Patent Publication Number: US-6991514-B1

Title: Optical closed-loop control system for a CMP apparatus and method of manufacture thereof

Description:
TECHNICAL FIELD OF THE INVENTION 
   The present invention is directed, in general, to a semiconductor wafer polishing apparatus and, more specifically, to an optical closed-loop control system for use with a chemical mechanical polishing apparatus for polishing a semiconductor wafer. 
   BACKGROUND OF THE INVENTION 
   The manufacture of an integrated circuit device requires the formation of various materials onto a base substrate to form necessary circuit structures. During the manufacturing process, chemical-mechanical polishing (CMP) is employed to remove certain layers or reduce a layer to a precise thickness. More specifically, CMP employs the combination of chemical etching and mechanical abrasion to remove excess material. In the case of dielectric films, CMP is typically employed to planarize the surface. For metal films, such as copper, CMP is typically used to remove excess material so as to permit the delineation of electrically isolated circuit interconnects. Also, it might be assumed that semiconductor manufacturing processes produce precisely uniform layers of conductive, semiconductive and non-conductive materials. As with any physical process, however, there are imperfections in the processes that can contribute to non-planarity of the wafer. 
     FIG. 1  illustrates a portion of a typical CMP tool  100 . The CMP tool  100  includes a platen  110  coupled to a spindle  120 . The platen  110  may be capable of movement relative to a wafer carrier  160  and a wafer  170 . The platen may rotate about the spindle  120  or other axes, translate in a plane, or orbit about an axis. Multiple variations of these types of movements are well known in the prior art. Coupled to the top of the platen  110  is a polishing pad  130 . Within the polishing pad  130  are probe windows  132 ,  134  for probes  140 ,  142 . The wafer  170  is held in the wafer carrier  160  by a wafer ring  162 . 
   During the CMP process, a slurry  150  is applied to the top of the polishing pad  130  and the wafer  170  in the wafer carrier  160  is simultaneously moved (translated, rotated and/or orbited) relative to the platen  110  and pressed against the polishing pad  130  and the slurry  150 . The action of the pressure and relative motion of the wafer carrier  160  and/or the platen  110  causes the removal and planarization of the material (also called film layers) that cover the wafer  170 . The CMP process, however, may remove material faster from one portion of the wafer versus another portion of the wafer. For example, the CMP process may remove more material from the annular portion of the edge of the wafer than from the center of the wafer. This inconsistency is based upon the slurry  150 , temperature, the material on the wafer, the amount of pressure, the movement of the wafer carrier  160  and the platen  110 , and other factors. 
   To help control the inconsistencies of the CMP process, it is desirable to monitor the characteristics of the film layers so that the removal process is controlled and stopped appropriately. Excessive or improper polishing may often result in severely damaged circuit structures on the wafer  170 . Some systems employ optical monitoring methods to help prevent excessive or improper polishing. These optical monitoring methods determine a thickness of the film layer by analyzing the optical reflectance spectrum from the film layer. However, in order for such an analysis to be practical, three criteria should be met: (1) the reflection spectrum should be obtained in situ from a wafer in a timely manner without interfering with the CMP process, (2) the quality of the reflection spectrum should be sufficiently good such that the analysis can yield reliable, accurate and relevant information, and (3) practical algorithms should exist with which to do the analysis. Previous optical monitoring systems have failed to meet at least one of the criteria listed above. 
   Accordingly, what is needed in the art is a system that overcomes the deficiencies of the prior art. 
   To address the above-discussed deficiencies of the prior art, the present invention provides, for use with a chemical mechanical polishing (CMP) apparatus for polishing a semiconductor wafer, the CMP apparatus having a platen, a polishing pad coupleable with a top surface of the platen and a wafer carrier, an optical closed-loop control system, a method of manufacture and a method of operation thereof. In one embodiment, the optical closed-loop control system includes a plurality of optical probes impacting a corresponding probe window and rigidly mountable through the platen. The probe window is positioned within the polishing pad. The optical closed-loop control system also includes a flash lamp configured to provide light to each of the plurality of optical probes and minimize an exposure time of the light onto the semiconductor wafer, and a spectrograph configured to spatially image light received by each of the plurality of optical probes to a common charge-coupled device (CCD) and produce real-time spectral reflectometry data therefrom. The optical closed-loop control system further includes a control subsystem configured to analyze the real-time spectral reflectometry data and determine at least one wafer state parameter therefrom, and cause the polishing to be adjusted based upon the at least one wafer state parameter. For purposes of the present invention, the phrase “configured to” means that the device, the system or the subsystem includes the necessary software, hardware, firmware or a combination thereof to accomplish the stated task. 
   In another embodiment, the present invention provides a method of manufacturing an optical closed-loop control system for use with a chemical mechanical polishing (CMP) apparatus for polishing a semiconductor wafer, the CMP apparatus having a platen, a polishing pad coupleable with a top surface of the platen and a wafer carrier, the method includes rigidly mounting through the platen a plurality of optical probes impacting a corresponding probe window, the probe window positioned within the polishing pad. The method also includes coupling a flash lamp to each of the plurality of optical probes to provide light thereto and configuring the flash lamp to minimize an exposure time of the light onto the semiconductor wafer. The method further includes configuring a spectrograph to spatially image light received by each of the plurality of optical probes to a common charge-coupled device (CCD) and producing real-time spectral reflectometry data therefrom. The method still further includes configuring a control subsystem to analyze the real-time spectral reflectometry data and determine at least one wafer state parameter therefrom, and cause the polishing to be adjusted based upon the at least one wafer state parameter. 
   The present invention also provides, in one embodiment, a method of operating an optical closed-loop control system for use with a chemical mechanical polishing (CMP) apparatus for polishing a semiconductor wafer, the CMP apparatus having a platen, a polishing pad coupleable with a top surface of the platen and a wafer carrier, the method including: (1) employing a plurality of optical probes impacting a corresponding probe window and rigidly mountable through the platen, the probe window positioned within the polishing pad, (2) providing light to each of the plurality of optical probes employing a flash lamp and minimizing an exposure time of the light onto the semiconductor wafer, (3) spatially imaging light received by each of the plurality of optical probes to a common charge-coupled device (CCD) of a spectrograph and producing real-time spectral reflectometry data therefrom, and (4) analyzing the real-time spectral reflectometry data, determining at least one wafer state parameter from the real-time spectral reflectometry data, and causing the polishing to be adjusted based upon the at least one wafer state parameter. 
   In another embodiment, the present invention also provides an optical closed-loop control system for use with a chemical mechanical polishing (CMP) apparatus for polishing a semiconductor wafer, the CMP apparatus having a platen, a polishing pad coupleable with a top surface of the platen, a plurality of probe windows within the polishing pad and a wafer carrier. The optical closed-loop control system includes: (1) a plurality of optical probes coupleable to corresponding ones of the plurality of probe windows and mountable through the platen, (2) a flash lamp configured to provide light to each of the plurality of optical probes, (3) a spectrograph configured to spatially image light received by each of the plurality of optical probes and produce real-time spectral reflectometry data therefrom, and (4) a control subsystem configured to employ a n-band analysis to analyze the real-time spectral reflectometry data and determine at least one wafer state parameter therefrom, and cause the polishing to be adjusted based upon the at least one wafer state parameter. 
   In yet another embodiment, the present invention provides an optical closed-loop control system for use with a chemical mechanical polishing (CMP) apparatus for polishing a semiconductor wafer, the CMP apparatus having a platen, a polishing pad coupleable with a top surface of the platen, a plurality of probe windows within the polishing pad and a wafer carrier. The optical closed-loop control system includes: (1) a plurality of optical probes coupleable to corresponding ones of the plurality of probe windows and mountable through the platen, (2) a flash lamp configured to provide light to each of the plurality of optical probes, (3) a spectrograph configured to spatially image light received by each of the plurality of optical probes and produce real-time spectral reflectometry data therefrom, and (4) a control subsystem configured to employ a transform analysis to analyze the real-time spectral reflectometry data and determine at least one wafer state parameter therefrom, and cause the polishing to be adjusted based upon the at least one wafer state parameter. 
   The present invention may also provide an optical closed-loop control system for use with a chemical mechanical polishing (CMP) apparatus for polishing a semiconductor wafer, the CMP apparatus having a platen, a polishing pad coupleable with a top surface of the platen, a plurality of probe windows within the polishing pad and a wafer carrier, where the optical closed-loop control system includes: (1) a plurality of optical probes coupleable to corresponding ones of the plurality of probe windows and mountable through the platen, (2) a flash lamp configured to provide light to each of the plurality of optical probes, (3) a spectrograph configured to spatially image light received by each of the plurality of optical probes and produce real-time spectral reflectometry data therefrom, and (4) a control subsystem configured to employ a metal breakthrough analysis to analyze the real-time spectral reflectometry data and determine at least one wafer state parameter therefrom, and cause the polishing to be adjusted based upon the at least one wafer state parameter. 
   The present invention, in another embodiment, may provide an optical closed-loop control system for use with a chemical mechanical polishing (CMP) apparatus for polishing a semiconductor wafer, the CMP apparatus having a platen, a polishing pad coupleable with a top surface of the platen, a plurality of probe windows within the polishing pad and a wafer carrier, where the optical closed-loop control system includes: (1) a plurality of optical probes coupleable to corresponding ones of the plurality of probe windows and mountable through the platen, (2) a flash lamp configured to provide light to each of the plurality of optical probes, (3) a spectrograph configured to spatially image light received by each of the plurality of optical probes and produce real-time spectral reflectometry data therefrom, and (4) a control subsystem configured to employ a model analysis to analyze the real-time spectral reflectometry data and determine at least one wafer state parameter therefrom, and cause the polishing to be adjusted based upon the at least one wafer state parameter. 
   The foregoing has outlined preferred and alternative features of the present invention so that those skilled in the art may better understand the detailed description of the invention that follows. Additional features of the invention will be described hereinafter that form the subject of the claims of the invention. Those skilled in the art should appreciate that they can readily use the disclosed conception and specific embodiment as a basis for designing or modifying other structures for carrying out the same purposes of the present invention. Those skilled in the art should also realize that such equivalent constructions do not depart from the spirit and scope of the invention. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     For a more complete understanding of the present invention, reference is now made to the following descriptions taken in conjunction with the accompanying drawings, in which: 
       FIG. 1  illustrates a portion of a typical CMP tool; 
       FIG. 2  illustrates an optical closed-loop control system for use with a chemical mechanical polishing apparatus constructed in accordance with the principles of the present invention; 
       FIG. 3  illustrates an alternative embodiment of an optical closed-loop control system of  FIG. 2  constructed in accordance with the principles of the present invention; 
       FIGS. 4A and 4B  illustrate a plan-view and a cross-sectional view, respectively, of an embodiment of an optical probe constructed in accordance with the principles of the present invention; 
       FIGS. 5A and 5B  illustrate exemplary placements of a probe tip to achieve an impaction into the probe window according to the principles of the present invention; 
       FIG. 6  illustrates a flow diagram of an embodiment of a method of operating an optical closed-loop control system for use with a chemical mechanical polishing apparatus for polishing a semiconductor wafer conducted according to the principles of the present invention; 
       FIG. 7  illustrates a flow diagram of an embodiment of a method of collecting normalization data from a reference wafer for use with a chemical mechanical polishing (CMP) apparatus conducted according to the principles of the present invention; 
       FIGS. 8A-D  illustrate exemplary graphs of acceptable and unacceptable reference spectra for a bare silicon reference wafer obtained by the method of  FIG. 7 ; 
       FIGS. 9A-C  illustrate a model and graphs that discuss how a flash lamp in combination with optical probes provide sampling spot isolation, thereby preserving the interference contrast of reflected light according to the principles of the present invention; 
       FIG. 10  illustrates a flow diagram of an embodiment of a method of performing a n-band analysis on real-time spectral reflectometry data conducted according to the principles of the present invention; 
       FIGS. 11A-D  illustrate an example of the raw spectra and derived real-time spectral reflectometry data analyzed at various stages of the n-band analysis of  FIG. 10 ; 
       FIG. 12  illustrates an example of a silicon wafer having trenches and employable in shallow trench isolation; 
       FIG. 13  illustrates a flow diagram of an embodiment of a method of performing a transform analysis on real-time spectral reflectometry data conducted according to the principles of the present invention; 
       FIG. 14  illustrates an example of a wafer having an interlayer dielectric deposited over the current features of the wafer; 
       FIGS. 15A-D  illustrate an example of the raw spectra and derived real-time spectral reflectometry data analyzed at various stages of the FFT type transform analysis of  FIG. 13 ; 
       FIGS. 16A and 16B  illustrate an example of the further processing of the derived real-time spectral reflectometry data of  FIGS. 15A-D , wherein the derivatives of the FFT signal are used to determine a wafer state parameter for the CMP processing of an interlayer dielectric; 
       FIG. 17  illustrates a flow diagram of an embodiment of a method of performing a metal breakthrough analysis on real-time spectral reflectometry data conducted according to the principles of the present invention; 
       FIG. 18  illustrates an example of a wafer having a metal layer deposited onto the entire top surface of the wafer; 
       FIGS. 19A-F  illustrate an example of the raw spectra and derived real-time spectral reflectometry data analyzed at various stages of the metal breakthrough analysis of  FIG. 16 ; 
       FIG. 20  illustrates a flow diagram of an embodiment of a method of determining a model for use with a model analysis conducted according to the principles of the present invention; 
       FIG. 21  illustrates an exemplary wafer and associated wafer state parameters employable in a chemical mechanical process according to the principles of the present invention; 
       FIG. 22  illustrates an exemplary silicon-on-insulator type wafer employable in a method of the present invention; 
       FIG. 23  illustrated is exemplary reflectances of a spot of light transmitted into a silicon-on-insulator type wafer of  FIG. 22 ; 
       FIG. 24  illustrates a flow diagram of an embodiment of a method of performing a model analysis on real-time spectral reflectometry data conducted according to the principles of the present invention; 
       FIGS. 25A-D  illustrate an example of the raw spectra and derived real-time spectral reflectometry data analyzed at various stages of the model analysis of  FIG. 24 ; and 
       FIG. 26  illustrates a spectrograph for spatially imaging light received by optical probes to a common charge-coupled device constructed according to the principles of the present invention. 
   

   DETAILED DESCRIPTION 
   Referring initially to  FIG. 2 , illustrated is an optical closed-loop control system, generally designated  200 , for use with a chemical mechanical polishing (CMP) apparatus constructed in accordance with the principles of the present invention. Although the current embodiment is illustrated using a conventional rotary-type platen type CMP polisher, the invention may be used with other types of CMP polishers that are well known in the art, such as orbital and fixed platen systems. In one embodiment, the CMP apparatus includes a platen  202  and coupled to a top surface of the platen  202  is a conventional polishing pad  210 . The platen  202  is also coupled to a spindle  204 . The spindle  204  may be coupled to a platen controller  206  that is configured to cause translations, rotations, orbits or other compound movements of the platen  202  and spindle  204 . The platen controller  206  also includes at least one platen sensor  208  that is configured to monitor the location of the platen  202  and the rotation speed of the spindle  204 . For purposes of the present invention, the phrase “configured to” means that the device, the system or the subsystem includes the necessary software, hardware, firmware or a combination, thereof to accomplish the stated task, of course, however, the present invention is not limited to a moving platen. In other embodiments, the platen may be a fixed platen or a rotating platen. 
   The portion of the CMP apparatus illustrated also includes a wafer carrier  270 . The wafer carrier  270  includes a ring  271  that holds a semiconductor wafer  260  in the wafer carrier  270 . In the illustrated embodiment, the wafer carrier  270  includes three controllable pressure zones  272 ,  273 ,  274  that can be individually controlled to adjust the pressure applied to different portions of the semiconductor wafer  280  during the CMP process. The wafer carrier  270  may also be coupled to a carrier controller  276  that is configured to cause translations and/or rotations of the wafer carrier  270 . The carrier controller  276  also includes at least one carrier sensor  278  that is configured to monitor the location and rotation speed of the wafer carrier  270 . The carrier controller  276  is also configured to adjust or cause to be adjusted the pressure applied at each of the controllable pressure zones  272 ,  273 ,  274 . Of course, however, the present invention is not limited to a single wafer carrier. Nor is the present invention limited to a wafer carrier having three controllable pressure zones. In other embodiments, the present invention may be configured to operate with a CMP apparatus having multiple wafer carriers and/or wafer carriers having any number of controllable pressure zones or no controllable pressure zones. 
   In the illustrated embodiment, the optical closed-loop control system  200  includes a plurality of optical probes  220 ,  222 ,  224  impacting a corresponding probe window  212 ,  214 ,  216 . The probe windows  212 ,  214 ,  216  are positioned within the polishing pad  210 . In a related embodiment, the optical probes may be positioned along the top surface of the platen  202  in such a manner to allow the monitoring of the semiconductor wafer  280  at specific radial locations. The impaction of the optical probes  220 ,  222 ,  224  with the probe windows  212 ,  214 ,  216  allows the optical probes  220 ,  222 ,  224  to maintain contact with their corresponding probe window  212 ,  214 ,  216  as the pressure applied to the semiconductor wafer  280  and to the polishing pad  210  changes. This impaction also substantially eliminates a water or air gap between the tip of the optical probe and the probe window, and, as such, decreases degradation of the optical signal. The optical probes  220 ,  222 ,  224  are also rigidly mountable through the platen  202  to help maintain a position of each of the optical probes  220 ,  222 ,  224 . If the optical probes  220 ,  222 ,  224  are not positioned to impact the probe windows  212 ,  214 ,  216  and the optical probes  220 ,  222 ,  224  are not rigidly restrained, temporal variations of the optical path may occur. These temporal variations would then cause degradation of the optical signal analysis, which may result in inaccuracies of the CMP of the semiconductor wafer  280 . See  FIGS. 5A and 5B  for a discussion of placement of a tip of an optical probe for impaction into the probe window employed. 
   The optical closed-loop control system  200  also includes a flash lamp  230  and a spectrograph  240 . The flash lamp  230  is configured to provide light to each of the optical probes  220 ,  222 ,  224  via an optical illumination fiber cable  232 . See  FIGS. 4A and 4B  for discussion of an optical probe and its connections. The flash lamp  230  is also configured to minimize an exposure time of the light onto the semiconductor wafer  280 . In another embodiment, the flash lamp  230  in combination with each of the plurality of optical probes  220 ,  222 ,  224  provide sampling spot isolation, thereby preserving the interference contrast of the reflected light. See  FIGS. 9A-C  for more discussion on interference contrast of the reflected light. 
   The spectrograph  240  is configured to be coupled to each of the optical probes  220 ,  222 ,  224  via individual optical collection fiber cables  242 . The spectrograph  240  is further configured to spatially image the light received by each of the optical probes  220 ,  222 ,  224 . In another embodiment, the spectrograph  240  is further configured to spatially image the light received by each of the optical probes  220 ,  222 ,  224  to a common charge-coupled device (CCD). In yet another embodiment, the light received from each of the optical probes  220 ,  222 ,  224  are collimated reflections from the semiconductor wafer  280 . The spectrograph  240  is also configured to produce real-time spectral reflectometry data from the spatially imaged light. The flash lamp  230  and the spectrograph  240 , however, are not limited to only the three optical probes illustrated in FIG.  2 . In other embodiments of the present invention, the flash lamp  230  may be configured to provide light to any number of optical probes and the spectrograph  240  may be configured to receive and spatially image light received from any number of optical probes. The flash lamp  230  may also be controlled by the spectrograph  240  via a control line  253 . The spectrograph  240  may control the triggering time of the flash lamp strobe as well as any other operational parameters of the flash lamp  230 . The spectrograph  240  may also directly monitor the light emitted by the flash lamp  230  using an additional fiber optic cable (not shown). See  FIG. 26  for a more detailed discussion of an embodiment of the spectrograph  240 . 
   In the illustrated embodiment, the optical closed-loop control system  200  also includes a control subsystem  250  that is configured to analyze the real-time spectral reflectometry data produced by the spectrograph  240  via a spectrograph/control data line  254  and determine at least one wafer state parameter therefrom. In a one embodiment, the control subsystem  250  is located within the CMP tool itself. In another embodiment, the control subsystem  250  may be individually mounted to the platen  202 . (See FIG.  3 ). In yet another embodiment, the control subsystem  250  may be embodied within the spectrograph  240 . In a related embodiment, the control subsystem  250  may be embodied within a conventional computer system employing specialized software, hardware or a combination thereof. For purposes of the present invention, the term “wafer state parameter” includes a reflection spectrum or any part thereof, an average of all or parts of one or more reflection spectra, a metrology data point or trends of data points derived from all or part of a reflection spectrum, a material layer removal rate, an error data point, an endpoint, a material layer thickness and a material layer change in thickness. Of course, however, a wafer state parameter may include other measurable or analytically derived data points not listed above. In another embodiment, the spectrograph data line  254  may be a high speed serial connection or part of a network. In yet another embodiment, the spectrograph  240  may communicate with the control subsystem  250  via wireless communications. 
   In the described embodiment, the platen controller  206 , the carrier controller  276 , the control subsystem  250  and the main tool controller  290  may be embodied within separate physical devices or computational systems, and may operate in a distributed control scheme. In a related embodiment, the platen controller  206 , the carrier controller  276 , the control subsystem  250  and the main tool controller  290  may be embodied within hardware, software, firmware or a combination thereof. In yet another embodiment, the platen controller  206 , the carrier controller  276 , the control subsystem  250  and the main tool controller  290  may be combined together, or grouped or sub-grouped in different combinations. Of course, however, the present invention is not limited to only the component described above. In other embodiments, the optical closed-loop control system  200  may include additional components than illustrated. 
   The control subsystem  250  is further configured to cause the CMP of the semiconductor wafer  280  to be adjusted based upon the at least one wafer state parameter. The control subsystem  250  may also be configured to control a movement of the wafer carrier  270  based upon one or more wafer state parameters. For purposes of the present invention, the phrase “control a movement” means to control a translation, a rotation, an orbit, in- or out-of-plane displacement or a combination thereof. Movement is considered in a vector sense, magnitude, direction and rates of change are implicit. These movements may be ascribed to the carrier  270  as well as to the platen  202 . In the illustrated embodiment, the control subsystem  250  may control the carrier controller  276  via a control line  256  to cause a movement of the wafer carrier  270 . In another embodiment, the control subsystem  250  may send a command to the main CMP tool controller  290  that may then engage the carrier controller  276  to act accordingly. The same may be done for the platen controller  206 . The control subsystem  250  may also employ positioning and rotation speed data from the carrier sensor  278  in controlling the wafer carrier  270 . In a related embodiment, the control subsystem  250  is configured to employ at least one wafer state parameter to individually control each of the controllable pressure zones  272 ,  273 ,  274  to adjust the pressure applied to different portions of the semiconductor wafer  280  in order to optimize the polishing of the semiconductor wafer  280 . 
   The control subsystem  250  may also be configured to control a movement of the platen  202  based upon at least one wafer state parameter if the platen  202  is a moving platen. In the illustrated embodiment, the control subsystem  250  may control the platen controller  206  via a control line  255  to cause a movement of the platen  202 . The control subsystem  250  may also employ positioning and rotation speed data from the platen sensor  208  in controlling the platen  202 . Also, the control subsystem  250  may transmit closed-loop control information to the main CMP tool controller  290  via control/data line  258 . In the illustrated embodiment, the control subsystem  250  may transmit closed-loop control information via the control/data line  258  to the main CMP tool controller to control and receive information concerning at least the wafer carrier  270 , the plurality of pressure zones  272 ,  273 ,  274 , the carrier controller  276 , the platen  202 , and the platen controller  206 . The main CMP tool controller  290  may also communicate closed-loop control and status information to the CMP apparatus and other devices via a local area network (not shown). 
   A moving platen, such as the platen  202  illustrated in  FIG. 2 , has unique problems with maintaining the integrity of the optical paths, especially the optical paths between the optical probes  220 ,  222 ,  224  and the flash lamp  230  and the spectrograph  240 . If the flash lamp  230  and/or the spectrograph  240  are not coupled to the moving platen, the optical cables would have to go through an optical rotating coupler connected to the spindle  204 . The optical coupler may introduce noise or cause degradation of the optical signal that would lead to a less accurate analysis. In one embodiment, the present invention advantageously increases the integrity of the optical paths by coupling the flash lamp  230 , the spectrograph  240  and at least a portion of the control subsystem  250  on the moving platen. In this configuration, the optical illumination fiber cable  232  of the optical probes  220 ,  222 ,  224  are directly connected to the flash lamp  230 . Also, the optical collection fiber cable  242  of the optical probes  220 ,  222 ,  224  are directly connected to the spectrograph  240 . The elimination of the optical rotating coupler and employing direct connections increases the integrity of the optical signals and, as such, increases the accuracy of the analysis. 
   As described above, the control subsystem  250  is configured to analyze real-time spectral reflectometry data obtained from the spectrograph  240  during the CMP process and determine at least one wafer state parameter therefrom. The control subsystem  250  may employ n-band analysis in analyzing the real-time spectral reflectometry data and determining the at least one wafer state parameter therefrom. In another embodiment, the control subsystem  250  may employ a transform analysis in analyzing the real-time spectral reflectometry data and determining the at least one wafer state parameter therefrom. In yet another embodiment, the control subsystem  250  may employ a metal breakthrough analysis in analyzing the real-time spectral reflectometry data and determining the at least one wafer state parameter therefrom. In still yet another embodiment, the control subsystem  250  may employ a model analysis in analyzing the real-time spectral reflectometry data and determining the at least one wafer state parameter therefrom. These analysis models are described in more detailed in  FIGS. 10-25 . 
   The control subsystem  250  may be further configured to perform a normalization using a reference wafer and employ the data obtained therefrom in at least the determination of ore or more wafer state parameters. The data from the normalization procedure is commonly composed of one or more spectra or an average of spectra. For example, the data from the normalization may be used as a target during the CMP processing of production semiconductor wafers. In another example, the normalization data is used to normalize the intensity of the reflected spectra. The method of acquisition of normalization spectra using a reference wafer is discussed in more detail in FIGS.  7  and  8 A-D. In another embodiment, the control subsystem may be configured to adjust for attenuation of the light received due to a slurry  260  or a probe window, such as probe window  212 , during the polishing of the semiconductor wafer  280 . One type of attenuation of the light received is due to the presence of abrasive and/or colored metallic oxide particles in the slurry causing the light to scatter. Another type of attenuation of the light received is due to the fact that probe window has some opacity and may cause some scattering. These attenuations may be wavelength specific and non-uniform. One skilled in the art understands that attenuation of the light received reduces the ability to correctly interpret or detect the current condition of the semiconductor wafer  280 . The present invention advantageously adjusts for attenuation of the light signals during the analysis process to increase the accuracy of the CMP process. A more detailed discussion of adjusting for the attenuation of the light received is discussed in association with  FIG. 7  (Normalization method) and  FIG. 13  (Transform Analysis method). 
   One skilled in the art should know that the placement of the elements of the optical closed-loop control system  200  are not limited to the locations illustrated. Nor is the routing of cables employed by the optical closed-loop control system  200  limited to the routing illustrated. Other embodiments of the present invention, the elements of the optical closed-loop control system  200  and associated cabling may be in any location and the location may be optimized in accordance with the requirements of a moving platen, such as maintaining gyroscopic stability. 
   Turning now to  FIG. 3 , illustrated is an alternative embodiment of an optical closed-loop control system of  FIG. 2 , generally designated  300 , constructed in accordance with the principles of the present invention. The optical closed-loop control system  300  is identical to and has the same functionality as the optical closed-loop control system  200  of  FIG. 2  except for what is discussed below. 
   The optical closed-loop control system  300  includes a control subsystem  350  that is coupled to said platen  202 , and is identical to the control subsystem  250  of FIG.  2 . The control subsystem  350  is further configured to employ a wireless interface module  352  to transmit closed-loop control information to the CMP apparatus to control at least the wafer carrier  270 . In the illustrated embodiment, the optical closed-loop control system  300  also includes a CMP wireless interface  392  coupled to the main CMP controller  290 . The control subsystem  350  may transmit and receive closed-loop control information and status to/from the main CMP tool controller  290  via the wireless interface module  352  and the CMP wireless interface  392 . The control subsystem  350  may still send and receive closed-loop control information and status to the carrier controller  276  and the platen controller  206 . In a related embodiment, the control subsystem  352  may control at least a portion of the flash lamp  230  and receive data from the flash lamp via a control/data line  353 . 
   The control subsystem  350  may also transmit closed-loop control information via the wireless interface module  352  to the CMP wireless interface module  392  and the main CMP tool controller  290  to control and receive information concerning at least the wafer carrier  270 , the plurality of pressure zones  272 ,  273 ,  274 , the carrier controller  276 , the platen  202 , and the platen controller  206 . The CMP wireless interface module  392  may also communicate closed-loop control and status information to the CMP apparatus and other devices via a local area network (not shown). In yet another embodiment, a portion of the control subsystem  350  may be coupled to the platen  202  and the remaining portion of the control subsystem  350  may be located within the CMP apparatus or the main CMP tool controller  290  and communication between each portion of the control subsystem  350  may be via the wireless interface module  352  and the CMP wireless interface module  392 . 
   Turning now to  FIGS. 4A and 4B , illustrated is a plan-view and a cross-sectional view, respectively, of an embodiment of an optical probe, generally designated  400 , constructed in accordance with the principles of the present invention. The optical probe  400  includes a probe tube  404  that rigidly contains a portion of the optical probe fibers  410  and  412 . The probe tube  404  also contains a lens  402  having one end planar with a distal end of the probe tube  404  forming a probe tip  401 . The lens  402  is also rigidly coupled to the optical probe fibers  410  and  412 . In one embodiment, the lens  402  may be configured to provide collimated light collection. In another embodiment, the lens  402  may be configured to provide collimated light illumination. In yet another embodiment, the lens  402  is an integral gradient index lens. 
   The optical probe  400  includes coupling means  406  that is configured to rigidly mount the probe tube  404  and the integral optical fibers  410  and  412  through a platen. The coupling means  406  allows for precise installation and adjustment, and also allows for optical contacting of the probe tip  401  with a probe window. The probe window may be one of the probe windows  212 ,  214 ,  216  of FIG.  2 . This precise installation./adjustment and optical contacting with the probe window also allow the integrity of the optical path to be maintained. In one embodiment, the coupling means  406  may be a threaded mechanism such as a nut  406   a  coupled with a ferrule  406   b . In another embodiment, the probe tube  404  and the coupling means  406  may be precisely adjusted/installed by use of a simple threaded mechanism such as a screw. 
   The probe tube  404  is also coupled to a transition tube  420 . The transition tube  420  permits the bifurcation of the bundled optical collection fiber cable  412  and optical illumination fibers  410 . Following the transition tube  420  the optical collection fiber  412  is encased in a protective jacket  430  that, along with connector  432 , is designated the “return leg” or “spectrograph leg” of the probe  400 . The name denotes the final device to which the leg of the probe  400  is connected: namely a spectrograph or other light detection means. For example, the spectrograph  240  of FIG.  2 . Similarly, the optical illumination fibers  410  are encased in a protective jacket  440  that along with connector  442  are designated the “illumination leg” or “flash lamp leg” of the probe  400 . Here the name denotes the final device to which the leg of the probe  400  is connected, namely the flash lamp or other light source. For example, the flash lamp  230  of FIG.  2 . The present invention advantageously employs direct coupling of the legs of the probe  400  to a spectrograph and a flash lamp in order to maintain the integrity of the optical path from the probe tip to the spectrograph and from the flash lamp to the probe tip. One skilled in the art should note that the addition of any extra connections in the fiber optic cables has the effect of degrading both the intensity of the illuminating and collected light signals. For a typical SMA905 type optical interconnects, available from AMP, the loss is typically 0.5 dB (˜12.5%) per connection. Adding one patch cable requires the addition of two connections for a total loss of signal of about 25%. The close placement of the spectrograph and flash lamp minimize the number of connections to the minimum required, namely two. 
   Turning now to  FIG. 4B , illustrated is a cross-sectional view of the optical probe cable of  FIG. 4A  constructed in accordance with the principles of the present invention. The probe tube  404  supports an optical collection fiber  412  at its core. In one embodiment, the optical collection fiber  412  may be a 300 micron fiber. The optical collection fiber  412  may be coupled to the lens  402  of the optical probe  400 . The probe tube  404  also encloses a plurality of optical illumination fibers  410  adjacent to the optical collection fiber  412  and are configured to provide illumination. In the illustrated embodiment, the optical illumination fibers  410  annularly encase the optical collection fiber  412 . The optical illumination fibers  410  may be 200 micron fibers. In a related embodiment, the plurality of optical illumination fibers  410  may be configured to provide collimated illumination. Also, the optical illumination fibers  410  may extend to the probe tip  401 . 
   Turning now to  FIGS. 5A and 5B , illustrated are exemplary placements of a probe tip to achieve an impaction into the probe window according to the principles of the present invention. Illustrated is a platen  504  with a conventional polishing pad  502  coupled to a ton surface of the platen  504 . Positioned within the polishing pad  502  is a probe window  510 . The probe window  510  is positioned over an optical probe  520  rigidly mountable through the platen  504 . The placement or positioning of a tip  525  of the optical probe  520  in the platen  504  depends upon achieving a specific range of impactions into the probe window  510 . It is desirable to maintain contact between the probe window  510  and the probe tip  525 . If there is a gap between the probe window  510  and the probe tip  525 , the optical path continuity may become diminished or impeded due to the use of a slurry in the CMP process. The transmission properties of the optical path may also become unstable during the wafer processing as the CMP process mechanically changes the gap between the probe tip  525  and the probe window  510  or forces slurry, air, or other fluids in the gap. This in turn may adversely affect the analysis of the light received by the optical probes and a spectrograph. One or more of these instability conditions are often observed during the data collection for normalization from a reference wafer as described in FIG.  7 . 
   The lower surface of the probe window  510  may be of three basic shapes: planar, convex, and concave.  FIG. 5A  illustrates the minimum height for the probe  520  to extend above the surface of the platen  504 . For probe windows with planar or convex surfaces, as illustrated by probe window  510 , the minimum height is 0.0 inches. For concave surfaces this minimum height should be increased to compensate for the curvature of the surface as by probe window  530  of FIG.  5 B. To ensure impaction and to simultaneously minimize the effects of altering the contour of the top surface of the probe window  510 , the probe  520  should not extend into the probe window  510  more than about 0.02 inches or equivalently about 10% of the probe window  510  thickness that is typically 0.040 to 0.180 inches. Distorting the top surface of the probe window  510  has the effect of creating a localized pressure point of the wafer that result in altered polishing performance or a dmaged wafer. With the probe  520  properly impacted into the probe window  510 , the normalization procedure of FIG.  7  and the corrections, such as those discussed in  FIG. 13 , may be readily applied to compensate or correct for attenuations from the window, probe tip/window interface, and slurry. Of course, however, the location and positioning of the maximum and minimm heights for the probe tips illustrated in  FIGS. 5A and 5B  are for illustrative purposes and the present invention is not limited to these illustrated locations and positions. 
   Turning now to  FIG. 6 , illustrated is a flow diagram of an embodiment of a method of operating an optical closed-loop control system, generally designated  600 , for use with a chemical mechanical polishing (CMP) apparatus for polishing a semiconductor wafer conducted according to the principles of the present invention. The CMP apparatus may have a platen, a polishing pad coupleable with a top surface of the platen and a wafer carrier. In  FIG. 6 , the method  600  first performs intitialization in a step  610 . 
   After initialization, the method  600  provides light to each of the optical probes employed by the optical closed-loop control system in a step  620 . In one embodiment, the light is provided by a flash lamp and minimizes an exposure time of the light onto the semiconductor wafer. In a related embodiment, the optical probes may include a plurality of illumination fibers that provide collimated illumination. In yet another embodiment, the optical probes may include collimated illumination optics. Next, the method  600  spatially images the light received by the optical probes after reflection from the wafer surface in a step  630 . In one embodiment, the method  600  spatially images the light received by the optical probes to a common charge-coupled device (CCD) of spectrograph. In a related embodiment, the optical probes may include collimated collection optics to collimate the reflections of the light received by the optical probes. The method  600  then produces real-time spectral reflectometry data from the spatially imaged light in a step  640 . 
   The method  600  analyzes the real-time spectral reflectometry data and determines at least one wafer state parameter therefrom in a step  650 . In one embodiment, the method  600  may employ a n-band analysis in analyzing the real-time spectral reflectometry data and determining at least one wafer state parameter. In a second embodiment, the method  600  may employ a transform analysis in analyzing the real-time spectral reflectometry data and determining at least one wafer state parameter. In a third embodiment, the method  600  may employ a metal breakthrough analysis in analyzing the real-time spectral reflectometry data and determining at least on wafer state parameter. In a fourth embodiment, the method  600  may employ a model analysis in analyzing the real-time spectral reflectometry data and determining at least one wafer state parameter. Of course, however, other analysis models may be employed by the method  600  to analyze the data and determine at lease one wafer state parameters. 
   Next, the method  600  employs the at least one wafer state parameter to determine if it has reached the end of the process in a decisional step  600 . If the end of the process has been reached, the method  600  stops in a step  670 . If the method  600  determined that it has not reached the end of the process, the method  600  then, employing the at least one wafer state parameter, determines if the process is to be adjusted in a step  680 . If the process is to be adjusted, the method  600  then employs the at least one wafer state parameter to adjust the process in a step  690 . In one embodiment, the optical closed-loop control system may include a wafer carrier having a plurality of controllable pressure zones. The method  600  employs the at least one wafer state parameter to individually control each of the plurality of controllable pressure zones to adjust the pressure applied to different portions of the semiconductor wafer in order to optimize the polishing of the semiconductor wafer. 
   The method  600  may also adjust the process by controlling a movement of the wafer carrier based upon the at least one wafer state parameter. In yet another embodiment, the method  600  may adjust the process by controlling a movement of a moving platen based upon the at least one wafer state parameter, if the CMP apparatus is equipped with a moving platen. In still yet another embodiment, the method  600  may adjust the process by controlling a movement of the wafer carrier and a movement of a moving platen based upon the at least one wafer state parameter, if the CMP apparatus is equipped with a movable wafer carrier and a movable platen. 
   After adjusting the process in the step  690 , the method returns to provide light to the optical probes again in the step  620 . In another embodiment, the method  600  may also perform as part of step  650  a normalization of the real-time spectral data using the data collected from a reference wafer (as per  FIG. 7 ) and employ the data obtained from the normalization in at least the determination of the at least one wafer state parameter. 
   One skilled in the art should know that the present invention is not limited to adjusting the process as described above. In other embodiments, the present invention and method may adjust or cause to adjust other devices or parameters of the CMP process. Also, other embodiments of the present invention may have additional or fewer steps than described above. 
   Turning now to  FIG. 7 , illustrated is a flow diagram of an embodiment of a method collecting normalization data using a reference wafer, generally designated  700 , for use with a chemical mechanical polishing (CMP) apparatus conducted according to the principles of the present invention. In one embodiment, the CMP apparatus may be a CMP apparatus that incorporates the optical closed-loop control system illustrated in  FIG. 2  or FIG.  3 . In  FIG. 7 , the method  700  first performs initialization in a step  710 . 
   After initialization, the CMP apparatus is prepared in a step  720 . In preparing the CMP apparatus, the CMP apparatus should be configured to operate in the same or substantially similar manner as the CMP apparatus would be in processing production wafers. It is important that the kinematical, optical and hydrodynamical conditions of the wafer, slurry, probe window, and probe interface are substantially consistent from the reference wafer to the production wafers. If the conditions are not substantially consistent, then analysis of the CMP process may produce flawed results. 
   The requirement for the usage of the same CMP process conditions permits the method  700  to remove a majority of the attenuation effects caused by the slurry, such as scattering due to oxidation of metal in the slurry. The method  700  may also remove a majority of the attenuation effects cause by the probe window, and window-probe interface. More specifically, the probe window is a generally transparent material often 0.040 to about 0.200 inches thick and typically has a wavelength transmission range is from about 200 nm (UV) to about 2000 nm (NIR). This includes the visible range where most current analysis is performed. The probe window is often made from polyurethane, acrylics, polycarbonates, nylons and polyesters or some combinations of these materials. These materials typically cause some scattering and attenuation of light signals as the light passes through the probe window. The attenuation is defined relative to the thickness (T) of the material and its extinction coefficient k(λ) for any specific wavelength. A common form of the transmission may be give as T=Exp(−k*T) therefore if a thicker window is used the attenuation is greater. Similarly for the scattering in the material; the scattering may be defined as the property of the material whereby a normally incident collimated beam of light is distorted as it passes through the material. This typically results in a decrease in the degree of collimation of the beam as well as spatial and wavelength-specific photometric changes to the distribution of the beam. For example, strong scattering will redden the center of the beam since blue wavelengths are most strongly scattered. 
   In addition, the CMP process causes the surfaces of the probe window to be worn. This is especially true of the top surface, which is abrasively conditioned (cleaned and textured) by the CMP tool, often for each wafer. This conditioning process produces a series of scratches on the top surface of the probe window. These scratches and their interaction with the slurry and particles add to the scattering and attenuation problems. The present invention, in one embodiment, advantageously accounts and adjusts for these problems during the normalization process and other processes defined later. Additional information concerning probe windows is discussed in the published PCT application entitled “POLISHING PAD WINDOW FOR A CHEMICAL-MECHANICAL POLISHING TOOL,” PCT Publication No. WO 01/94074 Al, which is hereby incorporated by reference in its entirety. 
   Mathematically, the attenuation can be equated to a function that is multiplied by the reflected light signal as follows: 
       S   =       (     1   -     F   a       )     ×     I   fl     ×     R   x           
 
wherein, S is the measured reflected light spectrum, I f1  is the flash lamp spectrum, R x  is the reflectance of a wafer, and F a  is the total wavelength-dependent attenuation of the optical path. R x  may designate a reference wafer (R norm ) or a wafer being processed (R wafer ). The typical normalization procedure includes the division of the spectrum S by that spectrum S′ that was recorded as a reference or normalization spectrum, i.e. S/S′. This function should result in the ration R wafer /R norm , since R norm  is commonly known (the reference wafer is most often a bare silicon wafer) then R wafer  is uniquely determined. However, if the same process conditions are not used then the attenuation effects are not equal to F a  but equal to some different F a ′. Then the ratio is then (R wafer /R norm )*(F a ′/F a ) and the normalized signal is now distorted and R wafer  is not uniquely determined.
 
   Next, the reference wafer is loaded into the CMP apparatus in a step  730 . Typically is bare silicon or oxide wafer is loaded into a wafer carrier of the CMP apparatus. In other embodiments, other types of wafers may be used if the wafer type is clearly defined and the optical properties of the substrate and film layers of the wafer are known. The method  700  then processes the wafer and collects data about the process in a step  740 . In one embodiment, the wafer is processed for a known period of time. For a bare silicon wafer the time period is typically one minute. For an oxide film wafer, the time period should be long enough for at least a few thousand Angstroms of material to be polished from the wafer. In one embodiment, the data may be collected by the optical probes and the spectrograph of  FIG. 2  or FIG.  3 . 
   The collected data is then analyzed for instability in a step  750 . Instability may include oscillations in the shape of the spectrum and the fluctuations in the intensity of the spectrum. Instabilities are typically indicative of problems with the optical stability of the CMP apparatus and control system that should be corrected prior to further operation. See  FIGS. 8A-D  for an example of instability problems isolated from reference data of a bare silicon wafer. In one embodiment, the collected data may be analyzed by the control subsystem of FIG.  2 . Next, the method  700  determines if the collected data contains significant instabilities in a decisional step  760 . A specific example of a significant instability is if the time variation of the data collected from a bare silicon wafer has a standard deviation that is greater than or equal to 5% of the averaged spectral signal. If the collected data contains significant instabilities, the method  700  stops processing in a step  765 . This allows for analysis and rectification of the cause of the instabilities. 
   If the collected data does not contain significant instabilities, the method  700  then averages the collected data in a step  770 . The method  700  averages the time series of the collected data, excluding definable first and last time periods of data collected to create the reference data. The first and last time periods of the data collection times are commonly prone to changes in the slurry flow dynamics or mechanical dynamics of the CMP apparatus that are not typical of the majority of the CMP process. The method  700  than saves the averaged data as the reference data in a step  780 . The reference data may be used in the analysis of the production wafers during the CMP process. The method  700  then stops processing in a step  790 . 
   One skilled in the art should know that the present invention is not limited to processing and collecting data based on a time period. In other embodiments, the present invention and method may process the wafer and collect data based on other predetermined criteria. Also, other embodiments of the present invention may have additional or fewer steps then described above. 
   Turning now to  FIGS. 8A-D , illustrated are exemplary graphs of acceptable and unacceptable reference spectra for a bare silicon reference wafer obtained by the method of FIG.  7 . These spectra are shown plotted from 420-500 nm for brevity. The spectra  810  of  FIG. 8A  represents the averaged signal for the collected normalization time series of spectra. (See  FIG. 7 , Step  770 ). The spectrum  820  is an individual sample spectra that portrays the maximum excursion from the average data. This variation is typically considered acceptably small.  FIG. 8B  illustrates a percent difference plot  830  for the spectra  810  and  820  of FIG.  8 A. The percent difference is randomly distributed and is about 5%. Typically, differences larger than what is illustrated in  FIG. 8B  are suspect and otherwise deemed unacceptable. 
   In  FIG. 8C , the spectra  810  represents the averaged signal for the collected normalization time series of spectra. The spectra  840  is an individual sample spectra that portrays an excursion from the average data.  FIG. 8D  illustrates a percent difference plot  850  for the spectra  810  and  840  of FIG.  8 C. The percent difference in this example is about 9% and is not randomly distributed. The collected set of normalization data represented by spectra  840  is unacceptable due to the size of the difference as well as the presence of structure. The structure may be due to an instability in the optical path (probe window, fiber, etc.) that should be corrected prior to operation of the CMP system. Of course, however, the spectra illustrated in  FIGS. 8A-D  are for illustrative purposes only and the present invention is not limited to the exact spectra illustrated. 
   Turning now to  FIGS. 9A-C , illustrated are a model and graphs that discuss how a flash lamp in combination with optical probes provide sampling spot isolation, thereby preventing interference contrast of reflected light according to the principles of the present invention. The preservation of the interference contrast is dependent on a probe spot size and a total area of the wafer sampled during a traverse of the spot over a wafer,  FIG. 9A  illustrates a simplified model of the optical interference from a single layer silicon dioxide film  910  deposited over a silicon wafer substrate  920 .  FIG. 9A  also illustrates how selected individual light rays that comprise a large sampled spot on the wafer will reflect and interfere upon interaction with a film of nonuniform thickness. 
   The silicon dioxide film  910  has a gradient in thickness that is typical of semiconductor films processed by CMP. The reflectometry data collected over such an area will have reduced interference contrast due to the incoherent summation of the reflected light  930 .  FIG. 9B  illustrates normalized reflectance spectra  940  for a limited series of silicon dioxide thicknesses within the sampled spot. More specifically, the spectra  940  illustrate the theoretical absolute thickness of the modeled films, where one curve represents each different thickness as shown in FIG.  9 A. Measuring the reflectometry data over the area shown in  FIG. 9A  yields, due to loss of interference contrast, the averaged reflectance spectrum  950  illustrated in  FIG. 9C , which is the average of the normalized reflectance spectra  940 . This averaged reflectance spectrum  950  is very similar to the spectrum of bare silicon  960  also illustrated in FIG.  9 C. In this example, the derived measurement of a wafer state parameter such as thickness of the silicon dioxide film  910  will be erroneous due to the reduced interference contrast. Also, the analysis will determine that the film is very thin or does not exist on the substrate  920 . 
   Since the wafer in a CMP tool moves, it is best to minimize the exposure time of the light signal onto the wafer. This further reduces the loss of contrast due to averaging of the non-uniformity of the wafer over the trajectory of the sampled spot. This is accomplished by the use of a light source with a very short exposure time, namely a flash lamp or very fast megahertz chopped CW lamp. In another embodiment, a very fast CCD or mechanically or electronically (CMOS) shuttered detector could be used. With the light now considered instantaneous, the probe diameter (spot size) may be selected. A rule may be developed to relate the planarization length to the limits for the probe diameter as well as the allowable maximum exposed and sampled wafer area. The planarization length is the characteristic length over which a stepped feature on the surface of the wafer is planarized. In other words the planarization length is the feature size over which the step height of that feature is reduced to zero. A typical range for planarization lengths may be from 3 to 10 mm. This condition allows the sampling to incoherently sum the reflectances of the different regions only over a region that is representative of the condition of the wafer and may be reduced to a wafer state parameter. 
   Turning now to  FIG. 10 , illustrated is a flow diagram of an embodiment of a method of performing a n-band analysis on real-time spectral reflectometry data, generally designated  1000 , conducted according to the principles of the present invention. N-band analysis may be used for shallow trench isolation (STI) or other wafer types. An STI type wafer has trenches etched into the silicon substrate and the areas between the trenches are covered with a silicon nitride layer. The silicon nitride layer is covered by and the trenches are filled with silicon dioxide.  FIG. 12  illustrates an example of a silicon wafer with trenches. The goal of shallow trench isolation CMP process is to planarize the silicon dioxide and the silicon nitride mask layer. Typically the CMP process would stop once the silicon nitride is exposed or at a given thickness into the silicon nitride layer. The n-band analysis method  1000 , in one embodiment, is used in determining a wafer state parameter for shallow trench isolation. In one embodiment, the wafer state parameter may be related to the clearing removal of the oxide over the nitride layer or to thinning of the nitride layer. 
   The method  1000  first performs initialization and selects the wavelength bands to use for the n-band analysis in a step  1010 . The number of bands n may be any number of bands automatically selected by a control subsystem based upon the overall spectral data or user selectable. To permit selection of the wavelength bands, a first test/setup wafer of the same type as the wafers to be processed should be polished. The data so collected is divided into multiple wavelength bands similar to those of  FIG. 11A   1120 , 1130 , 1140 , 1150  of equal spectral width. Most commonly the entire spectral range of the recorded spectrum is divided into these narrower spectral bands, although  FIG. 11A  only shows 4 bands for simplicity. The bands are typically more than 5 mm in width; more commonly 10 nm. These spectral data for each of these bands are then averaged or summed at each time step in the series. Next, each of the new time series ( 1125 ,  1135 ,  1145 ,  1155 ) generated from the averaged bands is analyzed for changes in amplitude or slope.  FIG. 11B  illustrates the time series  1125 ,  1135 ,  1145 ,  1155 , that were generated from the bands  1120 , 1130 , 1140 , 1150 , illustrating the strongest desired changes. The bands that show the greatest changes in amplitude or slope near or after the desired endpoint time are then selected to be used in the algorithm for further automated wafer processing. 
   Referring to the signal spectrum from the time series of spectra from a setup wafer in  FIG. 11A , four wavelength bands at 550 nm ( 1120 ), 600 nm ( 1130 ), 750 nm ( 1140 ) and 800 nm ( 1150 ) will be used to explain the method  1000 . In  FIG. 11A , the first wavelength band  110  selected for analysis is at 550 nm, which can range from 545 nm to 555 nm. The second wavelength band  1130  is at 600 nm, which can rage from 595 nm to 605 nm. The third wavelength band  1140  is at 750 nm, which can range from 745 nm to 755 nm. The fourth wavelength band  1150  is at 800 nm, which can range from 795 nm to 800 nm. Of course, however, the present invention is not limited to using only four wavelength bands or the exact wavelengths selected. Other embodiments of the present invention may use any number of wavelength bands at any wavelength. 
   The method  1000  then processes the wafer and collects data for each of the selected wavelength bands in a step  1020 . An example of the real-time spectral reflectometry data collected for the four wavelength bands is illustrated in FIG.  11 A and in reduced form in FIG.  11 B. It has been predetermined by the wavelength bands selected that the 550 nm wavelength band  1125  (Δλ 1 ) and the 600 nm wavelength band  1135  (Δλ 2 ) have upward transitions at or near a predetermined value of a wafer state parameter. Also, the 750 nm wavelength band  1145  (Δλ 3 ) and the 800 nm wavelength band  1155  (Δλ 4 ) have downward transitions at or near the predetermined value of a wafer state parameter. In the illustrated embodiment, the predetermined value of a wafer state parameter may be the point at which the silicon nitride layer is exposed or a given thickness of material has been removed. Of course, however, other predetermined values of wafer state parameters are within the scope of the present invention. 
   Next, the method  1000  individually averages the real-time spectral reflectometry data over the selected wavelength bands (e.g.,  1125 ,  1135 ,  1145 ,  1155  of  FIG. 11B ) in a step  1030 . In this example the method  1000  would individually average the data over the four bands Δλ 1 , Δλ 2 , Δλ 3 , Δλ 4 . In another embodiment, the method  1000  may sum the real-time spectral reflectometry data for the selected wavelength bands. The method  1000  then calculates a trend in a step  1040 . In one embodiment, the trend may be calculated by (Δλ 1 +Δλ 2 )/(Δλ 3 +Δλ 4 ). In the illustrated embodiment, the wavelength bands Δλ 1  and Δλ 2  have upward transitions at or near the predetermined value of a wafer state parameter, and the wavelength bands Δλ 3  and Δλ 4  have downward transitions at or near the predetermined value of a wafer state parameter. Additionally, the method  100  may smooth the time series data into trends with less noise as illustrated in  FIG. 11C , trends  1127 ,  1137 ,  1147  and  1157 . 
   The method  1000  then averages and/or normalizes the trend in a step  1050 . In one embodiment, the average trend is a moving average or an exponential filter. Normalization of the trend is by self-normalization. Self-normalization is defined as the division by the value of the trend at a user selected time after the start of the wafer processing. See  FIG. 11D  for an exemplary analysis trend for the n-band analysis that has been normalized. Next, the method  1000  determines if a predetermined value of a wafer state parameter has been reached in a decisional step  1060 . For this example, the predetermined value of a wafer state parameter is the endpoint  1190  of the shallow trench isolation CMP process. If the predetermined value of a wafer state parameter has been reached, the method  1000  stops processing in a step  1070 . In a related embodiment, the method  1000  may cause the CMP process to stop. 
   If the predetermined value of a wafer state parameter has not been reached, the method  1000  may cause the process to be adjusted in a step  1080 . In one embodiment, the control subsystem  250  of  FIG. 2  may adjust processing parameters or cause physical devices to be adjusted in order to optimally process the wafer. Next, the method  1000  returns to process the wafer and collect more data in the step  1020 . Other embodiments of the present invention may have additional or fewer steps than described above. 
   Turning now to  FIG. 13 , illustrated is a flow diagram of an embodiment of a method of performing a transform analysis on real-time spectral reflectometry data, generally designated  1300 , conducted according to the principles of the present invention. Typically, transform analysis may be used for interlayer dielectric or other semitransparent types of films. For example,  FIG. 14  illustrates a silicon wafer with a field oxide layer, metal vias within a borophosphosilicate glass (BPSG) or phosphosilicate glass (PSG) layer, and metal traces. The wafer also has a dielectric, such as silicon dioxide, deposited over the current features of the wafer resulting in a rough surface (non-planar). Typically, the goal for the CMP process for interlayer dielectric is to planarize the dielectric to a predetermined thickness or to a relative thickness of the dielectric above the topmost metal layer.  FIG. 14  illustrates an example threshold point for planarization of the dielectric. The transform analysis method  1300 , in one embodiment, is used in determining a wafer state parameter for interlayer dielectric. Wafer state parameters may include a reflectance or a thickness. Of course, however, the present invention is not limited to these wafer state parameters. 
   The method  1300  first performs initialization in a step  1310 . After initialization, the method  1300  processes the wafer and collects reflectometry data in a step  1315 . For example, see the spectra  1500  of FIG.  15 A. In one embodiment, the collection includes employing a plurality of optical probes and a spectrograph to obtain real-time reflectometry data of the wafer being processed. Next, the method  1300  normalizes the collected data with previously collected normalization data (Norm(λ)) in a step  1320 . The normalization data Norm(λ), in one embodiment, is the data obtained from the normalization method of FIG.  7 . The collected data may be normalized as follows: 
           R   norm     ⁡     (   λ   )       =         R   ⁡     (   λ   )       *       R   Silicon     ⁡     (   λ   )           Norm   ⁡     (   λ   )             
 
where R(λ) is an alternative mathematical name for the raw spectral data of the currently processing wafer, and R silicon (λ) is the theoretical reflectance of a bare silicon wafer. This mathematical expression assumes that the normalization wafer was a bare silicon wafer. If the normalization data was collected from a different type of wafer, R silicon  may be replaced with the theoretical expression for the wafer type used. Trend  1525  of  FIG. 15B  is an example of the normalized data.
 
   For further discussion of the method of FIG.  13  and associated  FIGS. 15A-D  and  16 A-B, it is assumed that the transform used is a Fourier transform commonly implemented as a “fast Fourier transform” (FFT). Alternatively other mathematical transforms may be employed to transform the data. These types of transforms include Laplace transforms, Z transforms, Legendre transforms, Gabor transforms, and wavelet transforms. Discussion and summary of these and other transforms is noted in “Numerical Recipes in C, the Art of Scientific Computing,” by William H. Press et al., Cambridge University press (2 nd  ed. 1992), which is hereby incorporated by reference. The goal of the transform is to mathematically convert or project the reflectance spectra into a new mathematical form or basis in which one or more wafer state parameters may be easily extracted. The mathematical basis may be selected on theoretical or phenomenological products. This is desired since the reflection spectra of patterned semiconductor wafers is often very complex and direct theoretical modeling often intractable. The FFT transform is often applied since this results in the mathematical functions and values that are easily understood and interpreted to determine desired wafer state parameters such as film thickness. Other transforms such as a Gaussian wavelet transform seeks to decompose the spectra into an easily interpreted basis of the Gaussian function. This function is defined by G(x)=B+A*Exp(−(x−xo)/2s)^2); wherein B is an offset, A an amplitude, xo is a center of the function, and s is the width of the function. These parameters can then be correlated to the wafer state parameters to control the process. 
   Next, the method  1300  performs a first transform by converting the normalized data R norm (λ) into a function of R norm (1/λ) or R norm (n(λ)/λ) in a step  1325 . (See  FIG. 15C , trend  1550 ). This conversion seeks to convert the spectral data into a function that is periodic with respect to the function of 1/λ. This functional form is a preferred basis for the analysis of dielectric films due to the theoretical formulation of the Frensel reflection equations. For additional background information on theoretical modeling of reflections from film stacks, see “Ellipsometry and Polarized Light,” by R. M. A. Azzam and N. M. Basara, Elsevier Science (1987), which is hereby incorporated by reference in its entirety. A review of the theoretical forms of the reflections often provides details for the selection of the best transforms to be selected in the analysis of the data. The procedure for converting the spectral data [data(i,:)] into a function that is periodic with respect to the function of 1/λ [ExpR] may be performed by Matlab code illustrated in Table 1. 
   
     
       
         
             
             
           
             
                 
               TABLE 1 
             
             
                 
                 
             
           
          
             
                 
               wls=250; wle=800; 
             
             
                 
               wl=wls:0.5:wle; 
             
             
                 
               wlindex = (wl−200)*2 + 1; 
             
             
                 
               indexfilm = ones(l,length(wl)); 
             
             
                 
               wnumarray = (indexfilm ./ wl); 
             
             
                 
               Nwlpoints = length(wl); 
             
             
                 
               NumpointsI = 1024; 
             
             
                 
               dwnum=(wnumarray(end)−wnumarray(1))/NumpointsI; 
             
             
                 
               iwnum=wnumarray(1)+0.5*dwnum:dwnum:wnumarray(end); 
             
             
                 
               ExpR = interp1(wnumarray,data(i,:),iwnum); 
             
             
                 
                 
             
          
         
       
     
   
   The method  1300  then fits the converted and normalized data R norm  into a low order polynomial function, typically cubic in order, or less, in a step  1330 . (See  FIG. 15C  trend  1560 ). This polynomial function may be replaced by other functions such as exponential, exp(x), or power law functions, x^y. Function 1/(x^4) is typical of attenuation due to scattering in slurry. The method  1300 , in the step  1330 , also divides or subtracts the result of step  1325  by that polynomial. For example, trend  1570  of  FIG. 15C  is the result of trend  1550  divided by trend  1560 , and trend  1580  is the result of trend  1560  subtracted from trend  1550 . This removes the wavelength-dependent effects of scattering and attenuation caused by the slurry and other effects, such as the transmission of the probe window. Trends  1570  and  1580  of  FIG. 15C  illustrates that this procedure recovers some or all of the decreased amplitude of the oscillation seen at the end of the trend  1550 . 
   Next, the method  1300  then scales and mean centers fitted data R norm  in a step  1335 . (See  FIG. 15D  trend  1590 ). In one embodiment, the method  1300  means centers R norm  and scales R norm  by dividing it by its standard deviation (StDev). For example: 
         R   norm     =       (       R   norm     -     Mean   ⁡     (     R   norm     )         )       STDEV   ⁡     (     R   norm     )             
 
Alternatively, the method  1300  scales and centers by: 
         R   norm     =       (       R   norm     -     Min   ⁡     (     R   norm     )         )       (       Max   ⁡     (     R   norm     )       -     Min   ⁡     (     R   norm     )         )           
 
This reduces the amplitude variation of the signal. One of the goals is to isolate only the oscillation components of the signal.
 
   Next, the method  1300  calculates a Fast Fourier Transform (FFT) or a Power Spectral Density (PSD) on R norm  in a step  1340 . The application of an FFT or PSD calculation to data is well known and is detailed in “Numerical Recipes in C, the Art of Scientific Computing,” by William H. Press et al., Cambridge University Press (2 nd  ed. 1992), which is hereby incorporated by reference. 
   Next, the method  1300  smoothes and interpolates the resultant data that is the output of the FFT transform in a step  1345 . (See  FIG. 16A  trend  1610 ). This process lessens the digitization of the data that is caused by application of the FFT process. The abscissa values of the FFT data are now proportional to the thickness of the film layer. The ordinate values are proportional to the amount of that film present on the wafer. The method  1300  also calculates first and second derivatives of the FFT data. (See  FIG. 16A  trend  1630  and trend  1640 , respectively). The smoothing and derivative may be obtained by applying a Savitski-Golay smoothing function. Spline functions may also be used to smooth and calculate derivatives. For more information concerning the application of these functions to data, see “Numerical Recipes” listed previously. 
   The method  1300  then locates and tracts each peak in the FFT signal in a step  1350 . In one embodiment, the peaks in the FFT signal are located by using a differencing filter acting upon the first derivative of the FFT signal in combination with the evaluation of the signal of the second derivative at the location of the peak. The possible peak locations are determined via the zero-crossing of the first derivative of the FFT signal. If the second derivative is negative at that point, then there is a peak. See  FIG. 16A  for an exemplary transform analysis trend illustrating first ( 1630 ) and second ( 1640 ) derivatives of the FFT signal. Also in  FIG. 16A , the intersections of lines  1620  and  1622  with the FFT transform trend  1610  illustrate an example of where two peaks occurred. These peaks are the identified maxima above a threshold of 0.25. This also relates to the film thicknesses that are present at 25% or greater in the compound signal. Table 2 illustrates a section of Matlab code that exemplifies the algorithm for finding peaks in the data. 
   
     
       
         
             
             
           
             
                 
               TABLE 2 
             
             
                 
                 
             
           
          
             
                 
               dersmdata = savgol(smdata,5,2,1); 
             
             
                 
               derdersmdata = savgol(dersmdata,5,2,1); 
             
             
                 
               intdata=sign(dersmdata); 
             
             
                 
               t=filter([l 1],1,intdata); 
             
             
                 
               clear zcarray; 
             
             
                 
               ss = find(smdata&lt;=0.25); 
             
             
                 
               t = sign(sign(sign(derdersmdata)+1)+sign(abs(t))); 
             
             
                 
               t(ss) = 1; 
             
             
                 
               t(round(NumpointsInterp):end)=1; 
             
             
                 
               zcarray = find(t==0); 
             
             
                 
                 
             
          
         
       
     
   
   Next, the method  1300  may transform the abscissa of the located peak or peaks into film thicknesses. This is done by applying the proper scaling factors to the abscissa data from the FFT process. These factors include division by the resolution of the data onto which the FFT was applied as well as the number of points to which the FFT was applied. Typically only the largest peak located or a peak within a specific thickness range is then used as the wafer state parameter. See trend  1650  of  FIG. 16B , which illustrates an exemplary trend of thickness that is determined by tracking the values of the peak at the intersection of line  1622  and trend  1610 . Of course, however, the present invention is not limited to only determining one film thickness as illustrated in FIG.  16 B. In other embodiments, the present invention can determine film thicknesses for every peak located or any number thereof. 
   Next, the method  1300  determines if a predetermined value of a wafer state parameter has been reached in a decisional step  1360 . For this example, the predetermined value of the wafer state parameter may be the planarization of the dielectric to a predetermined thickness or to a specific thickness above the topmost metal layer. See also,  FIG. 14  for an example predetermined value of the wafer state parameter (threshold point) in the dielectric layer of a wafer. The decision may be calculated by determining if the thickness that corresponds to the located peak or peaks is less than or equal to the predetermined threshold thickness. If the predetermined value of the wafer state parameter has been reached, the method  1300  stops processing in a step  1370 . In a related embodiment, the method  1300  may cause the CMP process to stop. 
   If the predetermined value of the wafer state parameter has not been reached, the method  1300  may cause the process to be adjusted in a step  1380 . In one embodiment, the control subsystem  250  of  FIG. 2  may adjust processing parameters or cause physical devices to be adjusted in order to optimally process the wafer. Next, the method  1300  returns to process the wafer and collect more data in the step  1315 . Other embodiments of the present invention may have additional or fewer steps than described above. 
   Turning now to  FIG. 17 , illustrated is a flow diagram of an embodiment of a method of performing a metal breakthrough analysis on real-time spectral reflectometry data, generally designated  1700 , conducted according to the principles of the present invention. Typically, metal breakthrough analysis may be used for monitoring the removal of a deposited layer of metal in order to isolate individual wires and vias.  FIG. 18  illustrates an example silicon wafer employable by the method  1700  and having a bottom field oxide layer and a second layer having metal vias within a borophosphosilicate glass (BPSG) or phosphosilicate glass (PSG) layer. The wafer also includes a third layer having metal traces and vias within a dielectric, such as silicon dioxide, and a first seal layer. The first seal layer may be a silicon nitride layer. After the first seal layer, the wafer includes another dielectric layer followed by a second seal layer and a final layer of deposited metal.  FIG. 18  also illustrates metal structures extending downward from the top layer through intermediate layers to the metal structure in the first dielectric layer. The CMP process would typically remove the top deposited layer of metal of this silicon wafer. 
   Referring back to  FIG. 17 , the metal breakthrough analysis detects the frequency transitions in a normalized signal from substantially straight line trends to multiple higher frequency components. The substantially straight line trend occurs when the CMP process is in the early stages of removing the metal layer and the multiple higher frequency components usually occurs when the metal layer is removed leaving the underlying dielectric layer. In one embodiment, the metal breakthrough analysis illustrated by the method  1700  is used in determining a wafer state parameter, such as a transition from straight line tread to multiple higher frequency components. This wafer state parameter is directly correlated to the removal of the bulk metal film above the underlying dielectric film. Also, this wafer state parameter is generally independent of the complications in the reflectance of the wafer that are caused by the deeper underlying layers or metal or dielectric. Of course, however, the present invention is not limited to this wafer state parameter. In addition, the method  1700  is a modified form of the more general transform method noted previously. 
   The method  1700  first performs initialization and starts initial processing of the wafer in a step  1710 . Also, the method  1700 , after a few seconds of processing to allow for stability, records a snapshot of the averaged raw spectra in the step  1710 . The snapshot (R snap (λ)) is used for self-normalization of the raw spectra. See  FIGS. 19A  trend  1910  for exemplary snapshot spectra. After initialization, the method  1700  processes the wafer and collects data in a step  1715 . In one embodiment, the collection includes employing a plurality of optical probes and a spectrograph to obtain real-time reflectometry data of the wafer being processed. Next, the method  1700  normalizes the collected data with previously snapshot data R snap (λ) in a step  1720 . The collected data may be normalized as follows: 
           R   norm     ⁡     (   λ   )       =       R   ⁡     (   λ   )           R   snap     ⁡     (   λ   )             
 
where R(λ) is an alternative mathematical name for the raw spectral data. Exemplary data prior to normalization are shown by spectrum  1920  and spectrum  1930  in FIG.  19 B. The spectrum  1920  is a spectrum recorded early in the CMP process when the metal film remains thick and the underlying dielectric is obscured. It is substantially similar to the snapshot of raw spectra  1910 . The spectrum  1930  is a spectrum recorded after some or all of the metal has been removed and the dielectric is exposed. The fringes are evident. Related normalized spectra are shown in  FIG. 19C  trend  1935  (metal removed) and trend  1925  (metal remaining).
 
   Next, the method  1700  performs a transform by converting the normalized data R norm (λ) into a function of R norm (1/λ) or R norm (n(λ)/λ) in a step  1725 . This conversion seeks to convert the spectral data into a function that is periodic with respect to the argument 1/λ. This functional form is a preferred basis for the analysis of dielectric films due to the theoretical formulation of the Frensel reflection equations. The procedure for converting the spectral data [(data(i,:)] into a function that is periodic with respect to the function of 1/λ [ExpR] may be performed by Matlab code illustrated in Table 1 described previously. 
   The method  1700  then fits the converted and normalized data R norm  into a low order polynomial function, typically cubic in order, or less, in a step  1730 . This polynomial function may be replaced by other functions such as exponential, exp(x), or power law functions, x^y. Function 1/(x^4) is typical of attenuation due to scattering in slurry. The method  1700 , in the step  1730 , also divides or subtracts the result of step  1725  by that polynomial. This removes the effect of scattering and attenuation caused by the slurry and other effects, such as the transmission of the probe window. See step  1330  of  FIG. 13  for additional discussion on removing the effects of scattering. 
   The method  1700  may then scale and mean center the fitted data R norm  in a step  1735 . In one embodiment, the method  1300  mean centers R norm  and scales R norm  by dividing it by its standard deviation (StDev). For example: 
         R   norm     =       (       R   norm     -     Mean   ⁡     (     R   norm     )         )       STDEV   ⁡     (     R   norm     )             
 
Alternatively, the method  1700  scales and centers by: 
         R   norm     =       (       R   norm     -     Min   ⁡     (     R   norm     )         )       (       Max   ⁡     (     R   norm     )       -     Min   ⁡     (     R   norm     )         )           
 
This reduces the amplitude variation of the signal. One of the goals is to isolate only the oscillating components of the signal.
 
   Next, the method  1700  calculates a FFT or a Power Spectral Density (PSD) on R norm  in a step  1740 . As discussed previously, the application of an FFT or PSD calculation to data is well known. An exemplary output of step  1740  is shown in FIG.  19 D. Therein, signal  1927  shows the FFT signal resulting from the FFT of the input signal  1925  indicative of the metal remaining on the wafer. Signal  1937  is the output from the FFT of signal  1935 , which indicates that the metal has been removed. Observation of the peak in the FFT signals  1927  and  1937  within the preselected bounds  1960  show that the peak amplitude is much greater when the metal is removed. The amplitude of this peak forms the basis of the wafer state parameter; namely the clearing of the metal film from the wafer. 
   Next, the method  1700  selects a maximum FFT intensity in a step  1745 . The maximum FFT intensity may be selected from a preselected range of FFT frequencies. These frequencies are directly related to the clearing of the metal layer over the underlying dielectric. The preselected range of frequencies is selected by running a first setup wafer and processing the data and observing where the amplitude of the frequencies change most strongly as the wafer approaches the desired endpoint. 
   The method  1700  then tests the selected maximum FFT intensity for an intensity threshold condition in a step  1750 . The threshold condition is a preselected value for the intensity that defines a demarcation for the two possible states of the wafer. The first state being uncleared (the metal is still thick and the normalized spectra remain substantially straight). The second state is that the metal is mostly removed (the normalizd spectra contain oscillations denoting the detection of the underlying dielectric). This threshold is selected similarly to the method used for determining the range from which to select the peak. The method  1700  then sets the output of the test to zero if the selected maximum intensity is greater than the intensity threshold condition and sets the output to one if the selected maximum intensity is less than the intensity threshold condition. This converts the data analysis into a binary decision of “1” meaning that the wafer remains covered with metal or “0” if clear of the metal.  FIG. 19E  shows the trend output  1970  for the step  1750  for part of a CMP process. 
   Next, the method  1700  calculates a moving time average of the results obtained in the previous step in a step  1755 . The moving average of signal  1970  is illustrated in  FIG. 19F  trend  1980 . Calculation of a moving time average is well known to one skilled in the art. 
   The method  1700  then determines if a threshold condition (predetermined value of a wafer state parameter) has been reached in a decisional step  1760 . For example, the threshold is a value below which the trend  1980  should surpass. For a simple endpoint of the removal of the metal from the wafer, the trend  1980  goes from one (fully covered with metal) to zero (fully cleared of metal). The threshold is then set at or near a value of zero. When trend  1980  surpasses this value, the method  1700  determines in the decisional step  1760  that the process is finished and the method  1700  stops processing in a step  1770 . 
   If the threshold condition has not been reached, the method  1700  may cause the process to be adjusted in a step  1780 . In one embodiment, the control subsystem  250  of  FIG. 2  may adjust processing parameters or cause physical devices to be adjusted in order to optimally process the wafer. Next, the method  1700  returns to process the wafer and collect more data in the step  1715 . Other embodiments of the present invention may have additional or fewer steps than described above. 
   Turning now to  FIG. 20 , illustrated is a flow diagram of an embodiment of a method of generating a model for use with a model analysis, generally designated  2000 , conducted according to the principles of the present invention. The model generated by the method  2000 , in one embodiment, is used as a theoretical optical model in a method of performing a model analysis on realtime spectral reflectometry data described in FIG.  24 . The method  2000  first performs initialization in a step  2010 . 
   After initialization, the method  2000  then identifies the wafer state parameters required to develop the model of the structure to be monitored during the chemical mechanical process in a step  2020 . For example,  FIG. 21  illustrates an exemplary wafer and associated wafer state parameters that are employable in a chemical mechanical process, such as shallow trench isolation, and employable by the present invention. The wafer state parameters that may be monitored by an embodiment of the present invention include a trench depth, a step height of the silicon dioxide, an area of the trench or active region of the semiconductor device, thicknesses of the silicon dioxide top and pad layers, and a thickness of the silicon nitride layer. For purposes of discussion only, the method  2000  and the method of  FIG. 24  will described employing a simpler type of wafer called a silicon-on-insulator (SOI) wafer.  FIG. 22  illustrates an exemplary SOI wafer having a structure that consists of three lamellae: a silicon substrate, a buried silicon dioxide layer on top of the silicon substrate, and a top silicon SOI layer. The wafer state parameters for this type of wafer are typically a thickness of the top silicon SOI layer and a thickness of the underlying buried oxide (BOX) layer. However, the thickness of the BOX layer is usually a known value or within a known range. For this example, the thickness of the BOX layer will be considered fixed and will have no substantial effect on the monitoring of the CMP process. Thus, the thickness of the SOI layer will be monitored and used as the wafer state parameter to adjust or stop the polishing process. See  FIG. 24  for more discussion on applying the model analysis method on real-time data. 
   After identifying the required wafer state parameters, the method  2000  then defines the model in a step  2030 . In one embodiment, the method  2000  employs the identified wafer state parameters and other necessary information, such as optical indices of the materials that comprise the type of wafer to be modeled, to define the model. In constructing an optical model for the SOI type wafer of  FIG. 22 , a simple optical model may be created since it is not required to compute a spectrum that will match the observed spectra precisely. Also, in constructing the optical model it is preferable to make as few assumptions about the structure as possible. For this example, it is assumed only that the reflection from the wafer is proportional to the coherent sum of the reflections from the lamellar interfaces.  FIG. 23  illustrates exemplary reflectances of a spot of light transmitted into the SOI type wafer of FIG.  22 .  FIG. 23  also illustrates that the spot of light transmitted into the SOI type wafer can have reflectances from each layer of the wafer. 
   The reflectivity of the surface of the SOI type wafer may be calculated as follows for any one wavelength: 
       R   =                (       r   01     +       r   12     ⁢     ⅇ     -     ⅈ2β   1             )     +       (         r   01     ⁢     r   12       +       r   01     ⁢     ⅇ     -     ⅈ2β   1             )     ⁢     r   23     ⁢     ⅇ     -     ⅈ2β   2                 (     1   +       r   01     ⁢     r   12     ⁢     ⅇ     -     ⅈ2β   1             )     +       (       r   12     +       r   01     ⁢     ⅇ     -     ⅈ2β   1             )     ⁢     r   23     ⁢     ⅇ     -     ⅈ2β   2                    2         
 
where r 01 , r 12  and r 23  are the reflection coefficients of the three interface regions, respectively. Also, β 1  is the phase thickness of the SOI layer, and β 2  is the phase thickness of the BOX layer. The reflection coefficients can be computed from Fresnel&#39;s equation: 
         r   nm     =         N   m     -     N   n           N   m     +     N   n             
 
where N x =n x −ik x . Similarly, the phase thickness is given by: 
         β   x     =         2   ⁢   π   ⁢           ⁢     d   x       λ     ⁢       N   x     ⁡     (   λ   )             
 
using the real and imaginary parts n and k of the refractive index of the material (for layer index 0=superstate [water], 1=SOI layer [silicon], 2=BOX layer [silicon dioxide], 3=substrate [silicon]).
 
   The reflection coefficients can be computed using the standard formalism for calculating the reflection coefficient of a multilayer stack. For additional discussion on the methodologies for defining the reflectance and transmission properties of thin film stacks and the above calculations, see “Ellipsometry and Polarized Light,” by R. M. A. Azzam and N. M. Basara, Elsevier Science pp. 332-40(1987), which is hereby incorporated by reference. As it stands, the optical model for the SOI wafer contains two unknown or variable wafer state parameters d 1  and d 2 , (the thickness of the SOI and BOX layers) assuming the optical constants of each of the constituent materials are known. Of course, however, the present invention is not limited to calculating an optical model only for a SOI type wafer. In other embodiments, an optical model can be created for any type of wafer capable of being analyzed by a model analysis method. 
   Next, the method  2000  calculates theoretical reflectance spectra in a step  2040 . In one embodiment, the reflectance values R(λ, wafer state parameter  1 , wafer state parameter  2 , . . . , wafer state parameter n) for the optical model are evaluated at predetermined values of wavelength throughout the wavelength region of interest or observation. A common wavelength region of observation may be from 200 to 800 nm. The predetermined wavelengths may be selected by requiring those wavelengths to provide a reduced subset of the data that facilitates fast computation but preserves the information content of the original spectrum. In a preferred embodiment, the wavelengths may be selected by subdividing the spectrum into N small regions whose endpoints have evenly spaced values of reciprocal wavelength, and then average the wavelength and the reflectivity within each region to obtain a single (wavelength, reflectivity) pair for each region. The number of regions should be chosen large enough so that the smallest features of interest in the reflectivity spectrum span four or more regions. The spectral data for fitting can then be thought of as a list R of length N without explicit reference to wavelength. An example of the calculated theoretical reflectance spectra is illustrated in spectra  2520  of FIG.  25 B. 
   The method  2000  then scales and mean centers the calculated theoretical reflectance spectra data R calc  in a step  2050 . (See  FIG. 25C  trend  2530 ). In one embodiment, the method  2000  mean centers R calc  and scales R calc  by dividing it by its standard deviation (StDev). For example: 
         R   calc     =       (       R   calc     -     Mean   ⁡     (     R   calc     )         )       STDEV   ⁡     (     R   calc     )             
 
Alternatively, the method  2000  scales and centers by: 
         R   calc     =       (       R   calc     -     Min   ⁡     (     R   calc     )         )       (       Max   ⁡     (     R   calc     )       -     Min   ⁡     (     R   calc     )         )           
 
The method  2000  scales and centers the calculated data based on the observation that vertical range of the observed real-time data provides a convenient scale, and the scale can be imposed on the calculated model rather than trying to accurately calculate it. Trend  2530  of  FIG. 25C  illustrates an exemplary scaled and centered calculated theoretical reflectance spectra. By transforming both the observed real-time data and the calculated model in such a way that their vertical extent and spectrally averaged values coincide, the present invention can advantageously tolerate large errors in both the observed data and the calculated model and still find a deep minimum in the appropriately constructed merit function at the correct values of the wafer state parameters. See  FIG. 24  for a discussion on a method of performing a model analysis on the observed data and the merit function. The method  2000  and the method disclosed in  FIG. 24  are typically most successful if interference minima and maxima occur in every spectrum, which will be more likely if the data includes a wide range of wavelengths.
 
   Next, the method  2000  stores the calculated model spectra in a step  2060 . The calculated model spectra will be used by the method disclosed in FIG.  24 . The method  2000  then stops processing in a step  2070 . Of course, however, other embodiments of the present invention may have additional or fewer steps than described above. 
     FIG. 24  illustrates a flow diagram of an embodiment of a method of performing a model analysis on real-time spectral reflectometry data, generally designated  2400 , conducted according to the principles of the present invention. As discussed previously, the method  2400  will be described employing the simpler type of wafer called the silicon-on-insulator (SOI) wafer. (See FIG.  22 ). One skilled in the art should know that the SOI type wafer is for discussion purposes only and the present invention is not limited to only performing model analysis on SOI type wafers. In other embodiments, the present invention may perform model analysis on other types of wafers. 
   The method  2400  first performs initialization in a step  2410 . After initialization, the method  2400  processes the wafer and collects reflectometry data in a step  2415 . For the example SOI type wafer, the method  2400  may collect reflectance spectra from a 4 mm diameter spot on the SOI wafer. (See FIG.  23 ). Each raw spectrum, as collected, spanned a range of wavelengths λ of 225 nm to 800 nm at a resolution of 0.5 nm. See  FIG. 25A  trend  2510  for an exemplary raw spectrum for the SOI type wafer. One skilled in the art should know that each time a sample is obtained of the raw spectra, the location of the spot on the SOI wafer is typically at a different location. This is done in order to sample across the wafer during the CMP process. Also, in order to simplify the discussion, the method  2400  is described in respect to analyzing reflectance spectra from only one spot (collected by an optical probe). This is for discussion purposes only and is not a limitation. In other embodiments of the present invention, the method  2400  may analyze information obtained from a plurality of optical probes in performing model analysis. 
   Next, the method  2400  normalizes the collected data with previously collected normalization data (Norm(λ)) in a step  2420 . The normalization data Norm(λ), in one embodiment, is the data obtained from the normalization method of FIG.  7 . The collected data may be normalized as follows: 
           R   norm     ⁡     (   λ   )       =         R   ⁡     (   λ   )       *       R   Silicon     ⁡     (   λ   )           Norm   ⁡     (   λ   )             
 
where R(λ) is an alternative mathematical name for the raw spectral data of the currently processing water, and R silicon (λ) is the theoretical reflectance of a bare silicon wafer. This mathematical expression assumes that the normalization wafer was a bare silicon wafer. If the normalization data was collected from a different type of wafer, R silicon  may be replaced with the theoretical expression for the wafer type used. Trend  2525  of  FIG. 25B  is an example of the normalized data.
 
   The method  2400  may then convert the normalized data R norm  to region data R region  in a step  2425 . In one embodiment, the method  2400  reduces the data to a minimal set of data that would facilitate fast computation and still substantially preserve the information content of the original spectrum. More specifically, the method  2400  may partition the normalized spectrum into a smaller number of regions and compute a single data point for each region. For example, if the normalized spectrum contained  1201  data points of 0.5 nm wavelength increments, the method  2400  may partition the normalized spectrum into 41 regions and compute a single data point for each region. In this example, 41 regions were chosen in order to facilitate fast computation. Of course, however, the present invention is not limited to  1201  data points nor 41 regions. Other embodiments of the present invention may have any number of data points and any number of regions satisfying the conditions set forth. Also, if computational speed is not an issue or a system can perform the computations within the bounds of in-situ requirements, than all of the data points may be used. 
   Given the selection of 41 regions, the method  2400  may then partition the data by computing a set of 42 wavelengths to serve as endpoints of the partitions (one more than the number of partitions desired in order to account for the beginning and ending points). It is preferable if the endpoints are chosen such that their wavelength reciprocals are approximately evenly distributed. Then from each partition, the method  2400  computes a single data point by averaging the nominal reflectivity over the entire region. After this transformation (conversion), at each time step t there is data in the form of a vector R i,t , where i is the index corresponding to wavelength, and runs from 1 to the number of partitions N (41 in this case). One skilled in the art should known that it is assumed that the calculated model generated by the method of  FIG. 20  has been partitioned to the same number and type of regions. 
   Next, the method  2400  scales and mean centers the region data R region  in a step  2430 . In one embodiment, the method  2400  mean centers R region  and scales R region  by dividing it by its standard deviation (StDev). For example: 
         R   region     =       (       R   region     -     Mean   ⁡     (     R   region     )         )       STDEV   ⁡     (     R   region     )             
 
Alternatively, the method  2400  scales and centers by: 
         R   region     =       (       R   region     -     Min   ⁡     (     R   region     )         )       (       Max   ⁡     (     R   region     )       -     Min   ⁡     (     R   region     )         )           
 
This reduces the amplitude variation of the signal. The vertical range of the data is also used to rescale the vertical range of the calculated model data. This relaxes the requirement of accurately calculating the reflectivity. The method  2400  is typically most successful if interference minima and maxima occur in every spectrum, which will be more likely if the data includes a wide range of wavelengths. In  FIG. 25C , trend  2535  illustrates the scaled and mean centered normalized real-time data R region  and trend  2530  illustrates the scaled and mean centered calculated model data R calc . Note that each circle on the trends  2530 ,  2535  represent the average of the nominal reflectivity over that region.  FIG. 25C  also illustrates that more sampling may be performed over wavelengths where it is known that changes in the data may be more important or occur more rapidly, and less sampling may be performed over wavelengths where changes do not occur as fast or follows a known estimation.
 
   The method  2400  then calculates a merit function of the data R region  in a step  2435 . In one embodiment, the method  2400  employs the merit function M(p 1 , p 2 , . . . , p n ) for comparison between the observed data R (R region ) and the model data R c  (R calc ), such that: 
         M   ⁡     (       p   1     ,     p   2     ,   …   ⁢           ,     p   n       )       =       ∑     j   =   1     N     ⁢       (       T   ⁡     [       R   j   c     ⁡     (       p   1     ,     p   2       )       ]       -     T   ⁡     [     R   j     ]         )     2           
 
with 
         T   ⁡     (     R   i     )       =         R   i     -       1   N     ⁢       ∑     j   =   1     N     ⁢     R   j               Max   ⁡     (     R   i     )       -     Min   ⁡     (     R   i     )               
 
where T(R i ) is the data vector representing the converted, scaled and centered data. Thus, the merit function produces a table having p n  dimensions that can be searched. That is, one dimension for every wafer state parameter employed in the method.
 
   Next, the method  2400  correlates a smallest value of the merit function to the wafer state parameters in the calculated model in a step  2440 . In one embodiment, the method  2400  may correlate by performing a minimization of the merit function by standard techniques, such as the Levenburg-Marquardt method. Also since the number of parameters being searched may be smaller due to partitioning by regions, an exhaustive search of the entire parameter space on a discrete grid may be done instead of by numerical minimization techniques. One skilled in the art is familiar with merit functions, minimization of merit functions, Levenburg-Marquardt method and exhaustive search methods. 
   In an alternative embodiment, the model and above described steps may be computed in advance to create a lookup table that can be searched exhaustively at run time. For example, given the SOI wafer and two wafer state parameters (thickness of the SOI layer d 1  and thickness of the BOX layer d 2 ) the merit function would be: 
           M   t     ⁡     (       d   1     ,     d   2       )       =       ∑     j   =   1     N     ⁢       (       T   ⁡     [       R     j   ,   t     c     ⁡     (       d   1     ,     d   2       )       ]       -     T   ⁡     [     R     j   ,   t       ]         )     2           
 
The lookup table would contain a set of vectors T[R j,t   c (d 1 ,d 2 )] for every possible SOI layer and BOX layer thickness pair on 1 nm intervals over the full range of expected values. This may be preferable to numerical minimization techniques because the results do not depend on an initial guess.
 
   At completion of the step  2440 , the method  2400  has the values for each of the wafer state parameters in the model in relation to the observed data at a specific point in time. Trend  2540  of  FIG. 25D  illustrates the results of the merit function and correlation for the wafer state parameter d 1  (SOI layer thickness). The wafer state parameter d 2  (BOX layer thickness) is not shown because it has not changed by the polishing process since the SOI layer fully covers the BOX layer. (See FIG.  22 ). 
   The method  2400  then determines if the wafer state parameter value(s) derived in the step  2440  has reached a predetermined value of the wafer state parameter(s) in a decisional step  2450 . If the predetermined value of the wafer state parameter(s) has been reached, the process stops in a step  2460 . For example, if the predetermined stopping thickness (endpoint) of the SOI layer was required to be 70 nm, the polishing process would have been automatically stopped about 40 seconds. See trend  2540  of FIG.  25 D. Further observation indicates that the trend  2540  begins to present more variation in thickness of the SOI layer as the polishing advances in time. (See trend section  2545 ). Ideally, the trend  2540  should be a straight line at fixed slope. This would denote a fixed removal rate and no emerging non-uniformity. This type of variation occurring after 40 seconds denotes emerging non-uniformity in the thickness of the film due to the polishing process. Information about this emerging non-uniformity may be employed to control the polishing process and limit the deleterious effects of the non-uniformity on the quality of the wafer. 
   If the predetermined value of the wafer state parameter(s) has not been reached in the decisional step  2450 , the method  2400  may adjust the polishing process in a step  2470 . For example, if the trend  2540  of  FIG. 25D  has variations, such as illustrated in section  2545 , occurring earlier in time, the method  2400  may cause the polishing process to correct for this imperfection. The method  2400  then returns to process and collect more data in the step  2415 . Of course, however, other embodiments of the present invention may have additional or fewer steps than described above. 
   Turning now to  FIG. 26 , illustrated is an embodiment of a spectrograph, generally designated  2600 , for spatially imaging light received by optical probes to a common charge-coupled device (CCD) constructed according to the principles of the present invention. The spectrograph  2600  includes an entrance slit,  2620 , a dispersive imaging system  2625 , an image plane  2630  and a CCD  2640 . The spectrograph  2600  receives individual light inputs (or channels) at a specific point on an entrance slit  2620 . The dispersive imaging system  2625  images the light that impinges upon the multiple sources at the entrance slit  2620  on to the image plane  2630  of the CCD  2640 . The image is separated physically by the independent incident channel in one dimension and, in a second dimension, is distributed over wavelength. See blow-up  2632  of the image plane  2630  for an example of how the individual inputs are spatially imaged. The CCD  2640  then captures and converts the spatially imaged light to digital information. An example of a commercial imaging spectrograph is the SD 1024 , available from Verity Instruments, Inc., of Carrollton, Tex. 
   While the methods disclosed herein have been described and shown with reference to particular steps performed in a particular order, it will be understood that these steps may be combined, subdivided, or reordered to form an equivalent method without departing from the teachings of the present invention. Accordingly, unless specifically indicated herein, the order and/or the grouping of the steps are not limitations of the present invention. 
   Although the present invention has been described in detail, those skilled in the art should understood that they can make various changes, substitutions and alterations herein without departing from the spirit and scope of the invention in its broadest form.