WO2022020551A1

WO2022020551A1 - Systems and methods for reduced swinging and dropping of silicon crystals during production of silicon

Info

Publication number: WO2022020551A1
Application number: PCT/US2021/042705
Authority: WO
Inventors: Zheng Lu; Chi-Yung Chen; Feng-Chien TSAI; Shan-hui LIN
Original assignee: Globalwafers Co., Ltd.
Priority date: 2020-07-23
Filing date: 2021-07-22
Publication date: 2022-01-27
Also published as: JP2023536410A; CN116096946A; TW202214918A

Abstract

A method for producing a silicon ingot by the Czochralski method includes rotating a crucible containing a silicon melt, contacting the silicon melt with a seed crystal, withdrawing the seed crystal from the silicon melt along an axis of symmetry while rotating the crucible about the axis of symmetry to form a silicon ingot, and inducing currents in the silicon ingot to oppose movement of the silicon ingot away from the axis of symmetry.

Description

SYSTEMS AND METHODS FOR REDUCED SWINGING AND DROPPING OF SILICON CRYSTALS DURING PRODUCTION OF SILICON

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claim priority to U.S. Provisional Patent Application No. 63/055,426 filed 23 July 2020, the entire disclosure of which is hereby incorporated by reference in its entirety.

FIELD

[0002] This disclosure generally relates to the production of silicon ingots, and more specifically, to methods and systems for reducing swinging and dropping of silicon crystal, for example because of earthquakes, during the production of silicon.

BACKGROUND

[0003] During Czochralski crystal growth, orbiting or swinging of silicon crystals that is detrimental to high quality crystal growth may occur due to vibration, mis-alignment, turbulent gas flow, and the like. Furthermore, in the event of an earthquake, the crystal swinging may be so severe that the crystal strikes the growth chamber or parts of the crystal puller. When crystals hit the chamber or parts, the crystal and the parts are often damaged. In some cases, the contact can lead to the breakage of the neck of the crystal and the drop of crystal. Any crystal drop can cause severe damage to parts and possibly to puller itself, as well as negative impact on tool time, materials and revenue, and the like. The dropped crystal itself is typically damaged and unusable. [0004] At least some known systems utilize a damping device that relies on active counter movement to reduce or cancel the movement in the crystal cause by orbiting or earthquake. Such systems may negatively impact normal crystal growth due to false positive signal processing or missing the abnormal event (such as a real earthquake) due to the lack of signal or signal sensitivity, or both.

[0005] Thus, there exists a need for methods and systems that automatically and reliably reduce swinging and dropping of crystals during silicon production without negatively impacting crystal growth through false detections.

[0006] This background section is intended to introduce the reader to various aspects of art that may be related to various aspects of the present disclosure, which are described and/or claimed below. This discussion 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. Accordingly, it should be understood that these statements are to be read in this light, and not as admissions of prior art.

BRIEF SUMMARY

[0007] One aspect of this disclosure is a crystal growing system for producing a silicon ingot. The system includes a vacuum chamber, a crucible disposed within the vacuum chamber, a pull shaft, a control unit, and at least one magnet. The crucible is rotatable about an axis of symmetry, and configured to hold a melt including molten silicon. The pull shaft is movable along the axis of symmetry and rotatable about the axis of symmetry, and configured to hold a seed crystal. The control unit includes a processor and a memory. The memory stores instruction that, when executed by the processor, cause the processor to withdraw the seed crystal from the melt in the crucible to form the silicon ingot. The at least one magnet induces currents in the silicon ingot to oppose movement of the silicon ingot away from the axis of symmetry. The at least one magnet is configured to generate a horizontal magnetic field having a nonzero magnetic flux gradient above a surface of the melt that reaches a maximum around the axis of symmetry.

[0008] Another aspect of this disclosure is a method for producing a silicon ingot by the Czochralski method. The method includes rotating a crucible containing a silicon melt, contacting the silicon melt with a seed crystal, withdrawing the seed crystal from the silicon melt along an axis of symmetry while rotating the crucible about the axis of symmetry to form a silicon ingot, and inducing currents in the silicon ingot to oppose movement of the silicon ingot away from the axis of symmetry.

[0009] Various refinements exist of the features noted in relation to the above-mentioned aspect. Further features may also be incorporated in the above- mentioned aspect as well. These refinements and additional features may exist individually or in any combination. For instance, various features discussed below in relation to any of the illustrated embodiments may be incorporated into the above-described aspect, alone or in any combination. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Fig. 1 is a top view of a crucible of one embodiment.

[0011] Fig. 2 is a side view of the crucible shown in Fig. 1.

[0012] Fig. 3 is a schematic illustrating a horizontal magnetic field applied to a crucible containing a melt in a crystal growing apparatus.

[0013] Fig. 4 is a block diagram of a crystal growing system.

[0014] Fig. 5 is an example coil for a magnet for the crystal growing system shown in Fig. 4.

[0015] Fig. 6 is a magnetic assembly including the coil shown in Fig. 5.

[0016] Fig. 7 is a graph comparing the flux density within the melt and the flux density above the melt as a function of distance from the axis of symmetry.

[0017] Like reference symbols in the various drawings indicate like elements.

DETAILED DESCRIPTION

[0018] Referring initially to Figs. 1 and 2, a crucible of one embodiment is indicated generally at 10. A cylindrical coordinate system for crucible 10 includes a radial direction R 12, an angular direction Q 14, and an axial direction Z 16. The crucible 10 contains a melt 25 having a melt surface 36. A crystal 27 (also referred to sometimes as ingot 27 or silicon ingot 27) is grown from the melt 25. The melt 25 may contain one or more convective flow cells 17, 18 induced by heating of the crucible 10 and rotation of the crucible 10 and/or crystal 27 in the angular direction Q 14. The structure and interaction of these one or more convective flow cells 17, 18 are modulated via regulation of one of more process parameters and/or the application of a magnetic field as described in detail herein below.

[0019] Fig. 3 is a diagram illustrating a horizontal magnetic field being applied to crucible 10 containing melt 25 in a crystal growing apparatus. As shown, crucible 10 contains silicon melt 25 from which a crystal 27 is grown. The transition between the melt and the crystal is generally referred to as the crystal-melt interface (alternatively the melt-crystal, solid-melt or melt-solid interface) and is typically non-linear, for example concave, convex or gull-winged relative to the melt surface. Two magnetic poles 29 are placed in opposition to generate a magnetic field generally perpendicular to the crystal-growth direction and generally parallel to the melt surface 36. The magnetic poles 29 may be a conventional electromagnet, a superconductor electromagnet, or any other suitable magnet for producing a horizontal magnetic field of the desired strength and flux gradient. Application of a horizontal magnetic field gives rise to Lorentz force along axial direction, in a direction opposite of fluid motion, opposing forces driving melt convection. The convection in the melt is thus suppressed, and the axial temperature gradient in the crystal near the interface increases. The melt-crystal interface then moves upward to the crystal side to accommodate the increased axial temperature gradient in the crystal near the interface and the contribution from the melt convection in the crucible decreases. The horizontal configuration has the advantage of efficiency in damping a convective flow at the melt surface 36. Moreover, the magnetic poles 29 are used to reduce swinging and dropping of the crystal 27, as will be described below.

[0020] Fig. 4 is a block diagram of a crystal growing system 100. System 100 employs a Czochralski crystal growth method to produce a silicon semiconductor ingot. In this embodiment, system 100 is configured to produce a cylindrical semiconductor ingot having an ingot diameter of one-hundred and fifty millimeters (150 mm), greater than one-hundred fifty millimeters (150 mm), more specifically in a range from approximately 150 mm to 460 mm, and even more specifically, a diameter of approximately three-hundred millimeters (300 mm). In other embodiments, system 100 is configured to produce a semiconductor ingot having a two-hundred millimeter (200 mm) ingot diameter or a four-hundred and fifty millimeter (450 mm) ingot diameter. In addition, in one embodiment, system 100 is configured to produce a semiconductor ingot with a total ingot length of at least nine hundred millimeters (900 mm). In some embodiments, the system is configured to produce a semiconductor ingot with a length of one thousand nine hundred and fifty millimeters (1950 mm), two thousand two hundred and fifty millimeters (2250 mm), two thousand three hundred and fifty millimeters (2350 mm), or longer than

2350 mm. In other embodiments, system 100 is configured to produce a semiconductor ingot with a total ingot length ranging from approximately nine hundred millimeters (900 mm) to twelve hundred millimeters (1200 mm), between approximately 900 mm and approximately two thousand millimeters (2000 mm), or between approximately 900 mm and approximately two thousand five hundred millimeters (2500 mm). In some embodiments, the system is configured to produce a semiconductor ingot with a total ingot length greater than 2000 mm.

[0021] The crystal growing system 100 includes a vacuum chamber 101 enclosing crucible 10. A side heater 105, for example, a resistance heater, surrounds crucible 10. A bottom heater 106, for example, a resistance heater, is positioned below crucible 10. During heating and crystal pulling, a crucible drive unit 107 (e.g., a motor) rotates crucible 10, for example, in the clockwise direction as indicated by the arrow 108. Crucible drive unit 107 may also raise and/or lower crucible 10 as desired during the growth process. Within crucible 10 is silicon melt 25 having a melt level or melt surface 36. In operation, system 100 pulls a single crystal 27, starting with a seed crystal 115 attached to a pull shaft or cable 117, from melt 25. One end of pull shaft or cable 117 is connected by way of a pulley (not shown) to a drum (not shown), or any other suitable type of lifting mechanism, for example, a shaft, and the other end is connected to a chuck (not shown) that holds seed crystal 115 and crystal 27 grown from seed crystal 115.

[0022] Crucible 10 and single crystal 27 have a common axis of symmetry 38. Crucible drive unit 107 can raise crucible 10 along axis 38 as the melt 25 is depleted to maintain melt level 36 at a desired height. A crystal drive unit 121 similarly rotates pull shaft or cable 117 in a direction 110 opposite the direction in which crucible drive unit 107 rotates crucible 10 (e.g., counter rotation). In embodiments using iso-rotation, crystal drive unit 121 may rotate pull shaft or cable 117 in the same direction in which crucible drive unit 107 rotates crucible 10 (e.g., in the clockwise direction). Iso rotation may also be referred to as a co-rotation. In addition, crystal drive unit 121 raises and lowers crystal 27 relative to melt level 36 as desired during the growth process.

[0023] According to the Czochralski single crystal growth process, a quantity of polycrystalline silicon, or polysilicon, is charged to crucible 10. A heater power supply 123 energizes resistance heaters 105 and 106, and insulation 125 lines the inner wall of vacuum chamber 101. A gas supply 127 (e.g., a bottle) feeds argon gas to vacuum chamber 101 via a gas flow controller 129 as a vacuum pump 131 removes gas from vacuum chamber 101. An outer chamber 133, which is fed with cooling water from a reservoir 135, surrounds vacuum chamber 101.

[0024] The cooling water is then drained to a cooling water return manifold 137. Typically, a temperature sensor such as a photocell 139 (or pyrometer) measures the temperature of melt 25 at its surface, and a diameter transducer 141 measures a diameter of single crystal 27. In this embodiment, system 100 does not include an upper heater. The presence of an upper heater, or lack of an upper heater, alters cooling characteristics of crystal 27. [0025] Magnetic poles 29 are positioned outside the vacuum chamber 101 to produce a horizontal magnetic field (shown in Fig. 3). Although illustrated approximately centered on the melt surface 36, the position of the magnetic poles 29 relative to the melt surface 36 may be varied to adjust the position of the maximum gauss plane (MGP) relative to the melt surface 36. A reservoir 153 provides cooling water to the magnetic poles 29 before draining via cooling water return manifold 137. A ferrous shield 155 surrounds magnetic poles 29 to reduce stray magnetic fields and to enhance the strength of the field produced.

[0026] A control unit 143 is used to regulate the plurality of process parameters including, but not limited to, at least one of crystal rotation rate, crucible rotation rate, and magnetic field strength. In various embodiments, the control unit 143 may include a memory 173 and processor 144 that processes the signals received from various sensors of the system 100 including, but not limited to, photocell 139 and diameter transducer 141, as well as to control one or more devices of system 100 including, but not limited to: crucible drive unit 107, crystal drive unit 121, heater power supply 123, vacuum pump 131, gas flow controller 129 (e.g., an argon flow controller), magnetic poles power supplies 149 and 151, and any combination thereof. The memory 173 may store instructions that, when executed by the processor 144 cause the processor to perform one or more of the methods described herein. That is, the instructions configure the control unit 143 to perform one or more methods, processes, procedures, and the like described herein. [0027] Control unit 143 may be a computer system. Computer systems, as described herein, refer to any known computing device and computer system. As described herein, all such computer systems include a processor and a memory. However, any processor in a computer system referred to herein may also refer to one or more processors wherein the processor may be in one computing device or a plurality of computing devices acting in parallel. Additionally, any memory in a computer device referred to herein may also refer to one or more memories wherein the memories may be in one computing device or a plurality of computing devices acting in parallel. Further, the computer system may located near the system 100 (e.g., in the same room, or in an adjacent room), or may be remotely located and coupled to the rest of the system via a network, such as an Ethernet, the Internet, or the like.

[0028] The term processor, as used herein, refers to central processing units, microprocessors, microcontrollers, reduced instruction set circuits (RISC), application specific integrated circuits (ASIC), logic circuits, and any other circuit or processor capable of executing the functions described herein. The above are examples only, and are thus not intended to limit in any way the definition and/or meaning of the term "processor." The memory may include, but is not limited to, random access memory (RAM) such as dynamic RAM (DRAM) or static RAM (SRAM), read-only memory (ROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), and non-volatile RAM (NVRAM). [0029] In one embodiment, a computer program is provided to enable control unit 143, and this program is embodied on a computer readable medium. The computer readable medium may include the memory 173 of the control unit 143. In an example embodiment, the computer system is executed on a single computer system. Alternatively, the computer system may comprise multiple computer systems, connection to a server computer, a cloud computing environment, or the like. In some embodiments, the computer system includes multiple components distributed among a plurality of computing devices. One or more components may be in the form of computer-executable instructions embodied in a computer-readable medium.

[0030] The computer systems and processes are not limited to the specific embodiments described herein.

In addition, components of each computer system and each process can be practiced independent and separate from other components and processes described herein. Each component and process also can be used in combination with other assembly packages and processes.

[0031] In one embodiment, the computer system may be configured to receive measurements from one or more sensors including, but not limited to: temperature sensor 139, diameter transducer 141, and any combination thereof, as well as to control one or more devices of system 100 including, but not limited to: crucible drive unit 107, crystal drive unit 121, heater power supply 123, vacuum pump 131, gas flow controller 129 (e.g., an argon flow controller), magnetic poles power supplies 149 and 151, and any combination thereof as described herein and illustrated in Fig. 4 in one embodiment. The computer system performs all of the steps used to control one or more devices of system 100 as described herein.

[0032] The magnetic poles 29 are additionally used to reduce and prevent swinging and dropping of the crystal 27, for example due to earthquakes.

[0033] When a silicon crystal, such as crystal 27, moves through a magnetic field, the eddy currents induced within the crystal cause an electromagnetic force opposing such motion. While such damping or braking force is very complex due the complexity of the typical magnetic field distribution and the complexity of the conductivity distribution in the crystal as it is being pulled during growth, the force is always proportional to: the magnet field flux density B going through the crystal, the spatial gradient of the flux in the direction of motion dB/dx, the electrical conductivity of the crystal, the velocity of the motion v, and the like. Silicon crystals are good conductors at or near growth temperature, with electrical conductivity o of about 10⁵ S/m. By using magnetic poles 29 with a flux density B ranging from 1000 Gauss to 5000 Gauss (0.1 T to 0.5 T) with highly conductive crystal, the damping force generated in the crystal in a noticeable off- center motion of the crystal is considerable. Increasing the magnetic flux gradient further increases the force generated to oppose movement of the crystal.

[0034] Thus, to reduce swinging and dropping of the ingot 27, the system 100 includes and uses a magnet (e.g., magnetic poles 29) to induce currents in the ingot 27 to oppose movement of the ingot 27 away from the axis of symmetry 38. The magnetic poles 29 are configured (i.e., designed, constructed, composed, oriented, positioned, and the like) to generate a horizontal magnetic field having a nonzero magnetic flux gradient above the surface 36 of the melt. The magnetic flux gradient reaches a maximum around the axis of symmetry 38.

[0035] The magnetic poles 29 deliver a strong and yet uniform horizontal magnetic field near or around the crystal 27 to melt interface as well as within the silicon melt 25 and is centered and positioned with the axis of symmetry 38. In the areas that do not impact normal crystal growth (e.g., above the melt surface 36) however, the coils of the magnetic poles 29 are configured to create a large magnetic flux gradient. With a strong magnetic field at the crystal 27 and a large magnetic flux gradient at the crystal 27 well above the melt 25, the eddy currents induced within the conducting crystal 27 whenever the crystal moves off of the axis of symmetry 38 are sufficiently strong to counter such undesired movement.

This results in self-centering the crystal 27 along the axis of symmetry 38 in response to any movement off of the axis of symmetry 38 without the need of any sensor. The larger and/or faster the undesired movement off of the axis of symmetry 38, the stronger the counter force to return the crystal 27 to its center axis along the axis of symmetry 38. When the crystal 27 is centered on the axis of symmetry 38, there is no counter force and thus no risk of false positive action and consequential negative impact to normal crystal growth.

[0036] Fig. 5 is an example coil 500 for a magnetic assembly for the crystal growing system 100. Fig. 6 is a magnetic assembly 600 including two of the coils shown in Fig. 5 to form the magnetic poles 29. The magnet flux gradient produced depends on the configuration, shape, dimension and number of turns of the coils 500. The magnet assembly 600 utilizes a pair of saddle shaped coils 500 lined up in the same direction and wrapped around within a magnet housing 602. In the example embodiment, the cylindrical magnet housing 602 has an ID of 1194mm, OD of 1556mm and height of 1088mm. Each coil 500 has 240 turns carrying up to 718 amps of current. Other embodiments may use coils and/or magnetic assemblies including different coils shapes, different numbers of turns, different spacings, and the like.

[0037] In the example embodiment, the magnetic poles 29 produce a maximum flux density of about 1500 Gauss. In some embodiments, the magnetic poles produce a maximum flux density of at least 1500 Gauss. In other embodiments, the magnetic poles 29 produce a maximum flux density of 2200 Gauss, or at least 2200 Gauss. In still other embodiments, the magnetic poles produce a maximum flux density between 1500 Gauss and 5000 Gauss. The coils (not shown) of the magnetic poles 29 are superconducting coils in the example embodiment. Alternatively, the coils may be made of a conventional conductor.

[0038] As explained above, the magnetic poles 29 produce a relatively uniform flux density (i.e., with a very low flux density gradient) within the melt 25 and at the interface between the crystal 27 and the melt surface 36. Above the melt 25, the magnetic poles 29 produce a magnetic field that varies along the horizontal direction and that has a maximum around the axis of symmetry 38.

Fig. 7 is a simulated graph 700 comparing the flux density 702 within the melt 25 and the flux density 704 above the melt 25 as a function of distance from the axis of symmetry 38 (indicated by radius 0 in the graph). Both the flux density 702 within the melt and the flux density 704 above the melt have a maximum of about 2200 Gauss. The gradient for the flux density 702 within the melt 25 is almost zero, with there being very little change as the distance from the axis of symmetry increases. However, as one can see, the variation, and thus the gradient, is significantly larger off the center of the axis (r=0) for the flux density 704 above the melt 25. In fact, the magnetic flux density 704 above the melt 25 shows a decrease in magnetic flux by about 250 Gauss (or at least ten percent of the maximum) within about 200 millimeters of the axis of symmetry 38. With such strong magnetic field at the crystal 27, with the large gradient in the crystal well above the melt 25, the eddy currents created within the conducting crystal 27 and hence the force opposing the movement whenever the crystal moved off the axis of symmetry 38 is sufficiently strong to damp such undesired movement.

[0039] Cusp magnetic systems provide no damping against movement of a crystal off of the axis of symmetry. Data regarding similar crystal growth systems using cusp magnets and no vibration damping had a drop rate of 24.2% during thirty-three earthquakes. That is in 24.2% of the thirty-three earthquakes experienced by the system, the crystal broke off the puller and fell. The example systems of this disclosure are expected, based on data and experimentation, to have a drop rate of 6.7% or better.

The drop rate of 6.7% is premised on the system using lower Gauss (e.g., 1500 Gauss) magnets. When 2200 Gauss magnets are used, the expected drop rate is about 0%.

[0040] Embodiments of the methods described herein achieve superior results compared to prior methods and systems. For example, the methods and systems described herein are non-contact and non-intrusive to normal crystal growth. The system is always active. There is no need for any sensor for cable or crystal movement, or any seismometer to detect the earthquake event. There is also no risk of missing a true abnormal even because counter movement or damping mechanism is always active. Moreover, the specially designed magnets induce forces that are sufficiently strong to damp undesired movement of the crystal.

[0041] When introducing elements of the present invention or the embodiment(s) thereof, the articles "a", "an", "the" and "said" are intended to mean that there are one or more of the elements. The terms "comprising", "including" and "having" are intended to be inclusive and mean that there may be additional elements other than the listed elements.

[0042] Approximating language, as used herein throughout the specification and claims, may be applied to modify any quantitative representation that could permissibly vary without resulting in a change in the basic function to which it is related. Accordingly, a value modified by a term or terms, such as "about," "approximately," and "substantially," is not to be limited to the precise value specified. In at least some instances, the approximating language may correspond to the precision of an instrument for measuring the value. Here and throughout the specification and claims, range limitations may be combined and/or interchanged; such ranges are identified and include all the sub-ranges contained therein unless context or language indicates otherwise.

[0043] As various changes could be made in the above without departing from the scope of the invention, 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

CLAIMS What is claimed is:

1. A crystal growing system for producing an ingot of crystalline material, the system comprising: a chamber; a crucible disposed within the chamber, the crucible rotatable about an axis of symmetry, and shaped to hold a melt; a pull shaft movable along the axis of symmetry and rotatable about the axis of symmetry, and configured to hold a seed crystal; a control unit comprising a processor and a memory, the memory storing instruction that, when executed by the processor, cause the processor to withdraw the seed crystal from the melt in the crucible to form the ingot, and a magnet to induce currents in the ingot to oppose movement of the ingot away from the axis of symmetry, the magnet disposed to generate a horizontal magnetic field having a nonzero magnetic flux gradient above a surface of the melt that reaches a maximum around the axis of symmetry.

2. The system of claim 1, wherein the magnet is disposed to produce the horizontal magnetic field with a lower magnetic flux gradient at the surface of the melt.

3. The system of claim 2, wherein the lower magnetic flux gradient at the surface of the melt is substantially zero.

4. The system of any preceding claim, wherein the magnet is configured to produce the nonzero magnetic flux gradient with a decrease in magnetic flux by at least ten percent of the maximum within about 200 millimeters of the axis of symmetry.

5. The system of any preceding claim, wherein the at least one magnet comprises an electromagnet having a conducting coil.

6. The system of claim 5, wherein the conducting coil comprises a superconducting coil.

7. The system of any preceding claim, wherein the magnet is configured to produce the horizontal magnetic field with a maximum magnetic flux density of at least 1500 gauss.

8. The system of claim 7, wherein the magnet is configured to produce the horizontal magnetic field with a maximum magnetic flux density of at least 2200 gauss.

9. A silicon ingot produced using the system of any preceding claim.

10. The silicon ingot of claim 9, wherein the silicon ingot was produced without breakage using the system of claim 1 during an earthquake.

11. A wafer produced from a silicon ingot of either of claims 9 and 10.

12. A method for producing a silicon ingot by the Czochralski method, the method comprising: rotating a crucible containing a silicon melt; contacting the silicon melt with a seed crystal; withdrawing the seed crystal from the silicon melt along an axis of symmetry while rotating the crucible about the axis of symmetry to form a silicon ingot; and inducing currents in the silicon ingot to oppose movement of the silicon ingot away from the axis of symmetry.

13. The method of claim 12, wherein inducing currents in the silicon ingot to oppose movement of the silicon ingot away from the axis of symmetry comprises using the magnet to generate a horizontal magnetic field having a nonzero magnetic flux gradient above a surface of the silicon melt that reaches a maximum around the axis of symmetry.

14. The method of claim 13, further comprising using the magnet to produce the horizontal magnetic field with a lower magnetic flux gradient at the surface of the melt.

15. The method of claim 14, wherein the lower magnetic flux gradient at the surface of the melt is substantially zero.

16. The method of any of claims 13 to 15, wherein using the magnet to generate the horizontal magnetic field comprises using the magnet to produce the nonzero magnetic flux gradient with a decrease in magnetic flux by at least ten percent of the maximum within about 200 millimeters of the axis of symmetry.

17. The method of any of claims 13 to 16, wherein using a magnet to generate the horizontal magnetic field comprises using an electromagnet having a conducting coil.

18. The method of claim 17, wherein using at least one electromagnet having a conducting coil comprises using a magnet having a superconducting coil.

19. The method of any of claims 13 to 18, wherein using a magnet to generate the horizontal magnetic field comprises using a magnet to generate the horizontal magnetic field with a maximum magnetic flux density of at least 1500 gauss.

20. The method of claim 19, wherein using a magnet to generate the horizontal magnetic field comprises using a magnet to generate the horizontal magnetic field with a maximum magnetic flux density of at least 2200 gauss.

21. A silicon ingot produced using the method of any of claims 13 to 20.

22.The silicon ingot of claim 21, wherein the silicon ingot was produced without breakage during an earthquake.

23. A wafer produced from a silicon ingot of either of claims 21 and 22.