Patent Publication Number: US-11658078-B2

Title: Using a trained neural network for use in in-situ monitoring during polishing and polishing system

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims priority to U.S. application Ser. No. 63/025,108, filed on May 14, 2020, the disclosure of which is incorporated by reference. 
    
    
     TECHNICAL FIELD 
     The present disclosure relates to reconstruction of measurements made near a substrate edge using in-situ monitoring during polishing of the 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 
     In one aspect, a method of polishing a substrate includes polishing a conductive layer on the substrate at a polishing station, monitoring the layer during polishing at the polishing station with an in-situ eddy current monitoring system to generate a plurality of measured signals values for a plurality of different locations on the layer, generating for each location of the plurality of different locations an estimated measure of thickness of the location, and at least one of detecting a polishing endpoint or modifying a polishing parameter based on each estimated measure of thickness. The conductive layer is formed of a first material having a first conductivity. Generating includes calculating initial thickness values based on the plurality of measured signals values and processing the initial thickness values through a neural network that was trained using training data acquired by measuring calibration substrates having a conductive layer formed of a second material having a second conductivity that is lower than the first conductivity to generated adjusted thickness values. 
     In another aspect, a method of training a neural network for use in an in-situ monitoring system includes scanning a sensor of an in-situ monitoring system across a calibration substrate having a conductive layer formed of a first material having a first conductivity, the monitoring system generating a first set of sensor measurements. Ground truth measurements of the thickness of the conductive layer of the calibrations substrate are obtained to provide a first thickness profile. The first thickness profile is scaled based the first conductivity and a target second conductivity that is greater than the first conductivity to provide a modified second thickness profile equivalent to a thickness profile that would be generated if the conductive layer were formed of a material of the second conductivity. A neutral network is trained to convert sensor measurements from the in-situ monitoring system to thickness measurements for a layer formed of the second material. The training is performed using training data including the modified training profile and calibration thickness values based on the first set of sensor measurements from the conductive layer formed of the first material. 
     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. The system can compensate for distortions in a portion of the signal that corresponds to the substrate edge. 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 water-to-wafer non-uniformity (WTWNU). The in-situ monitoring system can generate thickness measurements that are more accurate at very thin layers, e.g., during a clearing step. 
     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 A  is a schematic side view, partially cross-sectional, of a chemical mechanical polishing station that includes an eddy current monitoring system. 
         FIG.  1 B  is a schematic top view of a chemical mechanical polishing station. 
         FIG.  2    is a schematic top view of a substrate being scanned by a sensor head of a polishing apparatus. 
         FIG.  3    is a schematic graph of a static formula for determining substrate thickness based on measured signals. 
         FIG.  4    is a schematic graph of measured signals obtained while monitoring locations on a substrate. 
         FIG.  5    is an example neural network. 
         FIG.  6    is a schematic diagram of two calibration wafers of differing materials. 
         FIG.  7    is a flow diagram of an example process for polishing a substrate. 
         FIG.  8    is a flow diagram of an example process for generating estimated measures of thickness using a neural network. 
     
    
    
     Like reference symbols in the various drawings indicate like elements. 
     DETAILED DESCRIPTION 
     A polishing apparatus can use an in-situ monitoring system, e.g., an eddy current monitoring system, to detect the thickness of an outer layer that is being polished on a substrate. During polishing of the outer layer, the in-situ monitoring system can determine the thickness of different locations of the 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 locations of the outer layer. The polishing rate can be adjusted so that the locations of the layer are substantially the same thickness after polishing. The CMP system can adjust the polishing rate so that polishing of the locations of the layer completes at about the same time. Such profile control can be referred to as real time profile control (RTPC). 
     An in-situ monitoring system can be subject to signal distortion for measurements at locations close to the substrate edge. For example, an eddy current monitoring system can generate a magnetic field. Near the substrate edge, the signal can be artificially low because the magnetic field only partially overlaps the conductive layer of the substrate. If the eddy current sensor head is large, the signal could be further reduced due to earlier signal drop off due as the larger sensor head may need more time and space to pass over the edge region and lower spatial resolution. A technique to compensate for the distortions at the substrate is to use a neural network to generate modified signals based on the measured signals generated by the in-situ monitoring system. 
     However, near the end of a polishing operation, e.g., at or approaching clearing to expose the underlying layer, the thickness of the conductive layer becomes increasingly thin and the reconstruction of the signal by the neural network can become unreliable. Without being limited to any particular theory, neural networks may be trained for edge reconstruction using calibration substrates of differing materials that have relatively thick conductive layers; such training may not be suitable to configure the neural network to reconstruct the layer thickness for thin conductive layers at the substrate edge. In particular, thin layers on a calibration wafer can include discontinuities, e.g., regions where the underlying layer has been exposed. As a result, obtaining a ground truth measurement, e.g., using a four-point probe, from the calibration wafer may not be possible, and consequently reliable training data may not be available for thin layers. 
     However, by collecting signals using calibration wafers with layers that are thicker but composed of materials that have a lower conductivity, measurements can be obtained and then scaled based on the relative conductance ratio between the two calibration wafers to provide training data that is equivalent to thinner layers of higher conductivity. The neural network may be trained using this training data, thereby enhancing the ability of the neural network to generate estimated measures of thickness of the substrate edge for very thin layers made of high conductivity materials. 
       FIGS.  1 A and  1 B  illustrate 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  100  also includes an in-situ monitoring system  160 . The in-situ monitoring system  160  generates a time-varying sequence of values that depend on the thickness of a layer on the substrate. The in-situ monitoring system  160  includes a sensor head at which the measurements are generated; due to relative motion between the substrate and the sensor head, measurements will be taken at different locations 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 conductive layer on the substrate and a sensing system to detect eddy currents induced in the conductive 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 . The combination of the core  162  and coil  164  can provide the sensor head. 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. 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 conductive layer is present on substrate  10 , the oscillating magnetic field generates eddy currents in the conductive layer. The eddy currents cause the conductive layer to act as an impedance source that is coupled to the drive and sense circuitry  166 . As the thickness of the conductive layer changes, the impedance changes, and this can be detected by the drive and sense circuitry  166 . Different conductive layer materials have different conductive characteristics that result in different signal strengths from an eddy current sensor. Copper (Cu) has a high conductivity and is therefore a common material for a conductive layer. Other conductive materials (e.g., cobalt, tungsten, titanium nitride) may be used for the conductive layer based on the particular application, e.g., barrier layer, ferromagnetic memory, etc. 
     Alternatively or in addition, an optical monitoring system, which can function as a reflectometer or interferometer, can be secured to the platen  120  in the recess  128 . If both systems are used, the optical monitoring system and eddy current monitoring system can monitor the same portion of the substrate. 
     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  162  sweeps beneath substrate  10 . Alternatively 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 monitoring system  160 . The controller  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 electrical union  129 . Alternatively, the circuitry  166  could communicate with the controller  190  by a wireless signal. 
     Since the core  162  sweeps beneath the substrate with each rotation of the platen, information on the conductive layer thickness is accumulated in-situ and on a continuous real-time basis (once per platen rotation). The controller  190  can be programmed to sample measurements from the monitoring system when the substrate generally overlies the core  162  (as determined by the position sensor). As polishing progresses, the thickness of the conductive 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. 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. 
     The controller  190  can use a correlation curve that relates the measured signal value by the in-situ monitoring system  160  to the thickness of the layer being polished on the substrate  10  to compute a thickness value of the layer being polished. An example of a correlation curve  303  is shown in  FIG.  3   . In the coordinate system depicted in  FIG.  3   , the horizontal axis represents the value of the signal received from the in-situ monitoring system  160 , whereas the vertical axis represents the value for the thickness of the layer of the substrate  10 . For a given signal value, the controller  190  can use the correlation curve  303  to generate a corresponding thickness value. The correlation curve  303  can be considered a “static” formula, in that it predicts a thickness value for each signal value regardless of the time or position at which the sensor head obtained the signal. The correlation curve can be represented by a variety of functions, such as a polynomial function, or a look-up table (LUT) combined with linear interpolation. 
     Referring to  FIGS.  1 B and  2   , changes in the position of the sensor head with respect to the substrate  10  can result in a change in the signal from the in-situ monitoring system  160 . That is, as the sensor head scans across the substrate  10 , the in-situ monitoring system  160  will make measurements for multiple regions  94 , e.g., measurement spots, at different locations on the substrate  10 . The regions  94  can be partially overlapping (see  FIG.  2   ). 
       FIG.  4    illustrates a graph  420  that shows a signal  401  from the in-situ monitoring system  160  during a single pass of the sensor head below the substrate  10 . The signal  401  is composed of a series of individual measurements from the sensor head as it sweeps below the substrate. The graph  420  can be a function of measurement time or of position, e.g., radial position, of the measurement on the substrate. In either case, different portions of the signal  401  correspond to measurement spots  94  at different locations on the substrate  10  scanned by the sensor head. Thus, the graph  420  depicts, for a given location of the substrate scanned by the sensor head, a corresponding measured signal value from the signal  401 . 
     Referring to  FIGS.  2  and  4   , the signal  401  includes a first portion  422  that corresponds to locations in an edge region  203  of the substrate  10  when the sensor head crosses a leading edge of the substrate  10 , a second portion  424  that corresponds to locations in a central region  201  of the substrate  10 , and a third portion  426  that corresponds to locations in edge region  203  when the sensor head crosses a trailing edge of the substrate  10 . The signal can also include portions  428  that correspond to off-substrate measurements, i.e., signals generated when the sensor head scans areas beyond the edge  204  of the substrate  10  in  FIG.  2   . 
     The edge region  203  can correspond to a portion of the substrate where measurement spots  94  of the sensor head overlap the substrate edge  204 . The central region  201  can include an annular anchor region  202  that is adjacent the edge region  203 , and an inner region  205  that is surrounded by the anchor region  202 . The sensor head may scan these regions on its path  210  and generate a sequence of measurements that correspond to a sequence of locations along the path  210 . 
     In the first portion  422 , the signal intensity ramps up from an initial intensity (typically the signal resulting when no substrate and no carrier head is present) to a higher intensity. This is caused by the transition of the monitoring location from initially only slightly overlapping the substrate at the edge  204  of the substrate (generating the initial lower values) to the monitoring location nearly entirely overlapping the substrate (generating the higher values). Similarly, in the third portion  426 , the signal intensity ramps down when the monitoring location transitions to the edge  204  of the substrate. 
     When the bulk of the filler layer has been removed, the metal layer in the edge region  204  of the substrate becomes thin and may develop discontinuities as the raised pattern of the insulating layer is exposed. This leads to additional noise in the first  422  and third portions  426  as well as a second portion  424  of lower signal amplitude. Additionally, if larger eddy current sensors are used to detect the thin conductive filler layers, there is a loss in spatial resolution of the sensor. This results in the first  422  and third portions  426  being further elongated as the monitoring location overlaps earlier and longer with the edge  204  of the substrate, further increasing distortion in the signal due to sensor head overlap with the substrate edge. 
     Although the second portion  424  is illustrated as flat, this is for simplicity; a real signal in the second portion  424  would likely include fluctuations due both to noise and to variations in the layer thickness. The second portion  424  corresponds to the monitoring location scanning the central region  201 . The second portion  424  includes sub-portions  421  and  423  that are caused by the monitoring location scanning the anchor region  202  of the central region  201  and sub-portion  427  that is caused by the monitoring location scanning the inner region  205  of the central region  201 . 
     As noted above, the variation in the signal intensity in the regions  422 ,  426  is caused in part by measurement region of the sensor overlapping the substrate edge, rather than an intrinsic variation in the thickness or conductivity of the layer being monitored. Consequently, this distortion in the signal  401  can cause errors in the calculating of a characterizing value for the substrate, e.g., the thickness of the layer, near the substrate edge. To address this problem, the controller  190  can include a neural network, e.g., neural network  500  of  FIG.  5   , to generate a modified thickness value corresponding to one or more locations of the substrate  10  based on the computed thickness values corresponding to those locations. 
     Referring now to  FIG.  5   , the neural network  500  is configured to, when trained appropriately, generate modified thicknesses values that reduce and/or remove the distortion of computed thickness values near the substrate edge. The neural network  500  receives a group of inputs  504  and processes the inputs  504  through one or more neural network layers to generate a group of outputs  550 . The layers of the neural network  500  include an input layer  510 , an output layer  530 , and one or more hidden layers  520 . 
     Each layer of the neural network  500  includes one or more neural network nodes. Each neural network node in a neural network layer receives one or more node input values (from the inputs  504  to the neural network  500  or from the output of one or more nodes of a preceding neural network layer), processes the node input values in accordance with one or more parameter values to generate an activation value, and optionally applies a non-linear transformation function (e.g., a sigmoid or tanh function) to the activation value to generate an output for the neural network node. 
     Each node in the input layer  510  receives as a node input value one of the inputs  504  to the neural network  500 . 
     The inputs  504  to the neural network include initial thickness values from the in-situ monitoring system  160  for multiple different locations on the substrate  10 , such as a first initial thickness value  501 , a second initial thickness value  502 , through an n th  computed thickness value  503 . The initial thickness values can be individual thickness values calculated from the sequence of signal values in the signal  401  using the correlation curve. 
     In general, the multiple different locations include locations in the edge region  203  and the anchor region  202  of the substrate  10 . In some implementations, the multiple different locations are only in the edge region  203  and the anchor region  202 . In other implementations, the multiple different locations span all regions of the substrate. In other implementations, the multiple different locations may include locations in the edge region  203  and the anchor region  202  of a second substrate  10 . In some implementations, the multiple different locations are only in the edge region  203  and the anchor region  202  of the second substrate. In other implementations, the multiple different locations span all regions of the second substrate. 
     These initial thickness values are received at signal input nodes  544 . Optionally, the input nodes  504  of the neural network  500  can also include one or more state input nodes  516  that receive one or more process state signals  504 , e.g., a measure of wear of the pad  110  of the polishing apparatus  100 . 
     The nodes of the hidden layers  520  and output layer  530  are illustrated as receiving inputs from every node of a preceding layer. This is the case in a fully-connected, feedforward neural network. However, the neural network  500  may be a non-fully-connected feedforward neural network or a non-feedforward neural network. Moreover, the neural network  500  may include at least one of one or more fully-connected, feedforward layers; one or more non-fully-connected feedforward layers; and one or more non-feedforward layers. 
     The neural network generates a group of modified thickness values  550  at the nodes of the output layer  530 , i.e., “output nodes”  550 . In some implementations, there is an output node  550  for each measured signal from the in-situ monitoring system that is fed to the neural network  500 . In this case, the number of output nodes  550  can correspond to the number of signal input nodes  504  of the input layer  510 . 
     For example, the number of signal input nodes  544  can equal the number of measurements in the edge region  203  and the anchor region  202 , and there can be an equal number of output nodes  550 . Thus, each output node  550  generates a modified thickness value that corresponds to a respective measured signal supplied as an input to a signal input node  544 , e.g., the first modified thickness value  551  for the first measured signal  501 , the second modified thickness value  552  for the second measured signal  502 , and the nth modified thickness value  553  for the nth measured signal  503 . 
     In some implementations, the number of output nodes  550  is smaller than the number of input nodes  504 . In some implementations, the number of output nodes  550  is smaller than the number of signal input nodes  544 . For example, the number of signal input nodes  544  can equal the number of measurements in the edge region  203 , or equal to the number of measurements in the edge region  203  and anchor region  202 . Again, each output node  550  of the output layer  530  generates a modified thickness value that corresponds to a respective measured signal supplied as a signal input node  504 , e.g., the first modified thickness value  551  for the first measured signal  501 , but only for the signal input nodes  554  that receive signals from the edge region  203 . 
     The polishing apparatus  100  can use the neural network  500  to generate modified thickness values. The modified thickness values can then be used as the determined thickness for each location in a first group of locations of a substrate, e.g., the locations in the edge region (and possibly the anchor region). For example, referring back to  FIG.  4   , the modified thickness values for the edge region can provide a modified portion  430  of the signal  401 . 
     For example, the controller  190  can use the neural network  500  to determine modified thickness value for each of one or more locations in the edge region. Optionally, the controller  190  can use the neural network  500  to determine a modified thickness value for each of one or more locations in the anchor region of the substrate. In contrast, the controller  190  can use the initial thickness values for locations in other regions, e.g., the inner region  205 . That is, signal values from locations from other regions, e.g., the inner region  205 , can be converted to thickness values which are then used without being modified by the neural network. 
     In some implementations, for a modified thickness value that corresponds to a given measurement location, the neural network  500  can be configured such that only input signal values from measurement locations within a predetermined distance of that given location are used in determining the modified thickness value. For example, if signal values S 1 , S 2 , . . . S M , . . . S N  are received, corresponding to measurements at N successive locations on the path  210 , a modified thickness value S′M for the Mth location (indicate at R M ) can use only the thickness values S M−L (min 1) , . . . S M , . . . S M+L (max N)  to calculate the modified thickness value S′ M . The value of L can be selected such that measurements that are up to about 2-4 mm apart are used to generate a given modified thickness value S′ M ; measurements within about 1-2 mm, e.g., 1.5 mm, of the location of the measurement S M  can be used. For example, L can be a number from the range 0 to 4, e.g., 1 or 2. For example, if measurements within 3 mm are used, and the spacing between measurements is 1 mm, then L can be 1; if the spacing is 0.5 mm, then L can be 2; if the spacing is 0.25 then L can be 4. However, this can depend on the configuration of the polishing apparatus and the processing conditions. Values of other parameters, e.g., pad wear, could still be used in calculating the modified thickness value S′ M . 
     For example, there can be a number of hidden nodes  570  of the one or more hidden layers  520 , i.e., “hidden nodes”  570 , equal to the number of signal input nodes  544 , with each hidden node  570  corresponding to a respective signal input node  544 . Each hidden node  570  can be disconnected from (or have a parameter value of zero for) input nodes  544  that correspond to measurements for locations greater than the predetermined distance from the location of the measurement of the corresponding input node. For example, the M th  hidden node can be disconnected from (or have a parameter value of zero for) the 1 st  through (M−L−1) th  input nodes  544  and the (M+L+1) th  through N th  input nodes. Similarly, each output node  560  can be disconnected from (or have a parameter value of zero for) hidden nodes  570  that correspond to the modified thickness for locations that are greater than the predetermined distance from the location of the measurement of the output node. For example, the M th  output node can be disconnected from (or have a parameter value of zero for) the 1 st  through (M−L−1) th  hidden nodes  570  and the (M+L+1) th  through N th  hidden nodes. 
     In order to train the neural network, a training dataset is needed. This training dataset should include a plurality of records, with each record including a group of input values that would be input into the input nodes and a group of desired output values from the output nodes, i.e., the output values that would be desired for that group of input values. 
     One technique to generate this training dataset is to obtain a group of calibration substrates, each of which has a different thickness profile. Calibration substrates are a group of substrates that may have the same dimensions and regions as a substrate to be polished. The thickness of the layer may be accurately measured, e.g., using a four-point probe, to generate ground truth measurements. Generally, calibration substrates include a layer of the same material that is used as the conductive filler layer that is removed during polishing, e.g., a copper calibration layer for a copper conductive filler layer. 
     For each calibration substrate, the eddy current sensor of the polishing apparatus  100  can be scanned across the calibration substrate to generate a sequence of calibration signal values. These calibration signal values are similar to the sequence of signal values obtained during polishing, but no pressure or polishing liquid is applied so that no polishing of the calibration substrate is performed. The calibration signal values can be converted to calibration thickness values using the correlation curve. In addition, for each calibration substrate, ground truth thickness measurements are generated for multiple locations on the calibration substrate, e.g., using a four-point probe. The signal values and ground truth thickness measurements can be collected in a number of regions, e.g., the central region  201 , anchor region  202 , and edge region  203 . The calibration thickness values and ground truth thickness measurements for a particular calibration substrate thus provide a record for the training dataset. 
     Assuming the different calibration substrates have a sufficient variety of thickness profiles and span a sufficient range of thicknesses, it should be possible to train the neural network with the dataset. As such, in a polishing operation where a first substrate is being polished and monitored, a modified thickness value that is generated by the neural network  500  can be considered to be based on the thickness values from measurement locations on a second substrate (a calibration substrate). 
     Particular problems arise when generating modified thickness values at locations in the edge region if the bulk of the filler layer has been removed. Larger eddy current sensors may be required to detect thin conductive filler layers as the conductive filler layer is removed and the raised pattern of the insulating layer is exposed. Exposing the insulating layer leads to decreased signal quality as the eddy current sensor may span regions containing both conducting and insulating layer areas. A larger eddy current sensor covers a larger area, thereby covering more of both the conducting and insulating layer areas. This may cause a decrease in the slope and increased noise of the first portion of the signal  422 . Further decreases in signal arise when the path of the eddy current sensor  210  head attempts to measure the signal from an edge region  203 . As such, these regions can have a high variance between the measured initial thickness value and the actual Training data is particularly needed to train the neural network to accurately generate modified thickness values at locations in the edge region where the bulk of the filler layer has been removed. 
     However, obtaining such data, and hence reconstruction of the thickness of thin conductive layers at the edge region  203 , is more difficult because of difficulty to produce a calibration wafer of the same material and thickness as a conductive filler layer during later stages of polishing, e.g., clearing. This issue can be at least partially remedied by using a calibration wafer of a first material with a lower conductivity but similar conductance to perform the neural network training for a substrate of a second material. 
     Referring now to  FIG.  6   , calibration thickness values and ground truth thickness measurements, obtained using the four-point probe and eddy current sensor respectively, of a group of calibration wafers having a layer of a first material  601  may be used as training data to train the neutral network, even when the neural network is then used for in-situ monitoring of a group of substrates having a layer of a second material  602  of different conductivity. 
     In particular, in order to simulate a second calibration substrate having a thin layer of a second conductive material, a first calibration substrate with a layer of a first conductive material that is thicker layer but lower conductivity can be used, as the conductive layer of the first calibration substrate will have similar conductance to the simulated second calibration substrate. Conductance (G) is a measure of how a material conducts electricity and is defined as G=σ*A/l where σ is the conductivity, A is the cross sectional area, and l is the length or thickness of a material being measured. 
     If the conductivity of the first material  601  is lower than that of the second material  602 , e.g., 10×σ 1 =σ 2 , the thickness  610  of the first material can proportionally larger than the thickness  612  of the second material  611 , e.g., l 1 =10×l 2 , to maintain a similar conductance. This permits the operator to select the approximate range of thickness for the conductive layer in the calibration substrates. For example, if there is difficulty in obtaining a calibration substrates having a layer of copper (ρ=5.96×10 7 ) of 0.2-0.5 microns thickness, instead calibration substrates having a layer of titanium (ρ=2.38×10 6 ) of 5 to 12.5 microns thickness could be used. 
     For each calibration substrate having a layer of the second material, the eddy current sensor of the polishing apparatus  100  can be scanned across the calibration substrate to generate a sequence of calibration signal values. The calibration signal values can be converted to calibration thickness values using the correlation curve. The correlation curve assumes that the material has conductivity associated with the first material, but because the conductance of the layers is similar, the eddy current sensor will calibration thickness values that appear as a thinner layer of the first material. In addition, for each calibration substrate having a layer of the second material, ground truth thickness measurements are generated for multiple locations on the calibration substrate, e.g., using a four-point probe. The ground truth thickness measurements of the calibration wafers are then then be scaled by the ratio of conductivity between the first material and the second material to generate adjusted thickness values. For example, if the substrates to be polished have a copper layer and the correlation curve similarly assumes monitoring of the thickness of a layer of copper (ρ=5.96×10 7  Ωm), but the calibration substrates have a layer of titanium (ρ=2.38×10 6  Ωm), then the ground truth thickness measurements can be divided by a factor of about 25 (5.96×10 7 /2.38×10 6 ) to generate adjusted thickness values that correspond to a copper layer having the same conductance (and thus would generate the same calibration thickness measurements using the eddy current sensor). 
     For each calibration substrate having a layer of the second material, the calibration thickness values and the adjusted thickness measurements for that calibration substrate can provide a record for the training dataset. This permits generation of a training dataset that includes data that simulates substrates having very thin layers. This permits training of the neural network to properly convert the initial thickness values to adjusted thickness values where the layer is very thin, and thus improves accuracy and reliability of the in-situ monitoring system. 
     Possible materials for first and second materials include coper, aluminum, tungsten, cobalt, titanium, and titanium nitride. As noted above, the first material can have a higher conductivity than the second material. In some implementations, the first material is be copper, aluminum or tungsten. In some implementations, the second material is be cobalt, titanium or titanium nitride. 
     In some implementations, the training dataset includes data obtained only from calibration substrates having a conductive layer of different composition than the first material. In some implementations, the training dataset includes data obtained from a first group of calibration substrates that have a conductive layer of a second material that is different composition than the first material, and data obtained from a second group of calibration substrates that have a conductive layer of the first material. 
       FIG.  7    is a flow-diagram of an example process  700  for polishing a substrate  10 . The process  700  can be performed by the polishing apparatus  100 . 
     The polishing apparatus  100  polishes ( 702 ) a layer on the substrate  10  and monitors ( 704 ) the layer during the polishing to generate measured signal values for different locations on the layer. The locations on the layer can include one or more locations within the edge region  203  of the substrate (corresponding to the regions  422 / 426  of the signal  401 ), and one or more locations within an anchor region  202  on the substrate (corresponding to regions  421 / 423  of the signal). The anchor region  202  is spaced away from the substrate edge  204  and within a central region  201  of the substrate, and thus is not affected by the distortion created by the substrate edge  204 . However, the anchor region  202  can be adjacent to the edge region  203 . The anchor region  202  can also surround the inner region  205  of the central region  201 . The number of anchor locations can depend on the measurement spot size and measurement frequency by the in-situ monitoring system  160 . In some embodiments, the number of the anchor locations cannot exceed a maximum value, such as a maximum value of 4. 
     The polishing apparatus  100  generates ( 706 ) an initial thickness value for each location of the different locations based applying the static formula to the measured signal for the location. 
     The inputs to the neural network  500  may be computed thickness values generated by the in-situ monitoring system  160  for the different locations. In some embodiments, the apparatus  100  updates each measured signal by normalizing the value of the signals. Such normalization can increase the likelihood that at least some of the inputs  504  to the neural network system  500  fall within a particular range, which in turn can increase the quality of training of the neural network and/or the accuracy of the inference made by the neural network  500 . The normalized signal values may then be made into normalized thickness values by applying the static formula. 
     The outputs of the neural network  500  are modified thickness values each corresponding to an input computed thickness value. If the inputs are normalized thickness values, the modified thickness values corresponding to the computed thickness values will also be normalized thickness values. Therefore, the polishing apparatus  100  may need to convert such modified thickness values to non-normalized values before using modified signals to estimate thickness of substrate. 
     The polishing apparatus  100  detects ( 708 ) a polishing endpoint and/or modify a polishing parameter based on each modified thickness value. 
       FIG.  8    is a flow diagram of an example process  800  for generating modified thickness values using a neural network  500 . The process  800  can be performed by the polishing apparatus  100 . 
     The polishing apparatus  100  identifies ( 802 ) an anchor location of a group of locations of the substrate and obtains ( 804 ) measured signals for each location of the group of locations. In some embodiments, the anchor location is spaced away from the edge of the substrate. 
     The polishing apparatus  100  normalizes ( 806 ) each measured signal value based on the measured signal value of the anchor location, e.g., by dividing each measured signal value at every location by the measured signal of the anchor location, to update the measured signals. The polishing apparatus  100  then processes ( 808 ) the normalized measured signal values through the neural network  500  to generate modified thickness values for each normalized measured signal value. The polishing apparatus  100  then converts ( 810 ) the modified thickness values to non-normalized signal values using the measured signal value of the anchor location, e.g., by multiplying each measured signal value at every location by the measured signal of the anchor location, to update the measured signals. The polishing apparatus  100  then uses ( 612 ) non-normalized modified signal values to generate a computed thickness value of each location of the group of locations of the neural network  500 . 
     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 scan over an edge of substrate. In addition, although the discussion above focuses on a polishing system, the correction techniques can be applied to other sorts of substrate processing systems, e.g., deposition or etching systems, that include an in-situ monitoring system that scans over an edge of substrate. 
     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.