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Analysis of microdefects in a silicon single crystal by diffuse X-ray scattering using synchrotron radiation
810
Nuclear Instruments and Methods in Physics Research A246 (1986) 810-813 North-Holland, Amsterdam
A N A L Y S I S O F M I C R O D E F E C T S I N A S I L I C O N S I N G L E C R Y S T A L BY D I F F U S E X - R A Y SCATI'ERING USING SYNCHROTRON RADIATION H a n t e K I M ]), S h u n Ji G O T O H 2) T o s h i o T A K A H A S H I K I K U T A 2)
2> T e t s u y a I S H I K A W A -~> a n d Seishi
IJDepartment of Electronics, Faculty of Engineering, Korea University, Ogawa-cho, Kodaira, Tokyo 187, Japan 2~Department of Applied Physics, Faculty of Engineering, Uniuersity of Tokyo, Hongo, Bunl
Oxide precipitates (platelets in {100}) in Cz silicon single crystals induced by heat treatment at 750°C for 100 h and for 33 h have been investigated by diffuse X-ray scattering (Huang scattering). High angular resolution measurements of diffuse scattering have been carried out near the 400 reciprocal lattice point using a triple-crystal diffractometer in a parallel (n, -- n, n) setting. Diffuse X-ray scattering from oxide precipitates of several hundred hngstroms in size has been observed. The experimental results have been compared with the calculation based on the Huang scattering theory.
1. Introduction
Microdefects in silicon single crystals have been studied extensively by various techniques [1,2]. Information about the strain field around point defects and their clusters can be obtained by the technique of diffuse X-ray scattering. The size of the defects of oxygen clusters was observed from an integrated intensity of diffuse scattering by a double crystal diffractometer in a parallel setting [3]. Dislocation loops on {111 } planes were investigated by a triple crystal diffractometer in a parallel (n, - n , n) setting [4]. In this report, diffuse X-ray scattering from oxide precipitations in CZ silicon single crystals formed by heat treatment is described. High angular resolution measurements of diffuse scattering were performed by using a triple crystal diffractometer in a parallel (n, - n , n) setting with synchrotron radiation X-rays. The experimental results were compared with the calculation based on the Huang diffuse scattering theory.
2. Experimental
The experiment was carried out at the high precision X-ray optics station BL-15C of the Photon Factory. The experimental arrangement for diffuse X-ray scattering is shown schematically in fig. 1. As a preliminary crystal a Ge single crystal was used with the 220 reflection, and synchrotron radiation X-rays of wavelengths 1.0 ,~ were selected. In order to decrease the wavelength dispersion and to increase angular resolution, the triple crystal diffractometer in a parallel (n, - n , n) setting was used. The first, second and third crystals serve~as the mono0168-9002/86/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
chromator, the sample and the analyzer, respectively. The angular intensity distribution of X-rays scattered from the sample was measured by rotating the analyzer with an accuracy of 0.1 seconds of arc. For three crystals, silicon single crystal plates were used under the condition of the 400 symmetric Bragg case diffraction. 5R
•
Forecryst 220alGe - - ~ Monochromator Si 4 0 0 Ionitor Sample Si 400 Analyzer Si 400 Sc.counter Fig. 1. Schematic view of the measuring system for the diffuse X-ray scattering.
811
H. Kim et aL / Analysis of microdefects in a silicon single crystal
Here we denote 0s and 0A as angular deviations of the sample and analyzer from the Bragg angle, respectively. We also define q = K - h , where K is the scattering vector and h is the reciprocal lattice vector. The relation between 0s, 0A and q is given as
,
I liool,,
50
; ',1/)1 17' 4
(qx, % ) = (0A cos 0n, (0 A - 20B)sin 0B), where 0 B is the Bragg angle. The x and y coordinate axes are defined as the directions along h and perpendicular to h. The diffuse scattering intensity near the reciprocal lattice point in the direction parallel to the y-axis is measured by rotating 0s at a fixed 0A. The diffuse scattering intensity on the Ewals sphere is measured by changing 0A at fixed 0s. Three samples were used in the experiment. Sample l was an as-grown Czochralski silicon wafer of p-type with an interstitial oxygen concentration of 1018/cm 3. Samples II and III were of the same origin as the sample I. Sample II was heat-treated at 750°C for 100 h. It was determined by electron microscopy, chemical etching, and infrared spectroscopy that this sample contains square-shaped oxide precipitations in {100} planes with a concentration of about 10a2/cm 3 and a diagonal size of about 1000 ,~. Sample III was heat-treated at 750°C for 33 h. It contains oxide precipitation of the same type as sample II with a concentration of about 1 0 a l / c m 3 and diagonal size of about 400 A. U n d e r these heat treatment conditions, the other type of larger defects such as {111} loops and {110} loops were not induced.
3. Results and discussion
The diffuse scattering intensity distributions of samples I, II and III were measured near the 400 reciprocal lattice point in the (011) plane. Their iso-intensity contours are shown in fig. 2. The time required to obtain a contour map was about 1.5 h. The intensity contours of all samples show dynamical effects [4,5], that is, a main streak in the direction of the reciprocal lattice vector and pseudo-streaks in the directions which make the Bragg angle with the reciprocal lattice vector. Diffuse scattering caused by defects can be seen in samples II and III. Net diffuse scattering contours of samples II and III caused by defects without dynamical diffraction and thermal diffuse scattering etc, were obtained by subtracting the intensity of sample I, as shown in fig. 3. Asymmetry of contours can be observed in the direction of the reciprocal lattice vector ([100] direction). According to the Huang scattering theory [6] and previous experiments [7], the intensity distribution of diffuse scattering is divided into a symmetrical part and an antisymmetrical part with respect to q. We separated the measured diffuse scattering intensity into a symmetrical part and an antisymmetrical part. The symmetrical
t ,1oo,
(lOOi
,',X_
~'
/ "Jh" 7 '° fl;/,oo )
[
fi,,,,{
2x10-4,~ -1
2X'~0-4~-!
(a)
~xJt~l
2x10-4~-1
(b)
(c)
Fig. 2. Measured iso-lntensity contours near the 400 reciprocal lattice point in the (01]) plane. (a) Sample ! (no heat treatment); (b) sample II (750°C, 100 h); (c) sample IIl (750°C, 33 h). part of diffuse scattering contours of samples II and III are shown in fig. 4. The symmetrical part of the diffuse scattering along the [011] direction is shown in fig. 5. The double-logarithmic plots of the diffuse scattering intensity versus % / h shows the linear relation with slopes s = - 2 . This q - 2 dependence is a characteristic of Huang scattering. This means that the diffuse scattering contours shown in fig. 4 are the contours of Huang scattering caused by oxide precipitations. These experimental contours were compared with calculated contours on the basic of Huang scattering theory. The diffuse X-ray scattering contours were calculated on the
(lOOI
(lOOI
50
(0lt}
(011l
2×10-4~ -1
(a)
2x10-4~-1
(b)
Fig. 3. Net diffuse scattering intensity contours near the 400 reciprocal lattice point in the (011) plane. (a)Sample II (750°C, 100 h), (b) sample III (750°C, 33 h). V. RESEARCH APPLICATIONS
812
H. Kim et al. / Analysis of microdefects in a silicon single crystal
t [l oo)
oo)
Sphe r i c u [
loops
defects
n:{]O0} b=<]O0>
)
( (
>
(Oil)
[OllJ
(o) 2 x 1 0 - 4 ~ -1
2x10-4 ~,-1
(a)
[b)
Fig. 4. Symmetrical part of diffuse scattering (Huang scattering) near the 400 reciprocal lattice point in the (011) plane. (a) Sample II (750°C, 100 h), (b) sample III (750°C, 33 h).
assumptions of the model of spherical defects and the model of dislocation loops on {100} planes with Bergers vectors (100), as shown in fig. 6. Measured H u a n g diffuse scattering contours shown in fig. 4 do not agree with these theoretical contours. It seems that the strain
o~
10 5
o 750°C IOOH • 750°C 33H
¢.-.
([00~
(b)
Fig. 6. Calculated intensity contours of Huang scattering near the 400 reciprocal lattice point in the (011) plane. (a) Spherical defects; (b) dislocation loops with Burgers vector B = ~100) on {100} planes.
field around oxide precipitations is rather more complicated than the model of (100} loops, and further investigation is necessary. The measured a n d calculated antisymmetrical parts of diffuse scattering are shown in fig. 7. Measured contours show higher intensity for q . h > 0 and lower intensity for q . h < 0. F r o m theses results it is concluded that the strain field a r o u n d oxide precipitations is positive or in other words of interstitial type, a n d a good agreement between measured and calculated contours was found. The authors would like to t h a n k Dr. N. Inoue and the Atsugi Electrical C o m m u n i c a t i o n s Laboratory, NTT, for supplying the samples and valuable discussions. This study was performed through Special C o o r d i n a t i o n F u n d s for Promoting Science and Technology of Science and the Technology Agency.
tO lO ~
¢.-
10:
@, 102
1(
I
I
I irl+ll
10-4
i
i
l
lO-a
i
(a)
I
(b)
' ' 2x10-4~-1
(c)
q/h
Fig. 5. Huang diffuse scattering intensity near the 400 reciprocal lattice point in the [011] direction. Empty circle, sample II (750°C, 100 h); full circle, sample III~ (750°C, 33 h).
Fig. 7. Antisymmetrical part of diffuse scattering contours near the 400 reciprocal lattice point in the (011) plane. (a) Sample lI (750°C, 100 h); (b) sample III (750°C, 33 h); (c) calculated.
H. Kim et al. / Analysis of microdefects in a silicon single crystal
References [1] K. Wada, N. Inoue and K. Kohra, J. Cryst. Growth 49 (1980) 749. [2] A. Bourret, J. Thibault-Desseaux and D.N. Seidman, J. Appl. Phys. 55 (1984) 825.
813
[3] J.R. Pate1, J. Appl. Cryst. 8 (1975) 186. [4] A.A. Lomov, P. Zaumseil and U. Winter, Acta Cryst. A41 (1985) 223. [5] A. Iida and K. Kohra, Phys. Status Solidi A51 (1979) 533. [6] P.H. Dederichs, J. Phys. F3 (1973) 471. [7] B.C. Larson and W. Schmatz, Phys. Rev. B10 (1974) 2307.
V. RESEARCH APPLICATIONS
Nuclear Instruments and Methods in Physics Research A246 (1986) 810-813 North-Holland, Amsterdam
A N A L Y S I S O F M I C R O D E F E C T S I N A S I L I C O N S I N G L E C R Y S T A L BY D I F F U S E X - R A Y SCATI'ERING USING SYNCHROTRON RADIATION H a n t e K I M ]), S h u n Ji G O T O H 2) T o s h i o T A K A H A S H I K I K U T A 2)
2> T e t s u y a I S H I K A W A -~> a n d Seishi
IJDepartment of Electronics, Faculty of Engineering, Korea University, Ogawa-cho, Kodaira, Tokyo 187, Japan 2~Department of Applied Physics, Faculty of Engineering, Uniuersity of Tokyo, Hongo, Bunl
Oxide precipitates (platelets in {100}) in Cz silicon single crystals induced by heat treatment at 750°C for 100 h and for 33 h have been investigated by diffuse X-ray scattering (Huang scattering). High angular resolution measurements of diffuse scattering have been carried out near the 400 reciprocal lattice point using a triple-crystal diffractometer in a parallel (n, -- n, n) setting. Diffuse X-ray scattering from oxide precipitates of several hundred hngstroms in size has been observed. The experimental results have been compared with the calculation based on the Huang scattering theory.
1. Introduction
Microdefects in silicon single crystals have been studied extensively by various techniques [1,2]. Information about the strain field around point defects and their clusters can be obtained by the technique of diffuse X-ray scattering. The size of the defects of oxygen clusters was observed from an integrated intensity of diffuse scattering by a double crystal diffractometer in a parallel setting [3]. Dislocation loops on {111 } planes were investigated by a triple crystal diffractometer in a parallel (n, - n , n) setting [4]. In this report, diffuse X-ray scattering from oxide precipitations in CZ silicon single crystals formed by heat treatment is described. High angular resolution measurements of diffuse scattering were performed by using a triple crystal diffractometer in a parallel (n, - n , n) setting with synchrotron radiation X-rays. The experimental results were compared with the calculation based on the Huang diffuse scattering theory.
2. Experimental
The experiment was carried out at the high precision X-ray optics station BL-15C of the Photon Factory. The experimental arrangement for diffuse X-ray scattering is shown schematically in fig. 1. As a preliminary crystal a Ge single crystal was used with the 220 reflection, and synchrotron radiation X-rays of wavelengths 1.0 ,~ were selected. In order to decrease the wavelength dispersion and to increase angular resolution, the triple crystal diffractometer in a parallel (n, - n , n) setting was used. The first, second and third crystals serve~as the mono0168-9002/86/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
chromator, the sample and the analyzer, respectively. The angular intensity distribution of X-rays scattered from the sample was measured by rotating the analyzer with an accuracy of 0.1 seconds of arc. For three crystals, silicon single crystal plates were used under the condition of the 400 symmetric Bragg case diffraction. 5R
•
Forecryst 220alGe - - ~ Monochromator Si 4 0 0 Ionitor Sample Si 400 Analyzer Si 400 Sc.counter Fig. 1. Schematic view of the measuring system for the diffuse X-ray scattering.
811
H. Kim et aL / Analysis of microdefects in a silicon single crystal
Here we denote 0s and 0A as angular deviations of the sample and analyzer from the Bragg angle, respectively. We also define q = K - h , where K is the scattering vector and h is the reciprocal lattice vector. The relation between 0s, 0A and q is given as
,
I liool,,
50
; ',1/)1 17' 4
(qx, % ) = (0A cos 0n, (0 A - 20B)sin 0B), where 0 B is the Bragg angle. The x and y coordinate axes are defined as the directions along h and perpendicular to h. The diffuse scattering intensity near the reciprocal lattice point in the direction parallel to the y-axis is measured by rotating 0s at a fixed 0A. The diffuse scattering intensity on the Ewals sphere is measured by changing 0A at fixed 0s. Three samples were used in the experiment. Sample l was an as-grown Czochralski silicon wafer of p-type with an interstitial oxygen concentration of 1018/cm 3. Samples II and III were of the same origin as the sample I. Sample II was heat-treated at 750°C for 100 h. It was determined by electron microscopy, chemical etching, and infrared spectroscopy that this sample contains square-shaped oxide precipitations in {100} planes with a concentration of about 10a2/cm 3 and a diagonal size of about 1000 ,~. Sample III was heat-treated at 750°C for 33 h. It contains oxide precipitation of the same type as sample II with a concentration of about 1 0 a l / c m 3 and diagonal size of about 400 A. U n d e r these heat treatment conditions, the other type of larger defects such as {111} loops and {110} loops were not induced.
3. Results and discussion
The diffuse scattering intensity distributions of samples I, II and III were measured near the 400 reciprocal lattice point in the (011) plane. Their iso-intensity contours are shown in fig. 2. The time required to obtain a contour map was about 1.5 h. The intensity contours of all samples show dynamical effects [4,5], that is, a main streak in the direction of the reciprocal lattice vector and pseudo-streaks in the directions which make the Bragg angle with the reciprocal lattice vector. Diffuse scattering caused by defects can be seen in samples II and III. Net diffuse scattering contours of samples II and III caused by defects without dynamical diffraction and thermal diffuse scattering etc, were obtained by subtracting the intensity of sample I, as shown in fig. 3. Asymmetry of contours can be observed in the direction of the reciprocal lattice vector ([100] direction). According to the Huang scattering theory [6] and previous experiments [7], the intensity distribution of diffuse scattering is divided into a symmetrical part and an antisymmetrical part with respect to q. We separated the measured diffuse scattering intensity into a symmetrical part and an antisymmetrical part. The symmetrical
t ,1oo,
(lOOi
,',X_
~'
/ "Jh" 7 '° fl;/,oo )
[
fi,,,,{
2x10-4,~ -1
2X'~0-4~-!
(a)
~xJt~l
2x10-4~-1
(b)
(c)
Fig. 2. Measured iso-lntensity contours near the 400 reciprocal lattice point in the (01]) plane. (a) Sample ! (no heat treatment); (b) sample II (750°C, 100 h); (c) sample IIl (750°C, 33 h). part of diffuse scattering contours of samples II and III are shown in fig. 4. The symmetrical part of the diffuse scattering along the [011] direction is shown in fig. 5. The double-logarithmic plots of the diffuse scattering intensity versus % / h shows the linear relation with slopes s = - 2 . This q - 2 dependence is a characteristic of Huang scattering. This means that the diffuse scattering contours shown in fig. 4 are the contours of Huang scattering caused by oxide precipitations. These experimental contours were compared with calculated contours on the basic of Huang scattering theory. The diffuse X-ray scattering contours were calculated on the
(lOOI
(lOOI
50
(0lt}
(011l
2×10-4~ -1
(a)
2x10-4~-1
(b)
Fig. 3. Net diffuse scattering intensity contours near the 400 reciprocal lattice point in the (011) plane. (a)Sample II (750°C, 100 h), (b) sample III (750°C, 33 h). V. RESEARCH APPLICATIONS
812
H. Kim et al. / Analysis of microdefects in a silicon single crystal
t [l oo)
oo)
Sphe r i c u [
loops
defects
n:{]O0} b=<]O0>
)
( (
>
(Oil)
[OllJ
(o) 2 x 1 0 - 4 ~ -1
2x10-4 ~,-1
(a)
[b)
Fig. 4. Symmetrical part of diffuse scattering (Huang scattering) near the 400 reciprocal lattice point in the (011) plane. (a) Sample II (750°C, 100 h), (b) sample III (750°C, 33 h).
assumptions of the model of spherical defects and the model of dislocation loops on {100} planes with Bergers vectors (100), as shown in fig. 6. Measured H u a n g diffuse scattering contours shown in fig. 4 do not agree with these theoretical contours. It seems that the strain
o~
10 5
o 750°C IOOH • 750°C 33H
¢.-.
([00~
(b)
Fig. 6. Calculated intensity contours of Huang scattering near the 400 reciprocal lattice point in the (011) plane. (a) Spherical defects; (b) dislocation loops with Burgers vector B = ~100) on {100} planes.
field around oxide precipitations is rather more complicated than the model of (100} loops, and further investigation is necessary. The measured a n d calculated antisymmetrical parts of diffuse scattering are shown in fig. 7. Measured contours show higher intensity for q . h > 0 and lower intensity for q . h < 0. F r o m theses results it is concluded that the strain field a r o u n d oxide precipitations is positive or in other words of interstitial type, a n d a good agreement between measured and calculated contours was found. The authors would like to t h a n k Dr. N. Inoue and the Atsugi Electrical C o m m u n i c a t i o n s Laboratory, NTT, for supplying the samples and valuable discussions. This study was performed through Special C o o r d i n a t i o n F u n d s for Promoting Science and Technology of Science and the Technology Agency.
tO lO ~
¢.-
10:
@, 102
1(
I
I
I irl+ll
10-4
i
i
l
lO-a
i
(a)
I
(b)
' ' 2x10-4~-1
(c)
q/h
Fig. 5. Huang diffuse scattering intensity near the 400 reciprocal lattice point in the [011] direction. Empty circle, sample II (750°C, 100 h); full circle, sample III~ (750°C, 33 h).
Fig. 7. Antisymmetrical part of diffuse scattering contours near the 400 reciprocal lattice point in the (011) plane. (a) Sample lI (750°C, 100 h); (b) sample III (750°C, 33 h); (c) calculated.
H. Kim et al. / Analysis of microdefects in a silicon single crystal
References [1] K. Wada, N. Inoue and K. Kohra, J. Cryst. Growth 49 (1980) 749. [2] A. Bourret, J. Thibault-Desseaux and D.N. Seidman, J. Appl. Phys. 55 (1984) 825.
813
[3] J.R. Pate1, J. Appl. Cryst. 8 (1975) 186. [4] A.A. Lomov, P. Zaumseil and U. Winter, Acta Cryst. A41 (1985) 223. [5] A. Iida and K. Kohra, Phys. Status Solidi A51 (1979) 533. [6] P.H. Dederichs, J. Phys. F3 (1973) 471. [7] B.C. Larson and W. Schmatz, Phys. Rev. B10 (1974) 2307.
V. RESEARCH APPLICATIONS