- Email: [email protected]
Laser scattering experiments in VCz GaAs
Journal of Crystal Growth 210 (2000) 203}206
Laser scattering experiments in VCz GaAs M. Naumann, J. Donecker*, M. Neubert Institute of Crystal Growth, D-12489 Berlin, Max-Born-Strasse 2, Germany
Abstract The method of laser scattering tomography (LST) was adapted to investigate scatterers in semi-insulating GaAs grown by the vapour pressure controlled Czochralski (VCz) technique. The LST method was extended to evaluate quantitatively the scattering for macroscopic "elds. The LST images of as-grown VCz GaAs crystals showed a reduced number of scattering particles in comparison with conventional LEC crystals. The dependency of the total scattered intensities along a wafer radius and intensity histograms are discussed. ( 2000 Elsevier Science B.V. All rights reserved. PACS: 81.05.Ea; 61.72.Qq; 61.72.Ff; 78.30.Fs; 78.35.#i; 81.70.Fy Keywords: Gallium arsenide; Laser scattering tomography; Precipitates; Decorated defects
1. Introduction Vapour pressure controlled Czochralski (VCz) growth of semi-insulating GaAs promises to improve the quality of large GaAs crystals, especially the dislocation density. The lower temperature gradients and the control of arsenic pressure used by this growth technique in#uence other properties of the crystals, too. Here, we report on a proposal for quantitative studies of light scattering at the precipitates in the crystals by laser scattering tomography (LST). This method is well-accepted for studies of arsenic precipitates in LEC GaAs crystals [1}5]. The lower concentration of scatterers in the VCz crystals requires adapted LST techniques to recognize structures in the images. Moreover, LST is extended to characterize quantitatively macro-
* Corresponding author. Tel.: #49-30-6392-3090; fax: #4930-6392-3003. E-mail address: [email protected] (J. Donecker)
scopic dimensions of the crystals and to obtain statistically relevant information. 2. Experimentals The LST experiments were performed on 4A semi-insulating GaAs samples grown by the VCz technique [6]. Mainly halfwafers of about 4 mm thickness were used in the as-grown state. Both the large M1 0 0N surfaces and the small surface along a dividing diameter (mainly S1 1 0T) were chemically}mechanically polished. Fig. 1 shows the experimental arrangement. The beam of an Nd}YAG laser (c.w., 1 W, 1064 nm) is extended by a telescope. The subsequent anamorphotic optics consisting of a cylindrical and a spherical lens focuses the beam on the sample surface as a vertical line. The incident light irradiates the scatterers in a ribbon extended in the x}y plane to a few mm and in the z-direction with a di!raction-limited intensity pro"le with a full-width
0022-0248/00/$ - see front matter ( 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 0 2 4 8 ( 9 9 ) 0 0 6 7 9 - X
204
M. Naumann et al. / Journal of Crystal Growth 210 (2000) 203}206
3. Results
Fig. 1. Experimental set-up. 1 } laser, 2 } anamorphotic beam shaper, 3 } sample on translation stage 4, 5 } zoom microscope with CCD camera.
at half-maximum (FWHM) of about 15 lm. A zoom microscope images the irradiated scatterers on the target of a CCD matrix camera (688]512 pixels, 8 bit, C"1). Images with high resolution in large "elds in x- or y-direction are obtained by stringing adjacent images in a computer. For quantitative studies the intensities in the images have to be corrected for the inhomogeneity of the local irradiation in the y-direction and for the vignetting by the zoom microscope in the x}y plane. The di!raction-limited distribution of the irradiation intensity in z-direction spoils the proportionality between scattering cross-section and intensity of the image. This di$culty was removed by a procedure, which we called `depth integrationa. It means, the sample was translated relative to the "xed irradiation plane by a computercontrolled stage in the z-direction by *z. The images are added during the translation. The camera has to be moved accordingly to conserve the focus position in the irradiated plane in spite of the changing optical path in the sample for the imaging rays. In addition to the increased homogeneity of irradiation in the z-direction, there exist further advantages from the depth integration. It gives sharply focused images for ranges of depth up to some mm. Stereoscopic couples of depth-integrated images obtained for two di!erent directions of observation can be used for impressive visualizations of the spatial correlation of scatterers by usual stereoscopic means. Further, the depth integration acts like a projection of the scatterers to the x}y plane, and it can reveal hidden structures [7].
LST images obtained by using conventional experimental conditions show a lower precipitate concentration in VCz GaAs in comparison to the well-known images for LEC GaAs [1}5]. The LST images of VCz GaAs appear as nearly randomly distributed scatterers. It is di$cult to recognize the geometrical correlation of the scatterers without the use of the depth integration. Fig. 2 shows a depth-integrated image along a S1 1 0T radius of a (1 0 0) wafer. The original image with a capacity of about 6 MByte is prepared by the stringing of 20 corrected subimages. The di!erent arrangements of precipitates are shown evidently, e.g. in cells and lineages. To demonstrate the information capacity of the stripe, one has to imagine that for the perception of the single scatterers by the human eye, the image stripe has to be magni"ed to a length of more than 2 m. The addition of the intensity values i in a horizontal line of the camera pixels gives the total scattered intensity I, shown in Fig. 3 versus the radial distance r. The similarity of the curves for di!erent experimental conditions demonstrates the relevance of the radial dependency. The bump near i"40 in the upper curve presents the in#uence of too large *z intervals, if strong structures in the zdirection occur. In general, the half W-shape distribution is observed, well known for other properties of Czochralski-grown GaAs. To understand the radial dependency of I(r) we calculated the histograms of n(i)i versus the intensity i for the subimages. n(i) is the number of pixels detecting the intensity value i in the subimage. The n(i)i values represent the share of the pixels of intensity i to the total intensity I. Fig. 4 shows the histograms for typical subimages at di!erent radial positions indicated in Figs. 2 and 3 and the average for the full image in Fig. 2. The histograms of the other subimages lie in between these curves (exception: peripher subimage). Obviously, the main contributions to the total intensity I are due to the range i"10}70. It means that the large intensities do not contribute remarkably to the total intensity in contrast to their impressive appearance. The complicated di!erences of the curves of bright scatterers above i"50 are not discussed here.
M. Naumann et al. / Journal of Crystal Growth 210 (2000) 203}206
205
Fig. 3. Total intensities I for horizontal lines in Fig. 2 versus radial distance r for di!erent experimental conditions (e.g. *z"0.5 or 2.0 mm).
Fig. 4. Histograms of the product of the number of pixels n(i) times intensity i versus intensity i of selected subimages and the full image (mean) in Fig. 2.
Fig. 2. LST images of VCz GaAs obtained by stringing adjacent subimages along a wafer radius in the S1 1 0T direction in a stripe and typical subimages. Original dimension of the measured area: 3.3]48.6 mm2, integrated depth: *z"500 lm, intensities corrected for vignetting and laser irradiation inhomogeneity.
Because of the limited resolution of the optics, each scatterer is imaged onto several pixels of the camera with decrease in the intensity from its maximum. Therefore, an experimentally obtained n(i) versus i histogram is the result of the convolution of the true i distribution before imaging by the mean intensity histogram of a single scatterer due to the broadening. Since all measured intensities in the images result from convolution by the same function, we can compare the experimental histograms for n(i)i versus i, too. In the n(i)i versus i representation of Fig. 4, very similar curves with nearly equal maximum positions are observed below i"50. This means, the true n(i) distributions of the subimages di!er only by factors k independent of i. The scattered
206
M. Naumann et al. / Journal of Crystal Growth 210 (2000) 203}206
intensity is a measure of the volume v of the particle according to Rayleigh's law. Consequently, the relative v distribution of the precipitates is independent of r, rather the number of equally sized particles is changed by the factors k(r), and k(r) is found to be proportional to I(r). I(r) correlates coarsely with the average dislocation distance (the square root of the dislocation density). This result is restricted to scatterers observed in the dynamic range of our measurements. An enlarged dynamic range and improved evaluation procedures would be welcome to extract more information about the distribution of the volumes of the precipitates than was possible in this "rst attempt. We think the extended LST technique presented could become a valuable tool for quantitative precipitation studies in bulk GaAs, especially in qualities with low dislocation densities such as VCz and VGF crystals and for quantitative precipitate engineering studies.
Acknowledgements The authors are indebted to the colleagues of the Czochralski-semiconductor group of the institute
for growing the crystals and the preparation group for the surface preparation.
References [1] S. Kuma, Y. Otoki, K. Kurata, in: J.P. Fillard (Ed.), Defect Recognition and Image Processing, Elsevier, Amsterdam, 1985, pp. 19}25. [2] T. Ogawa, M. Nango, Rev. Sci. Instrum. 57 (1986) 1135. [3] T. Katsuma, H. Okada, T. Kikuta, T. Fukuda, Appl. Phys. A 42 (1987) 103. [4] J.P. Fillard, P. Gall, M. Castagne, J. Bonnafe, Solid State Phenom. 6&7 (1989) 403. [5] S. Kuma, Y. Otoki, in: J. Jiminez (Ed.), Defect Recognition and Image Processing, IOP Publishing, Bristol, Philadelphia, 1994; Inst. Phys. Conf. Ser. 49 (1995) 117. [6] P. Rudolph, M. Neubert, S. Arulkumaran, M. Seifert, Cryst. Res. Technol. 32 (1997) 135. [7] J. Donecker, G. Hempel, J. Kluge, M. Seifert, B. Lux, in: A.R. Mickelson (Ed.), Defect Recognition and Image Processing, IOP Publishing, Bristol and Philadelphia, 1995; Inst. Phys. Conf. Ser. 49 (1995) 349.
Laser scattering experiments in VCz GaAs M. Naumann, J. Donecker*, M. Neubert Institute of Crystal Growth, D-12489 Berlin, Max-Born-Strasse 2, Germany
Abstract The method of laser scattering tomography (LST) was adapted to investigate scatterers in semi-insulating GaAs grown by the vapour pressure controlled Czochralski (VCz) technique. The LST method was extended to evaluate quantitatively the scattering for macroscopic "elds. The LST images of as-grown VCz GaAs crystals showed a reduced number of scattering particles in comparison with conventional LEC crystals. The dependency of the total scattered intensities along a wafer radius and intensity histograms are discussed. ( 2000 Elsevier Science B.V. All rights reserved. PACS: 81.05.Ea; 61.72.Qq; 61.72.Ff; 78.30.Fs; 78.35.#i; 81.70.Fy Keywords: Gallium arsenide; Laser scattering tomography; Precipitates; Decorated defects
1. Introduction Vapour pressure controlled Czochralski (VCz) growth of semi-insulating GaAs promises to improve the quality of large GaAs crystals, especially the dislocation density. The lower temperature gradients and the control of arsenic pressure used by this growth technique in#uence other properties of the crystals, too. Here, we report on a proposal for quantitative studies of light scattering at the precipitates in the crystals by laser scattering tomography (LST). This method is well-accepted for studies of arsenic precipitates in LEC GaAs crystals [1}5]. The lower concentration of scatterers in the VCz crystals requires adapted LST techniques to recognize structures in the images. Moreover, LST is extended to characterize quantitatively macro-
* Corresponding author. Tel.: #49-30-6392-3090; fax: #4930-6392-3003. E-mail address: [email protected] (J. Donecker)
scopic dimensions of the crystals and to obtain statistically relevant information. 2. Experimentals The LST experiments were performed on 4A semi-insulating GaAs samples grown by the VCz technique [6]. Mainly halfwafers of about 4 mm thickness were used in the as-grown state. Both the large M1 0 0N surfaces and the small surface along a dividing diameter (mainly S1 1 0T) were chemically}mechanically polished. Fig. 1 shows the experimental arrangement. The beam of an Nd}YAG laser (c.w., 1 W, 1064 nm) is extended by a telescope. The subsequent anamorphotic optics consisting of a cylindrical and a spherical lens focuses the beam on the sample surface as a vertical line. The incident light irradiates the scatterers in a ribbon extended in the x}y plane to a few mm and in the z-direction with a di!raction-limited intensity pro"le with a full-width
0022-0248/00/$ - see front matter ( 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 0 2 4 8 ( 9 9 ) 0 0 6 7 9 - X
204
M. Naumann et al. / Journal of Crystal Growth 210 (2000) 203}206
3. Results
Fig. 1. Experimental set-up. 1 } laser, 2 } anamorphotic beam shaper, 3 } sample on translation stage 4, 5 } zoom microscope with CCD camera.
at half-maximum (FWHM) of about 15 lm. A zoom microscope images the irradiated scatterers on the target of a CCD matrix camera (688]512 pixels, 8 bit, C"1). Images with high resolution in large "elds in x- or y-direction are obtained by stringing adjacent images in a computer. For quantitative studies the intensities in the images have to be corrected for the inhomogeneity of the local irradiation in the y-direction and for the vignetting by the zoom microscope in the x}y plane. The di!raction-limited distribution of the irradiation intensity in z-direction spoils the proportionality between scattering cross-section and intensity of the image. This di$culty was removed by a procedure, which we called `depth integrationa. It means, the sample was translated relative to the "xed irradiation plane by a computercontrolled stage in the z-direction by *z. The images are added during the translation. The camera has to be moved accordingly to conserve the focus position in the irradiated plane in spite of the changing optical path in the sample for the imaging rays. In addition to the increased homogeneity of irradiation in the z-direction, there exist further advantages from the depth integration. It gives sharply focused images for ranges of depth up to some mm. Stereoscopic couples of depth-integrated images obtained for two di!erent directions of observation can be used for impressive visualizations of the spatial correlation of scatterers by usual stereoscopic means. Further, the depth integration acts like a projection of the scatterers to the x}y plane, and it can reveal hidden structures [7].
LST images obtained by using conventional experimental conditions show a lower precipitate concentration in VCz GaAs in comparison to the well-known images for LEC GaAs [1}5]. The LST images of VCz GaAs appear as nearly randomly distributed scatterers. It is di$cult to recognize the geometrical correlation of the scatterers without the use of the depth integration. Fig. 2 shows a depth-integrated image along a S1 1 0T radius of a (1 0 0) wafer. The original image with a capacity of about 6 MByte is prepared by the stringing of 20 corrected subimages. The di!erent arrangements of precipitates are shown evidently, e.g. in cells and lineages. To demonstrate the information capacity of the stripe, one has to imagine that for the perception of the single scatterers by the human eye, the image stripe has to be magni"ed to a length of more than 2 m. The addition of the intensity values i in a horizontal line of the camera pixels gives the total scattered intensity I, shown in Fig. 3 versus the radial distance r. The similarity of the curves for di!erent experimental conditions demonstrates the relevance of the radial dependency. The bump near i"40 in the upper curve presents the in#uence of too large *z intervals, if strong structures in the zdirection occur. In general, the half W-shape distribution is observed, well known for other properties of Czochralski-grown GaAs. To understand the radial dependency of I(r) we calculated the histograms of n(i)i versus the intensity i for the subimages. n(i) is the number of pixels detecting the intensity value i in the subimage. The n(i)i values represent the share of the pixels of intensity i to the total intensity I. Fig. 4 shows the histograms for typical subimages at di!erent radial positions indicated in Figs. 2 and 3 and the average for the full image in Fig. 2. The histograms of the other subimages lie in between these curves (exception: peripher subimage). Obviously, the main contributions to the total intensity I are due to the range i"10}70. It means that the large intensities do not contribute remarkably to the total intensity in contrast to their impressive appearance. The complicated di!erences of the curves of bright scatterers above i"50 are not discussed here.
M. Naumann et al. / Journal of Crystal Growth 210 (2000) 203}206
205
Fig. 3. Total intensities I for horizontal lines in Fig. 2 versus radial distance r for di!erent experimental conditions (e.g. *z"0.5 or 2.0 mm).
Fig. 4. Histograms of the product of the number of pixels n(i) times intensity i versus intensity i of selected subimages and the full image (mean) in Fig. 2.
Fig. 2. LST images of VCz GaAs obtained by stringing adjacent subimages along a wafer radius in the S1 1 0T direction in a stripe and typical subimages. Original dimension of the measured area: 3.3]48.6 mm2, integrated depth: *z"500 lm, intensities corrected for vignetting and laser irradiation inhomogeneity.
Because of the limited resolution of the optics, each scatterer is imaged onto several pixels of the camera with decrease in the intensity from its maximum. Therefore, an experimentally obtained n(i) versus i histogram is the result of the convolution of the true i distribution before imaging by the mean intensity histogram of a single scatterer due to the broadening. Since all measured intensities in the images result from convolution by the same function, we can compare the experimental histograms for n(i)i versus i, too. In the n(i)i versus i representation of Fig. 4, very similar curves with nearly equal maximum positions are observed below i"50. This means, the true n(i) distributions of the subimages di!er only by factors k independent of i. The scattered
206
M. Naumann et al. / Journal of Crystal Growth 210 (2000) 203}206
intensity is a measure of the volume v of the particle according to Rayleigh's law. Consequently, the relative v distribution of the precipitates is independent of r, rather the number of equally sized particles is changed by the factors k(r), and k(r) is found to be proportional to I(r). I(r) correlates coarsely with the average dislocation distance (the square root of the dislocation density). This result is restricted to scatterers observed in the dynamic range of our measurements. An enlarged dynamic range and improved evaluation procedures would be welcome to extract more information about the distribution of the volumes of the precipitates than was possible in this "rst attempt. We think the extended LST technique presented could become a valuable tool for quantitative precipitation studies in bulk GaAs, especially in qualities with low dislocation densities such as VCz and VGF crystals and for quantitative precipitate engineering studies.
Acknowledgements The authors are indebted to the colleagues of the Czochralski-semiconductor group of the institute
for growing the crystals and the preparation group for the surface preparation.
References [1] S. Kuma, Y. Otoki, K. Kurata, in: J.P. Fillard (Ed.), Defect Recognition and Image Processing, Elsevier, Amsterdam, 1985, pp. 19}25. [2] T. Ogawa, M. Nango, Rev. Sci. Instrum. 57 (1986) 1135. [3] T. Katsuma, H. Okada, T. Kikuta, T. Fukuda, Appl. Phys. A 42 (1987) 103. [4] J.P. Fillard, P. Gall, M. Castagne, J. Bonnafe, Solid State Phenom. 6&7 (1989) 403. [5] S. Kuma, Y. Otoki, in: J. Jiminez (Ed.), Defect Recognition and Image Processing, IOP Publishing, Bristol, Philadelphia, 1994; Inst. Phys. Conf. Ser. 49 (1995) 117. [6] P. Rudolph, M. Neubert, S. Arulkumaran, M. Seifert, Cryst. Res. Technol. 32 (1997) 135. [7] J. Donecker, G. Hempel, J. Kluge, M. Seifert, B. Lux, in: A.R. Mickelson (Ed.), Defect Recognition and Image Processing, IOP Publishing, Bristol and Philadelphia, 1995; Inst. Phys. Conf. Ser. 49 (1995) 349.