Patent Publication Number: US-8968468-B2

Title: Method of controlling single crystal diameter

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a method of controlling the diameter of a single crystal when the single crystal is pulled and grown from a raw material melt by the Czochralski method (hereinafter, referred to as the “CZ method”), and particularly to a method of controlling the diameter of a single crystal that enables the precise measurement of diameter of a growing single crystal. 
     2. Description of the Related Art 
     A single crystal silicon is a material for a silicon wafer used for a semiconductor device, and the CZ method excellent in mass production is widely adopted for the production of the single crystal silicon. During the growing of a single crystal by the CZ method, a seed crystal is dipped into a raw material melt of silicon retained in a crucible within a chamber maintained in an inert atmosphere under reduced pressure, and the dipped seed crystal is gradually pulled, thereby growing a single crystal silicon below the seed crystal. 
     When the single crystal is grown, the diameter of the single crystal is sequentially measured, and the diameter control that adjusts the pulling rate of the single crystal and the temperature of the raw material melt is performed so that the single crystal diameter becomes an aimed diameter. Conventionally, the approaches that measure the diameter of a single crystal include an optical system using an optical sensor such as a one-dimensional camera and two-dimensional camera and a weight system using a weight sensor such as a load cell. 
     In the optical system, the boundary (meniscus) between the single crystal and the raw material melt is imaged by the optical sensor, and the diameter of the single crystal is derived from the brightness distribution of the image data. This approach detects a ring-like portion (hereinafter, also referred to as a “fusion ring”) that appears along the boundary between the single crystal and the raw material melt and has the brightness higher than the surrounding thereof, and converts the ring-like portion into the diameter of the single crystal. 
     When a one-dimensional camera is used as an optical sensor, positions scanned in parallel to a line traversing the center of the fusion ring, i.e., the center of the single crystal, are imaged, and the diameter of the single crystal is determined from the distance between pixels where the peak of brightness appears. When a two-dimensional camera is used as an optical sensor, a half of the fusion ring is imaged, a circular arc formed by connecting pixels where the peak of brightness appears is calculated, and the center of the fusion ring is calculated from this circular arc so as to determine the diameter of the single crystal. 
     On the other hand, in the weight system, the weight of a single crystal is measured by a weight sensor, and the diameter of the single crystal is derived from the weight difference between the weight data and the model weight. 
     In the growing of a single crystal in which the diameter control by the optical system is adopted, a wire is typically used as a pulling shaft that holds a seed crystal and pulls the single crystal. While in growing a single crystal in which the diameter control by the weight system is adopted, a rod called a force bar is typically used as the pulling shaft. 
     In the diameter control of a single crystal, it is important to accurately measure the diameter of the growing single crystal. The reasons for this are as follows. If a measured diameter of a single crystal is misjudged to be larger than the actual diameter, the product quality is adversely influenced because the actual single crystal diameter is small, and further defective products are generated because the diameter of the single crystal does not reach the diameter of the product, which might incur an enormous loss. On the other hand, if the measured diameter of a single crystal is misjudged to be smaller than the actual diameter, the total length of the single crystal is shortened because the actual diameter of the single crystal is large, which might decrease the yield of the product. 
     However, in case of the diameter measurement by the optical system described above, since the fusion ring at the growth interface is measured and thus the response to an instantaneous diameter change is excellent, the spread of a microscopic diameter fluctuation at the measured site can be accurately detected. However, the distance from the optical sensor to the fusion ring to be measured may fluctuate due to the effects such as the strain of the wire (pulling shaft) in association with progression of the single crystal growth, and issues related to materials (quartz crucible, graphite crucible, and polysilicon) like dimensional accuracy, degradation and weight change. Therefore, in the diameter measurement by the optical system, it is difficult to detect the error of the diameter fluctuation occurring in the direction of the crystal growth, resulting in the lack of reliability in accuracy of the measured diameter of the single crystal. 
     On the other hand, in case of the diameter measurement by the weight system as described above, since the weight of a grown single crystal itself is measured, the change in the diameter fluctuation in the crystal growth direction in association with progression of single crystal growth is accurately detected. However, since it requires a processing for excluding the influence on the diameter fluctuation which is attributable to the buoyancy acting on the growing single crystal, its responsiveness is poor. Hence, it is difficult to detect the spread of the microscopic diameter fluctuation, resulting in the lack of reliability in accuracy of the measured diameter of the single crystal. 
     Accordingly, in the diameter control of a single crystal, an approach is desired that can accurately measure the diameter of a growing single crystal. 
     For example, Japanese Patent Application Publication No. 2003-176199 discloses a method of controlling the diameter of a single crystal in which, at the stage of growing a single crystal up until a cylindrical body portion, the diameter control is performed by the diameter measurement by the optical system, and at the stage of forming a tail portion subsequent to the body portion, in which the diameter of the single crystal is successively decreased, the diameter control is switched and performed by the diameter measurement by the weight system. In the method disclosed in this document, since the fusion ring is hidden by the body portion and cannot be sufficiently imaged at the stage of forming the tail portion, the weight system is adopted instead of the optical system so as to perform the diameter control of the single crystal. 
     However, also in the method of controlling the diameter of a single crystal disclosed in Japanese Patent Application Publication No. 2003-176199, the fact remains that the diameter measurement is carried out by either the optical system or the weight system at individual growth stages respectively, and therefore the diameter of a growing single crystal cannot be accurately measured. 
     SUMMARY OF THE INVENTION 
     The present invention has been made considering the above problems, and its object is to provide a method of controlling the diameter of a single crystal that can accurately measure the diameter of a growing single crystal when performing the diameter control during the growth of the single crystal. 
     The present inventor has rigorously studied for attaining the above objective and found that, for accurately measuring the diameter of a single crystal when performing the diameter control during the growth of the single crystal, it is effective to perform simultaneously the diameter measurement by the optical system and the diameter measurement by the weight system, and calculate a diameter value of the single crystal on the basis of measured values of the single crystal diameter derived from the respective diameter measurements. 
     The present invention has been completed on the basis of the above finding and its subject matter lies in the method of controlling the diameter of a single crystal as described below. That is, a method of controlling the diameter of a single crystal includes the steps of: when pulling and growing the single crystal from a raw material melt by the Czochralski method; imaging the boundary between the single crystal and the raw material melt by an optical sensor, and also measuring the weight of the single crystal by a weight sensor; calculating a diameter value of the single crystal on the basis of a first measured values of the diameter of the single crystal derived from image data captured by the optical sensor and a second measured values of the diameter of the single crystal derived from weight data captured by the weight sensor; and adjusting a pulling rate of the single crystal and the temperature of the raw material melt, wherever needed, on the basis of the calculated diameter value to thereby control the diameter of the single crystal. 
     In this method of controlling the diameter, it is preferable that a first and second measured values are sequentially accumulated, and the coefficient of a formula used for calculation of the diameter value is updated on the basis of average values of the accumulated first and second measured values within a predetermined period. 
     According to the method of controlling a single crystal diameter of the present invention, since the diameter measurement by the optical system and the diameter measurement by the weight system are simultaneously performed, and the diameter value of the single crystal is calculated on the basis of the first and second measured values of the diameter of the single crystal derived from the respective diameter measurements, the diameter of the growing single crystal can be accurately calculated and the diameter can be appropriately controlled as compared with the diameter value evaluated only by the diameter measurement by the optical system or only by the diameter measurement by the weight system. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  schematically shows the structure of a single crystal growth apparatus to which a method of controlling a single crystal diameter of the present invention can be applied. 
         FIG. 2  is a block diagram showing the configuration of a controller used in a method of controlling a single crystal diameter of the present invention. 
         FIGS. 3A to 3D  depict the test results of Inventive Example 1. 
         FIGS. 4A and 4B  depict the test results of Inventive Example 2. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Hereinafter, an embodiment will be described in detail about the method of controlling the single crystal diameter of the present invention. 
       FIG. 1  schematically shows the structure of a single crystal growth apparatus to which the method of controlling the single crystal diameter of the present invention can be applied. As shown in the drawing, the single crystal growth apparatus includes a chamber  1  as an exterior and a crucible  2  disposed at the central region of the chamber  1 . The crucible  2  has a double structure made up of an inner quartz crucible  2   a  and outer graphite crucible  2   b . This crucible  2  is fixed to the top end of a support shaft  3 , and rotated in a circumferential direction and axially raised or lowered by the rotation drive and raising or lowering drive of the support shaft  3 . 
     A resistance-heating heater  4  that surrounds the crucible  2  is disposed outside the crucible  2 , and outside the heater  4 , a heat insulator  5  is disposed along the inner surface of the chamber  1 . The heater  4  melts solid raw materials such as polysilicon loaded in the crucible  2 , thereby forming a raw material melt  6  in the crucible  2 . 
     The pulling shaft  7  such as a wire is provided above the crucible  2  along the same axis as the support shaft  3 . The pulling shaft  7  is rotated while being raised or lowered by a pulling mechanism  10  provided on the upper end of the chamber  1 . A seed crystal  8  is attached to the tip of the pulling shaft  7 . The seed crystal  8  is dipped in the raw material melt  6  in the crucible  2  along with the drive of the pulling shaft  7 , familiarized with the raw material melt  6 , and then gradually raised while being rotated to thereby grow a single crystal silicon  9  below the seed crystal  8 . 
     An optical sensor  11  and weight sensor  12  are provided in this single crystal growth apparatus to measure the diameter of the growing single crystal  9 . The optical sensor  11  is disposed outside the chamber  1  and images a fusion ring of boundary between the single crystal  9  and raw material melt  6  through an observation window  1   a  provided for the chamber  1 . A one-dimensional camera or two-dimensional camera can be used as the optical sensor  11 . The weight sensor  12  is disposed in the pulling mechanism  10  and weighs the growing single crystal  9 . A load cell can be used as the weight sensor  12 . 
     The optical sensor  11  and weight sensor  12  are wired/liaised to a controller  20 . The controller  20  simultaneously receives image data sequentially output from the optical sensor  11  as well as weight data sequentially output from the weight sensor  12  and performs the calculation as described below on the basis of both these image data and weight data to determine the diameter value of the growing single crystal  9 . In addition, the controller  20  adjusts the pulling rate of the single crystal and the temperature of the raw material melt, wherever needed, on the basis of the calculated diameter value so as to carry out the diameter control of the single crystal. 
       FIG. 2  is a block diagram showing the configuration of a controller used in the method of controlling the single crystal diameter of the present invention. As shown in the drawing, the controller  20  includes a first measured value processing section  21 , a second measured value processing section  22 , a diameter value determining section  23 , an output conversion section  24 , and a memory section  25 . 
     The first measured value processing section  21  is pursuant to the diameter measurement by the optical system and derives first measured values of the diameter of the single crystal on the basis of the image data received from the optical sensor  11 . The second measured value processing section  22  is pursuant to the diameter measurement by the weight system and derives the second measured values of the diameter of the single crystal on the basis of the weight data received from the weight sensor  12 . The diameter value determining section  23  calculates a diameter value of the single crystal on the basis of the first measured values derived in the first measured value processing section  21  and the second measured values derived in the second measured value processing section  22 . 
     The output conversion section  24  compares the diameter value calculated in the diameter value determining section  23  with a target diameter of the single crystal to be grown, converts it to an output value of the pulling mechanism  10  corresponding to the pulling rate and an output value of the heater  4  corresponding to the temperature of the raw material melt, and liaises the signals of these output values to the pulling mechanism  10  and heater  4  to thereby narrow the difference between the diameter value and the target diameter. As a result, the pulling rate of the single crystal and the temperature of the material melt are adjusted, if necessary, and the diameter control of the single crystal is performed. 
     In a memory section  25 , there are stored data related to calculation formulae used in the first measured value processing section  21 , second measured value processing section  22 , diameter value determining section  23 , and output conversion section  24 . Moreover, the memory section  25  sequentially in time series accumulates the first measured values derived in the first measured value processing section  21  and the second measured values derived in the second measured value processing section  22 . The accumulated first and second measured values can be utilized in calibration of the calculation formula used to determine the diameter value in the diameter value determining section  23 . 
     As described above, in the present invention, the diameter measurement by the optical system and the diameter measurement by the weight system are simultaneously performed to determine the diameter value of a single crystal on the basis of the first and second measured value of the single crystal diameter derived from each of the diameter measurements, and therefore the diameter of the growing single crystal can be accurately measured and the diameter can be appropriately controlled as compared with the diameter value determined by a mere single diameter measurement means either by the optical system or by the weight system, whereby it becomes possible to perform appropriate diameter control. 
     A specific example of calculation executed in the above controller  20  will be shown below. In this example, a one-dimensional camera is used as the optical sensor  11 . 
     The diameter value processing section  23  calculates the diameter value using the calculation formula (1) below.
 
 D=N×A×B   (1)
 
     wherein, D represents the diameter value [mm], N represents the number of pixels included in between brightness peaks in image data captured by the one-dimensional camera [number of pixels], A represents the weighted coefficient [dimensionless], and B represents the diameter conversion coefficient [mm/number of pixels] reflecting operating performance. 
     Here, the weighted coefficient A is a coefficient evaluated from the first measured value derived in the first measured value processing section  21  and the second measured value derived in the second measured value processing section  22  and updated for every execution of determination in the diameter value determining section  23  or at a predetermined frequency. The weighted coefficient A is defined, for example, by formula (2) below.
 
 A=A′×{ 1−( D 1− D 2)/ D 2}  (2)
 
     wherein, A represents the weighted coefficient after updated, A′ represents the weighted coefficient before updated, D 1  represents the average value, within a predetermined period, of the accumulated first measured values pursuant to the diameter measurement by the optical system, and D 2  represents the average value, within a predetermined period, of the accumulated second measured values pursuant to the diameter measurement by the weight system. The average value D 1  of the first measured values by the optical system is evaluated by the moving average, and the average value D 2  of the second measured values by the weight system is evaluated by the moving average or the average by the least squares method. In case of the least squares method, since the calculated average value may change suddenly, it is effective to incorporate correction pertinent to the sudden change. 
     The average value D 1  of the first measured values by the optical system can be evaluated by the moving average of formula (3) below.
 
 D 1=( D 1 m-o   +D 1 m-o+1   + . . . +D 1 m-1   +D 1 m )/( o+ 1)  (3)
 
     wherein m represents a measurement number, whereas o represents the prescribed number of measurements of first measured values for moving average relative to each measurement number. 
     In case of the moving average, the average value D 2  of the second measured values by the weight system can be defined by formula (4) below.
 
 D 2= D 2 m-o   +D 2 m-o+1   + . . . +D 2 m-1   +D 2 m )/( o+ 1)  (4)
 
     wherein m represents an intended measurement number, whereas o represents the prescribed number of second measured value D 2   i  for moving average relative to each measurement number. 
     In addition, D 2   i  is an average diameter converted from the measured values of the weight of the single crystal by the load cell in a specified interval and evaluated from formula (5) below (2.33: specific gravity of the single crystal silicon).
 
 D 2 i =2√{square root over ( )}(( W   i+1   −W   i )/(π×( X   i+1   −X   i )×2.33))  (5)
 
     wherein, X i  is an arbitrary position, in the pulling direction, of a cylindrical body portion of the single crystal, W i  is the weight of the single crystal at X i  (actual measured value by the load cell), X i+1  is a position which is a specified interval/distance away from X i , and W i+1  is the weight of the single crystal at X i+1  (actual measured value by the load cell). 
     Next, in case of the least squares method, the average value D 2  of the second measured values by the weight system can be defined by formula (6) below (2.33: specific gravity of the single crystal silicon).
 
 D 2=2√{square root over ( )}( W/ 2.33 πL )  (6)
 
     wherein, W is the weight of the single crystal for corresponding L which is the length of the specified interval for the cylindrical body portion of the single crystal, and is expressed by W=aL+b. 
     If W=aX+b is a linear function which is the best approximation to n data (X i , W i ): (X 1 , W 1 ), (X 2 , W 2 ), . . . , (X n , W n ) wherein X i  is an arbitrary position, in the pulling direction, of the cylindrical body portion of the single crystal, and W i  is the weight of the single crystal at X i  (actual measured value by the load cell), a and b are coefficients evaluated by formulae (7) and (8) below. 
     
       
         
           
             
               
                 
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     The number of pixels N in formula (1) above is evaluated as similarly as a conventional diameter measurement using a one-dimensional camera. That is, positions scanned in parallel to a line traversing the center of the fusion ring, i.e., the center of the single crystal, are imaged by a one-dimensional camera, the captured image data is analyzed to evaluate a brightness distribution, and the number of pixels included in between the brightness peaks is counted from the brightness distribution so as to evaluate the number of pixels N. 
     Moreover, the diameter conversion coefficient B in formula (1) above is a constant that can be set from the operating performance and can be a different value depending on production conditions and equipment configuration. The diameter conversion coefficient B can be set, for example, as follows: an image of a single crystal is captured, and the diameter of the single crystal actually measured by calipers or the like is divided by the number of camera pixels (the number of pixels between both right and left ends of the captured image of the single crystal) so as to evaluate a value from which the coefficient B is set. 
     During the growth of the single crystal, the weighted coefficient A of formula (1) above is updated using formula (2) above and formula (1) above is calibrated to thereby more accurately measure the diameter value D of the single crystal over the total length of the single crystal. This is because when a wire is used as the pulling shaft, although an error in the diameter value D to be calculated might occur due to the strain of and the degradation of the wire in association with the progression of the single crystal growth, the occurrence of the error is suppressed by the calibration of the calculation formula (formula (1) above) used in the diameter value determining section  23 . 
     However, in case of formula (2) above, if an updating time period for the weighted coefficient A is too short, an error may rather be occurred particularly in the average value D 2  of the second measured values by the weight system, as far as it concerns the average value D 1  of first measured values by the optical system and the average value D 2  of second measured values. Therefore, the updating time period should be appropriately set depending on the constitution of equipment to be used so as not to cause the error in the average value D 2 . 
     Additionally, if the period of time adopted to evaluate the average values D 1  and D 2  which are evaluated by the moving average in formula (2) above is too short, the scatter is likely to be generated in the average values D 1  and D 2 . Hence, the period of time adopted to evaluate the average values D 1  and D 2  should also be appropriately set so as not to generate the scatter in the average values D 1  and D 2 . 
     EXAMPLES 
     Example 1 
     A test was performed in which a single crystal ingot capable of assuring a diameter of 12 inches after processing its outer periphery was grown. In the test, the diameter measurement by the optical system using a one-dimensional camera and the diameter measurement by the weight system using a load cell were carried out, and the behavior of the diameter value by the measurement by the optical system and the behavior of the diameter difference (correction amount) when the measured value of the diameter by the optical system is corrected with the measured value of the diameter by the weight system were examined along a crystal length-wise direction. In the test of Inventive Example 1, the average value of the measured values of the diameter in formula (2) above was evaluated by the moving average, and 60, 45, 30 and 15 min are adopted as a period of time for the moving average. 
       FIGS. 3A to 3D  depict the test results of Inventive Example 1. The average values of the measurement values of the diameter for 60, 45, 30, and 15 min of time period are shown in  FIGS. 3A ,  3 B,  3 C and  3 D respectively. As illustrated in  FIGS. 3A to 3D , in case of 15 min calculation time period, the scatter of correction amount is noticeable and it cannot be used for the correction. In case of 30, 45 or 60 min as calculation time period, the scatter of correction amount is small, and stable correction is respectively achieved. 
     Example 2 
     In Example 2, a test of growing a single crystal ingot as well as an examination was carried out as similarly as in Example 1 above. In the test of Inventive Example 2, the average value of the measured values of the diameter was evaluated by the least squares method, and 60 and 15 min are adopted as a period of time for evaluating the average value. 
       FIGS. 4A and 4B  depict the test results of Example 2. The average values of the measurement values of the diameter for 60 and 15 min of time period are shown in  FIGS. 4A and 4B , respectively. As shown in  FIGS. 4A and 4B , in both cases of 15 and 60 min calculation time period, the scatter of correction amount is small, and therefore stable correction is possible. 
     According to the method of controlling a single crystal diameter of the present invention, since a diameter value of a single crystal is calculated on the basis of a first measured values of the single crystal diameter derived from the diameter measurement by the optical system and a second measured values of the single crystal diameter derived from the diameter measurement by the weight system, it is possible to accurately measure the diameter of a growing single crystal and therefore appropriately control the diameter as compared with a diameter value evaluated only by a mere single means for diameter measurement, either by an optical system or by a weight system.