Patent Publication Number: US-2023158636-A1

Title: Polishing apparatus and polishing method

Description:
CROSS REFERENCE TO RELATED APPLICATION 
     This document claims priority to Japanese Patent Application No. 2021-183999 filed Nov. 11, 2021, the entire contents of which are hereby incorporated by reference. 
     BACKGROUND 
     In a manufacturing process of a semiconductor device, various materials are repeatedly formed in film shapes on a silicon wafer to form a multilayer structure. In order to form such multilayer structure, a technique of planarizing a surface of an uppermost layer of the multilayer structure is becoming important. Chemical mechanical polishing (CMP) is used as one of such planarizing techniques. 
     The chemical mechanical polishing (CMP) is performed by a polishing apparatus. This type of polishing apparatus generally includes a polishing table that supports a polishing pad, a polishing head configured to hold a wafer having a film, and a polishing-liquid supply nozzle configured to supply a polishing liquid (for example, slurry) onto the polishing pad. The polishing apparatus is configured to supply the polishing liquid onto the polishing pad from the polishing-liquid supply nozzle while rotating the polishing head and the polishing table. The polishing head presses a surface of the wafer against the polishing pad to polish a film forming the surface of the wafer in the presence of the polishing liquid between the wafer and the polishing pad. 
     In order to measure a thickness of a non-metallic film, such as an insulating film or a silicon layer (hereinafter simply referred to as film thickness), the polishing apparatus generally includes an optical film-thickness measuring device. This optical film-thickness measuring device is configured to determine the film thickness of the wafer by directing light emitted by a light source to the surface of the wafer and analyzing a spectrum of reflected light from the wafer. The polishing apparatus can terminate polishing of the wafer or can change polishing conditions for the wafer based on the determined film thickness. 
     However, the spectrum of the reflected light from the wafer may vary even under the same conditions (e.g., same film thickness, same measuring point). Such a variation in the spectrum may lower stable measuring of a film thickness and may prevent accurate monitoring of a film thickness during polishing of a wafer. There is a film-thickness measuring device configured to measure a film thickness of a stationary wafer. This type of film-thickness measuring device can repeatedly measure a film thickness at the same measuring point and can obtain a stable measurement result by calculating an average of the obtained multiple measurement values. However, the optical film-thickness measuring device described above dynamically measures the film thickness of the wafer while the wafer is rotating, and such a process cannot be performed. 
     SUMMARY 
     Accordingly, there are provided a polishing apparatus and a polishing method capable of accurately measuring a film thickness of a workpiece, such as wafer, substrate, or panel, used in manufacturing of semiconductor devices during polishing of the workpiece. 
     Embodiments, which will be described below, relate to a polishing apparatus and a polishing method for polishing a workpiece, such as wafer, substrate, or panel, used in manufacturing of semiconductor devices and in particular relates to a technique for determining a film thickness of the workpiece based on optical information contained in reflected light from the workpiece. 
     The inventor has found that there are two reasons why a spectrum of reflected light from the workpiece is not stable. 
     The first reason is that a quantity of light from a light source may vary each time the light source emits light. In particular, in a flash light source configured to emit light by electric discharge, the quantity of light in each light emission is likely to vary due to fluctuation in the electric discharge. During polishing of the workpiece, the light source flashes multiple times to illuminate multiple measuring points on the workpiece in each rotation of the polishing table. There is a slight variation in the quantity of light that illuminates these measuring points. 
     The second reason is that each time the light source emits light, a path of the light traveling through an optical fiber cable may vary. The light source is coupled to the optical fiber cable through which the light is directed to the workpiece. The light source with a small irradiation diameter irradiates a different position on an end surface of the optical fiber cable each time the light source emits the light. As a result, the light is directed to the workpiece through a different part of the optical fiber cable. Such difference in optical path in the optical fiber cable may cause a variation in spectrum of the reflected light from the workpiece. 
     Accordingly, in an embodiment, there is provided a polishing apparatus for polishing a workpiece, comprising: a polishing table configured to support a polishing pad; a polishing head configured to press the workpiece against the polishing pad to polish the workpiece; a light source configured to emit light; a light-emitting optical fiber cable coupled to the light source arid configured to direct the light to the workpiece; a light-receiving optical fiber cable configured to receive reflected light from the workpiece; a first spectrometer coupled to the light-receiving optical fiber cable; a second spectrometer directly coupled to the light source; and a processing system including a memory storing a program and an arithmetic device configured to perform an arithmetic operation according to instructions included in the program, the memory storing therein first base intensity data indicating reference intensity of light measured by the first spectrometer before polishing of the workpiece, the memory storing therein second base intensity data indicating reference intensity of the light of the light source measured by the second spectrometer before polishing of the workpiece, the memory storing therein a calculation formula for calculating relative reflectance data, the processing system being configured to determine a film thickness of the workpiece based on the relative reflectance data, the calculation formula being expressed as 
       the relative reflectance data= MD 1/[ BD 1· k] 
 
     where MD1 represents first intensity measurement data indicating intensity of the reflected light from the workpiece measured by the first spectrometer, BD1 represents the first base intensity data, and k represents a rate of change in second intensity measurement data with respect to the second base intensity data, and the second intensity measurement data is indicative of intensity of the light of the light source measured by the second spectrometer during polishing of the workpiece. 
     In an embodiment, each of the first base intensity data, the second base intensity data, the first intensity measurement data, and the second intensity measurement data is data indicating intensities of light at a plurality of wavelengths, and the rate of change k comprises a plurality of rates of change corresponding to the plurality of wavelengths, respectively. 
     In an embodiment, the processing system is configured to: perform interpolation on the first base intensity data, the first intensity measurement data, the second base intensity data, and the second intensity measurement data such that the plurality of wavelengths of the first base intensity data and the first intensity measurement data coincide with the plurality of wavelengths of the second base intensity data and the second intensity measurement data; and then calculate the plurality of rates of change k. 
     In an embodiment, the plurality of wavelengths of the first base intensity data, the second base intensity data, the first intensity measurement data, and the second intensity measurement data are a plurality of integer wavelengths. 
     In an embodiment, the rate of change k is a rate of change in a representative intensity value of the second intensity measurement data with respect to a representative intensity value of the second base intensity data. 
     In an embodiment, the first spectrometer and the second spectrometer are configured to simultaneously measure the intensity of the reflected light from the workpiece and the intensity of the light of the light source. 
     In an embodiment, the polishing apparatus further comprises a direct-coupling optical fiber cable that directly couples the light source to the second spectrometer. 
     In an embodiment, there is provided a polishing apparatus for polishing a workpiece, comprising: a polishing table configured to support a polishing pad; a polishing head configured to press the workpiece against the polishing pad to polish the workpiece; a light source configured to emit light; a light-emitting optical fiber cable coupled to the light source and configured to direct the light to the workpiece; a light-receiving optical fiber cable configured to receive reflected light from the workpiece; a first spectrometer coupled to the light-receiving optical fiber cable; a second spectrometer directly coupled to the light source; and a processing system including a memory storing a program and an arithmetic device configured to perform an arithmetic operation according to instructions included in the program, the memory storing therein a plurality of different first base intensity data each indicative of reference intensity of light measured by the first spectrometer before polishing of the workpiece, the memory storing therein a plurality of different second base intensity data each indicative of reference intensity of the light of the light source measured by the second spectrometer before polishing of the workpiece, the plurality of different first base intensity data being associated with the plurality of different second base intensity data in one-to-one correspondence relationship, the processing system being configured to: obtain first intensity measurement data indicative of intensity of the reflected light from the workpiece measured by the first spectrometer; obtain second intensity measurement data indicative of intensity of the light of the light source measured by the second spectrometer during polishing of the workpiece; select second base intensity data that best matches the second intensity measurement data from the plurality of different second base intensity data; determine first base intensity data associated with the selected second base intensity data; calculate relative reflectance data by dividing the first intensity measurement data by the determined first base intensity data; and determine a film thickness of the workpiece based on the relative reflectance data. 
     In an embodiment, the first spectrometer and the second spectrometer are configured to simultaneously measure the intensity of the reflected light from the workpiece and the intensity of the light of the light source during polishing of the workpiece. 
     In an embodiment, the polishing apparatus further comprises a direct-coupling optical fiber cable that directly couples the light source to the second spectrometer, an end of the light-emitting optical fiber cable and an end of the direct-coupling optical fiber cable being bundled together to form a trunk optical fiber cable, and the trunk optical fiber cable being coupled to the light source. 
     In an embodiment, there is provided a polishing method of polishing a workpiece, comprising: before polishing of the workpiece, directing light, emitted by a light source, through a light-emitting optical fiber cable and a light-receiving optical fiber cable to a first spectrometer, and measuring intensity of the light by the first spectrometer to generate first base intensity data indicative of reference intensity of the light; before polishing of the workpiece, measuring intensity of the light, emitted by the light source, by a second spectrometer to generate second base intensity data indicative of reference intensity of the light, the second spectrometer being directly coupled to the light source; polishing the workpiece by pressing the workpiece against a polishing pad on a polishing table while rotating the polishing table; obtaining first intensity measurement data indicative of intensity of reflected light from the workpiece measured by the first spectrometer during polishing of the workpiece; obtaining second intensity measurement data indicative of intensity of the light of the light source measured by the second spectrometer during polishing of the workpiece; calculating a rate of change in the second intensity measurement data with respect to the second base intensity data; calculating corrected first base intensity data by multiplying the first base intensity data by the rate of change; calculating relative reflectance data by dividing the first intensity measurement data by the corrected first base intensity data; and determining a film thickness of the workpiece based on the relative reflectance data. 
     In an embodiment, each of the first base intensity data, the second base intensity data, the first intensity measurement data, and the second intensity measurement data is data indicating intensities of light at a plurality of wavelengths, and the rate of change comprises a plurality of rates of change corresponding to the plurality of wavelengths, respectively. 
     In an embodiment, the polishing method further comprises performing interpolation on the first base intensity data, the first intensity measurement data, the second base intensity data, and the second intensity measurement data such that the plurality of wavelengths of the first base intensity data and the first intensity measurement data coincide with the plurality of wavelengths of the second base intensity data and the second intensity measurement data, the interpolation being performed before calculating the plurality of rates of change. 
     In an embodiment, the plurality of wavelengths of the first base intensity data, the second base intensity data, the first intensity measurement data, and the second intensity measurement data are a plurality of integer wavelengths. 
     In an embodiment, the rate of change is a rate of change in a representative intensity value of the second intensity measurement data with respect to a representative intensity value of the second base intensity data. 
     In an embodiment, the first spectrometer and the second spectrometer simultaneously measure the intensity of the reflected light from the workpiece and the intensity of the light from the light source. 
     In an embodiment, there is provided a polishing method of polishing a workpiece, comprising: before polishing of the workpiece, repeatedly emitting light by a light source and transmitting the light through a light-emitting optical fiber cable and a light-receiving optical fiber cable to a first spectrometer; measuring intensity of the light by the first spectrometer to generate a plurality of different first base intensity data indicative of reference intensity of the light; measuring intensity of the light, repeatedly emitted by the light source, by a second spectrometer to generate a plurality of different second base intensity data indicative of reference intensity of the light from the light source, the second spectrometer being directly coupled to the light source; associating the plurality of different first base intensity data with the plurality of different second base intensity data in one-to-one correspondence relationship; polishing the workpiece by pressing the workpiece against a polishing pad on a polishing table while rotating the polishing table; obtaining first intensity measurement data indicative of intensity of reflected light from the workpiece measured by the first spectrometer during polishing of the workpiece; obtaining second intensity measurement data indicative of intensity of the light of the light source measured by the second spectrometer during polishing of the workpiece; selecting second base intensity data that best matches the second intensity measurement data from the plurality of different second base intensity data; determining first base intensity data associated with the selected second base intensity data; calculating relative reflectance data by dividing the first intensity measurement data by the determined first base intensity data; and determining a film thickness of the workpiece based on the relative reflectance data. 
     In an embodiment, the first spectrometer and the second spectrometer simultaneously measure the intensity of the reflected light from the workpiece and the intensity of the light from the light source during polishing of the workpiece. 
     The second base intensity data is original reference data, and the second intensity measurement data is reference data during polishing. According to the above-described embodiments, the rate of change in the second intensity measurement data with respect to the second base intensity data is used to correct the first base intensity data. Further, the first intensity measurement data obtained during polishing of the workpiece is divided by the corrected first base intensity data, so that the relative reflectance data is obtained. Such calculations remove the variation in the quantity of light of the light source from the relative reflectance data. As a result, an accurate film thickness can be determined from the relative reflectance data. 
     Furthermore, according to the above-described embodiments, the second base intensity data that best matches the second intensity measurement data(i.e., coincides with the second intensity measurement data most) is selected from the plurality of different base second intensity data. The plurality of different second base intensity data vary due to different optical paths of light traveling through the optical fiber cable. The second base intensity data that best matches the second intensity measurement data is data that reflects such difference in optical path. Therefore, the first base intensity data associated with the selected second base intensity data is also data reflecting the difference in the optical path. The operation of dividing the first intensity measurement data by the first base intensity data can determine the relative reflectance data from which the difference in optical path in the optical fiber cable is eliminated. As a result, an accurate film thickness can be determined from the relative reflectance data. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a schematic diagram showing one embodiment of a polishing apparatus; 
         FIG.  2    is a cross-sectional view showing detailed configurations of an optical film-thickness measuring device; 
         FIG.  3    shows a spectrum generated from first intensity measurement data; 
         FIG.  4    shows a spectrum generated from corrected first base intensity data; 
         FIG.  5    shows a spectrum generated from relative reflectance data; 
         FIG.  6    is a flow chart describing one embodiment of a polishing method for polishing a workpiece; 
         FIG.  7    is a graph showing intensities of light and their wavelengths measured by a first spectrometer and a second spectrometer; 
         FIG.  8    is a graph showing a state in which the wavelengths of the light intensities measured by the first spectrometer and the wavelengths of the light intensities measured by the second spectrometer coincide with each other by interpolation; 
         FIG.  9    is a schematic diagram showing a position of an incident spot of light on an end surface of a trunk optical fiber cable and optical paths of light in a light-emitting optical fiber cable and a direct-coupling optical fiber cable; 
         FIG.  10    is a flow chart describing one embodiment of a polishing method for polishing a workpiece; and 
         FIG.  11    is a schematic diagram showing another embodiment of the polishing apparatus. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Hereinafter, embodiments will be described below with reference to the drawings. 
       FIG.  1    is schematic view showing an embodiment of a polishing apparatus. As shown in  FIG.  1   , the polishing apparatus includes a polishing table  3  configured to support a polishing pad  2 , a polishing head  1  configured to press a workpiece W having a film against the polishing pad  2 , a table motor  6  configured to rotate the polishing table  3 , a polishing-liquid supply nozzle  5  configured to supply polishing liquid, such as slurry, onto the polishing pad  2 , and an operation controller  9  configured to control operations of the polishing apparatus. The polishing pad  2  has an upper surface that provides a polishing surface  2   a  for polishing the workpiece W. Examples of the workpiece W include wafer, substrate, panel, etc. used in manufacturing of semiconductor devices. 
     The polishing head  1  is coupled to a head shaft  10 , which is coupled to a polishing-head motor (now shown). The polishing-head motor is configured to rotate the polishing head  1  together with the head shaft  10  in a direction indicated by an arrow. The polishing table  3  is coupled to the table motor  6 , which is configured to rotate the polishing table  3  and the polishing pad  2  in a direction indicated by an arrow. The polishing head  1 , the polishing-head motor, and the table motor  6  are coupled to the operation controller  9 . 
     The workpiece W is polished as follows. While the polishing table  3  and the polishing head  1  are rotated in the directions indicated by the arrows in  FIG.  1   , the polishing liquid is supplied onto the polishing surface  2   a  of the polishing pad  2  from the polishing-liquid supply nozzle  5 . While the workpiece W is rotated by the polishing head  1 , the workpiece W is pressed by the polishing head I against the polishing surface  2   a  of the polishing pad  2  in the presence of the polishing liquid on the polishing pad  2 . A surface of the workpiece W is polished by a chemical action of the polishing liquid and a mechanical action of abrasive grains contained in the polishing liquid and the polishing pad  2 . 
     The operation controller  9  includes a memory  9   a  storing programs therein, and a processor  9   b  configured to perform arithmetic operations according to instructions included. in the programs. The operation controller  9  is composed of at least one computer. The memory  9   a  includes a main memory, such as a random access memory (RAM) and an auxiliary memory, such as a hard disk drive (HDD) or solid state drive (SSD). Examples of the processor  9   b  include a CPU (central processing unit) and a GPU (graphic processing unit). However, the specific configurations of the operation controller  9  are not limited to these examples. 
     The polishing apparatus includes an optical film-thickness measuring device  20  configured to measure a film thickness of the workpiece W. The optical film-thickness measuring device  20  includes a light source  22  configured to emit light, an optical sensor head  25  configured to direct the light from the light source  22  to the workpiece W and receive reflected light from the workpiece W, a first spectrometer  27  coupled to the optical sensor head  25 , a second spectrometer  28  directly coupled to the light source  22 , and a processing system  30  configured to determine a film thickness of the workpiece W based on relative reflectance data of the reflected light from the workpiece W. The optical sensor head  25  is arranged in the polishing table  3  and rotates together with the polishing table  3 . In an embodiment, a plurality of optical sensor heads  25  coupled to the first spectrometer  27  and the light source  22  may be provided. 
     The processing system  30  includes a memory  30   a  storing programs therein, and an arithmetic device  30   b  configured to perform arithmetic operations according to instructions included in the programs. The processing system  30  includes at least one computer. The memory  30   a  includes a main memory, such as a random access memory (RAM), and an auxiliary memory, such as a hard disk drive (HDD) or solid state drive (SSD). Examples of the arithmetic device  30   b  include a CPU (central processing unit) and a GPU (graphic processing unit). However, the specific configurations of the processing system  30  are not limited to these examples. 
     Each of the operation controller  9  and the processing system  30  may be composed of a plurality of computers. For example, each of the operation controller  9  and the processing system  30  may be configured from a combination of edge server and cloud server. In one embodiment, the operation controller  9  and processing system  30  may be composed of a single computer. 
       FIG.  2    is a cross-sectional view showing detailed configurations of the optical film-thickness measuring device  20 . The optical film-thickness measuring device  20  includes a light-emitting optical fiber cable  31  coupled to the light source  22 , a light-receiving optical fiber cable  32  coupled to the first spectrometer  27 , and a direct-coupling optical fiber cable  33  coupling the light source  22  to the second spectrometer  28  directly. A distal end  31   a  of the light-emitting optical fiber cable  31  and a distal end  32   a  of the light-receiving optical fiber cable  32  constitute the optical sensor head  25 . Specifically, the light-emitting optical fiber cable  31  directs the light from the light source  22  to the workpiece W on the polishing pad  2 , and the light-receiving optical fiber cable  32  receives the reflected light from the workpiece W and transmits the reflected light to the first spectrometer  27 . One end of the direct-coupling optical fiber cable  33  is coupled to the light source  22  and the other end is coupled to the second spectrometer  28 . 
     The first spectrometer  27  and the second spectrometer  28  are coupled to the processing system  30 . The light-emitting optical fiber cable  31 , the light-receiving optical fiber cable  32 , the direct-coupling optical fiber cable  33 , the light source  22 , the first spectrometer  27 , and the second spectrometer  28  are mounted to the polishing table  3  and rotate together with the polishing table  3  and the polishing pad  2 . The optical sensor head  25 , which is composed of the distal end  31   a,  of the light-emitting optical fiber cable  31  and the distal end  32   a  of the light-receiving optical fiber cable  32 , is arranged so as to face the surface of the workpiece W on the polishing pad  2 . The position of the optical sensor head  25  is such that the optical sensor head  25  traverses the surface of the workpiece W on the polishing pad  2  each time the polishing table  3  and polishing pad  2  make one rotation. The polishing pad  2  has a through-hole  2   b  located above the optical sensor head  25 . The optical sensor head  25  irradiates the workpiece W with the light through the through-hole  2   b  and receives the reflected light from the workpiece W through the through-hole  2   b  each time the polishing table  3  makes one rotation. 
     The light source  22  is a flash light source configured to repeatedly emit light at short time intervals. Examples of the light source  22  include xenon flash lamp. The light source  22  is electrically coupled to the operation controller  9  and emits the light upon receiving a trigger signal sent from the operation controller  9 . More specifically, while the optical sensor head  25  sweeps across the surface of the workpiece W on the polishing pad  2  the light source  22  receives multiple trigger signals from the operation controller  9  and emits the light multiple times. Therefore, the light is directed to multiple measuring points on the workpiece W each time the polishing table  3  makes one rotation. 
     The second spectrometer  28  is directly coupled to the light source  22  by the direct-coupling optical fiber cable  33 . The direct-coupling optical fiber cable  33  extends from the light source  22  to the second spectrometer  28 . The second spectrometer  28  is not coupled to the optical sensor head  25  and receives the light only from the light source  22 . The end of the light-emitting optical fiber cable  31  and the end of the direct-coupling optical fiber cable  33  are bundled together to form one trunk optical fiber cable  35 . This trunk optical fiber cable  35  is coupled to the light source  22 . Specifically, the trunk optical fiber cable  35  branches into the light-emitting optical fiber cable  31  and the direct-coupling optical fiber cable  33 . Therefore, the light emitted by the light source  22  splits into two lights, which are transmitted to the optical sensor head  25  and the second spectrometer  28  through the light-emitting optical fiber cable  31  and the direct-coupling optical fiber cable  33 , respectively. 
     Each of the light-emitting optical fiber cable  31  and the direct-coupling optical fiber cable  33  may be a bundle of a plurality of thin optical fibers (strand optical fibers). 
     The light emitted by the light source  22  is simultaneously transmitted to the optical sensor head  25  and the second spectrometer  28 . Specifically, the light is transmitted through the light-emitting optical fiber cable  31  to the optical sensor head  25  and emitted from the optical sensor head  25 . The light travels through the through-hole  2   b  of the polishing pad  2  and is incident on the workpiece W on the polishing pad  2 . The reflected light from the workpiece W travels through the through-hole  2   b  of the polishing pad  2  again and is received by the optical sensor head  25 . The reflected light from the workpiece W is transmitted through the light-receiving optical fiber cable  32  to the first spectrometer  27 . At the same time, the light emitted by the light source  22  is transmitted to the second spectrometer  28  through the direct-coupling optical fiber cable  33  without being sent to the optical sensor head  25 . 
     The first spectrometer  27  and the second spectrometer  28  are configured to decompose the light according to its wavelengths and measure the intensity of the reflected light at each of the wavelengths over a predetermined wavelength range. Specifically, the first spectrometer  27  decomposes the reflected light from the workpiece W according to its wavelengths and measures the intensity of the reflected light at each of the wavelengths over a predetermined wavelength range to generate first intensity measurement data. At the same time, the second spectrometer  28  decomposes the light of the light source  22  according to its wavelengths and measures the intensity of the light at each of the wavelengths over the wavelength range to generate second intensity measurement data. The intensity of light emitted by the light source  22  is measured simultaneously by the first spectrometer  27  and the second spectrometer  28 . The first intensity measurement data and the second intensity measurement data are sent to the processing system  30 . 
     The memory  30   a  of the processing system  30  stores therein first base intensity data indicating reference intensity of light measured by the first spectrometer  27  in advance before polishing of the workpiece W. The memory  30   a  of the processing system  30  further stores therein second base intensity data indicating reference intensity of the light of the light source  22  measured by the second spectrometer  28  in advance before polishing of the workpiece W. The first base intensity data and the second base intensity data are data obtained in advance before polishing of the workpiece W, while the first intensity measurement data and the second intensity measurement data discussed above are data obtained during polishing of the workpiece W. 
     Each of the first base intensity data, the second base intensity data, the first intensity measurement data, and the second intensity measurement data indicates intensifies of light at wavelengths within the predetermined wavelength range. For example, the first intensity measurement data indicates multiple intensities at multiple wavelengths of the reflected light from the workpiece W. The multiple intensities of light indicated by the above data may be intensities relative to dark levels (which are background intensities obtained under a condition that light is cut off) as light intensity reference. Specifically, an intensity of light included in each data may be a value obtained by subtracting a dark level from a measured intensity of light at each wavelength. For example, a light intensity E(λ) at a wavelength λ included in each data may be given by 
         E (λ)= M (λ)− D (λ)   (1)
 
     where λ represents a wavelength, M(λ) represents a measured value of light intensity at wavelength λ, and D(λ) represents a dark level at wavelength λ. 
     It is noted, however, that the light intensity of each data is not limited to this example. In an embodiment, the light intensities may be measured values as they are obtained by the first spectrometer  27  and the second spectrometer  28 . 
     The first intensity measurement data indicating the intensities of the reflected light from the workpiece W contains information on a film thickness of the workpiece W. In other words, the first intensity measurement data varies depending on the film thickness of the workpiece W. Accordingly, the processing system  30  can determine the film thickness of the workpiece W by processing the first intensity measurement data, as described below. 
     In contrast, the first base intensity data indicates the reference intensity of light measured in advance for each wavelength. The first base intensity data is obtained, for example, by irradiating a mirror with the light from the optical sensor head  25  and measuring intensity of reflected light from the mirror by the first spectrometer  27 . Alternatively, the first base intensity data may be obtained by measuring intensity of reflected light from a silicon wafer (or a bare wafer) having no film thereon by the first spectrometer  27  when the silicon wafer is water-polished or slurry-polished on the polishing pad  2  in the presence of water or slurry on the polishing pad  2 , or when the silicon wafer (or the bare wafer) is placed on the polishing pad  2 . 
     In the present embodiment, the relative reflectance data is determined by dividing the first intensity measurement data by the first base intensity data. The relative reflectance data is index (indexes) that indicates the intensity of the reflected light at each wavelength. By dividing the first intensity measurement data by the first base intensity data, unwanted noise (e.g., a variation in intensity inherent in the optical system of the apparatus and the light source  22 ) can be removed from the measured intensity. 
     Both the second base intensity data and the second intensity measurement data are measurement data of the intensity of the light of the light source  22  and are independent of the intensity of the reflected light from the workpiece W. The second base intensity data is data indicating the reference intensity of the light of the light source  22 , and the second intensity measurement data is data indicating the intensity of the light of the light source  22  while the workpiece W is being polished. In this embodiment, the second intensity measurement data and the second base intensity data are used for correction coefficient for eliminating a variation in the relative reflectance data caused by a change in the quantity of light of the light source  22  among the measurement points. 
     The second base intensity data is obtained before polishing of the workpiece W at the same timing as the above-described first base intensity data is obtained. Specifically, the first spectrometer  27  measures the intensities of light transmitted from the optical sensor head  25  over the predetermined wavelength range, while at the same time the second spectrometer  28  measures the intensities of light from the light source  22  over the same wavelength range. 
     The second intensity measurement data is obtained during polishing of the workpiece W at the same timing as the above-described first intensity measurement data is obtained. Specifically, the first spectrometer  27  measures the intensities of the reflected light from the workpiece W transmitted from the optical sensor head  25  over the predetermined wavelength range during polishing of the workpiece W, while at the same time the second spectrometer  28  measures the intensities of the light from the light source  22  over the same wavelength range during polishing of the workpiece W. 
     The memory  30   a  of the processing system  30  has a calculation formula stored therein for calculating the relative reflectance data. The processing system  30  is configured to determine the film thickness of the workpiece W based on the relative reflectance data. The above calculation formula is expressed as 
       Relative reflectance data= MD 1/[ BD 1· k]   (2)
 
     where, MD1 represents the first intensity measurement data indicating the intensity of the reflected light from the workpiece W measured by the first spectrometer  27  during polishing of the workpiece W, BD1 represents the first base intensity data indicating the reference intensity of the light measured by the first spectrometer  27  before polishing of the workpiece W, and k is rate of change in the second intensity measurement data with respect to the second base intensity data, wherein the second intensity measurement data indicates the intensity of the light of the light source  22  measured by the second spectrometer  28  during polishing of the workpiece W. 
     The change in the second intensity measurement data with respect to the second base intensity data does not depend on a change in the film thickness of the workpiece W, and depends only on the change in the quantity of light of the light source  22 . Therefore, the operation of multiplying the first base intensity data by the rate of change k can correct the first base intensity data. Specifically, the change in the quantity of light of the light source  22  is reflected in the first base intensity data. As well as the second intensity measurement data, the first intensity measurement data MD1 reflects the change in the quantity of light of the light source  22 . Therefore, the operation of dividing the first intensity measurement data MD1 by the corrected first base intensity data can remove (or cancel) the change in the quantity of light of the light source  22 . As a result, the processing system  30  can determine an accurate film thickness from the relative reflectance data. 
       FIG.  3    shows a spectrum generated from the first intensity measurement data,  FIG.  4    shows a spectrum generated from the corrected first base intensity data, and  FIG.  5    shows a spectrum generated from the relative reflectance data obtained by dividing the first intensity measurement data by the corrected first base intensity data. A shape of the spectrum generated from the relative reflectance data varies according to the film thickness of the workpiece W. The processing system  30  generates a spectrum as shown in  FIG.  5    from the relative reflectance data obtained by the above calculation formula, and determines the film thickness of the workpiece W based on the spectrum generated. 
     A known technique may be used for determining the film thickness of the workpiece W based on the spectrum. For example, the processing system  30  determines, from reference-spectra library, a reference spectrum that is closest in shape to the generated spectrum, and determines a film thickness associated with the determined reference spectrum. In another example, the processing system  30  performs a Fourier transform on the generated spectrum and determines a film thickness from a resultant frequency spectrum. 
       FIG.  6    is a flow chart describing one embodiment of a polishing method for polishing a workpiece W. 
     In step  101 , before polishing of the workpiece W, the light emitted by the light source  22  is directed through the light-emitting optical fiber cable  31  and the light-receiving optical fiber cable  32  to the first spectrometer  27 , and the intensity of the light is measured by the first spectrometer  27 , so that the first base intensity data indicating the reference intensity of light is generated. The processing system  30  obtains the first base intensity data from the first spectrometer  27  and stores the first base intensity data in the memory  30   a.    
     In step  102 , before polishing of the workpiece W, the light emitted by the light source  22  is directed through the direct-coupling optical fiber cable  33  to the second spectrometer  28 , and the intensity of the light is measured by the second spectrometer  28 , so that the second base intensity data indicative of the reference intensity of the light of the light source  22  is generated. The processing system  30  obtains the second base intensity data from the second spectrometer  28  and stores the second base intensity data in the memory  30   a.  The measuring of the light intensity by the first spectrometer  27  in the step  101  and the measuring of the light intensity by the second spectrometer  28  in the step  102  are performed simultaneously. 
     In step  103 , polishing of the workpiece W is started by pressing the workpiece W against the polishing pad  2  by the polishing head  1  while the polishing table  3  is rotated. 
     In step  104 , during polishing of the workpiece W, the processing system  30  obtains the first intensity measurement data indicative of the intensity of reflected light from the workpiece W measured by the first spectrometer  27 . 
     In step  105 , during polishing of the workpiece W, the processing system  30  obtains the second intensity measurement data indicative of the intensity of light from the light source  22  measured by the second spectrometer  28 . The measuring of the intensity of reflected light by the first spectrometer  27  in the step  104  and the measuring of the intensity of light of the light source  22  by the second spectrometer  28  in the step  105  are performed simultaneously. 
     In step  106 , the processing system  30  calculates the rate of change in the second intensity measurement data with respect to the second base intensity data. 
     In step  107 , the processing system  30  calculates the corrected first base intensity data by multiplying the first base intensity data by the rate of change. 
     In step  108 , the processing system  30  calculates the relative reflectance data by dividing the first intensity measurement data by the corrected first base intensity data. 
     In step  109 , the processing system  30  determines the film thickness of the workpiece W based on the relative reflectance data. 
     The rate of change k used in the above-described calculation formula may be a plurality of rates of change corresponding to a plurality of wavelengths, or may be a single rate of change determined for a plurality of wavelengths. The plurality of rates of change k(λ) corresponding to a plurality of wavelengths are given by 
         k (λ)= MV 2(λ)/ BV 2(λ), λ=λ LL,  to λ HL    (3)
 
     where λ represents a wavelength of light, k(λ) represents a rate of change at wavelength λ, MV2(λ) represents an intensity of light at wavelength λ contained in the second intensity measurement data, and BV2(λ) represents an intensity of light at wavelength λ contained in the second base intensity data, λLL represents a lower limit of the wavelength range of the light intensity measured by the first spectrometer  27  and the second spectrometer  28 , and λHL represents an upper limit of the above wavelength range. The wavelength λ is any one of wavelengths ranging from the lower limit λLL to the upper limit λHL. 
     According to this embodiment, since the rate of change is calculated for each wavelength, the first base intensity data can be corrected more accurately. 
     The above-described calculation formula (2) can be expressed as follows using formula (3), 
         R (λ)= MV 1(λ)/[ BV 1(λ)· k (λ)], λ=λ LL  to λ HL    (4)
 
     where, R(λ) represents a relative reflectance at wavelength λ, MV1(λ) represents an intensity of the reflected light at the wavelength λ contained in the first intensity measurement data MD1, and BV1(λ) represents a reference intensity of light at the wavelength λ contained in the first base intensity data BD1. 
     MV1(λ), BV1(λ), MV2(λ), and BV2(λ) included in the above formulas (3) and (4) are light intensities at the wavelength λ measured by the first spectrometer  27  and the second spectrometer  28 . Each of the first spectrometer  27  and the second spectrometer  28  is configured to decompose light according to wavelengths and measure the intensity of the light at each wavelength. However, due to a mechanical difference between the first spectrometer  27  and the second spectrometer  28 , there may be a difference between the wavelength of the intensity measured by the first spectrometer  27  and the wavelength of the intensity measured by the second spectrometer  28 . This issue will be described with reference to  FIG.  7   . 
       FIG.  7    is a graph showing the light intensities and their wavelengths measured by the first spectrometer  27  and the second spectrometer  28 . The first spectrometer  27  measures light intensities MV1(λ 1 ), MV1(λ 2 ), and MV1(λ 3 ) at wavelengths λ 1 , λ 2 , and λ 3 , and the second spectrometer  28  also measures MV2(λ 1 ), MV2(λ 2 ), and MV2(λ 3 ) at the wavelengths λ 1 , λ 2 , and λ 3 . However, as shown in  FIG.  7   , due to the mechanical difference between the first spectrometer  27  and the second spectrometer  28 , the wavelengths λ 1 , λ 2 , and λ 3  of the light intensities measured by the first spectrometer  27  are slightly different from the wavelengths λ 1 , λ 2 , and λ 3  of the light intensities measured by the second spectrometer  28 . Such difference in wavelength can adversely affect the accuracy of the relative reflectance data. 
     Thus, in one embodiment, the processing system  30  is configured to perform interpolation on the first base intensity data, the first intensity measurement data, the second base intensity data, and the second intensity measurement data such that the plurality of wavelengths of the first base intensity data and the first intensity measurement data coincide with the plurality of wavelengths of the second base intensity data and the second intensity measurement data. After the interpolation, the processing system  30  calculates the plurality of rates of change k and calculates the relative reflectance data. 
       FIG.  8    is a graph showing that the wavelengths λ 1 , λ 2 , and λ 3  of the light intensities measured by the first spectrometer  27  coincide with the wavelengths λ 1 , λ 2 , and λ 3  of the light intensities measured by the second spectrometer  28  as a result of the interpolation. In this example, the plurality of wavelengths λ 1 , λ 2 , λ 3  of the interpolated first intensity measurement data and the plurality of wavelengths λ 1 , λ 2 , λ 3  of the interpolated second intensity measurement data are integer wavelengths. Specifically, the processing system  30  performs the interpolation on the first intensity measurement data to determine light intensities MV1(λ 1 ), MV1(λ 2 ), MV1(λ 3 ) at integer wavelengths λ 1 , λ 2 , λ 3 , and further performs the interpolation on the second intensity measurement data to determine light intensities MV2(λ 1 ), MV2(λ 2 ), MV2(λ 3 ) at the integer wavelengths λ 1 , λ 2 , λ 3 . As a result, the wavelengths of the first intensity measurement data coincide with the wavelengths of the second intensity measurement data. 
     Similarly, the plurality of wavelengths λ 1 , λ 2 , and λ 3  of the interpolated first base intensity data and the plurality of wavelengths λ 1 , λ 2 , and λ 3  of the interpolated second base intensity data are integer wavelengths. Specifically, the processing system  30  performs the interpolation on the first base intensity data to determine light intensities BV1(λ 1 ), BV1(λ 2 ), BV1(λ 3 ) at integer wavelengths λ 1 , λ 2 , λ 3 , and further perform the interpolation on the second base intensity data to determine light intensities BV2(λ 1 ), BV2(λ 2 ), BV2(λ 3 ) at the integer wavelengths λ 1 , λ 2 , λ 3 . As a result, the wavelengths of the first base intensity data coincide with the wavelengths of the second base intensity data. 
     As a result of these operations, the wavelengths of the light intensities within the wavelength range measured by the first spectrometer  27  and the second spectrometer  28  are all the same. 
     In one embodiment, the rate of change k may be a single rate of change defined for a plurality of wavelengths. In this case, the interpolation described above is not necessary. The processing system  30  determines a representative intensity value for the second base intensity data and a representative intensity value for the second intensity measurement data, and calculates a rate of change k in the representative intensity value for the second intensity measurement data with respect to the representative intensity value for the second base intensity data. Examples of the representative intensity value include an average value, a local maximum value, and a maximum value of a plurality of intensities corresponding to the plurality of wavelengths. 
     According to the embodiments described above, the processing system  30  can not only remove a variation in the light emission of the light source  22 , but also can remove a change in the quantity of light of the light source  22  over time. Specifically, both the variation in the light emission of the light source  22  and the temporal change in the quantity of light of the light source  22  can be expressed as a change in the second intensity measurement data with respect to the second base intensity data. Therefore, the processing system  30  can eliminate not only the variation in the light emission of the light source  22  but also can eliminate the temporal change in the quantity of light of the light source  22  over time by executing the data processing using the calculation formula(s) discussed above. 
     Next, another embodiment of the polishing apparatus will be described. Configurations and operations of this embodiment, which will not be particularly described, are the same as those of the embodiments described with reference to  FIGS.  1  and  2   , and redundant descriptions thereof will be omitted. 
     As shown in  FIG.  2   , the light source  22  is coupled to the trunk optical fiber cable  35 . The light emitted by the light source  22  is first incident on the end surface of the trunk optical fiber cable  35 , and then distributed to the light-emitting optical fiber cable  31  and the direct-coupling optical fiber cable  33 .  FIG.  9    is a schematic diagram showing position of the incident spot of light on an end surface  35   a  of the trunk optical fiber cable  35  and optical paths of the light in the light-emitting optical fiber cable  31  and the direct-coupling optical fiber cable  33 . As shown in  FIG.  9   , an incident spot S of the light emitted by the light source  22  is smaller than the end surface  35   a  of the trunk optical fiber cable  35 , and the incident spot S is located within the end surface  35   a  of the trunk optical fiber cable  35 . 
     During polishing of the workpiece W, the light source  22  repeatedly emits the light at short time intervals. The position of the incident spot S of the light within the end surface  35   a  of the trunk optical fiber cable  35  is not constant and changes each time the light source  22  emits the light. An optical path P 1  of the light traveling through the light-emitting optical fiber cable  31  (i.e., a spot position of the light in the light-emitting optical fiber cable  31 ) and an optical path P 2  of the light traveling through the direct-coupling optical fiber cable  33  vary depending on the position of the incident spot S of the light within the end surface  35   a  of the trunk optical fiber cable  35 . Circles depicted by dotted line in  FIG.  9    indicate a change in the position of the incident spot S of the light and corresponding changes in the optical paths P 1  and P 2 . Such changes in the optical paths P 1  and P 2  in the light-emitting optical fiber cable  31  and the direct-coupling optical fiber cable  33  cause a change in the spectrum of the reflected light from the workpiece W. 
     Although the optical path P 1  in the light-emitting optical fiber cable  31  and the optical path P 2  in the direct-coupling optical fiber cable  33  change, there is a one-to-one relationship between the positions of the optical paths P 1  and P 2  in the optical fiber cables  31  and  33 . In other words, the position of the optical path P 1  of light traveling in the light-emitting optical fiber cable  31  uniquely corresponds to the position of the optical path. P 2  of light traveling in the direct-coupling optical fiber cable  33 . The second intensity measurement data representing the intensity of the light of the light source  22  measured by the second spectrometer  28  during polishing of the workpiece W varies depending on the optical path P 2  of the light traveling in the direct-coupling optical fiber cable  33 , i.e., depending on the position of the incident spot S of light within the end surface  35   a  of the trunk optical fiber cable  35 . Therefore, the first intensity measurement data indicating the intensity of the reflected light from the workpiece W measured by the first spectrometer  27  during polishing of the workpiece W also varies while maintaining one-to-one relationship with the second intensity measurement data. 
     In this embodiment, before polishing of the workpiece W, the light intensity is measured by the first spectrometer  27  and the second spectrometer  28  while the light source  22  repeatedly emits the light, so that a plurality of first base intensity data and a plurality of second base intensity data are generated. Each second base intensity data is generated at the same timing as each first base intensity data is generated before polishing of the workpiece W. Specifically, the first spectrometer  27  measures intensities of tight transmitted from the optical sensor head  25  over a predetermined wavelength range, while the second spectrometer  28  measures intensities of light from the light source  22  over the same wavelength range. 
     Each time the light source  22  emits light, the position of the incident spot S of the light within the end surface  35   a  of the trunk optical fiber cable  35  changes. Accordingly, the plurality of different first base intensity data and the plurality of different second base intensity data are generated. A reference library containing the plurality of different first base intensity data and the plurality of different second base intensity data is stored in the memory  30   a  of the processing system  30 . The plurality of different first base intensity data and the plurality of different second base intensity data are associated with each other in a one-to-one correspondence relationship. 
     The processing system  30  obtains the first intensity measurement data indicating the intensity of the reflected light from the workpiece W measured by the first spectrometer  27  during polishing of the workpiece W, and obtains the second intensity measurement data indicating the intensity of light of the light source  22  measured by the second spectrometer  28  during polishing of the workpiece W. The second intensity measurement data is generated during polishing of the workpiece W at the same timing as the first intensity measurement data is generated. Specifically, the first spectrometer  27  measures intensities of the reflected light from the workpiece W over a predetermined wavelength range, while the second spectrometer  28  measures intensities of the light from the light source  22  over the same wavelength range. 
     The processing system  30  selects, from the plurality of different base second intensity data contained in the reference library, one second base intensity data that best matches the second intensity measurement data (i.e., coincides with the second intensity measurement data most). The processing system  30  then determines the first base intensity data associated with the selected second base intensity data, “Best match (or coincide most)” includes not only being most similar, but also exact match. Curve fining, reproduction discrimination, or other technique can be used as a method for selecting the second base intensity data that best matches the second intensity measurement data (i.e., a method for determining the similarity of intensity data). 
     The spectrum of the reflected light from the workpiece W is affected by the optical path in the light-emitting optical fiber cable  31 . Therefore, if the intensity data of lights that have passed through different optical paths are used in the calculation of the relative reflectance from the first intensity measurement data and the first base intensity data, such different optical paths affect the calculation, and as a result, an accurate film thickness cannot be determined. On the other hand, the first base intensity data and the second base intensity data have a correspondence relationship, because these are the intensity data of light that has passed through the same optical path. Similarly, the first intensity measurement data and the second intensity measurement data have a correspondence relationship, because these are the intensity data of light that has passed through the same optical path. Therefore, the processing system  30  selects, from the plurality of second base intensity data, one second base intensity data having similarity of spectrum of light that is supposed to have passed through the same optical path in the direct-coupling optical fiber cable  33  as the light of the second intensity measurement data. Furthermore, the processing system  30  determines the first base intensity data corresponding to (i.e., measured at the same time as) the selected second base intensity data. The processing system  30  then calculates the relative reflectance from the first intensity measurement data and the determined first base intensity data. These operations can eliminate the effect of the optical path, and can therefore improve the accuracy of the film thickness measurement. 
     The processing system  30  calculates the relative reflectance data by dividing the first intensity measurement data by the determined first base intensity data, and determines the film thickness of the workpiece W based on the relative reflectance data. As a result of such dividing operation, the change in the position of the incident spot S of light within the end surface  35   a  of the trunk optical fiber cable  35  is removed from the relative reflectance data. As a result, the processing system  30  can determine an accurate film thickness from the relative reflectance data. 
       FIG.  10    is a flow chart describing one embodiment of a polishing method for polishing a workpiece W. 
     In step  201 , before polishing of the workpiece W, the light repeatedly emitted by the light source  22  is directed through the light-emitting optical fiber cable  31  and the light-receiving optical fiber cable  32  to the first spectrometer  27 , and the intensity of the light is measured by the first spectrometer  27 , so that a plurality of different first base intensity data each indicative of reference intensity of light are generated. The processing system  30  obtains the plurality of different first base intensity data from the first spectrometer  27  and stores them in the memory  30   a.    
     In step  202 , before polishing of the workpiece W, the light repeatedly emitted by the light source  22  is directed through the direct-coupling optical fiber cable  33  to the second spectrometer  28 , and the intensity of the light is measured by the second spectrometer  28 , so that a plurality of different second base intensity data each indicative of the reference intensity of the light of the light source  22  are generated. The processing system  30  obtains the plurality of different second base intensity data from the second spectrometer  28  and stores them in the memory  30   a.  Measuring of the light intensity by the first spectrometer  27  in the step  201  and measuring of the light intensity by the second spectrometer  28  in the step  202  are performed simultaneously. 
     In step  203 , polishing of the workpiece W is started by pressing the workpiece W against the polishing pad  2  by the polishing head  1  while the polishing table  3  is rotated. 
     In step  204 , during polishing of the workpiece W, the processing system  30  obtains the first intensity measurement data indicative of the intensity of the reflected light from the workpiece W measured by the first spectrometer  27 . 
     In step  205 , during polishing of workpiece W, the processing system  30  obtains the second intensity measurement data indicative of the intensity of the light from the light source  22  measured by second spectrometer  28 . Measuring of the intensity of the reflected light by the first spectrometer  27  in the step  204  and measuring of the intensity of the light of the light source  22  by the second spectrometer  28  in the step  205  are performed simultaneously. 
     In step  206 , the processing system  30  selects second base intensity data that best matches the second intensity measurement data (i.e., coincides with the second intensity measurement data most) from the plurality of different base second intensity data. 
     In step  207 , the processing system  30  determines first base intensity data associated with the selected second base intensity data. 
     In step  208 , the processing system  30  calculates the relative reflectance data by dividing the first intensity measurement data by the determined first base intensity data. 
     In step  209 , the processing system  30  determines the film thickness of the workpiece W based on the relative reflectance data. 
     Although one optical sensor head  25  is provided in the embodiments described previously, the present invention is not limited to the above embodiments, and a plurality of optical sensor heads  25  may be provided in the polishing table  3 . For example, as shown in  FIG.  11   , light-receiving optical fiber cables  32  constituting a plurality of optical sensor heads  25  may be coupled to the first spectrometer  27  via an optical-path switching device  40 , such as an optical switch or a shutter. Positions of the plurality of optical sensor heads  25  are not particularly limited. For example, the plurality of optical sensor heads  25  may be arranged at positions such that the plurality of optical sensor heads  25  move across the center and an edge portion of the workpiece W. In the embodiment shown in  FIG.  11   , two optical sensor heads  25  are provided, while three or more optical sensor heads  25  may be provided. 
     The previous description of embodiments is provided to enable a person skilled in the art to make and use the present invention. Moreover, various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles and specific examples defined herein may be applied to other embodiments. Therefore, the present invention is not intended to be limited to the embodiments described herein but is to be accorded the widest scope as defined by limitation of the claims.