Abstract:
A metrology system and method for measuring the thickness of thin-films of semiconductor wafer. This system and method analyze x-ray reflectivity data to determine transmission characteristics of thin-film layers. Based on these transmission characteristics the thickness of the thin-layer can be determined. Unlike some prior systems and methods, the system and method herein does not determine the thickness of the thin-film layer based on a fringe pattern in reflectivity for the thin-film layer. The fact that the system and method herein does not rely the fringe pattern is particularly advantageous in situations where the thin-film layer is of thickness which makes it very difficult to resolve the fringe pattern in the reflectivity data.

Description:
RELATED APPLICATION 
     The present application claims the benefit of U.S. Provisional Application Serial No. 60/323,255, filed Sep. 19, 2001, titled X-RAY REFLECTOMETRY MEASUREMENT OF LOW DENSITY FILMS which is incorporated herein by reference. 
    
    
     TECHNICAL FIELD 
     The present invention relates to the field of measurement of materials used in the fabrication of semiconductor devices. Specifically, the present invention pertains to using transmission characteristics of thin-film layers disposed on a substrate to determine the thickness of the thin-film layer. 
     BACKGROUND 
     Semiconductor wafers typically include thin-films formed on semiconductor substrates. There is a need to be able to measure and analyze characteristics of these films. Previous systems have provided a way to analyze the thickness and density of thin-films disposed on semiconductor substrates using X-ray reflectometry (XRR). For example, U.S. Pat. No. 5,619,548 and PCT Publication W01/71325 A2 (referred to herein as the &#39;325 application) discuss different aspects of XRR systems and are hereby incorporated by reference. 
     XRR systems of the prior art make use of the fact that x-rays reflected off of a thin-film disposed on a substrate are detected as having different characteristics depending on the x-ray&#39;s angle of reflection relative to the surface of the structure. FIG. 1 shows a view of a prior art XRR system for simultaneous measurements of the reflectivity over a range of angles. As shown in FIG. 1 a source  100  generates an x-ray beam  101  that is incident upon an x-ray reflector  102 , which is typically a monochromator. X-rays are then focused upon the sample being evaluated  106  which is positioned on a supporting stage  104 . X-rays incident upon the sample are reflected and then detected with a position-sensitive detector  108  (such as a photodiode array). 
     Reflected x-rays  110  are captured in the top half of the detector  108 , while the incident beam  112  can be measured by lowering the stage and reading the bottom half of the detector. By properly normalizing the two profiles (as described in the &#39;325 application) one can determine the reflectivity as a function of angle. Signals are generated by the detector  108 , and the information contained in these signals is then used by the processor system  114  to analyze the reflectivity characteristics of the sample  106 . The processor system  114  can then generate a display  116  to convey information about the sample  106  to user. 
     FIG. 2 shows a typical plot of angle-resolved XRR data, in a graph form which could be generated by the processor system  114 . This type of graph depicts the efficiency with which monochromatic x rays are reflected from a sample, and this type of information can characterize the reflectivity of a thin-film disposed on a substrate. Specifically, FIG. 2 shows a graph for reflectivity of x-rays incident on a 358 Å cobalt thin film, on a substrate taken at 6.4 keV. The reflectivity signal shows a fringe pattern having peaks  206 , and these peaks correlate to different reflection angles. It will be readily appreciated by one skilled in the art that as the thickness of the film increases the difference in the reflection angle between the peaks will decrease. For thin-films of sufficient thickness, prior systems may not be able to accurately resolve the fringe pattern, and as a result it may be difficult or impossible to determine the thickness of the thin-film. One approach for dealing with this problem is to modify the resolution of the system, but in general there is a limit to how much the resolution of the system can be increased, and further increasing the resolution of the system results in an increase in the amount of time it takes to make a measurement. (Aspects of one approach to varying the resolution of the system are disclosed in co-pending commonly assigned patent application Ser. No. 10/053,373 entitled X-RAY REFLECTANCE MEASUREMENT SYSTEM WITH ADJUSTABLE RESOLUTION, filed Oct. 24, 2001, which is incorporated herein by reference.) 
     One example of a semiconductor wafer structure where prior art XRR techniques are often unable to accurately determine the characteristics of a thin-film, is where a thin-film of porous SiO 2  is formed on a second film, or material, which is composed of a material which is denser than SiO 2 . Using previous systems and methods it was often difficult, or impossible to accurately determine the thickness of the porous SiO 2  material, because in many applications the SiO 2  layer is thick enough that it produces a very narrow fringe pattern which is beyond the resolution of the system. What is needed is a system and method for accurately determining the thickness of a thin film layer where the thin film layer is such that it produces an fringe pattern that is cannot be accurately resolved using standard XRR systems. 
     SUMMARY 
     Prior XRR systems utilize fringe patterns in reflectivity data to determine the thickness of a thin-film layer. In general terms, the fringe pattern is caused by the interference of x-rays reflected at the several density interfaces present in a thin-film structure, such as for a thin-film layer on a substrate. Changes in the thickness of the thin-film layer will result in changes in fringe pattern. 
     In contrast with prior methods which focus on using the reflectivity information to determine a fringe pattern and then use this information to determine the thickness of the thin-film, the present method and system use reflectivity information to determine transmission characteristics of the thin-film layer. The transmission characteristics are then used to determine the thickness of the thin-film. A system and method which evaluates the transmission characteristics of the thin-film, as disclosed herein, can be used to determine the thickness of the thin-film structures which could not be determined using many prior systems which utilized fringe pattern analysis. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 shows an XRR system of the prior art. 
     FIG. 2 is a graph showing the fringe profile for a thin film sample. 
     FIG. 3 is a graph showing the fringe profile for a thin film sample, where the thickness of the thin-film sample is such that the fringe pattern cannot be resolved using prior art techniques. 
     FIG. 4 shows a cross section of a sample being analyzed. 
    
    
     DETAILED DESCRIPTION 
     The system and method herein uses absorption characteristics of a thin-film to provide an analysis of XRR data that allows for the thickness·density product (ρ·T), and thereby thickness information, of certain low-density thin films to be deduced from angle-resolved x-ray reflectometry (XRR) data. The method is applicable to low-density thin-films deposited on substrates, or additional thin-films, of a higher density. 
     Commercially important structures having these characteristics include a porous silicon dioxide SiO 2  interlayer dielectric deposited on silicon; and barium strontium titanate (BST) deposited on platinum; and silicon deposited on silicon-germanium alloy. 
     FIG. 2 shows XRR data which is utilized in prior systems. The locations of interference fringes  206  are used to deduce the thickness of a film. The rapid decrease of the efficiency of the reflection occurs at a “critical angle”  204 . The critical angle is used to deduce the density of the film. For angles below the critical angle, the sample is nearly totally reflective for x rays. Above the critical angle, the rays penetrate into the film to some extent, and the reflectivity decreases. The value of critical angle scales with the density of the film, so that a low-density film will have a lower critical angle, and a higher density film, will have a higher critical angle. As will be seen below the method and system discussed herein takes advantage of the fact that the critical angle scales with the density of the film. 
     FIG. 3 shows XRR data for a different sample consisting of a thick porous SiO 2  film, sometimes referred to as Xerogel, deposited on a silicon substrate  302 , and XRR data for a bare silicon substrate  304  is shown for comparison. The invention herein makes use of the fact that important information can be obtained by analyzing the reflectivity data presented in FIG. 3, and in similar graphs where a low-density film is deposited on top of a denser substrate or a denser thin-film. As shown in FIG. 3 there are two critical angles  306  and  308 : where  306  corresponds to the critical angle for the SiO 2  layer, and  308  corresponds to the critical angle for the bare silicon. As discussed above, based on these critical angles the densities for the materials can be determined. In region A, below the critical angle  306  for SiO 2 , the x-ray beam is nearly totally reflected. In region B, between the two critical angles  306  and  308 , x-rays penetrate through the top film SiO 2 , and reflect off of the substrate or bottom film, and re-emerge as an externally observable signal that is received by a detector  108  as shown in FIG.  1 . In region C, above the substrate or bottom film critical angle  308 , the reflectivity of the substrate decreases rapidly. In the data shown in FIG. 3, the SiO 2  film is too thick to produce resolvable interference fringes, and thus the SiO 2  film&#39;s thickness cannot be deduced using prior XRR data analysis. As one skilled in the art will appreciate, however, the density can be determined from the location of the critical angle (at approximately 0.1°) to be about 0.3 grams/cc. 
     The invention uses information in the region between the two critical angles  306  and  308  (defined as region B above) to determine the thickness-density product of the low-density SiO 2  film, in a manner very different than the prior XRR data analysis methods. This analysis recognizes that if the substrate were left uncoated, then the observed reflectivity would have a value near unity in region B (i.e. the curve  302  would be the same as curve  304 ) and that the reflectivity is reduced below unity as a result of the absorption of x-rays in the low-density SiO 2  film. Essentially, the low-density film functions as an x-ray filter that attenuates the x-ray beam twice, once as it propagates down to the substrate and again as it is reflected by the substrate. This effect is shown graphically in FIG. 4, where the incident x-ray beam  406  penetrates into the SiO 2  layer  402  and travels through the layer  402  until it is incident with the layer  404  which is denser, and hence has a higher critical angle. Due to the fact that the layer  404  has a higher critical angle it will continue to reflect the x-rays until they reach the higher critical angle of the layer  404 . Thus, the reflected x-ray will be travel back through the SiO 2  layer  402  and be detected by the detector. As the angle of incidence with the surface of the film increases, the distance which the x-ray travels through the film is reduced which results in the reflected signal increasing in strength as the angle of incidence increases. This increase in strength is directly related to the fact that the distance which the x-ray  406  travels through the SiO 2  layer  402  is determined by the equation: 
     
       
         Distance x-ray travel in layer 402=(2 T )/sin Θ; 
       
     
     where T is the thickness of the layer  402 , and Θ is the angle of incidence of the x-ray  406  with the layer  404 . The fact that the reflectivity increases as the angle increases in the region B, is reflected in FIG.  3 . Specifically, the strength of the reflected x-rays increases in Region B as the reflection angle increases. Once the critical angle of the material  404  is reached than the reflectivity begins to rapidly decrease as the x-ray begins to penetrate into layer  404 . 
     This attenuation in region B can be modeled by the Lambert-Beers transmission law: I/I 0 =exp(−2μ/ρ·ρT/sin θ) to yield a calculation, independent of a fringe pattern analysis, of the thickness-density product, ρ·T of the layer of SiO 2    402 . Specifically, to solve for T (the thickness) one would take the natural log of the above equation, thereby reducing it to a linear equation. The reflectivity data for region B would then be used in connection with the resulting linear equation: In (I/I 0 )=−2 μ/ρ·ρT/sin θ, to determine a value for T. As one of skill the art would appreciate a least squares fitting algorithm can be used in conjunction with the linear equation and the reflectivity data to determine a value for the thickness T. Further, it may be desirable to use a theoretical model of the sample and to calculate its response to the incident x-rays. The result can be compared to the measured data using a curve fitting minimization algorithm to determine a value for T.    
     Use of the Lambert-Beers transmission law is in contrast with conventional XRR data analysis, which is based on the Fresnel equations where sin 2  Θ n =sin 2 Θ c +[(n+½) 2 (λ/2T) 2 ], n=1,2,3,4. . . ; where Θ n  is reflection angle corresponding to a peak of a fringe and λ is the wavelength of the probe beam; Θ c  is the critical angle; n corresponds to the order number of the fringe; and T is the thickness of the film. Where the fringe pattern can be resolved as in FIG. 1, the above Fresnel equation can be used to solve for T, as all of the other parameters can be determined. 
     In contrast in region B of FIG. 2 the peaks of the fringe pattern can not be resolved, so the Θ n  angle corresponding to peaks of a fringe pattern cannot be ascertained, and without knowing this value one cannot solve for the unknown T (the thickness of the film). To deal with this limitation of prior systems, the value of I/I 0  can be used in the Lambert-Beer equation, where I/I 0  is the observed transmission ratio of the low-density film, which is determined from the graph of FIG. 3 as the ratio of the expected reflectivity  304  of a material  404  without the top layer of film  402  to the reflectivity measured  302  with the film  402  disposed on the material  404 , in region B. The expected reflectivity of the material  404  can be determined based on modeling or referring to tabulated data for the expected reflectivity of the material  404 , or it can be obtained by actually measuring semiconductor wafer having a top layer defined by material  404 . A third alternative would be to assume that material  404  is totally reflective below the critical angle for the material  404 . Regardless of which of these methods is used for determining a value for reflectivity of the material  404 , the concept is the same. Herein, this approach, which could be implemented using any of the above methods, is described as comparing the reflectivity of the wafer with the thin-film layer with the reflectivity of a reference wafer, with the reflectivity of the reference wafer defining  10 . 
     The value μ/ρ is the mass absorption coefficient of the low-density film  404 . The mass absorption coefficient of the low-density film is determined by the composition of the film. Knowing the composition of the film one can refer to tabulated data to determine this value. The value Θ is the refraction corrected angle for the propagation angle in the film, which can be determined knowing the material of the film and the angle of reflection of the detected probe beam. The value of density, ρ, can be determined based on the location of the critical angle. The thickness T can be determined by solving the equation I/I 0 =exp(−2 μ/ρ·ρT/sin θ) for T. Thus, using the ratio of I/I 0  the value of T can be determined by the method and system of the present of the present invention where using prior art systems one could not determine this value because the peaks of the fringe pattern could not be resolved. Further, even where the resolution of a prior art system might be adjusted so that the fringe pattern could be determined, the present invention allows for determining the thickness without the need to increase the resolution of the system, which would result in increasing the amount of time needed to make the measurement. Thus, using the Lambert-Beers absorption law rather than the Fresnel equations, and using reflectivity data I/I 0  below the critical angle which in the past was ignored, the new measurement method and system is able to extract structural information characterizing a thin-film structure, where such information could frequently not be obtained in prior XRR systems. 
     To implement the system and method disclosed herein one could use a system very similar to that shown in FIG. 1, but the processor system would need to programmed such that it utilized the equations and relationship discussed herein to determine thickness of a low density film using the transmission properties of the thin-film. 
     While the method and apparatus of the present invention has been described in terms of its presently preferred and alternate embodiments, those skilled in the art will recognize that the present invention may be practiced with modification and alteration within the spirit and scope of the appended claims. The specifications and drawings are, accordingly, to be regarded in an illustrative rather than a restrictive sense. Further, even though only certain embodiments have been described in detail, those having ordinary skill in the art will certainly understand that many modifications are possible without departing from the teachings thereof. All such modifications are intended to be encompassed within the following claims.