Patent Publication Number: US-8119991-B2

Title: Method and apparatus for accurate calibration of VUV reflectometer

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a divisional of U.S. patent application Ser. No. 10/930,339, filed Aug. 31, 2004, which claims priority to Provisional Patent Application No. 60/600,599 filed Aug. 11, 2004; the disclosure of which is expressly incorporated herein by reference. 
    
    
     BACKGROUND OF THE INVENTION 
     The present invention relates to the field of optical metrology. More specifically, it provides a method by which broad-band vacuum ultraviolet (VUV) reflectance data may be accurately calibrated. Additionally, it also provides a method by which highly accurate thin film measurements may be performed. 
     Optical reflectometry techniques have long been employed in process control applications in the semiconductor manufacturing industry due to their non-contact, non-destructive and generally high-throughput nature. The vast majority of these tools operate in some portion of the spectral region spanning the deep ultraviolet and near-infrared wavelengths (DUV-NIR generally 200-1000 nm). The push towards thinner layers and the introduction of complicated new materials have challenged the sensitivity of such instrumentation. As a result, this has necessitated an effort to develop optical reflectometry equipment utilizing shorter wavelengths (below 200 nm), where greater sensitivity to subtle changes in material properties may be realized. One approach to performing such measurements is described in U.S. application Ser. No. 10/668,642, filed on Sep. 23, 2003, which discloses a system and method for a vacuum ultraviolet (VUV) reflectometer, the disclosure of which is incorporated herein by reference. 
     To obtain meaningful quantitative results from reflectometry data it is desirable to normalize or calibrate measured reflectance values in order to generate absolute reflectance spectra. At longer wavelengths in the DUV-NIR region this has traditionally been accomplished using a variety of techniques involving complicated optical arrangements that incorporate moving mirrors. Examples of such methods are provided in U.S. Pat. No. 4,368,983 (and references incorporated therein) which describes an apparatus and method to measure the absolute reflectivity of a sample using a multiple pass reflectometer. 
     While such methods offer a means of obtaining calibrated reflectance data, they generally suffer from the fact that they are time-consuming, involve considerable mechanical motion and can not easily be integrated into systems suitable for use in semiconductor manufacturing environments. Furthermore, many of these methods were designed for use in single wavelength reflectometers wherein a single wavelength detector is used in combination with a wavelength selecting pre-monochromator. 
     Ideally, it would be desirable to provide a technique by which broad-band reflectometry data could be simultaneously calibrated quickly and simply and in a manner that would lend itself suitable for use in semiconductor manufacturing environments. 
     One calibration approach is presented in U.S. Pat. No. RE 34,783 wherein a method is described that involves measuring the reflectance from a calibration sample whose absolute reflectance is well known, dividing the measured value by the absolute value to obtain a system efficiency coefficient and then, without changing the illumination or optics, measuring the reflectance of an unknown material and applying the coefficient to the measured value to obtain its absolute value. 
     In practice, single crystal silicon wafers are commonly employed as calibration samples since they are readily available, controllably manufactured and their optical properties in the DUV-NIR region have been well characterized. This approach works reasonably well at wavelengths above ˜250 nm where the reflectance of single crystal silicon is both stable and predictable. 
     At shorter wavelengths (&lt;250 nm) the reflectance of single crystal silicon wafers is neither stable nor predictable. Subtle variations in the thickness of the naturally (or “native”) formed silicon dioxide layer present on the wafer can significantly influence the measured reflectance. Additionally, ultra-thin layers of moisture and/or hydrocarbons are known to adsorb onto the surface further modifying the sample reflectance in this spectral region. As a result, it is generally not advisable to regard the reflectance of single crystal silicon wafers at wavelengths &lt;250 nm as a “known” property. 
     One approach to overcoming this problem is presented in U.S. Pat. No. 5,798,837, which describes an optical measurement system that includes a reference ellipsometer and at least one non-contact optical measurement device, such as a reflectometer. The reference ellipsometer is used to determine an optical property of the calibration sample. The optical measurement device is then calibrated by comparing the measured optical property from the optical measurement device to the determined optical property from the reference ellipsometer. 
     Integration of a separate reference ellipsometer into an optical measurement system in order to calibrate the first optical measurement device is both complicated and expensive. Furthermore, the reference ellipsometer itself must be properly aligned and calibrated if it is to yield accurate results. 
     It follows that it would be highly desirable to develop a means of quickly and accurately calibrating broad-band data from an optical reflectometer operating at wavelengths &lt;250 nm without the complication and expense associated with incorporating a second reference instrument into the system. 
     Additionally, it would be advantageous if this method specifically enabled the accurate calibration of reflectometry data at wavelengths encompassing the VUV spectral region, where small uncertainties in the properties of third party certified standards can result in substantial errors. It would be further desirable if this method was capable of independently determining the properties of such standards so as to reduce or altogether remove the need for their procurement and maintenance. 
     In addition to providing a technique to enable accurate calibration of reflectometry tools, it is desirable to provide a technique by which highly accurate thin film measurements may be performed. Optical reflectance measurements are used in a wide range of thin film applications. Ordinarily the absolute reflectance of a sample is recorded and subsequently analyzed using mathematical models in order to determine an assortment of physical properties. 
     Typically, the analysis is deemed complete when a quantitative indicator (generally referred to as the “goodness of fit” parameter) attains a specific value. Unfortunately, there are limits to the measurement accuracy that can be attained using conventional “goodness of fit” parameters. Hence, it follows that it would be desirable to develop a more sensitive measure of “goodness of fit” in order that higher levels of accuracy in thin film measurement may be obtained. 
     SUMMARY OF THE INVENTION 
     One embodiment of the current invention provides a means by which VUV reflectance data may be quickly and accurately calibrated. In one embodiment, the method enables simultaneous calibration of reflectance data covering a broad range of wavelengths. Additionally, the technique operates in a manner well suited for use in semiconductor manufacturing environments. 
     The method may be self-contained in that it may not require use of a second referencing instrument. It may provide a method by which calibration results may be autonomously verified such that use of third party certified standards will be reduced and/or altogether eliminated. 
     In one embodiment, the techniques include utilizing a standard (or “calibration”) sample that allows for calibration in the wavelengths of interest even when the standard sample may exhibit significant reflectance variations at those wavelengths for subtle variations in the properties of the standard sample. Thus, calibration may be achieved even in cases where traditionally significant calibration error in regions of wavelengths that a user is interested in would be expected to be encountered. In this regard the technique takes advantage of the presence of a certain amount of calibration error that may be referred to as a calibration error function. 
     In another embodiment, the calibration process may include a technique that utilizes a first sample and a second sample. The first sample may include significant reflectance variation in the spectral region of interest as a function of sample property variations and the second sample may have a relatively featureless reflectance spectrum over the same spectral region. The first sample may be considered a standard or calibration sample and the second sample may be considered a reference sample. In one embodiment the spectral region may include the VUV spectral region. 
     In another embodiment a calibration technique is provided in which a standard or calibration sample may have relatively unknown properties with the exception that it may be assumed to have a significant calibration error function in the spectral regions of interest. Thus, the exact properties of the standard sample need not be known if it can be assumed that the standard sample exhibits sharp changes in reflectance for changes in the sample property. 
     In another embodiment of the current invention a technique by which highly accurate thin film measurements may be performed is provided. The method may provide mathematical fitting algorithms with a more sensitive “goodness of fit” indicator that is less susceptible to noise present in the raw data. The fitting routine may be a spectrally driven fitting routine rather than relying solely on an amplitude driven routine (which typically incorporates difference calculations). In such an embodiment, the measurements may be obtained by utilizing the presence of sharp, narrow spectral features. 
     In one embodiment, the measurements are obtained by a spectrally driven fitting routine that utilizes a ratio of an expected reflectance spectrum of the sample being measured to the actual reflectance spectrum of the sample being measured. Thus, rather than being based upon a difference between the expected and actual values, the techniques provided herein utilize a ratio of the values. The techniques are particularly useful in spectral regions that contain sharp spectral features, for example the sharp features that are often exhibited in the VUV region for thin film samples. Thus, a data convergent technique is provided that may beneficially utilize an absorption edge effect of the material is disclosed. In this manner sharp spectral features, for example resulting from either interference or absorption effects are advantageously utilized to better determine a data minimum that is indicative of an actual measurement value. 
     In another embodiment, the data reduction techniques may utilize a two step approach. In such an embodiment a low resolution step such as an amplitude driven fitting routine may be used to first provide a “coarse” measurement. Then a high resolution step such as a spectrally-driven fitting routine that advantageously utilizes the presence of sharp spectral features may be used to provide a “fine” measurement. In one embodiment, the low resolution step may obtain a rough measurement value by using a difference based technique as in a “Chi-square” merit function. The high resolution step may be a spectrally driven step that includes a ratio based technique in the region of interest initially identified by the low resolution technique. 
     A further understanding of the nature of the advantages of the present invention may be realized following review of the following descriptions and associated drawings. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  illustrates a prior art calibration and measurement flowchart for a reflectometer. 
         FIG. 2  illustrates a prior art detailed calibration and measurement flowchart for a reflectometer. 
         FIG. 3  illustrates reflectance spectra from ultra-thin SiO2/Si samples. 
         FIG. 4  illustrates calibration error spectra for a 20 Å SiO2/Si sample generated for a series of assumed thicknesses. 
         FIG. 5  illustrates an exemplary calibration and measurement flowchart according to one embodiment of the present invention. 
         FIG. 6  illustrates calibration error spectra for a 10000 Å SiO2/Si sample generated for a series of assumed thicknesses. 
         FIG. 7  illustrates a reflectance spectra for a broad-band VUV mirror (#1200) manufactured by Acton Research Corp. 
         FIG. 8  illustrates a product of a reference sample reflectance spectrum and a calibration error function for a 10000 Å SiO2/Si sample obtained from the measurement of an arbitrary reference sample. 
         FIG. 9  illustrates a derivative of a calibration error function for a 10000 Å SiO2/Si sample generated for an assumed thickness of 10010 Å. 
         FIG. 10  illustrates a sensitivity plot calculated using a calibration error function integral for a 10000 Å SiO2/Si standard sample. 
         FIG. 11  illustrates a reflectance of a reference sample used in a calibration routine. 
         FIG. 12  illustrates an exemplary detailed calibration and measurement flowchart according to one embodiment of the present invention. 
         FIG. 12A  illustrates an exemplary reflectometer system which may utilize the calibration concepts of the present invention. 
         FIG. 13  illustrates the sensitivity plot calculated using a standard prior art merit function for a 10000 Å SiO2/Si sample. 
         FIG. 14  illustrates an expanded sensitivity plot calculated using a standard prior art merit function for a 10000 Å SiO2/Si sample in the presence of 1% noise on the measured reflectance data. 
         FIG. 15  illustrates an exemplary detailed measurement flowchart according to one embodiment of the present invention. 
         FIG. 16  illustrates an expanded sensitivity plot calculated using an MEF integral for a 10000 Å SiO2/Si sample in the presence of 1% noise on the measured reflectance data. 
         FIG. 17  illustrates a sensitivity plot calculated using an MEF integral for a 10000 Å SiO2/Si sample. 
         FIG. 18  illustrates a comparison of sensitivity plots calculated using an MEF integral and a standard prior art merit function for a 100 Å SiO2/Si sample. 
         FIG. 19  illustrates an expanded sensitivity plot calculated using an MEF integral for a 100 Å SiO2/Si sample in the presence of 1% noise on the measured reflectance data. 
         FIG. 20  illustrates an expanded sensitivity plot calculated using standard prior art merit function for a 100 Å SiO2/Si sample in the presence of 1% noise on the measured reflectance data. 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     The manner in which standard samples are typically used to calibrate reflectometers is generally presented in the flowchart  102  of  FIG. 1 . As is evident in the figure the first step  104  in the calibration process is to assume knowledge of the reflectance properties of the standard sample. With this information in hand, the intensity of light reflected from the sample as a function of wavelength can be recorded and the reflectometer calibrated in step  106 . Subsequently, the reflectance of unknown samples may then be absolutely determined with the device in step  108 . 
     A more detailed description of this calibration procedure is outlined in the flowchart  202  of  FIG. 2  wherein the mathematical relationships involved in calculating the absolute reflectance of an unknown sample are presented.  FIG. 2  illustrates the flowchart  202  for the calibration procedure. In a first step  204 , knowledge of reflectance properties of a standard sample is assumed. Then in step  206  the intensity from the standard sample is recorded. Next the source intensity profile is calculated in step  208  using knowledge of the assumed reflectance properties of the standard sample. In step  210 , the intensity from an unknown sample is recorded. The reflectance of the unknown sample may then be calculated as shown in step  212 . The reflectance of the unknown sample may then be expressed according to the equation of step  214 . From examination of the final step of the process it is evident that the measured reflectance of an unknown sample is directly proportional to the assumed reflectance of the calibration sample. Hence, if the assumed reflectance is inaccurate it follows that the measured reflectance will also be inaccurate. 
     Single crystal silicon wafers have long been used as calibration standards for reflectometers operating in the DUV-NIR. They have proved a sensible choice as they are ubiquitous, controllably manufactured and optically well characterized in this spectral region. In practice the assumed reflectance properties for the silicon wafer are calculated using the Fresnel Equations and an assumed knowledge of the optical properties and thickness of the native silicon dioxide surface layer and the optical properties of the silicon itself. 
     When employed for the calibration of reflectometers operating at wavelengths longer than about 250 nm silicon wafers work well since the underlying assumptions regarding their physical properties are relatively insensitive to error in this wavelength region. In other words, errors in the assumed thickness of the native oxide layer on the surface of the wafer do not significantly influence the expected reflectance of the sample and hence negatively impact the accuracy of the calibration process. 
     This point is further illustrated in  FIG. 3  wherein calculated reflectance spectra for a series of SiO 2 /Si samples with SiO 2  thicknesses ranging from 10 to 30 Å are presented. For example, reflectance spectrum  302  illustrates a Si sample having a 10 Å SiO 2  layer while reflectance spectrum  304  illustrates a Si sample having a 30 Å SiO 2  layer. While differences between the spectra are reasonably small above 250 nm, they become quite significant at shorter wavelengths. Hence, if the thickness of the native oxide layer is assumed to be 10 Å and is actually 20 Å then a considerable calibration error will be introduced at wavelengths lower than 250 nm. 
       FIG. 4  better illustrates the effect of such errors. Plotted in this figure are a series of curves corresponding to the ratios of pairs of reflectance spectra. The first spectrum in each pair corresponds to that expected from a SiO 2 /Si sample with an “assumed” native oxide thickness (ranging from 10 to 30 Å), while the second spectrum in each pair corresponds to a SiO 2 /Si sample with an “actual” native oxide thickness of 20 Å. Thus, curve  302  of  FIG. 4  corresponds to the ratio of the reflectance spectrum for an assumed native oxide thickness of 10 Å to the reflectance spectrum of a native oxide thickness of 20 Å. Similarly curve  304  of  FIG. 4  corresponds to the ratio of the reflectance spectrum for an assumed native oxide thickness of 15 Å to the reflectance spectrum of a native oxide thickness of 20 Å. In a similar fashion curves  306 ,  308  and  310  illustrate the ratio of an assumed native oxide thickness of 20, 25, and 30 Å (respectively) to the reflectance spectrum of a native oxide thickness of 20 Å. In this sense the ratio may be considered essentially as a measure of calibration error, herein referred to as the calibration error function (CEF). The closer CEF is to unity, the lower the error associated with the calibration. In the case where the “assumed” thickness is equal to the “actual” thickness of 20 Å as shown by curve  306 , the CEF is equal to one at all wavelengths and the calibration is perfectly accurate. In the situation where the “assumed” thickness is 25 Å (an error of just 5 Å) the CEF attains a value of greater than 1.3 at short wavelengths, while maintaining a value of less than 1.002 at wavelengths above 250 nm. This represents an error of greater than 30% in the VUV and less than ˜0.2% at longer wavelengths. Hence, while silicon wafers may be readily used to calibrate reflectometers at wavelengths greater than 250 nm, they do not provide a practical means of accurately calibrating reflectometers in the VUV. 
     An alternate approach to this problem is afforded by an embodiment of the current invention. The flowchart  502  depicted in  FIG. 5  provides a general overview of the steps involved in the process. As is evident from the figure the technique requires the use of two samples, a standard and a reference. The standard sample is chosen such that it is expected to exhibit a significant and spectrally sharp CEF over some spectral region. The reference sample, on the other hand, is selected such that it is expected to exhibit a relatively featureless reflectance spectrum over the same spectral region. 
     The first two steps  504  and  506  of the process are in effect identical to those described in the conventional method of  FIG. 1 . Namely, knowledge of the properties of the standard sample is assumed, following which the intensity of light reflected from the sample as a function of wavelength is recorded and used to calibrate the reflectometer. At this point the calibrated reflectometer is used to measure a reference sample and determine its reflectance as described in step  508 . Once this has been accomplished, in step  510  the “actual” properties of the standard sample are determined through evaluation of the measured reflectance properties of the reference sample and the CEF. With knowledge of the “actual” properties of the standard sample in hand, the reflectometer can then be accurately re-calibrated in step  512 , thereby removing imprecision resulting from errors associated with the “assumed” properties of the standard sample in the second step of the process. Once the instrument has been re-calibrated the absolute reflectance of unknown samples may be accurately determined as shown in step  514 . 
     In one embodiment, the calibration techniques are dependent on the choice of the standard sample. As discussed earlier, it is desirable for the standard to exhibit a significant and spectrally sharp CEF spectrum over some spectral region of the reflectometer. To a great degree this capacity will be dictated by the optical nature of the sample. Specifically, the CEF signal generated by a standard sample is expected to increase in the vicinity of an optical absorption edge corresponding to one or more of the materials comprising it. In this spectral region small changes in the properties of the sample can generate significant changes in the reflected signal and hence a large CEF contribution. It follows that it is thus desirable that the reflectometer has sufficient spectral resolution to ensure sharp features of the CEF signal are detected and accounted for. 
     In a preferred embodiment of the invention, designed to calibrate a VUV reflectometer, the standard sample is comprised of a relatively thick (˜10000 Å) layer of SiO 2  deposited on a silicon substrate.  FIG. 6  presents a CEF plot for such a standard, wherein the ratios of three pairs of reflectance spectra are plotted for “assumed” SiO 2  thicknesses of 9990, 10000 and 10010 Å. As is evident from the graph, the spectra  602  corresponding to the 9990 Å assumption and the spectra  604  corresponding to the 10010 Å assumption both exhibit substantial and spectrally sharp CEF features (in the case where the “assumed” thickness is equal to the “actual” thickness of 10000 Å the CEF is equal to one at all wavelengths). In fact, the data in the figure indicates that the 10 Å error (representing just 1 part in 1000) would introduce an inaccuracy of greater than 200% in the VUV reflectance results. 
     In contrast to the CEF plot for the 20 Å SiO 2 /Si sample presented in  FIG. 4 , wherein the CEF values at wavelengths longer than 250 nm displayed little in the way of error (owing to the fact that they all approached unity even when the assumed and actual thicknesses were not the same), the CEF values for the 10000 Å SiO 2 /Si sample plotted in  FIG. 6  exhibit measurable error at virtually all wavelengths when the assumed and actual thickness are not the same. It is important to note, however, that the sharpest and most intense features in the CEF again occur in the VUV (a direct consequence of the presence of the SiO 2  absorption edge in this region). 
     While the 10000 Å SiO 2 /Si sample provides an exemplary standard for the purposes of the current invention, as a result of the significant CEF signal it generates for small errors in “assumed” thickness, it will be clear to one skilled in the art that many other samples may function equally as well. In general, any sample that produces a substantial CEF signal for small error in “assumed” thickness or some other assumed sample property may be employed. 
     As defined within the scope of this disclosure, the CEF is essentially a ratio of the “assumed” and “actual” reflectance spectra for a standard (or “calibration”) sample. If the assumptions regarding the standard sample are completely accurate, the CEF assumes a value of one at all wavelengths. If instead the assumptions are to some extent flawed, the CEF will display values greater or less than one. The greater the inaccuracies in the assumptions, the greater the CEF values will deviate from unity. 
     While the CEF clearly provides a sensitive indicator of calibration accuracy it is not, itself, observable. One aspect to exploiting the CEF is therefore to use the reference sample to render the CEF features apparent. This follows since all measurements performed on samples following the initial calibration are in effect the product of the CEF and the “actual” reflectance spectrum of the sample under study. Hence if the reference sample, with its substantially smooth and featureless reflectance spectrum, is measured and if the CEF is not equal to unity then the intense sharp features in the CEF will be clearly evident in the reflectance spectrum recorded from the reference sample. Thus, even without prior intimate knowledge of the “actual” reflectance properties of the reference sample (other than that the reference sample is relatively featureless in the spectral region of interest) it is possible to readily evaluate the characteristics of the CEF and hence, gauge the accuracy of the initial assumptions regarding the properties of the standard sample. 
     While any sample with a substantially smooth and featureless reflectance spectrum may be employed as a reference sample a particularly well-suited choice may be a broad-band VUV mirror like the broad-band VUV mirror having coating #1200 manufactured by Acton Research Corporation of the United States. A typical reflectance spectrum  702  for this type of mirror is presented in  FIG. 7 . As is evident from the figure this broad-band mirror combines high reflectance throughout the entire VUV region with a largely featureless spectrum. It may be noted from  FIG. 7  that the reference sample does not display sharp features in a spectral region such as the VUV where the standard sample may display a significant CEF. The sample used for a reference sample need not provide a consistent reflectance spectrum from sample to sample. For example, the same type of broad-band VUV mirror with the same coating from the same manufacturer may show a difference in absolute reflectance from mirror to mirror. However, if for any given mirror a relatively smooth and featureless reflectance spectrum is provided (at least in the spectral range of interest), then the mirror may be suitable for use as a reference sample. Furthermore, even if the reference sample (such as the mirror described above) exhibits absolute reflectance changes over time, the sample may still be suitable as a reference sample. Thus, the repeatability of the manufacturing of the reference sample and the changes in properties over time are not as significant as the sample&#39;s featureless properties in the desired spectral range. 
     Thus, a technique is provided that includes utilizing a standard sample that allows for calibration in the wavelengths of interest even when the standard sample may exhibit significant reflectance variations at those wavelengths for subtle variations in the properties of the standard sample. Calibration may be achieved even in cases where traditionally significant calibration error in regions of wavelengths that a user is interested in would be expected to be encountered. In this regard the technique takes advantage of the presence of a certain amount of calibration error that may be referred to as a calibration error function. 
     The calibration process may thus include a technique that utilizes a first sample and a second sample. The first sample may include significant reflectance variation in the spectral region of interest as a function of sample property variations and the second sample may have a relatively featureless reflectance spectrum over the same spectral region. The first sample may be considered a standard or calibration sample and the second sample may be considered a reference sample. By first calibrating the system using a standard sample and then measuring a reference sample, any sharp changes in the reflectivity observed from the reference sample may be assumed to be a function of the inaccuracies in the assumptions regarding the calibration sample. With this knowledge, the system may then be recalibrated. 
     Further, the calibration technique may utilize a standard sample that may have relatively unknown properties with the exception that it may be assumed to have a significant calibration error function in the spectral regions of interest. Thus, the exact properties of the standard sample need not be known if it can be assumed that the standard sample exhibits sharp changes in reflectance for changes in the sample property. 
     Before the reference sample measurement can be used to evaluate the results of the calibration process it is desirable to mathematically construct a means of quantifiably assessing the CEF in light of its coupling with the reference sample reflectance spectrum. In one embodiment of the invention this may be generally accomplished in the following manner. 
     First, the derivative of the measured reflectance spectrum is calculated. This acts to reduce the coupling between the CEF and the “actual” reflectance spectrum of the reference sample and places greater emphasis on “sharp” reflectance structures (likely contributed by the CEF) than on slowly changing features (expected from the reference sample). Next, the absolute value of the derivative is calculated and the resulting function integrated. Taking the absolute value of the derivative prior to integration is necessary in order to constructively capture both positive and negative values of the function and to avoid canceling out contributions to the derivative arising from the reference sample reflectance spectrum. With the integration complete it is possible to quantitatively evaluate the results of the initial calibration procedure. 
     In this manner the integrated value can be fed back to an algorithm that iteratively adjusts the initial assumptions regarding the properties of the standard sample, re-calculates the CEF and re-determines the integrated value in an effort to minimize its value. When the minimum has been achieved the “actual” properties of the standard sample, and hence its “actual” reflectance have been determined. At this point the reflectometer can be accurately calibrated and measurements on unknown samples performed. 
     A further understanding of the steps involved in this method may be realized following a review of the data presented in  FIGS. 8-11 .  FIG. 8  presents the results of a measurement performed on an appropriate reference sample following calibration with a 10000 Å SiO 2 /Si standard sample using an “assumed” thickness of 10010 Å. The sharp structure evident in the measured spectrum of the reference sample (adjusted for the calibration) is a consequence of the 10 Å error introduced during the calibration process. Signal  802  shown in  FIG. 8  is a measured spectrum obtained from the reference sample. This signal is a result of the product of the reflectance of the reference sample and the CEF spectrum resulting from the inaccurate calibration. At this point in the process, the CEF and reference sample reflectance signals are essentially coupled, and as is evident exist largely at shorter wavelengths in the VUV. In the present example, this occurs because the CEF signal was largely present in the VUV region and the reference reflectance was substantially featureless in this same region. 
     The derivative of this spectrum is presented in  FIG. 9 . Not surprisingly, the bulk of the CEF/reference reflectance product derivative signal  902  still resides in the VUV region of the spectrum. The absolute value of the trace is then calculated prior to integration, which ultimately yields a quantitative measure of calibration accuracy. This integrated sum is then returned to an iterative routine that adjusts the “assumed” thickness of the standard sample and re-calculates the CEF/reference reflectance product integral until its value is minimized. 
     Values of the CEF/reference reflectance product integral as a function of “assumed” thickness are presented in the sensitivity plot of  FIG. 10  for the 10000 Å SiO 2 /Si standard sample with and without noise added to the system. Plot  1002  illustrates the values of the CEF/reference reflectance product integral including the presence of a 0.5% noise component while plot  1004  shows the data without noise. As is evident from examination of the data, the integral is extremely sensitive to small errors in the “assumed” thickness of the SiO 2  layer, even in the presence of a 0.5% noise component in the raw reflectance data. Needless to say, the minimum value of the CEF/reference reflectance product integral is achieved when the “assumed” thickness value matches the “actual” thickness of the standard sample. Following completion of the iterative process the “actual” properties of the standard sample are determined and the instrument is accurately calibrated. At this point in time the CEF function assumes a value of unity at all wavelengths and subsequent measurement of the reference sample yields its true reflectance spectrum  1102 , as illustrated in  FIG. 11 . 
     An exemplary and detailed description of this calibration procedure is outlined in the flowchart  1202  of  FIG. 12  wherein the mathematical relationships involved in calculating the absolute reflectance of an unknown sample are presented. As shown in  FIG. 12  step  1204 , first the assumed knowledge of a standard sample, expected to exhibit substantial calibration error features in a given spectral region is used to calculate the assumed reflectance of the standard sample. In step  1206  the intensity from the standard sample is recorded. In step  1208 , the source intensity profile is calculated using the assumed reflectance of the standard sample. The intensity from the reference sample that is expected to exhibit substantially smooth reflectance properties over the same spectral region is then recorded in step  1210 . Next, in step  1212  the reflectance of the reference sample is calculated. The reflectance of the reference sample may be then expressed according to the equation of step  1214 . The absolute value of the derivative of the reference sample reflectance spectrum may then be calculated in step  1216 . The integral of the absolute value of the derivative is then calculated in step  1218 . Next, in step  1220  an iterative adjustment of the assumptions regarding the properties of the standard sample is performed and the assumed reflectance of the standard is re-calculated. Control is returned to step  1214  from step  1220  until the value of the integral is minimized and the actual properties of the standard sample are thus obtained at which point the process proceeds from step  1220  to step  1222 . In step  1222  the source intensity profile is re-calculated using the actual reflectance of the standard. The intensity of an unknown sample is then recorded in step  1224 . Finally, the reflectance of the unknown sample is calculated and expressed according to the equation of step  1226 . 
     It will be recognized by those skilled in the art that many other methods exist for quantifying the CEF signal in such a manner as to render it useful for feedback to an iterative routine designed to minimize its value through adjustments in the “assumed” properties of the standard sample. In addition, while the above discussions have regarded the thickness of the standard sample as being the “assumed” property to be accurately determined during the calibration process, it will be further apparent to those skilled in the art that many other properties of the standard sample could also be treated as “assumed” properties and determined in the same manner. Such properties could include, but are not limited to, complex refractive index, composition, porosity and surface or interface roughness. These properties may be determined independently, or in some instances simultaneously along with other properties during the calibration procedure. 
     In certain circumstances additional mathematical steps may be performed to enhance the performance of the calibration routine. In the presence of significant noise in the measured reflectance data recorded from the reference sample it may be advantageous to filter the raw data prior to or after taking its derivative. While many appropriate smoothing filters exist in the prior art, the Savitzky-Golay filter is particularly well-suited to this application as it generally preserves the width and position of spectral features in the raw data. Additionally, in some situations it may prove beneficial to limit the range of wavelengths over which the integration is performed in order to further emphasize the contribution of the CEF signal. 
     It will be clear to those skilled in the art that the present invention readily lends itself to many modes of implementation. A particularly advantageous approach would be to integrate the reference sample into the reflectometer such that it could be effortlessly utilized. This approach is described in detail in U.S. application Ser. No. 10/668,644, filed on Sep. 23, 2003, which discloses a vacuum ultraviolet referencing reflectometer and in U.S. application Ser. No. 10/909,126 filed Jul. 30, 2004, the disclosures of which are incorporated herein by reference. An example of the use of the calibration techniques provided herein in combination with the systems described in the aforementioned prior filed U.S. Applications is illustrated in  FIG. 12A .  FIG. 12A  provides a broadband reflectometer system  3400  as described in more detail with regard to FIG. 34 in U.S. application Ser. No. 10/909,126 filed Jul. 30, 2004. The system  3400  may optionally include multiple sources  3201 ,  3206 , and  3302  and corresponding multiple spectrometers  3214 ,  3216 , and  3304 . Flip-in mirrors FM- 1  through FM- 4  and corresponding windows W- 3  through W- 6  may be utilized to select the various sources and spectrometers. Mirrors M- 1  through M- 5  are utilized to direct the beams as shown. A sample  3206  may be located in a sample beam  3210 . A reference beam  3212  is also provided. A beam splitter BS is provided and shutters S- 1  and S- 2  select which of the beams is being utilized. The various optics and samples may be included in environmentally sealed chambers  3202  and  3204  such that measurements in the VUV bandwidth may be obtained. 
     As shown in  FIG. 12A , a sample beam (or channel)  3210  is provided for obtaining measurements from a sample  3206 . A reference beam (or channel)  3212  is provided for referencing the system. Generally, the reference beam is configured to provide a mechanism that is indicative of environmental or other system conditions. The reference beam may be configured to provide a beam path that is similar in beam length and environmental conditions as the sample beam, however, the reference beam does not encounter the sample  3206 . In operation with the calibration techniques described herein, the standard sample may be placed at the sample  3206  location of  FIG. 12A . A separate reference sample need not be placed at the sample  3206  location however (although such a use of a separate reference sample placed at the sample  3206  location may be utilized). Rather, the entire reference beam  3212  path may be construed as the “reference sample.” For example, the cumulative effects of the beam splitter BS, mirror M- 4 , window W- 2 , and mirror M- 5  (i.e. the elements that are different between the sample and reference paths) may be construed as together forming the “reference sample.” Such use of an entire beam path for the reference sample is generally available if the combined effect of the optical elements provides a relatively smooth featureless reflectance spectrum in the spectral range of interest. It will be recognized that many other methods of utilizing the calibration techniques will be apparent to one skilled in the art and the calibration techniques described herein are not limited to the mechanical configurations referred to herein. Though not shown, the reflectometer system  3400  may include a processor, computer, other electronics, and/or software for calibrating the system according to the calibration techniques provided herein. The processor, computer, other electronics, and/or software may be constructed integral with the reflectometer optical hardware or may be a separate stand alone unit that together with the reflectometer optical hardware forms a reflectometer system configured to allow for calibration. 
     There are many advantages afforded by the current invention. One such advantage is that it provides a technique by which VUV reflectometry data may be accurately calibrated in light of the fact that uncertainties associated with commercially available thin film standard samples may be too large to enable accurate calibration using conventional methods. As a result, it may altogether eliminate the need for reflectometer tool users to purchase, maintain and re-calibrate expensive standard samples. 
     Furthermore, the current invention allows one to achieve highly accurate calibration results without prior knowledge of the exact properties of either the standard or reference samples. This capability is particularly useful since virtually all samples can be expected to undergo subtle changes in their properties as a function of time, as a result of either natural growth mechanisms or contamination. 
     While particularly well-suited to the purpose of calibrating VUV reflectometry data, the present invention may also be used to calibrate reflectometry data from other spectral regions. In such instances it may be advantageous to employ the use of other standard samples which could be expected to generate substantial CEF signals in the spectral region of interest. 
     A further advantage of the invention is that it does not require use of a secondary reference instrument, thereby greatly reducing system cost and complexity. 
     Once reflectance data has been recorded from a calibrated reflectometer it is typically sent to a processor unit where it is subsequently reduced via analytical algorithms. These algorithms generally relate optical data, such as reflectance, to other properties of the sample, which can then be measured and/or monitored like film thickness, complex refractive index, composition, porosity, surface or interface roughness, etc. 
     Data reduction is generally accomplished using some form of the Fresnel Equations in combination with one or more models to describe the optical properties of the materials comprising the sample. Regardless of the specific model used in the reduction of the data set, the greater goal is generally to use a mathematical expression to describe the measured data such that certain parameters, relating to the properties of the samples (as discussed above), can be obtained through an iterative optimization process. That is, the measured data set is compared to one calculated using an expression that depends on a set of parameters relating to the nature of the sample. The discrepancy between the measured and calculated data sets is minimized by iteratively adjusting the values of the parameters until such time as adequate agreement between the two data sets is achieved. This discrepancy is usually quantified in terms of a “goodness of fit” (GOF) parameter. 
     Numerous mathematical expressions for calculating GOF exist in the prior art. Most of these techniques are to some degree based on a determination of the difference between the measured and calculated spectra. While these methods are generally applicable and do a reasonable job of locating the general region of the absolute minimum in parameter space, they often exhibit shortcomings upon convergence at that minimum, particularly in the presence of increasing levels of noise in the measured data. 
       FIG. 13  presents a sensitivity plot  1302  for a prior art GOF expression (known to those skilled in the art as the “Chi-square” merit function) as calculated for a 10000 Å SiO 2 /Si test sample. As is evident this standard merit function provides an effective means of locating the general region of the “actual” thickness of the film, as it exhibits a relatively smooth line shape with a well-defined minimum. On closer examination, however, the sensitivity of the function is seen to degrade significantly in the immediate vicinity of the minimum. This point is better illustrated in  FIG. 14 , which presents an expanded view  1402  of the sensitivity plot  1302  of  FIG. 13  in the presence of 1% noise in the measured reflectance data. 
     As is evident upon examination of the data in  FIG. 14  the 1% noise resident in the raw reflectance data significantly reduces the ability of the merit function to enable the minimization routine to converge upon the “actual” thickness of the test sample. Hence, it would be desirable to develop a superior method of determining the “actual” thickness once the routine has located the general vicinity of the solution. 
     Another preferred embodiment of the present invention provides this capability. Namely, it provides a highly sensitive measure of convergence that can be used in combination with an appropriate minimization routine to efficiently reduce measured reflectance data, thus yielding results exhibiting a higher level of accuracy then attainable using conventional techniques alone. While designed to be used in conjunction with traditional merit functions, the current invention may in some instances altogether supplant the use of such methods. 
     A general overview of one embodiment of the data reduction techniques described herein is presented in the flowchart  1502  of  FIG. 15 , wherein the mathematical relationships involved in an iterative data fitting routine associated with the measurement of an unknown sample using a reflectometer are presented. The first step  1504  in the process is to obtain the absolute reflectance spectrum of the unknown sample using an accurately calibrated reflectometer. Once this spectrum has been recorded the initial assumptions regarding the physical properties of the sample are used to calculate the “expected” reflectance properties of the sample in step  1506 . With these two spectra in hand the ratio of the “expected” to “measured” spectra is determined as shown in the equation of step  1508 . 
     This ratio, termed herein as the measurement error function (MEF), is similar in nature to the CEF discussed earlier. While both functions relate the ratio of “assumed” to “actual” data sets, the MEF is somewhat simpler to evaluate as it is not coupled with the reflectance of the reference sample. That is, during minimization the CEF is evaluated through examination of the reference sample reflectance spectrum, while the MEF is evaluated through examination of the reflectance of the unknown sample itself. 
     Before the MEF (or reflectance spectrum ratio) can be used to evaluate the results of the minimization routine a suitable merit function must again be constructed. Following the approach undertaken with the CEF earlier, the next step in the flowchart  1502  is to calculate the absolute value of the derivative of the MEF as shown in step  1510 . This acts to accentuate sharp spectral features in the MEF, resulting largely from wavelengths in the vicinity of the absorption edge for one or more materials comprising the unknown sample. At this point the absolute value of the derivative is calculated and then the resulting function is integrated as shown in step  1512 . As before, taking the absolute value of the derivative prior to integration is desirable in order to constructively capture both positive and negative values. Once the integration is complete it is possible to quantitatively evaluate the results of the reduction process. More particularly, an iterative process of adjusting assumptions regarding properties of the unknown sample and recalculating the expected reflectance spectrum of the unknown sample may occur as shown in step  1514 . After the recalculation of the expected reflectance spectrum, control passes again to step  1508  and steps  1508 - 1514  are repeated until a value of the integral is minimized at which point the actual properties of the unknown sample are determined to have been obtained and control is passed to step  1516  where the actual properties of the unknown sample are provided as an output. 
     It is noted that this technique is insensitive to fixed offsets between the “assumed” and “measured” reflectance spectra. That is, it can not be effectively used to reduce long wavelength reflectometry data collected from samples comprised of very thin films (i.e. thin enough so as not to give rise to significant interference effects) since such data sets are unlikely to contain sharp spectral features that are required by this method. Fortunately, in the VUV region virtually all thin film samples exhibit some form of sharp structure in their reflectance spectra, resulting from either interference or absorption effects. 
     To better demonstrate the superior performance of this approach, relative to that of the conventional Chi-square method,  FIG. 16  presents an expanded sensitivity plot  1602  calculated using an embodiment of the current invention for the same 10000 Å SiO 2 /Si test sample of  FIG. 14 . Comparing the results in these two figures it is shown that the present invention is less affected by the 1% noise level present in the raw reflectance data, than is the Chi-square method. This establishes that the current invention provides the optimization routine with a more effective measure of the fit minimum and hence, the “actual” thickness of the film. This improved performance demonstrates that at least when the “assumed” thickness value is in the general vicinity of the “actual” thickness the current invention is capable of achieving a more accurate and repeatable result than is possible using conventional methods. 
     Exploration of a larger parameter space demonstrates why, in some situations, the current invention is best utilized in conjunction with prior art methods. The reasons for this become evident upon examination of  FIG. 17  which presents a sensitivity plot  1702  calculated using the current invention for the 10000 Å SiO 2 /Si sample graphed over a wider range of “assumed” thickness values. While the value of the MEF integral at the “actual” thickness is clearly distinguishable from its value at all other “assumed” thicknesses, the sharp features in the line shape of the MEF integral render it computationally arduous to fit. Hence, it would more efficient to begin searching for the minimum using a Chi-square based merit function and then once apparent convergence had been achieved, switch over and continue searching for the “actual” minimum using the current invention. In this sense the use of the current invention represents a high resolution mode of reflectometer operation. 
     In other situations, it may be possible to recognize the benefits afforded by the current invention without also employing the use of conventional Chi-square methods. An example of one such situation is the measurement of a 100 Å SiO 2 /Si sample in the presence of 1% noise in the measured reflectance data. In this circumstance the global search performance of the present invention is comparable to that of the standard Chi-square method. Evidence of this is provided by the sensitivity plot comparison presented in  FIG. 18 . As shown in  FIG. 18 , a sensitivity plot  1802  of the standard Chi-square method is compared to a sensitivity plot  1804  utilizing the MEF techniques according to the present invention. While both functions exhibit relatively smooth line shapes it is noted that the influence of the 1% noise in the reflectance data is already evident in the Chi-square results. 
       FIGS. 19 and 20  present expanded sensitivity plots covering a 4 Å region in the vicinity of the “actual” thickness of the 100 Å SiO 2 /Si sample calculated using the MEF technique of the present invention (sensitivity plot  1902  of  FIG. 19 ) and the Chi-square method (sensitivity plot  2002  of  FIG. 20 ) respectively. Comparisons of these two figures demonstrate the advantageous performance of the present invention in this situation. 
     Thus, data measurements may be obtained by utilizing a fitting routine that includes at least a portion of the routine that is a spectrally driven fitting routine rather than relying solely on an amplitude driven routine (which typically incorporates difference calculations). More particularly, measurements may be obtained by utilizing the presence of sharp, narrow spectral features. In one embodiment utilizing a spectral driven routine, a ratio of an expected reflectance spectrum of the sample being measured to the actual reflectance spectrum of the sample being measured. Rather than being based upon a difference between the expected and actual values, the techniques provided herein utilize a ratio of the values. The derivative of this ratio may be utilized to accentuate sharp spectral features. 
     These spectrally driven techniques are particularly useful in spectral regions that contain sharp spectral features, for example such as the sharp features that thin films often exhibited in the VUV region. Thus, a data convergent technique is provided that may beneficially utilize an absorption edge effect of the material is disclosed. In this manner sharp spectral features, for example resulting from either interference or absorption effects are advantageously utilized to better determine a data minimum that is indicative of an actual measurement value. The merit function presented in the present disclosure may therefore be driven by the absorption properties of the material being measured with an emphasis on regions that encompass large changes in absorption (the absorption edges) for small changes in sample properties. 
     The data reduction techniques may utilize a two step approach. In such an embodiment a low resolution step such as an amplitude driven fitting routine may be used to first provide a “coarse” measurement. Then a high resolution step such as a spectrally-driven fitting routine that advantageously utilizes the presence of sharp spectral features may be used to then provide a “fine” measurement. In one approach for such a technique, a low resolution approach may be utilized to obtain a rough measurement value by using a difference based technique such as in a “Chi-square” merit function and then a more accurate determination of the actual measurement value may be obtained by utilizing the spectrally driven ratio based technique in the region of interest initially identified by the low resolution technique. 
     The techniques provided herein may be construed as dynamically weighting the results for regions in which the sharp spectral features are present. For example with regard to sharp spectral edges present in the VUV range, these techniques may be construed as applying a weighting function which strongly emphasizes the VUV and strongly de-emphasizes the DUV and longer wavelength data where sharp spectral features may not be expected for a given sample. Further, the process may be weighted such that only measured data that could reasonably be expected to contain useful information may be included. This weighting method may be dynamic since the decision making process (which measured data should be considered) could be repeated after each iteration. 
     While the examples presented herein have addressed utilization of the technique to facilitate accurate measurements of film thickness, it will be apparent to those skilled in the art that other preferred embodiments of the invention can be employed equally well in the measurement of other material properties including, but not limited to complex refractive index, composition, porosity, surface or interface roughness, etc. Additionally, while the examples presented herein have dealt specifically with the measurement of SiO 2 /Si samples, it will be clear that many other types of samples may be measured equally well using the described methods. For example, the techniques provided herein may be utilized when analyzing more complex stacks of thin films. 
     Examples of such stacks include thin film SiO 2 /SiN stacks on a substrate or thin film SiN/SiO 2 /SiN stacks on a substrate. 
     As discussed earlier, the heightened levels of sensitivity afforded by the current invention results largely from the fact that it exploits the substantial changes in reflectance signal that accompany small changes in the properties of samples when in the vicinity of the optical absorption edge of one or more of the materials comprising such samples. While such features commonly lie in the VUV spectral region, the technique can also be generally applied at longer wavelengths in situations where substantially sharp features are expected in the MEF as a result of subtle changes in the physical properties of the samples under study. 
     It will be recognized by those skilled in the art that many other methods for quantifying the MEF signal in such a manner as to render it useful for feedback to an iterative routine designed to minimize its value through adjustments in the “assumed” properties of the measured sample exist. Furthermore, it will also be readily apparent that in some circumstances additional mathematical steps may be performed to enhance the performance of the measurement routine. 
     Further modifications and alternative embodiments of this invention will be apparent to those skilled in the art in view of this description. Accordingly, this description is to be construed as illustrative only and is for the purpose of teaching those skilled in the art the manner of carrying out the invention. It is to be understood that the forms of the invention herein shown and described are to be taken as presently preferred embodiments. Equivalent elements may be substituted for those illustrated and described herein and certain features of the invention may be utilized independently of the use of other features, all as would be apparent to one skilled in the art after having the benefit of this description of the invention.