System and method for producing low oxygen content silicon

Abstract

A method and system for producing silicon ingots having a low oxygen concentration is provided. A method for producing a silicon ingot includes withdrawing a seed crystal from a melt containing molten silicon in a crucible enclosed in a vacuum chamber including a cusped magnetic field. At least one process parameter is adjusted in at least two stages, including a first stage corresponding to forming the silicon ingot to an intermediate ingot length and a second stage corresponding to forming the silicon ingot from the intermediate ingot length to a full ingot length. During the second stage, adjusting the process parameter relative to the first stage can include decreasing the crystal rotation rate, decreasing the crucible rotation rate, and / or increasing the magnetic field strength.

Description

[Technical field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims priority to U.S. patent application 62 / 263,355, filed December 4, 2015, which is hereby incorporated by reference in its entirety. Technical Field

[0002] The present disclosure relates generally to the production of silicon ingots, and more particularly to methods and systems for producing silicon ingots having low oxygen concentrations. [Background technology]

[0003] Monocrystalline silicon is the starting material for many processes that manufacture semiconductor electronic components and solar cell materials. For example, semiconductor wafers produced from silicon ingots are commonly used in the production of integrated circuit chips. In the solar cell industry, monocrystalline silicon can be used instead of multicrystalline silicon due to the lack of grain boundaries and dislocations. Monocrystalline silicon ingots are processed into the desired shape, e.g., silicon wafers, from which semiconductor or solar cell wafers may be produced.

[0004] Existing methods for producing high purity monocrystalline silicon ingots include the float zone method and the magnetic Czochralski (MCZ) process. The float zone method involves melting a narrow region of a rod of ultra-pure polycrystalline silicon and slowly transferring the molten region along the rod to produce a high purity monocrystalline silicon ingot. The MCZ process produces monocrystalline silicon ingots by melting polycrystalline silicon in a crucible, immersing a seed crystal in the molten silicon, and withdrawing the seed crystal in a manner sufficient to achieve the desired diameter of the ingot. Horizontal and / or vertical magnetic fields can be applied to the molten silicon to inhibit the incorporation of impurities, such as oxygen, into the growing monocrystalline silicon ingot. Although float zone silicon ingots typically contain relatively low concentrations of impurities, such as oxygen, the diameter of ingots grown using the float zone method is typically as large as about 150 mm, due to limitations imposed by surface tension. MCZ silicon ingots can be produced in larger ingot diameters compared to float zone ingots, but MCZ silicon ingots typically contain higher concentrations of impurities.

[0005] During the process of producing single crystal silicon ingots using the MCZ method, oxygen is introduced into the silicon crystal ingot through the solid-liquid or crystal-melt interface. The oxygen may cause various defects in the wafers produced from the ingot and reduce the yield of semiconductor devices manufactured using the ingot. For example, insulated-gate bipolar transistors (IGBTs), high quality radio-frequency (RF), high resistivity silicon on insulator (HR-SOI), and charge trap layer SOI (CTL-SOI) applications usually require low oxygen concentration (Oi) to achieve high resistivity.

[0006] At least some known semiconductor devices are fabricated using float zone silicon materials to achieve low Oi and high resistivity. However, float zone materials are relatively expensive and are limited in use to the production of ingots having diameters less than about 200 mm. Thus, float zone silicon materials are expensive and cannot produce large diameter silicon crystal ingots with relatively low oxygen concentrations.

[0007] 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. It is believed that this discussion is 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

[0008] In one aspect, a method for producing a silicon ingot includes withdrawing a seed crystal from a melt containing molten silicon in a crucible. The crucible is enclosed in a vacuum chamber including a cusped magnetic field. The method further includes adjusting at least one process parameter of at least two stages. The at least one process parameter includes one of a crystal rotation rate, a crucible rotation rate, and a magnetic field strength. The at least two stages include a first stage corresponding to forming a silicon ingot to an intermediate ingot length, and a second stage corresponding to forming a silicon ingot from the intermediate ingot length to a total ingot length. According to the method of this embodiment, adjusting the at least one process parameter during the second stage includes at least one of decreasing the crystal rotation rate relative to the crystal rotation rate during the first stage, decreasing the crucible rotation rate relative to the crucible rotation rate during the first stage, and increasing the magnetic field strength relative to the magnetic field strength during the first stage.

[0009] Another aspect is directed to wafers created from silicon ingots produced using the methods described above.

[0010] Yet another aspect is directed to a crystal growing system for producing silicon ingots. The system includes a vacuum chamber and a crucible disposed within the vacuum chamber. The crucible is rotatable about an axis of symmetry and configured to hold a melt including molten silicon. The pull shaft is operable along the axis of symmetry and rotatable about the axis of symmetry and configured to hold a seed crystal. The at least one magnet is capable of generating a controllable cusp magnetic field within the crucible. The control unit includes a processor and a memory, the memory storing instructions that, when executed by the processor, cause the processor to pull the seed crystal from the melt in the crucible to form a silicon ingot. The unit also adjusts at least one process parameter, the at least one process parameter being adjusted in at least two stages. The at least two stages include a first stage corresponding to forming the silicon ingot to an intermediate ingot length and a second stage corresponding to forming the silicon ingot from the intermediate ingot length to a full ingot length. The instructions, when executed by the processor, cause the processor to adjust at least one process parameter by at least one of: decreasing a crystal rotation rate relative to a crystal rotation rate during the first stage; decreasing a crucible rotation rate relative to a crucible rotation rate during the first stage; and increasing a magnetic field strength generated by the at least one magnet relative to a magnetic field strength generated by the at least one magnet during the first stage.

[0011] There are various refinements of the features described in connection with the above-mentioned aspects. Various features may be incorporated into the above-mentioned aspects as well. These refinements and additional features may exist individually or in any combination. For example, various features of the following discussion in connection with any of the described embodiments may be incorporated alone or in any combination into the above-mentioned aspects. [Brief description of the drawings]

[0012] [Figure 1] FIG. 2 is a top view of a crucible in one embodiment. [Diagram 2] FIG. 2 is a side view of the crucible shown in FIG. [Diagram 3] FIG. 1 is a schematic diagram illustrating a cusp magnetic field applied to a crucible containing melt in a crystal growing apparatus. [Figure 4] FIG. 2 is a block diagram of the same embodiment of the crystal growth system as FIG. 1. [Figure 5A] FIG. 1 is a cross-sectional view of a portion of a crucible showing flow lines and oxygen concentration near the crucible wall during intermediate body growth for a given crystal rotation rate. [Figure 5B] FIG. 11 is a cross-sectional view of a portion of an example crucible, mapping flow lines and oxygen concentration near the crucible wall during late body growth at crystal rotation rate. [Figure 5C] FIG. 11 is a cross-sectional view of a portion of a crucible mapping flow lines and oxygen concentration near the crucible wall during late body growth at different crystal rotation rates. [Figure 6] 1 is a graph plotting simulated oxygen concentration (Oi) versus position along the crystal (BL) as a function of crystal rotation rate during late body growth. [Figure 7A] 1 is a graph plotting oxygen concentration for post-body growth versus crucible rotation rate for a crystal body rotation rate of 6 rpm. [Figure 7B] 1 is a graph plotting oxygen concentration for post-body growth versus crucible rotation rate for a crystal body rotation rate of 8 rpm. [Figure 8A] 13 shows a cross-sectional view of an example crucible with mapping of flow lines and velocities near the crucible wall during post-body growth at a magnetic field strength corresponding to 50% equilibration. [Figure 8B] 13 shows a cross-section of an example crucible with mapping of flow lines and velocities near the crucible wall during post-body growth at a magnetic field strength corresponding to 95% equilibration. [Figure 8C]FIG. 13 shows a cross-sectional view of an example crucible with mapping of flow lines and velocities near the crucible wall during post-body growth at a balanced magnetic field strength corresponding to 150%. [Figure 9] 1 is a graph plotting oxygen concentration as a function of crystal body length for two different crystal rotation rate profiles. [Figure 10] FIG. 2 is a block diagram of a server system according to an embodiment. [Figure 11] FIG. 2 is a block diagram of an example computing device. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0013] Like reference symbols in the various drawings indicate like elements.

[0014] 1 and 2, a crucible of one embodiment is generally designated as 10. The cylindrical coordinate system of the crucible 10 includes a radial direction R12, an angular direction θ14, and an axial direction Z16. The coordinates R12, θ14, and Z16 are used herein to describe a method and system for producing a low oxygen content silicon ingot. The crucible 10 includes a melt 25 having a melt surface 36. A crystal 27 grows from the melt 25. The melt 25 can include one or more convective flow cells 17, 18 induced by heating the crucible 10 and rotating the crucible 10 and / or the crystal 27 in the angular direction θ14. The structure and interaction of these one or more convective flow cells 17, 18 can be adjusted by adjustment of one of the additional process parameters to reduce the oxygen content in the forming crystal 27, as described in detail herein below.

[0015] FIG. 3 is a block diagram illustrating a cusp magnetic field applied to a crucible 10 containing a melt 25 in a crystal growing apparatus. As shown, the crucible 10 contains a silicon melt 25 from which a crystal 27 is grown. The cusp magnetic field configuration is designed to overcome the deficiencies of axial and horizontal magnetic field configurations. A pair of coils 31 and 33 (e.g., Helmholtz coils) are placed coaxially above and below the melt surface 36. The coils 31 and 33 are operated in an opposing current mode to generate a magnetic field having a pure radial field component near the melt surface 36 (i.e., along R12) and a pure axial field component near the axis of symmetry 38 of the crystal 27 (i.e., along Z16). The combination of the upper magnetic field 40 and the lower magnetic field 42 generated by the coils 31 and 33, respectively, results in axial and radial cusp magnetic field components.

[0016] FIG. 4 is a block diagram of crystal growth system 100. Crystal growth system 100, its elements, and various operating parameters of crystal growth system 100 are described in additional detail in PCT Published Application No. 2014 / 190165, all of which are incorporated herein by reference. Referring again to FIG. 4, system 100 employs the Chokrakski crystal growth method for producing semiconductor ingots. In this embodiment, system 100 is configured to produce cylindrical semiconductor ingots having an ingot diameter greater than one hundred fifty millimeters (150 mm), more particularly in the range of about 150 mm to 460 mm, and more particularly greater than about three hundred millimeters (300 mm) ingot diameter. In other embodiments, system 100 is configured to produce semiconductor ingots having a two hundred millimeter (200 mm) ingot diameter or a four fifty millimeter (450 mm) ingot diameter. Additionally, in one embodiment, the system 100 is configured to produce semiconductor ingots with a total ingot length of at least nine hundred millimeters (900 mm). In another embodiment, the system 100 is configured to produce semiconductor ingots with a total ingot length in the range of about nine hundred millimeters (900 mm) to one thousand two hundred millimeters (1200 mm).

[0017] Referring again to FIG. 4, the crystal growth system 100 includes a vacuum chamber 101 in which a crucible 10 is contained. A side heater 105, e.g., a resistive heater, surrounds the crucible 10. A bottom heater 106, e.g., a resistive heater, is disposed below the crucible 10. During heating and pulling the crystal, a crucible drive unit 107 (e.g., a motor) rotates the crucible 10, e.g., in a clockwise direction as indicated by arrow 108. The crucible drive unit 107 can also raise and / or lower the crucible 10 as desired during the growth process. Within the crucible 10 is a silicon melt 25 having a melt level or melt surface 36. In operation, the system 100 pulls a single crystal 27, starting from a seed crystal 115 attached to a pull shaft or cable 117, from the melt 25. One end of the pull shaft or cable 117 is connected by way of a pulley (not shown) to a drum (not shown) or other suitable type of pulling mechanism, such as a shaft, and the other end is connected to a chuck (not shown) that holds the seed crystal 115 and the crystal 27 grown from the seed crystal 115.

[0018] The crucible 10 and the single crystal 27 have a common axis of symmetry 38. The crucible drive unit 107 can raise the melt 10 along the axis 38 as the melt 25 is consumed to maintain the melt level 36 at a desired height. The crystal drive unit 121 similarly rotates the pull shaft or cable 117 in a direction 110 opposite (e.g., counter-rotation) to the direction in which the crucible drive unit 107 rotates the crucible 10. In embodiments using co-rotation, the crystal drive unit 121 can rotate the pull shaft or cable 117 in the same direction (e.g., clockwise) that the crucible drive unit 107 rotates the crucible 10. Co-rotation can also be referred to as co-rotation. Additionally, the crystal drive unit 121 can raise and lower the crystal 27 relative to the melt level 36 as desired during the growth process.

[0019] According to the Czochralski single crystal growth process, a quantity of polycrystalline silicon, or polysilicon, is filled into crucible 10. A heater power supply 123 energizes resistive heaters 105 and 106, and insulators 125 line the inner wall of vacuum chamber 101. A gas supply 127 (e.g., a bottle) supplies argon gas to vacuum chamber 101 through gas flow controller 129, as a vacuum pump 131 removes the gas from vacuum chamber 101. An outer chamber 133, supplied with cooling water from reservoir 135, surrounds vacuum chamber 101.

[0020] The cooling water is then discharged into a cooling water return manifold 137. Typically, a temperature sensor, such as a photocell 139 (pyrometer), measures the temperature of the melt 25 at its surface, and a diameter transducer 141 measures the diameter of the single crystal 27. In this embodiment, the system 100 does not include a top heater. The presence of a top heater, or the absence of a top heater, alters the cooling characteristics of the crystal 27.

[0021] An upper magnet, such as solenoid coil 31, and a lower magnet, such as solenoid coil 33, in this embodiment, are located above and below, respectively, melt level 36. Shown in cross section, coils 31 and 33 surround a vacuum chamber (not shown) and share an axis with an axis of symmetry 38. In one embodiment, the upper and lower coils 31 and 33 have separate power supplies, including, but not limited to, an upper coil power supply 149 and a lower coil power supply 151, respectively, connected to and controlled by a control unit 143.

[0022] In this embodiment, current flows in opposite directions in the two solenoid coils 31 and 33 to generate a magnetic field (as shown in FIG. 3). A reservoir 153 supplies cooling water to the upper and lower coils 31 and 33 before discharging through a cooling water return manifold 137. An iron shield 155 surrounds the coils 31 and 33 to reduce stray magnetic fields and increase the strength of the generated magnetic field.

[0023] The control unit 143 is used to regulate a number of process parameters including, but not limited to, at least one of the crystal rotation rate, the crucible rotation rate, and the magnetic field strength. In various embodiments, the control unit 143 may include a processor 144 that processes signals received from various sensors of the system 100, including, but not limited to, the photocell 139 and the diameter transducer 141, and signals to control one or more devices of the system 100, including, but not limited to, the crucible drive unit 107, the crystal drive unit 121, the heater power supply 123, the vacuum pump 131, the gas flow controller 129 (e.g., an argon flow controller), the upper coil power supply 149, the lower coil power supply 151, and any combination thereof.

[0024] The control unit 143 may be a computer system. As described herein, a computer system refers to any known computing device and computer system. As described herein, all such computer systems include a processor and a memory. However, any processor of a computer system referred to herein may also refer to one or more processors, which may reside in one computing device or in multiple computing devices acting in parallel. Additionally, any memory of a computing device referred to herein may also refer to one or more memories, which may reside in one computing device or in multiple computing devices acting in parallel.

[0025] As used herein, the term processor refers to a central processing unit, microprocessor, microcontroller, reduced instruction set circuits (RISC), application specific integrated circuits (ASIC), logic circuits, and other circuits or processors capable of performing the functions described herein. The above are examples only and are therefore not intended to limit in any way the definition and / or meaning of the term processor.

[0026] As used herein, the term "database" refers to a body of data, a relational database management system (RDBMS), or both. As used herein, a database includes any collection of data, including hierarchical databases, relational databases, flat file databases, object-relational databases, object oriented databases, and other structured collections of records or data stored in a computer system. The above examples are examples only and are therefore not intended to limit in any way the definition and / or meaning of the term database. Examples of RDBMS include, but are not limited to, Oracle® Database, MySQL, IBM® DB2, Microsoft® SQL Server, Sybase®, and PostgreSQL. However, any database that enables the systems and methods described herein may be used. (Oracle is a registered trademark of Oracle Corporation, Redwood Shores, CA. IBM is a registered trademark of International Business Machines Corporation, Armonk, NY. Microsoft is a registered trademark of Microsoft Corporation, Redmond, WA. Sybase is a registered trademark of Sybase Inc., Dublin, CA.)

[0027] In one embodiment, a computer program is provided to enable the control unit 143, the program being embodied in a computer readable medium. The computer system runs on a single computer system without the need to connect to a server computer. In a further embodiment, the computer system runs on a Windows environment (Windows is a registered trademark of Microsoft Corporation, Redmond, Washington). In yet another embodiment, the computer system runs on a mainframe environment and a UNIX server environment (UNIX is a registered trademark of X / Open Ltd., Reading, Berkshire, England). Alternatively, the computer system runs on any suitable operating system environment. The computer program is designed to be flexible and to run in a variety of different environments without compromising any primary functionality. In some embodiments, the computer system includes multiple components distributed among multiple computing devices. One or more of the components may be in the form of computer executable instructions embodied in a computer readable medium.

[0028] The computer systems and processes are not limited to the specific embodiments described herein. Furthermore, each computer system and each process component can be implemented independently and are separate from other components and processes described herein. Each component and process can also be used in combination with other assembly packages and processes.

[0029] In one embodiment, the computer system may be configured as a server system. Figure 10 illustrates an example configuration of a server system 301 used to receive measurements from one or more sensors, including but not limited to, temperature sensor 139, diameter transducer 141, and any combination thereof, and 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., argon flow controller), upper coil power supply 149, lower coil power supply 151, and any combination thereof, as described herein and depicted in Figure 4 in one embodiment. Referring again to Figure 10, server system 301 may also include, but is not limited to, a database server. In this example embodiment, server system 301 performs all of the steps used to control one or more devices of system 100 as described herein.

[0030] The server system 301 includes a processor 305 for executing instructions. The instructions may be stored, for example, in a memory area 310. The processor 305 may include one or more processing units (e.g., a multi-core configuration) for executing instructions. The instructions may be executed within a variety of different operating systems of the server system 301, such as, for example, UNIX, LINUX, Microsoft Windows, etc. It should also be appreciated that at the start of the computer-based method, various instructions may be executed during initialization. Some operations may be required to perform one or more processes described herein, while other operations may be more general and / or specific to a particular programming language (e.g., C, C#, C++, Java, or other suitable programming language).

[0031] The processor 305 is operatively coupled to a communication interface 315 such that the server system 301 can communicate with a remote device, such as a user system or another server system 301. For example, the communication interface 315 may receive requests (e.g., requests to receive sensor inputs and provide interactive user interfaces to control one or more devices of the system 100 from a client system over the Internet).

[0032] The processor 305 may also be operatively coupled to a storage device 134. The storage device 134 is any suitable computer operating hardware for storing and / or retrieving data. In some embodiments, the storage device 134 is integrated into the server system 301. For example, the server system 301 may include one or more hard disk devices as the storage device 134. In other embodiments, the storage device 134 may be external to the server system 301 and accessed by multiple server systems 301. For example, the storage device 134 may include multiple storage units, such as hard disks, solid state disks, etc., in a redundant array of inexpensive disks (RAID) configuration. The storage device 134 may include a storage area network (SAN) and / or a network attached storage (NAS) system.

[0033] In some embodiments, the processor 305 is operatively coupled to the storage device 134 through a storage interface 320. The storage interface 320 is any component capable of providing the processor 305 with access to the storage device 134. The storage interface 320 may include, for example, an Advanced Technology Attachment (ATA) adapter, a Serial ATA (SATA) adapter, a Small Computer System Interface (SCSI) adapter, a RAID controller, a SAN adapter, a network adapter, and / or any component capable of providing the processor 305 with access to the storage device 134.

[0034] The memory area 310 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). The above memory types are by way of example only and therefore are not limiting as to the types of memory that may be used for the storage of computer programs.

[0035] In another embodiment, the computer system may be provided in the form of a computing device, such as, for example, computing device 402 (shown in FIG. 11). Computing device 402 includes a processor 404 for executing instructions. In some embodiments, executable instructions are stored in memory area 406. Processor 404 may include one or more processing units (e.g., a multiple core configuration). Memory area 406 is any device that permits information, such as, for example, executable instructions and / or other data, to be stored and retrieved. Memory area 406 may include one or more computer-readable media.

[0036] In another embodiment, the memory included in the computing device of the control unit 143 may include multiple modules. Each module may include instructions configured to execute using at least one processor. The instructions included in the multiple modules, when executed by one or more processors of the computing device, may perform at least a portion of a method for simultaneously adjusting multiple process parameters as described herein. Non-limiting examples of modules stored in the memory of the computing device include a first module for receiving measurements from one or more sensors and a second module for controlling one or more devices of the system 100.

[0037] The computing device 402 also includes a media output component 408 for presenting information to the user 400. The media output component 408 is any component capable of communicating information to the user 400. In some embodiments, the media output component 408 includes an output adapter, such as, for example, a video adapter and / or an audio adapter. The output adapter is operatively coupled to the processor 404 and further configured to be operatively coupled to an output device, such as, for example, a display device (e.g., a liquid crystal display (LCD), organic light emitting diode (OLED) display, cathode ray tube (CRT), or “electronic ink” display) or an audio output device (e.g., speakers or headphones).

[0038] In some embodiments, the client computing device 402 includes an input device 410 to receive input from the user 400. The input device 410 may include, for example, a keyboard, a pointing device, a mouse, a stylus, a touch sensor panel (e.g., a touchpad or touch screen), a camera, a gyroscope, an accelerometer, a position detector, and / or an audio input device. A single component, such as a touch screen, may function as both an output device of the media output component 408 and as an input device 410.

[0039] Computing device 402 also includes a communications interface 412 configured to be communicatively coupled to a remote device, such as, for example, server system 302 or a web server. Communications interface 412 may include a wired or wireless network adapter or a wireless data transceiver, for example, for use with a cellular network (e.g., Global System for Mobile communications (GSM), 3G, 4G, or Bluetooth) or other mobile data network (e.g., Worldwide Interoperability for Microwave Access (WIMAX)).

[0040] Memory 406 stores, for example, computer readable instructions for providing a user interface to user 400 through media output component 408 and, optionally, receiving and processing input from input device 410. The user interface may include a web browser and an application, among other possibilities. The web browser allows user 400 to view and interact with media and other information, typically embedded web pages or websites, from a web server. The application allows user 400 to interact with server applications. The user interface, through one or both of the web browser and the application, facilitates the display of information related to the process of producing low oxygen content monocrystalline silicon ingots.

[0041] In an example embodiment, system 100 produces silicon crystal ingots suitable for use in device fabrication. Advantageously, system 100 may be used to produce silicon crystals 27 that are substantially free of agglomerated intrinsic point defects, a substantial portion of which or all of which are substantially free of agglomerated intrinsic point defects. Additionally, system 100 may be used to produce crystals 27 that are substantially free of agglomerated defects, such as crystals having a diameter of about 120 nanometers (nm), or, more particularly, crystals having a diameter of greater than about 90 nm. The shape of the solid-liquid or crystal-melt interface and the strain rate are controlled during crystal growth to limit and / or inhibit the formation of agglomerated intrinsic point defects.

[0042] During production, oxygen is introduced into silicon crystal ingots by the solid-liquid or crystal-melt interface. However, oxygen can cause various defects in wafers produced from the ingots, reducing the yield of semiconductor devices. Therefore, it is desirable to produce silicon crystal ingots with low oxygen concentrations. Using the methods described herein, silicon crystal ingots are produced having oxygen concentrations below about 5 parts per million atoms (ppma).

[0043] Without being limited to any particular theory, oxygen is introduced into the growing silicon crystal ingot emerging from the melt by a series of interacting events, each of which is influenced by at least one process parameter as described herein below. SiO is introduced into the melt by melting of the crucible walls. SiO introduced at the crucible walls can be transported elsewhere in the melt through flows induced by buoyancy forces created by localized heating of the melt near the crucible walls. SiO can be further transported by additional flows induced by the rotation rate of the crystal at the solid-liquid interface and the rotation rate of the crucible itself. The concentration of SiO in the melt can be reduced by evaporation from the melt at exposed surfaces of the melt. The interaction of any combination of dissolution, convection, and evaporation of SiO in the melt affects the concentration of SiO in the melt located near the crystal-melt interface formed in the silicon crystal ingot. In various embodiments, any one or more process parameters are adjusted to simultaneously reduce the concentration of SiO located near the crystal-melt interface, thereby reducing the oxygen concentration in the silicon crystal ingot formed by the method.

[0044] In various embodiments, various process parameters are adjusted simultaneously to facilitate producing a silicon crystal ingot with a low oxygen concentration. In one embodiment, the various process parameters are adjusted in at least two stages, including a mid-body growth stage corresponding to growing the silicon crystal ingot to an intermediate ingot length of about 800 mm, and a late body growth stage corresponding to growing the silicon crystal ingot from the intermediate ingot length of about 800 mm to the full ingot length. In this embodiment, the adjustment of the various process parameters in the at least two different stages comprises changing the interaction behavior of dissolution, convection, and evaporation of SiO in the melt, the depth of the melt in the crucible, and a flow cell in the melt in the crucible as the silicon crystal ingot grows to length.

[0045] In particular, the role of convection is altered throughout the formation of the entire silicon crystal ingot due to the decrease in the depth of the melt in the crucible associated with the growth of the silicon crystal ingot, as described in detail below. As a result, the adjustment of at least one process parameter is altered differently in the late body growth stage relative to the adjustment of these same parameters in the intermediate body growth stage. In some embodiments, the adjustment of at least three process parameters is altered differently in the late body growth stage relative to the adjustment of these same parameters in the intermediate body growth stage. As described herein below, the adjustment of the process parameters adjusts various factors associated with the convection of SiO in the melt in the late body growth stage. In one embodiment, the adjustment process parameters that are altered during the late body growth stage include, but are not limited to, seed rotation rate, crucible rotation rate, and magnetic field strength.

[0046] Referring again to FIG. 4, seed rotation rate refers to the rate at which the pull shaft or cable 117 rotates the seed crystal 115 about axis 38. The seed rotation rate affects the rate of SiO flow from the crucible 10 to the crystal 27 and the rate of SiO evaporation from the melt 25. Referring again to FIG. 2, the flow of SiO from the crucible 10 to the crystal 27 is generally influenced by the interaction between the crystal flow cell 18, which is driven by the rotation of the crystal 27, and the buoyancy flow cell 17, which is driven by the heating of the melt 25 in the crucible 10, at the seed rotation rate in the melt 25. The effect of seed rotation rate on the flow of SiO from the crucible 10 to the crystal 27 varies depending on the stage of growth of the crystal 27.

[0047] FIG. 5A is a cross-sectional view of simulated flow lines and oxygen concentration in melt 25 at the mid-body growth stage, corresponding to growth of crystal 27 to a mid-ingot length of about 800 mm. At the mid-body growth stage, the depth 200 of melt 25 in crucible 10 is deep enough to effectively decouple the interaction between the fluid motion induced by crystal flow cell 18 and buoyancy flow cell 17. A high seed rotation rate (i.e., 12 rpm) reduces the boundary layer thickness between melt line 36 and gas above melt 25 to increase SiO evaporation. In addition, a high seed rotation rate reduces melt flow from crucible 10 to crystal 27 by suppressing buoyancy flow cell 17 with induced crystal flow cell 18 as depicted in FIG. 5A. In addition, a high seed rotation rate creates an outer radial flow that retards the internal flow (i.e., transport) of SiO from crucible 10, reducing the oxygen concentration in crystal 27.

[0048] 5B is a cross-sectional view of simulated flow lines and oxygen concentration in melt 25 in the late body growth stage corresponding to the growth of crystal 27 from mid-ingot length to full ingot length of about 800 mm. Due to the removal of melt 25 from crucible 10 associated with the formation of crystal 27, the depth 200 in the late body growth stage is shallower with respect to the depth 200 in the mid-body growth stage as depicted in FIG. 5A. At high speeds similar to those used to process the simulation depicted in FIG. 5A (i.e., 12 rpm), the crystal flow cell 18 contacts the inner wall of crucible 10, causing convection of SiO formed at the inner wall of crucible 10 into crystal 27 formed in the late body growth stage.

[0049] 5C is a cross-sectional view of simulated flow lines and oxygen concentration in melt 25 during the late body growth stage calculated at a low seed rotation rate (e.g., 8 rpm). The crystal flow cell 18 induced by the low seed rotation rate does not extend to the inner wall of crucible 10, but is instead excluded by buoyancy cell 17. As a result, the flow of SiO produced at the inner wall of crucible 10 to crystal 27 is impeded, thereby reducing the oxygen concentration in crystal 27 formed during the late body growth stage at reduced seed rotation rate.

[0050] As described herein, the transition from the intermediate to late body growth stage is a gradual transition. The transition can vary depending on various parameters of the process, such as, for example, crucible size, shape, melt depth, modeling parameters, etc. In general, in the intermediate body growth stage, the parameters are such that there is limited or no interaction between the fluid motions induced by the crystal flow cell 18 and the buoyancy flow cell 17, and the crystal flow cell 18 and the buoyancy flow cell 17 are effectively decoupled. In the late body growth stage, the parameters are such that there is interaction between the fluid motions induced by the crystal flow cell 18 and the buoyancy flow cell 17, and the crystal flow cell 18 and the buoyancy flow cell 17 are effectively coupled. By way of non-limiting example, the late body growth stage occurs when less than 37% of the initial mass of the melt 25 remains in the crucible 10 in an embodiment including an initial molten mass of 250 kg in a crucible 10 with an inner diameter of about 28 inches. In various embodiments, the depth 200 of the melt 25 in the crucible 10 is monitored to identify the transition from the intermediate to late body growth stage. In other embodiments, the late body growth stage occurs when less than about 35%, less than about 40%, less than about 45%, or less than about 50% of the initial mass of the melt 25 remains in the crucible 10. In some embodiments, the transition from the intermediate to late body growth stage is determined based on the depth of the melt 25, or other suitable parameters.

[0051] In various embodiments, the method includes adjusting the seed rotation rate in at least two stages, including, but not limited to, the mid-body growth stage and the late-body growth stage. In one embodiment, the method includes rotating the crystal 27 during the mid-body growth stage at a seed rotation rate in the range of about 8 to 14 rpm, more particularly 12 rpm. In this embodiment, the method further includes reducing the seed rotation rate in the late-body growth stage to a seed rotation rate in the range of about 6 to 8 rpm, more particularly 8 rpm.

[0052] In another embodiment, the seed rotation rate may be decreased by the intermediate ingot length. By way of non-limiting example, the seed rotation rate may be adjusted to about 12 rpm at intermediate ingot lengths up to about 850 mm as depicted in FIG. 9, and may be adjusted to linearly decrease to about 8 rpm at intermediate ingot lengths of about 950 mm, and then adjust the seed rotation rate to about 8 rpm up to the total ingot length. As also depicted in FIG. 9, the oxygen content of the crystal in the body length range of about 800 mm to the total ingot length is reduced compared to the crystal formed at a constant seed rotation rate of about 12 rpm. FIG. 6 is a graph comparing the simulated oxygen concentration of the crystal formed at seed rotation rates according to three rotation schedules: a) rotation at 12 rpm for the formation of the entire crystal, b) rotation at 12 rpm to the intermediate crystal length of 900 mm followed by rotation at 8 rpm for the formation of the remaining crystal length, and c) rotation at 12 rpm to the intermediate crystal length of 900 mm followed by rotation at 6 rpm for the formation of the remaining crystal length. As shown in FIG. 6, a low seed turnover rate reduced the oxygen concentration in some of the crystals formed in the later body growth stage.

[0053] The crucible rotation rate can also affect the oxygen concentration in the crystal 27 formed by the method embodiments. The crucible rotation rate refers to the rate at which the crucible 10 rotates about the axis 38 using the crucible drive unit 107. The crucible rotation rate affects the flow of SiO from the crucible 10 to the crystal 27 and the amount of SiO evaporated from the melt 25. A high crucible rotation rate reduces both the boundary layer thickness between the crucible 10 and the melt 25 and the boundary layer thickness between the melt line 36 and the gas above the melt 25. However, to minimize the oxygen concentration in the crystal 27, a thick boundary layer between the crucible 10 and the melt 25 is desirable to reduce the SiO transport rate, while a thin boundary layer between the melt line 36 and the gas above the melt 25 is desirable to increase the SiO evaporation rate. Thus, the crucible rotation rate is selected to balance the competing benefits of a high boundary layer thickness between the crucible 10 and the melt 25 resulting from a low crucible rotation rate and a low boundary layer thickness between the melt line 36 and the gas above the melt 25 resulting from a high crucible rotation rate.

[0054] The change in melt 10 depth 200 between the intermediate and late body growth stages described herein above affects the effect of adjusting the crucible rotation rate on oxygen concentration in a manner similar to the effect of seed rotation rate described herein above. In various embodiments, the method includes adjusting the crucible rotation rate in at least two stages, including but not limited to the intermediate and late body growth stages. In one embodiment, the method includes rotating the crucible 10 in the intermediate body growth stage at a crucible rotation rate in the range of about 1.3 rpm to about 2.2, more particularly 1.7 rpm. In this embodiment, the method further includes reducing the crucible rotation rate in the late body growth stage to a crucible rotation rate in the range of about 0.5 rpm to about 1.0 rpm, more particularly 1 rpm.

[0055] 7A and 7B are graphs showing simulated oxygen concentrations in silicon ingots as a function of crucible rotation rate during the late body growth stage. The silicon ingot of FIG. 7A was formed using an embodiment of the method in which the seed rotation rate was reduced from 12 rpm to 6 rpm during the late body growth stage, and the crucible rotation rate was reduced from about 1.7 rpm to 1 rpm or 1.5 rpm during the late body growth stage. The silicon ingot of FIG. 7B was formed using an embodiment of the method in which the seed rotation rate was reduced from 12 rpm to 8 rpm during the late body growth stage, and the crucible rotation rate was reduced from about 1.7 rpm to 0.5 rpm, 1 rpm, or 1.5 rpm during the late body growth stage. In both simulations, lower crucible rotation rates were associated with lower oxygen concentrations in the resulting silicon ingots.

[0056] The method further includes adjusting the magnetic field strength in at least two stages, including, but not limited to, a mid-body growth stage and a late-body growth stage. The magnetic field strength refers to the strength of the cusp magnetic field in the vacuum chamber. More specifically, the magnetic field strength is characterized by the current flowing through the coils 31 and 33, which are controlled to adjust the magnetic field strength. The magnetic field strength affects the flow of SiO from the crucible 10 to the crystal 27. That is, a high magnetic field strength minimizes the flow of SiO from the crucible 10 to the crystal 27 by suppressing the buoyancy flow in the melt 25. Because the magnetic field suppresses the buoyancy flow, it reduces the melting rate of the quartz crucible and therefore reduces the lattice oxygen incorporated in the crystal. However, as the magnetic field strength increases beyond a certain level, further impediment of the buoyancy flow results in a reduced evaporation rate at the melt free surface and therefore increases the lattice oxygen level. As previously described herein, due to the difference in the relative contribution of buoyant flow to the oxygen content of the crystals in the late body formation stage relative to the intermediate body formation stage, adjustment of the magnetic field strength in the late body formation stage allows for appropriate adjustment of the buoyant flow to reduce oxygen in the crystals formed in the late body formation stage.

[0057] In various embodiments, the method includes adjusting the magnetic field strength in at least two stages, including, but not limited to, an intermediate body growth stage and a late body growth stage. In one embodiment, the method includes adjusting the magnetic field strength in the intermediate body growth stage such that the magnetic field strength is about 0.02 to 0.05 Tesla (T) at the edge of the crystal 27 at the solid-liquid interface and about 0.05 to 0.12 T at the walls of the crucible 10. In another aspect, the method includes adjusting the magnetic field strength in the late body growth stage such that the magnetic field strength is about 150% of the magnetic field strength used during the intermediate body growth stage, which corresponds to about 0.03 to 0.075 T at the edge of the crystal 27 at the solid-liquid interface and about 0.075 to 0.18 T at the walls of the crucible 10.

[0058] Figures 8A, 8B, and 8C are cross-sectional views of simulated flow lines and total velocities in melt 25 during the late body growth stage. Figure 8A was simulated using a magnetic field strength corresponding to 50% of the magnetic field used during the intermediate body growth stage (i.e., about 0.01 to 0.025 T at the edge of crystal 27 at the solid-liquid interface and about 0.025 to 0.06 T at the wall of crucible 10). Figure 8B was simulated using a magnetic field strength corresponding to 95% of the magnetic field used during the intermediate body growth stage (i.e., about 0.019 to 0.0475 T at the edge of crystal 27 at the solid-liquid interface and about 0.0475 to 0.114 T at the wall of crucible 10). FIG. 8C was simulated using a magnetic field strength corresponding to 150% of the magnetic field used in the intermediate body growth stage (i.e., about 0.03 to 0.075 T at the edge of the crystal 27 at the solid-liquid interface and about 0.075 to 0.18 T at the wall of the crucible 10). Comparing FIGS. 8A, 8B, and 8C, as the strength of the magnetic field is increased, the flow 300 from the bottom of the crucible 10 to the crystal-melt interface 302 transitions from a relatively high convection flow to the crystal-melt interface 302 at low magnetic field strength (FIG. 8A) to a relatively low convection flow at high magnetic field strength. This suppression of buoyancy flow in the melt 25 by the increased magnetic field results in a lower oxygen concentration in the resulting silicon ingot, as summarized in Table 1 below. At 150% magnetic field strength, the simulated oxygen concentration was within the desired range of less than 5% parts per million atoms (ppma). Table 1: Effect of magnetic field strength during the late bulk growth stage on the oxygen concentration of silicon ingots.

[0059] [Table 1]

[0060] One or more additional process parameters may be adjusted to facilitate producing a silicon crystal ingot with a low oxygen concentration. However, the effect of these additional process parameters is not sensitive to changes in the depth 200 of the melt 25 in the crucible 10 during the growth of the crystal 27. As a result, the adjustments of the additional process parameters described herein remain essentially the same during different stages of crystal growth, as described in additional detail below.

[0061] One additional process parameter that is controlled, at least in some embodiments, is the temperature of the walls of the crucible 10. The temperature of the walls of the crucible 10 corresponds to the melting rate of the crucible 10. In particular, increasing the temperature of the walls of the crucible 10 causes portions of the crucible 10 to react with and dissolve in the melt 25 faster, generating SiO in the melt and potentially increasing the oxygen concentration of the crystal 27 through the crystal-melt interface. Thus, decreasing the temperature of the walls of the crucible 10, as used herein, is equivalent to decreasing the melting rate of the crucible 10. By decreasing the temperature of the walls of the crucible 10 (i.e., decreasing the melting rate of the crucible 10), the oxygen concentration of the crystal 27 can be decreased. The temperature of the walls can be adjusted by controlling one or more additional process parameters, including, but not limited to, heater power, melt-to-reflector gap.

[0062] Heater power is another process parameter that can be controlled in some embodiments to adjust the temperature of the walls of the crucible 10. Heater power refers to the power of the side and bottom heaters 105 and 106. In particular, by increasing the power of the side heater 105 and decreasing the power of the bottom heater 106 relative to a typical heating configuration, the heating spot on the walls of the crucible 10 is raised closer to the melt line 36. When the temperature of the walls of the crucible 10 at or below the melt line 36 is low, the amount of SiO generated by the melt 25 that reacts with the crucible 10 is also low. The heater power configuration also affects the melt flow by reducing the flow (i.e., transport) of SiO from the crucible 10 to the single crystal 27. In this embodiment, the power of the bottom heater 106 is about 0 to 5 kilowatts, more particularly about 0 kilowatts, and the power of the side heater 105 ranges from about 100 to 125 kilowatts. Variations in the power output of the side heaters 105 may be due to, for example, variations in heating zones from puller to puller.

[0063] In some embodiments, the melt-to-reflector gap is an additional process parameter that is controlled to adjust the temperature of the walls of the crucible 10. The melt-to-reflector gap refers to the gap between the melt line 36 and the heated reflector (not shown). The melt-to-reflector gap affects the temperature of the walls of the crucible 10. In particular, a large melt-to-reflector gap reduces the temperature of the walls of the crucible 10. In this embodiment, the melt-to-reflector gap is about 60 mm to 80 mm, more particularly 70 mm.

[0064] Seed lift is an additional process parameter controlled to regulate the flow of SiO from the crucible 10 to the crystal 27. Seed lift refers to the rate at which the pull shaft or cable 117 lifts the seed crystal 115 out of the melt 25. In one embodiment, the seed crystal 115 is lifted at a rate in the range of about 0.42 to 0.55 millimeters per minute (mm / min), more specifically 0.46 mm / min, for a 300 mm production. This pull rate is slower than pull rates typically used for smaller diameter (e.g., 200 mm) crystals. For example, for a 200 mm production, the seed lift can be in the range of about 0.55 to 0.85 mm / min, more specifically 0.7 mm / min.

[0065] The pull speed is an additional process parameter that can be adjusted to control the defect quality of the crystal. For example, using SP2 laser light scattering, the detected lattice point defects generated by the processes described herein can be less than 400 defects smaller than 60 nm, less than 100 defects between 60 and 90 nm, and less than 100 defects between 90 and 120 nm.

[0066] In some embodiments, inert gas flow is an additional process parameter that is controlled to regulate SiO evaporation from the melt 25. Inert gas flow, as described herein, refers to the rate at which argon gas flows through the vacuum chamber 101. Increasing the argon gas flow rate sweeps additional SiO gas above the melt line 36 away from the crystal 27, minimizing the partial pressure of SiO gas, which in turn increases SiO evaporation. In this embodiment, the argon gas flow rate ranges from about 100 slpm to 150 slpm.

[0067] Inert gas pressure is an additional process parameter that is also controlled in some embodiments to regulate SiO evaporation from melt 27. Inert gas pressure, as described herein, refers to the pressure of argon gas flowing through vacuum chamber 101. Decreasing the argon gas pressure increases SiO evaporation and thus decreases the SiO concentration in melt 25. In this embodiment, the argon gas pressure ranges from about 10 torr to 30 torr.

[0068] In a suitable embodiment, the cusp position is an additional process parameter that is controlled to regulate the temperature of the walls of the crucible 10 and the flow of SiO from the crucible 10 to the crystal 27. The cusp position refers to the location of the cusp of the magnetic field generated by the coils 31 and 33, as described herein. Maintaining the cusp position below the melt line 36 facilitates reducing the oxygen concentration. In this embodiment, the cusp position is set in the range of about 10 mm to 40 mm below the melt line 36, more particularly in the range of about 25 mm to 35 mm, and more particularly about 30 mm below the melt line 36.

[0069] By controlling the process parameters (i.e., heater power, crucible rotation rate, magnetic field strength, seed lift, melt-to-reflector gap, inert gas flow, inert gas pressure, seed rotation rate, and cusp position), as described above, multiple process parameters (i.e., crucible wall temperature, flow of SiO from the crucible to the single crystal, and evaporation of SiO from the melt) are adjusted to produce silicon ingots with low oxygen concentration. In one embodiment, the method described herein facilitates producing silicon ingots with an ingot diameter greater than about 150 millimeters (mm), a total ingot length of at least about 900 mm, and an oxygen concentration less than 5 ppma. In another embodiment, the method described herein facilitates producing silicon ingots with an ingot diameter in the range of about 150 mm to 460 mm, particularly about 300 mm, and an oxygen concentration less than 5 ppma. In yet another additional embodiment, the methods described herein facilitate producing silicon ingots with a total ingot length ranging from about 900 mm to 1200 mm and an oxygen concentration of less than 5 ppma.

[0070] Wafers having low oxygen concentration using the systems and methods described herein can be advantageous in various applications. For example, insulated-gate bipolar transistors (IGBTs), high quality radio-frequency (RF), high resistivity silicon on insulator (HR-SOI), and charge trap layer SOI (CTL-SOI) applications can benefit from low oxygen concentration because they achieve high resistivity and do not have p-n junctions. Wafers produced using the methods described herein for IGBT applications can have, for example, an N-type resistivity of 30 to 300 ohm centimeters (Ωcm) or an N / P-type resistivity of greater than 750 Ωcm. Additionally, wafers produced using the methods described herein for RF, HR-SOI, and / or CTL-SOI applications can have, for example, a P-type resistivity of greater than 750 Ωcm. Wafers produced using the systems and methods described can also be used as handle wafers.

[0071] For P-type wafers produced using the methods described herein, boron, aluminum, germanium, and / or indium can be suitably used as majority carriers, and red phosphorus, phosphorus, arsenic, and / or antimony can be used as minority carriers. For N-type wafers produced using the methods described herein, red phosphorus, phosphorus, arsenic, and / or antimony can be used as majority carriers, and boron, aluminum, germanium, and / or indium can be used as minority carriers.

[0072] To improve mechanical strength and sliding performance, wafers produced using the methods described herein can be co-doped with nitrogen or carbon (e.g., by doping the single crystal forming the ingot) so that the wafer has a relatively low Oi. For example, the nitrogen concentration can be from 0 to 8e15 atoms per cubic centimeter (atoms / cm 3 ) and the carbon concentration can vary from 0.0 to 2.0 ppma.

[0073] Exemplary systems and methods for producing relatively low oxygen concentration monocrystalline silicon ingots from a melt formed from polycrystalline silicon are described herein. These methods utilize a change in the structure of a melt flow cell during a first and second stage of the production of the ingot to produce relatively low oxygen concentration silicon. During the first stage, the silicon ingot is relatively small and the depth of the melt is relatively deep. The second stage is characterized by the depth of the melt being exhausted in the crucible by the formation of the silicon ingot. In this second stage, the flow cell induced by the rotation of the silicon ingot in the melt can come into contact with the bottom of the crucible, causing the undesired inclusion of silicon oxide formed at the bottom of the crucible in the growing crystal ingot. The methods and systems described herein control the production of the ingot to limit the inclusion of the undesired silicon oxide. Typically, at least one process parameter is changed during the second stage relative to its value during the first stage. Non-limiting examples of process parameter changes from the first stage to the second stage include a reduced crystal rotation rate, a reduced crucible rotation rate, an increased magnetic field strength, and any combination thereof. For example, in some embodiments, the silicon ingot is rotated more slowly during the second stage to reduce flow cell induced rotational contact at the bottom of the crucible, thereby reducing the amount of oxygen contained in the silicon ingot.

[0074] The systems and methods described herein allow for the formation of single crystal silicon ingots with sustained low oxygen concentrations over the length of the silicon ingot achieved using previous methods. A detailed description of the effect of these changes in process parameters on the configuration of the flow cell within the crucible and the oxygen content of silicon ingots formed using the methods of the various embodiments is described in further detail herein.

[0075] Embodiments of the methods described herein achieve superior results compared to previous methods and systems. For example, the methods described herein are easier to produce silicon ingots with lower oxygen concentrations than at least some known methods. Moreover, unlike at least some known methods, the methods described herein can be used to produce ingots having diameters greater than 150 mm.

[0076] When introducing elements of the invention or embodiments thereof, the articles "a," "an," "the," and "said" are intended to mean that there are one or more 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.

[0077] Range language, as used herein throughout the specification and claims, can be applied to modify expressions relating to any quantity that can be permissibly varied without resulting in a change in the basic function to which it pertains. Thus, for example, terms such as "about," "approximately," and "substantially" and the like, and values ​​modified by such terms, are not limited to the exact values ​​specified. In at least some instances, range language corresponds to the precision of the means for measuring the values. Here and throughout the specification and claims, range limitations can be combined and / or substituted. Such ranges include all subranges identified and included within the ranges unless the content or language indicates otherwise.

[0078] Since various changes may be made herein above without departing from the scope of the present invention, all matter contained in the above description and shown in the accompanying drawings is intended to be interpreted as illustrative and not in a limiting sense.

Claims

1. 1. A method for producing a silicon ingot, comprising: withdrawing a seed crystal from a melt comprising molten silicon in a crucible to form a silicon ingot, the crucible being enclosed in a vacuum chamber including a cusped magnetic field; adjusting at least one process parameter, wherein adjusting the at least one process parameter comprises adjusting a magnetic field strength, and wherein the at least one process parameter is adjusted in at least two stages; The at least two stages include: a first stage corresponding to forming the silicon ingot to an intermediate ingot length; a second stage corresponding to forming the silicon ingot from the intermediate ingot length to a full ingot length; adjusting the magnetic field strength during the first stage comprises adjusting the magnetic field strength at an end of the silicon ingot at a solid-liquid interface to a strength of 0.02 to 0.05 Tesla during the first stage and adjusting the magnetic field strength at a wall of the crucible to a strength of 0.05 to 0.12 Tesla; Adjusting the magnetic field strength during the second stage includes: increasing the magnetic field strength at the end of the silicon ingot at the solid-liquid interface relative to the first stage, wherein during the second stage, the magnetic field strength is increased to a magnetic field strength of 0.03 to 0.075 Tesla at the end of the silicon ingot at the solid-liquid interface; increasing the magnetic field strength at the wall of the crucible relative to the first stage, wherein during the second stage the magnetic field strength is increased to a magnetic field strength at the wall of the crucible of 0.075 to 0.18 Tesla; increasing the magnetic field strength during the second stage by 150% of the magnetic field strength during the first stage.

2. further comprising controlling a plurality of additional process parameters during the first and second stages; the plurality of additional process parameters comprising at least one of a heater power, a melt-to-reflector gap, a seed pull rate, an inert gas flow, an inert gas pressure, and a cusp position; 2. The method of claim 1 , wherein controlling the plurality of additional process parameters during the first and second stages comprises controlling the parameter to be substantially the same during the first and second stages for each parameter of the plurality of additional process parameters.

3. the first stage is an intermediate growth stage; the second stage being a late body growth stage; 2. The method of claim 1, wherein the transition from the intermediate growth stage to the late body growth stage is identified by determining the depth of the melt within the crucible or by determining that less than about 50% of the initial mass of the melt remains in the crucible.

4. 1. A crystal growth system for producing silicon ingots, comprising: A vacuum chamber; a crucible disposed within the vacuum chamber, the crucible rotatable about an axis of symmetry and configured to hold a melt comprising molten silicon; a pull shaft movable along and rotatable about an axis of symmetry and configured to hold a seed crystal; at least one magnet generating a controllable cusp magnetic field within the crucible; A control unit comprising a processor and a memory, The memory, when executed by the processor, causes the processor to: withdrawing the seed crystal from the melt in the crucible to form the silicon ingot; adjusting at least one process parameter, wherein adjusting the at least one process parameter comprises adjusting a magnetic field strength, and wherein the at least one process parameter is adjusted in at least two stages; a control unit for storing instructions to adjust the at least one process parameter, the at least two stages comprising a first stage corresponding to formation of the silicon ingot to an intermediate ingot length and a second stage corresponding to formation of the silicon ingot from the intermediate ingot length to a full ingot length; The memory, when executed by the processor, causes the processor to: storing instructions for adjusting the magnetic field strength by increasing the magnetic field strength at an end of the silicon ingot at a solid-liquid interface for the first stage and increasing the magnetic field strength at a wall of the crucible for the first stage, wherein during the first stage, the magnetic field strength is 0.02 to 0.05 Tesla at the end of the silicon ingot at the solid-liquid interface and 0.05 to 0.12 Tesla at the wall of the crucible, and during the second stage, the magnetic field strength is 0.03 to 0.075 Tesla at the end of the silicon ingot at the solid-liquid interface and 0.075 to 0.18 Tesla at the wall of the crucible; The memory stores instructions that, when executed by the processor, cause the processor to adjust the magnetic field strength by increasing the magnetic field strength during the second stage by 150% of the magnetic field strength during the first stage.

5. 5. The system of claim 4, wherein the memory further stores further instructions that, when executed by the processor, cause the processor to control a plurality of additional process parameters during the first and second stages.

6. 6. The system of claim 5, wherein the plurality of additional process parameters comprises at least one of heater power, melt-to-reflector gap, seed pull rate, inert gas flow, inert gas pressure, and cusp position.

7. 7. The system of claim 6, wherein the memory stores instructions that, when executed by the processor, cause the processor to control the process parameters to be substantially the same during the first and second stages for each parameter of the plurality of additional process parameters.

8. the first stage is an intermediate growth stage; the second stage being a late body growth stage; 5. The system of claim 4, wherein the transition from the intermediate growth stage to the late body growth stage is identified by determining a depth of the melt within the crucible or by determining that less than about 50% of the initial mass of the melt remains in the crucible.

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