A 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 50-2000 microns thickness, and miniature, fixed grating, linear detector array spectrometers. At wavelengths greater than one 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. In other embodiments, the invention provides a quality control and/or particle size measuring system for cmp slurries using transmission data through an as-used cmp slurry flow. The process of the invention detects transmission through the flow, at select wavelengths, and determines changes in the logarithmic slope of transmission versus wavelength to detect acceptable or unacceptable cmp slurries. The process can further determine cmp slurry particle size through empirical extinction data stored in memory.
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1. A quality control process for detecting physical and/or chemical changes in a cmp slurry, comprising the steps of:
transmitting radiation through a flow of an undiluted optically dense slurry as used in a chemical mechanical planarization (cmp) process, the radiation having one or more wavelengths;
determining transmission of the transmitted radiation at each of the said one or more wavelengths; and
monitoring transmission, over time, to detect physical and/or chemical changes of the cmp slurry.
26. A system for evaluating chemical mechanical planarization (cmp) slurry quality in a process, comprising:
a light source generating a beam of electromagnetic radiation for transmission through a flow of an undiluted optically dense slurry as used in a cmp process;
a spectral discriminator for isolating at least two wavelength bands of the radiation prior to transmission of the radiation through the flow;
a detector for detecting radiation transmitted through the flow; and
a processor for evaluating transmission of the wavelength bands through the flow to determine physical and/or chemical changes of the cmp slurry.
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(a) detecting changes in the particle size distribution of the cmp slurry;
(b) storing a plurality of reference transmissions, each reference transmission corresponding to a particular cmp slurry flow and particle distribution;and
(c) selecting one reference transmission and comparing the transmission to the selected reference transmission.
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This application is a continuation-in-part of commonly-owned and U.S. application Ser. No. 09/069,682, filed on Apr. 29, 1998,
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 TP(λ), which is the quantity of interest. Beer's Law is then solved for the particle volume extinction coefficient (βE(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 (QE), and the PSD (N(r)), where m is the particle's complex refractive index.
βE(λ)=−ln(TP(λ))/L (2)
βE(λ)=∫πr2QE(2πr/λ)N(r)dr (3)
Equation (3) is 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 πr2QE. 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·RNR=βλ (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 partide 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 particles 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 Cerni, 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 partide 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.
NP(I)(r)=[1+(rP(I-1)−1)πr2QE(2πr/λ,m)]NP(I-1)(r) (5)
rP(I-1)=βE(λ)/[∫πr2QE(2πr/λ,m)NP(I-1)(r)dr] (6)
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.
Possible reasons for the observed small differences between the two curves (theoretical and actual results) of
The experimental data shown in
In
At the conclusion of step P1108, step P1110 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 P1112, 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 P1114, CPU 164 uses stored detector signals from steps P1108, P1110, and P1112 to calculate, display and store a particle size distribution, as discussed above. Steps P1106-1114 are continuously repeated to perform real time measurements of the particle size distribution in the CMP slurry.
Source 1214 generates radiation 1212. By way of example, source 1214 can be a quartz tungsten halogen source, generating infrared and/or visible radiation 1212, or a deuterium source, generating ultraviolet radiation. Preferably, source 1214 is “broadband” so as to provide multiple wavelength bands which generate radiation 1212. However, multiple sources 1214a, 1214b . . . 1214n can be used, selectively, to generate desired radiation wavelengths 1212a, as required. For example, to generate ultraviolet light, source 1214b can represent a deuterium source; while to generate infrared or visible light wavelengths, source 1214a can represent a tungsten lamp. To switch between sources 1214, an arrangement such as shown in
In the preferred embodiment, filters 1216 spectrally discriminate source radiation wavelengths 1212a emitted from source 1214 such that only selected wavelengths 1214b pass through filters 1216. Multiple filters 1216a, 1216b can be used to alternatively pass and select different wavebands to illuminate sample 1208. By way of example, filters 1216 are shown arranged on filter wheel 1218 which is rotated about axis 1219 by motor controller 1218a, selectively, to alternatively position filters 1216a, 1216b in the path of radiation 1212a. Filter wheel 1218, controller 1218a, and filters 1216 are known those skilled in the art of optics. In this manner, radiation 1212b of desired waveband can be selected by a user of system 1200. Filters 1216 are moved to block radiation 1212a as needed to select the appropriate wavelength band as emitted from source(s) 1214.
Although two filters 1215 are shown, those skilled in the art should appreciate that one or more filters can be used in system 1200 to achieve the objectives herein.
Radiation 1212c transmitted through sample cell 1208 corresponds to radiation also transmitted through CMP slurry flow 1210. A detector 1220 detects radiation 1212c and generates signals indicative of transmission of radiation 1212b through sample and flow 1208, 1210. These signals are interpreted by processor 1220, e.g., a computer, to determine a transmission value as a function of wavelength (or waveband). By way of example, if source 1214 generates radiation 1212a that is filtered by filter 1216a to 2.5 microns +/−0.2 micron, then detector 1220a can correspond to a near infrared detector, e.g., InGaAs, to detect transmission of radiation 1212c through sample and flow 1208, 1210. Transmission is determined by computer 1220 and associated with “2.5 microns.” At times, multiple detectors 1220a, 1220b . . . 1220n are required to detect all the wavelengths of interest from sources 1214a, 1214b . . . 1214n. Detectors 1220 can be inserted within system 1200, as needed, to measure appropriate wavelengths, or an appropriate optical technique such as illustrated in
Different slurry supplies 1204a, 1204b . . . 1204m can also be coupled to system 1200 in a manufacturing process; and each CMP slurry 1202a, 1202b . . . 1202m can then be coupled to sample cell 1208 as required through appropriate flow pathways 1206. Alternative sample cells 1208a, 1208b . . . 1208q can be used in system 1200, as needed, to acquire appropriate optical path lengths corresponding to enhanced detection of radiation 1212b through sample cell and flow 1208, 1210. As before, sample cells 1208 can be switched into system 1200 manually, or mechanically, or an optical configuration such as
CMP slurry from flow 1210 leaves sample cell 1208 along slurry line 1222, which couples to semiconductor manufacturing process 1224. When system 1200 detects bad CMP slurry, as discussed herein (e.g., slurry with a particle distribution extending beyond a desirable range), then processor 1220 sends a warning signal to warning device 1226, e.g., a light, audible alarm or other device (e.g., a computer) coupled or proximate to manufacturing process 1224. In this manner, manufacturing process 1224 is informed, in real time, of CMP slurry quality control issues which can damage and destroy semiconductor surfaces used in integrated circuit devices.
Transmission values determined by system 1200 are preferably plotted with respect to wavelength, such as illustrated in FIG. 12A. Specifically, the natural log of transmission values (ln(t), axis 1240) is plotted against wavelength (λ, axis 1242), as shown. Accordingly, the slop of a line C which approximates ln(transmission(λ)) at time to may be determined, such as line C(t0). At a later time t, line C may for example be plotted as C(t0+t), indicating a change in the slope of ln(transmission(λ)). When the slope of line C changes by a sufficient amount, represented by angle β, determined empirically or by another measure, then the particle distribution sizes within the CMP slurry have changed and system 1200 sends a warning to manufacturing process 1224.
The function of source(s) 1214 and filter(s) 1216 can be replaced by laser diodes, if desired. Alternatively, filter(s) 1216 can be replaced by appropriate dispersive elements (e.g., gratings) located with detector(s) 1220, such as discussed in FIG. 1.
Processor 1220a preferably includes solid state memory to store one or more “reference transmission” data corresponding to a preferred transmission vs. wavelength curve, or ln(t) vs. λ data, for a known CMP slurry with acceptable particle size distribution. The reference transmission data further includes an acceptable variance of that data from optimal where CMP slurry is deemed “acceptable.” Accordingly, in this embodiment, system 1200 evaluates transmission data from flow 1210 in real time and compares that data to reference transmission data in memory 1220a, and generates a warning when the real time data exceeds the allowed variance, indicating an “unacceptable” CMP slurry. Memory 1220a can further include an array of curves or ln(t) vs. λ data corresponding to each CMP slurry 1202a, 1202b . . . 1202m, as appropriate, such that system 1200 can operate with multiple CMP slurries used in manufacturing process 1224. A user can select which reference transmission data to use at any one time through a user interface (e.g., a keyboard) at processor 1220.
Measuring particle size distributions within CMP slurry flow 1210 is also a feature of the invention. Typically, these distributions are centered about a particular particle size, e.g., 0.06 micron, as shown in FIG. 6. Other suitable center particle sizes in accord with the invention are between about 0.3 and 1.0 micron, though particle size distributions centered about a value between 0.1 and 0.3 micron, or 1.0 and 10 microns, are also envisioned and within the scope of the invention. Typically, the diameter of flow 1210 is approximately 100 microns for near-infrared wavelengths. Smaller flow diameters, i.e., down to 50 microns or smaller, are also envisioned, as are larger flow diameters up to approximately 2000 microns, all within the scope of the invention.
Mie theory can be used to determine particle size distributions in CMP slurry flow 1210. Alternatively, an empirical curve of extinction efficiency QE versus particle size diameter D is developed and stored in memory 1220a; and that empirical curve is compared to data obtained by system 1200 in real time. The particle size function preferably corresponds to πD/λ, where λ corresponds to the waveband of measurement.
The invention thus attains the objects set forth above, among those apparent from the preceding description. Since certain changes may be made in the above methods and systems without departing from the scope of the invention, it is intended that all matter contained in the above description or shown in the accompanying drawing be interpreted as illustrative and not in a limiting sense. It is also to be understood that the following claims are to cover all generic and specific features of the invention described herein, and all statements of the scope of the invention which, as a matter of language, might be said to fall there between.
Cerni, Todd A., Waisanen, Scott, Knowlton, Dennis J.
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