Crystal pulling method for reducing defect density of section of heavily arsenic-doped crystal orientation monocrystalline silicon and monocrystalline silicon rod
By using a predetermined thermal field and adjusting the pulling speed and CR/SR ratio during the single-crystal silicon pulling process, the problem of heavily arsenic-doped silicon was solved. <111> The high defect density of crystal-oriented monocrystalline silicon has been addressed, enabling high-quality production of monocrystalline silicon rods and improving device yield.
Patent Information
- Application Number
- CN202511390669.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-09-26
- Publication Date
- 2025-11-28
AI Technical Summary
In heavily arsenic-doped <111> During the crystal pulling process of crystal-oriented single-crystal silicon, a large number of dislocations and arsenic precipitates exist in the crystal, resulting in high defect density, which affects the quality of the epitaxial layer and the yield of devices.
Single crystals are pulled using a predetermined hot zone in a single crystal furnace to increase the height of the hot zone. During the constant diameter process, the pulling speed is gradually reduced and the crystal rotation/boiler rotation ratio (CR/SR) is adjusted to control heat conduction and the solid-liquid interface temperature gradient, thereby suppressing the formation of point defects and impurity decorations.
By controlling the crystal growth rate and heat conduction, the cross-sectional defect density of single-crystal silicon rods can be reduced, the quality of heavily arsenic-doped silicon rods can be improved, and the quality of epitaxial layers and device yield can be increased.
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Figure CN121023641A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of single crystal silicon pulling, in particular to a single crystal pulling method for reducing the cross-section defect density of heavily doped arsenic <111> crystal silicon and a single crystal silicon rod. BACKGROUND
[0002] In the process of crystal growth, thermal dynamics fluctuation will promote the formation of arsenic clusters, precipitates and lattice defects decorated by impurities in the cross-section microstructure of the crystal rod, especially in the growth of heavily doped arsenic <111> crystal silicon by the Czochralski method, the thermal convection of the silicon solution will cause the small periodic fluctuation of the temperature and the segregation of arsenic at the solid-liquid interface, resulting in the periodic oscillation distribution of arsenic concentration in the crystal.
[0003] Specifically, in the process of growing heavily doped arsenic <111> crystal silicon by the Czochralski method, since the covalent radius of arsenic atom is larger than that of silicon atom, when a large number of arsenic atoms replace the silicon lattice positions, significant lattice mismatch stress will be introduced, resulting in the increase of local lattice constant of silicon (lattice expansion). In order to release the stress, a large number of dislocations and other extended defects will be formed in the crystal, the defect density increases, and arsenic atoms tend to aggregate around these defects, forming the so-called "impurity decoration" phenomenon. In microscopic observation, arsenic enrichment areas distributed along the dislocation lines or defect clusters in the form of etch pits can be observed. The distribution reflects the density and morphology of dislocations and other defects in the crystal. From the substrate preparation to the epitaxial process, the above defects and arsenic precipitates will become carrier recombination centers and epitaxial growth disturbance sources, resulting in the decrease of the quality of epitaxial layer, which is manifested as the significant deviation of the forward voltage drop (VF) of the device, and seriously reduces the yield of the final product. SUMMARY
[0004] Therefore, in view of the above problems, it is necessary to provide a single crystal pulling method for reducing the cross-section defect density of heavily doped arsenic <111> crystal silicon to improve the quality of heavily doped arsenic crystal rods. It is also necessary to provide a single crystal silicon rod.
[0005] The technical scheme adopted by the present application to solve the technical problems is: On the one hand, the present application provides a single crystal pulling method for reducing the cross-section defect density of heavily doped arsenic <111> crystal silicon, comprising the following steps: S1: using the predetermined thermal field of the single crystal furnace to pull the single crystal, so as to improve the height of the thermal zone in the pulling process; S2: in the constant diameter process, the distance from the liquid to the mouth is constant, the pulling speed of the crystal rod is gradually reduced according to the length of the crystal rod, and the ratio (CR / SR) of the crystal rotation to the pot rotation is adjusted, so that the heat conduction is uniformly transmitted along the radial direction of the crystal rod, and the generation of point defects and impurity decoration is inhibited.
[0006] Preferably, the "drawing crystal in the predetermined thermal field of a single crystal furnace" in S1 is specifically: keeping the total height of the middle insulation cylinder and the upper insulation cylinder unchanged, increasing the height of the middle insulation cylinder to a predetermined height, adjusting the height size of the upper insulation cylinder, and increasing the installation height of the heater support and decreasing the vertical heating height of the heater heating ring.
[0007] Preferably, the total height of the middle insulation cylinder and the upper insulation cylinder is 630mm-650mm, the predetermined height of the middle insulation cylinder is 555mm-565mm, the height size of the upper insulation cylinder is 75mm-85mm, the installation height of the heater support is 315mm-325mm, and the vertical heating height of the heater heating ring is 295mm-305mm.
[0008] Preferably, S2 is specifically: S21: when drawing from the constant diameter to a first predetermined length, the meniscus distance is constant, and the crystal bar is drawn using a constant first target pulling speed and a constant first target CR / SR; S22: when drawing from the first predetermined length to a second predetermined length, the meniscus distance is constant, and the crystal bar is drawn using a constant second target pulling speed and a constant second target CR / SR; S23: when drawing from the second predetermined length to a third predetermined length, the meniscus distance is constant, and the crystal bar is drawn using a constant third target pulling speed and a constant third target CR / SR; S24: when drawing from the third predetermined length to the constant diameter end, the meniscus distance is constant, and the crystal bar is drawn using a constant fourth target pulling speed and a constant fourth target CR / SR; The first target pulling speed, the second target pulling speed, the third target pulling speed, and the fourth target pulling speed decrease in turn.
[0009] Preferably, the meniscus distance is 40mm-45mm.
[0010] Preferably, in S21, the first predetermined length is 100mm-110mm, the first target pulling speed is 1mm / min, and the upper and lower limit ranges of the first target pulling speed are 1.5mm / min-0.3mm / min, and the first target CR / SR is 8rpm / 18rpm.
[0011] Preferably, in S22, the second predetermined length is 200mm-210mm, the second target pulling speed is 0.9mm / min, and the upper and lower limit ranges of the second target pulling speed are 1.2mm / min-0.5mm / min, and the first target CR / SR is 7rpm / 17rpm.
[0012] Preferably, in the S23, the third predetermined length is 300mm-310mm, the third target pulling speed is 0.75mm / min, and the upper and lower limit ranges of the third target pulling speed are 0.9mm / min-0.55mm / min, and the first target CR / SR is 6rpm / 16rpm.
[0013] Preferably, in the S24, the fourth target pulling speed is 0.68mm / min, and the upper and lower limit ranges of the fourth target pulling speed are 0.78mm / min-0.58mm / min, and the first target CR / SR is 6rpm / 15rpm.
[0014] In another aspect, the present application provides a single crystal silicon rod, which is drawn by the method for reducing the cross-section defect density of heavy-doped arsenic <111> crystal direction single crystal silicon.
[0015] Compared with the prior art, the present application has the following beneficial effects: The method for reducing the cross-section defect density of heavy-doped arsenic <111> crystal direction single crystal silicon provided by the present application first uses a predetermined thermal field of a single crystal furnace to draw a single crystal, so as to improve the height of the thermal zone in the crystal drawing process; in the constant diameter process, the liquid port distance is kept constant, the pulling speed of the crystal rod is gradually reduced according to the length of the crystal rod, and the ratio (CR / SR) of the crystal rotation to the pot rotation is adjusted, so as to control the growth rate of the crystal, the temperature gradient of the solid-liquid interface, and the deposition of the oxide, so that the heat conduction is uniformly transmitted along the radial direction of the crystal rod, and the point defects such as interstitial atoms and vacancies have more opportunities to diffuse outward during the crystal growth process, thereby inhibiting the generation of point defects and impurity decoration, reducing the cross-section defect density of the single crystal silicon rod, and improving the quality of the heavy-doped arsenic crystal rod. BRIEF DESCRIPTION OF DRAWINGS
[0016] Figure 1 The flow chart of the method for reducing the cross-section defect density of heavy-doped arsenic <111> crystal direction single crystal silicon provided by the present application.
[0017] Figure 2 The structure diagram of the predetermined thermal field of the single crystal furnace in the method embodiment of the present application.
[0018] Figure 3 The cross-section defect detection result diagram of the crystal rod obtained by the method embodiment of the present application.
[0019] Figure 4 The structure diagram of the predetermined thermal field of the single crystal furnace in the traditional method.
[0020] Figure 5 The cross-section defect detection result diagram of the crystal rod obtained by the traditional method.
[0021] In the figure: middle insulation cylinder 10, upper insulation cylinder 20, heater support 30, heater heating ring 40. DETAILED DESCRIPTION
[0022] In order to further understand the present application, the preferred embodiments of the present application are described below in conjunction with the examples, but it should be understood that these descriptions are only for further illustrating the features and advantages of the present application, and are not limitations to the claims of the present application.
[0023] Please refer to Figure 1 The present application provides a method for reducing the defect density of a heavy arsenic-doped <111> single crystal silicon section, comprising the following steps: S1: using a predetermined thermal field of a single crystal furnace to draw a single crystal, so as to improve the height of the thermal zone in the crystal drawing process; S2: in the constant diameter process, the liquid port distance is constant, the pulling speed of the crystal bar is gradually reduced according to the length of the crystal bar, and the ratio of the crystal rotation to the pot rotation (CR / SR) is adjusted, so that the heat conduction is uniformly transmitted along the radial direction of the crystal bar, and the generation of point defects and impurity decoration is inhibited.
[0024] Compared with the prior art, the present application has the beneficial effects that: First, using a predetermined thermal field of a single crystal furnace to draw a single crystal, so as to improve the height of the thermal zone in the crystal drawing process; then in the constant diameter process, the liquid port distance is constant, the pulling speed of the crystal bar is gradually reduced according to the length of the crystal bar, and the ratio of the crystal rotation to the pot rotation (CR / SR) is adjusted, so that the heat conduction is uniformly transmitted along the radial direction of the crystal bar, and the generation of point defects and impurity decoration is inhibited, the defect density of the single crystal silicon bar section is reduced, and the quality of the heavy arsenic-doped crystal bar is improved.
[0025] Specifically, by using a predetermined thermal field of a single crystal furnace to draw a single crystal, the height of the thermal zone of the crystal drawing process is increased, thereby reducing the transverse temperature gradient in the crystal near the crystallization interface, and the in-situ heat treatment effect is enhanced, which provides sufficient diffusion and recombination conditions for point defects such as self-interstitial atoms and vacancies in the crystal. Under the condition of the thermal field, the use of gradually reduced crystal drawing speed helps the solid-liquid interface to form a flat or slightly convex melt, reduces the thermal disturbance in the growth process, and weakens the forced convection of the melt, reduces the erosion intensity of the melt to the quartz crucible wall, and inhibits the corrosion rate and oxygen dissolution rate of the crucible. At the same time, with the segmented adjustment of the ratio of crystal rotation to pot rotation (CR / SR) with the drawing speed, a stable and symmetrical melt flow field is established to avoid the occurrence of severe or unstable turbulent flow. The process of stable control of oxygen transport promotes the oxygen volatilization of the solid-liquid interface. In addition, by keeping the liquid port distance constant throughout the crystal drawing process, the stability and consistency of the crystal growth environment are further ensured, thereby inhibiting the generation of point defects and impurity decoration, and improving the quality of the heavily doped arsenic crystal rod.
[0026] Further, the "drawing crystal using a predetermined thermal field of a single crystal furnace" in S1 is specifically: in the predetermined thermal field, under the premise of keeping the total height of the middle insulation cylinder 10 and the upper insulation cylinder 20 unchanged, the middle insulation cylinder 10 is increased to a predetermined height, the height size of the upper insulation cylinder 20 is adjusted, and the installation height of the heater support 30 is increased, and the vertical heating height of the heater heating ring 40 is reduced.
[0027] Specifically, in the present application, the single crystal furnace adopts a 1806 furnace type, in step S1, the total height of the middle insulation cylinder 10 and the upper insulation cylinder 20 is 630mm-650mm, the predetermined height of the middle insulation cylinder 10 is 555-565mm, the height size of the upper insulation cylinder 20 is 75mm-85mm, the installation height of the heater support 30 is 315mm-325mm, and the vertical heating height of the heater heating ring 40 is 295mm-305mm. Preferably, the total height of the middle insulation cylinder 10 and the upper insulation cylinder 20 is 640mm, the predetermined height of the middle insulation cylinder 10 is 560mm, the installation height of the heater support 30 is 320mm, and the vertical heating height of the heater heating ring 40 is 300mm.
[0028] Further, S2 is specifically: S21: from the beginning of the constant diameter to the first predetermined length, the liquid port distance is constant and unchanged, and the crystal rod is drawn using a constant first target drawing speed and a constant first target CR / SR, which ensures that the crystal growth interface forms a moderate supercooling degree to maintain the single crystal growth power; S22: When pulling from the first predetermined length to the second predetermined length, the liquid outlet distance remains constant, and the crystal rod is pulled using a constant second target pulling speed and a constant second target CR / SR to ensure the stability of melt convection, promote the effective volatilization of oxygen content and reduce its transport to the crystal center, while maintaining a flat or slightly convex solid-liquid interface morphology. S23: When pulling from the second predetermined length to the third predetermined length, the liquid outlet distance remains constant, and the crystal rod is pulled using a constant third target pulling speed and a constant third target CR / SR to ensure that the segregation of arsenic impurities at the solid-liquid interface tends to be stable, reducing concentration fluctuations, thereby inhibiting the formation of arsenic clusters and precipitates. S24: From the third predetermined length to the end of the equal diameter, the liquid outlet distance remains constant, and the crystal rod is pulled using a constant fourth target pulling speed and a constant fourth target CR / SR to ensure that the crystal stays in the high temperature zone of the single crystal furnace for a sufficient time, so that vacancies and interstitial atoms have enough time to diffuse and recombine, effectively reducing the overall defect density of the crystal. The first, second, third, and fourth target pulling speeds decrease sequentially. A higher first target pulling speed helps to quickly pass through the high-temperature region where a large number of point defects are generated. The pulling speed is gradually reduced in the later stages to prolong the residence time of the crystal in the high-temperature region, providing a more sufficient time window for the mutual diffusion and recombination of vacancies and interstitial atoms. At the same time, different pulling speeds are adapted to different CR / SR ratios to avoid violent and unstable turbulence, thereby smoothly controlling oxygen transport. Specifically, crystal rotation (CR) helps oxygen volatilize near the crystal growth interface, while pot rotation (SR) determines the intensity of oxygen transport from the crucible wall to the center of the melt. The oxygen "vaporization-transport" balance is dynamically regulated by adjusting the CR / SR ratio.
[0029] Furthermore, the liquid nozzle distance is 44mm-45mm, preferably 45mm. Compared to a smaller liquid nozzle distance, the liquid nozzle distance in this invention slows down the cooling rate of the crystal. It works synergistically with the "segmented reduction of pulling speed" to extend the residence time of the crystal in the high-temperature region, providing a sufficient time window for the mutual diffusion and recombination of vacancies and interstitial atoms.
[0030] Furthermore, in S21, the first predetermined length is 100mm-110mm, the first target pulling speed is 1mm / min, and the upper and lower limits of the first target pulling speed are 1.5mm / min-0.3mm / min, and the first target CR / SR is 8rpm / 18rpm.
[0031] Furthermore, in S22, the second predetermined length is 200mm-210mm, the second target pulling speed is 0.9mm / min, and the upper and lower limits of the second target pulling speed are 1.2mm / min-0.5mm / min, and the first target CR / SR is 7rpm / 17rpm.
[0032] Furthermore, in S23, the third predetermined length is 300mm-310mm, the third target pulling speed is 0.75mm / min, and the upper and lower limits of the third target pulling speed are 0.9mm / min-0.55mm / min, and the first target CR / SR is 6rpm / 16rpm.
[0033] Furthermore, in S24, the fourth target pulling speed is 0.68 mm / min, and the upper and lower limits of the fourth target pulling speed are 0.78 mm / min-0.58 mm / min, and the first target CR / SR is 6 rpm / 15 rpm.
[0034] On the other hand, the present invention provides a single-crystal silicon rod that reduces heavy arsenic doping as described in the preceding aspect. <111> It is produced by a crystal pulling method that measures the cross-sectional defect density of single-crystal silicon.
[0035] To further understand the present invention, the following examples of heavily arsenic-doped methods and comparative examples of conventional methods illustrate the present invention. <111> The pulling process of crystal-oriented monocrystalline silicon and the detection results of cross-sectional defects.
[0036] Example: Using an 1806 single crystal furnace, pull 5-inch heavily arsenic-doped crystals. <111> For crystal orientation single-crystal silicon rods, please refer to [link / reference]. Figure 2 The total height of the middle insulation cylinder 10 and the upper insulation cylinder 20 of the 1806 single crystal furnace is 640 mm. The predetermined height of the middle insulation cylinder 10 is 560 mm, the height of the upper insulation cylinder 20 is 80 mm, the installation height of the heater support 30 is 320 mm, and the vertical heating height of the heater heating ring 40 is 300 mm. During the crystal rod pulling process, the liquid outlet distance is constant at 45 mm. The target pulling speed setting and the upper and lower limits of the pulling speed during the constant diameter process are shown in Table 1. The crystal rotation / pot rotation ratio (CR / SR) is shown in Table 2. After obtaining the crystal rod, the crystal rod is rolled, cut, and sliced to obtain six silicon wafers of equal diameters of 0mm, 300mm, 600mm, 900mm, 1100mm, and 1400mm. The six silicon wafers are placed in a high-temperature heat treatment at 1100℃ for 2 hours and then subjected to preferential etching in Sirtl liquid for 3 minutes. The cross-sectional defect detection results are observed using an electron microscope, as shown in Figure 3.
[0037] Table 1
[0038] Table 2
[0039] Comparative example: Using an 1806 single crystal furnace, 5-inch heavily arsenic-doped crystals were pulled. <111> For crystal orientation single-crystal silicon rods, please refer to [link / reference]. Figure 4 The total height of the middle insulation cylinder 10 and the upper insulation cylinder 20 of the 1806 single crystal furnace is 640 mm. The predetermined height of the middle insulation cylinder 10 is 500 mm, the height of the upper insulation cylinder 20 is 140 mm, the installation height of the heater support 30 is 120 mm, and the vertical heating height of the heater heating ring 40 is 400 mm. During the crystal pulling process, the liquid outlet distance is constant at 30 mm. The target pulling speed settings during the constant diameter process are shown in Table 3. The ratio of CR / SR is shown in Table 4. After obtaining the crystal rod, the crystal rod is rolled, cut, and sliced to obtain six silicon wafers of equal diameters of 0mm, 300mm, 600mm, 900mm, 1100mm, and 1400mm. The six silicon wafers are placed in a high-temperature heat treatment at 1100℃ for 2 hours and then subjected to preferential etching with Sirtl liquid for 3 minutes. The cross-sectional defect detection results are observed with an electron microscope, as shown in Figure 5.
[0040] Table 3
[0041] Table 4
[0042] Please refer to Figure 5 It can be clearly observed that the cross-section of the crystal rod obtained in the comparative example contains micro-defects and impurities, with a relatively high defect density. Please refer to [link / reference needed]. Figure 3 It can be observed that the cross-section of the crystal rod obtained by the method embodiment of the present invention is free of impurity contamination and the defect density is 0. The above comparison proves that the present application effectively improves the performance of heavily arsenic-doped crystals. <111> The quality of crystal-oriented single-crystal silicon rods improves the yield rate of devices.
[0043] The above-disclosed embodiments are merely preferred embodiments of the present invention and should not be construed as limiting the scope of the invention. Those skilled in the art will understand that implementing all or part of the above-described embodiments and making equivalent changes in accordance with the claims of the present invention are still within the scope of the invention.
Claims
1. A method for reducing the defect density of a heavy arsenic <111> oriented single crystal silicon wafer, characterized in that, The method comprises the following steps: S1: using a predetermined thermal field of a single crystal furnace to draw a single crystal, so as to increase the height of the thermal zone of the crystal drawing process; S2: in the constant diameter process, the liquid port distance is constant, the drawing speed of the crystal bar is gradually reduced according to the length of the crystal bar, and the ratio of the crystal rotation to the pot rotation (CR / SR) is adjusted, so that the heat conduction is uniformly transmitted along the radial direction of the crystal bar, and the generation of point defects and impurity decoration is inhibited.
2. The method for reducing heavy arsenic doping as described in claim 1 <111> A crystal pulling method for determining the cross-sectional defect density of single-crystal silicon with specific crystal orientation, characterized in that... In the S1, the "drawing a single crystal using a predetermined thermal field of a single crystal furnace" specifically refers to keeping the total height of the middle insulation cylinder and the upper insulation cylinder unchanged in the predetermined thermal field, increasing the height of the middle insulation cylinder to a predetermined height, adjusting the height size of the upper insulation cylinder, increasing the installation height of the heater support, and reducing the vertical heating height of the heater heating ring.
3. The method of claim 2 wherein the crystal is a <111> oriented single crystal silicon crystal having a high arsenic concentration, and the crystal is grown by the Czochralski method. The total height of the middle insulation cylinder and the upper insulation cylinder is 630mm-650mm, the predetermined height of the middle insulation cylinder is 555mm-565mm, the height size of the upper insulation cylinder is 75mm-85mm, the installation height of the heater support is 315mm-325mm, and the vertical heating height of the heater heating ring is 295mm-305mm.
4. The method for reducing heavy arsenic doping as described in claim 1 <111> A crystal pulling method for determining the cross-sectional defect density of single-crystal silicon with specific crystal orientation, characterized in that... The S2 specifically comprises: S21: from the beginning of the constant diameter to the first predetermined length, the liquid port distance is constant, and the crystal bar is drawn using a constant first target drawing speed and a constant first target CR / SR; S22: from the first predetermined length to the second predetermined length, the liquid port distance is constant, and the crystal bar is drawn using a constant second target drawing speed and a constant second target CR / SR; S23: from the second predetermined length to the third predetermined length, the liquid port distance is constant, and the crystal bar is drawn using a constant third target drawing speed and a constant third target CR / SR; S24: from the third predetermined length to the end of the constant diameter, the liquid port distance is constant, and the crystal bar is drawn using a constant fourth target drawing speed and a constant fourth target CR / SR; The first target drawing speed, the second target drawing speed, the third target drawing speed and the fourth target drawing speed decrease in turn.
5. The method for reducing heavy arsenic doping as described in claim 2 <111> A crystal pulling method for determining the cross-sectional defect density of single-crystal silicon with specific crystal orientation, characterized in that... The liquid port distance is 40mm-45mm.
6. The method of claim 4 wherein the reducing of the defect density of the <111> oriented single crystal silicon ingot comprises the steps of: growing the <111> oriented single crystal silicon ingot to a diameter of at least 200 mm; and annealing the <111> oriented single crystal silicon ingot at a temperature of at least 1200 °C for at least 24 hours. In the S21, the first predetermined length is 100mm-110mm, the first target drawing speed is 1mm / min, and the upper and lower limit ranges of the first target drawing speed are 1.5mm / min-0.3mm / min, and the first target CR / SR is 8rpm / 18rpm.
7. The method of claim 4 wherein the crystal is grown with a reduced density of surface defects by reducing the concentration of oxygen in the melt to less than 20 ppma. In the S22, the second predetermined length is 200mm-210mm, the second target drawing speed is 0.9mm / min, and the upper and lower limit ranges of the second target drawing speed are 1.2mm / min-0.5mm / min, and the first target CR / SR is 7rpm / 17rpm.
8. The method of claim 4 wherein the reducing of the defect density of the <111> oriented single crystal silicon ingot comprises the steps of: growing the <111> oriented single crystal silicon ingot from the melt to a diameter of at least 200 mm; and annealing the <111> oriented single crystal silicon ingot at a temperature of at least 1200 °C for at least 24 hours. 0 In the S23, the third predetermined length is 300mm-310mm, the third target drawing speed is 0.75mm / min, and the upper and lower limit ranges of the third target drawing speed are 0.9mm / min-0.55mm / min, and the first target CR / SR is 6rpm / 16rpm.
9. The method for reducing heavy arsenic doping as described in claim 4 <111> A crystal pulling method for determining the cross-sectional defect density of single-crystal silicon with specific crystal orientation, characterized in that... In the S24, the fourth target drawing speed is 0.68 mm / min, and the upper and lower limit ranges of the fourth target drawing speed are 0.78 mm / min-0.58 mm / min, and the first target CR / SR is 6 rpm / 15 rpm.
10. A single crystal silicon ingot, characterized by, grown by a crystal pulling method for reducing the defect density of a heavy-arsenic <111> crystal orientation single crystal silicon cross section as claimed in any one of claims 1-9.
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