Patent Publication Number: US-2017368661-A1

Title: Polishing apparatus, polishing method and polishing control program

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is based upon and claims the benefit of priority of the prior Japanese Patent Application No. 2016-127611, filed on Jun. 28, 2016, the entire content of which is incorporated herein by reference. 
     BACKGROUND OF THE INVENTION 
     Field of the Invention 
     The present invention relates to a polishing apparatus for polishing the surface of a polishing target, and particularly to a polishing apparatus for estimating data corresponding to a film thickness and a polishing method for performing polishing by using the apparatus. Furthermore, the present invention relates to a polishing control program for controlling a polishing apparatus. 
     Description of the Related Art 
     Recently, in connection with higher integration and higher density of semiconductor devices, wiring of circuits has been increasingly finer, and the distance between wires has been reduced. Therefore, it has been required to flatten the surfaces of semiconductor wafer as polishing targets, and polishing has been performed by a chemical mechanical polishing (CMP) device as one means of the flattening method. 
     A polishing apparatus includes a polishing table on which a polishing pad for polishing a polishing target is held, and a top ring for pressing the polishing target against the polishing pad while holding the polishing target. Each of the polishing table and the top ring is rotated by a driving unit (for example, a motor). Liquid (slurry) containing polishing agent is made to flow on the polishing pad, and the polishing target held by the top ring is pressed against the polishing pad, whereby the polishing target is polished. 
     When the polishing target is insufficiently polished by the polishing apparatus, there occurs a risk that insulation between circuits is not established and thus short-circuiting occurs. Furthermore, when the polishing target is over-polished, there occurs such a problem that the resistance value of a wire increases due to decrease of the cross-sectional area of the wire, or a wire itself is completely removed and thus a circuit itself is not formed. In addition, it is necessary to flatten the entire surface with high accuracy. Therefore, it is required in the polishing apparatus to detect a proper polishing endpoint and also detect a polishing amount over the entire surface with high accuracy. 
     An eddy current type endpoint detection sensor (hereinafter referred to as “eddy current sensor”) disclosed in Japanese Patent Laid-Open No. 2012-135865, etc. are known as techniques for satisfying the foregoing requirement. In the eddy current sensor described above, eddy current in a polishing target is detected by a solenoid type or spiral type coil. Variation of the film thickness of the polishing target increases or decreases eddy current. 
     As other methods of the polishing endpoint detection means are known a method of detecting variation of polishing frictional force when the film thickness of the polishing target varies and thus polishing shifts to a material having different quality of material, and also known a method of detecting variation of reflectivity of the surface of the polishing target. 
     Outputs of these sensors for measuring the film thickness of the polishing target during polishing are subjected to processing such as averaging processing of the output of the sensor, noise filter processing for noise removal and/or amplification processing. These processing is performed by a processing system based on an analog circuit or a digital circuit (software or the like). When these processing is complicated, a delay (time lag) occurs between the measurement time by a sensor and the processing end time. For these processing, data transmission/reception may be performed in a communication system within the polishing apparatus or between communication systems of the polishing apparatus and another polishing apparatus. A delay caused by a communication system for data transmission/reception may occur. As a result, the polishing apparatus cannot completely perform endpoint detection and grasp film thickness data used for various controls on a real-time basis. Since polishing is progressing even during execution of the processing by the processing system or the communication system which is based on an analog circuit or a digital circuit, an error occurs between the film thickness grasped at the end time of the processing by the processing system or the communication system and the actual film thickness at the end time of the processing. 
     As miniaturization of semiconductor devices progresses, the required polishing amount decreases and the polishing time is also shortened, whereas a requirement for enhancing the measurement accuracy of the film thickness is more and more increased. Therefore, the influence of a time delay on the film thickness grasped by the processing system or the communication system increases in connection with a processing delay of the processing system or the communication system. 
     The present invention has been implemented to solve the foregoing problem, and has an object to provide a polishing apparatus, a polishing method and a polishing control program that can correct a measurement error caused by a delay time of a processing system or the like, and estimate data corresponding to a film thickness at a processing end time of a processing system. 
     SUMMARY OF THE INVENTION 
     In order to attain the above object, a first aspect adopts a configuration of a polishing apparatus for polishing a polishing target, comprising: a polishing unit for polishing the polishing target; a measuring unit for measuring a physical quantity variable according to variation of a film thickness of the polishing target at a plurality of measurement times; a film thickness calculator for calculating data corresponding to the film thicknesses of the polishing target at the measurement times based on the physical quantity measured by the measuring unit; and a film thickness estimating unit for estimating the data with respect to at least some measurement times of the plurality of measurement times after lapse of a processing delay time from the at least some measurement times by using the calculated data. 
     According to this aspect, it is possible to correct a time lag between a measurement time at which the measuring unit performs a measurement and a processing end time at which the processing of a communication system, a processing system or the like has been finished, the time lag being caused by a processing time of the communication system, the processing system or the like after the measurement of the physical quantity, that is, it is possible to correct a measurement error caused by “processing delay time”. By the correction, the data corresponding to the film thickness at the processing end time can be more accurately estimated, so that the accuracy of the endpoint detection of polishing can be enhanced. That is, the delay of the processing system can be compensated, and the delay of the endpoint detection can be prevented. 
     Here, “the data corresponding to the film thickness” contain (1) film thickness, (2) data obtained by multiplying the film thickness by a predetermined number, (3) data obtained by adding or subtracting a predetermined number to or from the film thickness, (4) data obtained by combining (2) and (3) or the like. Variation of the film thickness can be monitored from the data of (1) to (4), and the endpoint detection of polishing or monitoring of a polishing state can be performed. The predetermined number in (2) to (4) may be set to a fixed numerical value during measurements, but it may be changed during measurements in consideration of time variation of the state of the polishing unit (for example, a polishing pad) or the like. 
     Furthermore, according to the aspect, since the data corresponding to the film thickness can be more accurately estimated as compared with the prior art, the performance of close-loop control (Close-loop control: CLC) is enhanced. The close-loop control is a system in which data of a polishing result (the data corresponding to the film thickness) is fed back to the control device of the polishing apparatus, the control device determines the polishing state and the polishing unit is controlled according to an instruction from the control device. 
     In an in-situ film thickness measurement during chemical mechanical polishing, the physical quantity variable according to the variation of the film thickness of a polishing target during polishing contains eddy current, optical reflectivity of the surface of a film, etc. The eddy current is dependent on the electrical conductivity and film thickness of a film. After these physical quantities are measured by a sensor (measuring unit), processing such as time-averaging processing, correction processing, etc. are performed on measurement values for the purpose of noise removal, signal amplification, etc., so that a time delay occurs. The data corresponding to the film thickness which the control system of the polishing apparatus uses for endpoint detection and control under various polishing states are data which are older by an amount dependent on a time required for the processing, etc. 
     The delay time ranges from about 0.2 to 1 second, for example. The delay time can be actually measured and incorporated as a processing delay time in the system. The delay caused by the communication system or the processing system may be assumed as a fixed value (fixed time). Furthermore, the delay may be changed according to the progress of polishing or according to a polishing condition. 
     Spline interpolation or the like may be used for the calculation of the data corresponding to a film thickness when a processing delay time elapses. The spline interpolation is an interpolation using a smooth curve (spline curve) passing through plural measurement data. On a spline interpolation curve, an individual polynomial, for example, a cubic polynomial is used for each section sandwiched between adjacent measurement data. 
     A second aspect adopts a configuration of a polishing apparatus in which the film thickness estimating unit estimates a variation amount of the data with respect to the at least some measurement times of the plurality of measurement times after lapse of the processing delay time from the at least some measurement times by using the calculated data, and estimates the data after lapse of the processing delay time from the at least some measurement times by using the estimated variation amount. 
     A third aspect adopts a configuration of a polishing apparatus in which the film thickness estimating unit calculates a polishing rate by using the calculated data, and estimates the variation amount by using the calculated polishing rate. The polishing rate is defined as a polishing amount (a variation amount of the data corresponding to the film thickness) per unit time (for example, per second). 
     In this aspect, the delay of the processing system can be compensated by using the polishing rate based on the time-sequence data of the data corresponding to the film thickness, whereby the delay of the endpoint detection can be prevented. 
     A fourth aspect adopts a configuration of a polishing apparatus in which the wording (phrasing or expression) of after lapse of the processing delay time from the at least some measurement times indicates times at which after the measuring unit measures the physical quantity at the at least some measurement times, it is possible for the film thickness calculator to finish calculation of the data of the polishing target based on the physical quantity. 
     A fifth aspect adopts a configuration of a polishing apparatus in which the wording of after lapse of the processing delay time from the at least some measurement times indicates times at which after the measuring unit measures the physical quantity at the at least some measurement times, it is possible for the film thickness estimating unit to finish estimation of the data by using the calculated data. 
     A sixth aspect adopts a configuration of a polishing method for polishing a polishing target, comprising: a polishing step of polishing the polishing target; a measuring step of measuring a physical quantity variable according to variation of a film thickness of the polishing target at a plurality of measurement times; a film thickness calculating step of calculating data corresponding to the film thicknesses of the polishing target at the measurement times based on the physical quantity measured in the measuring step; and a film thickness estimating step of estimating the data with respect to at least some measurement times of the plurality of measurement times after lapse of a processing delay time from the at least some measurement times by using the calculated data. 
     A seventh aspect adopts a configuration of a polishing method in which the film thickness estimating step estimates a variation amount of the data with respect to the at least some measurement times of the plurality of measurement times after lapse of the processing delay time from the at least some measurement times by using the calculated data, and estimates the data after lapse of the processing delay time from the at least some measurement times by using the estimated variation amount. 
     An eighth aspect adopts a configuration of a polishing control program used to control a polishing apparatus for polishing a polishing target, the polishing apparatus having a measuring unit for measuring a physical quantity variable according to variation of a film thickness of the polishing target at a plurality of measurement times, the program causing a computer to function as a film thickness calculator for calculating data corresponding to the film thicknesses of the polishing target at the measurement times based on the physical quantity measured by the measuring unit, and a film thickness estimating unit for estimating the data with respect to at least some measurement times of the plurality of measurement times after lapse of a processing delay time from the at least some measurement times by using the calculated data. 
     A ninth aspect adopts a configuration of a polishing control program in which the film thickness estimating unit estimates a variation amount of the data with respect to the at least some measurement times of the plurality of measurement times after lapse of the processing delay time from the at least some measurement times by using the calculated data, and estimates the data after lapse of the processing delay time from the at least some measurement times by using the estimated variation amount. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a diagram showing the basic configuration of a polishing apparatus according to an embodiment; 
         FIGS. 2A and 2B  are diagrams showing the configuration of an eddy current sensor, wherein  FIG. 2A  is a block diagram showing the configuration of the eddy current sensor, and  FIG. 2B  is an equivalent circuit diagram of the eddy current sensor; 
         FIG. 3  is a schematic diagram showing an example of the configuration of a sensor coil in the eddy current sensor of the embodiment; 
         FIG. 4A  is a graph showing an actual film thickness of a semiconductor wafer  18 ,  FIG. 4B  is a graph showing a film thickness of the semiconductor wafer  18  which is output from a sensor processor  28 , and  FIG. 4C  is a graph showing an estimated film thickness of the semiconductor wafer  18  which is output from a film thickness estimating unit  32 ; and 
         FIG. 5  is a flowchart showing a case where polishing is performed until a predetermined film thickness, and the polishing is finished at the time when the film thickness reaches a predetermined film thickness. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     A polishing apparatus according to an embodiment of the present invention will be described hereunder with reference to the drawings. First, the basic configuration of a polishing apparatus will be described, and then detection of a polishing endpoint of a polishing target will be described. 
       FIG. 1  is a diagram showing the basic configuration of a polishing apparatus  100  according to an embodiment. The polishing apparatus  100  for polishing a semiconductor wafer (polishing target)  18  includes a polishing unit  30  for polishing the semiconductor wafer  18 , an eddy current sensor (measurement unit)  50 , and a sensor processor (film thickness calculator)  28 . The eddy current sensor  50  measures a physical quantity variable according to variation of the film thickness of the semiconductor wafer  18  at plural measurement times. The sensor processor  28  calculates data corresponding to the film thickness of the semiconductor wafer  18  at each measurement time based on the eddy current measured by the eddy current sensor  50 . 
     The measurement times in this embodiment are set to times having a time interval of 0.5 second. The physical quantity in this embodiment is an eddy current in the semiconductor wafer  18 . Variation of the film thickness of the semiconductor wafer  18  increases or decreases the eddy current. In the present invention, the physical quantity which is variable according to the variation of the film thickness is not limited to the eddy current. The physical quantity may be polishing frictional force under polishing or reflectivity of the surface of the polishing target. 
     The polishing apparatus  100  further has a controller  29 . The controller  29  contains a film thickness estimating unit  32 . By using the data corresponding to the film thickness calculated by the sensor processor  28 , the film thickness estimating unit  32  estimates data corresponding to a film thickness after lapse of a processing delay time from a measurement time for each measurement time. The data corresponding to the film thickness in this embodiment is a film thickness obtained from the magnitude (absolute value) of an impedance Z described later. 
     The film thickness estimating unit  32  estimates the variation amount of the film thickness after lapse of the processing delay time for each measurement time by using a calculated film thickness, and estimates the film thickness after lapse of the processing delay time from the measurement time by using the estimated variation amount. The present invention is not limited to the method of estimating the film-thickness variation amount and then estimating the film thickness by using the estimated variation amount. For example, the film thickness may be directly estimated without estimating any film-thickness variation amount. As the method of directly estimating the film thickness, the film thickness after lapse of a processing delay time from a measurement time may be estimated by spline interpolation using a calculated film thickness. 
     The film thickness estimating unit  32  calculates a polishing rate by using the calculated film thickness, and estimates the variation amount by using the calculated polishing rate. The details of a method of calculating the polishing rate will be described later. 
     “After lapse of a processing delay time from a measurement time” in this embodiment corresponds to a time at which after the eddy current sensor  50  measures an eddy current at the measurement time, the sensor processor  28  has finished the calculation of the film thickness of the semiconductor wafer  18  based on the eddy current. “After lapse of the processing delay time” corresponds to, for example, the time after 0.2 second elapses from the measurement of an eddy current by the eddy current sensor  50 . In the present invention, the time after lapse of the processing delay time is not limited to the time when the sensor processor  28  has finished the calculation of the film thickness of the semiconductor wafer  18  based on the eddy current. For example, the time after lapse of the processing delay time from the measurement time may be set to the time when after the eddy current sensor  50  measures the eddy current at the measurement time, it is possible for the film thickness estimating unit  32  to finish the estimation of the film thickness using the calculated film thickness. 
     The details of the polishing unit  30  will be described with reference to  FIG. 1 . The polishing unit  30  includes a polishing table  12  having an upper surface onto which a polishing pad  10  can be fitted, a first electric motor  14  for rotating the polishing table  12 , a top ring  20  capable of holding a semiconductor wafer  18 , and a second electric motor  22  for rotating the top ring  20 . The rotor of the first electric motor  14  is connected to a motor shaft  15 , and the polishing table  12  is rotated by the motor shaft  15 . 
     The top ring  20  is caused to approach to and get away from the polishing table  12  by a holding device (not shown). When the semiconductor wafer  18  is polished, the top ring  20  is approached to the polishing table  12  so that the semiconductor wafer  18  held on the top ring  20  is brought into contact with the polishing pad  10  fitted to the polishing table  12 . 
     When the semiconductor wafer  18  is polished, the semiconductor wafer  18  held on the top ring  20  is pressed against the polishing pad  10  while the polishing table  12  is rotated. Furthermore, the top ring  20  is rotated by the second electric motor  22  around an axial line  21  which is eccentrically displaced from the rotational axis  13  of the polishing table  12 . When the semiconductor wafer  18  is polished, polishing abrasive liquid containing polishing agent is supplied from a polishing agent supply device (not shown) onto the upper surface of the polishing pad  10 . The semiconductor wafer  18  set on the top ring  20  is pressed against the polishing pad  10  supplied with the polishing abrasive liquid while the top ring  20  is rotated by the second electric motor  22 . 
     The eddy current sensor  50  is embedded in the polishing table  12 . A connection cable of the eddy current sensor  50  passes inside the motor shaft  15  of the polishing table  12  via a rotary joint (not shown) provided to the shaft end of the motor shaft  15  to the sensor processor  28 . 
     Next, the eddy current sensor  50  equipped to the polishing apparatus according to the embodiment will be described with reference to  FIGS. 2 and 3 . 
       FIGS. 2A and 2B  are diagrams showing the configuration of the eddy current sensor  50 , wherein  FIG. 2A  is a block diagram showing the configuration of the eddy current sensor  50 , and  FIG. 2B  is an equivalent circuit diagram of the eddy current sensor  50 . 
     As shown in  FIG. 2A , the eddy current sensor  50  is configured so that a sensor coil  51  is arranged in the neighborhood of a metal film (or conductive film) mf as a detection target, and an AC signal source  52  is connected to the coil. Here, the metal film (or conductive film) mf as the detection target is a thin film of Cu, Al, Au, W or the like formed on the semiconductor wafer  18 , for example. The sensor coil  51  is a coil for detection, and arranged in the neighborhood of, for example, at a distance of about 1.0 to 4.0 mm from the metal film (or conductive film) as the detection target. 
     There are two types of eddy current sensors. One type of eddy current sensors is a frequency type in which occurrence of an eddy current in the metal film (or conductive film) mf varies the oscillation frequency, and the metal film (or conductive film) is detected from this variation of the oscillation frequency, and the other type is an impedance type in which occurrence of an eddy current in the metal film (conductive film) mf varies the impedance, and the metal film (conductive film) is detected from this variation of the impedance. That is, in the frequency type, when an eddy current I 2  varies in an equivalent circuit shown in  FIG. 2B , the impedance Z varies. When the impedance Z varies, the oscillation frequency of the signal source (frequency-variable oscillator)  52  varies. When the oscillation frequency varies, the variation of the oscillation frequency is detected by a detection circuit  54 , whereby variation of the metal film (or conductive film) can be detected. The sensor processor  28  is configured by the AC signal source  52  and the detection circuit  54 . 
     In the impedance type, when an eddy current I 2  varies in the equivalent circuit shown in  FIG. 2B , the impedance Z varies. When the impedance Z varies, the impedance Z when viewed from the signal source (fixed frequency oscillator)  52  varies. This variation of the impedance Z is detected by the detection circuit  54 , and thus the variation of the metal film (or conductive film) can be detected. The data corresponding to the film thickness in this embodiment are obtained from the magnitude (absolute value) of the impedance Z by the sensor processor  28 . Specifically, for example, the detection circuit  54  multiplies the impedance Z by a predetermined number, and outputs a value coincident with an actual film thickness to the film thickness estimating unit  32 . Accordingly, in this embodiment, the output of the detection circuit  54 , that is, the output of the sensor processor  28  is the value coincident with the actual film thickness. 
     The impedance type eddy current sensor is capable of taking out signal outputs X, Y, the phase, the impedance Z, etc. The signal outputs X, Y represent the real-number component and imaginary-number component of the impedance Z, respectively. Measurement information of the film thickness of the metal film (or conductive film) Cu, Al, Au or W is obtained from the frequency F, the impedance Z or the like. The eddy current sensor  50  can be incorporated at an inner position of the polishing table  12  which is in the vicinity of the surface. The eddy current sensor  50  is arranged so as to face the semiconductor wafer as the polishing target through the polishing pad. The eddy current sensor  50  can detect variation of the film thickness of the metal film (or conductive film) from an eddy current flowing in the metal film (or conductive film) on the semiconductor wafer. 
       FIG. 3  schematically shows an example of the configuration of the sensor coil of the eddy current sensor  50  according to the embodiment. As shown in  FIG. 3 , the sensor coil  51  is configured so that a coil for forming an eddy current in the metal film (or conductive film) and a coil for detecting the eddy current in the metal film (or conductive film) are arranged to be separated from each other. The sensor coil  51  includes three layers of coils  72 ,  73  and  74  wound around a bobbin  71 . Here, the center coil  72  is an oscillation coil connected to the AC signal source  52 . The oscillation coil  72  forms an eddy current in the metal film (or conductive film) mf on the semiconductor wafer  18  arranged in the neighborhood of the oscillation coil  72  by magnetic field which is generated by a voltage supplied from the AC signal source  52 . The detection coil  73  is arranged at the upper side (the metal film (or conductive film) side) of the bobbin  71 , and detects magnetic field generated by the eddy current formed in the metal film (or conductive film). The balance coil  74  is arranged on the opposite side to the detection coil  73  with respect to the oscillation coil  72 . The balance coil  74  is used to perform balance adjustment in a resistance bridge circuit used for measurements. Adjustment of a zero point can be performed by the balance coil  74 . Accordingly, it is possible to detect the eddy current flowing in the metal film (or conductive film) from a state where the eddy current is equal to zero, and thus the detection sensitivity of the eddy current in the metal film (or conductive film) is enhanced. 
     Next, the processing of the film thickness estimating unit  32  in the controller  29  will be specifically described with reference to  FIGS. 4A to 4C .  FIG. 4A  is a graph showing an actual film thickness of the semiconductor wafer  18  which varies with lapse of the polishing time,  FIG. 4B  is a graph showing a film thickness of the semiconductor wafer  18  which is output from the sensor processor  28  with lapse of the polishing time, and  FIG. 4C  is a graph showing an estimated film thickness of the semiconductor wafer  18  which is output by the film thickness estimating unit  32 . The abscissa axes of these graphs are common to one another, and represent the time. The unit of the time is “second”. The ordinate axes of these graphs represent the film thickness, and have the same scale. The unit of the film thickness is “μm”. A curve  34  shown in  FIG. 4A  represents that polishing progresses and the film thickness decreases with lapse of the time. 
     The times t1 to t4, t6 to t10 represent times at which the measurement is performed by the eddy current sensor  50  and the output thereof is transmitted to the sensor processor  28 . In this embodiment, the outputs of the sensor processor  28  shown in  FIG. 4B  are values coincident with the actual film thicknesses. However, some deviation occurs between the graph of  FIG. 4A  and the graph of  FIG. 4B  because there is a time delay from the time when an input from the eddy current sensor  50  is received until the sensor processor  28  outputs a processing result. 
     In  FIGS. 4A to 4C , the measurement and the processing are performed until the time t4. The film thicknesses s1 to s4 are outputs of the sensor processor  28 , and correspond to results obtained by processing inputs from the eddy current sensor  50  at the times t1 to t4, respectively. There is a time lag  36  between each of the times t1 to t4 and the corresponding one of times at which the film thicknesses s1 to s4 are output. Film thicknesses r1 to r4 are film thicknesses output from the film thickness estimating unit  32 , and has been subjected to time-lag correction. The film thicknesses r1 to r4 are the values obtained by actually performing the measurement at the times t1 to t4, respectively. Therefore, the film thicknesses r1 to r4 are obtained by performing an operation of turning back the film thicknesses s1 to s4 by only the time lag  36 . The film thicknesses s1 to s4 and the film thicknesses r1 to r4 have the same values. The time lag  36  corresponds to a time which is required for the sensor processor  28  to perform the processing. A curve  40  is a curve representing the actual film thickness, and a curve  42  is a curve representing the estimated film thickness. 
     The time “after lapse of a processing delay time from a measurement time” in this embodiment corresponds to a time at which after the eddy current sensor  50  measures an eddy current at the measurement time, the sensor processor  28  has finished the calculation of the film thickness of the semiconductor wafer  18  based on the eddy current. The processing delay time corresponds to the time lag  36 . “After lapse of the processing delay time” corresponds to the time t5. The time lag  36  is, for example, the time after 0.2 second from the time t4 when the eddy current sensor  50  measures an eddy current. In this embodiment, the time required for the processing in the film thickness estimating unit  32  is negligible. In  FIGS. 4A to 4C , the film thicknesses r1 to r4 are past data  44 , and the film thickness r5 is the latest estimation data. 
     Actual measurement values can be obtained at the times t1 to t4, t6 to t10. However, the actual film thickness is unclear at an intermediate time between the times t1 to t4, t6 to t10, for example, at a time t5 at which the sensor processor  28  outputs the film thickness s4. The film thickness estimating unit  32  estimates the film thickness at the time t5. The film thickness estimating unit  32  calculates a polishing rate before the measurement time t4 by using the film thicknesses s1 to s4 which have been already calculated, and estimates the film thickness r5 at the time t5 by using the calculated polishing rate. The polishing rate R (t4) at the time t4 is calculated from the film thickness s3 at the time t3 and the film thickness s4 at the time t4 by the following expression (1): 
         R ( t 4)=( s 4− s 3)/( t 4− t 3)  (1)
 
     The film thickness r5 at the time t5 is calculated by the following expression (2): 
         r 5= r 4+ R ( t 4)*( t 5− t 3)  (2)
 
     The variation amount  38  shown in  FIG. 4C  is the difference between the film thickness r4 and the film thickness r5, and is equal to R(t4)*(t5−t3) of the expression (2). 
     A method of calculating the polishing rate is not limited to only the expression (1). That is, the calculation method is not limited to the method using only the polishing rate R(t4) as the polishing rate. As another calculation method, for the times t1 to t3, the polishing rates R(t1) to R(t3) may be likewise calculated as in the case of the expression (1), and the average value of these four polishing rates R(t1) to R(t4) may be used in place of the R(t4) of the expression (2). The film thickness r5 may be directly calculated from the film thicknesses r1 to r4 by spline interpolation without calculating the variation amount. 
     The controller  29  containing the film thickness estimating unit  32  executes a polishing control program used to control the entire polishing apparatus  100 . The controller  29  has a storage device such as a magnetic hard disc device or a semiconductor storage device (not shown), and stores film thickness data generated by the sensor processor  28  as a database. The storage device stores the film thickness data along a time sequence while associating each time with each film thickness at the time. The controller  29  has an operation unit (not shown), and it estimates the polishing rate based on the data stored in the storage device and estimates the film thickness. The controller  29  has CPU (Central Processing Unit), a memory and an auxiliary storage device which are connected to one another through a bus. The operation unit functions as the sensor processor  28  and the film thickness estimating unit by executing programs. 
     A polishing method of polishing the semiconductor wafer  18  in the polishing apparatus  100  configured described above will be described with reference to  FIG. 5 .  FIG. 5  is a flowchart showing a case where polishing is performed until a predetermined film thickness and the polishing is finished at the time when the film thickness reaches a predetermined film thickness. For example, a case where the film thickness at the time t5 is estimated will be described. The same processing is performed for the other times. 
     When the polishing of the semiconductor wafer  18  is started (polishing step S 10 ), an eddy current (specifically, an impedance Z) of the semiconductor wafer  18  is measured at each time (measuring step S 12 ). When the impedance Z is measured at the time t4, the data corresponding to the film thickness of the semiconductor wafer  18  at the time t4 is calculated based on the measured impedance Z (film thickness calculating step S 14 , S 16 ). For the time t4, data after only the time lag  36  elapses from the time t4 are estimated by using the calculated data as described above (film thickness estimating step S 18 , S 20 ). In the film thickness estimating step S 18 , the polishing rate R(t4) is calculated based on the time-sequential data of the film thickness. In the film thickness estimating step S 20 , the film thickness r5 at the current time is calculated based on an estimated value of the polishing rate. Subsequently, it is determined whether the polishing has been executed until a predetermined film thickness based on the film thickness r5 (step S 22 ). When the polishing has been executed until the predetermined film thickness (YES), the polishing is finished. When the polishing has not yet been performed until the predetermined film thickness (NO), the polishing is continued. 
     The examples of the embodiments of the present invention have been described above. The foregoing embodiments of the present invention are provided to make the understanding of the present invention easy, and do not limit the present invention. The present invention can be modified and improved without departing from the subject matter of the present invention, and contains equivalents thereto. In a range where at least a part of the foregoing problem can be solved or in a range where at least a part of the effect can be achieved, it is possible to make any combination or eliminate the respective constituent elements described in the claims and the specification. 
     This application claims priority under the Paris Convention to Japanese Patent Application No. 2016-127611 filed on Jun. 28, 2016. The entire disclosure of Japanese Patent Laid-Open No. 2012-135865 including specification, claims, drawings and summary is incorporated herein by reference in its entirety. 
     REFERENCE SIGNS LIST 
     
         
         
           
               12  . . . polishing table 
               18  . . . semiconductor wafer 
               28  . . . sensor processor 
               29  . . . controller 
               30  . . . polishing unit 
               32  . . . film thickness estimating unit 
               50  . . . eddy current sensor 
               51  . . . sensor coil 
               52  . . . AC signal source 
               54  . . . detection circuit 
               100  . . . polishing apparatus