Method for producing ingots in an ingot pulling apparatus and method for selecting side heater length for such an apparatus

By simulating and optimizing side heater length in ingot pullers, the method addresses inefficiencies in conventional systems, achieving reduced oxygen input and improved thermal efficiency for high-quality silicon ingot production.

JP7789065B2Active Publication Date: 2025-12-19GLOBALWAFERS CO LTD
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Patent Information

Application Number
JP2023528345
Authority / Receiving Office
JP · JP
Patent Type
Patents
Current Assignee / Owner
Filing Date
2020-11-12
Publication Date
2025-12-19
Estimated Expiration
2040-11-12

AI Technical Summary

Technical Problem

Conventional ingot pulling apparatuses face inefficiencies due to long side heaters that increase energy consumption, reduce thermal efficiency, and introduce excessive oxygen into the melt, necessitating costly magnetic field applications to manage oxygen input.

Method used

Selecting the side heater length in ingot pullers through temperature simulations to optimize crucible temperature profiles, reducing oxygen input and energy consumption by shortening the side heater length.

Benefits of technology

Reduces oxygen incorporation into ingots, enhances thermal efficiency, and maintains consistent resistivity, producing high-quality silicon ingots with reduced thermal donors and defects.

✦ Generated by Eureka AI based on patent content.

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Patent Text Reader

Abstract

A method for producing an ingot in an ingot puller is disclosed. A temperature simulation is performed by varying the length of a side heater of the ingot puller in the temperature simulation. An ingot puller having a selected side heater length is provided. A seed crystal is lowered into a melt in a crucible of the ingot puller, and an ingot is removed from the melt.
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Description

[Technical Field]

[0001] The field of the disclosure relates to methods of producing ingots in ingot pullers, and more particularly to methods of producing ingots involving selection of ingot puller side heater lengths for such systems. [Background technology]

[0002] Some conventional ingot pulling apparatuses include relatively long side heaters in the ingot pulling hot zone. To achieve a desired melt temperature profile and reduce oxygen input into the melt, insulation toward the bottom of the hot zone is removed. Removing the insulation can lower the temperature of the crucible floor, reducing oxygen dissolution from the crucible into the melt. However, removing the insulation increases the energy input of the side heaters, thereby reducing thermal efficiency. Furthermore, when raising the crucible during crystal growth, the relatively long heaters can heat the bottom of the crucible and the shaft used to raise the crucible, further reducing the energy efficiency of the process.

[0003] Other methods for reducing oxygen input from the crucible include applying a magnetic field to the silicon melt during ingot growth to slow the melt flow and transport the oxygen-rich melt from the melt-crucible interface to the melt-ingot interface, which can involve significant capital and increased operating costs to generate the magnetic field.

[0004] There is a need for a method of manufacturing ingots that reduces oxygen input from the crucible, is relatively thermally efficient, and is adaptable to a variety of ingot pulling hot zones.

[0005] This section is intended to introduce the reader to various aspects of technology that may be related to various aspects of the present disclosure, as described and disclosed below. This description is believed to be helpful in providing the reader with background information to facilitate a better understanding of the various aspects of the present disclosure. As such, it should be understood that these statements are to be read in this light, and not as admissions of prior art. Summary of the Invention

[0006] One aspect of the present disclosure is directed to a method for producing an ingot in an ingot puller. An ingot puller for producing an ingot is provided. The ingot puller includes a crucible for holding a silicon melt. The crucible has a floor and a sidewall extending from the floor. The ingot puller includes a growth chamber for extracting a silicon ingot from the melt along a pulling axis. The ingot puller includes an elevator mechanism for raising and lowering the crucible relative to the pulling axis during crystal growth. The ingot puller includes a bottom heater disposed below the floor of the crucible. A length of a side heater disposed radially outward of the crucible sidewall is selected. Selecting the length of the side heater includes modeling a temperature profile of the crucible of the ingot puller during removal of the ingot from the silicon melt in two or more temperature simulations. The length of the side heater is varied during the temperature simulations. A length of the side heater is selected based on the temperature of the crucible floor during two or more temperature simulations. A side heater is provided that is disposed radially outward of the crucible side wall. The side heater has a selected side heater length. A silicon melt is formed in the crucible. The melt contacts the seed crystal. An ingot is removed from the silicon melt.

[0007] Yet another aspect of the present disclosure is directed to a method for selecting a side heater length for an ingot puller. The ingot puller includes a crucible for holding a silicon melt. The crucible has a floor and a sidewall extending from the floor. The temperature of the crucible during crystal growth in the ingot puller is simulated with an ingot puller including a side heater having a first length. The temperature of the crucible during crystal growth in the ingot puller is simulated with an ingot puller including a side heater having a second length. The temperature of the crucible during the temperature simulation in which the side heater has the first length is compared with the temperature of the crucible during the temperature simulation in which the side heater has the second length. A heater length is selected based on the comparison of the temperature of the crucible during the temperature simulation in which the side heater has the first length with the temperature of the crucible during the temperature simulation in which the side heater has the second length.

[0008] Various refinements of the features mentioned with respect to the above aspects of the present disclosure exist. Additional features may also be incorporated into the above aspects of the present disclosure as well. These refinements and additional features may exist individually or in any combination. For example, the various features described below in connection with any of the illustrated embodiments of the present disclosure may be incorporated, alone or in any combination, into any of the above aspects of the present disclosure. [Brief explanation of the drawings]

[0009] [Figure 1] FIG. 2 is a cross-sectional view of the ingot pulling apparatus with the crucible in the lowest position.

[0010] [Figure 2] FIG. 1 is a cross-sectional view of an ingot pulling apparatus during ingot growth.

[0011] [Figure 3] FIG. 1 is a cross-sectional view of an ingot pulling apparatus with the crucible in a terminal position where the melt is depleted.

[0012] [Figure 4]1 is a graph showing the temperature of the crucible wall in the temperature simulation of Example 1.

[0013] [Figure 5] 1 is a graph of the axial oxygen profile of an ingot produced according to Example 2.

[0014] Corresponding reference characters indicate corresponding elements throughout the drawings. DETAILED DESCRIPTION OF THE INVENTION

[0015] An ingot puller (or more simply, an "ingot puller") is generally designated "100" in Figure 1. The ingot puller 100 includes a crucible 102 supported by a susceptor 106 for holding a melt 104 of semiconductor or solar-grade material, such as silicon. The ingot puller 100 includes a crystal pulling housing 108 defining a growth chamber 152 for pulling a silicon ingot 113 (Figure 2) from the melt 104 along a pulling axis A.

[0016] Crucible 102 includes a floor 129 and a sidewall 131 extending upwardly from floor 129. Sidewall 131 is generally vertical. Floor 129 includes a curved portion of crucible 102 that extends below sidewall 131. Crucible 102 includes a bottom 116, which is the lowest point of crucible 102 relative to pull axis A. Within crucible 102 is a silicon melt 104 having a melt surface 111 (i.e., a melt-ingot interface).

[0017] The susceptor 106 is supported by a shaft 105. The susceptor 106, crucible 102, shaft 105, and ingot 113 (FIG. 2) share a common longitudinal axis A or "pulling axis."

[0018] A pulling mechanism 114 is provided within the ingot pulling apparatus 100 to grow and pull an ingot 113 from the melt 104. The pulling mechanism 114 includes a pulling cable 118, a seed holder or chuck 120 coupled to one end of the pulling cable 118, and a seed crystal 122 coupled to the seed holder or chuck 120 for initiating crystal growth. One end of the pulling cable 118 is connected to a pulley (not shown), a drum (not shown), or some other suitable type of lifting mechanism, such as a shaft, and the other end is connected to the chuck 120, which holds the seed crystal 122. During operation, the seed crystal 122 is lowered into contact with the melt 104. The pulling mechanism 114 is operated to raise the seed crystal 122, thereby pulling a single crystal ingot 113 ( FIG. 2 ) from the melt 104.

[0019] A crucible drive unit 107 (e.g., a motor) rotates the crucible 102 and susceptor 106 during heating and crystal pulling. A lifting mechanism 112 raises and lowers the crucible 102 along the pulling axis A during the growth process. For example, as shown in FIG. 1 , the crucible may be in its lowest position (near the bottom heater 126) where a charge of solid polycrystalline silicon pre-added to the crucible 102 is melted. Crystal growth begins by contacting the melt 104 with a seed crystal 122 and raising the seed crystal 122 via the lifting mechanism 114. The crucible 102 may be raised a distance from its lowest position (i.e., raised to the "seed dip position") before the melt 104 contacts the seed crystal 122.

[0020] As the ingot grows, the silicon melt 104 is consumed and the melt height in the crucible 102 decreases. The crucible 102 and susceptor 106 may be raised to maintain the melt surface 111 at or near the same position relative to the ingot pulling apparatus 100. The crucible 102 may move axially between its lowest position (e.g., melt position) shown in FIG. 1 , a seed dip position where a seed crystal first contacts the melt to pull a silicon ingot from the melt, and an end position ( FIG. 3 ) where the melt in the crucible is depleted. The end position of the crucible 102 is above the seed dip position (and lowest position) of the crucible 102.

[0021] The crystal drive unit (not shown) may also rotate the pulling cable 118 and ingot 113 (FIG. 2) in a direction opposite (e.g., counter-rotation) from the direction in which the crucible drive unit 107 rotates the crucible 102. In embodiments using co-rotation, the crystal drive unit may rotate the pulling cable 118 in the same direction as the crucible drive unit 107 rotates the crucible 102. Additionally, the crystal drive unit raises and lowers the ingot 113 relative to the melt surface 111 as desired during the growth process.

[0022] The ingot pulling apparatus 100 may include an inert gas system for introducing and withdrawing an inert gas, such as argon, from the growth chamber 152. The ingot pulling apparatus 100 may also include a dopant delivery system (not shown) for introducing dopants into the melt 104.

[0023] According to the Czochralski single crystal growth process, a quantity of polycrystalline silicon or polysilicon is charged into a crucible 102. Semiconductor or solar-grade material introduced into the crucible is melted by heat provided by one or more heating elements. The ingot puller 100 includes bottom insulation 110 and side insulation 124 for maintaining heat within the puller. In the illustrated embodiment, the ingot puller 100 includes a bottom heater 126 positioned below a crucible floor 129. The crucible 102 can be moved relatively close to the bottom heater 126 to melt the polycrystalline silicon charged into the crucible 102.

[0024] To form an ingot, a seed crystal 122 contacts the surface 111 of the melt 104. A pulling mechanism 114 is operated to pull the seed crystal 122 out of the melt 104. Referring now to FIG. 2, the ingot 113 includes a crown portion 142 that transitions from the seed crystal 122 and tapers outward as the ingot reaches a target diameter. The ingot 113 includes a constant diameter portion 145 of the crystal, or cylindrical "body," which is grown by increasing the pulling rate. The body portion 145 of the ingot 113 has a relatively constant diameter. The ingot 113 includes a tail or end cone 149 ( FIG. 3 ), where the ingot tapers in diameter after the body portion 145. Once the diameter is small enough, the ingot 113 separates from the melt 104. The ingot 113 has a central longitudinal axis A that extends through the crown portion 142 and the terminal end 150 of the ingot 113 .

[0025] The ingot pulling apparatus 100 includes a side heater 135 and a susceptor 106 that surrounds the crucible 102 to maintain the temperature of the melt 104 during crystal growth. The side heater 135 is positioned radially outward of the crucible sidewall 131 as the crucible 102 moves up and down the pulling axis A (e.g., from a lowest position to an end position). The side heater 135 and the bottom heater 126 may be any type of heater that allows the side heater 135 and the bottom heater 126 to operate as described herein. In some embodiments, the heaters 135, 126 are resistive heaters. The side heater 135 and the bottom heater 126 may be controlled by a control system (not shown) so that the temperature of the melt 104 is controlled throughout the pulling process.

[0026] The ingot puller 100 may include a heat shield 151. The heat shield 151 may surround the ingot 113 such that the ingot 113 passes through an opening 160 formed by the heat shield 151. The heat shield 151 may be positioned inside the crucible 102 during crystal growth (e.g., as shown at the end position of the crucible 102 in FIG. 3). In some embodiments, the ingot crystal puller does not include a heat shield positioned below the side heater (e.g., positioned directly below the side heater).

[0027] According to an embodiment of the present disclosure for manufacturing an ingot 113 in an ingot pulling apparatus 100, the length L of the side heater 135 135 (FIG. 1) (i.e., height relative to the pulling axis A) is selected based on two or more temperature simulations of the ingot pulling apparatus 100 (e.g., of the crucible 102). In some embodiments, the length L of the heater 135 135 is selected and the selected length L 135 A side heater 135 including the heater 135 is provided in the ingot pulling apparatus 100. The ingot 113 is then pulled from the melt 104 formed in the crucible 102 of the ingot pulling apparatus 100.

[0028] Length L of side heater 135 135 In order to select the temperature profile of the crucible 102 of the ingot pulling apparatus 100, the length L of the side heater 135 during the temperature simulation is determined in two or more temperature simulations. 135 The removal of the ingot 113 from the silicon melt 113 while varying the temperature is modeled (e.g., as described in Example 1 below). Temperature simulations were performed using commercially available tools such as CrysVun (CrysVun software, Crystal Growth Laboratory, Fraunhofer Institute USB, Erlangen, Germany) and CGSim (CGSim software, commercialized by STR Group, Inc., St. Petersburg, Russia). These tools are exemplary, and other software codes that model heat transfer in the pull during crystal growth may be used (e.g., any steady-state 2D simulation). The crucible temperature may also be measured experimentally through the use of temperature sensors. In some embodiments, the temperature of the crucible floor 129 (e.g., any portion of the crucible extending inward from the sidewall 131, including the curvature) during one or more steps of ingot growth is modeled.

[0029] During a first temperature simulation, the side heater 135 is selected to have a first length, and during a second temperature simulation, the side heater 135 is selected to have a second length that is different from the first length. The length of the side heater used in the ingot pulling apparatus 100 (i.e., the physical unit, not the modeled apparatus) can be selected from the first and second lengths. In some embodiments, additional temperature simulations are performed to select the side heater length L during the simulation. 135 (e.g., different side heater lengths L 135 (Use 3, 4, or 5 or more temperature simulations).

[0030] When the temperature simulation is performed, the length L of the side heater 135 135is selected based on the modeled temperature of the crucible 102 (e.g., the modeled temperature of the crucible floor 129) obtained from the simulation. For example, the length L of each of the side heaters 135 modeled during the temperature simulation 135 The temperature of the crucible 102 (e.g., the crucible floor 129) during the simulation for 135 can be compared and / or influenced by various criteria for selecting

[0031] Generally, the arbitrary length L of the side heater 135 135 may be selected based on the temperature of the crucible and criteria set by the user. In some embodiments, the selected side heater length L 135 corresponds to the length used in the temperature simulation where the temperature of the crucible floor is below about 1490° C. as determined from the model, or below 1482° C. or 1450° C. as determined from the model in other embodiments. In some embodiments, the selected side heater length L 135 corresponds to the length used in the temperature simulation, where the temperature of the crucible floor is about 1425°C to about 1450°C as determined by the model.

[0032] Selected side heater length L 135 may also be selected to minimize radial gradient changes at the melt surface 111 to reduce (or eliminate) loss of dislocation-free ingots, and to minimize point defects in the ingots (e.g., by maintaining sufficient heat and temperature at an elevation near the top of the crucible).

[0033] Selected side heater length L 135 may vary for different types of hot zone configurations. In some embodiments, the selected length L of the side heater 135 135is less than about 550 mm, less than about 525 mm, less than about 500 mm, less than about 475 mm, or less than about 450 mm (for example, 350 mm to about 500 mm, or 350 mm to about 450 mm).

[0034] Side heater length L 135 When is selected, the selected length L 135 A side heater 135 having a side heater 135 is provided in the ingot puller 100. The ingot puller 100 can then be used to produce a silicon ingot. As further described above, a silicon melt 104 (FIG. 1) is prepared in the crucible 102 of the ingot puller 100 having the side heater 135. The melt 104 is contacted with the seed crystal 122, and the seed crystal 122 and the ingot 113 attached to the seed crystal 122 are removed from the melt 104.

[0035] According to embodiments of the present disclosure, the side heater 135 may have a relatively short length L135 relative to conventional ingot pulling, which may reduce the amount of oxygen introduced into the ingot 113. In some embodiments, the length L135 of the side heater 135 135 may be about 550 mm or less (for example, less than about 525 mm, less than about 500 mm, less than about 475 mm, less than about 450 mm, 350 mm to about 500 mm, or 350 mm to about 450 mm).

[0036] The method of the disclosed embodiments has several advantages over conventional ingot pullers. By temperature simulating the temperature of the crucible (e.g., the floor of the crucible) to select the side heater length to be used in the ingot puller, the amount of oxygen incorporated into the ingot during ingot growth can be reduced. By shortening the side heater length with the use of temperature simulation, the temperature of the crucible floor can be reduced (e.g., lower than the crucible side walls but above the freezing point of silicon) without increasing energy consumption. The reduced temperature of the crucible floor reduces melting of the crucible, reduces convective transport of oxygen-rich melt from the crucible floor to the melt-ingot interface, and reduces the contribution of oxygen from the crucible to the melt. Reducing oxygen within the ingot reduces thermal donors within the ingot, facilitating the production of relatively high-resistivity silicon with more consistent resistivity (e.g., from ingot to ingot and axially within the ingot). In some embodiments, the disclosed methods may enable wafers with concentrations of less than 8 ppma, less than 6 ppma, or even less than 4 ppma to be achieved. Reducing the length of the side heater may also increase the temperature near the top of the crucible sidewall, reducing condensation of gaseous oxides on the crucible walls. Such condensed oxides may flake off and fall into the melt, causing loss of the single-crystal structure. Increasing the temperature near the top of the crucible also increases the radial temperature gradient of the melt, reducing the nucleation of solid silicon (i.e., "icing") on the crucible walls. Increasing the temperature near the top of the crucible also increases the radial temperature gradient of the melt, reducing the risk of rod distortion (i.e., deviations in the crystal's tendency from a cylinder). The temperature simulation to determine the side heater length generally fits most hot zone configurations. [Example]

[0037] The methods of the present disclosure are further illustrated by the following examples, which should not be construed in a limiting sense. Example 1: Temperature simulations performed with different side heater lengths

[0038] Figure 4 shows temperature simulations of an ingot pulling hot zone similar to the hot zones in Figures 1-3, normalized along its length ("0" is the bottom, "200" is the top). The ingot pulling apparatus was a 24-inch puller and included cusp-configured magnets capable of generating a magnetic field of several hundred gauss. The temperature simulations included a 550 mm long side heater. One temperature simulation included the same ingot pulling apparatus (i.e., the same side heater length), but with the bottom insulation of the side heater removed. Other temperature simulations included the same ingot pulling apparatus with the side heater shortened in length by 100 mm, 125 mm, and 150 mm. Yet another simulation included a side heater shortened in length by 125 mm, with the bottom insulation removed. One simulation also included a smaller hot zone ("20") for comparison.

[0039] According to an embodiment of the present disclosure, the heater length may be selected based on the temperature simulation shown in Figure 4. As shown in Figure 4, an ingot puller may be selected that reduces the crucible floor temperature by 40°C or more (e.g., by selecting a side heater length that is reduced by 150 mm). The use of a reduced side heater length also increases the temperature toward the top of the crucible (left side of the plot). The temperature simulation estimates a 2% energy reduction in power when the side heater height is reduced by 125 mm. Example 2: Comparison of oxygen content when the side heater length is shortened

[0040] The ingots were produced in the ingot puller with a 550 mm long side heater in Example 1. The other ingots were produced in an ingot puller with a 125 mm shortened side heater length. The axial oxygen profiles of both ingots were measured and are shown in Figure 5. As shown in Figure 5, the oxygen concentration decreased from about 11 ppma to about 6-7 ppma by shortening the heater length by 125 mm. The power consumed in the two ingot pullers was substantially the same.

[0041] As used herein, when used in connection with a range of dimensions, concentrations, temperatures, or other physical or chemical properties or characteristics, the terms "about," "substantially," "essentially," and "approximately" are meant to encompass the variation that may exist at the upper and / or lower limits of the range of the property or characteristic, including, for example, variation resulting from rounding, measurement methodology, or other statistical variations.

[0042] When introducing elements of the present disclosure or embodiments thereof, the articles "a," "an," "the," and "said" are intended to mean that there are one or more elements. The terms "have," "include," "including," and "having" are intended to be inclusive and mean that there may be additional elements beyond the listed elements. Terms indicating specific orientations (e.g., "top," "bottom," "side," etc.) are for convenience of description and do not require any particular orientation of the described items.

[0043] Since various changes may be made in the structures and methods described above without departing from the scope of the present disclosure, it is intended that all matter contained in the above description and shown in the accompanying drawings shall be interpreted as illustrative and not in a limiting sense.

Claims

1. 1. A method for producing an ingot in an ingot puller, the method comprising: a crucible for holding a silicon melt, the crucible having a floor and a sidewall extending from the floor, the crucible having a top and the floor including a curved portion; a growth chamber for withdrawing a silicon ingot from the melt along a pulling axis; an elevation mechanism for raising and lowering the crucible relative to the pulling shaft during crystal growth; a bottom heater disposed below the floor of the crucible; an ingot pulling apparatus for producing an ingot, selecting a length of a side heater disposed radially outward of the side wall of the crucible; Here, selecting the length of the side heater is in two or more temperature simulations, varying the length of the side heater during the temperature simulations to model a temperature profile of the crucible of the ingot pulling apparatus during removal of an ingot from the silicon melt; selecting the length of the side heater based on a temperature of the floor of the crucible during the two or more temperature simulations, wherein the length of the side heater is selected based on the length of the side heater during a temperature simulation in which the temperature of a portion of the floor of the crucible is about 1450° C. or less and the temperature of the top of the crucible is at least 1715 K; providing the side heater having the selected side heater length disposed radially outward of the side wall of the crucible; It is equipped with forming a silicon melt in the crucible while the crucible is in a lowest position adjacent the bottom heater; contacting the melt with a seed crystal; removing an ingot from the silicon melt, wherein the crucible is elevated during ingot growth; A method comprising:

2. the length of the side heater is selected based on the length of the side heater during a temperature simulation in which the temperature of the floor of the crucible is about 1490° C. or less. The method of claim 1.

3. the length of the side heater is selected based on the length of the side heater during a temperature simulation in which the temperature of the floor of the crucible is about 1450° C. or less. The method of claim 1.

4. the length of the side heater is selected based on the length of the side heater during a temperature simulation in which the temperature of the floor of the crucible is between about 1425°C and about 1450°C. The method of claim 1.

5. the selected length of the side heater is less than about 550 mm; The method of claim 1.

6. the selected length of the side heater is less than about 500 mm; The method of claim 1.

7. the selected length of the side heater is less than about 450 mm; The method of claim 1.

8. The ingot pulling apparatus does not include a heat shield disposed below the side heater. The method of claim 1.

9. 1. A method of selecting a side heater length in an ingot pulling apparatus having a crucible for holding a silicon melt, the crucible having a floor and a sidewall extending from the floor, the crucible having a top, and the floor including a curvature, the method comprising: temperature simulation of the temperature of the crucible during crystal growth in the ingot pulling apparatus having a side heater having a first length; temperature simulation of the crucible temperature during crystal growth in the ingot pulling apparatus having a side heater having a second length; comparing the temperature of the crucible during the temperature simulation when the side heater has the first length with the temperature of the crucible during the temperature simulation when the side heater has the second length; selecting a heater length based on the comparison of the temperature of the crucible in the temperature simulation in which the side heater has the first length and the temperature of the crucible in the temperature simulation in which the side heater has the second length, wherein the length of the side heater is selected based on the length of the side heater during a temperature simulation in which a temperature of a portion of the floor of the crucible is about 1450° C. or less and a temperature of the top of the crucible is at least 1715 K or less, and a maximum temperature of the crucible is within the curved portion of the crucible; A method comprising:

10. the temperature of the floor of the crucible during the temperature simulation when the side heater has the first length is compared with the temperature of the floor of the crucible during the temperature simulation when the side heater has the second length; 10. The method of claim 9.

11. Performing 3, 4, or 5 or more temperature simulations with side heaters of different lengths; comparing the temperature of the crucible in the temperature simulation; selecting a length of the side heater based on the comparison of the temperature of the crucible in the temperature simulation; The method of claim 9 or 10, further comprising:

12. comparing the temperature of the crucible in the temperature simulation includes comparing the temperature of the floor of the crucible in the temperature simulation; The method of claim 11.

13. the length of the side heater is selected based on the length of the side heater during a temperature simulation in which the temperature of the floor of the crucible is between about 1425°C and about 1450°C; 10. The method of claim 9.

14. the selected length of the side heater is less than about 550 mm; 10. The method of claim 9.

15. the selected length of the side heater is less than about 500 mm; 10. The method of claim 9.

16. the selected length of the side heater is less than about 450 mm; 10. The method of claim 9.

17. The ingot pulling apparatus does not include a heat shield disposed below the side heater.

10. The method of claim 9.

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