Abstract:
An apparatus, as well as a method, brings a surface of a substrate into contact with a polishing pad that has a window, causes relative motion between the substrate and the polishing pad, and directs a light beam through the window so that the motion of the polishing pad relative to the substrate causes the light beam to move in a path across the substrate. An extreme intensity measurement is derived from a plurality of intensity measurements made as the light beam moves across the substrate. The beam sweeps across the substrate a plurality of times to generate a plurality of extreme intensity measurements, and a polishing endpoint is detected based on the plurality of extreme intensity measurements.

Description:
BACKGROUND  
         [0001]    The present invention relates generally to chemical mechanical polishing of substrates, and more particularly to methods and apparatus for detecting an end-point during a chemical mechanical polishing operation.  
           [0002]    An integrated circuit is typically formed on a substrate by the sequential deposition of conductive, semiconductive or insulative layers on a silicon wafer. One fabrication step involves depositing a filler layer over a patterned stop layer, and planarizing the filler layer until the stop layer is exposed. For example, a conductive filler layer may be deposited on a patterned insulative stop layer to fill the trenches or holes in the stop layer. After planarization, the portions of the conductive layer remaining between the raised pattern of the insulative layer form vias, plugs and lines that provide conductive paths between thin film circuits on the substrate.  
           [0003]    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 disk pad or belt 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.  
           [0004]    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.  
           [0005]    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.  
           [0006]    More recently, in-situ optical monitoring of the substrate has been performed, e.g., with an interferometer or reflectometer, in order to detect the polishing endpoint. For example, when polishing a metal layer to expose an underlying insulative or dielectric layer, the reflectivity of the substrate will drop abruptly when the metal layer is removed. This drop can be detected to signal the polishing endpoint. Unfortunately, even when there is a sharp change in reflectivity, it may be difficult to determine the proper endpoint.  
         SUMMARY  
         [0007]    In one aspect, the invention is directed to an endpoint detection method for chemical mechanical polishing. In the method, a surface of a substrate is brought into contact with a polishing pad, and relative motion between the substrate and the polishing pad is created. A light beam is directed to contact the surface of the substrate, and the light beam is moved in a path across the substrate surface. An intensity signal produced by the light beam reflecting off the substrate is monitored, and a plurality of intensity measurements are extracted from the intensity signal as the light beam moves across the substrate. A first extreme intensity measurement is derived from the plurality of intensity measurements. The steps are iterated for a plurality of sweeps of the light beam across the substrate to generate a first plurality of extreme intensity measurements, and a polishing endpoint is detected based on the first plurality of extreme intensity measurements.  
           [0008]    Implementations of the invention may include the following features. The first extreme intensity measurement is a maximum or minimum intensity measurement from the plurality of intensity measurements. A second extreme intensity measurement may be selected from the plurality of intensity measurements. The minimum intensity measurement for each iteration may be subtracted from the maximum intensity measurement from that iteration to create a plurality of differential intensity measurement. Detecting a polishing endpoint may include determining if criteria associated with either of the first or second plurality of extreme intensity measurements are satisfied. Alternatively, detecting a polishing endpoint may include determining if criteria associated with both the first and second plurality of extreme intensity measurements are satisfied. The substrate may include a filler layer, e.g., a metal layer, disposed over a stop layer, e.g., a dielectric layer, with the filler layer abutting the polishing pad. The polishing endpoint may indicate that the stop layer is at least partially exposed or that the stop layer is substantially exposed. An average intensity may be calculated from the plurality of intensity measurements for each iteration, and the polishing endpoint may be based on the average intensity measurements. The polishing pad may include a window, the light beam may be directed through the window, and the motion of the polishing pad relative to the substrate may cause the light beam to move across the substrate surface. A radial position for each intensity measurement may be determined. The intensity measurements may be divided into a plurality of radial ranges according to the radial positions. An extreme intensity measurement may be selected from the intensity measurements in each of the plurality of radial ranges. Polishing may be stopped at the polishing endpoint, or a polishing parameter, such as a polishing consumable, e.g., a slurry, may be changed at the polishing endpoint.  
           [0009]    Advantages of the invention include one or more of the following. A wider range of endpoint detection algorithms are available, making the optical monitoring system useful in a wider range of polishing procedures. The endpoint detection procedure is more robust and less likely to fail. Endpoint detection during metal polishing is improved. The polishing pressure, polishing speed, chemistry, and slurry composition may be altered when an underlying oxide layer is first exposed, and polishing may be stopped more precisely when the entire oxide and barrier layer have been removed. 
       
    
    
       [0010]    Other features and advantages of the invention will become apparent from the following description, including the drawings and claims.  
       BRIEF DESCRIPTION OF THE DRAWINGS  
       [0011]    [0011]FIG. 1 is an exploded perspective view of a chemical mechanical polishing apparatus.  
         [0012]    [0012]FIG. 2 is a side view of a chemical mechanical polishing apparatus including an optical reflectometer.  
         [0013]    [0013]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.  
         [0014]    [0014]FIG. 4 is a schematic view illustrating the path of a laser beneath the carrier head.  
         [0015]    [0015]FIG. 5 is graph showing intensity measurements from the optical monitoring system in arbitrary intensity units. FIGS.  6 A- 6 D are graphs showing a reflected intensity trace of the metal layer as a function of distance using the average, minimum, maximum, and differential intensity measurements.  
         [0016]    [0016]FIG. 7 is a schematic view illustrating the radial positions of the intensity measurements on the substrate.  
         [0017]    [0017]FIG. 8A is a flow chart of a method of determining the radial position of a sampling zone.  
         [0018]    [0018]FIG. 8B 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.  
         [0019]    [0019]FIG. 9 is a schematic view illustrating the calculation of the radial positions of the intensity measurements.  
         [0020]    [0020]FIG. 10 is a schematic diagram of a data structure to store intensity measurements. 
     
    
     DETAILED DESCRIPTION  
       [0021]    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. Patent 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  transfers the substrates between the carrier heads and a loading apparatus.  
         [0022]    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 or a fixed-abrasive pad with embedded abrasive particles. The final polishing station may include a relatively soft pad. 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.  
         [0023]    A two-layer 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, Delaware (IC-1000 and SUBA-4 are product names of Rodel, Inc.).  
         [0024]    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 .  
         [0025]    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. In addition, each carrier head  80  independently laterally oscillates in a radial slot  72  formed in carousel support plate  66 .  
         [0026]    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.  
         [0027]    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 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. Pat. application Ser. No. 08/861,260, filed May 21, 1997, the entire disclosure of which is incorporated by reference.  
         [0028]    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).  
         [0029]    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.  
         [0030]    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. Pat. application Ser. No. 08/689,930, filed Aug. 26, 1996, 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.  
         [0031]    An optical monitoring system  40 , which can function as a reflectometer or interferometer, is secured to platen  24  generally beneath hole  26  and rotates with the platen. The optical monitoring system 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 a laser and the light beam  42  may be a collimated laser beam. The light laser beam  42  can be 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 .  
         [0032]    The 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  while window  36  sweeps beneath substrate  10 .  
         [0033]    In operation, CMP apparatus  20  uses optical monitoring system  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 apply the endpoint detection logic to the measured signals to detect the polishing endpoint.  
         [0034]    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.  
         [0035]    Generally, the reflected intensity undergoes different changes during polishing for different radial positions on the substrate. This is because 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. However, with the optical monitoring system, the reflection data from the entire wafer is captured at a relatively fine time scale in the order of milliseconds and is available for determination of the polishing endpoint.  
         [0036]    Referring to FIG. 4, 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 . Referring to FIG. 5, as the laser beam sweeps across the substrate, optical monitoring system  40  generates a series of intensity measurements I 1 , I 2 , I 3 , . . . , I N  (the number N can differ from sweep to sweep). The sample rate F (the rate at which intensity measurements are generated) of optical monitoring system  40  may be about 500 to 2000 Hertz (Hz), or even higher, corresponding to a sampling period between about 0.5 and 2 milliseconds.  
         [0037]    Each time the window sweeps beneath the substrate, the  35  computer  48  extracts a value from the series of intensity measurements I 1 , I 2 , I 3 , . . . , I N . For example, the series of intensity measurements can be averaged to generate a mean intensity I MEAN . Alternately, the computer can extract the minimum intensity I MIN  from the series, or the maximum intensity I MAX . In addition, the computer can generate an intensity difference I DIF  equal to the difference between the maximum and minimum intensities, i.e., I MAX −I MIN .  
         [0038]    A series of values extracted by computer  48  for a series of sweeps can be stored in memory or non-volatile storage. Referring to FIGS.  6 A-  6 D, this series of extracted values (with one extracted value per sweep) can be assembled and displayed as a function of measurement time to provide the time-varying trace of the reflectivity of the substrate. This time-varying trace may also be filtered to remove noise. FIG. 6A shows a reflectivity trace generated from the mean intensity I MEAN  of each sweep, FIG. 6B shows a reflectivity trace generated from the maximum intensity I MAX  of each sweep, FIG. 6C shows a reflectivity trace generated from the minimum intensities I MIN  of each sweep, and FIG. 6D shows a reflectivity trace generated from the intensity difference I DIF  of each sweep.  
         [0039]    The overall shapes of the minimum, maximum and average intensity traces may be explained as follows. Initially, 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. As the bulk of the metal layer is removed, the intensity remains relatively stable. Once the oxide layer begins to be exposed, the overall signal strength declines until the polishing operation is completed. Although the overall shapes of the minimum, maximum and average intensity traces are similar, the different traces have different shapes because different procedures have been used to extract the data points of the traces from the underlying intensity measurements.  
         [0040]    The maximum intensity trace, minimum intensity trace and differential intensity trace are particularly useful in the endpoint analysis during metal polishing. Specifically, the minimum intensity trace will tend to begin to drop as soon as the oxide layer is first exposed. In contrast, the maximum intensity trace will tend to begin to drop only after the metal layer is almost entirely removed and the oxide layer is entirely exposed, i.e., after the minimum intensity trace has begun to drop. Thus, the minimum intensity trace can be used for detection of the initial clearing of a spot on the oxide, and the maximum intensity trace can be used for detection of complete metal removal. The average intensity trace will fall somewhere between the minimum and maximum intensity traces. The differential intensity trace provides a measure of the non-uniformity of the substrate, since it will be largest when the metal has been removed to expose some, but not all, of the underlying oxide.  
         [0041]    Given the four intensity traces, a wide variety of endpoint detection algorithms can be implemented. Separate endpoint criteria (e.g., based on local minima or maxima, slope, or threshold values) can be created for each type of trace. Then the endpoint conditions for the various traces can be combined with Boolean logic. For example, polishing could be stopped when the endpoint conditions for either the maximum intensity trace or the differential trace have been met. As another example, polishing could be stopped only when the endpoint conditions for both the minimum intensity trace and the average intensity trace have been met. As noted, any combination of endpoint criteria for two or more of the traces is possible.  
         [0042]    The different endpoint traces may also be used to trigger different polishing events. The minimum intensity trace may be used to trigger a change in polishing parameters. For example, the polishing pressure, polishing speed, chemistry, and slurry composition may be altered when the underlying oxide layer is first exposed. Specifically, the system may change from a high-selectivity to a low-selectivity slurry in order to avoid dishing. Polishing may be halted based on the detection of the endpoint in the maximum intensity signal, since this will occur only once the metal has been entirely removed.  
         [0043]    The average, minimum, maximum and differential intensity traces may also be created for a plurality of radial ranges on the substrate. The generation of intensity traces for a plurality of radial ranges is discussed in U.S. application Ser. No. 09,184,767, filed Nov. 2, 1998, the entirety of which is incorporated by reference. As previously noted, 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 . Turning now to FIG. 7, the radial positions R 1 , R 2 , . . . , R n  of the corresponding intensity measurements I 1 , I 2 , . . . , I n  can be determined. One way to determine the radial position of an intensity measurement is to calculate the position of the laser beneath the substrate based on the measurement time, 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 intensity measurements is shown in FIG. 8A. 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 intensity measurements are determined from the time difference between the measurement time T measure  and the symmetric time T sym  (step  134 ).  
         [0044]    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 positions of the intensity measurements on the substrate are not known.  
         [0045]    Referring to FIG. 8B, 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 , 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 trail , 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 intensity measurement  96 . Similarly, computer  48  stores the trail times T trail1 , T trail2 , . . . T trailN  and the associated number of rotations  1 ,  2 , . . . N of each trailing measurement. Assuming that platen  24  rotates at a substantially constant rate, the times T lead 1 , T lead 2 , . . . 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)   
         [0046]    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.  
         [0047]    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                             
 
         [0048]    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 is substantially reduced, thereby significantly reducing uncertainty in the symmetry time T sym .  
         [0049]    Once computer  48  has calculated the time T sym  at which laser beam  42  crosses midline  124 , the radial distance R 1 , R 2 , . . . R N  of each intensity measurement 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} 
       {square root over (d  2 +L 2 − 2 dLcosθ)} 
     
         [0050]    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= ƒplaten · 2 π(T measure −T sym ) 
         [0051]    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   0 + A·cos(ω·   T   measure ) 
         [0052]    where ω is the sweep frequency, A is the amplitude of the sweep, and L O  is the center position of the carrier sweep.  
         [0053]    In another embodiment, position sensor  160  could be used to calculate the time T sym  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 an 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 start  and T end . In yet another embodiment, the platen and carrier head positions could be determined at each measurement time from optical encoders connected to the platen drive motor and radial drive motor, respectively.  
         [0054]    Once the radial positions R 1 , R 2 , . . . R N  of the intensity measurements have been calculated, some of the intensity measurement may be disregarded. If the radial position R of an intensity measurement is greater than the radius of the substrate, then that intensity measurement includes radiation reflected by the retaining ring or background reflection from the window or slurry. The intensity measurements made beneath the retaining ring can be ignored. This ensures that spurious intensity measurements are not used in the calculation of the thin film layer reflected intensity.  
         [0055]    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, the time and intensity measurements are sorted into bins in a data structure  140 . Each bin is associated with a radial range on the substrate. For example, intensity measurements made up to  20  mm from the center of the substrate may be placed in a first bin  142 , intensity measurements made between  20  and  30  mm from the center of the substrate may be placed in a second bin  144 , intensity measurements made between  30  and  40  mm from the center of the substrate may be placed in a third bin  146 , 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.  
         [0056]    Once the intensity measurements have been sorted into radial ranges, the calculations discussed above to determine the average, minimum, maximum or difference in intensity are performed for each bin, thereby providing four types of intensity traces for each radial range across the surface of the substrate. Separate endpoint criteria (e.g., based on local minima or maxima, slope, or threshold values) can be created for each type of intensity trace in each radial range. The endpoint conditions for the various traces and radial ranges can be combined with Boolean logic. For example, an endpoint may be triggered if the conditions for any of several radial ranges are met, or the endpoint may be triggered only if the conditions for multiple radial ranges are met. Thus, a wide variety of endpoint detection algorithms can be implemented.  
         [0057]    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.