Abstract:
A method of chemical mechanical polishing a substrate includes polishing a layer on the substrate at a polishing station, monitoring the layer during polishing at the polishing station with an in-situ monitoring system, the in-situ monitoring system monitoring an elongated region and generating a measured signal, computing an angle between a primary axis of the elongated region and a tangent to an edge of the substrate, modifying the measured signal based on the angle to generate a modified signal, and at least one of detecting a polishing endpoint or modifying a polishing parameter based on the modified signal.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims priority to U.S. Provisional Application Ser. No. 61/724,218, filed Nov. 8, 2012, the entire disclosure of which is incorporated by reference. 
    
    
     TECHNICAL FIELD 
     The present disclosure relates to in-situ monitoring of an elongated region during chemical mechanical polishing of a substrate. 
     BACKGROUND 
     An integrated circuit is typically formed on a substrate (e.g. a semiconductor wafer) by the sequential deposition of conductive, semiconductive or insulative layers on a silicon wafer, and by the subsequent processing of the layers. 
     One fabrication step involves depositing a filler layer over a non-planar surface, and planarizing the filler layer until the non-planar surface is exposed. For example, a conductive filler layer can be deposited on a patterned insulative layer to fill the trenches or holes in the insulative layer. The filler layer is then polished until the raised pattern of the insulative layer is exposed. 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. In addition, planarization may be used to planarize the substrate surface for lithography. 
     Chemical mechanical polishing (CMP) is one accepted method of planarization. This planarization method typically requires that the substrate be mounted on a carrier head. The exposed surface of the substrate is placed against a rotating polishing pad. The carrier head provides a controllable load on the substrate to push it against the polishing pad. A polishing liquid, such as slurry with abrasive particles, is supplied to the surface of the polishing pad. 
     During semiconductor processing, it may be important to determine one or more characteristics of the substrate or layers on the substrate. For example, it may be important to know the thickness of a conductive layer during a CMP process, so that the process may be terminated at the correct time. A number of methods may be used to determine substrate characteristics. For example, optical sensors may be used for in-situ monitoring of a substrate during chemical mechanical polishing. Alternately (or in addition), an eddy current sensing system may be used to induce eddy currents in a conductive region on the substrate to determine parameters such as the local thickness of the conductive region. 
     SUMMARY 
     An in-situ monitoring system that monitors an elongated region can provide improved signal strength at the substrate edge. However, if the relative angle between the region and the substrate edge changes over time, e.g., due to sweep of the carrier head, significant noise can be introduced into the portion of the signal generated by the monitoring system that corresponds to the substrate edge. By calculating the angle and feeding the data into a controller, this noise can be significantly reduced. 
     In one aspect, a method of chemical mechanical polishing a substrate includes polishing a layer on the substrate at a polishing station, monitoring the layer during polishing at the polishing station with an in-situ monitoring system, the in-situ monitoring system monitoring an elongated region and generating a measured signal, computing an angle between a primary axis of the elongated region and a tangent to an edge of the substrate, modifying the measured signal based on the angle to generate a modified signal, and at least one of detecting a polishing endpoint or modifying a polishing parameter based on the modified signal. 
     In another aspect, a method of chemical mechanical polishing a substrate includes polishing a layer on the substrate at a polishing station, monitoring the layer during polishing at the polishing station with an in-situ monitoring system, the in-situ monitoring system including an anisotropic sensor and generating a measured signal, computing an angle between a primary axis of the anisotropic sensor and a tangent to an edge of the substrate, modifying the measured signal based on the angle to generate a modified signal, and at least one of detecting a polishing endpoint or modifying a polishing parameter based on the modified signal. 
     In another aspect, a polishing system includes a carrier to hold a substrate, a support for a polishing surface, an in-situ monitoring system having a sensor, the in-situ monitoring system configured to monitor an elongated region and generate a measured signal, a motor to generate relative motion between the sensor and the substrate, and a controller configured to receive the measured signal from the in-situ monitoring system, compute an angle between a primary axis of the elongated region and a tangent to an edge of the substrate, modify the measured signal based on the angle to generate a modified signal, and at least one of detect a polishing endpoint or modify a polishing parameter based on the modified signal. 
     In another aspect, a polishing system includes a carrier to hold a substrate, a support for a polishing surface, an in-situ monitoring system having an anisotropic sensor configured to generate a measured signal, a motor to generate relative motion between the sensor and the substrate, and a controller configured to receive the measured signal from the in-situ monitoring system, compute an angle between a primary axis of the anisotropic sensor and a tangent to an edge of the substrate, modify the measured signal based on the angle to generate a modified signal, and at least one of detect a polishing endpoint or modify a polishing parameter based on the modified signal. 
     Implementations of any of the above aspects may include one or more of the following features. The angle may be the angle at a time when the elongated region or sensor is adjacent the edge of the substrate. Edge portions of the signal may be detected. Modifying the measured signal may include compressing or decompressing the edge portions. A compression ratio of the compressing or decompressing may be a function of the angle. The function of the angle may be such that the compression increases as the angle increases. Modifying the measured signal may include multiplying the signal by a gain factor. The gain factor may be a function of the angle. The function of the angle may be such that the gain factor decreases as the angle increases. The in-situ monitoring system may be an eddy current monitoring system having an elongated core. 
     Certain implementations can include one or more of the following advantages. An in-situ monitoring system, e.g., an eddy current monitoring system, can generate a signal as a sensor scans across the substrate. Noise in a portion of the signal that corresponds to the substrate edge can be reduced. The signal can be used for endpoint control and/or closed-loop control of polishing parameters, e.g., carrier head pressure, thus providing improved within-wafer non-uniformity (WIWNU) and wafer-to-wafer non-uniformity (WTWNU). 
     The details of one or more implementations are set forth in the accompanying drawings and the description below. Other aspects, features and advantages will be apparent from the description and drawings, and from the claims. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a schematic side view, partially cross-sectional, of a chemical mechanical polishing station that includes an eddy current monitoring system. 
         FIGS. 2A and 2B  show side and perspective views of an eddy current monitoring system with three prongs. 
         FIG. 3  shows a top view of a chemical mechanical polishing station. 
         FIGS. 4A and 4B  are schematic views of a core of the eddy current monitoring system passing below an edge of a substrate. 
         FIGS. 5A and 5B  are schematic graphs of a signal from the eddy current monitoring system. 
         FIG. 6  illustrates a modification of a signal from the eddy current monitoring system. 
         FIG. 7  illustrates a time-varying sequence of characterizing values generated from the signal from the monitoring system. 
         FIG. 8  illustrates fitting a function to the time-varying sequence of characterizing values. 
     
    
    
     Like reference symbols in the various drawings indicate like elements. 
     DETAILED DESCRIPTION 
     CMP systems can use eddy current monitoring systems to detect thickness of a top metal layer on a substrate. During polishing of the top metal layer, the eddy current monitoring system can determine the thickness of different regions of the metal layer on the substrate. The thickness measurements can be used to trigger a polishing endpoint and/or to adjust processing parameters of the polishing process in real time. For example, a substrate carrier head can adjust the pressure on the backside of the substrate to increase or decrease the polishing rate of the regions of the metal layer. The polishing rate can be adjusted so that the regions of the metal layer are substantially the same thickness after polishing. The CMP system can adjust the polishing rate so that polishing of the regions of the metal layer completes at about the same time. Such profile control can be referred to as real time profile control (RTPC). 
     Some eddy current monitoring systems have an elongated core such that the monitoring system monitors an elongated region on the substrate. Such a monitoring system can provide improved signal strength at the substrate edge while maintaining high resolution at the substrate edge. In addition, an elongated region can reduce sensitivity to angular variations in thickness at the substrate edge. However, if the relative angle between the region and the substrate edge changes over time, e.g., due to sweep of the carrier head, significant noise can be introduced into the portion of the signal generated by the monitoring system that corresponds to the substrate edge. By calculating the angle and feeding the data into a controller, this noise can be significantly reduced. 
       FIG. 1  illustrates an example of a polishing apparatus  100 . The polishing apparatus  100  includes a rotatable disk-shaped platen  120  on which a polishing pad  110  is situated. The platen is operable to rotate about an axis  125 . For example, a motor  121  can turn a drive shaft  124  to rotate the platen  120 . The polishing pad  110  can be a two-layer polishing pad with an outer polishing layer  112  and a softer backing layer  114 . 
     The polishing apparatus  100  can include a port  130  to dispense polishing liquid  132 , such as slurry, onto the polishing pad  110 . The polishing apparatus can also include a polishing pad conditioner to abrade the polishing pad  110  to maintain the polishing pad  110  in a consistent abrasive state. 
     The polishing apparatus  100  includes at least one carrier head  140 . The carrier head  140  is operable to hold a substrate  10  against the polishing pad  110 . The carrier head  140  can have independent control of the polishing parameters, for example pressure, associated with each respective substrate. 
     In particular, the carrier head  140  can include a retaining ring  142  to retain the substrate  10  below a flexible membrane  144 . The carrier head  140  also includes a plurality of independently controllable pressurizable chambers defined by the membrane, e.g., three chambers  146   a - 146   c , which can apply independently controllable pressures to associated zones on the flexible membrane  144  and thus on the substrate  10 . Although only three chambers are illustrated in  FIG. 1  for ease of illustration, there could be one or two chambers, or four or more chambers, e.g., five chambers. 
     The carrier head  140  is suspended from a support structure  150 , e.g., a carousel or a track, and is connected by a drive shaft  152  to a carrier head rotation motor  154  so that the carrier head can rotate about an axis  155 . Optionally the carrier head  140  can oscillate laterally, e.g., on sliders on the carousel  150  or track; or by rotational oscillation of the carousel itself. In operation, the platen is rotated about its central axis  125 , and the carrier head is rotated about its central axis  155  and translated laterally across the top surface of the polishing pad. 
     While only one carrier head  140  is shown, more carrier heads can be provided to hold additional substrates so that the surface area of polishing pad  110  may be used efficiently. 
     The polishing apparatus also includes an in-situ monitoring system  160 . The in-situ monitoring system generates a time-varying sequence of values that depend on the thickness of a layer on the substrate. 
     The in-situ-monitoring system  160  can be an eddy current monitoring system. The eddy current monitoring system  160  includes a drive system to induce eddy currents in a metal layer on the substrate and a sensing system to detect eddy currents induced in the metal layer by the drive system. The monitoring system  160  includes a core  162  positioned in a recess  128  to rotate with the platen, at least one coil  164  wound around a portion of the core  162 , and drive and sense circuitry  166  connected by wiring  168  to the coil  164 . In some implementations, the core  162  projects above the top surface of the platen  120 , e.g., into a recess  118  in the bottom of the polishing pad  110 . 
     The drive and sense circuitry  166  is configured to apply an oscillating electric signal to the coil  164  and to measure the resulting eddy current. A variety of configurations are possible for the drive and sense circuitry and for the configuration and position of the coil(s), e.g., as described in U.S. Pat. Nos. 6,924,641, 7,112,960 and 8,284,560, and in U.S. Patent Publication Nos. 2011-0189925 and 2012-0276661, each of which is incorporated by reference. The drive and sense circuitry  166  can be located in the same recess  128  or a different portion of the platen  120 , or could be located outside the platen  120  and be coupled to the components in the platen through a rotary electrical union  129 . 
     In operation the drive and sense circuitry  166  drives the coil  164  to generate an oscillating magnetic field. At least a portion of magnetic field extends through the polishing pad  110  and into substrate  10 . If a metal layer is present on substrate  10 , the oscillating magnetic field generates eddy currents in the metal layer. The eddy currents cause the metal layer to act as an impedance source that is coupled to the drive and sense circuitry  166 . As the thickness of the metal layer changes, the impedance changes, and this can be detected by the drive and sense circuitry  166 . 
     Optionally an optical monitoring system, which can function as a reflectometer or interferometer, can be secured to the platen  120  in the recess  128  to monitor the same portion of the substrate being monitored by the eddy current monitoring system  160 . 
     The CMP apparatus  100  can also include a position sensor  180 , such as an optical interrupter, to sense when the core  162  is beneath the substrate  10 . For example, the optical interrupter could be mounted at a fixed point opposite the carrier head  140 . A flag  182  is attached to the periphery of the platen. The point of attachment and length of flag  182  is selected so that it interrupts the optical signal of sensor  180  while the core  164  sweeps beneath substrate  10 . Alternately or in addition, the CMP apparatus can include an encoder to determine the angular position of platen. 
     A controller  190 , such as a general purpose programmable digital computer, receives the intensity signals from the eddy current sensing system  160 . The computer  190  can include a processor, memory, and I/O devices, as well as an output device  192  e.g., a monitor, and an input device  194 , e.g., a keyboard. 
     The signals can pass from the eddy current monitoring system  160  to the controller  190  through the rotary coupler  129 . Alternatively, the circuitry  166  could communicate with the controller  190  by a wireless signal. 
     Since the core  164  sweeps beneath the substrate with each rotation of the platen, information on the metal layer thickness is accumulated in-situ and on a continuous real-time basis (once per platen rotation). The computer  190  can be programmed to sample measurements from the monitoring system when the substrate generally overlies the core  164  (as determined by the position sensor). As polishing progresses, the thickness of the metal layer changes, and the sampled signals vary with time. The time varying sampled signals may be referred to as traces. The measurements from the monitoring systems can be displayed on the output device  192  during polishing to permit the operator of the device to visually monitor the progress of the polishing operation. 
     In operation, the CMP apparatus  100  can use the eddy current monitoring system  160  to determine when the bulk of the filler layer has been removed and/or to determine when the underlying stop layer has been substantially exposed. Possible process control and endpoint criteria for the detector logic include local minima or maxima, changes in slope, threshold values in amplitude or slope, or combinations thereof. 
     The controller  190  may also be connected to the pressure mechanisms that control the pressure applied by carrier head  140 , to carrier head rotation motor  154  to control the carrier head rotation rate, to the platen rotation motor  121  to control the platen rotation rate, or to slurry distribution system  130  to control the slurry composition supplied to the polishing pad. In addition, the computer  190  can be programmed to divide the measurements from the eddy current monitoring system  160  from each sweep beneath the substrate into a plurality of sampling zones, to calculate the radial position of each sampling zone, and to sort the amplitude measurements into radial ranges, as discussed in U.S. Pat. No. 6,399,501, the entirety of which is incorporated herein by reference. After sorting the measurements into radial ranges, information on the film thickness can be fed in real-time into a closed-loop controller to periodically or continuously modify the polishing pressure profile applied by a carrier head in order to provide improved polishing uniformity. 
       FIGS. 2A and 2B  show an example of a core  164  from the eddy current monitoring system  160 . The core  164  is formed of a non-conductive material with a relatively high magnetic permeability (e.g., μ of about 2500 or more). The core  164  can be coated with a water repellant material. For example, the core  164  can be coated with a material such as parylene to prevent water from entering pores in the core  164 , and to prevent coil shorting. 
     The core  164  is elongated, with a length Lt along the primary axis of the core  164  greater than its width Wt along a secondary axis perpendicular to the primary axis. When the core is installed in the platen, both the primary axis and secondary axis are parallel to the surface of the platen  120 , e.g., parallel to the faces of the substrate and polishing pad during the polishing operation. The elongated structure of the core causes the region measured on the substrate to be similarly elongated. The core  164  can include one or more prongs  172 ; when installed in the platen the prongs  172  project perpendicular to the plane of the platen, e.g., vertically. 
     In some implementations, the core  164  has an E-shaped cross-section in the plane perpendicular to the primary axis. The core  164  can include a back portion  170  and three prongs  172   a - 172   c  extending from the back portion  170 . The prongs extend away from the back portion  170  along a third axis that is perpendicular to both the primary axis and secondary axis. In addition, the prongs  172   a - 172   c  are substantially linear and extend in parallel to each other and along the primary axis. The prongs are spaced apart from each other in the secondary axis. Each prong can have a length Lt along the primary axis that is greater than its width W 1  along the secondary axis. The two outer prongs  172   a ,  172   c  are on opposite sides of the middle prong  172   b . The outer prongs  172   a ,  172   c  can be equidistant from the middle prong  172   b.    
       FIG. 3  shows the CMP system  100  with the elongated core  164  as part of the eddy current monitoring system. In some implementations, the elongated core  164  can be oriented so that the primary axis  174  passes through the axis of rotation  125  of the platen. As the platen  120  rotates (shown by arrow  300 ), the core  164  will traverse a circular path  310 , a portion of which passes below the substrate  10 . As the core  164  passes below the substrate  10 , the eddy current monitoring system can take measurements at a sequence of positions  312  along the path  310 . At each position  312 , the monitoring system monitors an elongated region on the substrate. Although only five positions  312  are illustrated in  FIG. 3 , the sampling rate could be much higher, e.g., measurements could be taken at hundreds of positions. In addition, although  FIG. 3  illustrates the regions as non-overlapping, if the positions are sufficiently close together then the measured regions could partially overlap. 
     As shown in  FIG. 4A , the elongated core  164  can be oriented in the platen  120  such that, for at least some lateral positions of the substrate  10 , when the core  164  is positioned immediately below the edge  12  of the substrate  10 , e.g., the center of the core  164  coincides with the substrate edge, the primary axis  174  of the core  164  forms an angle α less than a critical angle, e.g., less than 15°, e.g., less than 5°. e.g., less than 1°, with the line  14  that is tangent to the substrate edge  12 . That is, when the core  164  is at the position  314 , the primary axis of the core  164  is approximately perpendicular to a radius r of the substrate  10  that passes through the center of the core  164 . Therefore, for measurements near the substrate edge, the portion of the conductive layer on the substrate  10  that couples with the magnetic field produced by the coil is generally at the same radial distance from the center of the substrate. Consequently, the monitoring system can provide improved signal strength at the substrate edge without significant loss of resolution at the substrate edge. 
     If the carrier head  140  is laterally fixed during polishing, then the angle α will remain constant during the polishing operation. However, for some polishing operations, the carrier head sweeps laterally, changing its relative distance D (see  FIG. 3 ) from the axis of rotation  125  of the platen  120 . Comparing  FIGS. 4A and 4B , this causes the relative angle α between the region and the substrate edge  12  to change over time, so that the angle α will be different for different sweeps of the core  164  below the substrate  10 . 
     Referring to  FIGS. 5A and 5B , this change in angle α can result in a change in the signal from the eddy current monitoring system  160 .  FIG. 5A  illustrates a signal  320  from the eddy current monitoring system  160  during a single pass of the core  164  below the substrate  10 . The signal includes a first time period  322  that corresponds to the time during which the measurement region passes across the leading edge of the substrate  10 , a second time period  324  that corresponds to the time during which the measurement region scans across the substrate  10 , and a third time period  326  that corresponds to the time during which the measurement region passes across the trailing edge of the substrate  10 . The first time period  322  and the third time period  326  are referred to as edge time periods. 
     In the first time period  322 , the signal intensity ramps up from an initial intensity (typically the signal resulting when no substrate and no carrier head is present) to an intensity I. This is caused by the transition of the monitoring region from initially only slightly overlapping the substrate (generating the initial lower values) to the monitoring region nearly entirely overlapping the substrate (generating the higher values). As shown in  FIG. 5A , this transition can occur over a time period from Ta to Tb, with a duration ΔT. Similarly, during the third time period  326 , the signal intensity ramps down. 
     Although the second time period  324  is illustrated a flat, this is for simplicity, and a real signal in the second time period  324  would likely include fluctuations due both to noise and to variations in the metal layer thickness. 
     As shown  FIG. 5B , if the angle α increases (compare  FIGS. 4A and 4B ), and assuming that the rotation rate of the platen is the same, it will take a longer time αT&#39; for the monitoring region to transition from only slightly overlapping the substrate to nearly entirely overlapping the substrate. Consequently, the slope of the signal during the first time period  322 ′ and the last time period  326 ′ will be lower. Conversely, if the angle α decreases, the time ΔT′ is smaller and the slope of the signal during the first time period  322 ′ is greater. 
     In addition, the change in the angle α can cause variations in sensitivity or gain. Even if the layer thickness is the same, if the angle α changes, the signal at the midpoint T 0  of the edge time period can change (T 0  should be the time at which the center of the core is aligned with the substrate edge  12 ). In particular, in the case of an eddy current monitoring system having the prong configuration and orientation illustrated in  FIGS. 2A ,  2 B, and  3 , as the angle α increases, the gain of the monitoring system increases for positions of the core  164  near the substrate edge  12 . Thus, as shown in  FIGS. 5A and 5B , if the angle α′ increases, the signal at the midpoint T 0  can increase from I 0  to I 0 ′. The gain levels off as the core  164  moves further below the substrate  10 , so that by the time the core  164  is completely below the substrate  10 , the same signal intensity I should result regardless of the angle α. Without being limited to any particular theory, the change in gain can be caused by the anisotropic magnetic field lines generated by the core  164 . 
     This variation in the shape of the signal  320  can cause errors in the calculating of a characterizing value for the substrate, e.g., the thickness, near the substrate edge. To compensate for this, the angle α can be fed into an edge reconstruction algorithm. The edge reconstruction algorithm can compensates for the variances caused by sweep-to-sweep variances in the angle α. 
     The angle α can be calculated from the distance D between the axis of rotation  125  of the platen  120  and the center of the substrate  10  (which can be measured by an linear encoder that measures the sweep of the carrier head  140 ), the radius r of the substrate  10  (which can be input by a user), the distance B between the axis of rotation  125  of the platen  120  and the center of the core  164  (which can be input by a user), and the angle β, if any, between the primary axis  174  and a line that passes through the axis of rotation  125  and the core  164 . 
     For example, the angle α at the time that the center of core coincides with the substrate edge can be calculated as 
     
       
         
           
             α 
             = 
             
               
                 
                   cos 
                   
                     - 
                     1 
                   
                 
                 ⁢ 
                 
                   
                     
                       D 
                       2 
                     
                     - 
                     
                       r 
                       2 
                     
                     - 
                     
                       B 
                       2 
                     
                   
                   
                     2 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     rB 
                   
                 
               
               + 
               β 
               - 
               
                 90 
                 ⁢ 
                 ° 
               
             
           
         
       
     
     Each intensity measurement fed into the edge reconstruction algorithm can be accompanied by a calculated angle α. 
     The edge reconstruction algorithm can find the start and end times of the first time portion  322 , i.e., Ta and Tb, and the start and end times of third time portion  326  of the signal. For example, the controller  190  can calculate a derivative of the intensity signal  320  and identify the regions with slope above a threshold. The edge reconstruction algorithm can also limit evaluation of the signal  320  based on input from the position detector  180 . For example, evaluation can be limited to portions of the signal  320  within a threshold time of a time that the position sensor  180  indicates that the core  164  is passing below the substrate edge  12 . 
     The angle α for the first time portion  322  and third time portion  326  can be determined. For example, the angle α for the each time portion can be calculated as an average of the angles α associated with the intensity measurements received within that time portion. Alternatively, the angle α at a time that the position sensor  180  indicates that the platen is at a particular angular orientation could be used. 
     Once an angle α has been established for the time portion, a reconstructed edge signal can be calculated. The reconstructed edge signal at least partially compensates for the variation in the angle α from rotation to rotation of the platen  120 . 
     In some implementations, the edge time portions are compressed or decompressed. For example, referring to  FIG. 6 , the initial signal  320  can have a first time period  322  that extends from time Ta to time Tb. If the angle α is larger than a threshold angle, the portion of the signal in the edge time periods  322 ,  326  can be time-compressed to generate a modified signal  330 . As shown, in the modified signal  330 , due to the compression the duration of the edge time periods  322 ,  326  has been reduced and the slope of the signal in the edge time periods  322 ,  326  is increased. The amount of compression, e.g., the ratio ΔT/ΔTm can be a function of the angle α, e.g., be proportional to the angle α. 
     In some implementations, which can be combined with the compression or decompression, the intensity of the edge time portions (and optionally also the center time portion  324 ) is adjusted. For example, intensity values in the initial signal  320  during the edge time periods  322 ,  326  can be divided (or multiplied) by a gain factor to generate the modified signal  330 . In general, the gain factor is calculated to compensate for the change in sensitivity of the monitoring system that depends on the angle α. 
     As noted above, in general, at a higher angle α, the eddy current monitoring system  160  can be more sensitive. The gain factor can be a function of the angle α. Assuming the initial signal is multiplied by the gain factor, the gain factor can decrease as the angle α increases. In addition, the gain factor can be a function of time within the edge time period. Again assuming the initial signal is multiplied by the gain factor, the gain factor can decrease as the time distance from the center time period  334  increases. For example, as shown in  FIG. 6 , in the modified signal  330 , due to multiplication by the gain factor, the intensity at the midpoint T 0  of the edge time periods  322  has been reduced from I 0  to I 0   m . The gain factor can be calculated using an algebraic function of the angle α and the time, or using a look up table. 
     Due to this compensation, the effect of variation of the angle α between the elongated monitoring region and the substrate edge can be significantly reduced, making calculation of the characterizing value more accurate, and thus improving endpoint control and/or closed-loop control of polishing parameters to give better within-wafer non-uniformity (WIWNU) and water -to-wafer non-uniformity (WTWNU). 
     Referring to  FIG. 7 , which illustrates the results for only a single zone of a substrate, a time-varying sequence of characterizing values  212  is illustrated. The characterizing values  212  are generated from the signal  320  from the monitoring system  160 . This sequence of values can be termed a trace  210 . In general, for a polishing system with a rotating platen, the trace  210  can include one, e.g., exactly one, value per sweep of the sensor of the optical monitoring system below the substrate. If multiple zones on a substrate are being monitored, then there can be one value per sweep per zone. For a zone at the substrate edge  12 , the characterizing values  212  can be determined based on the modified edge portion  332 ,  336  of the signal  320 . Multiple measurements within a zone can be combined to generate a single value that is used for control of the endpoint and/or pressure. 
     Prior to commencement of the polishing operation, the user or the equipment manufacturer can define a function  214  that will be fit to the time-varying sequence of values  212 . For example, the function can be a polynomial function, e.g., a linear function. As shown in  FIG. 8 , the function  214  is fit to the sequence of values  212 . Multiple techniques exist to fit generalized functions to data. For linear functions such as polynomials, a general linear least squares approach can be employed. 
     Optionally, the function  214  can be fit to the values collected after time TC. Values collected before the time TC can be ignored when fitting the function to the sequence of values. For example, this can assist in elimination of noise in the measured spectra that can occur early in the polishing process, or it can remove spectra measured during polishing of another layer. Polishing can be halted at an endpoint time TE that the function  214  equals a target value TT. 
     The monitoring system can be used in a variety of polishing systems. Either the polishing pad, or the carrier head, or both can move to provide relative motion between the polishing surface and the substrate. The polishing pad can be a circular (or some other shape) pad secured to the platen, a tape extending between supply and take-up rollers, or a continuous belt. The polishing pad can be affixed on a platen, incrementally advanced over a platen between polishing operations, or driven continuously over the platen during polishing. The pad can be secured to the platen during polishing, or there can be a fluid bearing between the platen and polishing pad during polishing. The polishing pad can be a standard (e.g., polyurethane with or without fillers) rough pad, a soft pad, or a fixed-abrasive pad. 
     Although the discussion above focuses on an eddy current monitoring system, the correction techniques can be applied to other sorts of monitoring systems, e.g., optical monitoring systems, that monitor an elongated region on the substrate. In addition, although the discussion above focuses on a monitoring system with an elongated monitoring region, the correction techniques can be applied even if the monitoring region is not elongated but an anisotropic sensor generates a signal that depends on the relative orientation of the sensor to the substrate edge. 
     A number of embodiments of the invention have been described. Nevertheless, it will be understood that various modifications may be made without departing from the spirit and scope of the invention. Accordingly, other embodiments are within the scope of the following claims.