Patent Publication Number: US-8990961-B2

Title: Non-linearity determination of positioning scanner of measurement tool

Description:
REFERENCE TO PRIOR APPLICATIONS 
     This application is a Divisonal application of co-pending U.S. patent application Ser. No. 12/013,787, filed on Jan. 14, 2008, which is hereby incorporated by reference. 
    
    
     BACKGROUND 
     1. Technical Field 
     The disclosure relates generally to measurement systems, and more particularly, to calibration of measurement systems. 
     2. Background Art 
     Calibration of measurement systems used in, for example, measuring IC chips during or after manufacturing, is essential to attain accurate measurements. Current practices of checking linearity and calibrating vertical displacement of a measurement tool use several step height standards. The same is true for horizontal displacement. That is, the tool is used to measure a number of structures having known heights or known pitch standards for horizontal displacement. Limitations on the availability of these standards and the uncertainty of the standards make this approach inadequate. 
     SUMMARY 
     Determination of non-linearity of a positioning scanner of a measurement tool is disclosed. In one embodiment, a method may include providing a probe of a measurement tool coupled to a positioning scanner; scanning a surface of a first sample with the surface at a first angle relative to the probe to attain a first profile; scanning the surface of the first sample with the surface at a second angle relative to the probe that is different than the first angle to attain a second profile; repeating the scannings to attain a plurality of first profiles and a plurality of second profiles; and determining a non-linearity of the positioning scanner using the different scanning angles to cancel out measurements corresponding to imperfections due to the surface of the sample. The non-linearity may be used to calibrate the positioning scanner. 
     A first aspect of the disclosure provides a method comprising: providing a probe of a measurement tool coupled to a positioning scanner; scanning a surface of a first sample with the surface at a first angle relative to the probe to attain a first profile; scanning the surface of the first sample with the surface at a second angle relative to the probe that is different than the first angle to attain a second profile; repeating the scannings to attain a plurality of first profiles and a plurality of second profiles; and determining a non-linearity of the positioning scanner using the different scanning angles to cancel out measurements corresponding to imperfections due to the surface of the sample. 
     A second aspect of the disclosure provides a system comprising: a measurement tool including a probe coupled to a positioning scanner; a fixture for holding a sample for scanning a surface of the sample with the surface at a first angle relative to the probe to attain a plurality of first profiles, and scanning the surface of the sample with the surface at a second angle relative to the probe that is different than the first angle to attain a plurality of second profiles; and a determinator for determining a non-linearity of the positioning scanner using the different scanning angles to cancel out measurements corresponding to imperfections due to the surface of the sample. 
     A third aspect of the disclosure provides a program product stored on a computer-readable medium, which when executed, determines a non-linearity of a positioning scanner of a measurement tool, the program product comprising: program code for controlling scanning a surface of a sample with the surface at a first angle relative to a probe coupled to the positioning scanner to attain a first profile; program code for controlling scanning the surface of the sample with the surface at a second angle relative to the probe that is different than the first angle to attain a second profile; program code for controlling repeating the scannings to attain a plurality of first profiles and a plurality of second profiles; and program code for determining a non-linearity of the positioning scanner using the different scanning angles to cancel out measurements corresponding to imperfections due to the surface of the sample. 
     A fourth aspect of the disclosure includes a scanning probe microscope comprising: a probe coupled to a positioning scanner; a fixture for holding a sample for scanning a surface of the sample with the surface at a first angle relative to the probe to attain a plurality of first profiles, and scanning the surface of the sample with the surface at a second angle relative to the probe that is different than the first angle to attain a plurality of second profiles; and a determinator for determining a non-linearity of the positioning scanner using the different scanning angles to cancel out measurements corresponding to imperfections due to the surface of the sample. 
     A fifth aspect of the disclosure provides a computer-readable medium that includes computer program code to enable a computer infrastructure to determine a non-linearity of a positioning scanner of a measurement tool, the computer-readable medium comprising computer program code for performing the method steps of the disclosure. 
     A sixth aspect of the disclosure provides a method of generating a system for determining a non-linearity of a positioning scanner of a measurement tool, the method comprising: obtaining a computer infrastructure; and deploying means for performing each of the steps of the disclosure to the computer infrastructure. 
     The illustrative aspects of the present disclosure are designed to solve the problems herein described and/or other problems not discussed. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       These and other features of this disclosure will be more readily understood from the following detailed description of the various aspects of the disclosure taken in conjunction with the accompanying drawings that depict various embodiments of the disclosure, in which: 
         FIG. 1  shows a block diagram of an illustrative environment including a non-linearity determining system according to the disclosure. 
         FIG. 2  shows a flow diagram of embodiments of the non-linearity determining system of  FIG. 1  according to the disclosure. 
         FIGS. 3A-3B  show schematic diagrams of the non-linearity determining according to the disclosure. 
         FIG. 4  shows a comparison of profiles illustrating the non-linearity determining according to the disclosure. 
         FIG. 5  shows residuals of profiles after linear regression. 
         FIG. 6  shows a difference between the profiles for determining non-linearity. 
         FIG. 7  shows an illustrative calibrated Z height measurement sample. 
     
    
    
     It is noted that the drawings of the disclosure are not to scale. The drawings are intended to depict only typical aspects of the disclosure, and therefore should not be considered as limiting the scope of the disclosure. In the drawings, like numbering represents like elements between the drawings. 
     DETAILED DESCRIPTION 
     Turning to the drawings,  FIG. 1  shows an illustrative environment  100  of a measurement tool according to the disclosure. To this extent, environment  100  includes a computer infrastructure  102  that can perform the various process steps described herein for determining a non-linearity of a positioning scanner  92  of a measurement tool  90 . In particular, computer infrastructure  102  is shown including a computing device  104  that comprises a non-linearity determination system  106 , which enables computing device  104  to determine and/or correct a non-linearity of a positioning scanner of a measurement tool by performing the process steps of the disclosure. 
     Computing device  104  is shown including a memory  112 , a processor (PU)  114 , an input/output (I/O) interface  116 , and a bus  118 . Further, computing device  104  is shown in communication with an external I/O device/resource  120  and a storage system  122 . As is known in the art, in general, processor  114  executes computer program code, such as non-linearity determining system  106 , that is stored in memory  112  and/or storage system  122 . While executing computer program code, processor  114  can read and/or write data, such as measurements, scanning profiles, etc., to/from memory  112 , storage system  122 , and/or I/O interface  116 . Bus  118  provides a communications link between each of the components in computing device  104 . I/O device  118  can comprise any device that enables a user to interact with computing device  104  or any device that enables computing device  104  to communicate with one or more other computing devices. Input/output devices (including but not limited to keyboards, displays, pointing devices, etc.) can be coupled to the system either directly or through intervening I/O controllers. 
     In any event, computing device  104  can comprise any general purpose computing article of manufacture capable of executing computer program code installed by a user (e.g., a personal computer, server, handheld device, etc.). However, it is understood that computing device  104  and non-linearity determining system  106  are only representative of various possible equivalent computing devices that may perform the various process steps of the disclosure. To this extent, in other embodiments, computing device  104  can comprise any specific purpose computing article of manufacture comprising hardware and/or computer program code for performing specific functions, any computing article of manufacture that comprises a combination of specific purpose and general purpose hardware/software, or the like. In each case, the program code and hardware can be created using standard programming and engineering techniques, respectively. 
     Similarly, computer infrastructure  102  is only illustrative of various types of computer infrastructures for implementing the disclosure. For example, in one embodiment, computer infrastructure  102  comprises two or more computing devices (e.g., a server cluster) that communicate over any type of wired and/or wireless communications link, such as a network, a shared memory, or the like, to perform the various process steps of the disclosure. When the communications link comprises a network, the network can comprise any combination of one or more types of networks (e.g., the Internet, a wide area network, a local area network, a virtual private network, etc.). Network adapters may also be coupled to the system to enable the data processing system to become coupled to other data processing systems or remote printers or storage devices through intervening private or public networks. Modems, cable modem and Ethernet cards are just a few of the currently available types of network adapters. Regardless, communications between the computing devices may utilize any combination of various types of transmission techniques. 
     Measurement tool  90  may include any now known or later developed system for measuring that includes positioning scanner  92  and probe  94 , e.g., a scanning probe microscope (SPM), atomic force microscope, profilometer or other form of mechanical probe system, including electron and optical probing systems. Probe  94  may be contacting or non-contacting. Measurement tool  90  may be a contact type tool or a non-contact type tool, or may have a selective contact mode and a non-contact mode. As understood, probe  94  is scanned over a surface of sample  96  and measures an interaction between the surface and the probe, resulting in an electronic profile, i.e., an image including, for example, surface topography. Measurement tool  90  may include non-linearity determining system  106  or it may be a separate system. In any event, measurement tool  90  can include a capacitance gauge  95 , or some other gauge as a feedback control for positioning scanner  92 . Capacitance gauge  95  is used to monitor the position of positioning scanner  92 . Feedback from capacitance gauge  95  can be used to moderate the input voltage to positioning scanner  92  so the scanner will move in a controlled motion to precisely determine vertical position (height) versus lateral position. That is, piezoelectric material is used to finely position positioning scanner  92  and thus probe  94  laterally (X-Y plane) and vertically (Z plane). This functioning may be incorporated in a closed-loop feedback system, or the feedback system may be omitted. Positioning scanner  92  controls voltage to the actuator to extend probe  94  towards sample  96  so that the probe tracks the surface. As one with skill in the art will recognize, measurement tool  90  may include a variety of other sub-systems and components not illustrated in  FIG. 1 . Measurement tool  90  is shown for use with one or more samples  96  positioned on a fixture  98 . 
     Fixture  98  may include any now known or later developed sample holding mechanism capable of angling the sample(s)  96  about a horizontal axis (see  FIG. 3 ), and consistently holding sample  96  such that reproducible results can be obtained. Fixture  98  may have predefined angles of tilt to hold sample  96  to achieve a desired vertical (Z) translation for a given amount of lateral (X or Y) axis translation. More specifically, fixture  98  may include any now known or later developed structure to allow the necessary lateral, vertical and angling of sample  96 , e.g., motors, cams, electronic controls, etc. The method described here is also applicable for determining the non-linearity of scanners in the X,Y plane. A sample for doing this would have its scan surface perpendicular to the X, Y plane and be positioned and scanned at two different angles to cancel the scan surface roughness from the intrinsic non-linearity of the X or Y scanners. 
     As previously mentioned and discussed further below, non-linearity determining system  106  enables computing infrastructure  102  to, among other things, determine a non-linearity of positioning scanner  92  of measurement tool  90 . To this extent, non-linearity determining system  106  is shown including a scanner control  130 , a fixture control  132 , a determinator  134  including an averager  136 , a best line fitter  138 , an aligner  140 , a differencer  142  and an evaluator  144 . In addition, a calibrator  150  for calibrating positioning scanner  92  may also be provided. Operation of each of these systems is discussed further below. However, it is understood that some of the various systems shown in  FIG. 1  can be implemented independently, combined, and/or stored in memory for one or more separate computing devices that are included in computer infrastructure  102 . Further, it is understood that some of the systems and/or functionality may not be implemented, or additional systems and/or functionality may be included as part of environment  100 . 
     Referring to  FIGS. 2-3  in conjunction with  FIG. 1 , embodiments of a method of operation of non-linearity determining system  106  will now be described for the case of determining vertical displacement nonlinearity. In process P 1 , probe  94  of measurement tool  90  is provided coupled to positioning scanner  92 . As shown in  FIGS. 2-3 , a sample  96  is positioned on a fixture  98  that is capable of angling about a horizontal axis  140 . (Axis  140  could be a vertical axis to enable the X or Y non-linearity determination.) Fixture  98  movement is controlled by fixture control  132 , as will be described herein. 
     In process P 2 , scanner control  130  controls scanning of a surface  150  of sample  96  at a first angle (α 1 ) relative to probe  94  to attain a first profile, i.e., measured electronic representation of surface  150 . That is, scanner control  130  controls the data recordation by measurement tool  90 , positioning scanner  92 , and any other required component of measurement tool  90 . As illustrated, first angle (α 1 ) is substantially 90° relative to the probe such that sample  96  is at or near horizontal; however, other angles may be used. (In the X or Y non-linearity assessment, the first angle is substantially parallel to either the X or the Y axis while the second angle (as in process P 3 ) is any angle sufficient to achieve the desired travel in the X or Y axis.) Sample  96  may include, for example, a patterned integrated circuit (IC) chip. Preferably, sample  96  provides a smooth surface and the patterned silicon provides a navigation aid to ensure the return of subsequent scanning to the same starting position to minimize sample surface  150  variation due to stage positioning variance. 
     In process P 3 , scanner control  130  controls scanning surface  150  of first sample  96  with the surface at a second angle (α 2 ) relative to probe  92  that is different than the first angle to attain a second profile. As illustrated, second angle (α 2 ) is approximately 81° relative to the probe; however, other angles may be used. That is, fixture control  132  tilts sample  96  about horizontal axis  140  by approximately 9°, e.g., by activating a motorized tilting mechanism in fixture  98 . In any event, second angle (α 2 ) results in sample  96  being inclined, causing positioning scanner  92  to move probe  94  both laterally (X and/or Y direction) and vertically (Z direction) to accommodate the inclined sample  96 . 
     In process P 4 , scanner control  130  repeats the scannings (process P 2 -P 3 ) to attain a plurality of first profiles and a plurality of second profiles. It is understood that the repeating of scanning of sample  96  does not necessarily have to occur with intermittent first angle and second angle positions, as shown in  FIG. 2 . If this intermittent process was chosen, an alternative approach could be to use a single iteration of scans, do the fitting, the scan alignment of the residuals, subtraction, and then repeat this process to compare result  180  (collection of scans) for evaluation. That is, as shown in  FIG. 4 , repetitive scanning at first angle could occur, followed by repetitive scanning at second angle. Any number of repetitive scans to ensure accurate measurement may be used. 
     In process P 5 , determinator  134  determines a non-linearity of positioning scanner  92  using the different scanning angles to cancel out measurements corresponding to imperfections due to surface  150  of sample  96 . This process may take a variety of forms. In one embodiment, in process P 5 A, as shown in  FIG. 4 , averager  136  averages plurality of first profiles  160  and averages plurality of second profiles  162 , resulting in averaged first profiles  164  and averaged second profiles  166 . As shown in  FIG. 5 , in process P 5 B, best-line fitter  138  performs a linear regression (e.g., a Mandel or ordinary least squares regression) on averaged first profiles  164  and averaged second profiles  166  to fit them to a first order best-fit line, and calculates residuals (shown in dashed lines) from the first order best-fit lines. That is, the data is normalized by the process of fitting the data to a straight line and capturing the residuals. The residuals of the linear regression are the vertical deviations (both − and +) about the line. The residuals, by definition, have the slope of the line (and tilt of the sample) removed. Therefore, the residuals are the deviations from perfect linear behavior. This “normalization” allows comparison of the flat state of the sample with next to no Z displacement with that of tilted state with lots of Z displacement. As also shown in  FIG. 5 , in process P 5 C, aligner  140  aligns residuals of a best-fit line  170  of averaged first profiles  164  and residuals of a best fit-line  172  of averaged second profiles  166 . The vertical dashed lines over residuals of best-fit line  170  of averaged first profiles  164  and residuals of best-fit line  172  of averaged second profiles  166  illustrate a potential non-linearity, which can be used for the alignment of residuals  172  to residuals  170 .  FIG. 6  shows the result of process P 5 D in which differencer  142  subtracts the residuals of averaged first profiles  164  from the residuals of averaged second profiles  166  after the aligner  140  positions residuals  170  and  172  relative to each other. A result  180  identifies non-linearities of positioning scanner  92  since subtracting cancels out measurements corresponding to imperfections due to surface  150  of sample  96 . This principle is due to the invariance of surface  150  at the two different tilt angles shown in  FIGS. 3A and 3B . The tilt of sample surface  150  at second angle (α 2 ) exercises the vertical Z displacement of positioning scanner  92  thus the subtraction of sample surface  150  variations leaves the remaining Z displacement non-linearity. In process P 5 E, evaluator  144  evaluates a result  180  ( FIG. 6 ) of the subtracting to identify the non-linearity of the positioning scanner, e.g., the areas that are not zero represent non-linearities in positioning scanner  92  operation. 
     In the example illustrated, the behavior shown in profiles  162  of  FIG. 4  indicates the non-linearity may be systematic. The Root-Mean-Square (RMS) of result  180  will result in a good estimate of the standard deviation multiple (e.g., 3-sigma) uncertainty of the scanner due to non-linearity. If uncertainty is too large, then a higher order regression can remove this systematic non-linearity. This regression equation would be used to correct for this systematic non-linearity of the scanner, and a new RMS would be calculated smaller than the previously calculated RMS yielding a smaller non-linear uncertainty. Returning to  FIG. 2  in conjunction with  FIG. 7 , in an optional embodiment, scanner control  130  may further be used to measure a calibrated Z height measurement sample  190 , i.e., a calibrated sample including a minimum of one known Z height standard, thus linking all of the Z values. A single calibrated step height standard is needed if the surfaces of sample  190  have the similar roughness thus similar scanning probe  94  to sample  150  interaction for the substrate and step surfaces of  190  in  FIG. 7 . If these probe to sample interactions are significantly different, a minimum of 2 calibrated standards would be required to test that the scaling of the scanner is significantly different from unity. Based on this measurement, calibrator  150  ( FIG. 1 ) may calibrate an entire Z range of measurement tool  90  based on the Z height measurement sample. Once the non-linearity  180  of the vertical displacement is determined, this information with a single standard fully describes the deviation from perfect linear behavior of the Z displacement for the tested range of the Z displacement. Similarly, for the cases of the assessment of the X and Y linearity, a single pitch standard would be required to calibrate the entire assessed X and Y scanner range. 
     As discussed herein, various systems and components are described as “obtaining” data (e.g., measurements, etc.). It is understood that the corresponding data can be obtained using any solution. For example, the corresponding system/component can generate and/or be used to generate the data, retrieve the data from one or more data stores (e.g., a database), receive the data from another system/component, and/or the like. When the data is not generated by the particular system/component, it is understood that another system/component can be implemented apart from the system/component shown, which generates the data and provides it to the system/component and/or stores the data for access by the system/component. 
     While shown and described herein as a method and system for determining non-linearity of positioning scanner  92 , it is understood that the disclosure further provides various alternative embodiments. That is, the disclosure can take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment containing both hardware and software elements. In a preferred embodiment, the disclosure is implemented in software, which includes but is not limited to firmware, resident software, microcode, etc. In one embodiment, the disclosure can take the form of a computer program product accessible from a computer-usable or computer-readable medium providing program code for use by or in connection with a computer or any instruction execution system, which when executed, enables a computer infrastructure to determine the non-linearity of positioning scanner  92 . For the purposes of this description, a computer-usable or computer readable medium can be any apparatus that can contain, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device. The medium can be an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system (or apparatus or device) or a propagation medium. Examples of a computer-readable medium include a semiconductor or solid state memory, such as memory  122 , magnetic tape, a removable computer diskette, a random access memory (RAM), a read-only memory (ROM), a tape, a rigid magnetic disk and an optical disk. Current examples of optical disks include compact disk-read only memory (CD-ROM), compact disk-read/write (CD-R/W) and DVD. 
     A data processing system suitable for storing and/or executing program code will include at least one processing unit  114  coupled directly or indirectly to memory elements through a system bus  118 . The memory elements can include local memory, e.g., memory  112 , employed during actual execution of the program code, bulk storage (e.g., memory system  122 ), and cache memories which provide temporary storage of at least some program code in order to reduce the number of times code must be retrieved from bulk storage during execution. 
     In another embodiment, the disclosure provides a method of generating a system for determining non-linearity of positioning scanner  92 . In this case, a computer infrastructure, such as computer infrastructure  102  ( FIG. 1 ), can be obtained (e.g., created, maintained, having made available to, etc.) and one or more systems for performing the process described herein can be obtained (e.g., created, purchased, used, modified, etc.) and deployed to the computer infrastructure. To this extent, the deployment of each system can comprise one or more of: (1) installing program code on a computing device, such as computing device  104  ( FIG. 1 ), from a computer-readable medium; (2) adding one or more computing devices to the computer infrastructure; and (3) incorporating and/or modifying one or more existing systems of the computer infrastructure, to enable the computer infrastructure to perform the process steps of the disclosure. 
     As used herein, it is understood that the terms “program code” and “computer program code” are synonymous and mean any expression, in any language, code or notation, of a set of instructions that cause a computing device having an information processing capability to perform a particular function either directly or after any combination of the following: (a) conversion to another language, code or notation; (b) reproduction in a different material form; and/or (c) decompression. To this extent, program code can be embodied as one or more types of program products, such as an application/software program, component software/a library of functions, an operating system, a basic I/O system/driver for a particular computing and/or I/O device, and the like. 
     The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the disclosure. As used herein, the singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises” and/or “comprising,” when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. 
     The corresponding structures, materials, acts, and equivalents of all means or step plus function elements in the claims below are intended to include any structure, material, or act for performing the function in combination with other claimed elements as specifically claimed. The description of the present disclosure has been presented for purposes of illustration and description, but is not intended to be exhaustive or limited to the disclosure in the form disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the disclosure. The embodiment was chosen and described in order to best explain the principles of the disclosure and the practical application, and to enable others of ordinary skill in the art to understand the disclosure for various embodiments with various modifications as are suited to the particular use contemplated.