Patent Publication Number: US-6986699-B2

Title: Method and apparatus for determining polishing endpoint with multiple light sources

Description:
The present application is a continuation of U.S. patent application Ser. No. 09/237,472, filed Jan. 25, 1999, now U.S. Pat. No. 6,247,998. 

   BACKGROUND 
   This invention relates generally to chemical mechanical polishing of substrates, and more particularly to a method and apparatus for determining the thickness of a substrate layer during chemical mechanical polishing. 
   An integrated circuit is typically formed on a substrate by the sequential deposition of conductive, semiconductive or insulative layers on a silicon wafer. After each layer is deposited, the layer is etched to create circuitry features. As a series of layers are sequentially deposited and etched, the outer or uppermost surface of the substrate, i.e., the exposed surface of the substrate, becomes increasingly non-planar. This non-planar surface presents problems in the photolithographic steps of the integrated circuit fabrication process. Therefore, there is a need to periodically planarize the substrate surface. 
   Chemical mechanical polishing (CMP) is one accepted method of planarization. This planarization method typically requires that the substrate be mounted on a carrier or polishing head. The exposed surface of the substrate is placed against a rotating polishing pad. The polishing pad may be either a “standard” pad or a fixed-abrasive pad. A standard pad has a durable roughened surface, whereas a fixed-abrasive pad has abrasive particles held in a containment media. The carrier head provides a controllable load, i.e., pressure, on the substrate to push it against the polishing pad. A polishing slurry, including at least one chemically-reactive agent, and abrasive particles if a standard pad is used, is supplied to the surface of the polishing pad. 
   The effectiveness of a CMP process may be measured by its polishing rate, and by the resulting finish (absence of small-scale roughness) and flatness (absence of large-scale topography) of the substrate surface. The polishing rate, finish and flatness are determined by the pad and slurry combination, the carrier head configuration, the relative speed between the substrate and pad, and the force pressing the substrate against the pad. 
   In order to determine the effectiveness of different polishing tools and processes, a so-called “blank” wafer, i.e., a wafer with one or more layers but no pattern, is polished in a tool/process qualification step. After polishing, the remaining layer thickness is measured at several points on the substrate surface. The variations in layer thickness provide a measure of the wafer surface uniformity, and a measure of the relative polishing rates in different regions of the substrate. One approach to determining the substrate layer thickness and polishing uniformity is to remove the substrate from the polishing apparatus and examine it. For example, the substrate may be transferred to a metrology station where the thickness of the substrate layer is measured, e.g., with an ellipsometer. Unfortunately, this process can be time-consuming and thus costly, and the metrology equipment is costly. 
   One problem in CMP is determining whether the polishing process is complete, i.e., whether a substrate layer has been planarized to a desired flatness or thickness. Variations in the initial thickness of the substrate layer, the slurry composition, the polishing pad material and condition, the relative speed between the polishing pad and the substrate, and the load of the substrate on the polishing pad can cause variations in the material removal rate. These variations cause variations in the time needed to reach the polishing endpoint. Therefore, the polishing endpoint cannot be determined merely as a function of polishing time. 
   One approach to determining the polishing endpoint is to remove the substrate from the polishing surface and examine it. If the substrate does not meet the desired specifications, it is reloaded into the CMP apparatus for further processing. Alternatively, the examination might reveal that an excess amount of material has been removed, rendering the substrate unusable. There is, therefore, a need for a method of detecting, in-situ, when the desired flatness or thickness had been achieved. 
   Several methods have been developed for in-situ polishing endpoint detection. Most of these methods involve monitoring a parameter associated with the substrate surface, and indicating an endpoint when the parameter abruptly changes. For example, where an insulative or dielectric layer is being polished to expose an underlying metal layer, the coefficient of friction and the reflectivity of the substrate will change abruptly when the metal layer is exposed. 
   In an ideal system where the monitored parameter changes abruptly at the polishing endpoint, such endpoint detection methods are acceptable. However, as the substrate is being polished, the polishing pad condition and the slurry composition at the pad-substrate interface may change. Such changes may mask the exposure of an underlying layer, or they may imitate an endpoint condition. Additionally, such endpoint detection methods will not work if only planarization is being performed, if the underlying layer is to be over-polished, or if the underlying layer and the overlying layer have similar physical properties. 
   In view of the foregoing, there is a need for a polishing endpoint detector which more accurately and reliably determines when to stop the polishing process. There is also a need for an means for in-situ determination of the thickness of a layer on a substrate during a CMP process. 
   SUMMARY 
   The present invention relates to in-situ optical monitoring of a substrate during chemical mechanical polishing. The thickness of a layer in the substrate can be measured, and the thickness determination may be used to determine an endpoint of the CMP process, determine the thickness of a film remaining on the wafer during the CMP process, and determine thickness of material removed from a wafer in the CMP process. 
   In one aspect, the invention is directed to an apparatus for chemical mechanical polishing a substrate having a first surface and a second surface underlying the first surface. The apparatus has a first optical system, a second optical system, and a processor. The first optical system includes a first light source to generate a first light beam to impinge on the substrate, the first light beam having a first effective wavelength, and a first sensor to measure light from the first light beam that is reflected from the first and second surfaces to generate a first interference signal. The second optical system includes a second light source to generate a second light beam that impinges the substrate, the second light beam having a second effective wavelength that differs from the first effective wavelength, and a second sensor to measure light from the second light beam that is reflected from the first and second surfaces to generate a second interference signal. The processor is configured to determine a thickness from the first and second interference signals. 
   Implementations of the invention may include the following, the first and second light beams may have different wavelengths or different incidence angles on the substrate. The first effective wavelength may be greater than the second effective wavelength without being an integer multiple of the second effective wavelength. Each optical system may be an off-axis or an on-axis optical system. At least one of the first and second light sources may include a light emitting diode. The first light source may be a first light emitting diode with a first coherence length and the second light source may be a second light emitting diode having a second coherence length. The first coherence length may be greater than a optical path length of the first light beam through the surface layer, and the second coherence length may be greater than an optical path length of the second light beam through the surface layer. The apparatus may have a polishing pad which contacts the first surface of the substrate during polishing and a platen to support the polishing pad. The platen may include an aperture through which the first and second light beams pass, or the platen may include a first aperture through which the first light beam passes and a second aperture through which the second light beam passes. The polishing pad may include a transparent window through which the first and second light beams pass, or the polishing pad may include a first window through which the first light beam passes and a second window through which the second light beam passes. The first light beam may have a first wavelength, e.g., between about 600 and 1500 nanometers, and the second light beam may have a second wavelength, e.g., between about 300 and 600 nanometers, that is shorter than the first wavelength. The first light beam may have an incidence angle on the substrate that is less than a second incidence angle of the second light beam on the substrate. 
   The processor may be configured to determine an initial thickness during polishing of the substrate. The processor may be configured to determine a first model intensity function for the first interference signal and a second model intensity function for the second interference signal. The first and second model intensity functions may be sinusoidal functions, e.g., described by a first period and a first phase offset and a second period and a second phase offset, respectively. The first period and the first phase offset may be computed from a least square fit of the first model intensity function to intensity measurements from the first interference signal, and the second period and the second phase offset may be computed from a least square fit of the second model function intensity to intensity measurements from the second interference signal. The thickness may be estimated by a first model thickness function which is a function of a first integer, the first effective wavelength, the first period and the first phase offset, and by a second model thickness function which is a function of a second integer, the second effective wavelength, the second period and the second phase offset. The processor is configured to determine a first value for the first integer and a second value for the second integer which provide approximately equal estimates of the thickness from the first and second model thickness functions. The processor may be configured to determine the first and second values by finding solutions to the equation: 
       M   =         (         ϕ   2       Δ   ⁢           ⁢     T   2         +   N     )     ·       λ   eff2       λ   eff1         -       ϕ   1       Δ   ⁢           ⁢     T   1               
 
where M is the first integer, N is the second integer, λ eff1  is the first effective wavelength, λ eff2  is the second effective wavelength, ΔT 1  is the first period, ΔT 2  is the second period, φ 1  is the first phase offset, and φ 2  is the second phase offset.
 
   In another aspect, the invention is directed to an apparatus for use in chemical mechanical polishing a substrate having a first surface and a second surface underlying the first surface. The apparatus has a first optical system including a first light source to generate a first light beam to impinge on the substrate, and a first sensor to measure light from the first light beam that is reflected from the first and second surfaces to generate a first interference signal, and a second optical system including a second light source to generate a second light beam that impinges the substrate, and a second sensor to measure light from the second light beam that is reflected from the first and second surfaces to generate a second interference signal. The first light beam has a first effective wavelength and the second light beam has a second effective wavelength which differs from the first effective wavelength. 
   In another aspect, the invention is directed to an apparatus for use in chemical mechanical polishing a substrate having a first surface and a second surface underlying the first surface. The apparatus has a first optical system and a second optical system. The first optical system includes a first light emitting diode to generate a first light beam that impinges the substrate, and a first sensor to measure light from the first light beam that is reflected from the first and second surfaces to generate a first interference signal. The second optical system includes a second light emitting diode to generate a second light beam that impinges the substrate, and a second sensor to measure light from the second light beam that is reflected from the inner and outer surfaces to generate a second interference signal. The first light beam has a first effective wavelength, and the second light beam has a second effective wavelength that differs from the first effective wavelength. 
   Implementations of the invention may include the following. The first light beam may have a first wavelength, e.g., between about 700 and 1500 nanometers, and the second light beam may have a second wavelength, e.g., between about 300 and 700 nanometers, that is shorter than the first wavelength. The substrate may have a layer in a thin film structure disposed over a wafer, amd the first and second light beams may have coherence lengths sufficiently large to maintain coherence of the first and second light beams as they pass through the layer. 
   In another aspect, the invention is directed to an apparatus for detecting a polishing endpoint during chemical mechanical polishing of a substrate having a layer disposed over a wafer, the substrate having a first surface and a second surface underlying the first surface. The apparatus has a light emitting diode to generate a light beam that impinges the layer of the substrate, a sensor to measure light from the light beam that is reflected from the first and second surfaces to generate an interference signal, and a processor configured to determine an polishing endpoint from the interference signal. The light beam emitted by the light emitting diode has a coherence length equal to or greater than the optical path length of the light beam through the layer. 
   In yet another aspect, the invention is directed to an endpoint detector for use in chemical mechanical polishing a substrate having a layer in a thin film structure disposed over a wafer. The substrate has has a first surface and a second surface underlying the first surface. The endpoint detector has a first optical system, a second optical system, and a processor. The first optical system includes a first light source to generate a first light beam that impinges the substrate, and a first sensor to measure light from the first light beam that is reflected from the inner and outer surfaces to generate a first interference signal. The second optical system includes a second light source to generate a second light beam that impinges the substrate, and a second sensor to measure light from the second light beam that is reflected from the inner and outer surfaces to generate a second interference signal. The first light beam has a first effective wavelength, and the second light beam has a second effective wavelength that differs from the first effective wavelength. The processor is configured to compare the first and second interference signals and detect the polishing endpoint. 
   In yet another aspect, the invention is directed to an apparatus for determining a thickness during chemical mechanical polishing of a substrate having a first surface and a second surface underlying the first surface. The apparatus has means for generating first and second light beams having different effective wavelengths to impinge on the substrate, means for detecting light from the first and second light beams that is reflected from the first and second surfaces to generate a first and second interference signals, and means for determining a thickness from the first and second interference signals. 
   In yet another aspect, the invention is directed to an apparatus for measuring a thickness during chemical mechanical polishing of a substrate having a first surface and a second surface underlying the first surface. The apparatus has means for generating first and second light beams having different effective wavelengths to impinge on the substrate, means for detecting light from the first and second light beams that is reflected from the first and second surfaces to generate a first and second interference signals, and means for determining a thickness from the first and second interference signals. 
   In still another aspect, the invention is directed to a method of determining a thickness in a substrate undergoing chemical mechanical polishing. A first interference signal is generated by directing a first light beam having a first effective wavelength onto the substrate and measuring light from the first light beam reflected from the substrate, and a second interference signal is generated by directing a second light beam having a second effective wavelength onto the substrate and measuring light from the second light beam reflected from the substrate. The first effective wavelength differs from the second effective wavelength. The thickness is determined from the first and second interference signals. 
   Implementations of the method may include the following. First and second model intensity functions may be determined for the first and second interference signals. The first and second model intensity functions are sinusoidal functions, and may each be described by a period and a phase offset. The period and offset of each model intensity function may be computed from a least square fit of the model intensity function to the intensity measurements from the interference signal. The thickness may be estimated by a first model thickness function which is a function of a first integer, the first effective wavelength, the first period and the first phase offset, and by a second model thickness function which is a function of a second integer, the second effective wavelength, the second period and the second phase offset. A first value for the first integer and a second value for the second integer may be determined which provide approximately equal estimates of the thickness from the first and second model thickness functions. Determining the first and second value may include finding solutions to the equation 
       M   =         (         ϕ   2       Δ   ⁢           ⁢     T   2         +   N     )     ·       λ   eff2       λ   eff1         -       ϕ   1       Δ   ⁢           ⁢     T   1               
 
where M is the first integer, N is the second integer, λ eff1  is the first effective wavelength, λ eff2  is the second effective wavelength, ΔT 1  is the first period, ΔT 2  is the second period, φ 1  is the first phase offset, and φ 2  is the second phase offset. The first and second light beams have different wavelengths or different incidence angles on the substrate.
 
   In still another aspect, the invention is directed to a method of detecting a polishing endpoint during polishing of a substrate. A first interference signal is generated by directing a first light beam having a first effective wavelength onto the substrate and measuring light from the first light beam reflected from the substrate, and a second interference signal is generating by directing a second light beam having a second effective wavelength onto the substrate and measuring light from the second light beam reflected from the substrate. The first effective wavelength differs from the second effective wavelength. The first and second interference signals are compared to determine the polishing endpoint. 
   Advantages of the invention include the following. With two optical systems, an estimate of the initial and remaining thickness of the layer on the substrate can be generated. Employing two optical systems operating at different effective wavelengths also allows more accurate determination of parameters that were previously obtained with a single optical system. 
   Other features and advantages of the invention will become apparent from the following description, including the drawings and claims. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a schematic exploded perspective view of a CMP apparatus according to the present invention. 
       FIG. 2  is schematic view, in partial section, of a polishing station from the CMP apparatus of  FIG. 1  with two optical systems for interferometric measurements of a substrate. 
       FIG. 3  is a schematic top view of a polishing station from the CMP apparatus of  FIG. 1 . 
       FIG. 4  is a schematic diagram illustrating a light beam from the first optical system impinging a substrate at an angle and reflecting from two surfaces of the substrate. 
       FIG. 5  is a schematic diagram illustrating a light beam from the second optical system impinging a substrate at an angle and reflecting from two surfaces of the substrate. 
       FIG. 6  is a graph of a hypothetical reflective trace that could be generated by the first optical system in the CMP apparatus of  FIG. 2 . 
       FIG. 7  is a graph of a hypothetical reflectance trace that could be generated by the second optical system in the CMP apparatus of  FIG. 2 . 
       FIGS. 8A and 8B  are graphs of two hypothetical model functions. 
       FIG. 9  is a schematic cross-sectional view of a CMP apparatus having a first, off-axis optical system and a second, normal-axis optical system. 
       FIG. 10  is a schematic diagram illustrating a light beam impinging a substrate at a normal incidence and reflecting from two surfaces of the substrate. 
       FIG. 11  is a schematic cross-sectional view of a CMP apparatus having a two optical systems and one window in the polishing pad. 
       FIG. 12  is a schematic cross-sectional view of a CMP apparatus having two off-axis optical systems and one window in the polishing pad. 
       FIG. 13  is a schematic cross-sectional view of a CMP apparatus having two optical modules arranged alongside each other. 
       FIGS. 14 and 15  are unfiltered and filtered reflectivity traces, respectively, generated using a light emitting diode with a peak emission at 470 nm. 
   

   DETAILED DESCRIPTION 
   Referring to  FIGS. 1 and 2 , one or more substrates  10  will be polished by a chemical mechanical polishing (CMP) apparatus  20 . A description of a similar polishing apparatus may be found in U.S. Pat. No. 5,738,574, the entire disclosure of which is incorporated herein by reference. Polishing apparatus  20  includes a series of polishing stations  22  and a transfer station  23 . Transfer station  23  serves multiple functions, including receiving individual substrates  10  from a loading apparatus (not shown), washing the substrates, loading the substrates into carrier heads, receiving the substrates from the carrier heads, washing the substrates again, and finally, transferring the substrates back to the loading apparatus. 
   Each polishing station includes a rotatable platen  24  on which is placed a polishing pad  30 . The first and second stations may include a two-layer polishing pad with a hard durable outer surface, whereas the final polishing station may include a relatively soft pad. If substrate  10  is an “eight-inch” (200 millimeter) or “twelve-inch” (300 millimeter) diameter disk, then the platens and polishing pads will be about twenty inches or thirty inches in diameter, respectively. Each platen  24  may be connected to a platen drive motor (not shown). For most polishing processes, the platen drive motor rotates platen  24  at thirty to two hundred revolutions per minute, although lower or higher rotational speeds may be used. Each polishing station may also include a pad conditioner apparatus  28  to maintain the condition of the polishing pad so that it will effectively polish substrates. 
   Polishing pad  30  typically has a backing layer  32  which abuts the surface of platen  24  and a covering layer  34  which is used to polish substrate  10 . Covering layer  34  is typically harder than backing layer  32 . However, some pads have only a covering layer and no backing layer. Covering layer  34  may be composed of an open cell foamed polyurethane or a sheet of polyurethane with a grooved surface. Backing layer  32  may be composed of compressed felt fibers leached with urethane. A two-layer polishing pad, with the covering layer composed of IC-1000 and the backing layer composed of SUBA-4, is available from Rodel, Inc., of Newark, Del. (IC-1000 and SUBA-4 are product names of Rodel, Inc.). 
   A slurry  36  containing a reactive agent (e.g., deionized water for oxide polishing) and a chemically-reactive catalyzer (e.g., potassium hydroxide for oxide polishing) may be supplied to the surface of polishing pad  30  by a slurry supply port or combined slurry/rinse arm  38 . If polishing pad  30  is a standard pad, slurry  36  may also include abrasive particles (e.g., silicon dioxide for oxide polishing). 
   A rotatable carousel  40  with four carrier heads  50  is supported above the polishing stations by a center post  42 . A carousel motor assembly (not shown) rotates center post  42  to orbit the carrier heads and the substrates attached thereto between the polishing and transfer stations. A carrier drive shaft  44  connects a carrier head rotation motor  46  (see  FIG. 2 ) to each carrier head  50  so that each carrier head can independently rotate about it own axis. In addition, a slider (not shown) supports each drive shaft in an associated radial slot  48 . A radial drive motor (not shown) may move the slider to laterally oscillate the carrier head. In operation, the platen is rotated about its central axis  25 , and the carrier head is rotated about its central axis  51  and translated laterally across the surface of the polishing pad. 
   The carrier head  50  performs several mechanical functions. Generally, the carrier head holds the substrate against the polishing pad, evenly distributes a downward pressure across the back surface of the substrate, transfers torque from the drive shaft to the substrate, and ensures that the substrate does not slip out from beneath the carrier head during polishing operations. A description of a carrier head may be found in U.S. patent application Ser. No. 08/861,260, entitled a CARRIER HEAD WITH a FLEXIBLE MEMBRANE FOR a CHEMICAL MECHANICAL POLISHING SYSTEM, filed May 21, 1997, by Steven M. Zuniga et al., assigned to the assignee of the present invention, the entire disclosure of which is incorporated herein by reference. 
   Referring to  FIGS. 2 and 3 , two holes or apertures  60  and  80  are formed in platen  24 , and two transparent windows  62  and  82  are formed in polishing pad  30  overlying holes  60  and  80 , respectively. The holes  60  and  80  may be formed on opposite sides of platen  24 , e.g., about 180° apart. Similarly, windows  62  and  82  may be formed on opposite sides of polishing pad  30  over holes  60  and  80 , respectively. Transparent windows  62  and  82  may be constructed as described in U.S. patent application Ser. No. 08/689,930, entitled METHOD OF FORMING A TRANSPARENT WINDOW IN A POLISHING PAD FOR A CHEMICAL MECHANICAL POLISHING APPARATUS by Manoocher Birang, et al., filed Aug. 26, 1996, and assigned to the assignee of the present invention, the entire disclosure of which is incorporated herein by reference. Holes  60 ,  80  and transparent windows  62 ,  82 , are positioned such that they each alternately provide a view of substrate  10  during a portion of the platen&#39;s rotation, regardless of the translational position of carrier head  50 . 
   Two optical systems  64  and  84  for interferometric measurement of the substrate thickness and polishing rate are located below platen  24  beneath windows  62  and  82 , respectively. The optical systems may be secured to platen  24  so that they rotate with the platen and thereby maintain a fixed position relative to the windows. The first optical system is an “off-axis” system in which light impinges the substrate at a non-normal incidence angel. Optical system  64  includes a first light source  66  and a first sensor  68 , such as a photodetector. The first light source  66  generates a first light beam  70  which propagates through transparent window  62  and any slurry  36  on the pad (see  FIG. 4 ) to impinge the exposed surface of substrate  10 . The light beam  70  is projected from light source  66  at an angle α 1  from an axis normal to the surface of substrate  10 . The propagation angle α 1  may be between 0° and 45°, e.g., about 16°. In one implementation, light source  66  is a laser that generates a laser beam with a wavelength of about 600–1500 nanometers (nm), e.g., 670 nm. If hole  60  and window  62  are elongated, a beam expander (not illustrated) may be positioned in the path of light beam  70  to expand the light beam along the elongated axis of the window. 
   The second optical system  84  may also be an “off-axis” optical system with a second light source  86  and a second sensor  88 . The second light source  86  generates a second light beam  90  which has a second wavelength that is different from the first wavelength of first light beam  70 . Specifically, the wavelength of the second light beam  90  may be shorter than the wavelength of the first light beam  70 . In one implementation, second light source  86  is a laser that generates a light beam with a wavelength of about 300–500 nm or 300–600 nm, e.g., 470 nm. The light beam  90  is projected from light source  86  at an angle of α 2  from an axis normal to the exposed surface of the substrate. The projection angle α 2  may be between 0° and 45°, e.g., about 16°. If the hole  80  and window  82  are elongated, another beam expander (not illustrated) may be positioned in the path of light beam  90  to expand the light beam along the elongated axis of the window. 
   Light sources  66  and  86  may operate continuously. Alternately, light source  66  may be activated to generate light beam  70  when window  62  is generally adjacent substrate  10 , and light source  86  may be activated to generate light beam  90  when window  82  is generally adjacent substrate  10 . 
   The CMP apparatus  20  may include a position sensor  160 , to sense when windows  62  and  82  are near the substrate. Since platen  24  rotates during the CMP process, platen windows  62  and  82  will only have a view of substrate  10  during part of the rotation of platen  24 . To prevent spurious reflections from the slurry or the retaining ring from interfering with the interferometric signal, the detection signals from optical systems  64 ,  84  may be sampled only when substrate  10  is impinged by one of light beams  70 ,  90 . The position sensor is used to ensure that the detection signals are sampled only when substrate  10  overlies one of the windows. Any well known proximity sensor could be used, such as a Hall effect, eddy current, optical interrupter, or acoustic sensor. Specifically, position sensor  160  may include two optical interrupters  162  and  164  (e.g., LED/photodiode pairs) mounted at fixed points on the chassis of the CMP apparatus, e.g., opposite each other and 90° from carrier head  50 . A position flag  166  is attached to the periphery of the platen. The point of attachment and length of flag  166 , and the positions of optical interrupters  162  and  164 , are selected so that the flag triggers optical interrupter  162  when window  62  sweeps beneath substrate  10 , and the flag triggers optical interrupter  164  when window  82  sweeps beneath substrate  10 . The output signal from detector  68  may be measured and stored while optical interrupter  162  is triggered by the flag, and the output signal from detector  88  may be measured and stored while optical interrupter  164  is triggered the flag. The use of a position sensor is also discussed in the above-mentioned U.S. patent application Ser. No. 08/689,930. 
   In operation, CMP apparatus  20  uses optical systems  64 ,  84  to determine the amount of material removed from the surface of the substrate, or to determine when the surface has become planarized. The light source  66 ,  86 , detectors  68 ,  88  and sensor  160  may be connected to a general purpose programmable digital computer or processor  52 . A rotary coupling  56  may provide electrical connections for power and data to and from light sources  66 ,  86  and detectors  68 ,  88 . Computer  52  may be programmed to receive input signals from the optical interrupter, to store intensity measurements from the detectors, to display the intensity measurements on an output device  54 , to calculate the initial thickness, polishing rate, amount removed and remaining thickness from the intensity measurements, and to detect the polishing endpoint. 
   Referring to  FIG. 4 , substrate  10  includes a wafer  12 , such as a silicon wafer, and an overlying thin film structure  14 . The thin film structure includes a transparent or partially transparent outer layer, such as a dielectric layer, e.g., an oxide layer, and may also include one or more underlying layers, which may be transparent, partially transparent, or reflective. 
   At the first optical system  64 , the portion of light beam  70  which impinges on substrate  10  will be partially reflected at a first surface, i.e., the surface of the outer layer, of thin film structure  14  to form a first reflected beam  74 . However, a portion of the light will also be transmitted through thin film structure  14  to form a transmitted beam  76 . At least some of the light from transmitted beam  76  will be reflected by one or more underlying surfaces, e.g., by one or more of the surfaces of the underlying layers in structure  14  and/or by the surface of wafer  12 , to form a second reflected beam  78 . The first and second reflected beams  74 ,  78  interfere with each other constructively or destructively depending on their phase relationship, to form a resultant return beam  72  (see also  FIG. 2 ). The phase relationship of the reflected beams is primarily a function of the index of refraction and thickness of the layer or layers in thin film structure  14 , the wavelength of light beam  70 , and the angle of incidence α 1 . 
   Returning to  FIG. 2 , return beam  72  propagates back through slurry  36  and transparent window  62  to detector  68 . If the reflected beams  74 ,  78  are in phase with each other, they cause a maxima (I max1 ) on detector  68 . On the other hand, if reflected beams  74 ,  78  are out of phase, they cause a minima (I min1 ) on detector  68 . Other phase relationships will result in an interference signal between the maxima and minima being seen by detector  68 . The result is a signal output from detector  68  that varies with the thickness of the layer or layers in structure  14 . 
   Because the thickness of the layer or layers in structure  14  change with time as the substrate is polished, the signal output from detector  68  also varies over time. The time varying output of detector  68  may be referred to as an in-situ reflectance measurement trace (or “reflectance trace”). This reflectance trace may be used for a variety of purposes, including detecting a polishing endpoint, characterizing the CMP process, and sensing whether the CMP apparatus is operating properly. 
   Referring to  FIG. 5 , in the second optical system  84 , a first portion of light beam  90  will be partially reflected by the surface layer of thin film structure  14  to form a first reflected beam  94 . A second portion of the light beam will be transmitted through thin film structure  14  to form a transmitted beam  96 . At least some of the light from transmitted beam  96  is reflected, e.g., by one of the underlying layers in structure  14  or by wafer  12 , to form a second reflected beam  98 . The first and second reflected beams  94 ,  98  interfere with each other constructively or destructively depending on their phase relationship, to form a resultant return beam  92  (see also  FIG. 2 ). The phase relationship of the reflected beams is a function of the index of refraction and thickness of the layer or layers in structure  14 , the wavelength of light beam  90 , and the angle of incidence α 2 . 
   The resultant return beam  92  propagates back through slurry  36  and transparent window  82  to detector  88 . The time-varying phase relationship between reflected beams  94 ,  98  will create a time-varying interference pattern of minima (I min2 ) and maxima (I max2 ) at detector  88  related to the time-varying thickness of the layer or layers in thin film structure  14 . Thus, the signal output from detector  88  also varies with the thickness of the layer or layers in thin film structure  14  to create a second reflectance trace. Because the optical systems employ light beams that have different wavelengths, the time varying reflectance trace of each optical system will have a different pattern. 
   When a blank substrate, i.e., a substrate in which the layer or layers in thin film structure  14  are unpatterned, is being polished, the data signal output by detectors  68 ,  88  are cyclical due to interference between the portion of the light beam reflected from the surface layer of the thin film structure and the portion of the light beam reflected from the underlying layer or layers of thin fiilm structure  14  or from wafer  12 . Accordingly, the thickness of material removed during the CMP process can be determined by counting the cycles (or fractions of cycles) of the data signal, computing how much material would be removed per cycle (see Equation 5 below), and computing the product of the cycle count and the thickness removed per cycle. This number can be compared with a desired thickness to be removed and the process controlled based on the comparison. The calculation of the amount of material removed from the substrate is also discussed in the above-mentioned U.S. patent application Ser. No. 08/689,930. 
   Referring to  FIGS. 6 and 7 , assuming that substrate  10  is a “blank” substrate, the resulting reflectance traces  100  and  110  (shown by the dots) from optical systems  64  and  84 , respectively, will be a series of intensity measurements that generally follow sinusoidal curves. The CMP apparatus uses reflectance traces  100  and  110  to determine the amount of material removed from the surface of a substrate. 
   Computer  52  uses the intensity measurements from detectors  68  and  88  to generate a model function (shown by phantom lines  120  and  130 ) for each reflectance trace  100  and  110 . Preferably, each model function is a sinusoidal wave. Specifically, the model function I 1 (T measure ) for reflectance trace  100  may be the following: 
                 I   1     ⁡     (     T   measure     )       =         k   1     ·         I   max1     +     I   min1       2       +           I   max1     -     I   min1       2     ·     cos   ⁡     (           Φ   1     +     T   measure         Δ   ⁢           ⁢     T   1         ⁢   2   ⁢   π     )                   (   3   )             
 
where I max1 , and I min1  are the maximum and minimum amplitudes of the sine wave, φ 1  is a phase difference of model function  120 , ΔT 1  is the peak-to-peak period of the sine wave of model function  120 , T measure  is the measurement time, and k 1  is an amplitude adjustment coefficient. The maximum amplitude I max1  and the minimum amplitude I min1  may be determined by selecting the maximum and minimum intensity measurements from reflectance trace  100 . The model function  120  is fit to the observed intensity measurements of reflectivity trace  100  by a fitting process, e.g., by a conventional least square fit. The phase difference φ 1  and peak-to-peak period ΔT 1  are the fitting coefficients to be optimized in Equation 1. The amplitude adjustment coefficient k 1  may be set by the user to improve the fitting process, and may have a value of about 0.9.
 
   Similarly, the model function I 2 (T measure ) for reflectance trace  110  may be the following: 
                 I   2     ⁡     (     T   measure     )       =         k   2     ·         I   max2     +     I   min2       2       +           I   max2     -     I   min2       2     ·     cos   ⁡     (           Φ   2     +     T   measure         Δ   ⁢           ⁢     T   2         ⁢   2   ⁢   π     )                   (   4   )             
 
where I max2  and I min2  are the maximum and minimum amplitudes of the sine wave, φ 2  is a phase difference of model function  130 , ΔT 2  is the peak-to-peak period of the sine wave of model function  130 , T measure  is the measurement time, and k 2    is an amplitude adjustment coefficient. The maximum amplitude I   max2  and the minimum amplitude I min2  may be determined by selecting the maximum and minimum intensity measurements from reflectivity trace  110 . The model function  130  is fit to the observed intensity measurements of reflectivity trace  110  by a fitting process, e.g., by a conventional least square fit. The phase difference φ 2  and peak-to-peak period ΔT 2  are the fitting coefficients to be optimized in Equation 2. The amplitude adjustment coefficient k 2  may be set by the user to improve the fitting process, and may have a value of about 0.9.
 
   Since the actual polishing rate can change during the polishing process, the polishing variables which are used to calculate the estimated polishing rate, such as the peak-to-peak period, should be periodically recalculated. For example, the peak-to-peak periods ΔT 1  and ΔT 2  may be recalculated based on the intensity measurements for each cycle. The peak-to-peak periods may be calculated from intensity measurements in overlapping time periods. For example, a first peak-to-peak period may be calculated from the intensity measurement in the first 60% of the polishing run, and a second peak-to-peak period may be calculated from the intensity measurements in the last 60% of the polishing run. The phase differences φ l  and φ 2  are typically calculated only for the first cycle. 
   Once the fitting coefficients have been determined, the initial thickness of the thin film layer, the current polishing rate, the amount of material removed, and the remaining thin film layer thickness may be calculated. The current polishing rate P may be calculated from the following equation: 
             P   =     λ     Δ   ⁢           ⁢     T   ·   2     ⁢     n   layer     ⁢   cos   ⁢           ⁢     α   ′                 (   5   )             
 
where λ is the wavelength of the laser beam, n layer  is the index of refraction of the thin film layer, and α′ is the angle of laser beam through the thin film layer, and ΔT is the most recently calculated peak-to-peak period. The angle α′ may be determined from Snell&#39;s law, n layer  sinα′=n air  sinα, where n layer  is the index of refraction of the layer in structure  14 , n air  is the index of refraction of air, and α (α 1  or α 2 ) is the off-vertical angle of light beam  70  or  90 . The polishing rate may be calculated from each reflectance trace and compared.
 
   The amount of material removed, D removed , may be calculated either from the polishing rate, i.e.,
 
 D   removed   =P·T   measure   (6)
 
or by counting the number or fractional number of peaks in one of the reflectivity trace, and multiplying the number of peaks by the peak-to-peak thickness ΔD for that reflective trace (i.e., ΔD 1  for reflectance trace  100  and ΔD 2  for reflectance trace  110 ), where 
               Δ   ⁢           ⁢   D     =     λ     2   ⁢     n   layer     ⁢   cos   ⁢           ⁢     α   ′                 (   7   )             
 
   The initial thickness D initial  of the thin film layer may be calculated from the phase differences φ 1  and φ 2 . The initial thickness D initial  will be equal to: 
               D   initial     =       (         ϕ   1       Δ   ⁢           ⁢     T   1         +   M     )     ·       λ   1       2   ⁢     n   layer     ⁢   cos   ⁢           ⁢     α   1   ′                   (   8   )             
 
and equal to 
               D   initial     =       (         ϕ   2       Δ   ⁢           ⁢     T   2         +   N     )     ·       λ   2       2   ⁢     n   layer     ⁢   cos   ⁢           ⁢     α   2   ′                   (   9   )             
 
where M and N are equal to or close to integer values. Consequently, 
             M   =         (         ϕ   2       Δ   ⁢           ⁢     T   2         +   N     )     ·       cos   ⁢           ⁢     α   1   ′         cos   ⁢           ⁢     α   2   ′         ·       λ   2       λ   1         -       ϕ   1       Δ   ⁢           ⁢     T   1                   (   10   )             
 
   For an actual substrate, the manufacturer will know that the layers in structure  14  will not be fabricated with a thickness greater than some benchmark value. Therefore, the initial thickness D initial  should be less than a maximum thickness D max , e.g., 25000 Å for a layer of silicon oxide. The maximum value, N max , of N can be calculated from the maximum thickness D max  and the peak-to-peak thickness ΔD 2  as follows: 
               N   max     =         D   max       Δ   ⁢           ⁢     D   2         =           D   max     ·   2     ⁢     n   layer     ⁢   cos   ⁢           ⁢     α   2   ′         λ   2                 (   11   )             
 
Consequently, the value of M may be calculated for each integer value of N=1, 2, 3, . . . , N max . The value of M that is closest to an integer value may be selected, as this represents the mostly likely solution to Equation 6, and thus the most likely actual thickness. Then the initial thickness may be calculated from Equation 6 or 7.
 
   Of course, a value of N could be calculated for each integer value of M, in which case the maximum value, M max , of M would be equal to D max /ΔD 1 . However, it may be preferable to calculate for each integer value of the variable that is associated with the longer wavelength, as this will require fewer computations of the other integer variable. 
   Referring to  FIGS. 8A and 8B , two hypothetical model functions  140  and  150  were generated to represent the polishing of a silicon oxide (SiO 2 ) surface layer on a silicon wafer. The fitting coefficients that represent the hypothetical model functions  140  and  150  are given in Table 1. 
                                   TABLE 1                          phase offset   φ 1  = 12.5 s   φ 2  = 65.5 s           peak-to-peak period   ΔT 1  = 197.5 s   ΔT 2  = 233.5 s                        
These fitting coefficients were calculated for polishing rate of 10 Å/sec and utilizing the polishing parameters in Table 2.
 
                                   TABLE 2                           1st optical   2nd optical               system   system                          material   silicon oxide   silicon oxide           initial thickness   10000 Å   10000 Å           polishing rate   10 Å/sec   10 Å/sec           refractive index   n layer  = 1.46   n layer  = 1.46           wavelength   λ 1  = 5663 Å   λ 2  = 6700 Å           incidence angle in air   α 1  = 16°   α 2  = 16°           angle in layer   α 1 ′ = 10.88°   α 2 ′ = 10.88°           peak-to-peak thickness   ΔD 1  = 1970 Å   ΔD 2  = 2336 Å                        
Using Equation 8, the M-values can be calculated for integer values of N, as shown in Table 3.
 
   
     
       
         
             
             
             
             
             
             
           
             
               TABLE 3 
             
             
                 
             
             
                 
                 
               integer 
               thickness 
               thickness 
               thickness 
             
             
               N 
               M 
               of M 
               for N 
               for M 
               difference 
             
             
                 
             
           
          
             
                 
             
          
         
         
             
             
             
             
             
             
          
             
               0 
               0.27 
               0 
               655 
               125 
               530 
             
             
               1 
               1.45 
               1 
               2992 
               2100 
               892 
             
             
               2 
               2.63 
               3 
               5329 
               6050 
               −721 
             
             
               3 
               3.82 
               4 
               7665 
               8025 
               −360 
             
             
               4 
               5.00 
               5 
               10002 
               9999 
               2 
             
             
               5 
               6.18 
               6 
               12338 
               11974 
               364 
             
             
               6 
               7.37 
               7 
               14675 
               13949 
               725 
             
             
               7 
               8.55 
               9 
               17011 
               17899 
               −888 
             
             
               8 
               9.73 
               10 
               19348 
               19874 
               −526 
             
             
               9 
               10.92 
               11 
               21684 
               21849 
               −165 
             
             
               10 
               12.10 
               12 
               24021 
               23824 
               197 
             
             
               11 
               13.28 
               13 
               26357 
               25799 
               559 
             
             
               12 
               14.47 
               14 
               28694 
               27774 
               920 
             
             
               13 
               15.65 
               16 
               31030 
               31723 
               −693 
             
             
               14 
               16.83 
               17 
               33367 
               33698 
               −331 
             
             
               15 
               18.02 
               18 
               35704 
               35673 
               30 
             
             
               16 
               19.20 
               19 
               38040 
               37648 
               392 
             
             
               17 
               20.38 
               20 
               40377 
               39623 
               754 
             
             
               18 
               21.56 
               22 
               42713 
               43573 
               −860 
             
             
                 
             
          
         
       
     
   
   As shown, the best fit, i.e., the choice of N that provides a value of M that is closest to an integer, is for N=4 and M=5, with a resulting initial thickness of approximately 10000 Å, which is acceptable because ti is less than the maximum thickness. The next best fit is N=15 and M=18, with a resulting initial thickness of approximately 35700 Å. Since this thickness is greater than the expected maximum initial thickness D max  of 25000 Å, this solution may be rejected. 
   Thus, the invention provides a method of determining the initial thickness of a surface layer on a substrate during a CMP process. From this initial thickness value, the current thickness D(t) can be calculated as follows:
 
 D ( t )= D   initial   −D   removed (t)  (12)
 
   As a normal thickness for a deposited layer typically is between 1000 A and 20000 A, the initial as well as the current thickness can be calculated. The only prerequisite to estimate the actual thickness is to have sufficient intensity measurements to accurately calculate the peak-to-peak periods and phase offsets. In general, this requires at least a minima and a maxima for each of the wavelengths. However, the more minima and maxima in the reflective trace, and the more intensity measurements, the more accurate the calculation of the actual thickness will be. 
   Some combinations of wavelengths may be inappropriate for in-situ calculations, for example, where one wavelength is a multiple of the other wavelength. A good combination of wavelengths will result in an “odd” relationship, i.e., the ratio of λ 1 /λ 2  should not be substantially equal to a ratio of small integers. Where the ratio of λ 1 /λ 2  is substantially equal to a ratio of small integers, there may be multiple integer solutions for N and M in Equation 8. In short, the wavelengths λ 1  and λ 2  should be selected so that there is only one solution to Equation 8 that provides substantially integer values to both N and M within the maximum initial thickness. 
   In addition, preferred combinations of wavelengths should be capable of operating in a variety of dielectric layers, such as SiO 2 , Si 3   N   4 , and the like. Longer wavelengths may be preferable when thick layers have to be polished, as less peaks will appear. Short wavelengths are more appropriate when only minimal polishing is performed. 
   The two optical systems  64 ,  84  can be configured with light sources having different wavelengths and the same propagation angle. Also, light sources  66 ,  86  could have different wavelengths and different respective propagation angles α 1 , α 2 . It is also possible for light sources  66 ,  86  to have the same wavelength and different respective propagation angles α 1 , α 2 . 
   The available wavelengths may be limited by the types of lasers, light emitting diodes (LEDs), or other light sources that can be incorporated into an optical system for a polishing platen at a reasonable cost. In some situations, it may impractical to use light sources with an optimal wavelength relationship. The system may still be optimized, particularly when two off-axis optical systems are used, by using different angles of incidence for the light beams from the two sources. This can be seen by from the expression for the peak-to-peak thickness ΔD, ΔD=λ/(2 n*cosα′), where λ is the wavelength of the light source, n is the index of refraction of the dielectric layer, and α′ is the propagation angle of the light through the layer in the thin film structure. Thus, an effective wavelength λ eff  can be defined as λ/cosα′, and it is the effective wavelength λ eff  of each light source that is important to consider when optimizing the wavelengths of the different light sources. However, one effective wavelength should not be an integer multiple of the other effective wavelength, and the ratio of λ eff1 /λ eff2  should not be substantially equal to a ratio of small integers. 
   Referring to  FIGS. 9 and 10 , CMP apparatus  20   a  has a platen  24  configured similarly to that described above with reference to  FIGS. 1 and 2 . CMP apparatus  20   a , however, includes an off-axis optical system  64  and a normal-axis optical system  84   a . The normal axis optical system  84   a  includes a light source  86   a , a transreflective surface  91 , such as a beam splitter, and a detector  88   a . A portion of light beam  90   a  passes through beam splitter  91 , and propagates through transparent window  82   a  and slurry  36   a  to impinge substrate  10  at normal incidence. In this implementation, the aperture  80   a  in platen  24  can be smaller because light beam  90   a  passes through the aperture and returns along the same path. 
   Referring now to  FIG. 11 , in another implementation, CMP apparatus  20   b  has a single opening  60   b  in platen  24   b  and a single window  62   b  in polishing pad  30   b . An off-axis optical system  64   b  and a normal-axis optical system  84   b  each direct respective light beams through the same window  62   b . The light beams  70   b  and  90   b  may be directed at the same spot on substrate  10 . This implementation needs only a single optical interrupter  162 . Mirrors  93  may be used to adjust the incidence angle of the laser on the substrate. 
   Referring now to  FIG. 12 , in yet another implementation, CMP apparatus  20   c  has two off-axis optical systems  64   c  and  84   c  that direct light beams  70   c  and  90   c  at the same spot on substrate  10 . Light source  66   c  and detector  68   c  of optical system  64   c  and light source  86   c  and detector  88   c  of optical system  84   c  may be arranged such that a plane defined by light beams  70   c  and  72   c  crosses a plane defined by light beams  90   c  and  92   c . For example, optical systems  64   c ,  84   c  can be offset by about 90° from each other. This implementation also needs only a single optical interrupter  162 , and permits the effective wavelength of the first light beam  70   c  to be adjusted by modifying the incidence angle. 
   Although the optical systems  64   c ,  84   c  are illustrated as using different propagation angles α 1  and α 2 , the propagation angles can be the same. In addition, the light sources could be located side by side (horizontally), the light beams could reflect off a single mirror (not shown), and the return beams could impinge two areas of a single detector. This would be conducive to combining the two light sources, mirror and detector in a single optical module. Furthermore, the light beams could impinge different spots on the substrate. 
   In another implementation, shown in  FIG. 13 , two optical systems  64   d ,  84   d  are arranged next to each other in separate modules. Optical systems  64   d ,  84   d  have respective light sources  66   d ,  86   d , detectors  68   d ,  88   d , and mirrors  73   d  and  93   d  to direct the light beams onto the substrate at the described propagation angles α 1  and α 2 . 
   It will be understood that other combinations of optical systems and window arrangements are also within the scope of the invention, as long as the optical systems operate at different effective wavelengths. For example, different combinations of off-axis optical systems and normal-axis optical systems can be arranged to direct light beams through either the same or different windows in the platen. Additional optical components such as mirrors can be used to adjust the propagation angles of the light beams before they impinge the substrate. 
   Rather than a laser, a light emitting diode (LED) can be used as a light source to generate an interference signal. The important parameter in choosing a light source is the coherence length of the light beam, which should be on the order of or greater than twice the optical path length of the light beam through of the polished layer. The optical path length OPL is given by 
             OPL   =       2   ⁢     d   ·     n   layer           cos   ⁢           ⁢     α   ′                 (   13   )             
 
where d is the thickness of the layer in structure  14 . In general, the longer the coherence length, the stronger the signal will be. Similarly, the thinner the layer, the stronger the signal. Consequently, as the substrate is polished, the interference signal should become progressively stronger. As shown in  FIGS. 14 and 15 , the light beam generated by an LED has a sufficiently long coherence length to provide a useful reflectance trace. The traces in  FIGS. 14 and 15  were generated using an LED with a peak emission at 470 nm. The reflectance traces also show that the interference signal becomes stronger as the substrate is polished. The availability of LEDs as light sources for interference measurements permits the use of shorter wavelengths (e.g., in the blue and green region of the spectrum) and thus more accurate determination of the thickness and polishing rate. The usefulness of an LED for this thickness measurement may be surprising, given that lasers are typically used for interferometric measurements and that LEDs have short coherence lengths compared to lasers.
 
   Because the apparatus of the invention uses more than one optical system operating at more than one effective wavelength, two independent end point signals can be obtained. The two end point signals can be cross-checked when used, for example, to stop the polishing process. This provides improved reliability over systems having only one optical system. Also, if only one end point comes up and if within a predetermined time the other end point does not appear, then this can be used as a condition to stop the polishing process. In this way, a combination of both end point signals, or only one end point signal may be used as a sufficient condition to stop the polishing process. 
   Before the end point appears, signal traces from different optical systems may be compared with each other to detect irregular performance of one or the other signal. 
   When the substrater has an initially irregular surface topography to be planarized, the reflectance signal may become cyclical after the substrate surface has become significantly smoothed. In this case, an initial thickness may be calculated at an arbitrary time beginning once the reflectance signal has become sinusoidal. In addition, an endpoint (or some other process control point) may be determined by detecting a first or subsequent cycle, or by detecting some other predetermined signature of the interference signal. Thus, the thickness can be determined once an irregular surface begins to become planarized. 
   The invention has been described in the context of a blank wafer. However, in some cases it may be possible to measure the thickness of a layer overlying a patterned structure by filtering the data signal. This filtering process is also discussed in the above-mentioned U.S. patent application Ser. No. 08/689,930. 
   In addition, although the substrate has been described in the context of a silicon wafer with a single oxide layer, the interference process would also work with other substrates and other layers, and with multiple layers in the thin film structure. The key is that the surface of the thin film structure partially reflects and partially transmits, and the underlying layer or layers in the thin film structure or the wafer at least partially reflect, the impinging beam. 
   The present invention has been described in terms of a preferred embodiment. The invention, however, is not limited to the embodiment depicted and described. Rather, the scope of the invention is defined by the appended claims.