of the spectrophotometry is exemplified by the measurement of carbon distribution in silicon rods.

ALTHOUGHIR spectrophotometry is widely used for the determination of carbon in high-purity silicon, the modern semiconductor industry requires the improvement of its accuracy and sensitivity. The presently-used calibration curve has been offered by Newman and Willis, who discovered the I R absorption band due to substitutionally dissolved carbon a t about 600 cm-l and used it for carbon determination ( I ) . As the sample for obtaining the calibration curve, they prepared 14C-containingcrystals by adding Ba14C03 t o molten silicon and measured the incorporated l4C radioactivity t o determine the absolute l4C content. Although their pioneering work should be highly appreciated, the determined absorptivity of carbon cannot be believed very accurate when judged from their experimental method. Their samples contained significant amounts of oxygen from the BaC03, showing IR absorption bands due t o C-0 bondings ( I , 2 ) . Since carbon forming the C-0 bondings does not take part in the absorption at the wavenumber of the carbon determination, their observed absorptivity for the carbon was naturally underestimated. This, as they themselves noted, leads to a calibration curve giving overestimated carbon contents ( I ) . Also, a n accurate absolute determination of I4C in bulk silicon is very difficult by any nondestructive way because of the unprofitable radiation character of 'F. Radioactivation analysis usually is the only method or the most reliable method for the determination of sub-ppm level impurities in high-purity matrices. For oxygen in silicon, several workers have compared the results of activation analysis with those of IR spectrophotometry using the calibration curve obtained by vacuum fusion (3-5). By the use of (1) R. C. Newman and J. B. Willis, J . Phys. Chem. Solids, 26, 373 (1965). (2) R. C. Newman and R . S. Smith, ibid., 30, 1493 (1969). (3) G. I. Aleksandrova, A. M. Demidov, G. A. Kotelnikov, G. P. Pleshakova, G. V. Sukhov, D . Ya. Choporov, and G. I. Shmanenkova, A t . Energ. (USSR),18, 569 (1967). (4) C. K. Kimm, Rudioclrem. Radioand. L e f t . ,2, 53 (1969). (5) E. A. Schweikert and H. L. Rook, ANAL. CHEM.,42, 1525 (1970). 2258

charged particle activation analysis, we searched and found a convenient procedure for determining carbon in semiconductor silicon (6). This method proved to have sensitivity down to several ppb and also enough accuracy for concentrations of 100 ppb and less (see Table I). (In this paper, ppm and ppb are used for wt ppm and wt ppb.) We have analyzed various kinds of commercial semiconductor silicon for carbon and have studied its concentration and behavior (7). Thus, we now possess silicon single crystals of known carbon concentrations from 3 ppm down to about 20 ppb. Using these silicon samples, we have intended to draw calibration curves for the IR spectrophotometry. By the use of ultra-pure silicon as the reference of the spectrophotometry, the substitutional carbon concentration down to 50 ppb has proved detectable a t room temperature. In principle, the IR spectrophotometry and the charged particle activation analysis give different information. The former is sensitive only to the substitutionally dissolved carbon, but the latter gives either the total carbon or dissolved carbon plus some fraction of precipitated carbon according t o the method of chemical separation used in the analysis (8). As-grown silicon crystals, which we used for obtaining the calibration curve, d o not contain any notable amount of coagulates of S i c unless the total carbon concentration is over about 3 ppm. In this paper, the calibration curve is shown and compared with the curve of the former workers; discussions are made on the carbon insensitivity t o spectrophotometry; the sensitivity and accuracy of the spectrophotometry are estimated; and its usefulness is exemplified by the measurement of carbon distribution in single-crystal silicon rods. A comparison of charged particle activation analysis and IR spectrophotometry for caxbon in silicon is given in Table I. The following abreviations are used. Transmittance through the sample. Transmittance through the reference. D Differential transmittance. Spectrophotometer reading with one beam passing through the sample and the other through the reference (D = TJT,). R = Reflectivity of silicon for the I R radiation (R = 0.30). b = Sample thickness. c = Concentration of the carbon. a = Absorptivity of the carbon. a, = Absorptivity of the matrix silicon itself. T, T,

~~

= = =

~~

(6) T. Nozaki, Y . Yatsurugi. and N. Akiyama, J . Radioaml. Chrm.. 4, 87 (1970). (7) T. Nozaki. Y. Yatsurugi, and N. Akiyama. J . Elrcrrochem. SOC., 117, 1566 (1970). (8) T. Nozaki, Y . Makide, Y. Yatsurugi, Y. Endo, and N . Akiyama, Bull. Cliem. Soc. Jup., 45, 2776 (1972).

ANALYTICAL CHEMISTRY, VOL. 44, NO. 14, DECEMBER 1972

Table I. Comparison of Activation Analysis and IR Spectrophotometry for Carbon in Silicon

Activation Sensitive state of Total carbon or dissolved carbon plus carbon some fraction of Sic coagulates Several ppb Detection limit Limitation in sam- Little ple property Relative standard deviation for:" 20-ppb level 4% 50-100 ppb 20-107; 500-ppb level 7% 1--3 ppm 5% Estimated overall relative error

Spectrophotometry Substitutionally dissolved carbon 50 PPb Considerable

Under detection limit 4C-lOZ 3z 3%

for :

20-ppb level 50-100 ppb 500-ppb level 1-3 ppm Accessibility Person and time required per sample Other main differences

3~20

Under detection limit 70-20 Z

15% 10%

10% 10%

50 %

z

Limited 5 persons, 1.5 hr

Popular Single person, 0.5 hr

Destructive Nondestructive Difficulty in autoEase of automation mation Difficulty in spatial Convenience for spatial scanning scanning Based on the observed results for 5 runs.

EXPERIMENTAL Sample Preparation. Disks of 2 m m in thickness were cut out of as-grown single-crystal silicon rods of various origins and their surfaces were polished mirror-flat with the aid of diamond paste. Thickness variation was within 5 pm. For the determination of carbon concentration of each disk, usually the adjacent part of the rods were cut into 1-mm disks and were analyzed by activation. In some cases, the sample was analyzed by activation after I R measurement. Also, sets of silicon disks with various given thicknesses (1 to 5 mm) were prepared out of both a highly purified rod and a rod containing homogeneously about 0.6 ppm of carbon. They were used for the examination of the range of the transmittance in which no apparent deviation from Lambert's law is observed, and the transmission of IR beam through well-contacted silicon surfaces. F o r the examination of the IR-sensitive carbon content by heat treatment, some carbon-rich samples were kept a t 1200, 1230, and 1300 " C for many days. Activation Analysis. The 12C(3He,a)11Creaction was used in the activation analysis. The silicon wafer was bombarded with a 3He beam (15 MeV, 1 to 8 pA, usually 20 min), with the beam current being measured by a current recorder and a current integrator. After the removal of the surface layer (20 to 25 pm) by etching with HF-HN03, the sample was decomposed with HF-HN03-KI04 and the product was mixed with a NaOH-KMn04 solution containing N a C 0 3 carrier, all within a closed system. The resultant alkaline mixture was treated with H&O? to give l1COZ,which was converted into BallCO,, precipitate for activity measurement. As activation standard, a graphite disk was covered with a n aluminum foil having a thickness equivalent to the sample surface to be removed by etching and was bombarded with a lower flux and for a shorter duration (0.1 t o 0.3 PA, 10 to 50 sec).

-

0

575

600 Wavenumber

(cm-1)

Figure 1. IR absorption spectra of carbon in high-purity silicon at room temperature Curve 1. Transmittance for reference silicon Curve 2. Transmittance for silicon containing about 1.7 wt ppm of carbon Curve 3. Differential transmittance between the above two silicons

Detailed description about this procedure is given in Reference 6 together with a discussion on possible interferences. The oxygen interference due to the l 6 0 (3He,2a)11C reaction was corrected after the determination of the oxygen content by activation analysis using the 1 6 0 ( 3He,p)18F reaction. In order to ascertain the reliability of the chemical process, l'C-containing silicon prepared by the following techniques was subjected to the process and the behavior of lC was examined by proton bombardment of boron-doped silicon, and by fusion of high-purity silicon in an ambient containing carrier-free l1CO, (8). IR Measurement. A popular IR spectrophotometer of grating type (Japan Spectroscopic Co., Model IR-G) was used for most of the work. Extremely pure silicon which contained 20 i 10 ppb of carbon by activation was used as the reference. For some samples, T , and D were measured from 400 to 4000 cm-l a t room temperature and also under cooling with liquid nitrogen o r liquid helium. Then, D a t 602 cm-' was measured by scanning a narrow wavenumber region about it at room temperature. Because of the considerably large uo at 602 cm-', D should be measured under the energy-limited condition (9). After examination of the measurement condition, the spectrophotometer was set as follows: IR beam cross section, 10 mm X 5 mm; scanning velocity, 100 cm-lihr; mechanical slit width, 1.3 mm (observed spectral half-width, 8 cm-1). RESULTS AND DISCUSSION Spectra and Calibration Curve. The absorption spectra are shown in Figure 1. The absorption due to silicon lattice (9) J. W. Potts and A. L. Smith, Appl. Opt., 6,257 (1967).


2259

reason for this discrepancy is quite obvious from the description in the introduction. Correction for Multiple Reflection and Thickness Variation. When the multiple reflection of the IR radiation in the silicon disk is taken ipto account, the carbon concentration is given as (2) :

0.5

1.5

1.0 I

c IR

1 2 3 a b s o r p t i o n by t h e c a r b o n

4

Figure 2. Calibration curve for the IR spectrophotometry of carbon in high-purity silicon at room temperature Curve A . The present curve Curve B. By Newman and Willis Circles. Present experimental plots Units of the ordinate: I, wt ppm; 11, atomic ppm; 111, 10” atoms/cm3 .4bscissa: i, Absorbance for 1-cm sample; ii, Absorption coefficient

Since a, = 4.2 cm-l and a = 0.62 (cmswt ppm)-l a t room temperature, the relative contribution of the second term of Equation 1 can be calculated to be always less than 2.8, 1.1, and 0.5% for the sample thicknesses of 1.0, 1.5, and 2.0 mm, respectively, but equal t o 18% for an infinitely thin sample. Thus, the correction for multiple reflection need not be considered in the present spectrophotometry unless the sample is thinner than 1 mm. When the sample thickness (b) is slightly different from the reference thickness ( b Ab), the carbon concentration is given as :

+

1 T , a, Ab c = - - l og-+--+ ab T, a b

vibration itself has its maximum at 607 cm-I and overlaps with the absorption of the carbon for which the maximum is at 602 cm-l, both at room temperature. In the IR spectrophotometry of oxygen in silicon, liquidhelium cooling has been shown to be very effective t o improve the sensitivity, because the oxygen absorption peak is made sharper and higher and the three-phonon silicon lattice absorption is made unobservably small by the cooling (10). The peak height of the two-phonon silicon lattice absorption a t the wavenumber of carbon determination has been reported t o be reduced to about ‘ 1 2 by liquid-nitrogen cooling (11). According to our observation, the carbon peak was made higher by a factor of about two by liquid-nitrogen cooling; the silicon absorption at the wavenuinber of carbon determination could not be made so small as described in Reference 11 by liquid-nitrogen and liquid-helium cooling; and the silicon absorption a t the wavenumber of oxygen determination disappeared in liquid-helium cooling. In the carbon determination, therefore, no such marked sensitivity improvement by cooling as in the oxygen determination can be expected. Cooling is expensive and time-consuming, and a considerable amount of the beam intensity is lost in passing through the windows of the cooling vessel. For the routine analysis of carbon, therefore, measurement under cooling cannot be regarded as suitable for semiconductor manufacturers today, though it will give valuable information in fundamental research laboratories. Figure 2 gives the calibration curve for the spectrophotometry of carbon at room temperature together with the curve of Newman and Willis ( I ) . Their curve gives carbon concentrations higher by a factor of about 1.3 than our curve. The

Since the third term of Equation 2 can usually be neglected as just shown above, the effect of thickness variation can be corrected by the second term of Equation 2 , where a,/a = 6.9 (wt ppm) at room temperature. Reliability of Spectrophotometer Reading. Figure 3 shows the change of thc transmittance (T,) and the carbon absorbance (acb) Hith the sample thickness under our measurement conditions. The references were highly purified silicon with the same thicknesses as the samples. The optimum thickness to get the highest sensitivity is determined from this curve. When T, > 0.05, it was usually easy to determine D within a precision range of 3 %. For smaller T,, the response of the spectrophotometer became slower and the precision in the determination of D became poorer with the decrease of T,. The thickness of our samples was always so chosen as to make T, > 0.05, although some reproducibility in measured D was found in the region of 0.05 > T, > 0.03. For the mechanical slit width from 0.9 to 1.4 mm, T, was almost constant. For a narrower slit width, the reproducibility in the measured T, and D was likely t o be lost owing to the energy limitation; for wider width, the absorbance a t the absorption peak was underestimated, as naturally understandable. IR Insensitive Carbon. Bean and Newman have recently reported the solubility of carbon in silicon crystals (12). They followed the change of the IR absorbance for the substitutional carbon in the course of heat treatment under various conditions until the absorbance became constant at a given temperature. We independently undertook similar study and obtained results agreeing well with their results. The change was very slow in general, and at 13OO0C,it usually took more than 10 days for the substitutional carbon concentration t o reach a constant value which is regarded as the solid solubility. Any significant change in the result of activation analysis was not found after the heat treatment. The solid solubility

( I O ) B. Pajot, So/id-State EI~crror7ics,12, 923 (1969). ( 1 1 ) F. A. Johnson, Proc. Pkys. Soc., 73, 265 (1959).

(12) A. R. Bean and R. C. Newman, J . Phys. Chem. Solids, 32, 1211 (1971).

(cm-l)

2260


determined by us is expressed as 80 exp ( - A H / R T ) in atomic fraction [3.4 x 107 exp ( - A H / R T ) in wt ppm or 4.0 X l o z 4 exp ( - A H / R T ) in atoms/cm3], with A H = 55 i 4 Kcal/mol, where A H is the heat of solution, R the gas constant, and T absolute temperature. Bean and Newman have reported almost exactly the same value for AH, but a slight difference is found in the absolute solubility between our and their results due obviously to the difference in the calibration curves used. As is clear from the phase diagram (3, the thermodynamically stable state of carbon in solid silicon with its concentration over the solubility is S i c . In the heat treatment of carbon-containing silicon, therefore, coagulates of S i c are likely to form, resulting in the decrease of the I R absorbance. Bean and Newman have found that the heat-treated samples exhibit new I R spectra attributable to the precipitated S i c particles (12), in agreement with our results. The rate of the precipitation, however, is so low that as-grown crystals can safely be regarded as free from S i c particles unless the total carbon content is over 3 ppm, which is the solid solubility at the melting point of silicon (7). Thus, it is least probable that the samples we used for drawing the calibration curve contained any notable amount of S i c particles. Carbon once precipitated as S i c usually did not dissolve readily in heating, even to near the melting point of silicon. As is seen in Figure 2 , some samples of low carbon contents gave the experimental plots lying above the straight line of the calibration curve. A so-called dislocation-free crystal, for which well reproducible results were obtained in the repetition of both activation analysis (about 320 ppb) and I R spectrophotometry, belonged to them. A certain part of carbon in such a sample is thus considered to be in some form insensitive to I R radiation of the measurement wavenumber. Whether the insensitiveness is due to the combination of carbon with other impurities or to some other reasons is not yet known; this should be made clear in the future. At present, it is not always possible to obtain correct total carbon concentration by I R spectrophotometry. Reliability of the Activation Analysis. To estimate the precision in the activation analysis, two silicon rods containing homogeneously different concentrations of carbon were prepared and analyzed. The results for each five runs were 62 ppb and 2.28 ppm with relative standard deviations of 15 and 4 %, respectively. In the examination of the accuracy in the activation analysis, possible errors in the chemical separation and in the charged particle beam measurement should be considered. The chemical process was checked by the chemical treatment of 15 pieces of the llc-containing silicon (see Experimental Section). The carbon content obtained by our method should be corrected by a factor of 1.03. The accuracy of the charged particle beam measurement (beam integrator reading) cannot be estimated easily. The error in it, however, is not regarded as serious, because only the ratio of the integrator reading for the sample to that for the activation monitor is needed and because well-reproducible results were obtained for bombardments under different beam intensities and in different cyclotron machine times. Sensitivity and Accuracy of the Spectrophotometry. Sample disks containing about 50 ppb of carbon gave the absorption peak with D = 0.98, which was twice as high as the noise level. This impurity content can be regarded as the detection limit in practical routine analysis. As is obvious from the preceding descriptions, the relative error can be estimated to be within 10 % for the substitutional carbon concentrations over 500 ppb but about 50% for that of 80 ppb. Therefore,

0.121

Sample thickness (rnm)

Figure 3. Apparent deviation from Lambert-Beer’s law Curve A . Observed transmittance us. sample thickness (for reference-gradesilicon) Curve B. Observed differential absorbance cs. sample thickness (for silicon containing about 0.6 wt ppm of carbon)

Distonce from the center ( m r n )

Figure 4. Carbon distribution in silicon rods along diameter Crystal-pulling rate for the sample of: Curve A , 3 mm/min; Curve B, 2 mm/min; Curve C, 0.5 mm/min

the I R spectrophotometry has proved to be sufficiently sensitive and accurate for the analysis of most kinds of semiconductor silicon now being produced (7). For the determination of a ppb-level of carbon by this method, reference silicon of extremely low carbon content is required. It can be prepared by the following process: single pass of a molten zone through a semiconductor silicon rod loaded with a small quantity of high-purity S O ? ; and a few zone passes through the resultant silicon rod in a high vacuum carefully made free from any carbon source. Carbon escapes as C O in the first step, and oxygen sublimes from the melt as S i 0 in the second step (13). (13) T. Nozaki, Y. Makide, Y. Yatsurugi, N . Akiyama, and Y. Endo, Itit. J . Appl. Radiat. Isotopes, 22, 607 (1971).


2261

Usefulness, Limitation, and Possible Improvement. The IR spectrophotometry is nondestructive, and is much simpler, much more easily accessible, and usually more precise than activation analysis. This method, further, is convenient for the measurement of carbon distribution by automatized spatial scanning. Although the I R beam cross section cannot be made very small because of the energy limitation, the repetition of the scanning with subsequent data reduction can usually give more reliable and more detailed information about the carbon distribution than does the destructive activation analysis. I n the latter method, the bombardment by a sharp charged particle beam with a high total flux often damages the sample by heat evolution within its limited part. Relatively high carbon contents can be measured with the IR beam sharper and the sample thinner than described in the Experimental Section. Radial carbon distributions in Czochralski crystals pulled with various rates are shown in Figure 4. In the course of the crystal formation, the growing solid continuously excludes carbon onto the solid-liquid boundary, because the equilibrium distribution coefficient of carbon is 0.07 i 0.01 (7). The carbon is then gradually removed i ito the bulk liquid phase by diffusion and by macroscopic flow in it. The solid is slowly rotated in the process, and the flow caused by the rotation is the calmest near the center of the solid, becoming more active along with its radius. Also, carbon in the presence of oxygen is known t o escape readily from a silicon melt (13). The escape is the most difficult from just below the center of the solid becoming easier with the distance from it. These two mechanisms of the carbon removal give resultant carbon distributions in the solid product highest in the center decreasing with the radius, just as shown in Figure 4. The effect of the pulling rate on the resultant carbon distribution, seen in Figure 4, is also clearly explained from these mechanisms. Float-zone crystals have not exhibited such marked differences in carbon concentration depending on the location in them and on the crystallization rate. In the float zonemelting of silicon, the molten zone is automatically homogenized fairly efficiently by turbulence caused by radiofrequency heating. When two silicon disks with extremely flat surfaces were intimately contacted with each other, the I R beam traversed through the contact with a n intensity loss less than 10%. As is described in textbooks of optics, intensity loss of a photon beam (-Aril) through a very narrow air gap is given as:

_ -AII

-

2R[1 - COS (4~d/X)] 2R[1 - C O S ( ~ T ~ / X ) ] (1 - R)’

+

I

)~ - R ( 4 ~ d l X= 96 (d/X)2 (1

- R)’

(4)

An IR beam, hence, can be transmitted through an intimate contact of sample disks with much less intensity loss than a UV or visible light. Therefore, a carefully prepared disk pile can be used as the sample or reference of the present spectrophotometry when accuracy demand is not serious, with the spectrophotometer being so set as to make the reading of D as close to 100% as possible in wavenumbers where a = 0 (575590 cm-1 and 615-630 cm-I). The IR spectrophotometry, however, can be applied only single crystals which show n o birefringence and which are free from any notable amount of electrically active impurities (14). The sensitivity is determined by the apparent disobedience t o Beer’s law when the transmittance becomes small. Efforts were made t o minimize the disobedience region by some modifications of the spectrophotometer itself. The strengthening of the beam intensity by the adjustment of the shape and size of the IR source was found t o be the sole way directly effective for this purpose. As is obvious from the theory of the black-body radiation, however, only some limited intensity for IR radiation of desired wavenumber can be emitted from a unit source area of a heated body, whatever its constituents and temperature may be. The use of specially prepared reflectors and lenses may increase the beam intensity, but this is quite expensive. In the future, a new spectrophotometer applicable t o the present determination may be developed using a radiation source other than heated matter with a well-suited detection system to improve markedly the sensitivity and accuracy. The measured absorbance may be slightly variable according t o the measurement conditions. The use of standard samples of known impurity contents, if accessible, is clearly preferred to the use of the calibration curve alone. It will be highly appreciated when reliable standard samples are made commercially available. ACKNOWLEDGMENT

The authors would like t o express their thanks to the Cyclotron Group of the Institute of Physical and Chemical Research for their bombardment services.

RECEIVED for review March 3,1972. Accepted July 20,1972. (3)

where d i s the gap width and X is the photon wavelength. For 4 ~

Infrared spectrophotometry for carbon in silicon as calibrated by

Recommend Documents