inventions for accurately determining an endpoint or a thickness of a wafer layer are provided . in one embodiment , a plurality of sinusoidal signals generated by a plurality of complementary sensors is averaged generating a sinus - suppressed signal configured to substantially correlate with the thickness of the wafer layer being processed . in one embodiment , the signals generated by a set of complementary sensors defined along a circle of a wafer carrier are averaged generating a sinus - suppressed signal significantly correlating with the thickness of the wafer layer being processed or being removed . as used herein , the term “ complementary sensors ” refers to a set of two or more sensors substantially uniformly distributed along a circle of the wafer carrier such that the sinusoidal component in the average of generated sine signals is substantially suppressed so as to precisely correlate with thickness of a wafer layer being processed . in preferred embodiments , the sinusoidal component of the noise is eliminated by averaging the alternative phase signals generated by the plurality of complementary sensors . the term “ noise ,” as used herein , refers to any factor affecting the generated signals ( e . g ., undulating disturbance , etc .). in this manner , the suppression sine signal can be implemented to determine the sensor signal with significantly improved signal - to - noise ratio . in one example , the plurality of sensors is eddy current sensors ( ecs ) sensors . in the following description , numerous specific details are set forth in order to provide a thorough understanding of the present invention . it will be understood , however , to one skilled in the art , that the present invention may be practiced without some or all of these specific details . in other instances , well known process operations have not been described in detail in order not to unnecessarily obscure the present invention . fig3 a is a simplified schematic diagram of an exemplary wafer carrier 118 including a pair of complementary sensors 128 a and 128 a &# 39 ; measuring a thickness of a layer of a wafer 122 , in accordance with one embodiment of the present invention . in one embodiment , the complementary sensors 128 a and 128 a &# 39 ; are ecs sensors . as shown in the embodiment of fig3 a , the wafer carrier 118 is mounted on a carrier spindle 133 using a gimbal 135 . the gimbal 135 positioned above the wafer carrier 118 is implemented to align the wafer carrier 118 and the wafer 122 to the moving polishing pad 130 during the polishing operations . as can be seen , the gimbal 135 mounted on the carrier spindle 133 is designed to rotate in the direction of wafer rotation 134 . the carrier spindle 133 is configured to apply the wafer carrier 118 and thus the wafer 122 on to the moving polishing pad 130 . in one example , while the wafer carrier 118 and thus the wafer 122 rotate in the rotation direction 134 , the wafer carrier 118 and the wafer 122 are applied to the polishing pad 130 with the force f . in some embodiments , despite including the gimbal 135 to align the wafer carrier 118 and the wafer 122 with a surface of the polishing pad 130 , the wafer 122 is applied to the polishing pad 130 such that initially , a leading edge 122 a of the wafer 122 digs into the polishing pad 130 . thereafter , the center of the wafer 122 c and a trailing edge 122 b come into contact with the polishing pad 130 . in another embodiment , the leading edge 122 a digging into the polishing pad 130 leads to a decrease in the carrier film 120 thickness close to the leading edge 122 a of the wafer . as a consequence , the standoff and thus the ecs signals being detected by the ecs sensor 128 a are modified . the wafer leading edge 122 a digging into the polishing wafer also increases the temperature at the wafer leading edge 122 a affecting the sinusoidal undulation close to the wafer leading edge 122 a . as will be described in more detail below , in one embodiment , the ecs signal detected by the ecs sensors 128 a and 128 a &# 39 ; at the wafer leading edge 122 a and trailing edge 122 b , respectively , are implemented to suppress the ecs signal undulations . reference is made to fig3 b , depicting a simplified schematic top view of the wafer carrier 118 of fig3 a being applied to the polishing pad 130 , in accordance with one embodiment of the present invention . as can be seen , while the ecs sensor 128 a is defined on a radius r of a hypothetical circle 123 a defined within the wafer 122 , the complementary ecs sensor 128 a &# 39 ; is defined on a radius − r of the hypothetical circle 123 a . in this manner , as will be explained below , variation in signal undulation amplitude can be eliminated ( i . e ., eliminating any sinusoidal component of the noise ) beneficially using one of the functions of sinus . as can be appreciated , the resulting suppressed sine signal substantially correlates with the true thickness of the target layer . fig3 c is a simplified schematic top view of the wafer carrier 118 of fig3 a showing the two ecs sensors 128 a and 128 a &# 39 ; being defined 180 degrees out of phase to one another , in accordance with one embodiment of the present invention . that is , the signal from one sensor 128 a is offset by the signal from the other sensor 128 a &# 39 ;. as can be seen , the ecs sensor 128 a creates an angle α with reference to an angle 0 degree 131 while the ecs sensor 128 a &# 39 ; creates an angle 180 + α with reference to the angle 0 degree 131 . as further shown , the ecs sensor 128 a is defined at the radius r as opposed to the ecs sensor 128 b that is defined at the radius − r . in accordance with one embodiment , suppressing the variation in sinusoidal amplitude in the embodiment of fig3 c can further be understood as shown in table 1 below . in one embodiment , assuming that s 0 is the true signal magnitude sinusoidally modulated by the carrier rotation . as a result , the true signal magnitude s is configured to oscillate as : furthermore , the signal traces s 1 and s 2 for corresponding sensor 1 and sensor 2 located at a given circle , each located at diametrically alternative positions , also follow oscillating equations provided in table 1 . by averaging the sine components of the signal traces s 1 and s 2 , at the same time , the true non - oscillating signal amplitude in real time can be obtained . thus , as can be seen , where a pair of complementary ecs sensors is implemented , the sinusoidal signals generated by the respective sensors are synchronously recorded . the sine components of the sinusoidal signals are then averaged in accordance with the number of sensors implemented ( e . g ., 2 , in this example ). in this manner , variation in the amplitude of the ecs sinusoidal signals is suppressed , creating a signal that is substantially unaffected by the rotational sinusoidal noise that precisely correlates with the true thickness of the processed layer . reference is made to the embodiment of fig3 d , depicting a simplified schematic top view of the wafer carrier 118 including three sets of complementary ecs sensors built therein , in accordance with one embodiment of the present invention . as can be seen , a first set of complementary ecs sensors 128 a and 128 a ′ are defined at radii r 1 and − r 1 , respectively . in a like manner , a second set of complementary ecs sensors 128 b and 128 b ′ are defined at radii r 2 and − r 2 while a third set of complementary ecs sensors 128 c and 128 c ′ are defined at radii r 3 and − r 3 . in accordance with one embodiment , the sine component of the sinusoidal signals of each pair of complementary ecs sensors is synchronously recorded and averaged , generating a combination sine suppressed sinusoidal signal that significantly correlates with the thickness of the wafer layer . that is , by offsetting the sinusoidal signals between each pair of ecs sensors , the electromagnetic field produced by each pair of sensors will suppress each other . as can be appreciated , the average of each complementary pair of ecs sensors 128 a and 128 a ′, 128 b and 128 b ′, and 128 c and 128 c ′ are substantially equivalent to zero . as shown , the radius r 3 is shown to be greater than radius r 2 that in turn is greater than the radius r 1 . as will be described in more detail below , the greater the radius is , the greater the gradiance becomes . however , the embodiments of the present invention eliminate such variance in gradience by averaging the sine component of the sinusoidal signals recorded synchronously using the complementary ecs sensors . suppressing the variance in sinusoidal signal amplitude of ecs sensors are further illustrated in the graphs of signals generated by complementary esc sensors shown in fig4 , in accordance with one embodiment of the present invention . a graph 134 a plots an eddy current sensor output in volts ( i . e ., the y - axis 112 ) versus the time ( i . e ., the x - axis 110 ) as generated by the ecs sensor 128 a ′. similarly , a graph 134 a ′ plots an eddy current sensor output in volts versus the time , as generated by the ecs sensor 128 a . a graph 134 a ” represents the average of the sine components of the sinusoidal esc sensor signals 128 a and 128 a &# 39 ;. as can be appreciated , by averaging the sine component of the sinusoidal ecs signals of the ecs sensor defined on angle a on a circle having a radius r and the ecs signal of the ecs sensor defined on angle 180 + α a on a radius − r , the sine component of the noise affecting the sinusoidal signals is substantially eliminated . thus , in this manner , the thickness of the metal layer being processed substantially correlates with the amplitude of the sine suppressed combination signal . in one embodiment , the signal intensity is linearly related to the distance of the respective sensors 128 a and 128 a ′ from the wafer layer being processed . a change in the intensity of each signal caused by movement of the wafer layer toward the sensor 128 a is offset by a substantially opposite change in the intensity resulting from moving the wafer layer from the sensor 128 a ′. in this manner , advantageously , changes in the amplitude of the sinusoidal signals caused by the sine component of the noise are substantially eliminated . for instance , at the point the signals are shown to be at their lowest , the ecs sensors have substantially the least distance from the continuous metal film to be removed . thereafter , as the thickness of the metal film becomes less , the intensity of the signals is shown to be increasing , as illustrated by graphs 134 a and 134 a ′. the increase in signal intensity continues until the metal film ( e . g ., copper film ) is substantially completely removed from the wafer surface at which point , the sinusoidal graphs 134 a and 134 a ′ assume a more smooth path . as can be seen , signals generated by each sensor contains a sinusoidal component illustrated in the graphs 134 a and 134 a ′, which as can be appreciated are substantially equivalent but out of phase . thus , the average of the two sinusoidal ecs signals having equal but out of phase amplitudes , the combo graph 134 a ″, is a graph in which the sine component of the noise has been eliminated . in this manner , the combo sine suppressed signal can be implemented as a measure of the true thickness of the target layer ( i . e ., the metal film ), as the sinusoidal ecs signal correlates with the thickness of the metal film . in one embodiment , the ecs sensors implemented are ecs sensors commonly available such as gp - a series analog displacement sensors available from sunx limited . fig5 a is an exploded , simplified , diagram of graphs 136 a and 136 a ′ of a pair of complementary ecs sensors , in accordance with one embodiment of the present invention . as shown , the graph 136 a represents the ecs signal from a sensor located at a radius r while the graph 136 a ′ represents the ecs signal from a sensor located 180 degrees out of phase with respect to the first sensor , defined on the radius − r . one of ordinary skill in the art can appreciate variation in signal amplitude for the graphs 136 a and 136 a ′. in accordance with one embodiment of the present invention , by implementing pairs of sensors being defined 180 degrees out of phase , the variation in signal amplitude can be eliminated substantially by simply averaging the sine components of the two signal graphs 136 a and 136 a ′, generating a sine suppressed graph 136 a ″. reference is made to the exploded simplified graphs 136 a , 136 a ′, and 136 a ″ shown in fig5 c , in accordance with one embodiment of the present invention . as shown , both graphs 136 a and 136 a ′ are sinusoidal with varied amplitudes , with the two graphs 136 a and 136 a ′ being generated by ecs signals defined at substantially 180 degrees out of phase angles . despite the two graphs 136 a and 136 a ′ having evident amplitude variation and undulations caused by the noise , the combo graph 136 a ″ is shown to be a sine suppressed signal graph in which undulations caused by the noise have been eliminated . as a result , the combo graph signal 136 a ″ can be implemented to determine a true thickness of the metal film being removed . implementing a set of complementary ecs sensors including a plurality of complementary ecs sensors so as to create a sine suppressed combination graph is shown in embodiments of fig6 a - 6h , in accordance with some embodiments of the present invention . fig6 a shows a carrier head 118 including a set of three complementary sensors 128 a , 128 b , and 128 c , with sensors 128 a - c being defined 120 degrees out of phase with each other . in this manner , spatial coverage of the metal film ( i . e ., the target layer ) increases , beneficially allowing a more accurate measurement of the metal film thickness . table 2 below provides further explanation as to suppression of sensor signals generated by exemplary triplet - sensor complementary sensors , allowing synchronous measuring of the sensor signals and averaging of the sine components of the sensor signals . in a like manner , fig6 b shows a carrier head 118 including a set of complementary sensors consisting of four sensors 128 a , 128 b , 128 c , and 128 d with sensors 128 a - d being defined along a circle having a radius r at 90 degrees out of phase with each other , in accordance with one embodiment of the present invention . in one embodiment , this configuration can be configured to be two pairs of sensors located diametrically opposite to one another . fig6 c depicts the wafer carrier 118 including five complementary sensors 128 a - 128 e defined along a circle being 72 ° out of phase from each other , in accordance with still another embodiment . fig6 d shows six complementary sensors 128 a - 128 f being defined 60 ° out of phase from each other , in accordance with another embodiment . fig6 e and 6f depict the wafer carrier 118 including seven complementary sensors 128 a - 128 g being defined 52 ° out of phase with respect to each other , and eight complementary sensors 128 a - 128 h being defined 45 ° out of phase from one another , respectively . as was explained in more detail above , multi sets of complementary sensors can be implemented so as to create a sinus suppressed combination signal wherein the sine component of the noise has been eliminated , providing sensor signals that substantially correlate with the metal film thickness . implementing multiple combinations of complementary sensors is depicted in the embodiments of fig6 g and 6h , in accordance with one embodiment . as shown in fig6 g , complementary sensors 128 a - 128 i are defined 40 ° out of phase and along a radius r within the wafer carrier 118 while the sensors 138 a and 138 a ′ are defined 180 ° out of phase along a radius r ′, in accordance with one embodiment . in this manner , the average of sine components of the signals generated by the sensors 138 a and 138 a ′ defined 180 ° out of phase with respect to one another provides the sine suppressed signal that substantially correlates to the thickness of the film at and around radius r ′. in a like manner , the average of signals from the sensors 128 a - 128 i defined 40 ° out of phase with respect to one another provides the sine suppressed signal that substantially parallels with the thickness of the film at and around radius r . in one embodiment , temperature , pressure , or standoff gradiance becomes greater as the radius of the circle along which the sensors are defined increases . thus , in the embodiment of fig6 g , due to the radius r being greater than the radius r ′, the temperature , pressure , or standoff gradience is larger . as a result , the generated sinusoidal sensor signals have a higher amplitude than the sinusoidal sensor signals generated along the radius r ′. fig6 h depicts a carrier head 118 including another combination of complementary sensors , in accordance with one embodiment of the present invention . as can be seen , ten complementary sensors 128 a - 128 j are defined along the radius r and 36 ° out of phase with one another . additionally , a combination of two complementary sensors 138 a and 138 a ′ are defined along a radius r ′ and 180 ° out of phase with each other . although the embodiments of the present invention have been shown to include two through ten complementary sensors , one of ordinary skill in the art must appreciate that the embodiments of the present invention may implement any suitable combination of uniformly and equally distributed sensors defined along the same circle of the carrier head to produce sinusoidal signals substantially correlating with the wafer layer thickness . furthermore , one must appreciate that a multiplicity of combination of the equally distributed sensors defined along respective circles can be implemented to correlate with the thickness of wafer layer at respective locations of the sensors . furthermore , although some embodiments of the present invention have been described with ecs sensors , the embodiments of the present invention can be implemented to suppress signals generated by any suitable type of sensor ( e . g ., infrared , capacitance , sonic , etc .). for instance , the infrared sensors may be implemented to measure the temperature of the polishing belt over time . it must be appreciated by one having ordinary skill in the art that as silicon substrate is transparent to the infrared signal , the infrared signal can detect the temperature of the thin film ( i . e ., target layer ) of the wafer being processed by the surface of the polishing pad . in one embodiment , the wafer temperature is monitored to observe temperature variation during the cmp process . in one implementation , the temperature of the wafer and the temperature of the polishing pad begin to decrease at the endpoint . fig7 is a flowchart diagram 700 depicting operations performed to determine the thickness of a metal film using a plurality of complementary sensors , in accordance with one embodiment of the present invention . the method begins in operation 702 in which a plurality of complementary sensors is provided . in one embodiment the plurality of sensors are ecs sensors . the plurality of complementary sensors is defined within a wafer carrier configured to hold a wafer to be processed . in one embodiment , the wafer to be processed includes a metal film . then , a combination signal is created using signals generated by the plurality of sensors . a thickness of the metal film defined on the wafer surface is then determined using the combination signal . as described in more detail above , the sine suppressed combination signal is substantially unaffected by the sine component of the noise , significantly correlating with the thickness of the film layer being removed . reference is made to the flowchart 800 depicted in fig8 illustrating method operations performed in detecting etch endpoint implementing a plurality of complementary sensors , in accordance with another embodiment of the present invention . the method begins in operation 802 in which a plurality of sensors is provided . next , in operation 804 , a particular circle defined by the radius on a wafer carrier is defined . thereafter , the plurality of sensors is defined along the particular radius within the wafer carrier in operation 806 , creating a set of anti - phase complementary sensors . in one example , the sensors are complementary so long as the sensors are uniformly distributed along the particular radius in the wafer carrier generating a significantly suppressed sine signal . for instance , the set of complementary sensors may include two sensors , each being 180 degree out of phase with respect to the other , threes sensors being 120 degrees out of phase with each other , four sensors being 90 degrees out of phase with each other , etc . the method then continues to operation 808 in which the signals generated by each sensor in the set of complementary sensors are measured proceeding to operation 810 in which the sine component of the generated signals are averaged , creating a combination signal . continuing to operation 812 , an etch endpoint of a metal film defined on the wafer surface is determined using the combination signal . it should be appreciated that although in one embodiment the wafer carrier is aligned with the polishing pad using a gimbal , the embodiments of the present invention are not limited to cmp systems including that implement a gimbal . additionally , although one embodiment of the present invention is shown to be implemented in cmp systems including linear polishing pads , in a different embodiment , any appropriate polishing table may be implemented ( e . g ., rotary , etc .) furthermore , while the embodiments of the present invention have been described in terms of a cmp process , the complementary sensors are not limited to a cmp process . for example , the sensors can be used within any semiconductor process that removes or deposits a layer or film on a substrate , such as etch and deposition processes . the invention has been described herein in terms of several exemplary embodiments . other embodiments of the invention will be apparent to those skilled in the art from consideration of the specification and practice of the invention . the embodiments and preferred features described above should be considered exemplary , with the invention being defined by the appended claims .