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Quantitative phonon spectroscopy of interstitial oxygen in silicon
ELSEVIER
Physica B 219&220 (1996) 763 765
Quantitative phonon spectroscopy of interstitial oxygen in silicon C. Wurster a, ,, E. Dittrich a, W. Scheitler a, K. LalSmann a, W. Eisenmenger a, W. Zulehner b a 1. Physikalisches Institut, Universitiit Stuttgart, PJaffenwaldrin9 57, D-70550 Stuttgart, Germany b Wacker-Chemitronic GmbH, D-84479 Burghausen, German),
Abstract
By means of phonon spectroscopy with superconducting tunneling junctions, resonant phonon scattering by interstitial oxygen in silicon at 878 GHz is investigated. The acoustic scattering cross section obtained by comparison of experimental and calculated phonon transmission spectra is anisotropic with values of 2.4 x 10-14 c m 2 in (1 0 0)-direction and 5.0 x 10-14 c m 2 in (1 1 1)-direction and used for calibration. The fitting procedure takes into account crystal-related parameters like orientation, phonon focusing, multiple phonon scattering as well as the sample and junction dimensions. By comparing the phonon scattering by the JSO-isotope it is shown that oxygen concentrations of 7x 1013 cm -3 can be determined with high accuracy.
1. Introduction
Oxygen is the most important impurity in silicon incorporated during crystal growth by the Czochralski technique. Thermal treatment of such crystals changes technologically relevant material parameters: Annealing up to 450°C leads to a change of the electrical properties due to the formation of oxygen-related thermal donors [ 1], whereas annealing at temperatures above 700°C induces the growth of oxygen precipitates [2] which are a source of metal gettering in silicon. Recently, very pure silicon with oxygen concentrations below l014 c m -3 has been discussed to be a material well-suited for a new kilogram standard [3]. Such low concentrations are at or below the sensitivity limit of all analytical methods. We have, therefore, investigated the possibility to determine quantitatively extremely low concentrations of oxygen in silicon by phonon spectroscopy. The detection limit is determined by the possibility to detect the ~SO-isotope in its natural abundance of 2 x 10 -3 relative to z60 and comparing the phonon scattering by the latter with IR calibration at intermediate 160-concentrations in the range of 1016cm -3.
2. Interstitial oxygen
Oxygen in as-grown silicon is mainly interstitial (Oi) [4] such as to form a nearly stretched Si-O-Si-quasi-molecule oriented in (1 1 1)-direction. The IR-absorption depth induced by the transition at 1136cm - t is used to determine the oxygen concentration [4]. In phonon spectroscopy we use the strength of the low-energy vibrational-rotational ]0, 0) ~ ]0, 1)-transition induced by resonant phonon scattering at 878 GHz (29.3 cm -1 ) [5] for the determination of the oxygen concentration.
3. Phonon spectroscopy
High-resolution, wide range phonon spectroscopy is possible with superconducting A1- and Sn-tunneling junctions as phonon generators and detectors [6]. For bias U > 2AGe,/e to the Al-junction quasi-particles are excited from the ground state in both films via single particle tunneling. Single particle relaxation and two particle recombination processes determine the emitted phonon spectrum. Essential for spectroscopy is the sharp upper edge at eU 2/IAI of the relaxation spectrum. By superposition of a small modulation voltage to the bias U and lock-in-technique for the detection one obtains effectively the differentiated phonon emission spectrum ~N/~U consisting of a tunable nearly -
* Corresponding author. 0921-4526/96/$15.00 @ 1996 Elsevier Science B.V. All rights reserved SSDI 092 1-4526(95)00878-0
764
C Wurster et al. / Physica B 219&220 (1996) 763-765
monochromatic line and a residual non-monochromatic portion [6]. For computation of the differentiated phonon emission spectrum, the first and second quasiparticle decay steps are taken into account and, in addition, inelastic phonon scattering in the generator. The latter is rapidly increasing with phonon frequency reducing the monochromatic part of the spectrum [7]. It turns out that the differentiated normal conductor spectrum "quenched" by a factor (hf2 - 2 A ) / ( e U - 2A) is a good analytical approximation of the non-monochromatic part of the spectrum for numerical simulation [7, 8]. The height of the monochromatic line is proportional to AAj/eU [6]. The phonon detector is a superconducting Sn-tunneling junction with a wideband characteristic m(f2) consisting of a detector threshold at 2A Sn = 285 GHz, a constant sensitivity up to 570 GHz and a sensitivity proportional to the phonon frequency f2 for f2 > 570 GHz. Due to the inelastic phonon decay at the boundary between Sn-tunneling junction layer and the silicon surface rn(f2) has to be modified [5]. The signal output is proportional to the phonon transmission characteristic d S / d U which is defined by a convolution integral with g(f2) symbolizing the phonon scattering function of the sample: dS _ +~0~D ~ N ~
U)g(~)m(~2) dEL
5. Experimental results and evaluation The phonon transmission spectra of (100)-oriented FZ-silicon (thickness d = 1.8mm, oxygen concentration co = 2.5 x 1015 cm-3) and of (111)-oriented FZ-silicon (d = 2.0ram, co = 1.3 x 101s cm -3) are shown in Fig. 1, Besides the steep signal increase at the detector threshold 2Aaet = 285 GHz [6] the narrow dip at 878 GHz is due to resonance scattering by interstitial oxygen. As indicated in Fig. 1 a frequency resolution between 2.5 and 5 GHz can be achieved. The results of the Monte-Carlo simulation for the constants a,b used in Eq. (2) are strongly dependent on crystal orientation: aloo = 0.544 m m - 1 , alll 0.648 mm-~, bill = 0.736 mm, bl0o = 0.231 mm. Including further fit parameters describing inelastic phonon scattering in the generator and at the silicon-detector boundary the best agreement between measured and calculated spectra was achieved using c~0,100= (6.0 4- 0.5)mm-',c~0.1ti = (6.6 + 0.5)mm - j and a common line width F = (4.5 4- 1.5)GHz in agreement with the results of other authors [9, 10]. :
(1)
The phonon transmission spectra are obtained at 1.0 K with the sample in a 4He-cryostat. if) "O t-
4. Phonon scattering function g(~2)
¢-
._o
The correlation between g((2) and the reciprocal elastic or inelastic mean free path e(~2) = l-l(12) of the phonons has to be determined by Monte-Carlo simulation taking into account the characteristic of the scatterer together with area, distance d and position of the junctions and also the anisotropy of the phonon propagation in the crystal. A simple analytical fit to the Monte-Carlo results is possible if we write g(f2) = exp(-C~e~(f2)d). For a fixed d [7, 8] we get ~efr(c~) = aln(1 + boO,
G " C.
c O cO ee~ N
O e-
(2)
where c~ is the running parameter in the simulation. Multiple scattering occurs in the case of elastic scattering. The fit parameters a and b contain the above-mentioned factors including d. In the case of a lifetime broadened resonant transition the shape function f(f2) of cffQ) = e0f(Q) is a Lorentzian with the line width given by the reciprocal lifetime F. Scattering cross section a and concentration c of the scatterer are proportionality factors given by O~O =
¢-
0
200
400
600
800
1000
1200
phonon frequency [GHz]
Fig. l. Measured and calculated phonon transmission spectra of (100)-FZ-silicon and (11 l}-FZ-silicon. The frequency resolution is 2.5-5 GHz indicated by the bars in the magnified inset.
765
C. Wurster et al. /Physica B 219&220 (1996) 763-765
5-
6. Calibration The acoustic scattering cross section a of interstitial oxygen is determined by dividing the fit parameter c~0by the oxygen concentration c as obtained from IR spectroscopy. We find that the acoustic scattering cross section a is anisotropic:
frequency resolution --.-i1----
ex~
//
"o 4"
"o,
.~ 3-
FZ-silicon pulled frOm CZ-silicon
<111>-orientated J /V
v
"o.
experimental
//
t v
I t
trio0 -- (2.4 4- 0.3) × l0 -14 cm 2, 0"111
: (5.04- 1.5) × lO-14cm 2.
g2. ,~J i~
7. Detection limit Since silicon containing interstitial oxygen below 1015 cm -3 has not been available so far the maximum sensitivity of phonon spectroscopy is obtained from the phonon scattering by the 180-isotope (natural abundance: 0.2%) at 818 GHz. The evaluation of the phonon transmission spectrum of ( 111)-FZ-silicon pulled from CZ-silicon shown in Fig. 2 yields the following results: Assuming the same scattering cross section as obtained for 160 by calibration with the previous sample and taking the natural abundance of 180 we obtain concentrations of(7.0 ± 1.5) x 1013 cm 3 for 180 and (3.5 4- 0.7) x 1016cm -3 for 160. It is seen from Fig. 2 that the 180-resonance is just discernible from noise. A 160-concentration of (2.9 4- 0.6) × 1016cm 3 found by IR spectroscopy confirms the good agreement of both methods in this case.
^
8
0
~
250
measuredoxygen concentration: 160:3.5x10 ~ cm 3
500 750 phononfrequency[GHz]
1000
Fig. 2. Determination of the detection limit of 7 × 1013cm -3 from resonant phonon scattering by interstitial lSo at 818 GHz (abundance: 0.2%) by comparison of the measured and a calculated phonon transmission spectrum of FZ-pulled (111)-CZ-silicon. Thus, phonon spectroscopy is one order of magnitude more sensitive than IR spectroscopy [11] for the determination of small oxygen concentrations in silicon.
References 8. Conclusion Frequency-resolved phonon spectroscopy with superconducting tunnelingjunctions by interstitial oxygen at 878 GHz was found to be a very sensitive method to determine small oxygen concentrations in silicon. Measured and calculated phonon transmission spectra were compared using the absorption coefficient and the Lorentz line width as fit parameters. Because of the elastic character of the phonon scattering process effects of multiple scattering and the influence of the geometry of crystal, generator and detector have to be taken into account. Calibration of phonon spectroscopy was made by determination of the acoustic scattering cross section using IR-obtained data. The IR calibration of one sample makes it possible to determine the 160-concentration in another for which the junction details will be different. A detection limit in the upper 1013 cm -3 range was found by investigation of phonon scattering by the ISO-isotope.
[1] D. Wruck and P. Gaworzewski, phys. stat. sol. (a) 56 (1979) 557. [2] P. Gaworzewski, E. Hild, F.-G. Kirscht and L. Vecsernys, phys. stat. sol. (a) 85 (1984) 133. [3] P. Becker and G. Mana, Metrologia 31 (1994) 203. [4] D.R. Bosomworth, W. Hayes, A.R.L. Spray and G.D. Watkins, Proc. Roy. Soc. A 317 (1970) 133. [5] E. Dittrich, W. Scheitler and W. Eisenmenger, Jpn. J. Appl. Phys. 26 (Suppl. 3) (1987) 873. [6] W. Eisenmenger, Physical Acoustics, Vol. XII (Academic Press, New York, 1976) p. 79. [7] W. Scheitler, Thesis, University of Stuttgart (1989). [8] E. Dittrich, Thesis, University of Stuttgart (1989) [9] U. Werling and K.F. Renk, Phys. Rev. B 42 (1990) 1286. [10] A.A. Volkov, Yu.G. Goncharov, V.P. Kalinushkin, G.V. Kozlov and A.M. Prokhorov, Fiz. Tverd. Tela 32 (1990) 1249; Sov. Phys. Solid State 32 (1990) 799. [11] B. Pajot and B. Cales, Mat. Res. Soc. Symp. Proc. 59 (1986) 39.
Physica B 219&220 (1996) 763 765
Quantitative phonon spectroscopy of interstitial oxygen in silicon C. Wurster a, ,, E. Dittrich a, W. Scheitler a, K. LalSmann a, W. Eisenmenger a, W. Zulehner b a 1. Physikalisches Institut, Universitiit Stuttgart, PJaffenwaldrin9 57, D-70550 Stuttgart, Germany b Wacker-Chemitronic GmbH, D-84479 Burghausen, German),
Abstract
By means of phonon spectroscopy with superconducting tunneling junctions, resonant phonon scattering by interstitial oxygen in silicon at 878 GHz is investigated. The acoustic scattering cross section obtained by comparison of experimental and calculated phonon transmission spectra is anisotropic with values of 2.4 x 10-14 c m 2 in (1 0 0)-direction and 5.0 x 10-14 c m 2 in (1 1 1)-direction and used for calibration. The fitting procedure takes into account crystal-related parameters like orientation, phonon focusing, multiple phonon scattering as well as the sample and junction dimensions. By comparing the phonon scattering by the JSO-isotope it is shown that oxygen concentrations of 7x 1013 cm -3 can be determined with high accuracy.
1. Introduction
Oxygen is the most important impurity in silicon incorporated during crystal growth by the Czochralski technique. Thermal treatment of such crystals changes technologically relevant material parameters: Annealing up to 450°C leads to a change of the electrical properties due to the formation of oxygen-related thermal donors [ 1], whereas annealing at temperatures above 700°C induces the growth of oxygen precipitates [2] which are a source of metal gettering in silicon. Recently, very pure silicon with oxygen concentrations below l014 c m -3 has been discussed to be a material well-suited for a new kilogram standard [3]. Such low concentrations are at or below the sensitivity limit of all analytical methods. We have, therefore, investigated the possibility to determine quantitatively extremely low concentrations of oxygen in silicon by phonon spectroscopy. The detection limit is determined by the possibility to detect the ~SO-isotope in its natural abundance of 2 x 10 -3 relative to z60 and comparing the phonon scattering by the latter with IR calibration at intermediate 160-concentrations in the range of 1016cm -3.
2. Interstitial oxygen
Oxygen in as-grown silicon is mainly interstitial (Oi) [4] such as to form a nearly stretched Si-O-Si-quasi-molecule oriented in (1 1 1)-direction. The IR-absorption depth induced by the transition at 1136cm - t is used to determine the oxygen concentration [4]. In phonon spectroscopy we use the strength of the low-energy vibrational-rotational ]0, 0) ~ ]0, 1)-transition induced by resonant phonon scattering at 878 GHz (29.3 cm -1 ) [5] for the determination of the oxygen concentration.
3. Phonon spectroscopy
High-resolution, wide range phonon spectroscopy is possible with superconducting A1- and Sn-tunneling junctions as phonon generators and detectors [6]. For bias U > 2AGe,/e to the Al-junction quasi-particles are excited from the ground state in both films via single particle tunneling. Single particle relaxation and two particle recombination processes determine the emitted phonon spectrum. Essential for spectroscopy is the sharp upper edge at eU 2/IAI of the relaxation spectrum. By superposition of a small modulation voltage to the bias U and lock-in-technique for the detection one obtains effectively the differentiated phonon emission spectrum ~N/~U consisting of a tunable nearly -
* Corresponding author. 0921-4526/96/$15.00 @ 1996 Elsevier Science B.V. All rights reserved SSDI 092 1-4526(95)00878-0
764
C Wurster et al. / Physica B 219&220 (1996) 763-765
monochromatic line and a residual non-monochromatic portion [6]. For computation of the differentiated phonon emission spectrum, the first and second quasiparticle decay steps are taken into account and, in addition, inelastic phonon scattering in the generator. The latter is rapidly increasing with phonon frequency reducing the monochromatic part of the spectrum [7]. It turns out that the differentiated normal conductor spectrum "quenched" by a factor (hf2 - 2 A ) / ( e U - 2A) is a good analytical approximation of the non-monochromatic part of the spectrum for numerical simulation [7, 8]. The height of the monochromatic line is proportional to AAj/eU [6]. The phonon detector is a superconducting Sn-tunneling junction with a wideband characteristic m(f2) consisting of a detector threshold at 2A Sn = 285 GHz, a constant sensitivity up to 570 GHz and a sensitivity proportional to the phonon frequency f2 for f2 > 570 GHz. Due to the inelastic phonon decay at the boundary between Sn-tunneling junction layer and the silicon surface rn(f2) has to be modified [5]. The signal output is proportional to the phonon transmission characteristic d S / d U which is defined by a convolution integral with g(f2) symbolizing the phonon scattering function of the sample: dS _ +~0~D ~ N ~
U)g(~)m(~2) dEL
5. Experimental results and evaluation The phonon transmission spectra of (100)-oriented FZ-silicon (thickness d = 1.8mm, oxygen concentration co = 2.5 x 1015 cm-3) and of (111)-oriented FZ-silicon (d = 2.0ram, co = 1.3 x 101s cm -3) are shown in Fig. 1, Besides the steep signal increase at the detector threshold 2Aaet = 285 GHz [6] the narrow dip at 878 GHz is due to resonance scattering by interstitial oxygen. As indicated in Fig. 1 a frequency resolution between 2.5 and 5 GHz can be achieved. The results of the Monte-Carlo simulation for the constants a,b used in Eq. (2) are strongly dependent on crystal orientation: aloo = 0.544 m m - 1 , alll 0.648 mm-~, bill = 0.736 mm, bl0o = 0.231 mm. Including further fit parameters describing inelastic phonon scattering in the generator and at the silicon-detector boundary the best agreement between measured and calculated spectra was achieved using c~0,100= (6.0 4- 0.5)mm-',c~0.1ti = (6.6 + 0.5)mm - j and a common line width F = (4.5 4- 1.5)GHz in agreement with the results of other authors [9, 10]. :
(1)
The phonon transmission spectra are obtained at 1.0 K with the sample in a 4He-cryostat. if) "O t-
4. Phonon scattering function g(~2)
¢-
._o
The correlation between g((2) and the reciprocal elastic or inelastic mean free path e(~2) = l-l(12) of the phonons has to be determined by Monte-Carlo simulation taking into account the characteristic of the scatterer together with area, distance d and position of the junctions and also the anisotropy of the phonon propagation in the crystal. A simple analytical fit to the Monte-Carlo results is possible if we write g(f2) = exp(-C~e~(f2)d). For a fixed d [7, 8] we get ~efr(c~) = aln(1 + boO,
G " C.
c O cO ee~ N
O e-
(2)
where c~ is the running parameter in the simulation. Multiple scattering occurs in the case of elastic scattering. The fit parameters a and b contain the above-mentioned factors including d. In the case of a lifetime broadened resonant transition the shape function f(f2) of cffQ) = e0f(Q) is a Lorentzian with the line width given by the reciprocal lifetime F. Scattering cross section a and concentration c of the scatterer are proportionality factors given by O~O =
¢-
0
200
400
600
800
1000
1200
phonon frequency [GHz]
Fig. l. Measured and calculated phonon transmission spectra of (100)-FZ-silicon and (11 l}-FZ-silicon. The frequency resolution is 2.5-5 GHz indicated by the bars in the magnified inset.
765
C. Wurster et al. /Physica B 219&220 (1996) 763-765
5-
6. Calibration The acoustic scattering cross section a of interstitial oxygen is determined by dividing the fit parameter c~0by the oxygen concentration c as obtained from IR spectroscopy. We find that the acoustic scattering cross section a is anisotropic:
frequency resolution --.-i1----
ex~
//
"o 4"
"o,
.~ 3-
FZ-silicon pulled frOm CZ-silicon
<111>-orientated J /V
v
"o.
experimental
//
t v
I t
trio0 -- (2.4 4- 0.3) × l0 -14 cm 2, 0"111
: (5.04- 1.5) × lO-14cm 2.
g2. ,~J i~
7. Detection limit Since silicon containing interstitial oxygen below 1015 cm -3 has not been available so far the maximum sensitivity of phonon spectroscopy is obtained from the phonon scattering by the 180-isotope (natural abundance: 0.2%) at 818 GHz. The evaluation of the phonon transmission spectrum of ( 111)-FZ-silicon pulled from CZ-silicon shown in Fig. 2 yields the following results: Assuming the same scattering cross section as obtained for 160 by calibration with the previous sample and taking the natural abundance of 180 we obtain concentrations of(7.0 ± 1.5) x 1013 cm 3 for 180 and (3.5 4- 0.7) x 1016cm -3 for 160. It is seen from Fig. 2 that the 180-resonance is just discernible from noise. A 160-concentration of (2.9 4- 0.6) × 1016cm 3 found by IR spectroscopy confirms the good agreement of both methods in this case.
^
8
0
~
250
measuredoxygen concentration: 160:3.5x10 ~ cm 3
500 750 phononfrequency[GHz]
1000
Fig. 2. Determination of the detection limit of 7 × 1013cm -3 from resonant phonon scattering by interstitial lSo at 818 GHz (abundance: 0.2%) by comparison of the measured and a calculated phonon transmission spectrum of FZ-pulled (111)-CZ-silicon. Thus, phonon spectroscopy is one order of magnitude more sensitive than IR spectroscopy [11] for the determination of small oxygen concentrations in silicon.
References 8. Conclusion Frequency-resolved phonon spectroscopy with superconducting tunnelingjunctions by interstitial oxygen at 878 GHz was found to be a very sensitive method to determine small oxygen concentrations in silicon. Measured and calculated phonon transmission spectra were compared using the absorption coefficient and the Lorentz line width as fit parameters. Because of the elastic character of the phonon scattering process effects of multiple scattering and the influence of the geometry of crystal, generator and detector have to be taken into account. Calibration of phonon spectroscopy was made by determination of the acoustic scattering cross section using IR-obtained data. The IR calibration of one sample makes it possible to determine the 160-concentration in another for which the junction details will be different. A detection limit in the upper 1013 cm -3 range was found by investigation of phonon scattering by the ISO-isotope.
[1] D. Wruck and P. Gaworzewski, phys. stat. sol. (a) 56 (1979) 557. [2] P. Gaworzewski, E. Hild, F.-G. Kirscht and L. Vecsernys, phys. stat. sol. (a) 85 (1984) 133. [3] P. Becker and G. Mana, Metrologia 31 (1994) 203. [4] D.R. Bosomworth, W. Hayes, A.R.L. Spray and G.D. Watkins, Proc. Roy. Soc. A 317 (1970) 133. [5] E. Dittrich, W. Scheitler and W. Eisenmenger, Jpn. J. Appl. Phys. 26 (Suppl. 3) (1987) 873. [6] W. Eisenmenger, Physical Acoustics, Vol. XII (Academic Press, New York, 1976) p. 79. [7] W. Scheitler, Thesis, University of Stuttgart (1989). [8] E. Dittrich, Thesis, University of Stuttgart (1989) [9] U. Werling and K.F. Renk, Phys. Rev. B 42 (1990) 1286. [10] A.A. Volkov, Yu.G. Goncharov, V.P. Kalinushkin, G.V. Kozlov and A.M. Prokhorov, Fiz. Tverd. Tela 32 (1990) 1249; Sov. Phys. Solid State 32 (1990) 799. [11] B. Pajot and B. Cales, Mat. Res. Soc. Symp. Proc. 59 (1986) 39.