Sample rod growth and resistivity measurement during single crystal silicon ingot production

Abstract

This application relates to sample rod growth and resistivity measurement during single crystal silicon ingot production. A method for forming a single crystal silicon ingot with improved resistivity control is disclosed. The method involves growth and resistivity measurement of a sample rod. The sample rod can have a diameter that is less than the diameter of a product ingot. The resistivity of the sample rod can be measured directly by contacting a resistivity probe with a flat segment formed on the sample rod. The sample rod can be annealed in a thermal donor elimination cycle prior to measuring the resistivity.

Description

Cross-citation of related applications

[0001] This application is a divisional application of U.S. Patent Application No. 201980043704.8, filed June 25, 2019, entitled "Sample Rod Growth and Resistivity Measurement During Single Crystal Silicon Ingot Production". That application claims priority to U.S. Patent Application No. 16 / 020,698, filed June 27, 2018, the entire disclosure of which is incorporated herein by reference. Technical Field

[0002] The present invention relates to methods for forming single-crystal silicon ingots with improved resistivity control, and more particularly, to methods for growing sample rods and measuring resistivity. In some embodiments, the sample rods have a diameter smaller than that of the product ingot. Background Technology

[0003] Single-crystal silicon (the starting material for most processes used to manufacture semiconductor electronic components) is typically prepared using the so-called Czochralski (Cz) process, in which a single seed crystal is immersed in molten silicon and then grown by slow extraction. The molten silicon is contaminated with various impurities, primarily oxygen, during its containment in a quartz crucible. Some applications (such as advanced wireless communication applications, insulated-gate bipolar transistors (IGBTs), and low-power, low-leakage devices) require wafers with relatively high resistivity (e.g., 1500 ohm-cm (Ω-cm) or more).

[0004] High-purity polycrystalline silicon is used in the production of high-resistivity ingots. High-purity polycrystalline silicon is characterized by an extended impurity profile, which results in a wide range and variety of intrinsic resistivity in undoped materials. Calibration of seed-end resistivity in such high or ultra-high resistivity materials is difficult due to the variability of boron and phosphorus in the starting materials (including surface boron and phosphorus in polycrystalline silicon materials) and due to impurities in the crucible and / or oxygen levels that alter resistivity after heat donor elimination cycles. Furthermore, such high-resistivity applications are susceptible to increased errors in resistivity measurements.

[0005] There is a need for methods for preparing high-resistivity silicon ingots that allow for relatively rapid sampling of impurity concentration and / or resistivity of polycrystalline silicon starting materials and / or relatively rapid measurement of resistivity with relatively small amounts of silicon consumed for resistivity measurement and / or better resistivity control and / or simplification of the intrinsic doping process.

[0006] This section aims to introduce the reader to various aspects of the invention that may relate to the various aspects of the invention described and / or claimed below. It is believed that this discussion will help provide the reader with background information to facilitate a better understanding of the various aspects of the invention. Therefore, it should be understood that these statements should be read in this sense and not as an endorsement of prior art. Summary of the Invention

[0007] One aspect of the present invention relates to a method for producing a single-crystal silicon ingot from a silicon melt held in a crucible. Polycrystalline silicon is added to the crucible. The polycrystalline silicon is heated to cause a silicon melt to form in the crucible. A sample rod is pulled from the melt. The sample rod has a diameter. The sample rod is annealed to eliminate heat donors. After eliminating the heat donors, the resistivity of the sample rod is measured. A product ingot is pulled from the melt. The product ingot has a diameter. The diameter of the sample rod is smaller than the diameter of the product ingot.

[0008] Another aspect of the invention relates to a method for determining the resistivity of a polycrystalline silicon melt held in a crucible. A sample rod is pulled from the melt. The sample rod is annealed in a heat donor elimination cycle. A current is applied to the sample rod. While the current is applied to the sample, the sample rod is brought into contact with a resistivity probe to measure the resistivity of the rod. Various refinements exist for the features described with respect to the foregoing aspects of the invention. Similarly, further features may be incorporated into the foregoing aspects of the invention. These refinements and additional features may exist individually or in any combination. For example, various features discussed below with respect to any of the illustrated embodiments of the invention may be incorporated individually or in any combination into any of the foregoing aspects of the invention. Attached Figure Description

[0009] Figure 1 This is a schematic side view of a Czochralski (Czochralski) device used to form single-crystal silicon ingots;

[0010] Figure 2 It is a sample rod grown from silicon melt;

[0011] Figure 3 It is a sample rod with flat segments formed on its surface;

[0012] Figure 4 It is a measuring device used to measure the resistivity of a sample rod;

[0013] Figure 5 It is an IV curve used to measure the resistivity of a sample rod; and

[0014] Figure 6 This is a scatter plot of the resistivity of the sample rod at various locations from the seed end.

[0015] Throughout the accompanying drawings, corresponding reference symbols indicate the corresponding parts. Detailed Implementation

[0016] The invention relates to a method for producing single-crystal silicon ingots via the Chuklaski method, wherein a sample rod is grown to determine the resistivity of the melt. The sample rod has a diameter smaller than that of the product ingot.

[0017] According to embodiments of the present invention and with reference to Figure 1 The product ingot is grown using the so-called Chuklaski process, in which the ingot is withdrawn from a silicon melt 44 held within a crucible 22 in a puller 23. The puller 23 includes a housing 26 that defines a crystal growth chamber 16 and a lifting chamber 20 having a smaller lateral dimension than the growth chamber. The growth chamber 16 has a generally dome-shaped upper wall 45 that transitions from the growth chamber 16 to the narrowing lifting chamber 20. The puller 23 includes an inlet port 7 and an outlet port 12, which are used to introduce process gases into and remove process gases from the housing 26 during crystal growth.

[0018] The crucible 22 within the puller 23 contains the molten silicon 44 from which the silicon ingot is withdrawn. The molten silicon 44 is obtained by melting the polycrystalline silicon loaded into the crucible 22. The crucible 22 is mounted on a turntable 31 for rotating the crucible 22 about the central longitudinal axis X of the puller 23.

[0019] A heating system 39 (e.g., a resistance heater) surrounds the crucible 22 for melting the silicon charge to produce melt 44. The heater 39 may also extend below the crucible, as shown in U.S. Patent No. 8,317,919. The heater 39 is controlled by a control system (not shown) to precisely control the temperature of melt 44 throughout the pulling process. An insulating body (not shown) surrounding the heater 39 reduces the amount of heat lost through the housing 26. The ingot puller 23 may also include a heat shield assembly (not shown) above the melt surface to shield the ingot from the heat of the crucible 22, increasing the axial temperature gradient at the solid-melt interface.

[0020] A lifting mechanism (not shown) is attached to a lifting wire 24 extending downward from the mechanism. The mechanism is capable of raising and lowering the lifting wire 24. Depending on the type of puller, the ingot puller 23 may have a lifting shaft instead of a wire. The lifting wire 24 terminates in a lifting assembly 58, which includes a seed chuck 32 for holding a seed crystal 6 for growing a silicon ingot. During ingot growth, the lifting mechanism lowers the seed crystal 6 until it contacts the surface of the molten silicon 44. Once the seed crystal 6 begins to melt, the lifting mechanism slowly raises the seed crystal upward through the growth chamber 16 and the lifting chamber 20 to grow a single-crystal silicon ingot. The speed at which the lifting mechanism rotates the seed crystal 6 and the speed at which the lifting mechanism raises the seed crystal (i.e., the lifting rate v) are controlled by a control system.

[0021] Process gas is introduced into housing 26 through inlet port 7 and withdrawn from outlet port 12. The process gas creates an atmosphere within housing 26, and the melt and atmosphere form a melt-gas interface. Outlet port 12 is in fluid communication with the venting system of the puller (not shown).

[0022] On this point, Figure 1 The ingot puller 23 shown and described herein is exemplary and other crystal puller configurations and arrangements may be used to pull single-crystal silicon ingots from the melt, unless otherwise stated.

[0023] According to an embodiment of the invention, after polycrystalline silicon is added to crucible 22 and heating system 39 is operated to melt the polycrystalline silicon, a sample ingot or rod is pulled from the melt. Figure 2 An exemplary sample rod 5 is shown. Rod 5 includes a crown portion 21 in which the rod transitions outward from the seed crystal and tapers to achieve a target diameter. Rod 5 includes a constant-diameter portion 25 or cylindrical body, or simply "body," of the crystal grown by increasing the pulling rate. The body 25 of sample rod 5 has a relatively constant diameter. Rod 5 includes a tail or end taper 29 in which the rod tapers in diameter after the body 25. When the diameter becomes sufficiently small, the rod then separates from the melt. Rod 5 has a central longitudinal axis A extending through the crown 21 and end 33 of the ingot.

[0024] The growth conditions for sample rod 5 can generally be selected from any suitable growth conditions available to those skilled in the art. Sample rod 5 can be grown using locked seed lifting (i.e., a fixed pulling speed, where the diameter varies, for example, by + / - about 5 mm) or active seed lifting (variing the pulling speed to maintain the target diameter).

[0025] The sample rod 5 has a diameter smaller than that of the product ingot grown after the sample rod. For example, the diameter of the sample rod may be less than 0.75 times, less than 0.5 times, less than about 0.25 times, or less than 0.1 times the diameter of the product ingot. In some embodiments, the diameter of the sample rod is less than about 150 mm, less than about 100 mm, less than about 50 mm, less than about 25 mm, or less than about 20 mm (e.g., from about 5 mm to about 150 mm, from about 5 mm to about 100 mm, from about 5 mm to about 50 mm, from about 5 mm to about 25 mm, or from about 10 mm to about 25 mm). Generally, the diameter of the rod 5 is measured by measuring the rod at several axial locations (e.g., within a constant diameter portion of the rod if the rod has a crown and / or tapered end) and averaging the measured diameters (e.g., measuring 2, 4, 6, 10, or more diameters across a length and averaging). In some embodiments, the maximum diameter of the sample rod is less than about 150 mm or less than about 100 mm, less than about 50 mm, less than about 25 mm or less than about 20 mm (e.g., from about 5 mm to about 150 mm, from about 5 mm to about 100 mm, from about 5 mm to about 50 mm, from about 5 mm to about 25 mm or from about 10 mm to about 25 mm).

[0026] In some embodiments, the rod 5 has a diameter that typically corresponds to the diameter of the neck portion of the product ingot grown in the crystal puller. For example, the rod may have a diameter of less than 50 mm, less than 25 mm, or less than 20 mm.

[0027] The sample rod 5 may have any suitable length. In some embodiments, the rod (e.g., after trimming) has a length of less than about 300 mm, less than about 200 mm, or less than about 100 mm (e.g., from about 25 mm to about 300 mm).

[0028] After sample rod 5 is grown, its resistivity is measured. Rod 5 is removed from the puller 23 and processed to allow for resistivity measurement. The crown and tail of the rod can be removed, for example, using a wire saw. In some embodiments, the trimmed ends of rod 5 are ground to flatten the ends. The rod ends can be etched (e.g., with a mixed acid). Rod 5 can be modified to include ohmic contacts (e.g., ohmic contacts at its first end 15 and second end 17). For example, the trimmed ends 15, 17 of rod 5 can be sprayed with colloidal silver coating and dried.

[0029] A flat segment 11 is formed on the surface of rod 5. Figure 3The flat segment 11 may extend axially along the rod 5. In some embodiments, the flat segment 11 extends axially from a first end 15 of the rod 5 to a second end 17. In other embodiments, the flat segment 11 extends only partially along its length.

[0030] A flat segment 11 can be formed, for example, by abrading the surface of the sample rod 5 using an abrasive pad (e.g., a diamond coarse-grained pad). In some embodiments, the flat segment has a width sufficient to allow contact with a voltage probe (e.g., about 2 to 4 mm). The flat segment 11 can be cleaned, for example, by washing and drying with deionized water prior to resistivity measurement.

[0031] In some embodiments, sample rod 5 undergoes rapid thermal annealing prior to resistivity measurement. Rapid thermal annealing can serve as a heat donor elimination cycle (e.g., elimination of heat donors) by dissociating interstitial oxygen clusters. In some embodiments, annealing is performed at a temperature of about 500°C or more, about 650°C or more, or about 800°C or more (e.g., 500°C to about 1000°C, from about 500°C to about 900°C, or from about 650°C to about 1100°C) for at least about 5 seconds, at least about 30 seconds, at least about 1 minute, or at least about 3 minutes or more (e.g., from about 5 seconds to 15 minutes, from about 5 seconds to about 5 minutes, or from about 5 seconds to about 3 minutes).

[0032] The resistivity of rod 5 can be measured from the flat segment 11. In some embodiments of the invention, a driving current is passed through rod 5 and contacts a resistivity probe at one or more locations along the length of rod 5. The current can be applied to rod 5 through one of ends 15, 17.

[0033] In some embodiments, rod 5 is fixed to the measuring device (e.g., Figure 4 The device 43 shown in the illustration includes a clamp 51 for fixing a rod 5. The clamp 51 has a first support 53 fixing the rod 5 toward a first end 15 and a second support 55 fixing the rod 5 toward a second end 17. The supports 53, 55 are configured to secure the rod between the supports 53, 55 (e.g., screwed together for adjustment and clamping). The supports 53, 55 are accessible to ohmic contacts on the trimmed end of the rod 5. This causes a probe tip 61 to contact the rod 5 on a flat segment of the rod. Current is passed through the supports 53, 55, and voltage is measured through the probe tip 61. The probe tip 61 is manually moved along the axis of the rod 5, wherein the applied current / voltage is measured at each point. In the illustrated device 43, the probe tip 61 is moved manually. In other embodiments, the probe tip 61 is moved by an actuator.

[0034] Figure 4The measuring device 43 is an exemplary device and any suitable device for fixing the rod and / or measuring the resistivity of the rod can be used, unless otherwise stated. The use of the rod (e.g., typically a narrow diameter rod (e.g., less than 100 mm, 50 mm, or less than 25 mm)) and the measuring device 43 allows for the measurement of resistivity without cutting the rod into wafers or ingots.

[0035] The resistivity probe may be a two-point probe in contact with the flat segment 11 at two of its tips. The voltage difference is measured across the two probe tips. For example, resistivity can be measured using a two-point probe according to SEMI standard MF397-0812 entitled "Test Method for Resistivity of Silicon Bars using a Two-Point Probe," which is incorporated herein by reference for all relevance and consistency purposes. A two-terminal or three-terminal rectification method can be used to determine the crystal type (i.e., N-type or P-type). This type determination can be performed according to SEMI standard MF42-0316 entitled "Test Method for Conductivity Type of Extrinsic Semiconducting Materials," which is incorporated herein by reference for all relevance and consistency purposes. Both two-terminal and three-terminal rectification methods are robust methods for very high resistivity silicon.

[0036] Voltage can be measured at various points along the length. Resistivity can be calculated, for example, by determining the slope of the current-voltage curve, using the measured voltage, sample length, and average diameter (Example 1 below).

[0037] In some embodiments, sample rod 5 has a relatively low oxygen content (e.g., less than about 5.5 ppma). In other embodiments, the oxygen content of the sample rod is less than 5.2 ppma, less than 5.0 ppma, less than 3.5 ppma, less than about 3 ppma, or even less than about 2.5 ppma. In some embodiments, sample rod 5 is dislocation-free.

[0038] The measured resistivity of rod 5 provides information related to the resistivity of the polycrystalline silicon melt in the crucible (i.e., the initial dopant impurity concentration (i.e., the net donor-acceptor concentration)). The measured resistivity of rod 5 can be used to adjust the manufacturing conditions of the subsequently grown ingot. For example, a certain amount of dopant can be added to the polycrystalline melt, wherein the doping dose is adjusted at least in part based on the measured resistivity (e.g., by using a model that predicts the resistivity of the product ingot). Suitable dopant includes p-type dopant (e.g., boron, aluminum, gallium, and indium) and n-type dopant (e.g., phosphorus, arsenic, and antimony).

[0039] In some embodiments, a certain amount of dopant is added to the melt before the resistivity of the sample rod and the measuring rod is measured, and a certain amount of dopant (e.g., the same dopant or different dopant) is added after the sample rod is grown. In other embodiments, all dopant (if any) (e.g., boron or phosphorus) is added after the sample rod is grown and the resistivity is measured.

[0040] Polysilicon from which dopants are added and from which sample ingots and product ingots are pulled can be semiconductor-grade polysilicon. When semiconductor-grade polysilicon is used, in some embodiments, the polysilicon has a resistivity greater than 4,000 Ω-cm and contains no more than 0.02 ppba of boron or phosphorus.

[0041] After the sample bar is pulled up and, optionally, dopant is added to the melt, the product ingot is withdrawn from the melt. The product ingot has a diameter larger than that of the sample bar (i.e., the diameter of the constant diameter portion of the sample bar is smaller than the diameter of the constant diameter portion of the ingot). The product ingot may have a diameter of about 150 mm or, as in other embodiments, about 200 mm, about 300 mm or more (e.g., 450 mm or more).

[0042] In some embodiments, polysilicon is not added during the growth of the ingot (e.g., in a batch process). In other embodiments, polysilicon is added to the melt as the product ingot is grown (e.g., in a continuous Chuklaski process).

[0043] The doping amount added to the melt can be controlled (with or without the addition of the first dopant prior to sample rod growth) to achieve a target resistivity in at least a portion of the body of the ingot (e.g., the main portion of the ingot). In some embodiments, the target resistivity is a minimum resistivity. In some embodiments, the entire length of the ingot (e.g., the length of the ingot body) has a target resistivity (e.g., a minimum resistivity). In some embodiments, the target resistivity of at least a portion of the product ingot is at least about 1,500 Ω-cm or, as in other embodiments, at least about 2,000 Ω-cm, at least about 4,000 Ω-cm, at least about 6,000 Ω-cm, at least about 8,000 Ω-cm, at least about 10,000 Ω-cm, or a minimum resistivity from about 1,500 Ω-cm to about 50,000 ohm-cm or from about 8,000 Ω-cm to about 50,000 Ω-cm. Alternatively or additionally, the sample rod may have a resistivity of at least about 1,500 Ω-cm, or at least about 2,000 Ω-cm, at least about 4,000 Ω-cm, at least about 6,000 Ω-cm, at least about 8,000 Ω-cm, at least about 10,000 Ω-cm, from about 1,500 Ω-cm to about 50,000 ohm-cm, or from about 8,000 Ω-cm to about 50,000 Ω-cm.

[0044] Compared to conventional methods for producing monocrystalline silicon ingots, the method of the present invention has several advantages. The relatively high-purity polycrystalline silicon used to produce relatively high-resistivity monocrystalline silicon has a wide range of boron and phosphorus impurities, resulting in a wide range of intrinsic resistivity. By growing sample rods with relatively small diameters (e.g., smaller than product ingots, such as less than 100 mm, less than 50 mm, less than 25 mm, or even less than 10 mm, compared to sample ingots of substantially the same size as product ingots (e.g., at least 200 mm), the resistivity of the melt can be sampled relatively quickly. The measured resistivity can be used for more precise addition of dopants to achieve better calibration of high-resistivity or ultra-high-resistivity products (e.g., at least about 3000 ohm-cm, 5000 ohm-cm, or at least 7000 ohm-cm or more), and specifically, for better seed-end resistivity calibration. The relatively small diameter sample rods consume a relatively small amount of melt (e.g., less than 1 kg, less than 0.5 kg, or about 0.25 kg or less, compared to full-diameter short ingots that can consume 15 kg, 20 kg, or 50 kg or more of melt) and reduce impurity accumulation attributable to the sampling process. The sample rods can be grown relatively quickly (e.g., about 12, 10, or even 5 hours or less, compared to full-size short ingots that can involve growth times of 20, 30, 40, or 50 hours). The sample rods can have a relatively low oxygen content (e.g., less than about 5 ppma or less than 4 ppma), which improves the accuracy of resistivity measurements (e.g., the accuracy of the rods after heat donor elimination cycles).

[0045] In embodiments where a flat segment is formed on the surface of the sample rod, resistivity can be measured using a two-point probe. Compared to a four-point probe, such a two-point probe reduces sample preparation, is less sensitive to geometric correction factors, and allows for better current contact. The use of a two-point probe also allows for the use of two-terminal or three-terminal rectification methods for ingot type determination.

[0046] The reduced sample bar growth time and the reduced resistivity measurement time decrease the processing time for resistivity measurements (e.g., a reduction of 20, 30, or 40 hours in process time), which reduces the accumulation of impurities caused by crucible dissolution. Reduced impurities also improve the predictability of resistivity for future operations. The reduction in thermal hours per batch (i.e., between product ingots) allows for crucible reloading in additional cycles without increased losses due to zero dislocations.

[0047] Example

[0048] The process of the present invention is further illustrated by the following examples. These examples should not be considered as limiting.

[0049] Example 1: Determining resistivity from IV curves

[0050] (For example, for example, using) Figure 4 The device measures the voltage of a sample rod axially, recording the applied current and the measured voltage. Figure 5 The resulting IV curve is shown. Using the geometry of the sample and the slope of the IV curve, the resistivity of the sample is determined to be 6139 ohm-cm.

[0051] Example 2: Comparison of short ingots and sample bars

[0052] In similar Figure 1 A single-crystal short sample ingot (“short ingot”) with a diameter approximately the size of the product bar (e.g., approximately 200 mm in a 200 mm Czochralski apparatus) is grown in a Czochralski apparatus. The crystal is trimmed and subjected to mixed acid etching (MAE). The crystal ingot is then rapidly thermally annealed at 800°C for 3 minutes and polished. The ingot is brought into contact with a four-point probe to measure resistivity, wherein the resistivity is averaged over three measurements.

[0053] Following the growth of the short ingot, a sample rod (“Sample Rod”) was grown in the same Czochralski apparatus using a locked seed-lift mode. The diameter of the rod varied across its length and ranged from 17 to 23 mm, with an average of 20 mm. The sample rod was trimmed and ground to form a flat segment extending from one end of the rod to the other. The rod was then rapidly thermally annealed at 800°C for 3 minutes. This process was similar to... Figure 4 The measuring equipment shown in the image utilizes a two-point probe to measure the resistivity of the ingot. The differences between growth conditions are illustrated in Table 1 below:

[0054]

[0055] Table 1: Growth conditions for sample ingots with a diameter of 200 mm and sample rods with a diameter of approximately 17 to 23 mm.

[0056] exist Figure 6 The measured resistivity across the length of the sample bar and the resistivity of the ingot from the sample bar are shown in the figure.

[0057] Sample preparation for short ingots takes 26 hours and involves trimming, mixed acid etching, rapid thermal annealing, plate cutting, grinding (e.g., using a diamond pad), polishing, and measurements using a 4-point probe. Sample preparation for sample bars takes 6 hours and involves trimming, mixed acid etching, rapid thermal annealing, grinding (using a diamond pad), polishing, and measurements using a 2-point probe.

[0058] As used herein, when used in conjunction with ranges of size, concentration, temperature or other physical or chemical properties or characteristics, the terms “about,” “substantially,” “basically,” and “approximately” mean to cover variations that may exist in the upper and / or lower limits of the range of properties or characteristics, including, for example, variations arising from rounding, variations in measurement methods, or other statistical variations.

[0059] When describing elements of the present invention or several embodiments thereof, the articles “a” and “described” are intended to indicate the presence of one or more elements. The terms “comprising,” “including,” “containing,” and “having” are intended to be inclusive and indicate that additional elements may be present in addition to those listed. Terms indicating a particular orientation (e.g., “top,” “bottom,” “side,” etc.) are used for convenience of description and do not require any particular orientation of the described items.

[0060] Since various changes can be made to the above-described structure and method without departing from the scope of the invention, it is intended that all matters contained in the above description and shown in (some) the accompanying drawings be interpreted as illustrative and non-limiting.

Claims

1. A method for producing single-crystal silicon ingots from silicon melt held in a crucible, comprising: Add polycrystalline silicon to the crucible; The polycrystalline silicon is heated to form a silicon melt in the crucible; A sample rod is pulled from the melt, the sample rod having an average diameter of less than about 20 mm and a resistivity of at least about 1,500 Ω-cm; The sample rod is subjected to rapid thermal annealing at a temperature of at least 500°C for approximately 5 seconds to 15 minutes to eliminate the heat donor, and the sample rod has an oxygen content of less than 5.5 ppma. After the heat donor is eliminated, the resistivity of the sample rod is measured, wherein a current is applied to the sample rod to measure its resistance. The resistivity of the sample rod is measured without slicing it into a wafer or ingot. The sample rod is held in place by a measuring device, which includes a clamp that holds the sample rod in place when it comes into contact with a resistivity probe. The product ingot is pulled from the melt, the product ingot having a diameter, the diameter of the sample rod being less than 0.1 times the diameter of the product ingot, wherein the product ingot has a resistivity of at least about 1,500 Ω-cm.

2. The method of claim 1, further comprising forming a flat segment on the sample rod, and measuring the resistivity of the sample rod on the flat segment.

3. The method of claim 2, wherein the flat segment extends axially from one end of the sample rod toward a second end of the sample rod.

4. The method of claim 3, wherein the probe is brought into contact with the flat segment to measure the resistivity of the sample rod.

5. The method according to claim 4, wherein the probe is a two-point probe.

6. The method of claim 1, wherein the sample rod has a length of less than about 300 mm.

7. The method of claim 1, wherein the sample rod is annealed at a temperature of about 800°C or higher.

8. The method of claim 1, further comprising adding a dopant to the melt, the amount of dopant added to the melt depending on the resistivity of the sample rod being measured.

Images