Improved resistivity stabilization measurements of fat neck slabs for growing high and ultra-high resistivity single crystal silicon ingots

Abstract

A method for producing single crystal silicon ingots with improved resistivity control is disclosed. The method includes growing a sample rod. The sample rod may have a diameter smaller than that of the product ingot. The sample rod is cropped to form a central slab. The resistivity of the central slab may be measured directly, such as with a four-point probe. The sample rod, or optionally the central slab, may be annealed in a thermal donor annihilation cycle before measuring the resistivity, and the annealed rod or slab is irradiated with light to increase the relaxation rate and enable more rapid resistivity measurements.

Description

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to U.S. Provisional Application No. 62 / 785,432, filed December 27, 2018, the disclosure of which is incorporated herein by reference as if set forth in its entirety. [Technical field]

[0002] The field of the disclosure relates to methods for making single crystal silicon ingots with improved resistivity control, and in particular to methods that involve the growth and resistivity measurement of a central slab cut from a sample rod having a smaller diameter than the product ingot. [Background technology]

[0003] Single crystal silicon, the starting material for most processes for the manufacture of semiconductor electronic components, is typically prepared by the so-called Czochralski (CZ) process, in which a single seed crystal is immersed in molten silicon and then slowly extracted and grown. The molten silicon becomes contaminated with various impurities, mainly oxygen, during its time in the quartz crucible. Some applications, such as advanced wireless communication applications, insulated gate bipolar transistors (IGBTs), and low-power and low-leakage devices, require wafers with relatively high resistivity, such as 1500 Ω·cm or higher.

[0004] High-purity polycrystalline silicon is used for high resistivity ingot production. High-purity polycrystalline silicon is characterized by a spread in impurity profile, which results in a large spread in the range of intrinsic resistivity values ​​for undoped materials and their varieties. Targeting the seed-end resistivity of such high-resistivity or ultra-high-resistivity materials is difficult due to variations in boron and phosphorus (including surface boron and phosphorus in polycrystalline silicon materials) in the starting material, impurities in the crucible, and / or oxygen levels that change the resistivity after thermal donor annihilation cycles. Furthermore, such high-resistivity applications may be susceptible to increased errors in resistivity measurements.

[0005] What is needed is a method for preparing high resistivity silicon ingots that allows the impurity concentration and / or resistivity of a polycrystalline silicon starting material to be sampled relatively quickly and reliably with a relatively small amount of silicon consumed for resistivity measurements.

[0006] This section is intended to introduce the reader to various aspects of art that may be related to various aspects of the present disclosure that 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. As such, it should be understood that these statements are not admissions of prior art, and are to be read in this light. Summary of the Invention

[0007] The present application provides a method for controlling the resistivity of a single crystal silicon ingot grown by the Czochralski method, the method including the steps of contacting a silicon seed with a silicon melt, the silicon melt contained in a crucible and containing molten silicon, pulling the silicon seed from the silicon melt to form a sample rod containing single crystal silicon, the sample rod having a generally cylindrical shape including a central axis, a circumferential edge and a radius extending from the central axis to the circumferential edge, slicing a slab from the sample rod, the slab including a longitudinal plane that encircles at least a portion of the central axis of the sample rod and has a thickness, annealing the slab to annihilate thermal donors, lapping the slab, irradiating the slab with infrared radiation, and measuring the resistivity of the slab after the temperature of the slab has decreased to below 30°C.

[0008] There are various refinements of the features mentioned in relation to the above-mentioned aspects of the present disclosure. Further features may also be incorporated into the above-mentioned aspects of the present disclosure as well. These refinements 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 the present disclosure may be incorporated into any of the above-mentioned aspects of the present disclosure alone or in any combination. [Brief description of the drawings]

[0009] [Figure 1] FIG. 1 is a schematic side view of a pulling apparatus for producing a single crystal silicon ingot. [Diagram 2] This is a sample rod grown from a silicon melt. [Diagram 3] FIG. 1 is a schematic perspective view of a sample rod showing two crop planes where the rod is cut to form a central slab. [Figure 4] FIG. 1 is a schematic perspective view of a cut sample rod including a central slab. [Diagram 5] This is the IV curve used to measure resistivity. [Figure 6] FIG. 13 is a scatter plot of resistivity of sample rods at various positions from the seed end. [Figure 7] FIG. 1 is a scatter plot of the resistivity of a flat polished sample rod, a short ingot, and a product ingot. [Figure 8A] FIG. 1 is a schematic top view of three sample rods that were successively polished to form flat segments (flats). [Figure 8B] FIG. 8B is a scatter plot of the resistivity of the successively polished sample rods of FIG. 8A and the resistivity of the short ingots and the product ingots. [Figure 9] FIG. 13 is a scatter plot of the resistivity of a half-cut sample rod and a central slab cut from the sample rod, as well as the resistivity of a short ingot and a product ingot. [Figure 10]FIG. 13 is a scatter plot of the resistivity of a continuously polished sample rod and a central slab cut from the sample rod, as well as the resistivity of a short ingot and a product ingot. [Figure 11] Scatter plot of resistivity of a central slab cut from a production ingot, and resistivity of a short ingot and a production ingot, measured by a two-point probe and a four-point probe. [Figure 12] 13 is a graph showing resistivity measurements of the central slab at .about.5K.OMEGA.cm as a function of time after thermal donor annihilation anneal and lapping. [Figure 13] 1 is a graph showing the temperature profile of the fat neck central slab during irradiation, where time zero is when the IR lamps are turned on. [Figure 14A] Figure 1 shows the resistivity relaxation of the fat neck central slab ~1.5KΩcm with (new method) and without (POR test #1 and #2) IR irradiation annealing started 1 hour after the thermal donor annihilation annealing. [Figure 14B] 1 is a graph showing the relative resistivity drop versus time for a central slab at 1.5 K with (new method) and without (POR test #2) IR irradiation. [Figure 15A] This graph compares the resistivity relaxation of the fat neck central slab ~5KΩcm with and without IR irradiation (new method) (POR test #1, #2). The IR irradiation anneal was started 1 hour after the thermal donor annihilation anneal. [Figure 15B] 1 is a graph showing the relative resistivity drop versus time for a central slab at 5K with (new method) and without IR irradiation (POR test #2). [Figure 16A] This is a graph comparing resistivity relaxation of the fat neck central slab at ~20KΩcm with (new method) and without (POR test #1 and #2) IR irradiation annealing was started 1 hour after the thermal donor annihilation annealing. [Figure 16B]1 is a graph showing the relative resistivity drop versus time for a central slab at 20K with (new method) and without (POR test #2) IR irradiation.

[0010] Corresponding reference characters indicate corresponding parts throughout the drawings. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0011] The provisional application of the present disclosure relates to a method for producing a single crystal silicon ingot by the Czochralski method, in which a sample rod is grown to determine the resistivity of the melt. The sample rod has a smaller diameter than the product ingot. The sample rod is slabized and the resistivity of the slab is measured, such as with a four-point probe. In some embodiments, the resistivity of the slab is measured after irradiation, for example with infrared light. The irradiation has the effect of accelerating the relaxation of the resistivity, thereby allowing for more rapid resistivity measurement.

[0012] 1, in accordance with an embodiment of the present disclosure, a product ingot is grown by the so-called Czochralski process in which an ingot is pulled from a silicon melt 44 held in a crucible 22 in an ingot puller 23. The ingot puller 23 includes a housing 26 that defines a crystal growth chamber 16 and a pull 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 narrowed pull chamber 20. The ingot puller 23 includes an inlet port 7 and an outlet port 12 that are used to introduce and remove process gases into and from the housing 26 during crystal growth.

[0013] The crucible 22 in the ingot pulling apparatus 23 contains a silicon melt 44 from which a silicon ingot is pulled. The silicon melt 44 is obtained by heating and melting polycrystalline silicon loaded in the crucible 22. The crucible 22 is mounted on a turntable 31 for rotation about a central longitudinal axis X of the ingot pulling apparatus 23.

[0014] Surrounding the crucible 22 is a heating system 39 (e.g., an electrical resistance heater) for melting the silicon charge to produce a melt 44. The heating system 39 may extend below the crucible as shown in U.S. Pat. No. 8,317,919. The heating system 39 is controlled by a control system (not shown) such that the temperature of the melt 44 is precisely controlled throughout the pulling process. Insulation (not shown) surrounding the heating system 39 may reduce the amount of heat lost through the housing 26. The ingot pulling apparatus 23 may also include a heat shield assembly (not shown) on the melt surface to shield the ingot from the heat of the crucible 22 to increase the axial temperature gradient at the solid-melt interface.

[0015] A pulling mechanism (not shown) is attached to a pulling wire 24 that extends downward from the mechanism. The mechanism can raise and lower the pulling wire 24. The ingot puller 23 may have a pulling shaft rather than a wire, depending on the type of pull. The pulling wire 24 terminates in a pulling assembly 58 that includes a seed chuck 32 that holds a seed crystal 6 used to grow a silicon ingot. When growing an ingot, the pulling mechanism lowers the seed crystal 6 until it contacts the surface of the silicon melt 44. Once the seed crystal 6 begins to melt, the pulling mechanism slowly pulls the seed crystal through the growth chamber 16 and the pulling chamber 20 to grow a single crystal ingot. The speed at which the pulling mechanism rotates the seed crystal 6 and the speed at which the pulling mechanism pulls the seed crystal (i.e., the pulling speed v) are controlled by a control system.

[0016] Process gas is introduced into the housing 26 through the inlet port 7 and removed through the outlet port 12. The process gas creates an atmosphere within the housing 26, and the melt and the atmosphere form a melt-gas interface. The outlet port 12 is in fluid communication with the exhaust system (not shown) of the ingot puller.

[0017] In this regard, the ingot pulling apparatus 23 shown in FIG. 1 and described herein is exemplary, and other crystal pulling apparatus configurations and arrangements may be used to pull a single crystal silicon ingot from a melt, unless otherwise specified.

[0018] According to an embodiment of the present disclosure, after polycrystalline silicon is added to the crucible 22 and the heating system 39 operates to melt down the polycrystalline silicon, a sample ingot or rod is pulled from the melt. An example of a sample rod 5 is shown in FIG. 2. The rod 5 includes a crown portion 21 where the rod transitions and tapers outward from the seed to reach a target diameter. The rod 5 includes a central axis A and a constant diameter portion 25 or cylindrical body or simply "body" of the crystal that is grown by increasing the pulling rate. The body portion 25 of the sample rod 5 has a relatively constant diameter. The rod 5 includes a tail cone or end cone 29 where the rod tapers in diameter after the body 25. Once the diameter is small enough, the rod 5 is separated from the melt. The rod 5 has a central longitudinal axis A that extends through the crown 21 and the terminal end 33 of the ingot.

[0019] The growth conditions for the sample rod 5 can be selected from about any suitable growth condition available to one of skill in the art. The sample rod 5 may be a single crystal with the body of the sample rod having zero dislocations. The sample rod 5 may be grown with locked seed lift (i.e., a fixed pulling rate while varying the diameter, such as about ±5 mm) or active seed lift (pulling rate that varies to maintain a target diameter).

[0020] The sample rod 5 has a smaller diameter than the product ingot that will be grown after the sample rod. For example, the diameter of the sample rod may be less than 0.75 times, less than 0.50 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, or less than about 100 mm, less than about 50 mm, less than about 25 mm, or less than about 20 mm (e.g., about 5 mm to about 150 mm, about 5 mm to about 100 mm, about 5 mm to about 50 mm, about 5 mm to about 25 mm, or about 10 mm to about 25 mm). In general, the diameter of the rod 5 is measured by measuring the rod along several axial positions (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 and averaging 2, 4, 6, 10 or more diameters along the length). In some embodiments, the maximum diameter of the sample rod is less than about 150 mm, or less than about 100 mm, or less than about 50 mm, or 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).

[0021] In some embodiments, the rod 5 has a diameter that generally 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, e.g., about 17 mm.

[0022] The sample rod 5 may have any suitable length. In some embodiments, the rod (e.g., after cropping) has a length between about 100 millimeters and about 500 millimeters, e.g., between about 150 millimeters and about 300 millimeters, e.g., about 200 millimeters. In some embodiments, the rod (e.g., after cropping) has a length less than about 300 millimeters, less than about 200 millimeters, or less than about 100 millimeters (e.g., about 25 millimeters to about 300 millimeters, e.g., about 200 millimeters).

[0023] After the sample rod 5 is grown, it is processed, e.g., sliced, to form a central slab 40 (FIG. 4). Slicing the central slab 40 from the sample rod 5 can improve the reliability of the resistivity measurement. The fat neck should be measured as close to the axisymmetric center as possible, where the radial variation of resistivity is minimal. To achieve this, the fat neck is sliced ​​at the center (or close to the widest diameter of the fat neck) into a thin slab. The crown and tail of the sample rod 5 may be removed, e.g., sliced ​​using a wire saw. The sample rod 5 is then cut to form a slab 40, as shown in FIG. 4. The sample rod 5 may be cut by a benchtop saw (e.g., Minitom available from Streuers, Westlake, Ohio) or with a diamond wire saw (e.g., DTW wire saw). The sample rod 5 is cut along a first crop surface 42 (FIG. 3) and cut along a second crop surface 46 to form first and second crop portions 49, 52 (FIG. 4) and a slab 40. The first crop surface 42 and the second crop surface 46 are parallel to each other and to a central longitudinal axis A of the sample rod 5. The slab 40 may have any thickness suitable for resistivity measurements, such as, for example, a thickness between about 5 mm and about 0.1 mm, between about 3 mm and about 0.5 mm, between about 3 mm and about 1 mm, between 2 mm and 1 mm, or about 1.1 mm. The slab 40 may be generally square or rectangular in cross section. The first and second sides 62, 64 of the slab 40 may be slightly rounded due to the contour of the sample rod 5, or the slab 40 may be further cut to form planar sides 62, 64.

[0024] Generally, the central slab 40 includes at least a portion of the central axis A of the uncropped sample rod 5. In some embodiments, the cropping method may be varied to account for axial non-uniformity in the diameter of the sample rod, such that the central slab 40 captures as much of the axisymmetric centerline of the rod 5 as possible. For example, the central slab 40 may include at least about 10% of the central axis A of the sample rod 5 (i.e., the sample rod immediately prior to cropping to form the central slab), or at least about 25%, at least about 50%, at least about 75%, or at least about 90% of the central axis A of the sample rod 5. In some embodiments, after cropping, the central axis A of the cropped sample rod 5 extends through the entire length of the central slab 40 (e.g., from the first end 54 to the second end 56 of the central slab 40).

[0025] In some embodiments, the cropped ends of the rods 5 or central slab 40 are polished to make the ends flat. The ends of the rods may be etched (e.g., mixed acid etch). The central slab 40 may be modified to include ohmic contacts at its first and second ends 54, 56. For example, the first and second ends 54, 56 of the central slab 40 may be painted with colloidal silver paint and allowed to dry.

[0026] In some embodiments, the sample rod 5 or a central slab 40 sliced ​​from the sample rod 5 (see FIG. 4) undergoes a thermal donor annihilation anneal prior to measuring resistivity. The thermal donor annihilation anneal may act as a thermal donor annihilation cycle (i.e., annihilation of the thermal donor) by dissociating interstitial oxygen clusters. In some embodiments, the thermal donor annihilation anneal is performed at a temperature of about 500° C. or higher, or about 600° C. or higher, about 650° C. or higher, or about 800° C. or higher (e.g., from about 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) for no more than 60 minutes, or no more than 30 minutes. In some embodiments, the anneal to extinguish the thermal donor comprises annealing the sample rod 5 or the slab 40 sliced ​​from the sample rod 5 to a temperature of greater than about 600° C. for 60 minutes or less, or for 30 minutes or less. In some embodiments, the anneal to extinguish the thermal donor comprises annealing the sample rod 5 or the slab 40 sliced ​​from the sample rod 5 to a temperature of about 720° C. for about 2 minutes.

[0027] The first and second cropped planar surfaces 57, 59 of the central slab 40 may be polished to flatten the surfaces. In some embodiments, the central slab 40 is lapped prior to resistivity measurements to form a lapped surface with reduced surface morphology (e.g., before or after a thermal donar-chill cycle). The purpose of lapping includes removing subsurface damage of the sliced ​​central slab 40, thinning the central slab 40 to a target thickness, and achieving a high degree of parallelism and flatness of the surface of the central slab 40. Both single-side and double-side lapping processes can be used to lap the central slab 40. In double-side lapping (DSL), loose abrasive particles are suspended in a colloidal slurry to scrape material from the surface of the central slab 40. The central slab 40 is held in a geared carrier and driven with a planetary motion. A batch of central slabs 40 can be manually placed into the holes of the carrier, and the top plate is pressed down by a certain pressure (or weight), for example, about 1 kg to about 30 kg, or about 5 kg to about 20 kg, for example, about 10 kg. The two plates start to rotate either in the same direction or in the opposite direction. In double-sided lapping, both sides of the central slab 40 are lapped simultaneously. The colloidal slurry is continuously filled into the lapping machine, and there is usually a thin film of the slurry between the central slab 40 and the two plates. The slurry performs material removal via the abrasive grains as it slides or rolls between the wafer surface and the two plates. The lapping is performed for at least 1 minute, at least 5 minutes, at least 10 minutes, at least 15 minutes, at least 20 minutes, at least 25 minutes, for example, about 10 minutes. The lapping parameters, including lapping pressure, plate rotation speed, plate material, abrasive and grain size, slurry concentration, slurry flow rate, and carrier design, may follow conventional techniques. For example, the particle size of the lapping slurry may range from about 1 to about 250 micrometers, such as from about 1 to about 50 micrometers, for example, from about 5 to about 20 micrometers.The rotation speed may range from about 10 to about 150 rpm, or from about 25 to about 150 rpm, such as about 50 rpm, about 75 rpm, or about 100 rpm. In some embodiments, the central slab 40 may contact an alumina (Al2O3) slurry. In some embodiments, the central slab 40 may contact a slurry containing single crystal diamond particles. In some embodiments, the central slab 40 may contact a slurry containing boron carbide particles. In some embodiments, the central slab 40 may contact a slurry containing silicon carbide particles.

[0028] In embodiments where the goal is for the ingots grown by the Czochralski method to have high resistivity, it has been observed that accurate resistivity measurements require a time-dependent relaxation following the thermal donor annihilation anneal and lapping to prepare the sample. For example, up to 72 hours at room temperature are required for the resistivity to relax to a stable value. Also, causes of delayed relaxation and stabilization include surface treatments (surface morphology such as etching, polishing, grinding, lapping, etc.) affecting the transient profile. These transient effects interfere with the measurement of true dopant concentration determinations, which are necessary to accurately "sample" polycrystalline silicon. Accurate sampling resistivity measurements are necessary to determine whether additional dopants are required in the silicon melt when growing single crystal silicon ingots intended for prime rods for HR (high resistivity) or UHR (ultra-high resistivity) applications. Thus, it is important to allow this transient behavior to relax sufficiently to derive the true net melt dopant concentration measured by resistivity. Accurate resistivity measurements may require waiting at least 4 hours after the thermal donor annihilation anneal and lapping for the resistivity to decay by 90% and up to 12 hours for the resistivity to decay by 95% or more. Figure 12 shows the relaxation curves of a central slab after two different treatments of the same slab followed by a thermal donor annihilation anneal and lapping. As shown in Figure 12, it can take 36 hours or more for the resistivity of the sample slab to fully relax and stabilize (open circle curve). The open white diamond curve in Figure 12 shows the resistivity stabilization time after an additional thermal donor annihilation anneal and lapping on the same slab. The two curves have slightly different transient behavior for the first few hours but become identical after a longer time. This reflects the true stable dopant concentration after extended relaxation at room temperature. The time required to allow resistivity stabilization affects the overall cycle time of the process of "sampling" the polycrystalline silicon melt to determine the appropriate dopant addition to grow the desired HR or UHR full-size monocrystalline silicon ingot, thereby affecting the process throughput.

[0029] According to the method of the present invention, the central slab 40 sliced ​​from the sample rod 5 is irradiated to promote a transient relaxation process, thereby shortening the stabilization period required to obtain accurate resistivity measurements. In some embodiments, the central slab 40 is irradiated with infrared light. In some embodiments, the central slab 40 is irradiated with light having a wavelength between about 0.75 micrometers and about 1000 micrometers. In some embodiments, the central slab 40 is irradiated with light having a wavelength between about 400 nanometers and about 4.5 micrometers. In some embodiments, the central slab 40 is irradiated with light having a wavelength between about 0.75 micrometers and about 4.5 micrometers. Any commercially available lamp capable of irradiating within these ranges is suitable for the method of the present invention. In some embodiments, the central slab 40 may be irradiated for a duration of at least about 10 minutes, such as between about 10 minutes and about 2 hours, such as between about 10 minutes and 1 hour. Commercially available lamps may be used to irradiate the central slab 40, provided that such lamps irradiate within the desired wavelengths according to the method of the present invention. In some embodiments, the central slab 40 is irradiated with light of sufficient intensity to raise the temperature of the central slab 40 to a temperature of at least about 40° C., at least about 50° C., or at least about 60° C. The temperature is a close measurement of the photon flux sufficient to achieve a more rapid resistivity relaxation in these embodiments. In some embodiments, the central slab 40 is irradiated at a temperature of at least about 40° C., at least about 50° C., or at least about 60° C. for at least about 10 minutes. In some embodiments, the central slab 40 is irradiated at a temperature of at least about 40° C., at least about 50° C., or at least about 60° C. for a period of about 10 minutes to about 2 hours. In some embodiments, the central slab 40 is irradiated at a temperature of at least about 40° C., at least about 50° C., or at least about 60° C. for a period of about 10 minutes to about 1 hour. In some embodiments, the central slab 40 is irradiated at a temperature of at least about 40° C., at least about 50° C., or at least about 60° C. for about 10 minutes.In some embodiments, the central slab 40 is irradiated at a temperature of at least about 40° C., at a temperature of at least about 50° C., or at least about 60° C. for about 1 hour.

[0030] The appropriate duration and intensity of irradiation can be determined by measuring the temperature, but in some embodiments, the temperature increase is not critical for the enhanced relaxation and stabilization of the resistivity of the slab. That is, a temperature increase is not required to achieve the relaxation of resistivity that is the result of irradiation. The required photon flux is achieved in some embodiments without a temperature increase. Irradiation by the methods of the invention may involve heating, but it is believed that irradiation results in relaxation, meaning that photodissociation by light flux is the dominant mechanism of relaxation enhancement. The mechanism of photodissociation may involve photogenerated carriers, which means that the range of light suitable for relaxation may be broad, for example, from visible light (or near ultraviolet light) to near infrared light at about 1100 nm (corresponding to the band gap energy), which ranges from about 250 to 1100 nm. Photodissociation may also involve photoexcitation of low energy states, such as vibrational states and defect electronic states within the band gap, in which case photodissociation may extend into the mid-infrared range. Prior to resistivity measurements, the slabs are cooled to below 30° C., such as room temperature, which typically takes several minutes, such as up to 30 minutes, or 10 minutes, or 1-5 minutes.

[0031] The resistivity of the melt from which the product ingot is grown may be determined by measuring the resistivity of the central slab 40. In some embodiments, if the temperature of the central slab 40 is increased by irradiation, it is cooled to below 30° C. and the resistivity is measured after irradiation. In some embodiments of the present disclosure, a current is driven through the central slab 40 and a resistivity probe is contacted at one or more locations along the length of the central slab 40. The current may be applied to the rod 5 through either of the ends 54, 56.

[0032] In some embodiments, the resistivity of the central slab 40 is measured by a four-point resistivity probe (e.g., an in-line four-point probe) in which all four probe tips contact the slab 40. The slab 40 may be mounted in a fixture during resistivity measurement. According to some embodiments, a current (e.g., direct current) is passed through the slab 40 between the outer probe pins, and the resulting potential difference is measured between the inner probe pins. The resistivity is calculated from the measured current and potential values ​​based on appropriate coefficients from the geometry of the slab. In this regard, the resistivity may be measured in accordance with SEMI MF84-0307, ​​"Test Method for Measuring Resistivity of Silicon Wafers with an In-line Four-Point Probe," and / or SEMI MF43-0705, "Test Methods for Resistivity of Semiconductor Materials," which are incorporated herein by reference for all relevant consistent purposes. The voltage may be measured at various points along the length of the slab 40. The measured voltage, as well as the length and average thickness of the sample, may be used to calculate the resistivity, such as by determining the slope of the current-voltage curve (eg, Example 1 below).

[0033] In some embodiments, the sample rod 5 and central slab 40 have a relatively low oxygen content, such as an oxygen content of less than about 5.5 ppma. In other embodiments, the oxygen content of the sample rod 5 and slab 40 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, the sample rod 5 and slab 40 produced from the sample rod 5 are free of dislocations.

[0034] The measured resistivity of the slab 40 provides information related to the resistivity of the polycrystalline silicon melt in the crucible (i.e., the starting dopant impurity concentration (i.e., net donor-acceptor concentration)). The measured resistivity of the slab 40 may be used to adjust the manufacturing conditions of the subsequently grown ingot. For example, dopants may be added to the polycrystalline silicon melt, adjusting the amount of dopant based at least in part on the measured resistivity (e.g., using a model that predicts the resistivity of the product ingot). Suitable dopants include p-type dopants, such as boron, aluminum, gallium, and indium, and n-type dopants, such as phosphorus, arsenic, and antimony.

[0035] The measured resistivity can be an indirect measure of the total amount of p-type dopants, e.g., boron, or n-type dopants, e.g., phosphorus, contained in the incoming polycrystalline silicon. Depending on the measured resistivity and type, trace amounts of p-type dopants, e.g., boron, or n-type dopants, e.g., phosphorus, are added to achieve the appropriate seed-end resistivity target for ultra-high resistivity (>5KΩcm, more specifically >7.5KΩcm) material. The accuracy to the target is highly sensitive to the accuracy of the short body and / or fat neck resistivity results. During operation, the puller remains hot while waiting for the resistivity of the short body or fat neck to be determined. This increases the cycle time of the overall process and may have deleterious effects on oxygen or other impurities as the crucible is continuously melting. The fat neck sample rod may be slabbed to remove the cycle time for growing the "sample" material. Irradiating the center slab sample can further reduce the cycle time of the overall process by reducing the waiting time required for the resistivity to relax to near saturation from 6-12 hours to less than 1 hour. The method also offers an improvement over this precision for seed end targeting of long UHR rods by ensuring that the resistivity measured in the short body or fat neck is not less than ~95% fully relaxed to the final resistivity state.

[0036] In some embodiments, a predetermined amount of dopant is added to the melt before growing the sample rod and measuring the resistivity of the rod, and a predetermined amount of dopant (e.g., the same dopant or a different dopant) is added after growing the sample rod, in other embodiments, all dopant (if any) is added (e.g., boron or phosphorus) after growing the sample rod and measuring the resistivity.

[0037] The polycrystalline silicon to which the dopants are added and from which the sample ingots and product ingots are pulled may be semiconductor grade polycrystalline silicon. When semiconductor grade polycrystalline silicon is used, in some embodiments the polycrystalline silicon has a resistivity greater than 4,000 Ω·cm and does not contain more than 0.02 ppba of boron or phosphorous.

[0038] After the sample rod is drawn and optionally dopants are added to the melt, a product ingot is pulled from the melt. The product ingot has a diameter greater than that of the sample rod (i.e., the diameter of the constant diameter portion of the sample rod is less than the diameter of the constant diameter portion of the ingot). The product ingot may have a diameter of about 150 mm, or in other embodiments, about 200 mm, about 300 mm, or more (e.g., 450 mm or more).

[0039] In some embodiments, polycrystalline silicon is not added during the growth of the ingot (e.g., as in a batch process), while in other embodiments, polycrystalline silicon is added to the melt as the product ingot is grown (e.g., as in the continuous Czochralski process).

[0040] The amount of dopant added to the melt (with or without adding a first dopant before the sample rod is grown) may be controlled to achieve a target resistivity in at least a portion of the body of the ingot (e.g., a prime 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 body of the ingot) has a target resistivity (e.g., a minimum resistivity). In some embodiments, the target resistivity of at least a portion of the product ingot has a minimum resistivity of at least about 500 Ω·cm, at least about 1,000 Ω·cm, at least about 1,500 Ω·cm, 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 in a range from about 500 Ω·cm to about 50,000 Ω·cm, from about 1,000 Ω·cm to about 50,000 Ω·cm, from about 1,500 Ω·cm to about 50,000 Ω·cm, or from about 8,000 Ω·cm to about 50,000 Ω·cm. Alternatively or additionally, the sample rod (and resulting central slab) is at least about 500 Ω·cm, at least about 1,000 Ω·cm, at least about 1,500 Ω·cm, 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, or at least about 10,000 Ω·cm, or from about 500 Ω·cm to about 50,000 Ω·cm, from about 1,000 Ω·cm to about 50,000 Ω·cm, from about 1,500 Ω·cm to about 50,000 Ω·cm, or from about 8,000 Ω·cm to about 50,000 Ω·cm.

[0041] In some embodiments, the target is a p-type single crystal silicon ingot. If the resistivity of the sample slab is below the target value, the dopant added is selected from the group consisting of phosphorus, arsenic, and antimony, and the dopant is added to increase the resistivity of the p-type single crystal silicon ingot.

[0042] In some embodiments, for p-type single crystal silicon ingots, if the resistivity of the sample slab is above target or the resistivity measurement indicates that the slab is n-type, the dopant added is selected from the group consisting of boron, gallium, and aluminum, and the dopant is added to reduce the resistivity of the p-type single crystal silicon ingot.

[0043] In some embodiments, the target is an n-type single crystal silicon ingot. If the resistivity of the sample slab is equal to or lower than the target, the dopant is added to the sample slab, and the dopant is selected from the group consisting of boron, gallium, and aluminum, and the dopant is added to increase the resistivity of the n-type single crystal silicon ingot.

[0044] In some embodiments, for n-type single crystal silicon ingots, if the resistivity of the sample slab exceeds the target, or if the resistivity measurement indicates that the slab is p-type, the dopant added is selected from the group consisting of phosphorus, arsenic, and antimony, and the dopant is added to reduce the resistivity of the n-type single crystal silicon ingot.

[0045] Compared with the conventional method of producing single crystal silicon ingots, the method of the present disclosure has several advantages. The relatively high purity polycrystalline silicon used to produce single crystal silicon with relatively high resistivity has a range of boron and phosphorus impurity amounts, which results in a range of intrinsic resistivity. By growing a sample rod with a relatively small diameter (e.g., less than 100 mm, less than 50 mm, less than 25 mm, or even less than 10 mm, smaller than the product ingot, compared to a sample ingot having substantially the same size as the product ingot, such as at least 200 mm), and forming a slab from the sample rod, the resistivity of the melt can be sampled relatively quickly and reliably.

[0046] The measured resistivity can be used for more precise doping of dopants to achieve better targets for high or ultra-high resistivity products (e.g., at least about 3000 Ω·cm, 5000 Ω·cm, or at least 7000 Ω·cm or higher), especially for better seed-end resistivity targets. The relatively small diameter sample rod consumes a relatively small amount of melt (e.g., less than 1 kg, less than 0.5 kg, or less than about 0.25 kg, compared to a full diameter short ingot that may consume 15 kg, 20 kg, or 50 kg or more of melt), reducing the accumulation of impurities due to the sampling process. The sample rod can be grown in a relatively short time (e.g., about 12 hours, 10 hours, or 5 hours or less, compared to a full size short ingot that may require 20 hours, 30 hours, 40 hours, or 50 hours of growth time). Slabs cut from the sample rod may have a relatively low oxygen content (e.g., less than about 5 ppma or less than 4 ppma), which may improve the accuracy of the resistivity measurement (e.g., after a thermal donor kill cycle).

[0047] Variations in resistivity measurements from sample rods can be caused by (1) diameter correction of resistivity measured by a two-point probe, contact noise due to the preparation of planar segments on the sample rod, and / or (3) large morphology variations. Forming a slab from the sample rod allows the resistivity to be measured in a portion closer to the axisymmetric center of the sample rod. This improves the accuracy of the resistivity measurement by reducing or eliminating radial variations in resistivity. Also, in embodiments where the slab is lapped to reduce morphology due to polishing and improve thickness uniformity, the resistivity measurement may be more accurate. In embodiments where a four-point probe is used to measure resistivity, the resistivity measurement may be further improved.

[0048] The shorter growth time of the sample rod and the shorter resistivity measurement time shortens the processing time over which resistivity measurements are taken (e.g., shortening processing times to 20, 30 or 40 hours), which reduces the buildup of impurities resulting from melting the crucible. Fewer impurities improve the predictability of future resistivities. Reducing the hot hour time between each batch (i.e., between product ingots) allows the crucible to be refilled for additional cycles without increasing the loss of zero dislocations.

[0049] The processes of the present disclosure are further illustrated by the following examples, which should not be viewed in a limiting sense.

[0050] Example 1: Determining resistivity from an IV curve The voltage across the sample rod was measured in the axial direction, and the applied current and measured voltage were recorded. Figure 5 shows the generated I-V curve. From the shape of the sample and the slope of the I-V curve, the resistivity of the sample was calculated to be 6139 Ω·cm. The resistivity of the central slab cut from the sample rod can also be calculated in the same way.

[0051] Example 2: Comparison of short ingot and sample rod A single crystal short sample ingot ("short ingot") with a diameter on the order of the size of the product ingot (e.g., about 200 mm for a 200 mm puller) was grown in a puller similar to that shown in Figure 1. The crystal was cropped and subjected to mixed acid etching (MAE). The crystal slab was rapid thermal annealed at 800°C for 3 minutes and lapped. The resistivity of the slab was measured by contacting it with a four-point probe, and the resistivity was averaged over three measurements.

[0052] After growing the short ingots, sample rods ("sample rods") were grown in locked-sea drift mode on the same puller. The diameter of the rods varied over their length, ranging from 17 to 23 mm, with an average of 20 mm. The sample rods were cut and polished to form flat segments extending from one end of the rod to the other. The rods were rapid thermal annealed at 720 °C for 2 minutes. The resistivity of the ingots was measured with a two-point probe. The differences in the growth conditions are shown in Table 1 below. TIFF0007638871000001.tif52137 Table 3: Growth conditions for sample ingots with a diameter of 200 mm and sample rods with a diameter of approximately 17–23 mm.

[0053] The resistivity measured over the length of the sample rod and the resistivity of the slag from the sample ingot are shown in FIG.

[0054] The sample preparation time for the short ingot was 26 hours and included cropping, mixed acid etching, rapid thermal annealing, slab cutting, polishing (e.g., with a diamond pad), lapping, and resistivity measurement. The sample rod preparation time was 6 hours and included cropping, mixed acid etching, rapid thermal annealing, flat grinding (with a diamond grinder), lapping, and resistivity measurement. The sample rod processing time was 20% of the short ingot processing time (5 hours vs. 25 hours), and the total sample rod processing time was 22% of the short ingot processing time (11 hours vs. 51 hours). In some embodiments, the sample rod processing time and total time range from about 15% to about 25% of the short ingot processing time and total time.

[0055] Example 3: Comparison of resistivity of sample rod, short ingot, and seed end of product ingot A single crystal short sample ingot ("short ingot") and two sample rods ("sample rods") were grown under the conditions of Example 2. One sample rod was grown before growing the short ingot, and one sample rod was grown after growing the short ingot. In addition, a product ingot was grown with a target seed end resistivity of approximately 8,000 Ω·cm (p-type). Because the resistivity of the short ingot was approximately 5,000 Ω·cm, an amount of phosphorus dopant was added to target a resistivity of at least 7,500 Ω·cm for the product ingot.

[0056] The resistivity of the sample rod was measured with a two-point probe, and the resistivity of the slug of the short ingot was measured with a four-point probe, and the results are shown in Figure 7. Also shown in Figure 7 is the resistivity near the seed end of the product ingot. From Figure 7, the variability of the two-point measurements of the sample rod is observed. The variability in the resistivity measurements of the sample rod grown before the short ingot would cause overdoping (e.g., if an average had been used). Similar variability (not shown) was observed when the sample rod was cut in half (center cut).

[0057] Example 4: Proximity of sample rod to center of axisymmetric and variability in resistivity measurements A single crystal short sample ingot ("short ingot") and a sample rod ("sample rod") were grown under the conditions of Example 2. A product ingot was also grown to a target seed end resistivity of approximately 7,500 Ω·cm (p-type). The sample rod was polished three times to form planar segments on the sample rod that gradually approached the central axis of the sample rod (FIG. 8A). After each planar segment was formed, resistivity was measured with a two-point probe along the rod, and the resistivity of each planar segment is shown in FIG. 8B. The resistivity of the short ingot and the resistivity of the product rod, which were used to determine the dopant amount in the product ingot, are also shown in FIG. 8B.

[0058] As shown in Figure 8B, the axial measurements for each planarization become flatter with each removal and have less axial variation. For each planarization, the initial seed resistivity of the sample rod is well below the mid-to-late body average of the rod. The average value for each planarization is below the average value for the short ingot, which would require the use of additional phosphorus dopant and would move the production ingot away from the 7,500 Ω-cm target.

[0059] Example 5: Comparison of resistivity measurements between center-cut sample rods and central slabs Prior to the growth of the short ingots, sample rods were grown under the conditions of Example 2. One sample rod was center cut and one sample rod was processed into a central slab with a thickness of about 1.1 mm. After the growth of the short ingots, sample rods were grown under the conditions of Example 2, one sample rod was center cut and the other sample rod was processed to form a central slab with a thickness of about 1.1 mm. To prepare the center-cut sample rods, after thermal donor annihilation anneal and a waiting time of 4 hours, the top and tail of the sample rod were removed and the rod was cut axially along the centerline to create two half pieces. To prepare the central slabs, the top and tail of the sample rod were removed and the rod was cut to form the central slab. After mixed acid etching (MAE), the central slab was subjected to thermal donor annihilation anneal. After a waiting time of 4 hours, the resistivity was measured. The resistivity of the center-cut sample rods was measured with a two-point probe and the resistivity of the central slab was measured with a four-point probe. In addition, a product ingot was grown and the resistivity of the seed end was measured. The resistivity measurement results are shown in Figure 9.

[0060] As shown in Figure 9, the center cut sample rods show axial variation. The center slab measurements contain some random fluctuations in the axial measurements, but the average resistivity is relatively close to the short body (~6200 Ω·cm). If the resistivity of the center slab is used to determine the dopant addition, the resulting dopant addition will be of the same order of magnitude (e.g., a small amount of phosphorus addition).

[0061] Example 6: Comparison of resistivity of successive planarization polishing of sample rods and central slabs A sample rod was grown according to Example 2. The sample rod was polished in sequence and the resistivity was measured after each polish with a two-point probe as in Example 4. The sample rod was also grown and processed to form a central slab about 1.1 mm thick. The resistivity of the central slab was measured with a four-point probe. Also, after the sample rod was formed, a short ingot and a product ingot were grown and the resistivity of the seed end was measured from the slag. The resistivity is shown in FIG. 10.

[0062] As shown in Figure 10, each planarization measurement (first, third, and fifth polishes shown) contains an axial trend from the seed end to the opposite end, with the overall average resistivity being lower than that of the short ingot. Measurements of the center slab show a flat axial trend with the overall average very similar to the resistivity of the short body, resulting in a similar dopant loading.

[0063] Example 7: Accuracy of resistivity prediction Table 1 compares the resistivity of the short ingots measured by four-point probe ("4PP") of a central slab cut from the sample rod with the resistivity of the sample rod with a flat segment polished into it measured by two-point probe ("2PP"). The short ingots were grown prior to the sample rods. The resistivity of the short ingots was measured at the opposite end (~250 mm) of the short ingots. The data points for the sample rods are the average of axial resistivity measurements taken every 10 mm from the seed end to the opposite end. The product ingots were grown with the resistivity of the seed end (~150 mm body position) shown in Table 1. The sample rods, short ingots, and product ingots were grown in eight runs according to the conditions in Example 2. TIFF0007638871000002.tif78138 Table 1: Resistivity measurement results of sample rod, short ingot, and product ingot

[0064] As shown in Table 1, the resistivity of the short ingot and the center slab of the sample rod (4PP) are relatively similar, and both results indicate that the dopant addition was directional. The sample rod with planar segments (2PP) contains some results with the opposite directionality to the short body, where the wrong dopants (i.e., P-type and N-type) may be added. This indicates that the sample rod center slab with four-point probe resistivity measurement predicts the resistivity of the product ingot with better accuracy.

[0065] Example 8: Comparison of two-point probe resistivity measurements and four-point probe resistivity measurements of the central slab The resistivity of several central slabs cut from the sample rods was measured with two-point and four-point probes. The resistivity of a short ingot (4PP) was also measured. As shown in Figure 11, the two-point and four-point measurements track relatively well, with the average axial resistivity being similar to that of the short ingot. This indicates that the axial variation in measurements between the short sample rods with planar segments and the central slabs is due to the physical volume of the samples and the variation in thickness used.

[0066] Example 9: Slab irradiation to enhance resistivity relaxation A sample rod was grown and a central slab was cut from the sample rod. The central slab was subjected to thermal donor annihilation annealing at 720° C. for 2 min. The central slab was then wrapped in a carrier with a weight pressure of 10 kg.

[0067] The annealed and lapped slabs were irradiated with an infrared (IR) lamp. The IR lamp heated the sample fat-neck slab to approximately 50 °C over a period of 10 min. Irradiation and light flux measurements were taken using temperature measurements, but it is currently believed that heating is not the dominant relaxation mechanism. Irradiation involves heating, but photodissociation is currently believed to be the dominant mechanism. Varying the distance between the lamp and the sample changed both the temperature of the slab and the light flux on the sample, which changed the rate of photodissociation. Since both mechanisms are due to the radiation exposure, it may not be possible to separate their respective effects on resistance relaxation. However, it is currently believed that photodissociation may proceed at any temperature.

[0068] The sample was allowed to cool to room temperature for approximately 2 minutes and the resistivity was measured by a four-point probe at room temperature. Using the IR lamp setup, it was found that approximately 10 minutes of irradiation was required for the fat neck to come to equilibrium temperature. Figure 13 is a graph showing the temperature profile of the fat neck central slab during irradiation. Time zero is when the IR lamp was turned on. The temperature increase is monitored to reach the desired end point of approximately 50°C, but this temperature monitor is to approximate sufficient photon flux to result in sufficient photodissociation. The fat neck central slab was held at 50°C for more than 10 minutes to achieve the desired relaxation transient in resistivity within 2 hours. The sample can be held at the soak temperature for longer, but 10 minutes is the minimum required time.

[0069] Example 10: Slab irradiation to enhance resistivity relaxation Sample rods were grown with a target resistivity of 1500 Ω·cm, and central slabs were cut from the sample rods. The two central slabs were subjected to thermal donor annihilation annealing at 720 °C for 2 min. The central slabs were then placed in a carrier and lapped under a pressure of 10 kg.

[0070] One central slab was allowed to relax for 32 hours to stabilize the resistivity. The second central slab was irradiated with infrared radiation for 60 minutes to a temperature of at least 50°C. Figure 14A shows the relaxation of the resistivity of fat-neck central slabs ~1.5KΩcm with (new method) and without (POR test #1, #2) infrared radiation. The IR radiation annealing started 1 hour after the thermal donor annihilation annealing. As shown by the open circles, the unirradiated sample required approximately 32 hours of relaxation to reach near full saturation and stabilize in resistivity. The re-prepared white diamonds of the same sample have slightly different initial transient decays (likely due to RTA and / or lapping at the time), but the curves converge to similar resistivity values ​​after 12 hours. The black triangles are the decay curves observed with the new method of lapping followed by infrared radiation. The graph clearly shows that the low temperature annealing accelerates the relaxation, leading to full saturation of the resistivity 1 hour after annealing. Figure 14B shows the relative resistivity degradation vs. time for the fat-neck center slab with (new method) and without (POR test #2) IR irradiation on the 1.5K fat-neck slab. The results clearly show that a 1-hour low-temperature anneal is more than enough to relax the resistivity to nearly 100%. Meanwhile, in the POR process, waiting 12 hours after the RTA / Lap was enough to achieve about 95% of the final resistivity.

[0071] Example 11: Slab irradiation to enhance resistivity relaxation Additional sample rods with target resistivity of 5,000 Ω·cm and 20,000 Ω·cm were grown. A central slab was cut from each and subjected to a thermal donor annihilation anneal at 720 °C for 2 min. The central slabs were then placed in a carrier and wrapped under a 10 kg weight. One central slab from each sample rod was allowed to relax for 32 hours to stabilize the resistivity. A second central slab from each sample rod was irradiated with infrared radiation for 60 minutes to a temperature of at least 50 °C. Figure 15A shows a graph comparing the resistivity relaxation of fat-neck central slabs ~5K Ω·cm with (new method) and without (POR Test #1, #2) IR irradiation annealing was started 1 hour after the thermal donor annihilation annealing. Figure 15B shows the relative resistivity drop vs. time for 5K fat-neck slabs with (new method) and without (POR Test #2) IR irradiation. FIG. 16A is a graph comparing resistivity relaxation of fat neck center slabs ~20KΩcm with (new method) and without (POR test #1 and #2) IR irradiation. The IR irradiation anneal started 1 hour after the thermal donor annihilation anneal. FIG. 16B is a graph showing the relative resistivity decay vs. time for 20K fat neck slabs with (new method) and without (POR test #2) IR irradiation. The results clearly show that a 1 hour low temperature anneal is more than enough to relax the resistivity to near saturation, whereas the POR process allows for waiting 12 hours after RTA / wrap to achieve about 95% of the final resistivity.

[0072] As used herein, the terms "about," "substantially," "essentially," and "approximately" when used in connection with a range of dimensions, concentrations, temperatures, or other physical or chemical properties or characteristics are meant to cover variations that may exist at the upper and / or lower limits of the range of the property or characteristic, including variations due to, for example, rounding, measurement method, or other statistical variations.

[0073] When introducing elements of the disclosure or embodiments thereof, the articles "a," "an," "the," and "said" are intended to mean that there are one or more elements. The terms "comprising," "including," "containing," and "having" are intended to be inclusive and mean that there may be additional elements other than the listed elements. The use of specific orientation terms (e.g., "top," "bottom," "side," etc.) is for convenience of description and does not require a particular orientation of the described items.

[0074] Because various changes can be made in the structure and methods described above without departing from the scope of the disclosure, it is intended that all matter contained in the above description and shown in the accompanying drawings be interpreted in an illustrative and not a limiting sense.

Claims

1. 1. A method for controlling resistivity of a single crystal silicon ingot grown by the Czochralski process, comprising: contacting a silicon seed crystal with a silicon melt, the silicon melt being contained in a crucible and containing molten silicon; withdrawing a silicon seed crystal from the silicon melt to form a sample rod comprising single crystal silicon, the sample rod having a generally cylindrical body having a central axis, a periphery, and a relatively constant diameter; Slicing a slab from the sample rod, the slab including a longitudinal plane that encircles at least a portion of a central axis of the sample rod and has a thickness; annealing the slab to annihilate the thermal donors; lapping the slab; irradiating the slab with infrared light; measuring the resistivity of the slab after the temperature of the slab has decreased to below 30°C.

2. 2. The method of claim 1, wherein the central axis of the sample rod is between 100 mm and 500 mm in length, such as between 150 mm and 300 mm in length.

3. 2. The method of claim 1, wherein the diameter of the sample rod is less than 150 mm, less than 100 mm, less than 50 mm, less than 25 mm, or less than 20 mm (e.g., 5 mm to 150 mm, 5 mm to 100 mm, 5 mm to 50 mm, 5 mm to 25 mm, or 10 mm to 25 mm).

4. 10. The method of claim 1, wherein the slab has a thickness between 1 millimeter and 3 millimeters.

5. 10. The method of claim 1, further comprising growing a single crystal silicon ingot from the silicon melt.

6. 6. The method of claim 5, wherein the single crystal silicon ingot has a resistivity of at least 500 Ω-cm, at least 1,000 Ω-cm, at least 1,500 Ω-cm, at least 2,000 Ω-cm, at least 4,000 Ω-cm, at least 6,000 Ω-cm, at least 8,000 Ω-cm, or at least 10,000 Ω-cm, or from 500 Ω-cm to 50,000 Ω-cm, from 1,000 Ω-cm to 50,000 Ω-cm, from 1,500 Ω-cm to 50,000 Ω-cm, or from 8,000 Ω-cm to 50,000 Ω-cm.

7. Furthermore, after the slab temperature was reduced to less than 30° C., the resistivity of the slab was measured, adding a dopant to the silicon melt; and growing a single crystal silicon ingot from the silicon melt, the single crystal silicon ingot having a resistivity different from that of the sample rod.

8. 8. The method of claim 7, wherein the resistivity of the single crystal silicon ingot is at least 500 Ω cm, at least 1,000 Ω cm, at least 1,500 Ω cm, at least 2,000 Ω cm, at least 4,000 Ω cm, at least 6,000 Ω cm, at least 8,000 Ω cm, or at least 10,000 Ω cm, or from 500 Ω cm to 50,000 Ω cm, from 1,000 Ω cm to 50,000 Ω cm, from 1,500 Ω cm to 50,000 Ω cm, or from 8,000 Ω cm to 50,000 Ω cm.

9. 8. The method of claim 7, wherein the single crystal silicon ingot is a p-type single crystal silicon ingot, and the added dopant is selected from the group consisting of phosphorus, arsenic, and antimony, and the dopant is added to increase the resistivity of the p-type single crystal silicon ingot.

10. 10. The method of claim 9, wherein the resistivity of the single crystal silicon ingot is at least 500 Ω cm, at least 1,000 Ω cm, at least 1,500 Ω cm, at least 2,000 Ω cm, at least 4,000 Ω cm, at least 6,000 Ω cm, at least 8,000 Ω cm, or at least 10,000 Ω cm, or from 500 Ω cm to 50,000 Ω cm, from 1,000 Ω cm to 50,000 Ω cm, from 1,500 Ω cm to 50,000 Ω cm, or from 8,000 Ω cm to 50,000 Ω cm.

11. 8. The method of claim 7, wherein the single crystal silicon ingot is a p-type single crystal silicon ingot, and the added dopant is selected from the group consisting of boron, gallium, and aluminum, and the dopant is added to reduce the resistivity of the p-type single crystal silicon ingot.

12. 12. The method of claim 11, wherein the resistivity of the single crystal silicon ingot is at least 500 Ω-cm, at least 1,000 Ω-cm, at least 1,500 Ω-cm, at least 2,000 Ω-cm, at least 4,000 Ω-cm, at least 6,000 Ω-cm, at least 8,000 Ω-cm, or at least 10,000 Ω-cm, or in the range of 500 Ω-cm to 50,000 Ω-cm, 1,000 Ω-cm to 50,000 Ω-cm, 1,500 Ω-cm to 50,000 Ω-cm, or 8,000 Ω-cm to 50,000 Ω-cm.

13. 8. The method of claim 7, wherein the single crystal silicon ingot is an n-type single crystal silicon ingot, and the added dopant is selected from the group consisting of boron, gallium, and aluminum, and the dopant is added to increase the resistivity of the n-type single crystal silicon ingot.

14. 14. The method of claim 13, wherein the resistivity of the single crystal silicon ingot is at least 500 Ω cm, at least 1,000 Ω cm, at least 1,500 Ω cm, at least 2,000 Ω cm, at least 4,000 Ω cm, at least 6,000 Ω cm, at least 8,000 Ω cm, or at least 10,000 Ω cm, or in the range of 500 Ω cm to 50,000 Ω cm, 1,000 Ω cm to 50,000 Ω cm, 1,500 Ω cm to 50,000 Ω cm, or 8,000 Ω cm to 50,000 Ω cm.

15. 8. The method of claim 7, wherein the single crystal silicon ingot is an n-type single crystal silicon ingot, and the added dopant is selected from the group consisting of phosphorus, arsenic, and antimony, and the dopant is added to reduce the resistivity of the n-type single crystal silicon ingot.

16. 16. The method of claim 15, wherein the resistivity of the single crystal silicon ingot is at least 500 Ω cm, at least 1,000 Ω cm, at least 1,500 Ω cm, at least 2,000 Ω cm, at least 4,000 Ω cm, at least 6,000 Ω cm, at least 8,000 Ω cm, or at least 10,000 Ω cm, or from 500 Ω cm to 50,000 Ω cm, from 1,000 Ω cm to 50,000 Ω cm, from 1,500 Ω cm to 50,000 Ω cm, or from 8,000 Ω cm to 50,000 Ω cm.

17. A method according to any one of claims 1 to 16, wherein the step of quenching the thermal donors comprises annealing the slab at a temperature of 600°C or higher for up to 60 minutes, or for 30 minutes.

18. A method according to any one of claims 1 to 16, wherein the step of quenching the thermal donors comprises annealing the slab at a temperature of 720°C for 2 minutes.

19. A method according to any one of claims 1 to 18, wherein the step of irradiating the slab with infrared light comprises irradiating the slab with light having a wavelength between 0.75 micrometers and 1000 micrometers.

20. A method according to any one of claims 1 to 18, wherein the step of irradiating the slab with infrared light comprises irradiating the slab with light having a wavelength between 400 nanometers and 4.5 micrometers.

21. A method according to any one of claims 1 to 18, wherein the step of irradiating the slab with infrared light comprises irradiating the slab with light of sufficient intensity to raise the temperature of the slab to a temperature of at least 50°C.

22. A method according to any one of claims 1 to 18, comprising the step of irradiating the slab with infrared light, wherein the slab is irradiated at a temperature of at least 50°C for at least 10 minutes.

23. A method according to any one of claims 1 to 18, comprising the step of irradiating the slab with infrared light, the slab being irradiated at a temperature of at least 50°C for a period of from 10 minutes to 2 hours.

24. A method according to any one of claims 1 to 18, comprising the step of irradiating the slab with infrared light, the slab being irradiated at a temperature of at least 50°C for a period of 10 minutes to 1 hour.

25. A method according to any one of claims 1 to 24, wherein the step of measuring the resistivity of the slab comprises measuring the resistivity of the slab at a plurality of points along the central axis.

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