Patent Publication Number: US-2022228291-A1

Title: Systems and methods for production of silicon using a horizontal magnetic field

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a divisional of U.S. patent application Ser. No. 17/115,154 filed Dec. 8, 2020, which claim priority to U.S. Provisional Patent Application No. 62/947,785 filed Dec. 13, 2019, the entire disclosures of which are hereby incorporated by reference in their entireties. 
    
    
     FIELD 
     This disclosure generally relates to the production of silicon ingots, and more specifically, to methods and systems for achieving a high success ratio producing silicon ingots in the Czochralski process using a horizontal magnetic field. 
     BACKGROUND 
     During the 1990&#39;s, at least some high quality silicon growth was mainly controlled by the thermal condition of the puller and more specifically the hot zone (HZ) design itself, because the ratio of the pulling speed to the thermal gradient (v/G) was considered the dominant factor. In the late 1990&#39;s, further consideration of the crystal/melt interface at the same v/G was included in the growth of at least some high quality silicon. At that time, application of high quality silicon to memory devices really expanded as more customers transitioned from epi to polished and from 200 mm to 300 mm silicon. Soon after, it became established that high quality silicon growth requires very stable process growth conditions and controlled melt flow to achieve the specific crystal/melt needed to achieve the desired low crystal defectivity during growth. 
     Peripherally, as silicon crystal growth transitioned from 200 mm to 300 mm and corresponding charge sizes increased to maintain productivity, the need for magnetic field application to stabilize melt flow in the increasing melt volume was recognized as a dominate feature. 
     Several silicon manufactures transitioned to a horizontal magnetic field Czochralski process (HMCZ) in the early 2000&#39;s when high quality 300 mm silicon production started in order to control the crystal/melt interface effectively. Other silicon manufactures used a cusp magnetic field for 300 mm production of high quality silicon. In both cases, magnetic field in the silicon melt had a dramatic impact on crystal quality and performance and every manufacturer developed their own technique to optimize performance and quality from the onset. 
     During the process of producing single crystal silicon ingots with the CZ process and a magnetic field, oxygen may be introduced into silicon crystal ingots through a melt-solid or melt crystal interface. The oxygen may cause various defects in wafers produced from the ingots, reducing the yield of semiconductor devices fabricated using the ingots. For example, memory devices, 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 typically require a low interstitial oxygen concentration (Oi) in order to achieve high resistivity. In the case of HMCZ process, it was believed that the process typically requires a very low crucible rotation (C/R) to control oxygen in the growing crystal, particularly to control oxygen inclusion to the desired range applicable for memory devices. Further, a higher occurrence ratio of lost zero dislocation (LZD) from the crown to the end of body was found in HMCZ as compared to processes using a cusp magnetic field. 
     Thus, there exists a need for methods and systems that reduce LZD losses with HMCZ growth and provide an improved ZD success ratio for high quality silicon growth from crown to body. 
     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 
     In one aspect of this disclosure, a method for producing a silicon ingot by the horizontal magnetic field Czochralski method includes rotating a crucible containing a silicon melt, applying a horizontal magnetic field to the crucible, contacting the silicon melt with a seed crystal, and withdrawing the seed crystal from the silicon melt while rotating the crucible to form a silicon ingot. The crucible has a wettable surface with a cristobalite layer formed thereon 
     Another aspect is a wafer generated from a silicon ingot produced using the method described above. 
     Another aspect is a system for producing a silicon ingot. The system includes a crucible to contain a silicon melt, magnetic poles to produce a horizontal magnetic field, and a controller. The crucible has a wettable surface with a cristobalite layer formed thereon. The controller is programmed to produce a silicon ingot by rotating the crucible containing the silicon melt, applying a horizontal magnetic field to the crucible using the magnetic poles, contacting the silicon melt with a seed crystal, and withdrawing the seed crystal from the silicon melt while rotating the crucible to form a silicon ingot. 
     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 
       The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee. 
         FIG. 1  is a top view of a crucible of one embodiment. 
         FIG. 2  is a side view of the crucible shown in  FIG. 1 . 
         FIG. 3  is a schematic illustrating a horizontal magnetic field applied to a crucible containing a melt in a crystal growing apparatus. 
         FIG. 4  is a block diagram of a crystal growing system. 
         FIG. 5  presents temperature field in melt free surface by MGP in mm and crucible rotation in RPM. 
         FIG. 6  is a graph of crystallization rate as a function of time. 
         FIG. 7  is a graph of the thickness of the layer formed as a function of time at a temperature of 1360° C. 
         FIG. 8  is a contour plot of ZD success ratio by crucible rotation and the quantity of melt modifier in a natural sand crucible. 
     
    
    
     Like reference symbols in the various drawings indicate like elements. 
     DETAILED DESCRIPTION 
     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 θ  14 , and an axial direction Z  16 . The crucible  10  contains a melt  25  having a melt surface  36 . A crystal  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 θ  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. 
       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. 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 . 
       FIG. 4  is a block diagram of a crystal growing system  100 . System  100  employs a Czochralski crystal growth method to produce a 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. 
     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 . 
     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. 
     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 . 
     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 . 
     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. 
     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 supply  149 , 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. 
     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. 
     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). 
     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. 
     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. 
     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 supply  149 , 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. 
     The loss of zero dislocation (ZD) structure (quantified by LZD rate) is generally higher during silicon crystal Cz growth in a horizontal magnet (HMCZ) field versus growth in a Cusp (or vertical) magnetic field. However, the LZD rate in HMCZ can be lowered dramatically if the crystal is grown in a synthetic lined crucible versus a natural sand lined crucible. But while the ZD rate is better, the cost of synthetic lined crucibles is higher than natural sand. Additionally, the thin (roughly 2 mm thickness) synthetic liner dissolves in a relatively short process time, leaving the backing sand layer exposed to the melt, which allows quartz particles to enter the melt and hit the growing crystal. Thus, the exposure of bubbles in the liner or even from the backing sand into the melt is higher. To avoid bubble exposure and/or backing sand contamination by dissolution when using synthetic lined crucibles, the process hot hours are generally limited to less than ˜250 hours, which is much shorter process time than achievable for natural sand crucibles (approximately 400-500 hours or more). Because the hot time for crystal growth depends on the process conditions, HZ configuration, and attempts, recharge capability and multiple rod growth per batch can be impacted using synthetic lined crucibles. Therefore, silicon growth using HMCZ in synthetic lined crucibles generally requires optimization of the crucible condition to ensure the best ZD rate and lowest attempts so that maximum recharge capability can be achieved. 
     Further, a horizontal magnet in Cz growth enhances the melt flow with an irregular velocity melt wave continuously knocking against the crucible wall surface with a strong force in a transient behavior. In this case, the crucible surface condition is very critical for quartz piece generation which directly relates to the ZD success. This is illustrated in  FIG. 5 , in which the melt flow and temperature field of the melt are significantly impacted by the magnetic field strength and MGP position. As shown in the figure, the temperature variation of the circumferential direction at the melt surface is markedly changed by the magnetic field direction. 
     These and other difficulties may be overcome or mitigated in embodiments of the present disclosure through use of one or both of two techniques described in detail below. Generally, in the first aspect, a cristobalite layer is formed on the wettable surface of the interior of the crucible. The wettable surface generally refers to the surface of the crucible that may be in contact with the melt during silicon production. The wettable surface generally includes the interior bottom of the crucible, at least a portion of the interior sidewalls of the crucible, and the interior portions connecting the interior sidewalls and bottom of the crucible. In  FIG. 2 , the wettable surface is all of the interior surface of the crucible  10  below and including the melt surface  36 . The wettable surface may also extend above the melt surface  36 . The second technique described in this disclosure is to increase the rotational speed of the crucible. 
     In general, a strong and unsteady melt flow is induced by an HMCZ magnetic field and this can generate strong thermo-mechanical stress and mechanical impact on the crucible wall causing quartz particle generation. However, high crucible rotation (C/R) will produce faster convective flow near the crucible wall surface, which can interfere with the melt flow driven by a magnetic field. This will reduce the stress and impact on the wall surface. Consequently, the generation of quartz particles at the wall surface is reduced which in turn reduces LZDs during crystal growth. 
     LZDs may also be reduced by enabling the formation of a generally uniform crystalline SiO2 layer (referred to as cristobalite layer) on the crucible&#39;s wettable surface. This layer is more stable and stronger than amorphous quartz itself, and thereby it is more resistant to melt attack by stress or mechanical impact. Thus, the cristobalite layer reduces quartz particle generation. 
     There are at least two methods to promote crystalline layer growth on quartz crucibles. The first method is to use pre-coated crucibles precoated with a compound, such as BaOH, that will promote cristobalite growth, and the other is to add a suitable melt modifier (MM) into the melt before crystal growth. Nonlimiting examples of suitable MMs include barium (Ba) and strontium (Sr). More specifically, nonlimiting example of suitable MMs include barium carbonate (BaCO3), barium oxide (BaO), and strontium carbonate (SrCO3). 
     Cristobalite formation on the amorphous quartz inner wall is governed by pressure, Oi concentration, H2O and hydrogen content, temperature, and the like. As shown in  FIGS. 6 and 7 , the formation and growth of a crystalline layer on the crucible wall is governed by the temperature of the crucible wall and concentration of the MM, which is consumed by the crucible.  FIG. 6  compares the crystallization rate as a function of time for no MM and an 8% AL2O3 MM.  FIG. 7  compares the thickness of the layer formed as a function of time at a temperature of 1360° C. for no MM, an 8% AL2O3 MM, and a barium based MM. These charts indicates that a proper MM addition (e.g., a barium based MM) into the melt or a pre-coating of a barium compound generates a uniform and thick crystalline (i.e., cristobalite) layer on the wall of natural sand crucibles giving similar behavior and performance to synthetic lined crucibles. Because the cristobalite layer has slower dissolution rate than the fused quartz, the generation of quartz pieces by thermo or mechanical stress is decreased so the crystal LZD occurrence is decreased thereafter. Further, the generation of secondary bubbles in the Bubble Free Layer (BFL) of the natural sand crucible and its propagation into the melt is much less than that of synthetic lined crucible in general due to the difference of material properties. 
     The formation and growth of a uniform cristobalite layer either through pre-coating on the crucible or post addition of melt modifier into the melt is started during stabilization mode prior to crystal growth (i.e. after melting of poly silicon or during the melting). In case of a post MM addition, the MM is introduced after meltdown, so the formation speed of the cristobalite is slower than otherwise pre-coated case. However, post addition of the MM can yield lower air pocket (APK) losses because bubbles formed and trapped at the crucible wall can be released to the surface prior to the formation of the stable cristobalite layer. Because it typically takes 3˜7 hours from the start of the stabilization step to the start of body growth, the cristobalite thickness is estimated to be greater than about 2 mm with an appropriate amount of MM added to increase the formation rate of the cristobalite. In practice, a cristobalite layer of less than about 1.0 mm is typically formed on the surface of the crucible (whether natural sand or synthetic). Some special case, such as heavily doped process for P++ or N++, yield a thicker cristobalite layer by adding a large amount of MM. In such cases a cristobalite layer of approximately 1.0 mm (+/−) is formed. These thicknesses differ from the 2.0 mm because although the cristobalite layer is grown by hot time as shown in  FIG. 7 , wet cristobalite layer is continuously being dissolved to melt. Other embodiments include a cristobalite layer of approximately 2.0 mm, greater than 1.5 mm, greater than 1.0 mm, greater than 0.75 mm, greater than 0.5 mm, or greater than 0.25 mm formed on the wettable surface of the crucible. In some embodiments the cristobalite layer is less than 3.0 mm thick, less than 2.0 mm thick, less than 1.25 mm thick, or less than 1.0 mm thick. In some embodiments, the cristobalite layer falls within a range defined by the minima and maxima above, such as between 0.25 mm and 1.25 mm. Generally, too thin a cristobalite layer may be insufficient to provide the benefits described herein, while too thick a cristobalite layer may be more likely to break and enter the melt (potentially contributing to an LZD) during silicon production. 
     Melt modifier addition described above forms a uniform crystalline layer at the crucible wettable surface and this crystalline structure has a strong resistance against the thermomechanical stress induced by the irregular (transient) melt flow produced during HMCZ. The formation of a thick and uniform cristobalite can resist the stress and impact from the melt flow, reducing crucible surface damage (i.e., resisting damage generating quartz particles in the melt) which will increase the ZD success. 
     As mentioned previously, a strong convective flow caused by higher crucible rotation will reduce the variation of temperature in the melt free surface and reduce the melt flow induced by a horizontal magnet as seen in Case  6  in  FIG. 5 . In case  6 , C/R is 1.6 RPM as compared to 0.6 RPM in cases  1 - 5  and  7 . In other words, the force produced by the magnetic field from the melt to the crucible wall surface is reduced or blocked by the convective flow related with higher crucible rotation. Thereby, the possibility of quartz piece generation due to damage of crucible wall surface is decreased, also improving the potential of ZD success. 
     A test condition was performed to understand ZD success and on both synthetic lined and natural sand crucibles in a horizontal magnet as a function of crucible rotation speed and the quantity of melt modifier addition. The synthetic crucible showed high ZD success ratio across a broad range of crucible rotation and MM. For the natural sand lined crucible, a total of 96 trials with  19  different conditions were completed and the results are summarized with a contour plot in  FIG. 8 . The data for  FIG. 8  was from approximately 200 mm body length to approximately OE of the crystal. In  FIG. 8 , CR is the crucible rotation in RPM, a Success %_3 of 0.0 is a ZD fail (LZD), and a Success %_3 of 1.0 is 100% ZD success. The sign of the crucible rotation indicates direction of rotation of the crucible. For some pulls, the crucible rotation ramped between speeds during portions of the pull, an arbitrary value of crucible rotation was selected for plotting, and the data was collected from greater than 1000 mm body length to approximately OE of the crystal. Results clearly show that higher ZD success ratio is achieved with increasing the absolute value of the speed of crucible rotation and quantity of melt modifier (in this case, Ba based). 
     The use of increased speed of crucible rotation and the creation of a cristobalite layer are shown to individually and in combination result in improved ZD outcomes. At lower C/R, such as between about 0 and about 2 RPM, addition of suitable MM (or use of precoated crucible) is needed to increase the ZD success ratio. As the C/R is increased to between about 2 RPM and about 5 RPM, the amount of MM needed to gain an equivalent success rate decreases and may even be zero MM. Within this range, additional gains in ZD success ratio may be obtained through use of at least some MM. When the C/R exceeds about 5 RPM there is generally no ZD concern from the crucible and no MM is likely to be needed. However, at such speeds, additional process condition will likely be required to control the quality of the products, because it may have other issues such as oxygen control due to melt flow velocity, melt level control caused by centrifugal force, and the like. 
     Thus, some embodiments of the present disclosure use a MM more than 1.7 grams per square meter of the wettable surface area of crucible during an HMCZ process at any C/R rate to improve the ZD success rate. In some embodiments, a MM between 1.7 and 2.0 grams/m 2  of the wettable surface of the crucible is used. In still other embodiments, a MM between 1.7 and 5.4 grams/m 2  of the wettable surface of the crucible is used. In still other embodiments, a MM greater than 5.4 grams/m 2  of the wettable surface of the crucible may be used, but the large amount of MM might cause LZD in multiple recharge processes. The quantities above (e.g., 1.7 grams/m 2 ) are based on BaCO3 as the MM. Similar embodiments using BaO or SrCO3 include an amount of the particular MM functionally equivalent to the amount of BaCO3. 
     Some embodiments use a MM between about 0 and 0.5 g/m 2  and a crucible rotation greater than about 2.0 RPM. In some such embodiments, the crucible is a natural sand crucible. Alternatively, the crucible may be a synthetic crucible. 
     Embodiments of the methods described herein achieve superior results compared to prior methods and systems. For example, the methods described herein facilitate producing silicon with a higher ZD success rate than some other methods. 
     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. 
     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. 
     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.