Particle size selection for doped particulate silicon

Abstract

A method for doping a silicon molten material using doped particulate silicon is disclosed. The maximum particle size of the doped particulate silicon may be controlled based on the impact region of the doped particulate silicon on the silicon molten material.

Description

Cross-reference of related applications

[0001] This application claims priority to U.S. Provisional Patent Application No. 63 / 499,307, filed on 1 May 2023, the contents of which are incorporated herein by reference in their entirety. [Technical Field]

[0002] The technical aspects of this disclosure relate to methods for doping a silicon molten material with doped particulate silicon. [Background technology]

[0003] Solid-phase dopant doping of silicon molten material is desirable because it can achieve nearly 100% doping efficiency compared to gas-phase doping, which is far less efficient. Solid-phase doping also provides more precise doping control. However, in solid-phase doping, the relatively long dissolution time of the solid dopant on the free surface of the molten material makes zero dislocation loss (LZD) in the ingot likely to occur. Floating solid dopants can collide with growing crystals, causing LZD.

[0004] There is a need for doping methods for silicon molten material using solid dopants to reduce or eliminate zero dislocation loss in growing crystals.

[0005] This section aims to introduce readers to various aspects of the technical field that may relate to the various aspects of the disclosure described below. We believe this explanation will be useful in providing background information to help readers better understand the various aspects of this disclosure. Therefore, these descriptions should be read in this context and not as an endorsement of prior art. [Overview of the Initiative]

[0006] One aspect of the present disclosure relates to a method for forming a single-crystal silicon ingot. An initial charge of polycrystalline silicon is placed in a crucible. The crucible has a bottom surface and side walls extending from the bottom surface. The initial charge of polycrystalline silicon is heated to form a silicon molten material in the crucible. The silicon molten material has a surface. A seed crystal is brought into contact with the surface of the silicon molten material. The seed crystal is pulled out of the molten material to grow a single-crystal silicon ingot. A distance D exists between the single-crystal silicon ingot and the side wall of the crucible, extending along the surface of the molten material. An impact region is determined on the surface of the molten material where doped particulate silicon is added to the molten material. The flow and melting rate of the doped particulate silicon in the molten material are modeled. The particle size or weight of the doped particulate silicon to be added to the molten material during the growth of the single-crystal silicon ingot is selected based on the modeled flow and melting rate of the doped particulate silicon in the molten material. Doped particulate silicon with a selected particle size is added to the molten material in the impact region during the growth of a single-crystal silicon ingot.

[0007] Another aspect of this disclosure relates to a method for forming a single-crystal silicon ingot. An initial charge of polycrystalline silicon is added to a crucible. The crucible has a bottom and side walls extending from the bottom. The initial charge of polycrystalline silicon is heated to form a silicon molten material in the crucible. The silicon molten material has a surface. A seed crystal is brought into contact with the silicon molten material. The seed crystal is pulled out of the molten material to grow a single-crystal silicon ingot. A distance D exists between the single-crystal silicon ingot and the side wall of the crucible, extending along the surface of the molten material. During the growth of the single-crystal silicon ingot, doped particulate silicon is added to the molten material. The dopant concentration in the doped particulate silicon is at least 1 × 10⁻¹⁶. 14 atoms / cm 3 The doped particulate silicon impacts the molten surface in an impact region extending from a distance of 0.08 × D from the ingot towards the crucible sidewall. The weight of the doped particulate silicon is less than 10 milligrams (mg).

[0008] Various improvements exist to the features relating to the above embodiments of this disclosure. Furthermore, additional features can be incorporated into the above embodiments of this disclosure. These improvements and additional features may exist individually or in any combination. For example, the various features discussed below in relation to any of the illustrated embodiments of this disclosure may be incorporated individually or in any combination into any of the above embodiments of this disclosure. [Brief explanation of the drawing]

[0009] [Figure 1] Figure 1 is a cross-sectional view of the ingot lifting device. [Figure 2] Figure 2 is a plan view of the ingot and crucible showing the impact region in the molten material for doping doped particulate silicon. [Figure 3] Figure 3 includes box plots of zero dislocations and zero dislocation yield when 5 mg sized doped particulate silicon is added to a melt where the distance ratio between the crystal and the crucible sidewall is 0.08 to 0.1. [Figure 4] Figure 4 includes a reconstructed photograph of doped particulate silicon cut from a doped single-crystal silicon wafer. [Figure 5] Figure 5 shows a simulation of the dopant behavior of doped particulate silicon at different dropping positions. [Figure 6] Figure 6 shows a simulation of the radial temperature profile of the free surface of the molten material. [Figure 7] Figure 7 shows models of molten material flow in the cusp method and the magnetic field Czochralski method. [Figure 8] Figure 8 is a graph showing the resistivity profiles of calculated and experimental values ​​during the counter-doping procedure. [Figure 9] Figure 9 is a graph showing the maximum particle size of doped particulate silicon as a function of the distance ratio between the ingot and the crucible sidewall. [Figure 10] Figure 10 shows a schematic diagram of a tool used to crush silicon wafers and a photograph of a crushed wafer. [Figure 11]FIG. 11 is a replica of a silicon wafer diced with a dicing tool.

[0010] Corresponding reference symbols indicate corresponding parts throughout the drawings.

DETAILED DESCRIPTION OF THE INVENTION

[0011] The provisions of the present disclosure relate to a method of adding a solid-phase dopant to a silicon melt during ingot growth. An example of an ingot pulling apparatus (or simply an “ingot puller”) for growing a single-crystal silicon ingot and adding a dopant is shown generally at 100 in FIG. 1. The ingot pulling apparatus 100 includes a crystal pulling housing 108 that defines a growth chamber 152 for pulling a silicon ingot 113 from a silicon melt 104. The ingot pulling apparatus 100 includes a crucible 102 disposed within the growth chamber 152 for holding the silicon melt 104. The crucible 102 is supported by a susceptor 106.

[0012] The crucible 102 includes a bottom surface 129 and sidewalls 131 extending upward from the bottom surface 129. The sidewalls 131 are generally vertical. The bottom surface 129 includes a curved portion of the crucible 102 that extends below the sidewalls 131. Within the crucible 102 is a silicon melt 104 having a melt surface 111 (i.e., the melt-ingot interface). The susceptor 106 is supported by a shaft 105. The susceptor 106, crucible 102, shaft 105, and ingot 113 have a common longitudinal axis A or “pulling axis” A.

[0013] Inside the ingot lifting device 100, a lifting mechanism 114 for growing and lifting the ingot 113 from the melt 104 is provided. The lifting mechanism 114 includes a lifting cable 118, a seed crystal holder or chuck 120 connected to one end of the lifting cable 118, and a seed crystal 122 for starting crystal growth. The seed crystal 122 is connected to the seed crystal holder or chuck 120. One end of the lifting cable 118 is connected to another appropriate hoisting mechanism such as a pulley (not shown) or a drum (not shown), or a shaft, and the other end is connected to the chuck 120 that holds the seed crystal 122. During operation, it is lowered until the seed crystal 122 contacts the melt 104. The lifting mechanism 114 is activated to lift the seed crystal 122 from the melt 104 and raise the seed crystal 122. Thereby, the single crystal ingot 113 is lifted from the melt 104.

[0014] During heating and crystal pulling, the crucible drive unit 107 (for example, a motor) rotates the crucible 102 and the susceptor 106. The lift mechanism 112 moves the crucible 102 up and down along the pulling axis A during the growth process. As the ingot grows, the silicon melt 104 is consumed and the height of the melt in the crucible 102 decreases. The crucible 102 and the susceptor 106 can be raised to maintain the melt surface 111 at the same position or in the vicinity thereof with respect to the ingot lifting device 100.

[0015] A crystal drive unit (not shown) can also rotate the lifting cable 118 and the ingot 113 in a direction opposite to the direction in which the crucible drive unit 107 rotates the crucible 102 (for example, counter-rotation). In an embodiment using constant speed rotation, the crystal drive unit can rotate the lifting cable 118 in the same direction as the direction in which the crucible drive unit 107 rotates the crucible 102. Further, the crystal drive unit raises and lowers the ingot 113 with respect to the melt surface 111 as needed during the growth process.

[0016] The ingot lifting device 100 may include an inert gas system for introducing and discharging an inert gas such as argon from the growth chamber 152. The ingot lifting device 100 may also include a dopant supply system (not shown) for introducing a dopant into the molten material 104.

[0017] According to the Czochralski single-crystal growth process, solid-phase silicon, such as polycrystalline silicon, is charged into a crucible 102. The semiconductor or solar cell grade material introduced into the crucible 102 is melted by heat supplied from one or more heating elements. The ingot pulling device 100 includes a bottom insulator 110 and side insulators 124 for retaining heat within the pulling device 100. In the illustrated embodiment, the ingot pulling device 100 includes a bottom heater 126 located below the bottom surface 129 of the crucible. The crucible 102 is moved to a position relatively close to the bottom heater 126 so that the polycrystalline silicon charged into the crucible 102 can be melted.

[0018] To form an ingot, a seed crystal 122 is brought into contact with the surface 111 of the molten material 104. The pull-up mechanism 114 is activated to pull the seed crystal 122 from the molten material 104. The ingot 113 includes a tapering crown portion 142 that moves outward from the seed crystal 122 until it reaches a target diameter. The ingot 113 includes a constant diameter portion 145 or cylindrical "body" of the crystal that is grown by increasing the pull-up rate. The body 145 of the ingot 113 has a relatively constant diameter. The ingot 113 has a tail portion or end cone portion (not shown) behind the body 145 where the diameter tapers. When the diameter becomes sufficiently small, the ingot 113 separates from the molten material 104. The ingot 113 has a central longitudinal axis A that passes through the crown portion 142 and the end of the ingot 113.

[0019] The ingot pulling apparatus 100 includes side heaters 135 and a susceptor 106 surrounding the crucible 102 to maintain the temperature of the molten material 104 during crystal growth. The side heaters 135 are positioned radially outward relative to the crucible sidewalls 131 as the crucible 102 moves up and down along the pulling axis A. The side heaters 135 and bottom heater 126 can be any type of heater that can operate as described herein. In some embodiments, the heaters 135 and 126 are resistance heaters. The side heaters 135 and bottom heater 126 are controlled by a control system (not shown) to control the temperature of the molten material 104 throughout the pulling process.

[0020] The ingot lifting device 100 also includes a heat shield 151 located within the growth chamber 152 and above the molten material 104, which covers the ingot 113 during ingot growth. The heat shield 151 defines a central passage 160 for receiving the ingot 113 as it is lifted by the lifting mechanism 114. The ingot lifting device may include magnetic coils for applying a cusp magnetic field or a horizontal magnetic field during ingot growth.

[0021] The ingot lifting device 100 includes a dopant supply system 132. The dopant supply system 132 includes a dopant feeder 164 and a dopant tube 130 extending through the ingot lifting housing 108, thereby adding solid-phase dopant to the crucible 102. The solid-phase dopant passes through the dopant tube 130 into contact with the molten material 104, doping the molten material 104. The dopant tube 130 includes an inlet 125 located outside the growth chamber 152 and an outlet 127 located inside the growth chamber 152 and relatively close to the surface of the molten material 104.

[0022] The dopant feeder 164 is located outside the growth chamber 152. The dopant feeder 164 includes a dopant feeder housing 136 and one or more dopant storage containers or "cups" 137 located within the housing 136 for adding solid-phase dopant to the molten material 104. In the illustrated embodiment, the dopant feeder 164 includes a first cup 137A, a second cup 137B, a third cup 137C, and a fourth cup 137D. A process gas (e.g., argon) may be circulated within the dopant feeder 164. In the illustrated embodiment, the dopant supply system 132 does not include a shut-off valve because the dopant is located inside the dopant feeder housing 136, which isolates the system from the ambient atmosphere. In other embodiments, a shut-off valve may be used. The dopant feeder housing 136 is located outside the ingot pull-up housing 108.

[0023] Before ingot growth, each dopant cup 137 is pre-loaded with doped particulate silicon. During ingot growth, a rotating mechanism (not shown) is operated to sequentially rotate each cup 137 according to a predetermined doping protocol, supplying the pre-loaded doped particulate silicon from the feeder 164 to the dopant tube 130 and then to the molten material 104. The dopant feeder 164 comprises one or more funnels 157 (in the illustrated embodiment, first and second funnels 157A and 157B are shown) positioned below the dopant cups 137. The funnels 157A and 157B are connected to the dopant tube 130.

[0024] According to an embodiment of the present disclosure, during the growth of the single crystal silicon ingot 113, doped particulate (i.e., solid phase) silicon is added to the melt 104. Any suitable method can be used to produce the doped particulate silicon (also referred to herein as "silicon alloy"). For example, the particulate silicon may be silicon that is pulverized or cut from a silicon wafer (i.e., the particulate silicon is single crystal silicon). To cut the particulate silicon, the wafer can be scribed and divided. The wafer can be pulverized using a tool (Figure 10) or diced using a dicing saw (Figure 11).

[0025] The dopant concentration in the particulate silicon is at least 1×10 14 atoms / cm 3 (e.g., 1×10 14 atoms / cm 3 to 1×10 20 atoms / cm 3 ). In other embodiments, the concentration is at least 1×10 15 atoms / cm 3 , at least 5×10 15 atoms / cm 3 , at least 1×10 16 atoms / cm 3 , at least 1×10 17 atoms / cm 3 , or at least 1×10 18 atoms / cm 3 . The doped particulate silicon is P-type or N-type. In some embodiments, the dopant in the particulate silicon is boron (e.g., the concentration is at least 1×10 15 atoms / cm 3 ). The doped particulate silicon contains an amount of dopant that exceeds the amount of dopant inherent in the particulate silicon (e.g., the amount present in polycrystalline silicon grown by the Siemens process or a fluidized bed reactor).

[0026] In one embodiment of the present disclosure, the initial molten material 104 is initially doped either before or after melting and before silicon ingot growth. This first dopant may be of a different type from the second dopant (for example, a dopant added during ingot growth, as in a counter-doping embodiment). For example, the first dopant may be P-type and the second dopant may be N-type. Alternatively, the first dopant may be N-type and the second dopant may be P-type.

[0027] Referring to Figure 2, a distance D exists between the body of the single-crystal silicon ingot 113 and the side wall 131 of the crucible 102, extending along the surface of the molten material 104. The doped silicon particles fall into the molten material 104, colliding with the surface of the molten material 104 in the impact region 140. The location of the impact region 140 may be selected based on the particle size of the doped silicon particles. Once the particle size and / or weight of the doped silicon particles added during ingot growth are determined, the flow and melting rate of the doped particulate silicon in the molten material can be modeled (see Example 4 below). For example, the melting flow and melting rate of particulate silicon in the molten material may include modeling the possibility of zero dislocation loss in the single-crystal silicon ingot (e.g., correlating the size or weight of the particulate silicon with the impact region where zero dislocation loss is least likely to occur).

[0028] The impact region in which doped particulate silicon is added to the molten material on the molten surface is selected based on the modeled melt flow and melting rate of particulate silicon in the molten material. The position of the tube 130 between the ingot 113 and the crucible sidewall 131 is either preset in the ingot lifting device (i.e., when the hot zone is set) or adjusted by a dopant tube moving device (not shown). In some embodiments, the hot zone (e.g., by the design of the heat shield) restricts the position of the dopant tube from 0.08 × D to 1.0 × D.

[0029] According to one embodiment of the present disclosure, the weight of the doped silicon particles is less than 10 milligrams (mg) (e.g., at least 50%, at least 75%, at least 90%, at least 95%, at least 99%, or substantially all particles have a weight of less than 10 mg). The weight and / or size of the doped silicon particles can be controlled to less than 10 mg by sorting the doped particulate silicon before adding it to the melt. In other embodiments, the weight of the silicon particles is less than 9 mg, less than 7 mg, less than 5 mg, or in the range of 1 mg to 10 mg, or 1 mg to 5 mg. The particulate dopant may have a thickness typical of single-crystal silicon wafers (e.g., 0.5 mm to 1 mm).

[0030] In some embodiments, the amount of doped particulate silicon added to the molten material is determined based on the measured resistance of a single-crystal silicon wafer that has been crushed or cut to produce the doped particulate silicon.

[0031] In one embodiment of this disclosure, the impact region extends from 0.08 × D to 0.1 × D from the silicon ingot (for example, the weight of the silicon particles is less than 10 mg to reduce or eliminate LZD). In the impact region of approximately 0.1 × D to 0.6 × D, the weight of the silicon particles may be less than 400 mg (e.g., 25 to 400 mg). In the impact region greater than 0.6 × D, the weight of the silicon particles may be less than 800 mg.

[0032] Compared to conventional doping methods for silicon melts, the method described herein offers several advantages. By controlling the size of the doped particulate silicon added to the melt, the success rate of zero dislocations can be improved (e.g., when the doping position is limited by reflector design). The use of doped particulate silicon allows for rapid and effective dissolution on the molten surface after impact with the molten surface (i.e., 100% doping efficiency). It also allows the use of conventional doping supply systems. By using relatively fine particles directly on the molten surface, melt vibrations (e.g., within a cusp magnetic field) that can cause zero dislocation losses in the growing crystal can be reduced. The use of doped particulate silicon makes the control and production of the dopant relatively easy. [Examples]

[0033] The processes described herein are further illustrated by the following embodiments, which should not be constrained.

[0034] Example 1: Effect of particle size of added particulate silicon on zero dislocation loss The dopant tubes in the 200 mm ingot crystal pulling apparatus were positioned so that the doped particulate silicon would collide with the molten surface at a range of 0.08 × D to 0.1 × D during ingot growth (i.e., during re-doping or counter-doping) (where D is the distance between the silicon ingot and the crucible sidewall, and D=0 at the crystal edges). As shown in Table 1, smaller sized doped particulate silicon (represented by particles with less total grams) resulted in a higher zero-dislocation success rate (e.g., sizes of 0.01 grams or less).

[0035] TIFF2026519747000002.tif73156 Table 1: Zero dislocation success rate in doped silicon of different sizes

[0036] As a result, as shown in Figure 3, the zero dislocation yield improved as the zero dislocation yield decreased. Although the zero dislocation yield decreased, a higher prime yield was achieved by extending the prime length, which is related to the resistivity specification range. The bar graph on the right in Figure 3 shows the relative effect of counter-doping on the zero dislocation yield. Counter-doping increases the loss of zero dislocations compared to no counter-doping ("reference"). This increase in zero dislocation loss is offset by "fallout" (as shown in the box plot on the left). Fallout is the amount by which the opposite end of the crystal is out of specification, resulting in an increase in the overall prime yield.

[0037] Example 2: Melt vibrations dependent on the size of doped particulate silicon When solid dopant particles are dropped directly onto a molten surface, molten vibrations (e.g., within a cusp magnetic field) are generated, potentially causing zero dislocation losses (LZDs) in the growing crystal. Table 2 shows a qualitative comparison of molten vibrations depending on dopant size. As the weight of the doped particles decreased, the molten vibrations decreased. This result depends on the landing position of the dopant alloy on the free molten surface (distance from the crystal surface), the molten flow velocity due to crucible rotation and magnetic field, and the type of magnetic field, such as cusp magnetic field or horizontal flux.

[0038] TIFF2026519747000003.tif67144 Table 2: Detection of molten vibrations at different particle sizes

[0039] Example 3: Zero dislocation success rate dependent on the size of doped particulate silicon The dopant alloy shown in Figure 4 (n-type, pulverized n++ wafer, diagonal length less than 6 mm) was supplied to the molten free surface through a pre-installed quartz supply tube in a 32-inch ingot puller. The supply position was located at the third supply point shown in Figure 5 (crystal radius (R) / 2 × distance D between the crystal edge and the crucible wall, or 0.28 × D). Figure 5 shows the dopant behavior from different drop positions with diagonal lengths from 0.1 to 3.0 mm and thicknesses of 0.725 mm. The contour lines indicate the argon gas velocity.

[0040] The droplet placement is primarily at the landing point on the molten surface shown in Figure 5, but fine dopant particles may be affected by eddy currents directly beneath the bottom surface of the reflector. The particle path varies depending on the reflector design, and by considering the eddy current path, a safe path can be selected to avoid zero dislocation losses.

[0041] Figure 6 shows the radial temperature distribution on the free molten surface. Since the radial temperature increases from the crystal towards the crucible wall, the landing position determines the dissolution rate of the dopant particles. Figure 6 shows that particles that land near the crucible wall dissolve extremely quickly, even if they are large additive particles. The radial temperature distribution on the free molten surface differs depending on the hot zone configuration. This temperature distribution (except in the meniscus region) is higher than the melting point of silicon. This indicates that silicon particles melt rapidly even when they land on the free molten surface with a crystal-to-crucible distance ratio in the range of 0.08 to 0.1.

[0042] Figure 7 shows model images of the molten channel in cusp magnetic field (side view of the molten region) and horizontal magnetic field (plan view of the free molten surface) processes. The molten channel in the cusp magnetic field shows that floating particles move from the crucible surface to the crystal surface. The horizontal magnetic field tends to push the floating particles towards the crucible wall. Doped particulate silicon is more likely to reach the crystal surface in the cusp magnetic field process if it does not melt relatively quickly after contact with the molten surface.

[0043] The experimental results at the intermediate doping position in Figure 5 show that the actual resistivity closely follows the calculated curve, as shown in Figure 8. When phosphorus-containing particulate silicon was dropped during P-type crystal growth with a solidification rate of approximately 0.76, the resistivity increased instantaneously due to the N-type dopant. Since the doping efficiency was 100%, the resistivity after doping agreed very well with the calculated value, as shown in Figure 8.

[0044] Example 4: Modeling the maximum particle size of doped particulate silicon as a function of the landing position. Figure 9 shows the determined maximum dopant size relative to the landing site from the crystal surface, modeled by the method described herein. The dopant size and the zero dislocation success rate are related as a function of the landing site, which is directly influenced by the temperature of the molten surface. The temperature of the molten free surface on which the dopant lands determines the time constant required to melt the particles. Convection of the molten fluid (which also depends on the type of magnet) determines the transient motion of the particles after landing, i.e., the direction of growth towards or away from the meniscus. Taken together, the further away from the crystal meniscus the particles land, the higher the zero dislocation success rate. Experimental results showed that doped particulate silicon with a size of less than 0.01 grams is usable with a crystal-to-crucible distance ratio of 0.08 to 0.1. Results indicate that zero dislocation is possible with larger particles (0.35 grams / particle) when the crystal-to-crucible distance ratio is 0.4 to 0.5. By extrapolating the results, Figure 9 plots the estimated maximum particle size (weight-based) against the normalized distances of the crystal meniscus and crucible wall.

[0045] In this specification, the terms “about,” “substantially,” “essentially,” and “approximately,” when used in conjunction with dimensions, concentrations, temperatures, or other physical or chemical properties or ranges, are intended to include any variations that may exist at the upper and / or lower limits of those properties or ranges (including, for example, variations resulting from rounding errors, measurement methods, or other statistical variations).

[0046] When describing the components of this disclosure or its embodiments, articles such as “a,” “an,” “the,” and “said” indicate that there are one or more components. Terms such as “comprising,” “including,” “containing,” and “having” are comprehensive and indicate that additional elements other than those listed may exist. The use of terms indicating specific orientations (e.g., “top,” “bottom,” “side,” etc.) is for explanatory convenience and does not require a specific orientation of the described article.

[0047] Since various modifications can be made to the above structure and method without departing from the scope of disclosure, all matters included in the above description and shown in the attached drawings are intended to be illustrative and not to be interpreted in an restrictive sense.

Claims

1. A method for forming a single-crystal silicon ingot, A step of loading an initial charge of polycrystalline silicon into a crucible, wherein the crucible has a bottom surface and side walls extending from the bottom surface; A step of heating an initial charge of polycrystalline silicon to form a silicon molten material in a crucible, wherein the silicon molten material has a surface; A step of bringing a seed crystal into contact with the surface of a silicon molten material; A process of growing a single-crystal silicon ingot by pulling a seed crystal from a molten material, wherein there is a distance D between the single-crystal silicon ingot and the side wall of the crucible that extends along the surface of the molten material; A process in which impact regions are identified on the surface of the molten material, and doped particulate silicon is added to the molten material in those impact regions; A process for modeling the flow and melting rate of doped particulate silicon in a molten material; A step of selecting the particle size or weight of doped particulate silicon to be added to the molten material during the growth of a single-crystal silicon ingot, based on the modeled flow and melting rate of the doped particulate silicon in the molten material; and, A method comprising the step of adding doped particulate silicon having a selected particle size to the molten material in an impact region during the growth of a single-crystal silicon ingot.

2. The method according to claim 1, comprising the step of cutting or crushing one or more single-crystal silicon wafers to produce doped particulate silicon.

3. The method according to claim 1 or 2, wherein the step of modeling the flow and melting rate of doped particulate silicon in the molten material includes a step of modeling the possibility of zero dislocation disappearance in a single-crystal silicon ingot.

4. The method according to any one of claims 1 to 3, wherein the step of modeling the flow and melting rate of doped particulate silicon in a molten material includes a step of correlating the size or weight of the doped particulate silicon with an impact region in which zero dislocation loss is least likely to occur.

5. A method for forming a single-crystal silicon ingot, A step of adding an initial charge of polycrystalline silicon to a crucible, wherein the crucible has a bottom surface and side walls extending from the bottom surface; A step of heating an initial charge of polycrystalline silicon to form a silicon molten material in a crucible, wherein the silicon molten material has a surface; The process of bringing a seed crystal into contact with molten silicon; A step of growing a single-crystal silicon ingot by pulling up a seed crystal from the molten material, wherein there is a distance D between the single-crystal silicon ingot and the side wall of the crucible that extends along the surface of the molten material; and, A step in which doped particulate silicon is added to the molten material during the growth of a single-crystal silicon ingot, wherein the dopant concentration in the doped particulate silicon is at least 1 × 10⁻¹⁶ １４ atoms / cm ３ A method comprising the steps of: the doped particulate silicon impacts the surface of the molten material in an impact region extending from a distance of 0.08 × D from the silicon ingot toward the crucible sidewall, wherein the weight of the doped particulate silicon is less than 10 milligrams (mg).

6. The method according to claim 5, wherein the impact region extends from 0.08 × D from the silicon ingot to 0.1 × D from the silicon ingot.

7. The method according to claim 5 or 6, wherein the doped particles are crushed or cut from one or more single-crystal silicon wafers.

8. The method according to any one of claims 5 to 7, comprising the step of cutting a single-crystal silicon wafer to produce doped granular silicon.

9. A process for determining the resistivity of a single-crystal silicon wafer; and, The method according to any one of claims 5 to 8, comprising the step of determining, at least partially, the amount of doped particulate silicon to be added to the molten material based on the resistivity of a single-crystal silicon wafer.

10. The Dopant is the second Dopant, The method according to any one of claims 5 to 9, comprising the step of doping a molten material with a first dopant before a single-crystal silicon ingot is grown, wherein the first dopant is of a different type from the second dopant.

11. The method according to claim 10, wherein the first dopant is of type p and the second dopant is of type n.

12. The method according to claim 10, wherein the first dopant is of type n and the second dopant is of type p.

13. The method according to any one of claims 5 to 12, wherein the dopant is boron.

14. The boron concentration in doped particulate silicon is 1 × 10⁻⁶ １４ atoms / cm ３ from 1 x 10 ２０ atoms / cm ３ The method according to claim 13.

15. The method according to any one of claims 5 to 14, comprising the step of pre-loading doped particulate silicon into one or more dopant storage containers before ingot growth, wherein the containers are located within a dopant feeder housing and sealed from the surrounding atmosphere, and the containers are located outside the ingot pulling housing.

16. The method according to claim 15, comprising the step of supplying pre-loaded doped particulate silicon from a container during ingot growth, wherein the pre-loaded doped particulate silicon passes through a dopant tube that penetrates the ingot pulling housing.

17. The method according to any one of claims 5 to 16, wherein the weight of the doped particulate silicon is less than 9 mg, less than 7 mg, less than 5 mg, or 1 mg to 10 mg, or 1 mg to 5 mg.

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