Abstract:
An apparatus ( 295 ) using specular reflection spectroscopy to measure a temperature of a substrate ( 135 ). By reflecting light ( 100 ) from a substrate, the temperature of the substrate can be determined using the band-edge characteristics of the substrate. This in situ apparatus can be used as a feedback control in combination with a variable temperature substrate holder to more accurately control the processing conditions of the substrate. By utilizing a multiplicity of measurement sites, the variation of the temperature across the substrate can also be measured.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
   The present application claims priority to and is related to International Application Ser. No. PCT/US01/27767, filed on Oct. 12, 2001, which claims priority to U.S. Provisional Application Ser. No. 60/239,922, filed on Oct. 13, 2000. The present application is related to U.S. application Ser. No. 10/168,544, filed on Jul. 2, 2003 and U.S. application Ser. No. 10/088,504, filed on Mar. 28, 2002. Each of those applications is incorporated herein by reference in its entirety. 
   BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention is directed to an in-situ method of measuring the temperature of a substrate with a temperature dependent band-gap using band-edge thermometry (BET), and, more specifically, using specular reflection spectroscopy (SRS). 
   2. Discussion of the Background 
   The accurate measurement of semiconductor substrate temperatures during processing is highly desirable for semiconductor substrate processing. In particular, most processes are temperature sensitive, and therefore, accurate temperature measurement is a pre-requisite to the control of optimal conditions for etch and/or deposition chemistry. Moreover, a spatial variation of temperature across a semiconductor substrate can lead to non-uniform processing when either etching or depositing material. 
   There are three geometric modes or configurations of band-edge thermometry (BET) as illustrated in  FIGS. 1A–1D : (1) diffuse reflectance spectroscopy (DRS; see  FIGS. 1A  and  1 B), (2) transmission spectroscopy (TS; see  FIG. 1C ), and (3) specular reflection spectroscopy (SRS; see  FIG. 1D ). 
   In the DRS mode, the light source and detector are on the same side of the substrate with the detector placed in a non-specular position (see Johnson et al., U.S. Pat. Nos. 5,568,978 and 5,388,909 (hereinafter “the &#39;978 and &#39;909 patents” respectively)). A non-specular detector only sees the light that is transmitted through the wafer and that is diffusely back scattered into the solid angle of the detector. In the DRS method, the double-pass transmission of light through the substrate is measured as a function of wavelength or, equivalently, photon energy. As the wavelength increases, the photon energy decreases, and the onset of substrate transparency (or, equivalently, the band-gap energy) occurs as the photon energy becomes less than the band-gap energy. 
   In the TS mode, the onset of substrate transparency is determined by the transmission of light through the substrate as described in U.S. Pat. No. 5,118,200 (hereinafter “the &#39;200 patent”). In this geometry, the light source and the detection system are on opposite sides of the wafer. One difficulty with this approach is that it requires optical access to the chamber at opposite sides of the substrate. However, in comparison to the SRS mode, the TS mode results in an increase in the light intensity received by the optical detector. 
   In the SRS mode, the light source and detector are also on the same side of the substrate. The detector is placed in a specular position where it detects light that is specularly reflected from both surfaces of the wafer (see U.S. Pat. No. 5,322,361 (hereinafter “the &#39;361 patent)). The light that is reflected into the detector without traveling through the wafer contains no temperature information and consequently adds only a relatively constant background signal. The light component that is reflected from the opposite internal surface of the substrate travels back through the wafer and onto the detector. That reflected component, which passes twice though the wafer, contains the useful temperature information. 
   No matter what mode is used, a temperature signature must be extracted from the spectra. In general, three algorithms have commonly been used to extract substrate temperature from band-edge spectra: (1) the spectral position of the maximum of the first derivative or, equivalently, the inflection point, (2) a direct comparison of the spectrum to a predetermined spectral database, and (3) the position of the spectrum knee (i.e., the location of the maximum of the second derivative). The first method has been discussed in the &#39;200 patent. That method determined the substrate temperature as a function of the position of the inflection point of the spectrum in a previous calibration run where the temperature of each spectrum is known. The advantages of that method are that it is simple, fast and independent of the absolute intensity of measurement. The disadvantage is that it is very sensitive to interference effects that may occur at either surface of the processed silicon (Si) wafer. 
   In the second approach, the &#39;361 patent compares a given spectrum to a temperature-dependent database composed of spectra taken at known temperatures. One advantage is that it is reported to work well for Si wafers. A disadvantage is that it is sensitive to interference effects and requires an absolute reflectivity measurement. Accordingly, each wafer may require a separate normalization spectrum. 
   Lastly, the &#39;978 and &#39;909 patents disclose a DRS mode BET, using the position of the spectrum knee as a signature. Its advantage is that it is the closest distinct point to the onset of transparency of a substrate, and is therefore less sensitive to interference effects. A shortcoming of this approach is that it requires sophisticated fitting algorithms that may be too slow for some current applications. 
   In general, a BET system includes three main units, i.e., a light source, a dispersion device and a photo-detector. Currently, there are several commercially available systems; however, none of these systems is fully capable of satisfying the following criteria: 
   1) Non-contact thermometry from the bare backside of Si wafers during front side processing. 
   2) Use of optical methods and quartz rods to couple light in and out of the process chamber. 
   3) Two-dimensional snapshot of wafer temperature. 
   4) Simultaneous samples of several points (approximately 10) on large Si wafers with a response time of 100 msec or less. 
   5) Temperature range of 20 to 300° C. 
   6) Accuracy of temperature measurement to within 2 to 5° C. 
   SUMMARY OF THE INVENTION 
   It is an object of the present invention to provide a non-intrusive method of measuring (1) substrate temperature and (2) spatial variation of the substrate temperature. This measuring process can, in turn, be employed to (1) tune the thermal response of a chamber to a process and (2) concurrently modify temperature characteristics of the chamber in response to temperature measurements performed in-situ throughout that process. 
   Since the band-gap of most semiconductor materials decreases with temperature (linearly above the Debye temperature), the onset of transparency of semiconductor materials gives a precise reproducible measure of substrate temperature. This makes band-edge thermometry (BET) an ideal method for in-situ non-contact measurements of substrate temperature during semiconductor processing. This method is particularly useful for low temperature applications where pyrometry is not effective and in applications where the process has a detrimental effect on in-situ temperature sensors (e.g., thermocouples) or, conversely, where in-situ temperature sensors have a detrimental effect on the process. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     A more complete appreciation of the invention and many of the attendant advantages thereof will become readily apparent to those skilled in the art with reference to the following detailed description, particularly when considered in conjunction with the accompanying drawings, in which: 
       FIG. 1A  is a schematic illustration of a first configuration of an apparatus using diffuse reflectance spectroscopy; 
       FIG. 1B  is a schematic illustration of a second configuration of an apparatus using diffuse reflectance spectroscopy; 
       FIG. 1C  is a schematic illustration of a first configuration of an apparatus using transmission spectroscopy; 
       FIG. 1D  is a schematic illustration of a first configuration of an apparatus using specular reflection spectroscopy; 
       FIG. 2  is an illustration of a prior art inductively coupled plasma (hereinafter ICP) source; 
       FIG. 3  is an illustration of a prior art electrostatically shielded radio frequency (hereinafter ESRF) plasma source; 
       FIG. 4  is a schematic illustration of a first embodiment of a wafer temperature measurement system that uses feedback to control the temperature of a substrate; 
       FIG. 5  is a schematic illustration of a second embodiment of a wafer temperature measurement system that uses feedback to control the temperature of a substrate; 
       FIG. 6  is a schematic illustration of a third embodiment of a wafer temperature measurement system that uses feedback to control the temperature of a substrate; 
       FIG. 7  is a schematic illustration of a fourth embodiment of a wafer temperature measurement system that uses feedback to control the temperature of a substrate; 
       FIG. 8  is a graph showing the normalized specular reflectance of IR radiation from a Si substrate as a function of wavelength with temperature as a parameter; 
       FIG. 9  is a schematic illustration of a wafer including plural measurement sites; and 
       FIG. 10  is a schematic illustration of a computer. 
   

   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   Referring now to the drawings, wherein like reference numerals designate identical or corresponding parts throughout the several views,  FIG. 1D  is a schematic illustration of a first configuration using specular reflection spectroscopy. The following sections describe: (1) the fundamental principles behind the use of specular reflection spectroscopy (SRS); (2) embodiments used for measuring temperature, including a description of the light source(s), a description of the optics, and a description of the detection system; (3) a method for extracting temperature information; (4) the measurement speed; (5) the spectral resolution of the measurement, and (6) the tuning of the thermal characteristics of a substrate. 
   Fundamental Principles 
   The basic theory described herein is based on simulations of the Si band-edge when the absorption cross-section is assumed to be constant over the operating temperature and spectral ranges. Furthermore, the absorption coefficient near the band-edge is assumed to be proportional to the joint density of states of an indirect band-gap material with parabolic bands. Finally, the simulated band-edge reflectance spectra for Si are based on the SRS measurement configuration. 
   Assuming that absorption is proportional to the optical joint density of states and that the energy bands are parabolic, the absorption coefficient is quadratic in energy (for energies above the band-gap (in indirect band-gap materials)). Under those assumptions, the absorption edge for Si is described by:
 
α g =0, for  hv&lt;E   g ,
 
and
 
α g   =A   g ( hv−E   g ) 2 , for  hv≧E   g ,
 
where
 
 E   g   =E   g ( T )= E   g (0)−( aT   2 )/( T+B )
 
is the band-gap energy of Si as a function of temperature (see Thurmond, 1975), T is temperature, hv is the photon energy, and A g  is a constant. Semiconductors are typically never perfectly transparent below the band edge due to absorption caused by free carriers. This absorption is represented by the term:
 
α f =A f T 2 ,
 
where A f  is a constant. The total absorption is given by:
 
α=α g +α f .
 
Finally, for the SRS measurement configuration, the band-edge spectra are given by:
 
 R   T   =R +( R (1 −R   2 ) e   −αd )/(1 −R   2   e   −2αd ),
 
where R is the reflectivity at either wafer surface and d is the wafer thickness.
 
   Band-edge spectra simulations using the above equation for the reflectance that includes the reflections at both surfaces of the substrate (i.e., the values of R T ), are shown in  FIG. 8  for a 40 mil thick silicon wafer. For the purpose of these simulations, the band-gap parameters used are E g (0)=1.12 eV, a=0.000473 eV/K, and B=636 K (see Thurmond, 1975) and the other parameters used are A g =1000 cm −1 eV −2 , A f =0.000004 cm −1 K −2 , and R=0.313. These parameters may vary depending on the type of doping and the doping level of the substrate. In addition, the value of the total reflectance R T  depends upon the wafer thickness. Therefore, accuracy may be improved by providing a separate calibration curve for each doping type and level and for each wafer thickness. However, given a batch of wafers with uniform thickness and doping levels, this measurement technique will have a 1° C. reproducibility between wafers. The simulated spectra shown in  FIG. 8  cover the temperature range from 20° C. to 320° C. The temperature of each spectrum is listed at the right-hand side of the plot, with the lowest temperature corresponding to the left-most spectrum. The temperature increases 50° C. per spectrum moving to the right where the right-most spectrum corresponds to 320° C. Those simulated spectra depict, as a function of wavelength and temperature, the fraction of incident radiation that is reflected from the substrate. Some of the incident light is reflected without having first passed through the substrate; some passes through the substrate, is reflected from the second substrate surface, and then emerges from the substrate at the first substrate surface. Multiple transmissions and reflections must be considered. The useful temperature information is contained in the reflectance curves for reflectances in a corresponding range (e.g., between approximately 0.3 and 0.5). In this range the incident light is both absorbed within the substrate and partially reflected from the substrate surfaces. The absorption is a function of the photon energy or, equivalently, the wavelength of the incident light. For photon energies greater than the band gap energy, the light is absorbed within the substrate to such an extent that any light reflected from the second substrate surface does not emerge from the substrate at the first substrate surface. This condition corresponds to the horizontal portions of the spectra shown in  FIG. 8  for which the reflectance is about 0.3. For photon energies less than the band gap energy, the incident light is not absorbed; the substrate is transparent, and the reflectance is essentially independent of the wavelength. This condition corresponds to the horizontal portions of the spectra shown in  FIG. 8  for which the reflectance is between about 0.4 and 0.5. 
   The reflected light is analyzed by the wavelength sensitive detection system, and from a determination of the wavelength at which the onset of transparency occurs, the substrate temperature may be inferred. 
   The accuracy of the determination of substrate temperature can be improved through the use of additional information. Such additional information includes, but is not limited to: (1) the extent of process chamber use since its most recent cleaning, (2) condition of the wafer surface, (3) wafer type (i.e., p-type or n-type and impurity concentration), (4) the characteristics of any surface coatings on the wafer, and (5) the size of the measurement elements in comparison to the wafer size and the sizes of any features on the wafer. 
   A first embodiment of the present invention is shown in  FIG. 4 . It comprises a radiation source with an emission spectrum that includes at least the range of wavelengths of interest as shown in  FIG. 8 , and a wavelength sensitive detection system utilizing a spectrometer comprising an acousto-optic tunable filter (hereinafter AOTF), and, as shown in  FIG. 4 , a two-dimensional (hereinafter 2-D) photo-detector array (e.g., a 2-D charge-coupled-device (CCD) array or a 2-D charge-injection-device (CID) array). As would be appreciated by one of ordinary skill in the art, the band-gap energy can be determined as a function of temperature from  FIG. 8 . 
   A CID array has two distinct advantages relative to a CCD array for the purposes described herein. Firstly, a CID array is not subject to “blooming,” which may occur when a pixel is saturated and light intensity “spills” over into adjacent pixels. Secondly, pre-selected pixels within the pixel array may be sampled without scanning the entire pixel array. However, CCD arrays are typically faster and more sensitive than their CID counterparts. CID arrays may have a maximum pixel interrogation frequency of about 100 kHz (with zero gain). As the interrogation frequency decreases, the gain increases. For example, a gain of about 50 is attainable for an interrogation frequency of about 33 kHz. However, CCD arrays may be used at frequencies as high as about 100 kHz. 
   One advantage of the present invention is due to the use of an AOTF to replace mechanically rotated grating/single detector methods. In doing so, superior speed can be achieved over traditional methods while obtaining a 2-D representation of the temperature distribution across a substrate. 
   Furthermore, high speed extraction of temperature information from band-gap spectra is attainable using a method that utilizes digital filters based upon a higher-order derivative of the spectrum. The method presented herein can reduce the time necessary for temperature extraction and minimize interference effects that are inherent to prior temperature extraction methods. 
   A first embodiment of the system of the present invention is illustrated in  FIG. 4 . For clarity, only two measurement sites are shown in  FIG. 4 , but a plurality of measurement sites (e.g., 10) is possible. An optical system  295  views the light reflected from a plurality of sites on a substrate being processed. In the illustrated embodiment, the light reflected from the plurality of measurement sites is transmitted by means of optical fibers  199 B through fiber optic vacuum feedthroughs  195 A and  195 B located in an upper surface of the process chamber in an ICP or ESRF plasma processor. Other locations are possible and may indeed be preferable. In particular, it would be advantageous for the optical fibers to enter and leave the vacuum chamber below the plane of the wafer to lessen the likelihood of particulate contamination of the wafer. The ICP and ESRF plasma processors include at least one induction coil  129 , which establishes the plasma  196 , Moreover, an ESRF processor includes an electrostatic shield  128  as well. Ideally the axis of the optical system coincides with the axis of either the substrate or the wafer chuck. 
   The optical system  295  of  FIG. 4  includes: (a) a band-pass filter  127  that passes (preferably with minimal attenuation) signals at all wavelengths within a selected range (e.g., between 1.00 and 1.35 μm) and, preferably, significantly attenuates signals at all wavelengths outside that range; and (b) a neutral density filter or a mechanical iris  200 , either of which may be electrically controlled, that permits uniform adjustment of the intensity of those signals at wavelengths within the range transmitted by the band-pass filter  127 ; and (c) a lens system  110 B (e.g, including multiple elements) having a field of view encompassing all of the optical fibers  199 C, transmitting reflected light from the plurality of measurement sites; and (d) a 2-D detection array  145  (e.g., a CCD array or a CID array) on which the IR-transmitting lens system  110 B forms an image of the wafer  135 , by means of the IR radiation reflected from the wafer  135  at the multiplicity of measurement sites (e.g., as illustrated in  FIG. 9 ). 
   The band-pass filter  127  improves the signal-to-noise ratio (hereinafter “S/N ratio”) of the measurement system by reducing to acceptable levels the effect of radiation at wavelengths outside a region of interest (e.g., outside of a region between 1.00 and 1.35 μm) on the detection array  145 . The neutral density filter or mechanical iris  200  provides the ability to reduce the intensity of the IR radiation with wavelengths within the region of interest, that impinges on the 2-D detection array  145  to prevent saturation of elements of the 2-D detection array  145 . In this way, erroneous data due to the saturation of individual elements of the 2-D detection array  145  is ameliorated. 
   The measurement system according to the present invention uses the SRS mode arrangement generally shown in  FIG. 1D . A schematic representation of one embodiment of the present invention is shown in  FIG. 4 . It includes a broad spectrum light source  100 , an acousto-optical tunable filter (hereinafter AOTF)  140 , the wavelength sensitive optical system  295  described above, and a lock-in amplifier  150 . 
   A broad spectrum light source  100  (e.g., a tungsten-halogen light source or an array of IR light emitting diodes (hereinafter “LEDs”)) emits IR radiation that is focused by lens  110 A (either a single-or multi-element lens) onto the entrance aperture of collimator  111 . The radiation passing through collimator  111  is periodically chopped (i.e., interrupted) by the mechanical chopper  105  driven by the motor  155 . The radiation that passes through the mechanical chopper  105  impinges on the input aperture of the AOTF  140 , which is driven by the radio frequency (hereinafter “RF”) driver  141 . The frequency of the signal from the RF driver  141  determines the narrow band of frequencies that will pass through the AOTF  140 . An exemplary AOTF  140  selects signals having wavelengths within the range from about 1.00 μm to about 1.35 μm with a response time of approximately 5 μsec, but other ranges and response times are possible. The angle at which the radiation with the selected wavelength leaves the AOTF  140  depends, in general, on the wavelength. However, it is advantageous for all IR radiation that leaves the AOTF  140  to travel in the same direction when it enters reaction chamber  125  through IR-transmitting vacuum window  120 . To achieve this end, the prism  184  is included in the optical path between the AOTF  140  and the IR-transmitting vacuum window  120 . 
   In one embodiment, the IR radiation passes through IR-transmitting vacuum window  120  and impinges upon optical beam splitter  130 , which divides the IR radiation into plural parts (either equal or dissimilar), the number of parts being determined by the number of measurement sites on the wafer  135  at which the temperature is to be determined. In an alternate embodiment, in which only one measurement site is used, the optical beam splitter  130  is omitted.  FIG. 4  shows a division into only two equal parts for simplicity, but a division into many (e.g., ≧10) equal parts is possible. The IR-transmitting vacuum window  120  maintains the vacuum integrity of the reaction chamber  125 . Some of the IR radiation passes through optical fibers  199 A through the wafer chuck  182  to the underside of the wafer  135 , is reflected from the wafer  135  and transmitted through optical fibers  199 B and fiber optic feedthroughs  195 A and  195 B and optical fibers  199 C to the wavelength sensitive optical system  295 . The optical vacuum feedthroughs  195 A and  195 B are shown in the upper surface of the process chamber, but other locations are possible and may, indeed, be preferable. In particular, it would be advantageous for the optical fibers to enter and leave the vacuum chamber below the plane of the wafer to lessen the likelihood of particulate contamination of the wafer. 
   In  FIG. 5 , a second embodiment in which the plasma  196  is established within an ICP or an ESRF plasma processor, the IR radiation passes through vacuum window  120  and impinges upon optical beam splitter  130 , which divides the IR radiation into at least two parts (e.g., 10 parts, where the number of parts is determined by the number of sites on wafer  135  at which the temperature is to be determined). Vacuum window  120  maintains the vacuum integrity of reaction chamber  125 . Optical fibers  199 A conduct IR radiation through wafer chuck  182  to the under side of each of the at least two sites on wafer  135  at which the temperature is to be determined. Some of the IR radiation reflected from the underside of the wafer  135  is collected by optical fibers  199 B and is conducted by them to optical vacuum feedthroughs  195 A and  195 B, optical filters  173 B and  173 D, lenses  110 B and  110 C, and filters  173 A and  173 C, which focus the IR radiation onto photodiodes  187 A and  187 B, respectively. In an alternative embodiment, filters  173 A and  173 C are omitted. In yet another alternate embodiment, filters  173 A and  173 C are used but filters  173 B and  173 D are omitted. In a further alternate embodiment, filters  173 A,  173 B,  173 C and  173 D are omitted. The amount of radiation coupled to the photodiodes  187 A and  187 B, thus is controlled to prevent saturation of the detector (or array as described below). The filters pass all wavelengths in a desired range (e.g., between 1.00 μm and 1.35 μm) and as nearly as possible significantly attenuate all wavelengths outside the desired range. In an embodiment in which those filters do not prevent saturation of the detectors, a suitable neutral density filter (e.g., an electrically controlled neutral density filter) is included with each band-pass filter. Filters of the types described herein are well known to persons of ordinary skill in the art. In a further alternate embodiment, neutral density filters can be replaced by a mechanical iris for limiting the amount of light passing therethrough. 
   Optical vacuum feedthroughs  195 A and  195 B maintain the vacuum integrity of reaction chamber  125 . The optical vacuum feedthroughs  195 A and  195 B are shown in the upper surface of the process chamber, but other locations are possible and may, indeed, be preferable. In particular, it would be advantageous for the optical fibers to enter and leave the vacuum chamber below the plane of the wafer to lessen the likelihood of particulate contamination of the wafer. In an embodiment in which focusing lenses are included in the packaged photodiodes, separate lenses  110 B and  110 C are omitted. The output of each of photodiodes  187 A and  187 B is selected sequentially by interrogator  190  according to a protocol provided by computer  160  and is conveyed to lock-in amplifier  150 . If a lock-in amplifier with a sufficient number of input channels is used, interrogator  190  is not necessary. The output signal from lock-in amplifier  150  is sent to computer  160 , which stores the data for each of photodiodes  187 A and  187 B. After output data for photodiodes  187 A and  187 B have been stored in computer  160 , computer  160  sends a signal to RF driver  141  for acousto-optical filter  140  and the RF drive frequency applied to acousto-optical filter by RF driver  141  is changed to another frequency (e.g., the second of ten pre-selected frequencies). When computer  160  has received data for diodes  187 A and  187 B corresponding to all pre-selected frequencies, it uses a program stored in its memory to calculate the temperature at the wafer site corresponding to photodiode  187 A and at the wafer site corresponding to photodiode  187 B. Such temperature measurements can be recorded in volatile or non-volatile storage. 
   A third embodiment of the feedback system of the present invention, suitable for use with a capacitively-coupled plasma processor, is shown in  FIG. 6 . In this embodiment, the plasma  196  is excited by means of the RF drive electrode  185  which may have mounted on its surface proximate to the plasma the silicon facing  183 . In at least one embodiment of the present invention, the upper and/or lower electrode may be movable. One such embodiment uses a vertically translatable chuck or lower electrode. The IR radiation passes through vacuum window  120  and impinges upon optical beam splitter  130 , which divides the IR radiation into at least two parts (e.g., 10 parts, where the number of parts is determined by the number of sites on wafer  135  at which the temperature is to be determined). As in the embodiment of  FIG. 4 , optical fibers  199 A conduct IR radiation through wafer chuck  182  to the under side of each of the at least two sites on wafer  135  at which the temperature is to be determined. As in the embodiment of  FIG. 4 , optical fibers  199 B conduct the IR radiation reflected from the substrate  135  to the optical vacuum feedthroughs  195 A and  195 B, to lens  110 D, and through filters  127  and  200  which focus the radiation on charge-coupled-device (CCD) array or charge-injection-device (CID) array  145  which may be either a linear array or a two-dimensional array. The optical vacuum feedthroughs  195 A and  195 B are shown in the upper surface of the process chamber, but other locations are possible and may, indeed, be preferable. In particular, it would be advantageous for the optical fibers to enter and leave the vacuum chamber below the plane of the wafer to lessen the likelihood of particulate contamination of the wafer. The output of each element of CCD or CID array  145  is selected sequentially by interrogator  190  according to a protocol provided by computer  160  and is conveyed to lock-in amplifier  150 . The filters  127  and  200  should pass all wavelengths between 1.00 μm and 1.35 μm and as nearly as possible completely attenuate all wavelengths outside this range. If the filter does not prevent saturation of the CCD or CID array, it may be necessary to include with the band-pass filter a suitable neutral density filter. An electrically controlled neutral density filter may be used. Filters of the types described herein are known to persons of ordinary skill in the art. 
   In  FIG. 7 , a fourth embodiment which is suitable for a capacitively-coupled plasma processor is shown. Except as noted here, the fourth embodiment is the same as the third embodiment. The plasma  196  is excited by means of the RF drive electrode  185  which may have mounted on its surface proximate to the plasma the silicon facing  183 . The IR radiation passes through vacuum window  120  and impinges upon optical beam splitter  130 , which divides the IR radiation into at least two parts (e.g., 10 parts, where the number of parts is determined by the number of sites on wafer  135  at which the temperature is to be determined). Vacuum window  120  maintains the vacuum integrity of reaction chamber  125 . As in the embodiment of  FIG. 5 , optical fibers  199 A conduct IR radiation through wafer chuck  182  to the under side of each of the at least two sites on wafer  135  at which the temperature is to be determined. Some of the IR radiation reflected from the underside of the wafer  135  is collected by optical fibers  199 B and is conducted by them to optical vacuum feedthroughs  195 A and  195 B, optical filters  173 B and  173 D, lenses  110 B and  110 C, and filters  173 A and  173 C, which focus the IR radiation onto photodiodes  187 A and  187 B, respectively. Filters may be selectively omitted as discussed with reference to  FIG. 5 , to prevent saturation of the detector or array. Similarly, optical vacuum feedthroughs can be used as discussed with reference to  FIG. 5 . In a further alternate embodiment, neutral density filters can be replaced by a mechanical iris for limiting the amount of light passing therethrough. 
   It will be apparent to a person of normal skill in the art that the invention described herein is also suitable for use with a plasma processor that employs both inductive and capacitive coupling means to excite the plasma. For example, an inductance coil  129  and an electrostatic shield may be incorporated into the embodiments of  FIGS. 6 and 7 . Moreover, the invention described herein is also suitable for use with other plasma generation means such as Helicon wave, electron cyclotron resonance (ECR), etc. 
   All of the embodiments described herein may also be realized using an AOTF having integral fiber optic input and output pigtails. When an AOTF of this type is used, some modifications of the optical elements proximate to the AOTF  140  shown in  FIGS. 4 ,  5 ,  6 , or  7  are required. For example, in the embodiment shown in  FIG. 5 , fiber collimators/focusers like the SMA  905  or SMA  906  manufactured by OZ Optics, Ltd. might be used advantageously with a pigtailed AOTF in conjunction with or in place of collimator  111  and prism  184 . Such modifications would be understood by a person of ordinary skill in the art and are, of course, consistent with the spirit of this invention. 
   The measurement procedure begins when the equipment operator enters a start command by means of the input terminal (e.g., keyboard  422  or mouse  424 ) of the computer  160 . RF driver  141  then sends to AOTF  140  a signal that selects the first narrow band of IR wavelengths for passage through the wafer  135 . The output of each element of the 2-D detection array  145  is selected sequentially or in parallel by the interrogator  190  according to a protocol provided by the computer  160  and is conveyed to the lock-in amplifier  150  and thereafter to the computer  160 , which stores the data for each element of the 2-D detector array  145 . (If a lock-in amplifier with a sufficient number of input channels is used, the interrogator  190  is not necessary.) After output data for each element of the 2-D detection array  145  have been stored in the computer  160 , the computer  160  sends a signal to the RF driver  141  for the AOTF  140  and the RF drive frequency applied to the AOTF  140  by the RF driver  141  is changed to another of, perhaps, ten pre-selected values. The computer  160 , having received data for all elements of the 2-D detector array  145  corresponding to all of the pre-selected frequencies, calculates the temperatures at the wafer sites corresponding to the respective elements of the 2-D detection array  145 . After calculating the temperature, the computer  160  regulates the temperature distribution. The computer may direct the wafer chuck heater controller  180 A to adjust the power delivered to the multi-element substrate heater  181 A to cause the substrate temperature to become either more or less uniform. The computer  160  may also direct the wafer chuck cooler controller  180 B to adjust the multi-element substrate cooler  181 B to cause the substrate temperature to become more or less uniform. To regulate cooling, the multiple element substrate cooler  181 B within the wafer chuck includes plural channels through which the flow of a coolant is controlled by the wafer chuck cooler controller  180 B. In an alternate embodiment, an array of thermoelectric coolers are embedded in the chuck. 
   Although the above discussion has assumed a spectral resolution of 30 nm, it is possible to obtain a spectral resolution of 3 nm if the measurement speed (i.e., the interrogation or sampling frequency) is reduced by an order of magnitude. This reduction in measurement speed produces system response times of 20 msec to 1 sec depending upon the light source (and the modulation frequency for lock-in detection). In general, the S/N ratio is greater when using the SRS mode rather than the DRS mode (in particular, for silicon wafer temperature measurement). However, in the event that the S/N ratio is low, it can be improved by using the lock-in amplifier  150 . The light source is modulated (e.g., using a mechanical chopper which communicates with the computer  160 ) and the resultant signal is amplified by the lock-in amplifier  150 . In this manner, the signal can be extracted from the noise by observing the response occurring at the frequency determined by the chopper  105 . However, the speed of the measurement becomes limited by the frequency of the mechanical chopper  105  (coupled to the broadband light source  100 ) and the subsequent lock-in amplifier  150 . 
   In an alternate embodiment, the broad spectrum light source  100  shown in  FIG. 4  includes plural infrared (IR) LEDs, because they are capable of responding to significantly higher modulation frequencies. For that reason, they can greatly improve the measurement speed. Accordingly, any other IR light source compatible with a high modulation frequency and having a broad spectrum output may also be used. 
   In still another embodiment, light source  100  in  FIG. 4  is replaced by an array comprising on the order of ten laser diodes (e.g., InGa x P 1-x  laser diodes with different values of the parameter x), each of which emits IR radiation over a very narrow range of wavelengths. The wavelength emitted by the nth laser diode is approximately given by λ(n)=1.00+(0.04)n μm where n is an integer with a value between 0 and approximately 9, but other relationships between the emitted wavelengths are possible. Consequently, the ten laser diodes provide ten approximately equally separated wavelengths that span the range of wavelengths of interest for this application (approximately 1.00 to 1.35 μm); so the AOTF  140 , RF driver  141 , and prism  184  are not necessary. However, RF driver  141  is replaced in this embodiment by a multi-output diode controller that sequentially causes one (and only one) of the approximately ten laser diodes to emit IR radiation. 
   Lastly, the high speed measurement (update time&lt;100 msec) of substrate temperature at a multiplicity of pre-arranged spatial locations on the substrate enables the chamber thermal characteristics to be optimized at the substrate. Moreover, with this rapid temporal response, it is possible to adjust the spatial distribution of the substrate temperature as the wafer is being processed. 
   Only a fraction of the light at each wavelength is passed through the substrate and reflected from the second substrate surface, whereupon it is received by the analyzer (e.g., a spectrometer). The AOTF  140  is capable of rapidly tuning the pass-band wavelength across the pre-selected spectral range (e.g., from approximately 1.00 μm to 1.35 μm). For each wavelength in the scan sequence the reflected light intensity is recorded using the 2-D detection array  145  shown in  FIG. 4 . The temperature at each measurement site on the substrate  135  is then obtained from the reflection spectrum using any of several known techniques to obtain a pre-determined calibration curve. 
   As already described, the system uses a broad band light source  100  (e.g., (1) a tungsten-halogen stabilized light source, or (2) an array of IR LEDs, or (3) an array of laser diodes). Due to the physical size of a conventional lamp filament, the coupling efficiency of the light into the AOTF  140  is low. Furthermore, if there are n measurement sites, only 1/n of the light intercepted by the AOTF  140  is coupled to the optical fibers  199 A for each measurement site. Therefore, the lock-in amplifier  150  is generally required. When using a tungsten-halogen stabilized lamp, the light source is modulated at 1 to 2 kHz using the mechanical chopper  105 . Lock-in detection is used to remove the incoherent signal (i.e., noise) due to any ambient background light that may impinge on the 2-D detection array  145  shown in  FIG. 4 . An advantage to using the tungsten-halogen stabilized light source is its relatively low cost, and its ability to provide a continuous spectrum across the spectral range of interest, (e.g., 1.00 μm to 1.35 μm). However, as stated, the tungsten-halogen lamp is less efficient in coupling light to the optical fibers  199 A than some other sources (e.g., laser diodes). 
   An important part of a lock-in amplifier is a low-pass filter, which may be characterized either by its upper half-power frequency (i.e., −3 dB frequency) or its time constant. The time constant is ½ πf c , where f c  is the −3 dB or cutoff frequency of the filter. Traditionally, the low-pass filters of lock-in amplifiers have been characterized by their time constant. (The concept of a time-constant is relevant here, because the output of the lock-in amplifier will be relatively time-independent.) The time-constant reflects how slowly the output responds to a change in the input, and, consequently, the degree of smoothing. A greater time-constant causes the output signal to be less affected by spurious causes and, therefore, to be more reliable. Hence, a trade-off must be considered because real changes in the input signal take many time constants to be reflected at the output. This is because a single-section RC filter requires about 5 time constants to settle to its final value. It is obvious that faster measurements require shorter time-constants and, therefore higher cutoff frequencies for the filters. Therefore, the conventional chopper at a chopping frequency of approximately 1 kHz provides a response time of approximately 5 msec for each wavelength increment at each measurement site. Hence, such a mechanical chopper-based design is a suitable for measurement of the substrate temperature every 50 msec for each selected band of IR wavelengths. (This result assumes measurements at ten sites and that the data extraction algorithm requires approximately 0.01 msec per measurement.). Therefore, for ten measurement sites and ten wavelength increments, approximately 500 msec is required for a complete scan of the substrate. An alternate embodiment obtains the data for all measurement sites and all wavelength increments according to other protocols. 
   Due to limitations imposed by the mechanical chopper  105 , the modulation frequency is constrained to values much lower than those attainable with LEDs. LEDs, operating in the range of wavelengths between 1.00 μm and 1.35 μm, typically have a spectral bandwidth of 10 to 30 nm. Therefore, approximately 9 to 10 LEDs will be necessary to span the wavelengths of interest. For improved S/N ratio, lock-in detection can be used wherein LEDs may be modulated at up to 200 MHz (a significant improvement over the combination of the mechanical chopper  105  and the tungsten-halogen broad band light source). Hence, the LEDs can solve many of the issues related to speed and light coupling. Although LEDs have considerably less total optical power than a typical tungsten-halogen light source, their power output in the portion of the spectrum of interest here is comparable. One additional advantage to using LEDs is that a separate LED per optical port (or channel) may be used to improve the S/N ratio. A disadvantage of using LEDs is their potentially reduced stability and cost. Either way, the background light source spectrum will be recorded as the reference spectrum at each measurement interval and each measurement site. 
   Use of a modulation frequency of approximately 100 kHz can provide a response time for each measurement on the order of 0.05 msec, which corresponds to about 0.06 msec per measurement when the data acquisition time is included. Hence, it is possible to obtain a total measurement response time of approximately 6 msec for ten wavelength increments and ten measurement sites. 
   In an alternate embodiment, plural parallel processors are used to acquire data from each element or detector simultaneously, hence reducing the measurement speed by a factor approximately equivalent to the number of measurement sites. 
   Method for Extracting Temperature Information 
   An important part of any technology relating to band-gap thermometry is the method of extracting temperature from the spectra. The present invention utilizes a digital filter that is based upon a higher-order derivative of the spectrum. Other means of extraction (e.g., a method based on wavelet transforms) may be possible. The primary advantage of the digital filter is its speed. This is important for achieving the 10 to 100 msec update times for fine-grain control. Current band-edge thermometry technology updates temperature on the order of once per second, in which case the computational speed of current personal computers is not an issue. The present invention, however, increases the measurement frequency by at least a factor of ten, without approaching the computational limits of those computers. 
   By providing accurate measurements, the system can use the substrate&#39;s temperature as a feedback in a control loop. Thus, the present invention provides a method to control the temperature distribution on a substrate during processing. In conjunction with the system described in the co-pending patent application entitled “Multi-zone resistance heater, U.S. Ser. No. 60/156,595” the contents of which are incorporated herein by reference, the multi-site temperature measurement system can provide an improved feedback control of substrate temperature. In that combination, the control signal is used to adjust the heating and/or cooling of individual zones (or sectors) pre-designed within the chuck (or substrate holder). Due to the speed of the measurement system (&lt;100 msec) relative to the thermal response to heating/cooling adjustments (˜1–2 seconds), information obtained from successive temperature measurements (e.g., rate of change or first derivative of the temperature with respect to time) can provide information to the design of a robust control algorithm. 
   A computer system  160  shown in  FIG. 10  monitors the temperature and signals any combination of heating and/or cooling zones to increase or decrease the current heat flux. In particular, the power to each heating or cooling element and/or the coolant flow rate can be adjusted to provide for the designated heat flux either into or out of an individual zone. The computer  160  of  FIG. 10  implements the method of the present invention, wherein the computer housing  402  houses a motherboard  404  which contains a CPU  406 , memory  408  (e.g., DRAM, ROM, EPROM, EEPROM, SRAM, SDRAM, and Flash RAM), and other optional special purpose logic devices (e.g., ASICs) or configurable logic devices (e.g., GAL and re-programmable FPGA). The computer  160  also includes plural input devices, (e.g., a keyboard  422  and mouse  424 ), and a display card  410  for controlling monitor  420 . In addition, the computer system  160  further includes a floppy disk drive  414 ; other removable media devices (e.g., compact disc  419 , tape, and removable magneto-optical media (not shown)); and a hard disk  412 , or other fixed, high density media drives, connected using an appropriate device bus (e.g., a SCSI bus, an Enhanced IDE bus, or a Ultra DMA bus). Also connected to the same device bus or another device bus, the computer  160  may additionally include a compact disc reader  418 , a compact disc reader/writer unit (not shown) or a compact disc jukebox (not shown). Although compact disc  419  is shown in a CD caddy, the compact disc  419  can be inserted directly into CD-ROM drives which do not require caddies. In addition, a printer (not shown) also provides printed listings of the temperature of the substrate, in one or more dimensions over time. 
   As stated above, the system includes at least one computer readable medium. Examples of computer readable media are compact discs  419 , hard disks  412 , floppy disks, tape, magneto-optical disks, PROMs (EPROM, EEPROM, Flash EPROM), DRAM, SRAM, SDRAM, etc. Stored on any one or on a combination of computer readable media, the present invention includes software for controlling both the hardware of the computer  160  and for enabling the computer  160  to interact with a human user. Such software may include, but is not limited to, device drivers, operating systems and user applications, such as development tools. Such computer readable media further include the computer program product of the present invention for measuring the temperature of a substrate. The computer code devices of the present invention can be any interpreted or executable code mechanism, including but not limited to scripts, interpreters, dynamic link libraries, Java classes, and complete executable programs. 
   Obviously, numerous modifications and variations of the present invention are possible in light of the above teachings. It is therefore to be understood that, within the scope of the appended claims, the invention may be practiced otherwise than as specifically described herein.