Abstract:
A very sensitive particle distribution probe uses special processing including a modified Twomey/Chahine iterative convergence technique and a specially constructed sample cell to obtain particle size distribution measurements from optically dense slurries, such as the slurries used in the semiconductor industry for chemical mechanical planarization. Spectral transmission data is taken over the spectral range of 0.20-2.5 microns, utilizing specially constructed, chemically resistant sample cells of 50-250 microns thickness, and miniature, fixed grating, linear detector array spectrometers. At wavelengths greater than 1 micron, the preferred design utilizes InGaAs linear detector arrays. An ultrasonic disrupter can be employed to breakup harmless soft agglomerates. In addition to direct particle size distribution measurement, the invention described here could be used to detect other fundamental causes of slurry degradation, such as foaming and jelling. The probe accomplishes continuous, real time sampling of undiluted slurry. A three-position chopper allows automated operation in an industrial environment without the need for frequent reference spectra, which would require taking the probe off-line.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention pertains to the field of measurements performed on slurries to determine the slurry particle size distribution. More specifically, the measurements concern a use of instrumentation to determine the particle concentration as a function of size in substantially opaque slurries, such as the chemical mechanical planarization (“CMP”) slurries that are currently used in semiconductor manufacturing. 
     2. Statement of the Problem 
     CMP processes are used in the semiconductor and optics industries to provide ultrasmooth surfaces. CMP slurries for use in these processes typically consist of SiO 2  or Al 2 O 3  particles suspended in an acid or base solution to a concentration of 4% to 18% solids by weight. The SiO 2  slurries are referred to in the art as ‘oxide’ slurries, and the Al 2 O 3  slurries are referred to as ‘metal’ slurries. It is difficult to check the quality of particle size distribution due to the submicron sizes of the particles and the substantially opaque nature of CMP slurries. 
     CMP slurries are used to facilitate the deposition of uniform planarized layers in multiple layer wafers. The use of CMP slurry results is ultrasmooth surfaces that enhance the resolution of embedded microfeatures in integrated circuits. Particles having dimensions that exceed a delimiting value for a particular application are analogous to sandpaper having grit that is too large, and disadvantageously score or scratch the surface that is being smoothed. Thus, it is an essential quality control operation to eliminate the use of slurries having particles that are too large. 
     The use of CMP slurries in semiconductor manufacturing has risen sharply over the last 5 years. It has emerged as the preferred method of planarization for manufacture of multiple layer semiconductor wafers having feature sizes less than or equal to 0.35 micron. It has been observed that semiconductor wafers can be scratched and thereby damaged if a significant concentration of large particles appear in the slurry through either contamination or agglomeration. The size threshold for particles that are large enough to damage wafers is a process dependent value that still poorly known, but is believed to be in the range of 0.5-3.0 microns. CMP slurry manufacturers attempt to produce slurries that consist predominantly of particles less than 0.5 micron in size. 
     Commercially available sensor devices are presently unable to meet the needs of those who wish to measure the particle size distribution of CMP slurries. It is desirable to perform continuous measurements of the CMP slurry particle size distribution in real time, in order to eliminate the risk of using slurries having particles or agglomerated particles that are too large. This enhanced process control, if available, would allow early detection and cure of slurry problems. The use of the term “real time” in this discussion means that the measurement results are available within a few seconds after sampling. It is also desirable to measure the particle size distribution of undiluted slurry because dilution and the subsequent change in pH can alter the distribution. Furthermore, dilution combined with continuous sampling creates large volumes of waste slurry. These needs characterize the present state of the art in measuring the particle size distribution of CMP slurries. 
     Existing commercial particle size sensors include those based on measurement of angular light scattering, dynamic light scattering or photon correlation spectroscopy, ultrasonic transmission, and capillary hydrodynamic fractionalization. These measurement techniques are problematic because they require substantial dilution of the optically dense CMP slurries, discontinuous batch sampling of the slurry, or have insufficient sensitivity to detect small changes in the particle size distribution over the critical size range of 0.5 to 3.0 microns. 
     The need to dilute CMP slurries for particle size measurements creates large amounts of waste that cannot be reinjected back into the CMP slurry. According to the data of Bare and Lemke: “Monitoring slurry stability to reduce process variability”, Micro. Vol. 15, No. 8, pp. 53-63 (1997), oxide slurries typically have 2×10 5 /cm 3  particles greater than one micron, and metal slurries typically have 7×10 8 /cm 3  particles greater than one micron. This data was obtained using a Particle Measurement Systems LiQuilaz SO5 particle size detector, which is specified for a maximum particle concentration of 12,000/cm 3  to keep coincidence errors less than ten percent. The SO5 detector is typical of commercially available single particle light scattering devices. Thus, a minimum dilution factor of 17 is required to reduce coincidence errors for oxide slurries, and a minimum dilution factor of 58,350 is required for metal slurries. These dilution factors represent significant amounts of process slurry waste, and the dilution itself is suspected of altering the size distribution through agglomeration. 
     U.S. Pat. No. 5,710,069 to Farkas et al. discusses an optical particle counter that detects only one particle at a time in CMP slurries. The single particle must flow through a sample volume consisting of the intersection of a light beam and a detector field of view. The &#39;069 patent does not discuss the difficulty in requiring the light beam to penetrate the slurry towards the measurement area (sample volume), nor in achieving detection of one particle at a time in slurries which typically contain of 10 13 -10 14  particles per cm 3 . The idea of being able to measure only one particle at a time is unsupported by any calculations, numerical arguments, or design details. It is unclear whether the &#39;069 patent uses Mie scattering calculations or empirical correlations to calculate a particle size distribution based upon the number of single particles that are counted. The technique of “photocorrelation” is said not to work, but no description is provided of a technique that does work. U.S. Pat. No. 5,616,457 to Garcia-Rubio teaches an apparatus for detecting the presence of a microorganism in a sample of liquid. A Twomey linear inversion with a smoothing constraint is used to calculate a particle size distribution for the organism. A standard commercial spectrophotometer having a one cm cell path length is used to perform the measurements. Additional detail regarding the Twomey linear inversion can be found in Twomey, “Comparison of constrained linear inversion and an iterative nonlinear algorithm applied to the indirect estimation of particle size distributions”, J. Comp. Phys. Vol. 18, No. 2, 188-200 (1975). The &#39;457 patent does not require dilution because it addresses solutions that are much less optically dense than CMP slurries. 
     Examples of the present state of the art in measuring particle size distribution in optically dense mixtures of submicron particles suspended in a liquid solution include two presentations at a recent American Chemical Society symposium, namely, Kourti and MacGregor, “Particle size determination using turbidimetry”, Particle Size Distribution II—Assessment and Characterization, pp. 35-63, Amer. Chem. Soc. Symposium No. 472 (1991); and Brandolin and Garcia-Rubio, “On-line partide size distribution measurements for latex reactors”, Particle Size Distribution II—Assessment and Characterization, pp. 65-85 (1991). These authors typically utilize measurements at 2-3 wavelengths in the range of 0.2-1.0 microns. Conventional sample cells on the order of 1.0 cm in thickness were apparently utilized. The limited wavelength range and conventional sample cell dimensions force significant sample dilution, which in turn results in generation of a large waste stream of diluted product. An off-line batch sampling system may also be used, but this type of system has an unacceptably slow time response. 
     There remains a need for a real-time probe for use in obtaining continuous particle size distribution measurements that do not require dilution of the CMP slurry. The probe must retrieve the particle distribution over a broad range of sizes, and be capable of consistently detecting small changes in the size distribution, while providing autonomous operation in an industrial environment. 
     SOLUTION 
     The present invention overcomes the problems that are outlined above, and advances the art by providing a real-time apparatus for continuous particle size distribution measurements of undiluted CMP slurry over a broad range of sizes, with high sensitivity to small changes in the size distribution and with autonomous operation in a industrial environment. These advantages are obtained by measuring spectral transmission through an undiluted sample of the slurry at many wavelengths over a broad wavelength range, with a novel sensor design. These spectral transmission measurements are made possible by using one or more flow through sample cells having widths as narrow as 50 microns. CMP slurries have very high optical extinction per unit length in the visible spectrum by virtue of the very high particle concentration and submicron sizes. A reasonable fraction of the incident light beam, i.e., an amount greater than approximately 5%, must penetrate the sample without being scattered, in order to obtain useful spectral transmission data. This goal is accomplished by extending the spectral transmission measurements to 2.5 microns in wavelength, which is well beyond the 1.0 micron limit used in past work, and utilizing specially constructed sample cells having a path length of 50-250 microns in thickness. A spectral wavelength range of 0.20-2.5 microns is used to retrieve the entire CMP slurry particle size distribution for the full range of CMP slurries that are currently used in semiconductor manufacturing. 
     A particle size distribution probe according to the invention is used for measuring the particle size distribution of optically dense slurries with undiluted, continuous, on-line sampling for real time process control. The probe includes a plurality of light sources, a detector system which may be comprised of a plurality of fixed grating linear detector array spectrometers, a plurality of sample cells, a three position chopper, and an optical pathway for transmitting light from the light sources through the sample cells and then to the detector system or spectrometers. A computer or microprocessor receives detector signals, and performs a particle size distribution measurement. The sample cells are specially constructed to reduce optical depth in the slurry, which permits particle size distribution measurements without dilution of the slurry. 
     Optical depth is the dimensionless extinction parameter in the exponential transmission function (Beer&#39;s law), and is defined as the product of an extinction per unit length in the slurry times a thickness of the slurry in an optical path through the sample cell. Optically dense slurry is hereby defined as a particulate polydispersion consisting of 1-30% solids by weight of submicron particles, suspended in a liquid. CMP slurries are optically dense slurries that typically exhibit an optical depth of greater than 10, at 0.5 microns wavelength in a conventional sample cell having a one centimeter path length, thus yielding a transmission of less than 0.00005. As stated above, the reduction in optical depth derives from a substantial narrowing of the conventional flow path length in the sample cell to a length ranging from 50 to 250 microns. 
     The sample cells are formed of a chemically resistant housing that retains first window and a second window in spaced relationship to provide a suitable optical depth. These windows are preferably made of a very hard, chemically resistant, artificial crystal, such as sapphire. The housing includes a tapered ramp that widens as it narrows from an inlet to the separation between the windows, and thins as it thickens from the separation to an outlet. The outlet preferably returns undiluted slurry to the day tank or main process slurry line after particle size distribution measurements have been obtained from the sample. The use of multiple sample cells yields measurements of greater accuracy by tuning the optical path length (window spacing) of each cell to a different wavelength regime. Specifically, greater accuracy measurements can be obtained by keeping the transmission, measured through the slurry, within the approximate range of 0.10-0.90. 
     A light chopper is positioned between the light source and the sample cell. The chopper contains a plurality of holes for transmitting light to the sample cell and a plurality of mirrors or solid regions means for blocking transmission of light to the sample cell. The mirrors allow measurement of the time and temperature drift of the sources, while the solid region allows measurement of the time and temperature drift of the spectrometers and their detectors. These features allow autonomous operation in an industrial environment and eliminate the need for frequent measurement of reference spectra, which would require taking the probe off-line. The computer or microprocessor preferably uses a modified Twomey/Chahine-based nonlinear iterative conversion to calculate a particle size distribution measurement from the spectral transmission measurements. A plurality of fixed grating spectrometers each having a detector array are used to assist in this calculation. An ultrasonic disrupter may be used to disrupt soft slurry agglomerations just prior to their entry into the ample cell. 
     The probe is operated continuously and in real time by diverting a portion of optically dense slurry from a main slurry line, introducing the slurry into a sample cell in undiluted form, narrowing flow of the optically dense slurry within the sample cell to reduce optical depth in the slurry, transmitting light through the slurry, detecting light transmitted through the slurry in the sample cell with production of corresponding detector signals, and calculating a particle size distribution through use of the detector signals. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 depicts a sample of a probe for use in measuring particle size distributions according to the invention; 
     FIG. 2 depicts a light chopper blade for use in the probe of FIG. 1; 
     FIG. 3 depicts a first specially constructed sample cell for use in the probe of FIG. 1; 
     FIG. 4 depicts a second specially constructed sample cell for use in the probe of FIG. 1; 
     FIG. 5 depicts a comparison between calculation data from an optical model according to the present invention and spectral transmission data obtained from a manufacturer&#39;s CMP slurry; 
     FIG. 6 depicts a manufacturer&#39;s scanning electron microscope-based particle size distribution corresponding to the spectral transmission data of FIG. 5; 
     FIG. 7 depicts a comparison between calculation data from an optical model according to the present invention and spectral transmission data obtained from a manufacturer&#39;s CMP slurry; 
     FIG. 8 depicts reported data for a particle size distribution corresponding to the spectral transmission data of FIG. 7; 
     FIG. 9 depicts the calculated spectral transmission data effects of varying a distribution size bin factor to adjust the particle size distribution data shown in FIG. 10; 
     FIG. 10 depicts the calculated concentration data effects of varying a distribution size bin; and 
     FIG. 11 depicts a schematic process diagram for use in operating the probe shown in FIG.  1 . 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     FIG. 1 is an optical system schematic of a CMP slurry particle size distribution probe  100 . A deuterium source  102  supplies ultraviolet radiation, while a quartz tungsten halogen source  104  supplies visible and infrared radiation. The light from each of sources  102  and  104  is collimated by a combination of a corresponding lens  106  and  108 , and a corresponding a mirror  110  and  112 , which provide respective collimated beams  114  and  116 . A long pass filter  118  combines the two collimated beams  114  and  116  into a single collimated beam  120 . 
     A motor-driven rotational chopper blade  122  intersects the combined collimated beam  120 , and provides three different measurements in quick succession. As shown in FIG. 2, chopper blade  122  contains three ellipsoid features, namely, hole  200 , mirror  202 , and solid, nonreflective disk  204 . Hole  200  permits transmission of light through chopper blade  122  for passage of collimated beam  120  onto pathway  124  (see FIG.  1 ). Mirror  202  allows measurement of source irradiance, which drifts with temperature and time, by reflecting light onto pathway  126 . The solid disk  204  allows measurement of the electronic offsets by preventing light from reaching the charge coupled device detector arrays within two miniature, fixed grating, linear detector array spectrometers  128  and  130 . These electronic offsets are a substantial source of error for the detector arrays if uncorrected, and the offsets drift with temperature and time. 
     Use of the mechanical chopper  122  permits real time calibration of probe  100  interspersed with actual measurement data, as facilitated by the respective optical pathways that are described below. Use of the mechanical chopper  122  also allows signal-to-noise enhancement that is associated with lock-in detection and signal processing techniques. 
     Light passing through hole  200  of chopper blade  122  travels on pathway  124  towards a long pass filter  132 , which is used as a beam splitter. For oxide CMP slurries, long wavelengths greater than about 0.55 microns pass through the long pass filter  132  onto pathway  134  while shorter wavelengths are reflected onto pathway  136 . For metal CMP slurries, the long pass filter will accomplish wavelength division at approximately 1.0 to 1.25 micron. 
     Light that is reflected from chopper blade  122  by mirror  202  travels along path  126  towards a 50/50 beam splitter  138  for splitting of the light on pathway  126  into two beams  140  and  142  of equal intensity. Beam  140  travels through an order sorting or blocking filter  144  and gathering lens  146  towards the fixed grating spectrophotometer  128 . Beam  142  travels through an order sorting or blocking filter  148  and gathering lens  150  towards the fixed grating spectrophotometer  130 . 
     The order sorting filters  144  and  148  are required because any grating will create higher orders of the fundamental wavelength. It is anticipated that the wavelength coverage of the two spectrometers  128  and  130  will be approximately be 0.20 to 0.50 microns and 0.50 to 1.0 microns respectively for oxide CMP slurries, and 0.5 to 1.0 microns and 1.25 to 2.5 microns respectively for metal CMP slurries. Spectrometers operating at wavelengths shorter than 1.0 micron will utilize Si detector arrays, and those operating at longer wavelengths will utilize InGaAs detector arrays. 
     Light passing through long pass filter  132  onto pathway  134  is directed towards a first mirror  152  for reflection through a first sample cell  154 . Light that has been transmitted through first sample cell  154  is reflected by a second mirror  156  along pathway  158  through long pass filter  160 . Long pass filter  160  is preferably identical to long pass filter  132 , and both filters may be changed to provide appropriate instrument sensitivity in the intended environment of use. Light on pathway  158  passes through long pass filter  160 , and is eventually split 50/50 by beam splitter  138  for delivery to spectrophotometers  128  and  130 . 
     Light reflected by long pass filter  132  onto pathway  136  travels through a second sample cell  162 . Light that has been transmitted through the second sample cell  162  is reflected by long pass filter  160  towards 50/50 beam splitter  138  for delivery of light to spectrophotometers  128  and  130 . The use of multiple sample cells yields measurements of greater accuracy by tuning the optical path length (window spacing) of each cell to a different wavelength regime. Tuning is accomplished by maintaining transmission through the cells in a range between about 0.10 to 0.90. 
     The spectrometers  128  and  130  are collectively referred to herein as a detector or detector group. Each spectrometer preferably includes an internal fixed grating to enhance speed of measurement and reliability, i.e.; the preferred spectrometers are not scanning spectrometers having a movable grating. The internal fixed grating is configured to place dispersed light having selected wavelengths on an internal array of conventional detector elements concealed within each spectrometer. Thus, each spectrometer is operable to detect a range of wavelengths. A computer  164  receives signals from the detector group including spectrophotometers  128  and  130 , and uses these signals to calculate a particle size distribution corresponding to the CMP slurry being measured. 
     In embodiments where the slurry is not optically dense, the sample cells  154  and  162  may be removed to provide an open pathway adapted to receive a pharmaceutical mist, such as a mist from a medical nebulizer for delivery of medication to asthmatics. The sample cells may also be replaced by an open tube or chamber. In this manner, the probe can be used to measure the particle size distribution of aerosol mists. 
     Specially Constructed Sample Cells Reduce Optical Depth 
     FIG. 3 gives a detailed assembly view of a preferred CMP slurry sample cell  162  (see FIG.  1 ), which is intended for use with optically dense slurries. Both cells  154  and  162  share the same basic features, but the depth of the cells may be selectively adjusted to accommodate the increasing transmissivity of longer wavelength radiation in cell  154  (see FIG.  1 ). 
     A housing is formed of top plate  300  and bottom plate  302 , which are each machined from a solid block of chemically resistant material such as Kel-F, polyvinyldifluoride (“PVDF”) or polyvinyldichloride (“PVDC”). Sample cell inlet line  303  is connected with an inlet port (not depicted) through which the undiluted CMP slurry from main CMP slurry line  304  enters the interior space  306  of sample cell  162 . Outlet port  308  drains the slurry from space  306  into outlet line  310 . Each of top plate  300  and bottom plate  302  are provided with an opposed pair of triangular tapered ramps, e.g., ramps  312  and  314 . These ramps are thickest at their respective tips proximate the corresponding port, e.g., tip  316  proximate outlet port  308 , and which widen and narrow towards a base remote from the port, e.g., base  318 . 
     Each of top and bottom plates  300  and  302  are respectively provided with centrally located circular apertures  320  and  322 . The interior portions of plates  300  and  302  contain a groove  324 , for receipt of corresponding elastomeric O-rings  326  and  328 . A bevel  330  receives sapphire windows  332  and  334 . A pair of opposed spacers  336  and  338  are retained against flow by corresponding retaining pins, e.g., retaining pins  340  and  342 , and fit between sapphire windows  332  and  334 . 
     The sapphire windows  332  and  334  and opposed spacers  336  and  338  define the optical viewing area available to path  136  (see FIG.  1 ). The optical viewing area preferably ranges between 50 and 250 microns in thickness between windows  332  and  334  for use with optically dense slurries. The slurry fills the space between the two sapphire windows, and the transmission path length through sample cell  162  equals the thickness of spacers  336  and  338 . The tapered ramps  312  and  314  are carefully machined into the respective plates  300  and  302  to provide a smooth transition between the input/output lines  168  and  310 , and the optical viewing area. This smooth transition prevents slurry agglomeration. Also the inside edges of the sapphire windows have been beveled, as at bevels  344  and  346  to prevent slurry accumulation and agglomeration. 
     An ultrasonic generator or disrupter  348  is optionally coupled with the sample cell input line  303  for disruption of soft slurry agglomerates. CMP slurry can contain both hard and soft agglomerates, and the soft agglomerates are believed not to scratch semiconductor wafers. The ultrasonic disrupter is used to break up the soft agglomerates before slurry enters the sample cell. 
     The slurry enters the space defined by spacers  336  and  338  and between windows  326  and  328 . Cell  162  is referred to herein as a nonvolumetric sample cell for the reason that some leakage may escape into the cavity  350  surrounding the opening  322 , e.g., through non-sealed openings at  352 ,  354 ,  356 , and  358 . This leakage, as well as the flow between windows  326  and  328 , is collected by ramp  312  and cell output line  310 . The slurry between windows  326  and  328  is exposed to light or electromagnetic radiation from pathways  134  or  136  for particle sensing and analysis by CPU  164  (see FIG.  1 ). 
     FIG. 4 depicts a second and most preferred volumetric sample cell  400  for use as an alternative to or in combination with the sample cells  162  or  154  of FIG. 3. A housing is formed of top plate  402  and bottom plate  404 , which are each machined from a solid, slightly deformable block of chemically resistant material such as TFE Teflon. Sample cell inlet line  406  is connected with an inlet port (not depicted) through which the undiluted CMP slurry from the main CMP slurry line enters the interior space  408  of sample cell  400 . Outlet port  410  drains the slurry from space  408  into outlet line  412 . Each of top plate  402  and bottom plate  404  are provided with an opposed pair of triangular tapered ramps, e.g., ramps  414  and  416 . These ramps are thickest at their respective tips proximate the corresponding port, e.g., tip  418  proximate outlet port  416 , and which widen and narrow towards a base remote from the port, e.g., base  420 . Ramp  414  contains a conical opening having a maximum volume proximate cell inlet line  406 . This volume decreases towards ramp  416  with decreasing volume in the conical opening  422  being equally compensated by increased volume in the portion of ramp  414  surrounding conical opening  422 . Conical opening terminates at tip  424  proximate a wedge  426  of increasing narrow width and steepness leading to an interior opening  428 . Ramp  416  has a similar conical opening  430  with tip  432  pointing towards ramp  414  and terminating prior to wedge  434 . 
     Each of top and bottom plates  402  and  404  are respectively provided with centrally located circular apertures  428  and  436 , which are slightly offset along the fluid flow axis. The interior portions of plates  402  and  404  each contain a first step surrounding the corresponding opening, e.g., first step  438  surrounding opening  428 , for receipt of a corresponding sapphire window. For example, a flat sapphire window  440  is received in sealing engagement against step  438 . Flat sapphire window  442  identical to window  440  is similarly received in sealing engagement against step  444 . A pair of opposed spacers  446  and  448  are retained against flow by corresponding retaining pins, e.g., retaining pins  450  and  452 , and fit between the sapphire windows  440  and  442 . Each spacer is retained within the confines of a correspondingly sized recess, e.g., as spacer  448  is retained within recess  454 . A deformable elastomeric wall  456  sealingly engages top plate  402  and bottom plate  404  to prevent leakage from sample cell  400 . The wedges  426  and  434  extend wide enough to meet the spacers  448  and  446 . The spacers each sealingly engage both windows  440  and  442 . Thus, there is no slurry leakage from the space between windows  440  and  442 , i.e., cell  400  is a volumetric cell because it does not leak into the space  458  circumscribing windows  440  and  442 .). The optical viewing area between windows  440  and  442  preferably ranges between 50 and 250 microns in thickness for use with optically dense slurries. 
     Sample cell  400  operates in a similar manner with respect to cell  162 , as shown in FIG,  3 , though there are volumetric flow differences between the two cells with respect to leakage from the space between the windows. The sapphire windows  440  and  442  together with opposed spacers  446  and  448  define the optical viewing area available to path  134  or  136  (see FIG.  1 ). The slurry fills the space between the two sapphire windows, and the transmission path length through sample cell  400  equals the thickness of spacers  446  and  448 . The tapered ramps  414  and  416  are carefully machined into the corresponding plates  402  and  404  to provide a smooth transition between the input/output lines  406  and  412  relative to the optical viewing area between windows  440  and  442 . This smooth transition prevents slurry agglomeration. 
     The various optical pathways depicted in FIG. 1 comprise a distance along which light may travel. In alternative embodiments, the pathways  114 ,  116 ,  120 ,  124 ,  126 ,  134 ,  140 ,  142 , and  158  may be constructed of optical fibers. In this alternative embodiment, mirrors  152  and  156  are not required. Long pass filters  118 ,  132 , and  160  may be replaced by 1:2 fiber optic couplers. A 1:2 fiber optic coupler may also replace the 50:50 beam splitter  138 . 
     Mie Theory 
     Measurement of light scattering as a function of angle is also a sensitive measurement technique for CMP slurry particle size distribution. A major disadvantage of this approach is that significant multiple scattering errors appear when the optical depth exceeds 0.1-0.2, where the optical depth is the product of the extinction per unit length times the sample cell thickness. This measurement technique relies upon an unambiguous definition of the scattering angle for each photon. For a doubly scattered photon, the scattering angle for each scattering event is undefined. This limitation necessitates a batch sampling mode of operation, with large amounts of dilution. 
     By comparison, the spectral transmission measurement technique can operate at optical depths as large as approximately 3.0, allowing one to sample undiluted slurry in a continuous, real time mode, with realistic sample cell dimensions. The spectral transmission measurement technique does not suffer from multiple scattering errors until the diffuse radiation field intercepted by sensor&#39;s narrow field of view (typically about 1°), becomes a significant percentage of that remaining in the direct beam. 
     Optical Model Calculations 
     Mie scattering gives a complete theoretical description of optical extinction by homogenous spheres. Although particles in all of the CMP slurries are chemically homogeneous, i.e., they are composed of a single known compound, most particles are not spherical. Even so, Mie theory has demonstrated success by modeling the optical extinction of naturally occurring, non-spherical particles, in terms of optically equivalent spheres. Furthermore, extinction is the sum of scattering over all angles plus absorption, and is not as sensitive to particle shape as is the scattering phase function (the angular scattering pattern). 
     The slurry particle size distribution (PSD) is retrieved from the spectral transmission measurements through utilization of a modified Twomey/Chahine nonlinear inversion algorithm. Equation (1) expresses the measured transmission (T) as a function of wavelength (λ) in terms of the transmission of sample cell windows (T W ), the transmission of the liquid portion of the slurry (T L ), and the transmission of the slurry particles (T P ). 
     
       
         T(λ)=T W (λ)T L (λ)T P (λ)  (1) 
       
     
     By first measuring the transmission of the sample cell filled only with the liquid portion of the slurry, then dividing that into the transmission expressed in Equation (1), one can isolate T P (λ), which is the quantity of interest. Beer&#39;s Law is then solved for the particle volume extinction coefficient (β E (λ)), as shown in Equation (2), where L is the transmission path length or sample cell width. Equation (3) represents the formula for calculating the particle volume extinction coefficient in terms of the particle radius (r), the Mie extinction efficiency (Q E ), and the PSD (N(r)), where m is the particle&#39;s complex refractive index. 
     
       
         β E (λ)=−In(T P (λ))/L  (2) 
       
     
     
       
         β E (λ)=∫πr 2 Q E (2πr/λ,m)N(r)dr  (3) 
       
     
     Equation (3) must be inverted to solve for the particle size distribution. One class of inversion algorithms is the linear inversion, which provides a less preferred model for reasons that are explained below. The less preferred inversion method transforms the measurement equation into a linear system of equations by replacing the integral with a summation and by representing the collection of equations in the matrix form given by Equation (4). In this latter equation, elements of matrix  Q  consist of πr 2 Q E . The  Q  matrix has m rows, one for each wavelength, and n columns, one for each radius; m must be greater than or equal to n. The  N  matrix is n by 1, and the elements consist of the particle size distribution. The  β  matrix is m by 1, and the elements consist of the measured spectral volume extinction coefficients. 
     
       
           Q   □R   N   R = β   80   (4) 
       
     
     Equation (4) can be formally inverted to solve for the particle size distribution, utilizing conventional inversion algorithms which constrain the solution to various conditions, such as smoothing (minimize the first or second derivative), or minimize the departure from a first guess, according to Twomey, “Comparison of constrained linear inversion and an iterative nonlinear algorithm applied to the indirect estimation of particle size distributions”, J. comp. Phys., Vol. 18, No. 2, pp. 188-200 (1975), which is hereby incorporated by reference to the same extent as though fully disclosed herein. 
     Constraints are required in all inversion algorithms because the existence of measurement error and quadrature error (replacing the integral with a sum) result in the fact that a family of particle size distributions will satisfy the measurement equation. For any inversion method, the uncertainty in the retrieved solution can be reduced by: (a) choosing a more sensitive measurement technique, (b) reducing the measurement error, (c) increasing the number of measurements, which reduces the effects of quadrature error. 
     Linear inversion techniques are computationally efficient, but they are a poor choice for the CMP slurry problem because the most popular constraint, i.e., that of smoothing, is a poor choice for slurry particle size distributions. These distributions are not necessarily smooth or continuous. Additionally, linear inversion algorithms can be unstable to an extent that produces physically unrealistic answers. 
     The CMP slurry measurement problem consists of detecting departures from the normal or specified particle size distribution, which makes a non-linear, iterative, inversion algorithm a natural choice and a more preferred model for use in practicing the invention. With the iterative approach, one can start with the normal particle size distribution as a first guess. The iterative calculations converge toward a final solution in an orderly fashion, where convergence is based upon a difference between the measured spectral extinction and that calculated from the last guess particle size distribution. Alternatively, one can start with a delta function as a first guess. Iteration is halted when this difference becomes less than some predetermined error bound. This preferred method of inverting equation (4) is based on previous work in the field of atmospheric remote sensing by Cemi, “Aircraft-based remote sensing or tropospheric profiles for meoscale studies”, Advances in Remote Sensing Retrievals, pp. 339-347 A. Deepak Publ., Hampton, Va. (1985); and Chahine, “Inverse problems in radiative transfer: Determination of atmospheric parameters”, J. Atmos. Sci., Vol. 27, pp 960-967 (1970) and Twomey (1975, referenced earlier), which are incorporated by reference herein to the same extent as though fully disclosed herein. 
     The algorithm given in Equations (5) and (6) is a preferred means of inverting the spectral transmission data to retrieve the particle size distribution. The superscripts I and I−1 refer to successive numbers of iterations. The subscripts P refer to different wavelengths, and indicate that all the measurements are utilized in adjusting the particle size distribution at a single r value. Additionally, one can improve the accuracy of the retrieval by adding conservation of mass (slurry percent solids by weight), and summing Equation (5) over all wavelengths. 
     
       
         N P   (I) (r)=[1+(r P   (I−1) −1)πr 2 Q E (2πr/λ,m)]N P   (I−1) (r)  (5) 
       
     
     
       
         r P   (I−1) =β E (λ)/[∫πr 2 Q E (2πr/λ,m)N P   (I−1) (r)dr]  (6) 
       
     
     EXAMPLE 1 
     VERIFICATION OF THE MODEL WITH EXPERIMENTAL RESULTS 
     The Mie theory optical model results were verified with the use of an Acton SP-305 spectrometer system retrofitted with a sample cell according to FIG.  3 . The sample cell was constructed to provide sapphire windows having a 40 mm diameter with the windows being held approximately 100 microns apart in a PVDF chemically resistant block. The detector module utilized one Si and one InGaAs photodiode to cover the broad 0.20-2.5 micron spectral range. 
     FIG. 5 shows a comparison between optical model predictions and experimental data for Solution Technology Klebosol 30N50 oxide slurry, which consists of SiO 2  particles immersed in a weak NH 4 OH solution with a pH of 10.9. The product as tested contained 30% solids by weight, which is the basic product produced by Solution Technology. The product it is typically diluted to 18% solids by weight just prior to use in CMP wafer planarization. Thus, the tested product was even more optically dense than an actual CMP slurry using the product. As an input, the optical model utilized a particle size distribution provided by Solution Technology, shown in FIG. 6, which the manufacturer purports to have been measured with an electron microscope. The comparison shown in FIG. 5 demonstrates a remarkably good agreement between measured transmission data and optical model predictions. 
     Possible reasons for the observed small differences between the two curves (theoretical and actual results) of FIG. 5 include: (1) departure of the optical behavior of this unusually dense particulate suspension from that predicted by Mie theory, (2) departures of the sample particle size distribution from the typical particle size distribution provided by the slurry manufacturer, (3) errors in the particle size distribution measurements provided by the slurry manufacturer, due to the poor sample statistics provided by analysis of electron microscope imagery, (4) unexpected slurry liquid absorption bands, and (5) errors in the experimental spectral transmission measurement technique. The combined effects of these error sources are minor in this example. Klebosol 30N50 is described by the manufacturer as consisting of individual spheres, which are grown from seed in a saturated SiO 2  solution. As such, one would expect accurate predictions from Mie theory. 
     The experimental data shown in FIG. 5 was truncated at a transmission value of 0.030, below which the measured data indicated a leveling off and then an increase in transmission as wavelength decreased and optical depth increased. Such a result is unphysical, and indicates that the multiply scattered radiation, which is scattered in a near forward direction, has become comparable to or greater than the transmitted radiation. This result is expected to occur at some point with increasing optical depth and with a finite instrument field of view. The detector system used the SP-305 spectrometer, which is designed to have a nominal 1° field of view, and this scattering effect was predicted to be observed at a transmission value of approximately 0.050, i.e., an optical depth of 3. 
     EXAMPLE 2 
     VERIFICATION OF THE MODEL WITH EXPERIMENTAL RESULTS 
     FIG. 7 shows optical model predictions and experimental data for Cabot SC-1 oxide slurry, which consists of SiO 2  particles immersed in a weak KOH solution having a pH of 10.3. This sample was diluted to 12% solids by weight, which is the concentration at which it is used for CMP wafer planarization. The particle size distribution used as input to the optical model is plotted in FIG. 8, and represents a modified version of the Cabot SC-1 PSD measured by Bare and Lemke: “Monitoring slurry stability to reduce process variability”, Micro. Vol. 15, No. 8, pp. 53-63 (1997) (the BH97 particle size distribution) using an Horiba LA-910 light scattering particle size distribution probe. A modification to the BH97 particle size distribution consisted of multiplying each particle size distribution size bin by 0.56. The 0.56 factor was chosen to obtain good fit to the measured transmission data. 
     FIGS. 9 and 10 show how changes in this distribution size bin factor affect the transmission spectrum, and serve as another indication of the sensitivity of the spectral transmission measurement technique. Cabot SC-1 is a fumed silica product produced by combining reactant gases in a flame, and is known to consist of chains of tiny spheres fused together. Hence, the diameter of such a particle chain is not well defined. The extinction cannot be accurately modeled by Mie theory, and one should expect differences in the particle size distribution obtained by different measurement techniques. Given this uncertainty, a factor of 0.56 is reasonable. 
     In FIG. 9, the measured spectrum was truncated at a transmission value of 0.079, due to apparent errors introduced by multiple scattering. This higher value of transmission cut-off for SC-1 versus 30N50 (0.079 versus 0.030), is consistent with the larger particles present in the former slurry, which is known to produce more forward scattering. It is also consistent with more forward scattering produced by non-spherical versus spherical particles. 
     FIG. 11 depicts a schematic process diagram of process P 1100  for use in operating the probe shown in FIG.  1 . In step P 1102 , optically dense CMP slurry is diverted from the main slurry line to the sample cells  154  and  162 . In step P 1104 ; the flow of slurry is narrowed through the sample cells to provide an optical depth that permits meaningful spectral transmission data. Light is transmitted through the narrowed slurry along pathways  134  and  136  in step P 1106 . Pathways  140  and  142  deliver this light to the spectrophotometers  128  and  130  in step P 1108 . The spectrophotometers produce signals representative of the detected light and particles in the cells  154  and  162 . These signals are transmitted to CPU  164  for processing according to the modified Twomey/Chahine technique according to equations 1-6. 
     At the conclusion of step P 1108 , step P 1110  includes the detection of light transmitted along pathway  126  to spectrophotometers  128  and  130  due to the rotation of chopper blade  122  and the reflective action of mirror  202 . The detector counts are transmitted to CPU  164  for registration of source lighting conditions without particle scattering from sample cells  154  and  162 . 
     In step P 1112 , the detector background count is measured with chopper blade  122  positioned to place solid disk  204  in path  120  for blocking the transmission of light along either path  126  or  134 . Spectrophotometers  128  and  130  again produce signals corresponding to detected light, and these signals are transmitted to CPU  164  which interprets the signals as background count information that can be subtracted from total counts received from light traveling along pathways  126  or  134 . 
     In step P 1114 , CPU  164  uses stored detector signals from steps P 1108 , P 1110 , and P 1112  to calculate, display and store a particle size distribution, as discussed above. Steps P 1106 - 1114  are continuously repeated to perform real time measurements of the particle size distribution in the CMP slurry. 
     Those skilled in the art will understand that the preferred embodiments described above may be subjected to apparent modifications without departing from the true scope and spirit of the invention. The inventors, accordingly, hereby state their intention to rely upon the Doctrine of Equivalents, in order to protect their full rights in the invention.