Method and apparatus for bandwidth measurement and bandwidth parameter calculation for laser light

<u style="single">Related application</u> This application is filed on July 7, 2003 by the inventor of Agent Docket No. 2003-0004-01, US Patent Application No. 10 entitled "Optical Bandwidth Measuring Instrument for Laser Light". / 615,321 is a partial continuation application, and also as the inventor of Agent Docket No. 2003-0056-01, filed on June 26, 2003 by Lafuck, "Method of measuring the bandwidth of the optical output of a laser. It is also a partial continuation application of US Patent Application No. 10 / 109,223 entitled "and Equipment", both of which have been transferred to the applicant of this application, the respective disclosures of which are incorporated herein by reference. There is. The present invention relates to determining the spectral bandwidth of a laser. More generally, the present invention relates to a light source using an interferometer or diffractometer (spectrometer) having a bandwidth approximately equal to or greater than the bandwidth of the light source whose impulse response function is being measured. For accurate estimation of bandwidth.

The output spectrum of a line narrow excimer laser source for DUV lithography is generally not constant over time. Although stability has improved significantly with technological advances, neither the bandwidth nor the functional form (shape) of the spectrum is completely fixed. The effect of spectral shape changes on lithography performance has not been fully characterized so far, but full width at half maximum (FWHM) and 95% encapsulation energy (I95%) on image contrast, log-slope, exposure tolerance, etc. The effect of irradiation bandwidth (also referred to as "E95" or sometimes "spectral purity") is incorporated herein by reference by A. Kroyan, I. Lalovic, NR Farrar, "Far Ultraviolet Lithography Related". Contribution of multicolor irradiation to the optical proximity effect of "21st Annual BACUS Symposium on Photomask Technology and Management", GT Dao and BJ Glenon (edit), Monterey, California, SPIE Vol. 4562, p. 1112 Page 1120, 2002, and K.Lai, I.Lalovic, R.Fair, A.Kroyan, C.Progler, NRFarrar, D.Ames, K.Ahmed, "Understanding the Effects of Abrasion on Lithographic Imaging", It has been found to be significant, as described in "Journal of the Society of Microlithography, Microprocessing, and Microsystems", Volume 2, Issue 2, pp. 105-111, 2003.

The dependence on the irradiation spectrum arises because, for example, some chromatic aberrations become unavoidable in projection lenses for KrF and ArF lithography due to optical material constraints at the DUV wavelength. The effect of color can be minimized with a spectrally narrowed light source, but the disclosure is incorporated herein by reference, A.Kroyan, JJBendik, O.Semprez, NRFarrar, CGRowan, And CAMack, "Modeling the Effect of Excimer Laser Bandwidth on Lithography Performance," SPIE, Vol. 4000, "Optical Microlithography XIII," pp. 658-664, March 2000. Even the spread of the irradiation spectrum below picometers cannot be completely ignored. This concern raises the industry's higher numerical aperture settings and lower k₁It becomes even more imminent when moving to the value of. To ensure that spatial image characteristics are maintained within a given processing window, therefore, reliable metric feedback from light sources reporting these spectral performance indices with high accuracy, reliability, and stability. Getting more and more important. Moreover, in more advanced applications, this information can actually be used to control the action of the light source in some way to stabilize the light source spectrum or otherwise modulate its bandwidth. .. In such techniques, the resulting improved spectral performance reproducibility is, for example, an enhanced feature that tightly controls bandwidth to some range, i.e., a range below a threshold but at the same time above a threshold. It means that you can think of a general optical proximity (OPC) solution that is effective and consistent over the life of the system, including the requirements for.

Commonly used bandwidth metrics such as FWHM and E59 are not necessarily accurate measures of spectral shape, especially when either is considered alone. For example, as the energy content of the far wing of the spectrum increases, the E95 bandwidth value can increase significantly, while the FWHM bandwidth value remains essentially and effectively unchanged. Other spectral shape changes, for example, change the FWHM while keeping the E95 constant, or, for example, the energy center of the spectrum or other performance of the spectrum while keeping both of these metrics constant. May change significant parameters. These shape changes can often be synchronized with, for example, bandwidth changes, and system performance that relies on the design of spectral weighing tools and accurate bandwidth estimation for effectiveness, especially weighing feedback and It has a significant impact on the performance of more commonly used systems that require the incidental control function to be pulse-by-pulse at repeat rates up to 4000 Hz and above.

Detailed shape and bandwidth variations of ultra-narrow excimer laser sources can originate from a variety of physical mechanisms. Some of these fluctuations are technically unavoidable, and some effective strategies to overcome them in the past have been largely optimized to minimize the effects of such fluctuations. It was to design the light source in. However, even with technical control, due to improper alignment, failure of optics, or failure to manage critical processing parameters (eg, laser gas mixture) inside the light source, the spectral shape or bandwidth Large changes can occur. The job of the on-board spectral weighing package is to correctly identify and accurately report the light source bandwidth so that it can be used as a reliable input to the lithography process controller. To illustrate these shape changes, the "Cymer XLA 100 ArF" measured with a high resolution double path Echelle grating spectrometer Some examples of common spectral shape variations found in MOPA (master oscillator / power amplifier) light sources are shown in Figures 1A-D. This gathering is not exhaustive and is considered to be representative of the current generation of light sources. The data are normalized to equalize the total energy content for a better comparison of spectral energy distributions and to better represent the integrated spectral content for exposure of, for example, 200 laser pulses.

<patcit num="1"><text>U.S. Patent Application Application No. 10 / 615,321</text></patcit><patcit num="2"><text>U.S. Patent Application Application No. 10 / 109,223</text></patcit><nplcit num="1"><text>A.Kroyan, I.Lalovic, NR Farrar, "Contribution of Multicolor Irradiation to Optical Proximity Effects Related to Far-UV Lithography", Lectures "21st Annual BACUS Symposium on Photomask Technology and Management", GT Dao and BJ Glenon ( Edit), Monterey, Calif., SPIE Vol. 4562, pp. 1112 to 1120, 2002</text></nplcit><nplcit num="2"><text>K.Lai, I.Lalovic, R.Fair, A.Kroyan, C.Progler, NRFarrar, D.Ames, K.Ahmed, "Understanding the Effects of Aberrations on Lithography Imaging", "Microlithography, Microprocessing, and Journal of Microsystems Society, Volume 2, Issue 2, pp. 105-111, 2003</text></nplcit><nplcit num="3"><text>A.Kroyan, JJBendik, O.Semprez, NRFarrar, CGRowan, and CAMack, "Modeling the Effect of Excimer Laser Bandwidth on Lithography Performance," SPIE, Vol. 4000, "Optical Microlithography XIII," pp. 658-664. Page, March 2000</text></nplcit><nplcit num="4"><text>A.Kroyan, I.Lalovic, NR Farrar, "Effect of 95% Integral on FWHM Bandwidth Specifications in Lithography Imaging," SPIE, Vol. 4346, "Optical Microlithography XIV," pp. 1244 to 1253, March 2001.</text></nplcit><nplcit num="5"><text>Berington, "Data Deduction and Error Analysis for Physical Sciences"</text></nplcit>

Disclosed is a method and apparatus for a bandwidth measuring instrument for measuring the bandwidth of a spectrum of light emitted from a laser and input to the bandwidth measuring instrument, which indicates the bandwidth of the light emitted from the laser. To calculate the actual bandwidth parameters with an optical bandwidth monitor that provides a first output representing one parameter and a second output representing the bandwidth of the light emitted by the laser. A real bandwidth calculator that utilizes a first output and a second output can be included as part of a multivariate equation that uses predetermined calibration variables specific to the optical bandwidth monitor. The real bandwidth parameter is the spectrum full width (FWXM) at the maximum value within the full width of the spectrum of light emitted from the laser, or the energetic percentage ratio of the whole spectrum of the light emitted from the laser. Can include the width (EX) between two points on the spectrum containing. Bandwidth monitors can include etalons, the first output being on a spectrum that includes the width of the fringe of the etalon's light output at the FWXM, or the energetic percentage of the entire spectrum of light emitted by the laser. Represents at least one of the widths (EX') between the two points of, and the second output represents at least one of the second FWX''M or EX''', where X X'' and X. ' X'''. Pre-computed calibration variables can be derived from measurements of real bandwidth parameter values correlated with the occurrence of first and second outputs to the calibration spectrum using reliable criteria. The value of the real bandwidth parameter is the estimated real BW parameter = K^*w₁+ L^*w₂Calculated from the formula + M, but w₁= 1st measurement output representing FWXM or EX', and w₂Is the second measurement output representing FWX''M or EX'''. This device and method can be implemented in laser lithography light sources and / or integrated circuit lithography tools.

Example I of FIG. 1A reveals the effect of significantly enriching the fluorine concentration in the gain medium of a laser gas or single oscillator, eg, an ArF single-chamber source, in the MOPA master oscillator. Adding extra fluorine to a gas mixture at a constant total pressure increases the bandwidth. In these measurements, it was found that FWHM remained constant within the accuracy of the measurements when fluorine was concentrated to a concentration above 13% of the initial concentration. However, E95 was not constant, but increased by 18% for the same enrichment. This shows, for example, a significant change in the functional form of the spectrum, but does not, for example, simply indicate rescaling of the wavelength axis. Such a large excess concentration of the laser gas mixture is uncommon and may represent a virtual failure mode of the internal controller of the light source, in which case a smaller increase in the fluorine content in the laser chamber. It shows a symptomatic change in the shape of the bandwidth spectrum associated with it.

Example II shown in FIG. 1B shows the effect of, for example, acoustic disturbance, time tuned to pass through, for example, the electrode gap during laser oscillation. The wing of the spectrum remains fixed, while the shape of the spectral profile changes in response to the so-called bandwidth resonant peak event, as evidenced by the fact that the central peak of the spectrum flattens and spreads. Can be seen. The effect of this shape change in spectral shape is opposite to that of the previous example in Figure 1A. In this case, the FWHM bandwidth increases by 52% above the nominal value obtained away from the time-of-flight (TOF) resonance, also known as acoustic resonance, while the E95 increases by only 8% above the nominal value. The magnitude of the effect of TOF resonance can be significantly reduced by careful design of the discharge chamber, but it is present to some extent in all high repetition rate systems, including laser discharge operation, output pulse repetition rate, temperature, and so on. And other parameters of laser operation may occur randomly.

Example III, shown in Figure 1C, shows a change due to a very large static error in the relative timing of the discharge initiation of the gain medium between the two chambers of the MOPA light source. This phenomenon occurs, for example, because the spectral shape and bandwidth of the MO output are time-dependent. Therefore, this behavior is somewhat unique to MOPA systems (the MOPO architecture has yet another spectral complexity due to gain competition between power oscillator injections and self-excited modes). In normal operation, the delay in ignition of the two chambers corresponds to the peak of the electrical-to-light conversion efficiency of the MOPA system.₀Is selected to be. In this shape-to-time delay measurement, the bandwidth has a delay of τ.₀When increased to + 10ns, it decreased by about 10% in FWHM and 25% in E95. The delay is τ₀When reduced to -10ns, the bandwidth was found to increase by about the same amount. Although this delay change can be used to control bandwidth in a MOPA configuration, such a large offset from the efficiency peak introduces a trade-off for control of other characteristics of the laser output. This result also helps to further show that the spectral shape is affected, for example, by failure of internal control of the light source.

The final example IV shown in FIG. 1D shows, for example, the response of the laser spectrum to, for example, the exaggerated wave surface curvature inside the resonator of a grating narrow laser oscillator (MO or single chamber oscillator). In this experiment, the surface optics inside the line narrowing subsystem are mechanically strained to simulate the effects of defect components inside the laser cavity. It is a thing. The effect on the spectral shape was quite large, as can be seen in the figure. This is the second example in which there was almost no change in FWHM due to shape change, but the change in E95 was almost 1/3. The symmetry of the spectrum was also broken by this perturbation. This type of variation is not normal for a well-designed light source and can manifest itself with defects or failures due to, for example, excessive thermal loading, different thermal expansion between the catoptric component and its attachment. Has been observed by.

These four figures relate to the major types of spectral shape variation seen in ongoing research and development work at the assignee of the Applicant. However, these figures illustrate the types of spectral changes that can occur and occur fairly often, which can lead to false metrics, for example, real bandwidth to specifications. When not, whatever is selected for the specification, it may report bandwidth within the specification and report out-of-specification when the actual bandwidth is not out of specification. In each case, the repetition rate is extremely high and is detrimental to laser operation in tightly controlled wavelength / bandwidth, bandwidth stability, dose stability, and other strict operating parameter measurement and control requirements. The challenge is always to deal with spectral changes that can negatively affect the lithography performance of the irradiated exposure tool, and to do this accurately despite, for example, spectral function or shape changes. To develop an external measurement method.

There are many examples of bandwidth measurement and estimation techniques for DUV light sources. However, it is technically very difficult to develop an accurate and powerful measurement method for each pulse for a high repetition rate excimer laser light source, and at least it has been highly evaluated in the conventional measurement system. It's far more technically difficult than you might think. For next-generation light sources, the ideal spectral measurement solution will have most, if not all, of the following five features: The solution is, for example, a very high spectroscopy that can be modified more precisely by requiring that the impact response (instrument function) of the spectrometer have a bandwidth that is many times smaller than the source spectrum. Resolution may be required. This solution will also require, for example, a wide inspection range in wavelength (λ) space. It has been previously suggested that even small changes in the distant wing of the irradiation spectrum can have a significant effect on spatial image characteristics, and similarly, this requirement is incorporated herein by reference. A.Kroyan, I.Lalovic, NR Farrar, "Effects of 95% Integral on FWHM Bandwidth Specifications in lithography Imaging," SPIE, Vol. 4346, "Optical Microlithography XIV," pp. 1244 to 1253, 2001. Required for direct calculation of E95, as explained in March of the year. The solution also provides, for example, the band of the light source spectrum from the instrument function of the spectrometer.Accurate and powerful methods for unwinding (reverse convolution) will be needed, which are generally not negligible in ensuring proper measurements and are becoming more and more important. It has become. This could be, for example, a direct inverse convolution using independent measurements of instrument functions, or some sort of mathematical or semi-experimental model with, for example, similar results or estimates. This solution will also require, for example, a high signal-to-noise ratio (SNR) for single pulse measurements. Ideally, for example, this is needed for pulse-by-pulse evaluation of spectral quality and judgment of lithographic processing. The system may also require, for example, optical and mechanical simplicity and robustness, which is required, for example, for calibration stability, measurement reproducibility, and, for example, long life in a lithography manufacturing environment. There is a possibility of becoming.

Satisfying all of these requirements for current technology at the same time will be difficult, if not impossible. For example, as shown in Figure 2, multipath diffraction grating spectrometers can provide excellent spectral resolution, a wide inspection range, and the ability to inverse convolve the effects of instrument functions using the Fourier method or other methods. it can. As shown in FIG. 2, such a spectrometer 20 can include, for example, a spectral intensity detector 30, an inlet slit 22, a diffraction grating 24, and a maximum reflectance mirror 26. However, such instruments are bulky and fragile, generally require moving parts for adjustment, and can be difficult to install, align, calibrate, and maintain. High-resolution grating spectrometers, due to their low acceptance, require long irradiations to ensure proper signal-to-noise ratio (SNR), making it impractical for pulse-by-pulse reporting of spectral quality. .. It is also expensive and at a price that can correspond to most of the total cost of a high performance light source, such as a laser lithography tool light source. Grating spectrometers are essential for system quality assurance in the role of research where very fine details of spectral shape and out-of-band energy distribution must be accurately characterized for spectral purity, line width asymmetry, etc. It is a tool. It is generally impractical for onboard real-time wavelength or bandwidth metrology applications, for example in lithography manufacturing applications.

For example, a "Fabry-Perot" Etalon spectrometer, as shown in Figure 3, could be another solution. It is optically simple, has no moving parts, and can be made mechanically strong. Such a spectrometer 40 as shown in FIG. 4 can include, for example, a beam homogenizer 42, a collimator lens 44, an etalon 465, an imaging lens 50, and, for example, a transverse photodiode array 54. Can be included. The absence of the need for slits means that for a particular input, for example a PDA45, a large irradiance can be obtained in the detector plane despite poor beam quality, for example. To this end, the planar-mirror etalon 46 can capture useful spectral information from a single short irradiation pulse by utilizing the angular distinction between beams transmitted at different wavelengths.

Long Free Spectral Range (FSR), High Transparency, and High Finesse to compete purely with grating spectrometers based on spectroscopic resolution and inspection intervals

<img file="JP2007536498A_D0001.tif" />

Etalon is needed. Commercially available double-path Echelle grating spectrometers used in DUV light sources can achieve a fixed inspection range of 15 pm and instrument functions in the 50 fmFWHM band when operating at higher orders. To adapt this performance to the Etalon spectrometer, FSR 15pm and

<img file="JP2007536498A_D0002.tif" />

Finesse will be needed. This type of performance is routinely exceeded for long wavelengths, but is not practical for DUVs, in which case surface morphology (parallelism, flatness, roughness) and mirror coating limitations are generally full. Finesse

<img file="JP2007536498A_D0003.tif" />

Limit to. Finesse loss due to geometric imperfections is mode-modified because the focusing effect of the spherical mirror results in a small mode diameter on the mirror surface and thus the effect of geometric imperfections is suppressed. It can be reduced by using a spherical confocal etalon. Unfortunately, in this configuration, the optical path length between the mirrors must be scanned for spectral analysis, which makes the analysis impractical for short pulses isolated by this or even a few pulses within a pulse burst. There is a possibility of becoming. In addition, for a given interval, the FSR is halved using this method, and this mode conformance requirement can result in tremendously high insertion loss, for example for poor quality beams. It means that there is. Therefore, in the confocal configuration, many of the advantages of the Etalon spectrometer 40 are discarded when trying to obtain the same performance as the grating spectrometer. Similar conclusions can be drawn for other methods of obtaining high spectral resolution and large inspection range with a series of multiple etalons.

Despite these limitations, air-separated planar etalon spectrometers are often the best choice for many spectral measurement tasks. It does not provide maximum inspection range or resolution in DUVs, but retains the desired features, such as excellent single short pulse SNR and suitability for manufacturing applications that require physical strength and reliability. However, reasonable negotiation proposals can be reached in these areas. For example, for spectral monitoring of lithographic tool irradiation, planar etalons with FRS of 2 pm to 4 pm that achieve finesse values from 20 to 50 can be used. This means that these devices are used in regions where the FWHM bandwidth to light source spectrum bandwidth ratio of the spectrometer function is close to or greater than 1. In this region, as mentioned above, the etalon FWHM fringe width includes, for example, spectral purity, i.e. the amount of integrated energy within a portion of the spectrum on either side of the peak wavelength normally measured as E95% or E95. , FWHM has been found to have non-negligible sensitivity to light source spectral shape details, for example, the spectral purity increases as the width of E95 decreases.

As mentioned above, the spectral shape of the DUV light source can vary significantly, especially in the case of defect components or controllers. These shape changes can affect their output "hidden" under the instrument function of the spectrometer. Therefore, Applicants have a third requirement, i.e., the method used to estimate the bandwidth of the light source spectrum from etalon fringe measurements is a reliable system caused by changes in the shape of the light source spectrum. It was decided that the point that there was no target error should be given special importance.

The effect of spectral shape on the estimation of source bandwidth should be considered. Several techniques can be applied to recover the complete light source spectrum or light source bandwidth from the spectroscopic measurements. The signal output O (λ) by the spectrometer is the convolution of the light source spectrum S (λ) and the instrument function I (λ) of the spectrometer.

<img file="JP2007536498A_D0004.tif" />

Three methods are commonly used to determine the bandwidth of the light source spectrum S (λ) given the spectrometer signal O (λ). The output signal can be, for example, a fringe detection result from the light output of an etalon, eg, using a photodiode array (PDA), which can detect the light intensity distribution across the diodes of the array. Will be understood by those skilled in the art. Intensity plots can then be used to generate intensity plots, mathematically, eg, using interpolation techniques, eg, by a digital processor, eg, FWHM or summed up as an example. Positions within an array of intensities that are FW78% M or FW35% M and / or positions within an array of intensities that make up boundaries such as E95 or E75 values can be calculated. Thus, for example, the output signal of the detector in the form of an array of light intensity distributed along the linear arrangement of the photodiodes is another signal representing the value derived from the bandwidth detector output function O (λ). Converted, this bandwidth detector output function O (λ) is used throughout the system as a measurement result, such as FWHM or E95. This is one form of output from a bandwidth detector that represents a parameter, which represents the actual bandwidth of the light source, ie, the actual FWHM or E95.

The most complete of the commonly applied methods is the complete inverse convolution of the signal O (λ). Given the independent judgment of O (λ) and I (λ), the solution of Equation 1 can be found using, for example, the Fourier method or other methods. However, this can be a daunting task due to the large number of light source spectra S (λ) that are convoluted by I (λ) to give the same real output signal O (λ). The output signal O (λ) is a complete O (λ), from which the bandwidth detection imager, i.e. the PDA, actually "sees" only its individual parts, from which typical parameters such as FWHM Alternatively, the value of E95 is calculated by the bandwidth detector system.

In general, special efforts should be made to deal with noise in the measurement results and zeros in I (λ), which can take a considerable amount of processing time for finer spectra. There is sex. For these and other reasons, the method is generally not well suited for pulse-by-pulse light source spectrum bandwidth monitoring in high repetition rate applications. Nevertheless, this method is preferred when using high resolution grating spectrometers for basic research or in environments that require very detailed knowledge of the average spectrum.

The second method appeals to mathematical reasoning based on analytical inferences of light source spectra and instrument functions. If the spectral densities S (λ) and I (λ) are both completely Lorentz or both completely Gaussian, then the FWHM and E95 bandwidths of the source spectrum S (λ) are very simply O (λ). ) And I (λ) bandwidth. For example, the Lorenz distribution light source spectrum and instrument function respectively Г_SAnd Г_IConsider in.

<img file="JP2007536498A_D0005.tif" />

Therefore, in this case, the FWHM bandwidth of S (λ) Г_SIs obtained by subtracting a constant. The E95 value can be processed in the same way. The reason is,

<img file="JP2007536498A_D0006.tif" />

Here, E [...] indicates the E95 bandwidth of the spectral distribution in parentheses.

The third and widely used method of obtaining the source bandwidth without full reverse convolution begins with equations 2 and 3 as the first guess, but modifies its shape or an additional correction term. Is added to reduce systematic errors resulting from incomplete assumptions about the shape of the light source spectrum and / or instrument functions, for example. It is therefore characteristically semi-experimental and requires calibration against reliable measurements. In general practice, a light source is operated through some set of operating modes or conditions that vary its bandwidth. Light source FWHM bandwidth Г_SIs carefully determined during this test, for example using an external high resolution grating spectrometer and Fourier inverse convolution (or any other means). At the same time, the output of the weighing system being calibrated is recorded. As mentioned above, this output can be, for example, the FWHM fringe width w of the Etalon spectrometer housed inside the light source, or any digital or analog signal representing the detected w. If this data is available, light source bandwidth Г_SIs related Г_SIt can be estimated from f (w). The best choice of semi-experimental model f can be made from examination of the data and / or by resorting to mathematical reasoning as described in the preceding paragraph.

Looking at these semi-experimental models in more detail, for example, the simplest option for a model for FWHM bandwidth estimation is to subtract a constant experimentally determined offset. Г_S f (w) = w-δ (4) This model is mathematically accurate when both the light source spectrum and the instrument function of the spectrometer are purely Lorentz distribution, for example, as seen in Equation 2 above. It is a thing. Etalon spectrometers may have an instrument function I (λ) that is very close to the Lorenz distribution, but as mentioned above, the spectrum S (λ) of the DUV source is generally better with a Gaussian or Lorenz distribution. It is not approximated to, and it is actually quite difficult to parameterize. For example, as shown in the spectra shown in FIGS. 1A to 1D, the simple fact that the ratio E95 / FWHM is not constant is a simple indication that the Gaussian or Lorenz distribution assumptions are inadequate. This ratio remains constant for these analytical forms, as can be seen from Equation 3 and so on. Therefore, in the constant offset model (Equation 4), the source bandwidth Г is subject to systematic errors that depend on the details of the spectral shape._SEstimates will be incomplete. To show this point, the spectrum S, which has a shape very close to the "Voigt" profile._VConsider the hypothetical light source of (λ). The "Voigt" profile is a convolution of the Lorenz and Gaussian distributions with equal energy content as follows.

<img file="JP2007536498A_D0007.tif" />

Next, the light source spectrum shape is, for example, Г of FWHM of Lorenz component and Gauss component._Las well as

<img file="JP2007536498A_D0008.tif" />

It is fully characterized by two parameters. Output O of the Etalon spectrometer illuminated by this light source_V(λ) is purely Lorentz distribution instrument response I_VS by (λ)_VWell approximated by the convolution of (λ), the FWHMγ of this Lorenz distribution is its finesse of the Etalon FSR as follows:

<img file="JP2007536498A_D0009.tif" />

Given by the ratio to.

<img file="JP2007536498A_D0010.tif" />

Figure 4 shows the Etalon spectrometer output fringe O_VFWHM of (λ) and two independent shape parameters Г_L/ γ and Г_GLight source spectrum S for γ as a function of / γ_VThe difference between (λ) and FWHM is shown. Г_G When 0, the difference δ between the etalon fringe FWHM and the FWHM of the light source spectrum approaches the limit value of γ as expected. This is the condition described by Equation 2. However, as the width of the Gaussian distribution component increases, δ decreases and the constant offset model of Equation 3 does not give an accurate estimate of the source bandwidth within current and future accuracy and consistency requirements. The content described here, although somewhat artificial, clearly shows the variation between the limited cases of the Lorenz and Gaussian light sources.

The performance of the constant offset model can be improved by extending it to the point slope model as follows. Г_S f (w) = Aw-B (7) The point slope model is a hypothetical "Voigt" spectral distribution S_VIt fits well for (λ), but the parameter Г_LAnd Г_GWhen the fluctuation of is suppressed, for example, a linear relationship with m and b as constants Г_G= MГ_LOnly if there is + b and the overall bandwidth variation of SV (λ) is not too wide. However, if the spectral shape is not well constrained, the point slope model can be inaccurate and becomes unacceptable as it grows. It is also worth noting that in the case of FWHM estimation, the performance of these simple models is significantly improved when the FWHM band of the instrument function I (λ) is made very small. However, as also mentioned above, this is difficult or impossible to achieve even for a moderate FSR planar etalon assembly within a DUV.

Here, a more powerful method of bandwidth estimation using an etalon spectrometer will be described below. For any source spectrum S (λ), the only useful bandwidth estimation appears to be obtained from the exact inverse convolution of the spectrum obtained from a device with very high spectral resolution. Let's go. In addition, the E95 estimate may seem even more unacceptable as it requires integration of the source spectrum over a wide range of wavelengths. Fortunately, a clear understanding of the limitations of this technique still provides a powerful semi-experimental method of bandwidth estimation for both FWHM and E95 using relatively wide bandwidth etalons. Applicants and their collaborators have previously studied several techniques for estimating the bandwidth of the DUV excimer source spectrum, using, for example, the width of the etalon fringe as an input. Depending on the configuration, these techniques are designed to suppress or aggressively correct systematic errors caused by spectral shape changes. Most of the methods under investigation rely on three simple observations. First, the FWHM band of Etalon,

<img file="JP2007536498A_D0011.tif" />

The wider the fringe FWHM w, the greater the influence of the wing energy of the light source spectral distribution (and thus its E95). Second, when measuring the total width of the fringe peak intensity (FWX% or FWXM) at X%, when X 100%, the total width is large in the energy content near the center of the light source spectral line. Dependent. At X 0%, the overall width depends more on the energy content in the wings of the light source spectrum. Third, the bandwidth space and the spectral shape accessible to a single oscillator or MOPA light source are limited to a limited extent, even in the event of anomalous or failed internal components.

With these points in mind, Applicants and collaborators have maximum values that are relatively unaffected by systematic variation in spectral shape, such as FWHM bandwidth at a certain percentage or with encapsulation energy. Desktop that it is possible to "optimize" the selection of etalon band γ, fringe measurement techniques, and bandwidth estimation models to obtain accurate predictions of light sources in percentage ratios, eg E95 bandwidth. Found in the experiment. The applicant and collaborators have shown that the FWX% fringe width w (X%, γ) of an etalon spectrometer having a FWHM instrument band γ irradiated by a lithography laser light source is relatively well modeled by the following equation. I am observing that it will be done. w (X%, γ) A (X%, γ) Г_{light source}+ B (X%, γ) E_{light source}+ C (X%, γ) (8) However, A, B, and C are constants that depend on the spectroscopic instrument function and the total width of the fringe depending on a part of the measured intensity._{light source}And E_{light source}Are, in part, FWHM and E95 of the light source spectrum S (γ), which is the subject of patent application No. 10 / 109,223 previously referenced by the Applicant, respectively. Equation 8 is a further generalization of the model described herein, taking into account the dependence of the fringe width on the light source spectrum. Ratio E_{light source}/ Г_{light source}= Constant or E_{light source}When = constant, a point slope model is obtained, and when any of these conditions is maintained by A1, a constant offset model is obtained. The coefficients of Equation 8 can be determined by computer simulation or calibration against reliable criteria. In practice, it helps to use the simulation as a guide in selecting the parameters X, γ, and the functional form of the estimation model to obtain the desired sensitivity. The suitability of Equation 8 can be determined for a given population of spectral shapes by plotting the fringe width against E95 and FWHM of the light source spectra. This model can be validated by plots such as those shown in Figure 5, with a ratio of E_{light source}/ Г_{light source}Is not constant across its population, but the data are still (Г_{light source}, E_{light source}, W) Near a plane in three-dimensional space. This model is not perfect, but (Г_{light source}, E_{light source}, Gamma) seems to hold a useful range of values. In addition, E_{light source}/ Г_{light source}= Since a plane can be obtained at a constant time, it is important to confirm the behavior using a spectral sample with a significant variation in this ratio.

For the above-mentioned types of experimentally obtained spectral shapes, the applicant and collaborators have determined that γE._{light source}And it is discovered that A B when X = 50%. γ E_{light source}/ 2 Г_{light source}And when X = 50%, the applicant and collaborators have found that A3.5B. This confirms the expectation that when the FWHM of the etalon instrument function γ is narrowed, the fringe width w at 50% intensity tracks the light source spectrum FWHM more completely despite the shape change. Applicants have this meaning, i.e., when estimating the FWHM bandwidth of the light source spectrum from the FWHM of the etalon fringe when the choice of γ is too wide using the point slope model, for example, as shown in FIG. We considered the meaning of some E95s "flowing out" through instrumental functions. This is because the convolution with the instrument function draws some energy from the wing of the light source spectrum into the core of the etalon fringe. If the FWHM (~ core) and E95 (~ wing) of the light source spectrum fluctuate independently as shown above, the systematic error will be, for example, as shown in FIGS. 7A and 7B. It can be seen that it appears in the estimated value of the light source FWHM.

When designing an etalon spectrometer

<img file="JP2007536498A_D0012.tif" />

The available options are very constrained by high quality reflective coating low loss / high flatness substrates and cavity spacers with very low wedge angles. Therefore, optimal options are usually not available, especially for current and next generation DUV light sources and for current and future lithographic tool requirements. However, Applicants have found that a remedy for this situation can be found by adjusting the threshold parameter X for the specific spectral width detection utilized in the new model. For example, the simulation results as plotted in FIG. 8 are, for example, the point slope model and γ Г._{light source}For errors in estimating the FWHM bandwidth of a large population of light source spectra with shape variation when using, for example, when measured by a bandwidth detector, X is 25% to 50% of the fringe peak intensity ~ It is increased to 70% to show the effect of forming the bandwidth detector output. Increasing X reveals an improvement, which Applicants attribute to the reduced width sensitivity when increasing the threshold to the fluctuation of the energy balance between the core and wing of the light source spectrum. This can be attributed to, for example, the fact that the ratio A / B increases as the threshold X increases, which is I_VThis is because the reduction of energy from the wing of the light source spectrum contributes to FW75% as compared with FW25% by the process of convolution with (λ).

Applicants have found, for example, to apply this directly to the Measurement Act, such as the E95 Measurement Act. The fact that the E95 variation of the light source spectrum at a constant FWHM can be clearly distinguished within the FWX% of the etalon spectrometer fringe, eg, as shown in FIGS. 6 and 7A and 7B, is, for example, the inverse of the data. It shows that it is possible to estimate E95 with the required level of accuracy and measurement stability of the source spectrum without resorting to convolution and full-integration processing. For the model (Equation 8), by making the γ as small as possible for the application of the planar etalon spectrometer to the FWHM estimation and increasing X to the maximum level allowed by the angular resolution of the fringe detector, eg, the PDA. Often sufficient, PDAs have resolution that depends in part on the fineness of the pixels (diodes in the array) available for mathematical operations such as intensity measurement and thus interpolation. In such cases, the A / B can be, for example,&gt; 5, and the sensitivity to shape changes, for example, can be small enough to be acceptable. However, for E95 estimation, it is difficult to construct a scenario with an A / B much smaller than 1 while still satisfying the constraints placed on other aspects of the spectrometer design (detector resolution, signal-to-noise ratio, etc.). Therefore, the situation is still considered difficult.

The applicant and collaborators are γ Max {E_{light source}By verifying the behavior of the FW35% and FW75% fringe widths of experimental spectrometers with }, the usefulness of the etalon spectrometer for measurement methods, such as applications to the E95, was verified. This γ is chosen, for example, because it provides acceptable sensitivity to energy content in the light source spectrum without unduely compromising other performance aspects. In the experiment, within the normal working envelope and in the normal working envelope to generate significant variation in output bandwidth and spectral shape (corresponding to the conditions and fluctuations of types I-III in Figures 1A-1C). "Cymer XLA" over a wide range of conditions 100 Prototype laser DUV light source was operated. The light from this light source was homogenized and used, and both the double-pass Echelle grating spectrometer and the experimental Etalon spectrometer 40 were simultaneously irradiated. The grating spectrometer output is inverse-folded using the Fourier method, the corresponding E95 bandwidth is calculated, the etalon fringe patterns obtained during grating spectrometer irradiation are analyzed, and the separate fringe values w1 and w2, For example, FW35% and FW75% values were recorded. The results are shown in FIG. 9 as an E95 plot of the inverse convolution source spectra recorded by a grating spectrometer for fringe widths at two intensity thresholds. From the point of view of the point slope, it is as follows. E_{light source} m · w (X%, γ) + b (9) The fringe width follows, for example, the change in the light source E95 bandwidth due to the MOPA timing offset and fluorine enrichment with one slope m, but the chamber acoustic phenomenon, that is, Responds to completely different slopes m' m for changes in the light source E59 as a result of different types of simultaneous variations in bandwidth and spectral shape associated with different physical processes in the laser. The best-fitting intercept b also fluctuates as a function of the working point. Therefore, Applicants have concluded from the above and other experiments that full-width measurements at a single intensity threshold X are insufficient for a strong E95 estimate in the presence of shape variation.

Recognizing that the single-threshold technique is inadequate, Applicants and Collaborators considered several other techniques following the fringe width model (Equation 8). In one technique, obtain sufficiently different coefficients A, B, C for each, as is also the subject of the previously referenced patent application No. 10 / 615,321 in the name of the Applicant 2 Two etalon spectrometers can be designed. Such a spectrometer can be operated simultaneously and in parallel to obtain two different fringe widths, with these fringe widths and a set of six coefficients, a system of two multivariable linear equations. Can be solved for an unknown light source FWHM or E95. However, while this method is potentially very successful in itself, it has the disadvantages of cost and complexity of requiring two separate etalon spectrometers. However, as is the subject of the patent application referred to earlier, if the simulation results show that the coefficients are properly selected to meet certain detection constraints, then both FWHM and E95 of the light source are very emergency. It has been found that good estimates can be obtained.

According to embodiments of the present invention, equation 8 is applied differently, for example, in an alternative method that can provide a strong E95 estimate of the light source spectrum while using only a single etalon. In this approach, according to embodiments of the present invention, the etalon band γ is fixed by the choice of finesse and FSR, but nevertheless, the coefficients A, B in a significant way by changing the intensity threshold X for width measurement. , C values can be changed. For example, for two sufficiently different choices of X, the equation of a plane can be obtained again.

To test this embodiment of the invention, Applicants and Collaborators repeated the experiment, for example, with an E95 estimation model modified to use two intensity thresholds. In this set of measurements, the selected models are: E_{light source} K w (35%, γ) + L w (75%, γ) + M (10) However, K, L, and M are calibration constants determined by the best fit of the light source spectrum E95 measured with a grating spectrometer to the model. With this change, the light source E95 estimation accuracy over a wide range of spectral shape variations is sufficiently improved, as can be seen, for example, from the experimental results plotted in FIG. According to the model of Equation 8, the Applicant and collaborators, for example, say that the combination of two FWX% terms partially "senses" independent changes in the source spectral energy distribution within the core of the spectral line and the near wing. "I believe. Therefore, this model compensates for the independent variation of FWHM and E95, which is insensitive to simple one-dimensional (point slope) models. Although some systematic deviations still exist, the sigma of the error distribution of a given spectral population has been reduced by about half when the improved technique according to the embodiments of the present invention is applied. Similarly, Applicants and collaborators believe that the use of two well-separated EX% measurements as bandwidth detector output width measurements can have the same effect. The use of two separate separated X% values for FW or E measurements in a bandwidth detector, whether FW or E, eg FWHM or E95, is as described above for a given instrument, eg, a particular instrument. It can be said to be useful in determining the desired real bandwidth parameters, relying solely on the generation of the appropriate constants L, K, M for etalons. Similarly, the two measurements with etalon used for calibration and later actually sensed can be each of the differences between FW and E with the same result.

Also, those skilled in the art will use a single width detector, such as a PDA, to assume that if both are FW or E, then X X'' and X' X''', while w.₁, For example FWXM or EX', and w₂For example, you will find that the data needed to process the value of FWX''M or EX'''' is available. Then w₁And w₂The two values can be conveniently and quickly calculated simultaneously according to the operation of the detector and associated processor, for example from the intensity value obtained from the PDA.

The calculation of the energy width (EX%) of the Etalon spectrometer fringe used as an input to a point slope or other model can be computationally expensive, for example due to the required integrals, but is still achieved. This is a viable solution, with possible and improved computational speed and / or special DSP circuits optimized for, for example, integration work. However, it may even have some advantages when it comes to degrees of freedom in etalon selection and other aspects of spectrometer design.

It is also understood that the actual bandwidth parameters, such as FWHM or E95, which are the final outputs of the devices and methods according to the embodiments of the invention disclosed herein, are at best only estimates thereof. Let's go. However, as far as the laser light source and its measurement and control system and / or lithography system are concerned, it is an actual value. As used in this application, the "actual" or "estimated actual" value of the bandwidth measurement parameter, including its claims, will be reached in accordance with the disclosed embodiments of the present invention, followed by the specification. Means the final determined value of the desired bandwidth measurement parameters that the system can generate within the limits described in, eg, trusted by the rest of the system as the best and closest judgment of FWHM or E95. Used interchangeably as you do.

From the above, it will be understood by those skilled in the art that, despite various drawbacks, the Etalon spectrometer has clear advantages for application to the bandwidth measurement-equipped line narrow excimer light source used in DUV lithography. Will be done. It has been proven so far that these light sources show a dependence on the detailed shape or functional shape of the output spectrum, for example under some specific operating conditions. Such shape changes can lead to large systematic errors in the methods commonly used for bandwidth estimation due to the non-negligible effect of the bandwidth of the instrument functions of the practical embodiments of these spectrometers. is there. Fortunately, through the application of a simple etalon fringe width model according to an embodiment of the present invention, some special methods have been proposed that are less sensitive to these variations. In use, these techniques can suppress errors associated with spectral shape variation by introducing measurement sensitivity to the relative energy distribution between the core of the spectrum and the near wing. Due to the sensitivity of the lithography method to the irradiation bandwidth, this systematic error source management is important for current and future applications, especially those involving practical control and stabilization of the light source spectrum.

Also, at a more conceptual level, embodiments of the present invention make use of a bandwidth weighing method and, for example, a laser-generated plasma (LPP) or discharge-generated plasma (DPP), such as a laser DUV light source or, in some cases, an EUV light source. It will also be appreciated by those skilled in the art that it relates to devices that can include, for example, an optical dispersometer that can include an etalon that disperses the energy contained in the light output of the light source. Due to the dispersion, the output light in the intrinsic wavelength region is converted into a spatial or temporal region according to the wavelength dispersion of the light energy output from the light source. The present invention further records, for example, a spatial or temporal variation in the wavelength distribution of energy, for example, by utilizing a transverse photodiode array that records the light intensity along the range of the array, eg, a detector, for example. It envisions a photodiode array and can further provide an output signal based on the recorded spatial or temporal variation. The output signal is the spectrum full width (FWXM) and (FWX'M) at a percentage with the maximum value within the full spectrum of the light emitted from the light source or the energy of the whole spectrum of the spectrum of the light emitted from the light source. Represents the width (EX'') and (EX''') between two points on a spectrum that make up the content of a spectrum containing a percentage, eg multiple widths measured between pixels on an array. Can include.

In embodiments of the present invention, for example, any combination of at least two of these values can be used, such as X X'when the combination is FWXM and FWX'M, and the combination is, for example, EX. It is further assumed that X'' X'''when it is'' and EX''''. Also, the particular combination used and the difference between, for example, X and X'or X'' and X'''is, for example, at different planes of energy distribution in the spectrum being measured, eg, at X% of the maximum value. Light emitted by a light source to respond by width or width of encapsulation energy at Y%, i.e., generally by energy in different parts of the spectrum, such as the central part of the spectrum or the skirt (wing). It is understood by those skilled in the art that it can be empirically selected according to, for example, the type of dispersion element, the recording device, and the type and accuracy of the light source (eg, measured by SNR), including the type and probability of occurrence of distortions in the spectrum of. Will.

Embodiments of the invention are also based on the spatial or temporal variation of the wavelength distribution of energy recorded by each detector, i.e., of the light detected by each photodiode (pixel) in a lateral PDA array. As shown in the intensity distribution, it is assumed that, for example, a first computing device is used to calculate the width of the energy wavelength distribution in each space or time domain. According to an embodiment of the present invention, this first computing device, for example, spatially or temporally distributes (eg, sensed light intensity in a PDA) according to the optical properties of a dispersion meter, i.e., the width values described above. By obtaining it, it can be converted into a wavelength region and their width values can be output.

According to embodiments of the present invention, the second calculator utilizes at least one of these width values that represent the wavelength distribution of energy within the wavelength region when calculated by the first calculator to provide a light source. , Dispersometers, detectors, and apply them as arguments to multivariable equations that have a particular predetermined calibration variable in at least one width taken as an argument. That is, as described above, according to the embodiment of the present invention, a predetermined calibration value is a multivariable equation using a pre-calculated calibration variable when the same width output is input to the second computing device. At least one width output from a particular instrument, eg, a particular etalon spectrometer, so that use returns the same or essentially the same desired wavelength parameter (FWXM or EX) measured by a reliable reference in the calibration process. It is determined using reliable criteria to measure the actual wavelength of the spectrum correlated with. The embodiments of the present invention disclosed above relate to the use of two such width measurement results from a first computing unit, but as described herein, it is at least one. All you have to do is, and you could have more than two. Further, the first and second arithmetic units may be the same arithmetic unit according to another embodiment of the present invention. Calculate the value of the multivariable equation, group FWX^*M, EX^**Real bandwidth parameters are calculated that explain the spectral distribution of the energy output by the light source selected from.

Those skilled in the art will recognize that the aforementioned embodiments of the present invention are not limited to the particular disclosed embodiments of the present invention. It will be appreciated that many changes and amendments are available without departing from the claims, content and spirit. For example, diffractive optics that generate the required fringe pattern or other bandwidth detection measurement parameters can be utilized other than etalon. Similarly, a width measurement that is first calibrated and then used in operation, i.e. used in the equations of the embodiments of the invention other than, for example, the processing output from the PDA.₁(As some FWXM or EX function, eg instrument bandwidth function) and w₂Various means are available to reach (as some other FWXM or EX function, eg instrument bandwidth function). Furthermore, the final output is not derived from the processing of the PSA intensity value output, but can be derived from the PDA itself, for example by incorporating a digital signal processor (DSP) within the PDA, which is, for example, dedicated. W in the form of a programmed and, in some cases, FWXM or EX as a real-time output of the bandwidth detector and associated circuitry.₁And w₂It can have specialized arithmetic, algebraic, or trigonometric or similar circuits to handle some aspects of conversion of, for example, PDA intensity values to. Subsequent processing of the relevant equations, for example to obtain the desired real parameters, may then occur on another processor or, in some cases, on the DSP itself. For example, the bandwidth detector output can be further refined in that it increases the number of pixels (diodes) in the array to speed up processing and increase the signal-to-noise ratio. Other modifications and modifications may be made within the scope of the claims, and the present invention should interpret the scope only from the scope of such claims.

Further, although the embodiments described involve multivariable linear equations, those skilled in the art will recognize that there are examples in which non-linear terms may appear in transformation functions that include calibration coefficients. Also, these embodiments have been described in relation to, for example, the bandwidth of a laser output light having a relatively narrow bandwidth for use in lithography. However, for other light sources that may require narrow bandwidth judgment, such as EUV light sources and similar or other forms of monochromatic spectroscopes where similar inaccuracies are brought to the measurement results due to instrument characteristics. The present invention could also be utilized for use. In addition, we have described in some detail how to determine the calibration factor, but the actual bandwidth as determined by the so-called "reliable criteria" correlated in the light of the generation of the two values of the first and second bandwidth monitor outputs. It will also be appreciated by those skilled in the art that any measurement of width can be made by applying known and understood standard error propagation techniques. What is required for the performance (accuracy) of a "reliable standard" is reliable when judged using error propagation techniques, such as those shown in Berington's "Data Deformation and Error Analysis for Physical Sciences". The reference probabilistic error must be of the same order or less than the probabilistic error for, for example, an etalon measurement from a bandwidth monitor propagated through, for example, a multivariate transformation equation.

<figref num="1A">It is a figure which shows the various response of a bandwidth spectrum shape by changing some parameters of a laser operation.</figref><figref num="1B">It is a figure which shows the various response of a bandwidth spectrum shape by changing some parameters of a laser operation.</figref><figref num="1C">It is a figure which shows the various response of a bandwidth spectrum shape by changing some parameters of a laser operation.</figref><figref num="1D">It is a figure which shows the various response of a bandwidth spectrum shape by changing some parameters of a laser operation.</figref><figref num="2">It is a figure which shows the embodiment of the double path diffraction grating spectrometer.</figref><figref num="3">It is a figure which shows the spectroscope which utilizes the angular dispersion of a single plane etalon by embodiment of this invention.</figref><figref num="4">It is a figure which shows the contour line of the difference between the "Voigt" light source and the Lorenz instrument convolution spectrum FWHM bandwidth with respect to the shape parameter by the unit of Lorenz FWHM band γ.</figref><figref num="5">The two sets shown show the effect of different selections of the Etalon FWHM band γ, showing the simulation Etalon spectrometer FWHM fringe contours for ~ 5000 experimental light source spectra.</figref><figref num="6">A diagram showing how energy leakage from the near-spectrum wing widens the FWHM of the etalon fringe, following a simulation of a Lorenz spectrometer with a 0.12pm FWHM band convoluted with an actual light source spectrum, all with the same FWHM bandwidth of 0.11pm. Is.</figref><figref num="7A">Two measured laser spectra with the same 0.11 pmFWHM are shown, with different E95 bandwidth (I) and 0.12 pmFWHM bandwidth convolutions by the Lorenz instrument function, and the fringe width convoluted at various thresholds into two spectra. On the other hand, it is a figure which shows that it is different.</figref><figref num="7B">It is a figure in which the amount of difference such that the difference is a source of a constant offset due to a change in spectral shape and a systematic error with respect to the point slope FWHM model as described in the present application is shown as Δ in (II).</figref><figref num="8A">Of the intensity thresholds X% = 25%, 50%, 75% increased by the embodiments of the present invention using a population of, for example, ~ 5000 sample spectra, which is the same as that used in connection with FIG. It is a figure which shows the improvement of the point slope FWHM estimator model using the fringe width measurement at 25%.</figref><figref num="8B">Of the intensity thresholds X% = 25%, 50%, 75% increased by the embodiments of the present invention using a population of, for example, ~ 5000 sample spectra, which is the same as that used in connection with FIG. It is a figure which shows the improvement of the point slope FWHM estimator model using the fringe width measurement at 50%.</figref><figref num="8C">Of the intensity thresholds X% = 25%, 50%, 75% increased by the embodiments of the present invention using a population of, for example, ~ 5000 sample spectra, which is the same as that used in connection with FIG. It is a figure which shows the improvement of the point slope FWHM estimator model using the fringe width measurement at 75%.</figref><figref num="9">For example, the results of an experiment showing the systematic sensitivity of E95 fringe point slope model estimation to spectral shape variation induced by changes in laser operating conditions, including about 3130 measurement spectra, with gray squares using fringe FW 35% as input. However, the black circroid uses fringe FW 75%, with two or three distinct slopes and three distinct sections appearing, corresponding to different spectral shape subsets of the data.</figref><figref num="10">Group I, normal F with delayed MOPA timing₂Concentration; Group II, normal F₂And normal timing; Group III, Concentrated F₂Also, a normal F with shortened MOPA timing and better control of deviation from parity compared to the point slope model of FIG.₂For a spectral population that shows 3250 spectra from a combination of four separate experiments, such as, with a sigma of 12.1 fm, of which about 4 fm can be explained by the finite signal-to-noise ratio (SNR) of the source spectrum. It is a figure which shows the prediction of E95 using the bandwidth type 2 intensity threshold (FW35% + 75%) model with the inset figure which shows the distribution of the tracking error.</figref>

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