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Melt surface change measurement under different crucible rotations in Czochralski furnace using an image-processing method
Journal Pre-proofs Melt surface change measurement under different crucible rotations in Czochralski furnace using an image-processing method Yashun Xu, Xianshan Huang, Xutao Mo, Sihai Ma PII: DOI: Reference:
S0263-2241(20)30064-6 https://doi.org/10.1016/j.measurement.2020.107527 MEASUR 107527
To appear in:
Measurement
Received Date: Revised Date: Accepted Date:
26 October 2019 23 December 2019 16 January 2020
Please cite this article as: Y. Xu, X. Huang, X. Mo, S. Ma, Melt surface change measurement under different crucible rotations in Czochralski furnace using an image-processing method, Measurement (2020), doi: https://doi.org/ 10.1016/j.measurement.2020.107527
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2020 Elsevier Ltd. All rights reserved.
1
Melt surface change measurement under different crucible rotations in Czochralski furnace using an image-processing method Yashun Xu1, Xianshan Huang*2, Xutao Mo2，Sihai Ma1,3 1) School of Electrical and Information Engineering, Anhui University of Technology, Maanshan 243002, China 2) School of Mathematics and Physics, Anhui University of Technology, Maanshan 243002, China 3) Anhui Yixin Semiconductor Co., Ltd., Hefei 230000, China Abstract: Effect of different crucible rotations on the silicon melt surface in Czochralski furnace is studied using an image-based measurement system. The mathematical model on the relationship between the target feature in the image and the melt level is discussed. A new improved approach based on Otsu method is applied to segment the feature area from the imperfect image due to uneven illumination. The calibration experiment indicates that the measurement system has resolution of 0.00371 mm. The effectiveness experiment shows that system measurements are very accurate. The surfaces of silicon melt with different crucible rotation rates are measured and analyzed. The result reveals that the melt surface becomes a paraboloid shape with crucible rotation. Moreover, crucible rotations cause more fluctuation on the melt surface under less silicon melt mass. This work may provide us with an effective method to monitor the melt surface change during crystal growth. Key words: Melt surface; Czochralski furnace; Reflected image; Crucible rotations; Measurement
1 Introduction Czochralski (Cz) method of silicon single crystal growth is very important among all the techniques of manufacturing silicon single crystals[1]. To improve quality of the silicon single crystals produced by this method, measurement of surface melt flow in Cz furnace has always been a hot research issue. A great number of studies have been made to try to clarify the melt flow phenomena [2-10]. The wave patterns were observed in the 1980s [9] in Cz crystal growth system. Different forms of patterns appear on the melt surface in Cz crucible. Due to high temperature and closed environment of silicon in Cz furnace, experimental investigation of the melt flow activity is
* Corresponding author. E-mail address: [email protected]
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extremely difficult[11]. Therefore, many researchers have carried out experiments on Cz-type model [2], [6] and calculated melt flow by numerical simulations [5], [7], [8], [10]. A. Cramer et al. [2] used ultrasonic velocimetry immersed into the liquid metal to measure fluid velocities in a model of Cz puller. Their experiments revealed that an axisymmetric m = 0 mode and a mono-cellular m = 1 mode superimpose the convective pattern. Takeshi Azami et al. [4] found that the spacing between spokes of the 8-mm-deep-melt pattern was wider than that of the 3-mm-deep-melt pattern on the melt surface using Charge Coupled Device (CCD). Their result indicated that thermocapillary flow in the horizontal direction played an important role in forming the spoke pattern. According to massive three-dimensional numerical simulations of melt flow [8], the characteristic modes of wave patterns showed some general spatial features. Besides, dynamic process of the wave pattern was also analyzed, which indicated that traveling wave behavior of the characteristic mode pairs can attribute to the rotation of the original wave pattern. All the above studies give us better understanding of melt flow in Cz silicon single crystal system. However, there are few investigations on affecting the melt surface flow activities by measuring the melt surface level and shape with high temperature and closed Cz furnace previously. In fact, the melt surface level and shape can directly affect thermal gradient near the crystal melt interface which is one of the key factors affecting crystal quality and yield production according to defect theory of Voronkov [12]. Liang Zhu et al. [13] used a mirror image of the heat shield reflected on the melt surface to calculate the melt level. The reflection of the heat shield on the melt surface changed accordingly when melt level changed which can be captured by CCD camera. Senwei Xiang et al. [14] used image-based laser-triangulation system in the melt level measurement for Cz crystal growth. A line laser was used to project a laser line to the heat shield and melt surface which generated two laser bars then captured by camera. The distance between the two laser bars changed as the melt level changed. Both methods were effective and accurate to measure the melt level. However, due to the limit of the small observation window, the interference of the heat shield and the limitation of the laser life, laser-triangulation method brought the difficulties to installation and adjustment and increased equipment cost. Using only one camera to observe reflection of the heat shield can greatly overcome the difficulties. We mainly based on an image-processing method to extract the feature value in reflective image of the heat shield. The aim of our study is to investigate effect of different crucible rotations on melt surface in the real Cz furnace using CCD camera to observe the reflective image of the heat shield. Firstly, operating theory of the measurement system was introduced. The system was mainly based on camera vision, so we built a mathematical model on the relationship between target feature and the melt level. In our system, target feature was the area of the mirror image of the heat shield reflected on the melt surface. Then, we applied a unique image processing algorithm to segment the target. And as follow, the experiment result was shown on relationship between the detected target area and the melt level. Besides, an effectiveness experiment was performed to verify measurement performance. Finally, the comparison results of effect of silicon melt mass on surface flow driven by different crucible rotations were shown and analyzed.
2 System description 3D schematic illustration of the single crystal furnace structure is shown in Fig. 1. As we can see that the silicon rod is pulled from the silicon melt contained in heat crucible. Above the silicon melt with a gap distance, the heat shield is suspended. A camera is installed on the observation 2
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window to capture the image of the target. Fig. 2 is a schematic illustration observed from the camera. Because reflectivity of high-temperature melt surface reaches as high as 0.7 [14], the heat shield generates a reflected image on the melt surface. Particularly, the crescent part on the melt surface is the mirror image of the bottom rim of the heat shield. In fact, the crescent region is the target that we want to detect.
Fig. 1. Single crystal Cz furnace structure.
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Fig. 2. Schematic illustration of single silicon growth with Cz method.
In order to clarify the relationship between the target and the melt level, we first need to build their coordinate relation. As seen in Fig. 3(a), Cartesian coordinate system (X, Y, Z) called World Coordinate System (WCS) is set on the plane of inner bottom rim of the heat shield as follows: the coordinate origin (0, 0, 0) is the center of the upper green circle which denotes the inner bottom rim of the heat shield, while the lower red circle which denotes the reflected image of the inner bottom rim of the heat shield is located 2h below the green circle (h, the gap distance between the heat shield bottom and the melt surface level and less than 0, is regarded as melt level). The red circle is the same size and shape as the green one, assuming the melt surface is a stationary plane mirror. The second Cartesian coordinate system (X’, Y’, Z’) called Camera Coordinate System (CCS) is set on the image plane with X’-axis parallel to X-axis and Y’-axis forming an angle θ with the Y-axis. The relationship between WCS and CCS is given:
{
𝑋 = 𝑋′ 𝑌 = 𝑌′𝑐𝑜𝑠𝜃 ― 𝑍′𝑠𝑖𝑛𝜃 + 𝑎 𝑍 = 𝑌′𝑠𝑖𝑛𝜃 + 𝑍′𝑐𝑜𝑠𝜃 + 𝑏
(2.1)
where (0, a, b) is the coordinate origin of CCS in WCS. In WCS, the green circle is described by the following equation:
{𝑋
2
+ 𝑌2 = 𝑟2 𝑍=0
(2.2)
And the red one is given by the similar equation:
{𝑋
2
+ 𝑌2 = 𝑟2 𝑍 = 2ℎ
(2.3)
where r is the radius of the inner rim of the heat shield bottom. Therefore, by substituting equation (2.1) into equation (2.2) and (2.3) and simplifying them, the green circle and the red one can be described with the following equations in CCS, respectively:
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5
{
1
2
𝑋′ +
sin2 𝜃
2
(𝑍′ ― 𝑎𝑠𝑖𝑛𝜃 + 𝑏𝑐𝑜𝑠𝜃) = 𝑟2
(2.4)
𝑌′𝑠𝑖𝑛𝜃 + 𝑍′𝑐𝑜𝑠𝜃 + 𝑏 = 0
And
{
𝑋′2 +
1 2
sin 𝜃
2
(𝑍′ - 𝑎𝑠𝑖𝑛𝜃 - (2ℎ ― 𝑏)𝑐𝑜𝑠𝜃) = 𝑟2
(2.5)
𝑌′𝑠𝑖𝑛𝜃 + 𝑍′𝑐𝑜𝑠𝜃 + 𝑏 = 2ℎ
Fig. 3. Model of the heat shield bottom rim and reflected image on the melt surface.
Equations (2.4) and (2.5) indicate that in the image plane the green circle and the red one in WCS are regarded as the ellipses with the center coordinates (0, 𝑎𝑠𝑖𝑛𝜃 - 𝑏𝑐𝑜𝑠𝜃) and (0, 𝑎𝑠𝑖𝑛𝜃 +(2ℎ ―𝑏)𝑐𝑜𝑠𝜃) respectively. When angle θ equals
, center coordinates become (0,
0) and (0, 2ℎ𝑐𝑜𝑠𝜃) of the points O’ and Q as shown in Fig. 4. Therefore, distance between the points O’ and Q can be described as following equation: (2.6) ℎ′ = 2ℎ𝑐𝑜𝑠𝜃 A rectangle ABCD is plotted in Fig. 4, which is intersected at the points E, F, G and H with ellipses O’ and Q and where line segment AB is parallel to X' axis direction. Curve segment FG can be obtained by translating curve segment EH downward along Z'-axis direction, so the distance h’ between curve segment EH and FG in the Z'-axis direction is equal everywhere, then: 𝑘 × 𝑆𝐸𝐹𝐺𝐻 (2.7) ℎ′ = ― 𝑙𝐴𝐵 where SEFGH is the area of the enclosed graphic made of E, F, G and H, lAB is length of line segment and k is ratio of real area to pixel area. According to equations (2.6) and (2.7), we can obtain the relationship between the real melt level and the pixel area of the local crescent part in the camera image, as the following equation:
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ℎ= ― where
𝑘 × 𝑆𝐸𝐹𝐺𝐻 2𝑙𝐴𝐵𝑐𝑜𝑠𝜃
= ―𝐾 × 𝑆𝐸𝐹𝐺𝐻
(2.8)
, can be regarded as the measurement resolution of the system which
converts the pixel area to real gap distance. From equation (2.8), we can know that the melt level has linear relationship with the detected pixel area of the crescent part. Therefore, if we obtain area SEFGH, the melt level h can be calculated by equation (2.8). Note that the calibration process must be done to get parameter K.
Fig. 4. Simplified diagram of the heat shield bottom rim and reflected image on melt surface.
At first, an original image of the crescent part was captured by the camera as shown in Fig. 5(a). Then, we set a W×H rectangle region manually as the region of interest (ROI) shown in Fig. 5(b). Due to the uneven illumination of the image, using a multi-threshold[15] method and Otsu method [16] we were unable to segment the brightest area from ROI Image well, as seen in Fig. 6(a), (b) and (c). Therefore, we used a large template to smooth ROI Image and got a Smoothing Image. Then, we obtained Difference Image by subtracting Smoothing Image from ROI Image. Finally, we used Otsu method to binarize Difference Image and calculated the area of the target by counting the pixel number of the red region which can be seen in Fig. 6(d). The image result of our image processing method is quite good.
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Fig. 5. (a) An original image of the crescent part; (b) Set the detection area to W×H rectangle.
Fig. 6. (a) ROI image; (b) Thresholding image (a) by multi-threshold method; (c) Thresholding image (a) by Otsu method; (d) Thresholding image (a) by our method.
3 Results and Analysis In this section, three experiments were conducted. The first one was to observe relationship between the detected area of the target and the melt level which was performed before the crystal seeding process as the melt volume would not change. The second one was to test effectiveness of our measurement system. The third one was to compare the effects of two different masses of silicon melt on surface flow driven by different crucible rotations, which were performed before (much mass) and after (less mass) the growth process, respectively. In our system, a monochrome industrial camera of resolution 1292×964 pixels with gray levels of 8bits and camera lens of the focal length 50 mm was used. The acquisition frame rate was set into 5 fps (frame per second). The inner diameters of the crucible and the bottom rim of the heat shield in Cz puller were 686 mm and 360 mm, respectively.
3.1 Calibration experiment In this experiment, we performed the following steps to set up the relationship between the detected area and the crucible level (regarded as the melt level). 7
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First, the heat shield and the crucible were moved on an initial position while the crucible rotation rate was set to 0 rpm (round per minute). And the detected area of the target in the captured image processed was obtained, at the same time, the crucible position was recorded as the melt level because of constant melt volume by observing the ruler under the crucible. Then the crucible was moved downward a height from the initial position and the crucible position was recorded. To calculate the parameter K, we got a set of data sets on different crucible positions and the corresponding detected pixel areas. Finally, we used Least Square Method to fit the curve on the detected area and the crucible level and calculated the parameter K according to the data sets. The slope of the green line is -269.3 as seen the red points, which means the parameter K = 1/269.3 = 0.00371 mm/pixel, as shown in Fig.7. The relationship of the position and area can provide us a good way to measure and monitor the melt surface in real time.
Fig. 7. Relationship between the detected area and the crucible level.
3.2 Effectiveness experiment In order to test effectiveness of our method, the measurement system was performed when the crucible was moved down 1 mm continuously with a constant speed under the rotation rate of 0 rpm. With downward process of crucible, the camera captured the images continuously. The whole process lasted for 6 minutes, and the measured values were obtained by processing each 120 frames of pictures and then averaging the data. The comparison result between the measured value and the actual value is shown in Fig. 8. The red line of the measured value is highly consistent with the green line of the actual value. Fig. 8 shows differences between the measured values and the actual values which indicate an absolute error of less than 0.073 mm and the maximum relative error of 7.3% at 1 mm. The result also shows that to acquire more reliable measurement, the larger displacement of than 1 mm should be measured. In addition, if the absolute error of 0.073 mm is in all range of 30 mm, according to relative error of less than 5%, the measured displacement should be larger than 1.46 mm. This also reveals that the 8
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reliable range of our measurement system can be from 1.5 mm to 30 mm.
Fig. 8. Effectiveness experiment result.
3.3 Measurement experiment on the melt surface under different crucible rotations In this experiment, our purpose was to detect and analyze the melt surface change under different crucible rotations. According to our purpose, the melt level should be kept at the same position for image acquisition to control variables. However, during production process, the continuous consumption of melt inevitably led to the drop of the melt level. In order to keep the melt level constant, the lowered melt level needed to be supplemented by controlling the crucible. Because the regulation here was performed by manual intervention, a deviation was inevitable. The crucible rotation rates changed from 0 rpm to 12 rpm at intervals of 4 rpm, whereas the crucible location kept stable. Before the single silicon growth process the silicon melt mass in the crucible was 230 kg. And after that, there was about 20 kg left in the crucible. Fig. 9 shows the detected area fluctuations for different crucible rotations before and after the growth process, and corresponding frequency spectra. In Fig. 9(a) and (b), corresponding to before and after the crystal pulling, at crucible rotation rate of 0 rpm (red wave line), the average values of initial detected area are 26920 pixels and 27850 pixels respectively. At crucible rotation rate of 0 rpm, both the balance positions of the detected area fluctuations decrease with increase of the crucible rotation rate, but amplitude of the fluctuation suddenly increases in Fig.9 (b). As shown in Fig. 9(c), in the range of 0 to 0.5 Hz, amplitudes of frequency of the detected area are highly coincident with different crucible rotations. In the range of 0.5 to 2.5 Hz, the amplitudes at 0 rpm are the highest (red line), while the amplitudes at 8 rpm and 12 rpm are lower (blue line). As shown 9
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in Fig. 9(d), in the range of 0 to 0.5 Hz, main frequency of the detected area fluctuation is 0.059 Hz, 0.137 Hz, 0.205 Hz, respectively, and conversion frequencies of the crucible rotations are 0.067 Hz (4 rpm), 0.133 Hz (8 rpm), 0.2 Hz (12 rpm), respectively. By comparison, fluctuation frequency of the detected area is highly close to the crucible rotation rates, and amplitude of the main frequency of the detected area fluctuation at crucible rotation rate of 8 rpm (blue line) is the lowest, excluding 0 rpm. At crucible rotation rate of 12 rpm (blue-green line), in the range of 0.5 to 2.5 Hz, amplitudes of detected area fluctuations are substantially the maximum among all frequencies. Comparison of the results means that melt surface flow is more affected by the crucible rotation rate under less silicon melt mass than that under much.
Fig. 9. (a) Fluctuation of detected area with different rotation rates under much melt mass; (b) Fluctuation of detected area with different rotation rates under less melt mass; (c) Power spectral densities for the fluctuation in (a); (d) Power spectral densities for the fluctuation in (b).
Next are some explanations and analysis of above. Firstly, under much silicon melt mass, the average value of the detected area is 26920, which corresponds to the position of the crucible at 502.1 mm in Fig. 7. Under less melt mass, the average value of the detected area is 27850, while the position of the crucible has lost its reference value due to changing it during production. Since the calibration range in the calibration experiment is the crucible movement range by 525 - 495 = 30 mm, using the calibration coefficient of 269.3 obtained, the melt level movement can be 10
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calculated by (27850 - 26920) / 269.3＝3.45 mm. The result can be considered as detection valid due to less than the range of 30 mm. Then, at crucible rotation rate of none 0 rpm, the shape of the melt surface can be described by the well-known paraboloid shape of the liquid surface in absence of surface tension [17]. 𝑅2𝑤2 𝑤2 (3.1) 𝑧(𝑟,𝑤) = 𝑟2 ― + 𝑧0 2𝑔 4𝑔 where z0 is height of the still liquid, g is gravity acceleration, R is radius of the crucible, w is the rotation rate, r is radius variable, and z is height variable of the liquid. In our Cz puller, the r is fixed radius of the monitoring point location under the heat shield. Therefore, z is a unary quadratic function only with respect to w. However, the detected area which should have become larger at the location under the heat shield has become smaller as the rotation rate increases. As shown in Fig. 10, although the melt level under the heat shield moves downward with crucible rotation, the melt surface forms into a paraboloid mirror which magnifies the image of bottom inner rim of the heat shield. In Fig. 4, area SEFGH will decrease when the red curve becomes large while the green curve keeps constant. This is the reason that detected area decreases as the crucible rotation rate increases.
Fig. 10. Side view of the heat shield bottom and reflected image with and without crucible rotation.
Finally, under much silicon melt mass, thermal convection has dominant effect on the melt surface. As the growth process continues, the silicon melt mass has been decreasing, and external force driving effect is enhancing. This means that crucible rotation is severely detrimental to the melt level in later period of the growth process. Particularly, it is worthy noting that fluctuation of the melt free surface almost perfectly agrees with rotation of crucible, which might indicate either effect of rotation on the melt flow, or some imperfections in axis-symmetry of the furnace. Fluctuation generally looks more chaotic due to turbulent nature of the melt but such fluctuation is not seen well under much melt mass because of compensation on these imperfection by the large 11
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melt volume. Therefore, further study on splitting contribution of melt free surface deflection and surface curvature on detected area should be subject of future work.
4 Conclusions In this paper, we have investigated effect of different crucible rotations on silicon melt surface in Cz furnace, using an image-based measurement system. The results of calibration experiment and effectiveness experiment show that the system has high measurement resolution and accuracy. The result of the comparison experiments indicates that the crucible rotation has a significant impact in the melt surface, forming a paraboloid shape on it, and having great melt surface changes with crucible rotations, especially under less melt mass. In addition, further research on the contribution of melt surface deflection and surface curvature to splitting of the detection zone should be considered as a future work.
Acknowledgements We thank Dr. Chen Hongmei for her help in the language of this paper. This work was partially supported by the National Natural Science Foundation of China under Grant No. 11474003 and Grant No. 11504003, and Anhui Yixin Semiconductor Co., Ltd China.
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Conflict of Interest The authors declared that they have no conflicts of interest to this work.
Credit Author Statement Xianshan Huang: Conceptualization, Methodology， Yashun Xu: Software，Writing- Original draft preparation， Xutao Mo: Investigation，Writing- Reviewing and Editing, Sihai Ma1: Project administration.
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Highlights 1. A mathematical model between the feature image and the melt level is 18
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established. 2. The image processing algorithm perfectly segments the feature regions. 3. The measurement system has a high resolution of 0.00371 mm. 4. Abnormal changes in detected feature value are clearly analyzed. 5. The crucible rotations cause more fluctuations on the melt surface when the silicon melt mass is less.
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S0263-2241(20)30064-6 https://doi.org/10.1016/j.measurement.2020.107527 MEASUR 107527
To appear in:
Measurement
Received Date: Revised Date: Accepted Date:
26 October 2019 23 December 2019 16 January 2020
Please cite this article as: Y. Xu, X. Huang, X. Mo, S. Ma, Melt surface change measurement under different crucible rotations in Czochralski furnace using an image-processing method, Measurement (2020), doi: https://doi.org/ 10.1016/j.measurement.2020.107527
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2020 Elsevier Ltd. All rights reserved.
1
Melt surface change measurement under different crucible rotations in Czochralski furnace using an image-processing method Yashun Xu1, Xianshan Huang*2, Xutao Mo2，Sihai Ma1,3 1) School of Electrical and Information Engineering, Anhui University of Technology, Maanshan 243002, China 2) School of Mathematics and Physics, Anhui University of Technology, Maanshan 243002, China 3) Anhui Yixin Semiconductor Co., Ltd., Hefei 230000, China Abstract: Effect of different crucible rotations on the silicon melt surface in Czochralski furnace is studied using an image-based measurement system. The mathematical model on the relationship between the target feature in the image and the melt level is discussed. A new improved approach based on Otsu method is applied to segment the feature area from the imperfect image due to uneven illumination. The calibration experiment indicates that the measurement system has resolution of 0.00371 mm. The effectiveness experiment shows that system measurements are very accurate. The surfaces of silicon melt with different crucible rotation rates are measured and analyzed. The result reveals that the melt surface becomes a paraboloid shape with crucible rotation. Moreover, crucible rotations cause more fluctuation on the melt surface under less silicon melt mass. This work may provide us with an effective method to monitor the melt surface change during crystal growth. Key words: Melt surface; Czochralski furnace; Reflected image; Crucible rotations; Measurement
1 Introduction Czochralski (Cz) method of silicon single crystal growth is very important among all the techniques of manufacturing silicon single crystals[1]. To improve quality of the silicon single crystals produced by this method, measurement of surface melt flow in Cz furnace has always been a hot research issue. A great number of studies have been made to try to clarify the melt flow phenomena [2-10]. The wave patterns were observed in the 1980s [9] in Cz crystal growth system. Different forms of patterns appear on the melt surface in Cz crucible. Due to high temperature and closed environment of silicon in Cz furnace, experimental investigation of the melt flow activity is
* Corresponding author. E-mail address: [email protected]
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2
extremely difficult[11]. Therefore, many researchers have carried out experiments on Cz-type model [2], [6] and calculated melt flow by numerical simulations [5], [7], [8], [10]. A. Cramer et al. [2] used ultrasonic velocimetry immersed into the liquid metal to measure fluid velocities in a model of Cz puller. Their experiments revealed that an axisymmetric m = 0 mode and a mono-cellular m = 1 mode superimpose the convective pattern. Takeshi Azami et al. [4] found that the spacing between spokes of the 8-mm-deep-melt pattern was wider than that of the 3-mm-deep-melt pattern on the melt surface using Charge Coupled Device (CCD). Their result indicated that thermocapillary flow in the horizontal direction played an important role in forming the spoke pattern. According to massive three-dimensional numerical simulations of melt flow [8], the characteristic modes of wave patterns showed some general spatial features. Besides, dynamic process of the wave pattern was also analyzed, which indicated that traveling wave behavior of the characteristic mode pairs can attribute to the rotation of the original wave pattern. All the above studies give us better understanding of melt flow in Cz silicon single crystal system. However, there are few investigations on affecting the melt surface flow activities by measuring the melt surface level and shape with high temperature and closed Cz furnace previously. In fact, the melt surface level and shape can directly affect thermal gradient near the crystal melt interface which is one of the key factors affecting crystal quality and yield production according to defect theory of Voronkov [12]. Liang Zhu et al. [13] used a mirror image of the heat shield reflected on the melt surface to calculate the melt level. The reflection of the heat shield on the melt surface changed accordingly when melt level changed which can be captured by CCD camera. Senwei Xiang et al. [14] used image-based laser-triangulation system in the melt level measurement for Cz crystal growth. A line laser was used to project a laser line to the heat shield and melt surface which generated two laser bars then captured by camera. The distance between the two laser bars changed as the melt level changed. Both methods were effective and accurate to measure the melt level. However, due to the limit of the small observation window, the interference of the heat shield and the limitation of the laser life, laser-triangulation method brought the difficulties to installation and adjustment and increased equipment cost. Using only one camera to observe reflection of the heat shield can greatly overcome the difficulties. We mainly based on an image-processing method to extract the feature value in reflective image of the heat shield. The aim of our study is to investigate effect of different crucible rotations on melt surface in the real Cz furnace using CCD camera to observe the reflective image of the heat shield. Firstly, operating theory of the measurement system was introduced. The system was mainly based on camera vision, so we built a mathematical model on the relationship between target feature and the melt level. In our system, target feature was the area of the mirror image of the heat shield reflected on the melt surface. Then, we applied a unique image processing algorithm to segment the target. And as follow, the experiment result was shown on relationship between the detected target area and the melt level. Besides, an effectiveness experiment was performed to verify measurement performance. Finally, the comparison results of effect of silicon melt mass on surface flow driven by different crucible rotations were shown and analyzed.
2 System description 3D schematic illustration of the single crystal furnace structure is shown in Fig. 1. As we can see that the silicon rod is pulled from the silicon melt contained in heat crucible. Above the silicon melt with a gap distance, the heat shield is suspended. A camera is installed on the observation 2
3
window to capture the image of the target. Fig. 2 is a schematic illustration observed from the camera. Because reflectivity of high-temperature melt surface reaches as high as 0.7 [14], the heat shield generates a reflected image on the melt surface. Particularly, the crescent part on the melt surface is the mirror image of the bottom rim of the heat shield. In fact, the crescent region is the target that we want to detect.
Fig. 1. Single crystal Cz furnace structure.
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4
Fig. 2. Schematic illustration of single silicon growth with Cz method.
In order to clarify the relationship between the target and the melt level, we first need to build their coordinate relation. As seen in Fig. 3(a), Cartesian coordinate system (X, Y, Z) called World Coordinate System (WCS) is set on the plane of inner bottom rim of the heat shield as follows: the coordinate origin (0, 0, 0) is the center of the upper green circle which denotes the inner bottom rim of the heat shield, while the lower red circle which denotes the reflected image of the inner bottom rim of the heat shield is located 2h below the green circle (h, the gap distance between the heat shield bottom and the melt surface level and less than 0, is regarded as melt level). The red circle is the same size and shape as the green one, assuming the melt surface is a stationary plane mirror. The second Cartesian coordinate system (X’, Y’, Z’) called Camera Coordinate System (CCS) is set on the image plane with X’-axis parallel to X-axis and Y’-axis forming an angle θ with the Y-axis. The relationship between WCS and CCS is given:
{
𝑋 = 𝑋′ 𝑌 = 𝑌′𝑐𝑜𝑠𝜃 ― 𝑍′𝑠𝑖𝑛𝜃 + 𝑎 𝑍 = 𝑌′𝑠𝑖𝑛𝜃 + 𝑍′𝑐𝑜𝑠𝜃 + 𝑏
(2.1)
where (0, a, b) is the coordinate origin of CCS in WCS. In WCS, the green circle is described by the following equation:
{𝑋
2
+ 𝑌2 = 𝑟2 𝑍=0
(2.2)
And the red one is given by the similar equation:
{𝑋
2
+ 𝑌2 = 𝑟2 𝑍 = 2ℎ
(2.3)
where r is the radius of the inner rim of the heat shield bottom. Therefore, by substituting equation (2.1) into equation (2.2) and (2.3) and simplifying them, the green circle and the red one can be described with the following equations in CCS, respectively:
4
5
{
1
2
𝑋′ +
sin2 𝜃
2
(𝑍′ ― 𝑎𝑠𝑖𝑛𝜃 + 𝑏𝑐𝑜𝑠𝜃) = 𝑟2
(2.4)
𝑌′𝑠𝑖𝑛𝜃 + 𝑍′𝑐𝑜𝑠𝜃 + 𝑏 = 0
And
{
𝑋′2 +
1 2
sin 𝜃
2
(𝑍′ - 𝑎𝑠𝑖𝑛𝜃 - (2ℎ ― 𝑏)𝑐𝑜𝑠𝜃) = 𝑟2
(2.5)
𝑌′𝑠𝑖𝑛𝜃 + 𝑍′𝑐𝑜𝑠𝜃 + 𝑏 = 2ℎ
Fig. 3. Model of the heat shield bottom rim and reflected image on the melt surface.
Equations (2.4) and (2.5) indicate that in the image plane the green circle and the red one in WCS are regarded as the ellipses with the center coordinates (0, 𝑎𝑠𝑖𝑛𝜃 - 𝑏𝑐𝑜𝑠𝜃) and (0, 𝑎𝑠𝑖𝑛𝜃 +(2ℎ ―𝑏)𝑐𝑜𝑠𝜃) respectively. When angle θ equals
, center coordinates become (0,
0) and (0, 2ℎ𝑐𝑜𝑠𝜃) of the points O’ and Q as shown in Fig. 4. Therefore, distance between the points O’ and Q can be described as following equation: (2.6) ℎ′ = 2ℎ𝑐𝑜𝑠𝜃 A rectangle ABCD is plotted in Fig. 4, which is intersected at the points E, F, G and H with ellipses O’ and Q and where line segment AB is parallel to X' axis direction. Curve segment FG can be obtained by translating curve segment EH downward along Z'-axis direction, so the distance h’ between curve segment EH and FG in the Z'-axis direction is equal everywhere, then: 𝑘 × 𝑆𝐸𝐹𝐺𝐻 (2.7) ℎ′ = ― 𝑙𝐴𝐵 where SEFGH is the area of the enclosed graphic made of E, F, G and H, lAB is length of line segment and k is ratio of real area to pixel area. According to equations (2.6) and (2.7), we can obtain the relationship between the real melt level and the pixel area of the local crescent part in the camera image, as the following equation:
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ℎ= ― where
𝑘 × 𝑆𝐸𝐹𝐺𝐻 2𝑙𝐴𝐵𝑐𝑜𝑠𝜃
= ―𝐾 × 𝑆𝐸𝐹𝐺𝐻
(2.8)
, can be regarded as the measurement resolution of the system which
converts the pixel area to real gap distance. From equation (2.8), we can know that the melt level has linear relationship with the detected pixel area of the crescent part. Therefore, if we obtain area SEFGH, the melt level h can be calculated by equation (2.8). Note that the calibration process must be done to get parameter K.
Fig. 4. Simplified diagram of the heat shield bottom rim and reflected image on melt surface.
At first, an original image of the crescent part was captured by the camera as shown in Fig. 5(a). Then, we set a W×H rectangle region manually as the region of interest (ROI) shown in Fig. 5(b). Due to the uneven illumination of the image, using a multi-threshold[15] method and Otsu method [16] we were unable to segment the brightest area from ROI Image well, as seen in Fig. 6(a), (b) and (c). Therefore, we used a large template to smooth ROI Image and got a Smoothing Image. Then, we obtained Difference Image by subtracting Smoothing Image from ROI Image. Finally, we used Otsu method to binarize Difference Image and calculated the area of the target by counting the pixel number of the red region which can be seen in Fig. 6(d). The image result of our image processing method is quite good.
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Fig. 5. (a) An original image of the crescent part; (b) Set the detection area to W×H rectangle.
Fig. 6. (a) ROI image; (b) Thresholding image (a) by multi-threshold method; (c) Thresholding image (a) by Otsu method; (d) Thresholding image (a) by our method.
3 Results and Analysis In this section, three experiments were conducted. The first one was to observe relationship between the detected area of the target and the melt level which was performed before the crystal seeding process as the melt volume would not change. The second one was to test effectiveness of our measurement system. The third one was to compare the effects of two different masses of silicon melt on surface flow driven by different crucible rotations, which were performed before (much mass) and after (less mass) the growth process, respectively. In our system, a monochrome industrial camera of resolution 1292×964 pixels with gray levels of 8bits and camera lens of the focal length 50 mm was used. The acquisition frame rate was set into 5 fps (frame per second). The inner diameters of the crucible and the bottom rim of the heat shield in Cz puller were 686 mm and 360 mm, respectively.
3.1 Calibration experiment In this experiment, we performed the following steps to set up the relationship between the detected area and the crucible level (regarded as the melt level). 7
8
First, the heat shield and the crucible were moved on an initial position while the crucible rotation rate was set to 0 rpm (round per minute). And the detected area of the target in the captured image processed was obtained, at the same time, the crucible position was recorded as the melt level because of constant melt volume by observing the ruler under the crucible. Then the crucible was moved downward a height from the initial position and the crucible position was recorded. To calculate the parameter K, we got a set of data sets on different crucible positions and the corresponding detected pixel areas. Finally, we used Least Square Method to fit the curve on the detected area and the crucible level and calculated the parameter K according to the data sets. The slope of the green line is -269.3 as seen the red points, which means the parameter K = 1/269.3 = 0.00371 mm/pixel, as shown in Fig.7. The relationship of the position and area can provide us a good way to measure and monitor the melt surface in real time.
Fig. 7. Relationship between the detected area and the crucible level.
3.2 Effectiveness experiment In order to test effectiveness of our method, the measurement system was performed when the crucible was moved down 1 mm continuously with a constant speed under the rotation rate of 0 rpm. With downward process of crucible, the camera captured the images continuously. The whole process lasted for 6 minutes, and the measured values were obtained by processing each 120 frames of pictures and then averaging the data. The comparison result between the measured value and the actual value is shown in Fig. 8. The red line of the measured value is highly consistent with the green line of the actual value. Fig. 8 shows differences between the measured values and the actual values which indicate an absolute error of less than 0.073 mm and the maximum relative error of 7.3% at 1 mm. The result also shows that to acquire more reliable measurement, the larger displacement of than 1 mm should be measured. In addition, if the absolute error of 0.073 mm is in all range of 30 mm, according to relative error of less than 5%, the measured displacement should be larger than 1.46 mm. This also reveals that the 8
9
reliable range of our measurement system can be from 1.5 mm to 30 mm.
Fig. 8. Effectiveness experiment result.
3.3 Measurement experiment on the melt surface under different crucible rotations In this experiment, our purpose was to detect and analyze the melt surface change under different crucible rotations. According to our purpose, the melt level should be kept at the same position for image acquisition to control variables. However, during production process, the continuous consumption of melt inevitably led to the drop of the melt level. In order to keep the melt level constant, the lowered melt level needed to be supplemented by controlling the crucible. Because the regulation here was performed by manual intervention, a deviation was inevitable. The crucible rotation rates changed from 0 rpm to 12 rpm at intervals of 4 rpm, whereas the crucible location kept stable. Before the single silicon growth process the silicon melt mass in the crucible was 230 kg. And after that, there was about 20 kg left in the crucible. Fig. 9 shows the detected area fluctuations for different crucible rotations before and after the growth process, and corresponding frequency spectra. In Fig. 9(a) and (b), corresponding to before and after the crystal pulling, at crucible rotation rate of 0 rpm (red wave line), the average values of initial detected area are 26920 pixels and 27850 pixels respectively. At crucible rotation rate of 0 rpm, both the balance positions of the detected area fluctuations decrease with increase of the crucible rotation rate, but amplitude of the fluctuation suddenly increases in Fig.9 (b). As shown in Fig. 9(c), in the range of 0 to 0.5 Hz, amplitudes of frequency of the detected area are highly coincident with different crucible rotations. In the range of 0.5 to 2.5 Hz, the amplitudes at 0 rpm are the highest (red line), while the amplitudes at 8 rpm and 12 rpm are lower (blue line). As shown 9
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in Fig. 9(d), in the range of 0 to 0.5 Hz, main frequency of the detected area fluctuation is 0.059 Hz, 0.137 Hz, 0.205 Hz, respectively, and conversion frequencies of the crucible rotations are 0.067 Hz (4 rpm), 0.133 Hz (8 rpm), 0.2 Hz (12 rpm), respectively. By comparison, fluctuation frequency of the detected area is highly close to the crucible rotation rates, and amplitude of the main frequency of the detected area fluctuation at crucible rotation rate of 8 rpm (blue line) is the lowest, excluding 0 rpm. At crucible rotation rate of 12 rpm (blue-green line), in the range of 0.5 to 2.5 Hz, amplitudes of detected area fluctuations are substantially the maximum among all frequencies. Comparison of the results means that melt surface flow is more affected by the crucible rotation rate under less silicon melt mass than that under much.
Fig. 9. (a) Fluctuation of detected area with different rotation rates under much melt mass; (b) Fluctuation of detected area with different rotation rates under less melt mass; (c) Power spectral densities for the fluctuation in (a); (d) Power spectral densities for the fluctuation in (b).
Next are some explanations and analysis of above. Firstly, under much silicon melt mass, the average value of the detected area is 26920, which corresponds to the position of the crucible at 502.1 mm in Fig. 7. Under less melt mass, the average value of the detected area is 27850, while the position of the crucible has lost its reference value due to changing it during production. Since the calibration range in the calibration experiment is the crucible movement range by 525 - 495 = 30 mm, using the calibration coefficient of 269.3 obtained, the melt level movement can be 10
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calculated by (27850 - 26920) / 269.3＝3.45 mm. The result can be considered as detection valid due to less than the range of 30 mm. Then, at crucible rotation rate of none 0 rpm, the shape of the melt surface can be described by the well-known paraboloid shape of the liquid surface in absence of surface tension [17]. 𝑅2𝑤2 𝑤2 (3.1) 𝑧(𝑟,𝑤) = 𝑟2 ― + 𝑧0 2𝑔 4𝑔 where z0 is height of the still liquid, g is gravity acceleration, R is radius of the crucible, w is the rotation rate, r is radius variable, and z is height variable of the liquid. In our Cz puller, the r is fixed radius of the monitoring point location under the heat shield. Therefore, z is a unary quadratic function only with respect to w. However, the detected area which should have become larger at the location under the heat shield has become smaller as the rotation rate increases. As shown in Fig. 10, although the melt level under the heat shield moves downward with crucible rotation, the melt surface forms into a paraboloid mirror which magnifies the image of bottom inner rim of the heat shield. In Fig. 4, area SEFGH will decrease when the red curve becomes large while the green curve keeps constant. This is the reason that detected area decreases as the crucible rotation rate increases.
Fig. 10. Side view of the heat shield bottom and reflected image with and without crucible rotation.
Finally, under much silicon melt mass, thermal convection has dominant effect on the melt surface. As the growth process continues, the silicon melt mass has been decreasing, and external force driving effect is enhancing. This means that crucible rotation is severely detrimental to the melt level in later period of the growth process. Particularly, it is worthy noting that fluctuation of the melt free surface almost perfectly agrees with rotation of crucible, which might indicate either effect of rotation on the melt flow, or some imperfections in axis-symmetry of the furnace. Fluctuation generally looks more chaotic due to turbulent nature of the melt but such fluctuation is not seen well under much melt mass because of compensation on these imperfection by the large 11
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melt volume. Therefore, further study on splitting contribution of melt free surface deflection and surface curvature on detected area should be subject of future work.
4 Conclusions In this paper, we have investigated effect of different crucible rotations on silicon melt surface in Cz furnace, using an image-based measurement system. The results of calibration experiment and effectiveness experiment show that the system has high measurement resolution and accuracy. The result of the comparison experiments indicates that the crucible rotation has a significant impact in the melt surface, forming a paraboloid shape on it, and having great melt surface changes with crucible rotations, especially under less melt mass. In addition, further research on the contribution of melt surface deflection and surface curvature to splitting of the detection zone should be considered as a future work.
Acknowledgements We thank Dr. Chen Hongmei for her help in the language of this paper. This work was partially supported by the National Natural Science Foundation of China under Grant No. 11474003 and Grant No. 11504003, and Anhui Yixin Semiconductor Co., Ltd China.
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Conflict of Interest The authors declared that they have no conflicts of interest to this work.
Credit Author Statement Xianshan Huang: Conceptualization, Methodology， Yashun Xu: Software，Writing- Original draft preparation， Xutao Mo: Investigation，Writing- Reviewing and Editing, Sihai Ma1: Project administration.
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Highlights 1. A mathematical model between the feature image and the melt level is 18
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established. 2. The image processing algorithm perfectly segments the feature regions. 3. The measurement system has a high resolution of 0.00371 mm. 4. Abnormal changes in detected feature value are clearly analyzed. 5. The crucible rotations cause more fluctuations on the melt surface when the silicon melt mass is less.
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