Patent Publication Number: US-6659842-B2

Title: Method and apparatus for optical monitoring in chemical mechanical polishing

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of pending U.S. application Ser. No. 09/591,187, filed Jun. 8, 2000 now U.S. Pat. No. 6,296,548, which is a continuation-in-part of pending U.S. application Ser. No. 09/184,767, filed Nov. 2, 1998 now U.S. Pat. No. 6,280,289 and claims priority under 35 USC 119(e) to U.S. Provisional Application Serial No. 60/139,015, filed Jun. 14, 1999. 
    
    
     BACKGROUND 
     The present invention relates generally to chemical mechanical polishing of substrates, and more particularly to methods and apparatus for detecting an end-point of a metal layer during a chemical mechanical polishing operation. 
     An integrated circuit is typically formed on a substrate by the sequential deposition of conductive, semiconductive or insulative layers on a silicon wafer. After each layer is deposited, the layer is etched to create circuitry features. As a series of layers are sequentially deposited and etched, the outer or uppermost surface of the substrate, i.e., the exposed surface of the substrate, becomes increasingly non-planar. This non-planar surface presents problems in the photolithographic steps of the integrated circuit fabrication process. Therefore, there is a need to periodically planarize the substrate surface. 
     Chemical mechanical polishing (CMP) is one accepted method of planarization. This planarization method typically requires that the substrate be mounted on a carrier or polishing head. The exposed surface of the substrate is placed against a rotating polishing pad. The polishing pad may be either a “standard” pad or a fixed-abrasive pad. A standard pad has a durable roughened surface, whereas a fixed-abrasive pad has abrasive particles held in a containment media. The carrier head provides a controllable load, i.e., pressure, on the substrate to push it against the polishing pad. A polishing slurry, including at least one chemically-reactive agent, and abrasive particles if a standard pad is used, is supplied to the surface of the polishing pad. 
     One problem in CMP is determining whether the polishing process is complete, i.e., whether a substrate layer has been planarized to a desired flatness or thickness. Variations in the initial thickness of the substrate layer, the slurry composition, the polishing pad condition, the relative speed between the polishing pad and the substrate, and the load on the substrate can cause variations in the material removal rate. These variations cause variations in the time needed to reach the polishing endpoint. Therefore, the polishing endpoint cannot be determined merely as a function of polishing time. 
     One way to determine the polishing endpoint is to remove the substrate from the polishing surface and examine it. For example, the substrate may be transferred to a metrology station where the thickness of a substrate layer is measured, e.g., with a profilometer or a resistivity measurement. If the desired specifications are not met, the substrate is reloaded into the CMP apparatus for further processing. This is a time consuming procedure that reduces the throughput of the CMP apparatus. Alternatively, the examination might reveal that an excessive amount of material has been removed, rendering the substrate unusable. 
     Several methods have been developed for in-situ polishing endpoint detection. Most of these methods involve monitoring a parameter associated with the substrate surface, and indicating an endpoint when the parameter abruptly changes. For example, where an insulative or dielectric layer is being polished to expose an underlying metal layer, the coefficient of friction and the reflectivity of the substrate will change abruptly when the metal layer is exposed. 
     Where the monitored parameter changes abruptly at the polishing endpoint, such endpoint detection methods are acceptable. However, as the substrate is being polished, the polishing pad condition and the slurry composition at the pad-substrate interface may change. Such changes may mask the exposure of an underlying layer, or they may imitate an endpoint condition. Additionally, such endpoint detection methods will not work if only planarization is being performed, if the underlying layer is to be over-polished, or if the underlying layer and the overlying layer have similar physical properties. 
     SUMMARY 
     In one aspect, the invention is directed to a method of determining polishing parameters. In the method, a surface of a substrate is brought into contact with a polishing pad that has a window, relative motion is created between the substrate and the polishing pad, and a light beam is directed through the window. The motion of the polishing pad relative to the substrate causes the light beam to move in a path across the substrate. Light beam reflections from a layer in the substrate are detected, reflection data associated with the light beam reflections is generated, and the reflection data from a scan of the light beam across the substrate is displayed. Polishing parameters are selected to provide uniform polishing of the substrate based on the displayed reflection data. 
     Implemenations of the invention may include one or more of the following features. The displayed reflection data may show the reflectivity of the substrate as the light beam scans across the substrate. The reflectivity of the substrate may be displayed in real-time during polishing. The layer maybe a metal. The reflection data may include a plurality of intensity measurements made at a plurality of positions along the path across the substrate. A radial position relative to the center of the substrate may be calculated for each intensity measurement. The reflection data may be divided into a plurality of radial ranges, and which radial range is the last portion to be completely polished may be determined. The displayed reflection data may form at least one transient signal graph. Each transient signal graph may comprise reflection data from a single sweep of the window beneath the substrate. 
     In another aspect, the invention is directed to a method of generating endpoint parameters. A first substrate is polished, light beam reflections are detected during polishing the first substrate to generate a first plurality of intensity measurements, and a radial range to use for endpoint detection is determined from the first plurality of intensity measurements. A second substrate is polished, light beam reflections are detected during polishing of a layer in a second substrate to generate a second plurality of intensity measurements, a radial position relative to the center of the substrate is calculated for each of the second intensity measurements, and a polishing endpoint is determined from those second intensity measurements which are within the radial range. 
     Implementations of the invention may include one or more of the following features. Determining the radial range may include determining the last portion of the substrate to be completely polished. At least one process parameter may be determined for polishing of the second substrate from the first plurality of intensity measurements. 
     In another aspect, the invention relates to a method of determining process uniformity. In the method, light beam reflections are detected during polishing of a layer in first and second substrates. Reflection data associated with the light beam reflections is generated, and the reflection data is displayed from a first scan of the light beam across the first substrate and from a second scan of the light beam across the second substrate. The reflection data from the first scan is compared to the reflection data from the second scan to determine process uniformity. A polishing consumable may be changed between the polishing of the first and second substrates. 
     Advantages of the invention include one or more of the following. The reflection data from a wafer is captured using a high resolution data acquisition system at a relatively fine time scale, on the order of milliseconds. Further, reflection intensity changes during polishing are captured for different radial positions on the substrate. The high resolution data acquisition system provides precise time control of each process step in a multi-step operation. Detailed data is available on the progress of the metal polishing operation at different locations of the wafer. Additionally, parameters such as uniformity of the entire wafer and removal rate for different radial portions of the wafer are determined. The acquired high resolution data can be processed on-line or off-line to adjust various variables and parameters to minimize erosion and dishing of the surface layer. If the data is processed in real-time, the feedback data may be used for endpoint detection or for closed-loop control of process parameters. For instance, the polishing pressure, polishing speed, chemistry, and slurry composition may be altered in response to the feedback data to optimize the overall polishing performance and/or polishing quality. The reflection data is available for experimentation to improve the deposition process. 
     Other features and advantages of the invention will become apparent from the following description, including the drawings and claims. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is an exploded perspective view of a chemical mechanical polishing apparatus. 
     FIG. 2 is a side view of a chemical mechanical polishing apparatus including an optical reflectometer. 
     FIG. 3 is a simplified cross-sectional view of a substrate being processed, schematically showing a laser beam impinging on and reflecting from the substrate. 
     FIG. 4 is a graph showing a measured reflectance trace in arbitrary intensity units (a.u.). 
     FIGS. 5A-5E are simplified plan views illustrating the position of a window in a polishing pad as a platen rotates. 
     FIG. 6 is a flow chart of a method of determining the end-point of the polishing of a metal layer during CMP. 
     FIG. 7A is a schematic view illustrating the path of a laser beneath the carrier head. 
     FIG. 7B is a graph showing a hypothetical portion of a reflectance trace generated by a single sweep of the window beneath the carrier head. 
     FIG. 8 is a schematic view illustrating the radial positions of sampling zones from the path of the laser. 
     FIG. 9A is a flow chart of a method of determining the radial position of a sampling zone. 
     FIG. 9B is a graph showing the time at which the laser beam passes beneath the leading and trailing edges of the substrate as a function of the number of rotations of the platen. 
     FIG. 10 is a schematic view illustrating the calculation of the radial position of the sampling zones. 
     FIG. 11 is a schematic diagram of a data structure to store intensity measurements. 
     FIG. 12 is a graph illustrating an overlay of several reflectance traces taken at different times. 
     FIGS. 13A-13H are graphs showing the reflected intensity of the metal layer as a function of distance from the center of the substrate over a polishing period. 
    
    
     DETAILED DESCRIPTION 
     Referring to FIGS. 1 and 2, one or more substrates  10  may be polished by a CMP apparatus  20 . A description of a similar polishing apparatus  20  may be found in U.S. Pat. No. 5,738,574, the entire disclosure of which is incorporated herein by reference. Polishing apparatus  20  includes a series of polishing stations  22  and a transfer station  23 . Transfer station  23  serves multiple functions, including receiving individual substrates  10  from a loading apparatus (not shown), washing the substrates, loading the substrates into carrier heads, receiving the substrates from the carrier heads, washing the substrates again, and finally, transferring the substrates back to the loading apparatus. 
     Each polishing station includes a rotatable platen  24  on which is placed a polishing pad  30 . The first and second stations may include a two-layer polishing pad with a hard durable outer surface, whereas the final polishing station may include a relatively soft pad. If substrate  10  is an “eight-inch” (200 millimeter) or “twelve-inch” (300 millimeter) diameter disk, then the platens and polishing pads will be about twenty inches or thirty inches in diameter, respectively. Each platen  24  may be connected to a platen drive motor (not shown). For most polishing processes, the platen drive motor rotates platen  24  at about thirty to two hundred revolutions per minute, although lower or higher rotational speeds may be used. Each polishing station may also include a pad conditioner apparatus  28  to maintain the condition of the polishing pad so that it will effectively polish substrates. 
     Polishing pad  30  typically has a backing layer  32  which abuts the surface of platen  24  and a covering layer  34  which is used to polish substrate  10 . Covering layer  34  is typically harder than backing layer  32 . However, some pads have only a covering layer and no backing layer. Covering layer  34  may be composed of an open cell foamed polyurethane or a sheet of polyurethane with a grooved surface. Backing layer  32  may be composed of compressed felt fibers leached with urethane. A two-layer polishing pad, with the covering layer composed of IC-1000 and the backing layer composed of SUBA-4, is available from Rodel, Inc., of Newark, Del. (IC-1000 and SUBA-4 are product names of Rodel, Inc.). 
     A rotatable multi-head carousel  60  is supported by a center post  62  and is rotated thereon about a carousel axis  64  by a carousel motor assembly (not shown). Center post  62  supports a carousel support plate  66  and a cover  68 . Carousel  60  includes four carrier head systems  70 . Center post  62  allows the carousel motor to rotate carousel support plate  66  and to orbit the carrier head systems and the substrates attached thereto about carousel axis  64 . Three of the carrier head systems receive and hold substrates, and polish them by pressing them against the polishing pads. Meanwhile, one of the carrier head systems receives a substrate from and delivers a substrate to transfer station  23 . 
     Each carrier head system includes a carrier or carrier head  80 . A carrier drive shaft  74  connects a carrier head rotation motor  76  (shown by the removal of one quarter of cover  68 ) to each carrier head  80  so that each carrier head can independently rotate about it own axis. There is one carrier drive shaft and motor for each head. In addition, each carrier head  80  independently laterally oscillates in a radial slot  72  formed in carousel support plate  66 . A slider (not shown) supports each drive shaft in its associated radial slot. A radial drive motor (not shown) may move the slider to laterally oscillate the carrier head. 
     The carrier head  80  performs several mechanical functions. Generally, the carrier head holds the substrate against the polishing pad, evenly distributes a downward pressure across the back surface of the substrate, transfers torque from the drive shaft to the substrate, and ensures that the substrate does not slip out from beneath the carrier head during polishing operations. 
     Carrier head  80  may include a flexible membrane  82  that provides a mounting surface for substrate  10 , and a retaining ring  84  to retain the substrate beneath the mounting surface. Pressurization of a chamber  86  defined by flexible membrane  82  forces the substrate against the polishing pad. Retaining ring  84  may be formed of a highly reflective material, or it may be coated with a reflective layer to provide it with a reflective lower surface  88 . A description of a similar carrier head  80  may be found in U.S. patent application Ser. No. 08/745,679, entitled a CARRIER HEAD WITH a FLEXIBLE MEMBRANE FOR a CHEMICAL MECHANICAL POLISHING SYSTEM, filed Nov. 8, 1996, by Steven M. Zuniga et al., assigned to the assignee of the present invention, the entire disclosure of which is incorporated herein by reference. 
     A slurry  38  containing a reactive agent (e.g., deionized water for oxide polishing) and a chemically-reactive catalyzer (e.g., potassium hydroxide for oxide polishing) may be supplied to the surface of polishing pad  30  by a slurry supply port or combined slurry/rinse arm  39 . If polishing pad  30  is a standard pad, slurry  38  may also include abrasive particles (e.g., silicon dioxide for oxide polishing). 
     In operation, the platen is rotated about its central axis  25 , and the carrier head is rotated about its central axis  81  and translated laterally across the surface of the polishing pad. 
     A hole  26  is formed in platen  24  and a transparent window  36  is formed in a portion of polishing pad  30  overlying the hole. Transparent window  36  may be constructed as described in U.S. patent application Ser. No. 08/689,930, entitled METHOD OF FORMING A TRANSPARENT WINDOW IN A POLISHING PAD FOR A CHEMICAL MECHANICAL POLISHING APPARATUS by Manoocher Birang, et al., filed Aug. 26, 1996, and assigned to the assignee of the present invention, the entire disclosure of which is incorporated herein by reference. Hole  26  and transparent window  36  are positioned such that they have a view of substrate  10  during a portion of the platen&#39;s rotation, regardless of the translational position of the carrier head. 
     A reflectometer  40  is secured to platen  24  generally beneath hole  26  and rotates with the platen. The reflectometer includes a light source  44  and a detector  46 . The light source generates a light beam  42  which propagates through transparent window  36  and slurry  38  (see FIG. 3) to impinge upon the exposed surface of substrate  10 . For example, the light source  44  may be laser and the light beam  42  may be a collimated laser beam. The light laser beam  42  is projected from laser  44  at an angle α from an axis normal to the surface of substrate  10 , i.e., at an angle α from axes  25  and  81 . In addition, if the hole  26  and window  36  are elongated, a beam expander (not illustrated) may be positioned in the path of the light beam to expand the light beam along the elongated axis of the window. Laser  44  may operate continuously. Alternatively, the laser may be activated to generate laser beam  42  during a time when hole  26  is generally adjacent substrate  10 . 
     Referring to FIGS.  2  and  5 A- 5 E, CMP apparatus  20  may include a position sensor  160 , such as an optical interrupter, to sense when window  36  is near the substrate. For example, the optical interrupter could be mounted at a fixed point opposite carrier head  80 . A flag  162  is attached to the periphery of the platen. The point of attachment and length of flag  162  is selected so that it interrupts the optical signal of sensor  160  from a time shortly before window  36  sweeps beneath carrier head  80  to a time shortly thereafter. The output signal from detector  46  may be measured and stored while the optical signal of sensor  160  is interrupted. 
     In operation, CMP apparatus  20  uses reflectometer  40  to determine the amount of material removed from the surface of the substrate, or to determine when the surface has become planarized. A general purpose programmable digital computer  48  may be connected to laser  44 , detector  46  and sensor  160 . Computer  48  may be programmed to activate the laser when the substrate generally overlies the window, to store intensity measurements from the detector, to display the intensity measurements on an output device  49 , to store the intensity measurement, to sort the intensity measurements into radial ranges, and to detect the polishing endpoint. 
     Referring to FIG. 3, a substrate  10  includes a silicon wafer  12  and an overlying metal layer  16  disposed over an oxide or nitride layer  14 . The metal may be copper, tungsten, aluminum, among others. As different portions of the substrate with different reflectivities are polished, the signal output from the detector  46  varies with time. Particularly, when the metal layer  16  has been polished away to expose the oxide or nitride layer  14 , the reflectivity of the substrate drops. The time varying output of detector  46  may be referred to as an in-situ reflectance measurement trace (or more simply, a reflectance trace). As discussed below, this reflectance trace may be used to determine the end-point of the metal layer polishing operation. 
     Referring to FIGS.  4  and  5 A- 5 E, a measured reflectance trace with a transient intensity waveform  90  generated by polishing a metal-coated wafer is shown. The intensity waveform  90  is generated over a relatively long time scale (measured in seconds). Characteristic features of the waveform include top level plateau  97 , each of which is surrounded by left and right intermediate plateau  98 . One cycle of the waveform  90  includes left and right intermediate level plateau  98 , one of the top level plateau  97 , and a background level  94 . 
     The intermediate plateau  98  represent reflections from the retaining ring  84 , while the top level plateau  97  represent reflections from the substrate  10 . The background level represents scattered reflections from the window and slurry. The reflection from retaining ring  84  is higher than background level. As the substrate  10  is polished and the metal layer  16  is removed to expose the underlying layer  14 , the end-point waveform  90  drops toward or below the level of the intermediate plateau  98 . 
     Referring to FIGS.  4  and  5 A- 5 E, the large scale structure of reflectance trace  90  can be explained by reference to the angular position of platen  24 . Initially, window  36  does not have view of the substrate (see FIG.  5 A). Consequently, laser beam  42  is not reflected and the intensity measured by detector  46  is a result of background intensity, including reflection from slurry  38  and transparent window  36 . This low intensity corresponds to the background level  94 . As platen  24  rotates, window  36  first sweeps underneath retaining ring  84  of carrier head  80  (see FIG.  5 B). The lower surface  88  of retaining ring  84  reflects a portion of laser beam  42  into detector  46 , creating an intermediate intensity measurement that corresponds to intermediate plateau  98 . As window  36  sweeps beneath substrate  10  (see FIG. 5C) a portion of laser beam  42  is reflected by the substrate. In general, the metal layer of substrate  10  will have a high reflectivity, resulting in top level plateau  97  on reflectance trace  90 . As the platen continues to rotate, window  36  passes again beneath retaining ring  84  (see FIG.  5 D). Finally, window  36  sweeps out from beneath carrier head  80  (see FIG.  5 E), and the detector measures a low intensity that corresponds to the background  94 . 
     Computer  48  of CMP apparatus  20  may use the reflectance trace generated by reflectometer  40  to determine the end-point of the metal layer polishing operation. Each measurement may be performed at a plurality of radial positions. In addition, computer  48  may use the intensity measurements to determine the flatness of the substrate and the polishing uniformity for CMP tool and process qualification as explained below. 
     Referring now to FIG. 6, an end-point determining process is shown. First, several polishing parameters that will be used during the end-point determination are stored in the memory of computer  48  (step  101 ). The polishing parameters of interest include the platen rotation rate and the carrier head sweep profile. 
     A metal layer on a surface of the substrate  12  is polished (step  102 ) by bringing the surface of the substrate into contact with the polishing pad  30  (FIG.  2 ). The polishing pad  30  is rotated, causing relative motion between the substrate and the polishing pad. 
     Transient intensity data is monitored and collected for a plurality of sampling zones (step  104 ). This is done by directing a light beam generated by the reflectometer  40  through the window. The motion of the polishing pad  30  relative to the substrate  12  causes the light beam to move in a path across the substrate surface. Light beam reflections from the substrate  10  and the retaining ring  84  are detected by a sensor, which generates reflection data associated with the light beam reflections. 
     The transient intensity data is displayed on a monitor (step  106 ) for an operator to monitor the progress of the polishing operation. A pattern recognizer is applied to the transient intensity data to detect signal changes (step  108 ). The pattern recognizer may simply be a threshold detector which checks whether the intensity data has fallen below a predetermined threshold. Alternatively, in another embodiment, a window logic can be applied to the data to detect a sequence of signal changes. Three types of window logic are used to detect local maxima and minima: a window logic with a downwardly cusp to detect a downward trend in the reflection data; a window logic with an upwardly cusp to detect an upward trend in the reflection data; and a window logic with a substantially flat line to detect that the reflection data is relatively static. The signal changes may be averaged. More discussion of pattern recognition algorithms for endpoint detection may be found in above mentioned U.S. patent application Ser. No. 08/689,930. 
     The output of the pattern recognizer is a stop signal which, along with additional feedback data, is provided to a polisher controller (step  110 ). The polisher controller uses the feedback data to adjust various variables and parameters to minimize erosion and dishing of the surface layer. For instance, the polishing pressure, polishing speed, chemistry, and slurry composition may be deployed to optimize the overall polishing performance and/or polishing quality. The stop signal causes the polisher controller to stop the current metal layer polishing operation (step  112 ). 
     Concurrent with steps  106 - 112 , the process of FIG. 6 stores the transient intensity data onto a data storage device, e.g., a computer disk (step  114 ) for subsequent processing. In brief, the intensity for each sampling zone is determined (step  116 ), the radial position of each sampling zone is calculated (step  118 ), and the intensity measurements are sorted into radial ranges (step  150 ). The sorted intensity measurements are used to measure the polishing uniformity and removal rates at different radial ranges of the substrate (step  152 ). Each of these steps will be discussed in greater detail below. 
     Generally, the reflected intensity changes during polishing for different radial positions on the substrate. The metal layer may be removed at different rates for different portions of the substrate. For instance, the metal layer near the center of the substrate may be removed last, while the metal layer near the perimeter or edge of the substrate may be removed first, or vice versa. The reflection data from the entire wafer is captured at a relatively fine time scale in the order of milliseconds and is available for experimentation to improve the deposition process. By analyzing the recorded data, the process can be changed to make it faster, shorter or smoother. As can be appreciated, the stored data is useful for process research and development to optimize the process performance. 
     Referring to FIGS. 7A and 7B, the combined rotation of the platen and the linear sweep of the carrier head causes window  36  (and thus laser beam  42 ) to sweep across the bottom surface of carrier head  80  and substrate  10  in a sweep path  120 . As the laser beam sweeps across the substrate, reflectometer  40  integrates the measured intensity over a sampling period, T sample , to generate a series of individual intensity measurements I a , I b , . . . I j . The sample rate F (the rate at which intensity measurements are generated) of reflectometer  40  is given by F=1/T sample . Reflectometer  40  may have a sample rate between about 10 and 400 Hertz (Hz), corresponding to a sampling period between about 2.5 and 100 milliseconds. Specifically, reflectometer  40  may have a sampling rate of about 40 Hz and a sampling period of about 25 milliseconds. 
     Thus, each time that laser  44  is activated, reflectometer  40  measures the intensity from a plurality of sampling zones  122   a - 122   j . Each sampling zone corresponds to the area of the substrate over which the laser beam sweeps during a corresponding sampling period. In summary, in step  106 , reflectometer  40  generates a series of intensity measurements Ia, Ib, . . . Ij corresponding to sampling zones  122   a ,  122   b , . . . ,  122   j.    
     Although FIG. 7A illustrates ten sampling zones, there could be more or fewer zones, depending on the platen rotation rate and the sampling rate. Specifically, a lower sampling rate will result in fewer, wider sampling zones, whereas a higher sampling rate will result in a greater number of narrower sampling zones. Similarly, a lower rotation rate will result in a larger number of narrower sampling zones, whereas a higher rotation rate will result in a lower number of wider sampling zones. In addition, multiple detectors could be used to provide more sampling zones. 
     As shown in FIG. 7B, the intensity measurements Ia and Ij for sampling zones  122   a  and  122   j , respectively, are low because window  36  does not have a view of the carrier head, and consequently laser beam  42  is not reflected. Sampling zones  122   b  and  122   i  are located beneath retaining ring  84 , and therefore intensity measurements Ib and Ii will be of intermediate intensity. Sampling zones  122   c ,  122   d , . . .  122   h  are located beneath the substrate, and consequently generate relatively large intensity measurements I c , I d , . . . I h  at a variety of different radial positions across the substrate. 
     FIG. 12 is an overlay of several transient signal graphs  300 - 320 . Each of the transient signal graphs  300 - 320  represents intensity data over an interval associated with a sweep of the window beneath the carrier head. For instance, the graph  300  shows the end-point data between about 1.7 seconds to about 2.7 seconds, and the graph  320  shows the end-point data between about 350.8 seconds and about 351.8 seconds. Of course, the transient signal graphs can be stored in computer  48  for later reference. 
     FIG. 12 shows how the endpoint reflected intensity signal changes during the polishing operation. Initially, in period  300 , the metal layer on the surface of the substrate  10  is jagged. The metal layer  16  has some initial topography because of the topology of the underlying patterned layer  14 . Due to this topography, the light beam scatters when it impinges the metal layer. As the polishing operation progresses, the metal layer becomes more planar and the reflectivity of the polished metal layer increases during periods  302 - 308 . As such, the signal strength steadily increases to a stable level. From period  310 - 320 , as the metal layer  16  is increasingly cleared to expose the oxide layer  14 , the overall signal strength declines until the polishing operation is completed. Thus, in period  320 , only a small trace of metal remains in the center of the substrate  10 . 
     When entire surface of the substrate is covered with a metal layer, such as copper, the reflection from the substrate  10  has a square profile. As the metal layer is removed from the edge of the substrate  10 , the profile of the reflection from the substrate takes on a trapezoidal shape. Eventually, when the metal layer is nearly removed by the polishing operation, the profile of the reflection from the substrate  10  takes on a triangular shape. 
     The transient signal graphs  300 - 320  can be viewed by the operator on the display  49  either during or after the polishing operation. The operator can use the displayed transient signal graphs for a variety of diagnostic and process control decisions (which may be applicable to both reflectivity measurements in metal polishing and interference measurements in oxide polishing). The transient signal graphs can be used to select process parameters in order to optimize polishing uniformity. For example, a test wafer can be polished when initially selecting process parameters, such as the plate rotation rate, carrier head pressure, carrier head rotation rate, carrier head sweep profile, and slurry composition. High reflectivity areas represent regions where metal remains on the substrate, and low reflectivity area represent regions where metal has been removed from the substrate. A noisy transient signal graph indicates that the metal has not been evenly removed from the substrate, whereas a relatively flat transient signal graph indicates uniform polishing. Consequently, the operator can draw immediate conclusions, without resorting to measuring the substrate layer thickness with a metrology tool, regarding the effectiveness of the selected process parameters. The operator can then adjust the polishing parameters, polish another test wafer, and determine whether the new polishing parameters have improved the polishing uniformity. 
     An operator may also examine the transient signal graphs to determine whether the substrate has been polished to planarity, and whether polishing should be halted. Furthermore, if an operator notes during polishing of an actual device wafer that a portion of the substrate is being polished too slowly or too quickly, the process parameters can be changed while polishing is in progress to adjust the polishing rate profile. 
     The transient signal graphs can also be used as a measure of process repeatability. For example, if the transient signal graphs depart significantly from their expected shapes, this indicates that there is some problem in the polishing machine or process. 
     In addition, the transient signal graphs can be used to “qualify” a process. Specifically, when the polishing machine receives a new set of consumables, e.g., if the polishing pad or slurry is replaced, the operator may wish to verify that the polishing uniformity has not been affected. An operator can compare the transient signal graphs for the substrates polished before and after the change in consumables to determine whether the polishing uniformity has been affected. 
     Turning now to FIG. 8, in step  108  the radial positions R a , R b , . . . R j  of the corresponding sampling zones  122   a ,  122   b , . . .  122   j  are determined. One way to determine the radial position of a sampling zone is to calculate the position of the laser beneath the substrate based on the measurement time T measure  and the platen rotation rate and carrier head sweep profile. Unfortunately, the actual platen rotation rate and carrier head sweep profile may not precisely match the polishing parameters. Therefore, a preferred method  130  of determining the radial positions of the sampling zones is shown in FIG.  9 A. First, the time T sym  at which laser beam  42  passes beneath a mid-line  124  (see FIG. 5C) of the substrate is determined (step  132 ). Then the radial positions of the sampling zones are determined from the time difference between the measurement time Tmeasure and the symmetric time T sym  (step  134 ). 
     One method of determining the symmetry time T sym  is to average the times of the first and last large intensity measurements from each sweep, as these intensity measurements should correspond to the substrate edge. However, this results in some uncertainty in T sym  because the position of the sampling zones beneath the substrate are not known. 
     Referring to FIG. 9B, in order to compute the symmetric time T sym  in step  132 , computer  48  determines the first and last large intensity measurements from sweep path  120 , i.e., intensity measurements I c  and I h , and stores the corresponding measurement times T lead  and T trail . These lead and trail times T lead  and T trail  are accumulated on each sweep to generate a series of lead times T lead1 , T lead2 , . . . T leadN  and trail times T trail1 , T trail2 , . . . T trailN . Computer  48  stores lead times T lead1 , T lead2 , . . . T leadN  and the associate number of platen rotations 1, 2, . . . N for each leading spike  96 . Similarly, computer  48  stores the trail times T trail1 , T trail 2 , . . . T trailN  and the associated number of rotations 1, 2, . . . N of each trailing spike  98 . Assuming that platen  24  rotates at a substantially constant rate, the times T lead1 , T lead2 , . . . T leadN  form a substantially linear increasing function (shown by line  136 ). Similarly, the times T trail1 , T trail2 , . . . T trailN  also form a substantially linear increasing function (shown by line  137 ). Computer  48  performs two least square fits to generate two linear functions T lead(n)  and T trail(n)  as follows: 
     
       
           T   lead(n)   =a   1 +( a   2   *n ) 
       
     
     
       
           T   trail(n)   =a   3 +( a   4   *n ) 
       
     
     where n is the number of platen rotations and a 1 , a 2 , a 3  and a 4  are fitting coefficients calculated during the least square fit. Once the fitting coefficients have been calculated, the symmetry time T sym  at which laser beam  42  crosses mid-line  124  (shown by phantom line  138 ) may be calculated as follows:          T   sym     =       (           a   1     +     a   3       2     +         a   2     +     a   4       2       )        n                     
     By using a least square fit over several platen rotations to calculate the symmetry time T sym , uncertainty caused by the differences in the relative position of the sampling zone beneath the retaining ring are substantially reduced, thereby significantly reducing uncertainty in the symmetry time T sym . 
     Once computer  48  has calculated the time Tsym at which laser beam  42  crosses midline  124 , the radial distance R a , R b , . . . R j  of each sampling zone  122   a ,  122   b , . . .  122   j  from the center  126  of the substrate are calculated in step  132 . Referring to FIG. 10, the radial position may be calculated as follows: 
       R={square root over (d 2 +L 2 −2dL cosθ)}   
     where d is the distance between the center of the polishing pad and the center of window  36 , L is the distance from the center of the polishing pad to the center of substrate  10 , and θ is the angular position of the window. The angular position θ of the window may be calculated as follows: 
     
       
         θ= f   platen ·2π( T   measure   −T   sym ) 
       
     
     where f platen  is the rotational rate of the platen (in rpm). Assuming that the carrier head moves in a sinusoidal pattern, the linear position L of the carrier head may be calculated as follows: 
     
       
           L=L   O   +A ·(ω· T   measure ) 
       
     
     where ω is the sweep frequency, A is the amplitude of the sweep, and L O  is the center position of the carrier sweep. 
     In another embodiment, position sensor  160  could be used to calculate the time Tsym when the window crosses midline  124 . Assuming that sensor  160  is positioned opposite carrier head  80 , flag  162  would be positioned symmetrically across from transparent window  36 . The computer  48  stores both the trigger time T start  when the flag interrupts optical beam of the sensor, and the trigger time T end  when the flag clears the optical beam. The time T sym  may be calculated as the average of T star t and T end . In yet another embodiment, the platen and carrier head positions could be determined at each sample time T a , T b , . . . T h , from optical encoders connected to the platen drive motor and radial drive motor, respectively. 
     Once the radial positions R a , R b , . . . R m  of the sampling zones have been calculated, some of the intensity measurement may be disregarded. If the radial position R of a sampling zone is greater than the radius of the substrate, then the intensity measurement for that sampling zone includes mostly radiation reflected by the retaining ring or background reflection from the window or slurry. Therefore, the intensity measurements for any sampling zone that is mostly beneath the retaining ring is ignored. This ensures that spurious intensity measurements are not used in the calculation of the thin filn layer reflected intensity. 
     After several sweeps of laser beam  42  beneath the substrate, computer  48  accumulates a set of intensity measurements I 1 , I 2 , . . . I N , each associated with a measurement time T 1 , T 2 , . . . T N , and a radial position R 1 , R 2 , . . . R N . 
     Referring to FIG. 11, as the intensity, time, and radial position measurements are accumulated in steps  106  and  108 , the time and intensity measurements are sorted into bins in a data structure  140  in step  110 . Each bin is associated with a radial range of sampling zones. For example, intensity measurements for sampling zones located up to 20 mm from the center of the substrate may be placed in a first bin  142  (see FIG. 13A) which is discussed below, intensity measurements made for sampling zones located between 20 and 30 mm from the center of the substrate may be placed in a second bin  144  (see FIG.  13 B), intensity measurements made for sampling zones located between 30 and 40 mm from the center of the substrate may be placed in a third bin  146  (see FIG.  13 C), and so on. The exact number of bins and the radial ranges of the bins depend upon the information that the user desires to extract. In general, the radial range of each bin may be selected so that a sufficient number of intensity measurements are accumulated in the bin to provide visually meaningful information. 
     The calculations discussed above are performed for each bin, thereby providing reflected intensity measurements at a plurality of radial positions across the surface of the substrate. Graphs of the initial and final reflected intensity of the thin film layer as a function of radius are shown in FIG. 12 discussed above as well as in FIGS. 13A-13H. 
     Turning now to FIGS. 13A-13H, a number of traces which display how reflected intensity changes during polishing for different radial positions on the substrate  10  are shown. The charts of FIGS. 13A-13H illustrate that the metal layer is removed at different rates for different portions of the substrate. Generally, FIGS. 13A-13H show that the metal layer near the center of the substrate is removed last, while the metal layer near the perimeter or edge of the substrate is cleared first. For example, FIG. 13A shows that the metal layer within a radius range of 0-20 mm is removed at about 330 seconds. FIG. 13B shows that the metal layer within a radius range of 20-30 mm is removed at about 325 seconds. FIG. 13C shows that the metal layer within a radius range of 30-40mm is removed at about 318 seconds. FIG. 13D shows that the metal layer within a radius range of 40-50 mm is removed at about 310 seconds. FIG. 13E shows that the metal layer within a radius range of 50-60 mm is removed at about 295 seconds. FIG. 13F shows that the metal layer within a radius range of 60-70 mm is removed at about 290 seconds. FIG. 13G shows that the metal layer within a radius range of 70-80mm is removed at about 290 seconds; and FIG. 13H shows that the metal layer within a radius range of 80-90mm is removed as early as about 260 seconds. 
     As shown therein, the reflectance trace for several of the radial ranges exhibit two intensity levels (shown by lines  160  and  162 ). The distance between the two intensity levels increases with substrate radius. Without being limited to any particular theory, the two intensity levels may be caused by non-symmetric distribution of the slurry or the product of the reaction of the slurry and the metal layer on the substrate. Specifically, on each sweep of the laser beam across the substrate, two data points are usually entered in a bin: one data point which is closer to the leading edge of the substrate and one data point which is closer to the trailing edge of the substrate. However, due to non-symmetric distribution of the slurry and the reaction products beneath the substrate, the laser beam may be more attenuated when passing through slurry layer adjacent different regions of the substrate. Thus, the reflectance traces might also be used as a measure of the uniformity of slurry distribution beneath the substrate. 
     In another implementation, an operator might decide to use only a single bin. In this case, all of the intensity measurements for the specified radial range are used to determine a single intensity trace, which is used for determination of a polishing endpoint in the conventional fashion. The operator can specify this radial range based on examination of the transient signal graphs. For example, if the transient signal graphs show that the center of the substrate is the last portion to be polished, then the operator can select a radial range around the substrate center to ensure that the endpoint is not triggered until all of the metal has been polished away. 
     The reflection intensity changes during polishing are thus captured for different radial positions on the substrate. The high resolution data acquisition allows a precise time control of each process step in a multi-step operation. A wealth of parameters such as uniformity of the entire wafer and removal rate for different radial portions of the wafer are captured. The acquired high resolution data can be processed on-line or off-line to adjust various variables and parameters to minimize erosion and dishing of the surface layer. If the data is processed in real-time, the real-time feedback data allows a tighter closed-loop control with the process parameters. Further, the reflection data is available for process engineers to experiment with their processing parameters to improve the polishing process. 
     The present invention has been described in terms of a preferred embodiment. The invention, however, is not limited to the embodiment depicted and described. Rather, the scope of the invention is defined by the appended claims.