Optical technique for material characterization

Abstract

A polarized Raman Spectrometric system for defining parameters of a polycrystalline material, said system comprising: a polarized Raman Spectrometric apparatus, a computer-controlled sample stage for positioning a sample at different locations, and a computer comprising a processor and an associated memory.

Claims

1. A method for defining parameters of a polycrystalline material, said method comprising: illuminating, by a polarized Raman spectrometric apparatus, multiple locations of the polycrystalline material by multiple spots; wherein the polycrystalline material comprises grains; collecting, by the polarized Raman spectrometric apparatus, radiation emitted from the multiple spots; generating, by the polarized Raman spectrometric apparatus, a plurality of signals from the multiple locations of the polycrystalline material; determining, by a computer and based on the plurality of signals, Raman peaks of the multiple locations; determining, by the computer, and using a peak fitting algorithm, a distribution of Raman amplitudes of the Raman peaks; and determining, by the computer, an average dimension of the grains based on the distribution of Raman amplitudes of the Raman peaks.

2. The method according to claim 1, wherein the illumination and the collecting are executed without cross-talk between the multiple spots.

3. The method according to claim 1, wherein the multiple spots have sub-micron dimensions.

4. The method according to claim 1, wherein dimensions of the grains are smaller than an optical resolution of the polarized Raman spectrometric apparatus.

5. The method according to claim 1, comprising adjusting dimensions of the multiple spots by adjusting a numerical aperture (NA) of the polarized Raman spectrometric apparatus.

6. The method according to claim 5, comprising adjusting the NA using a variable aperture that is positioned at a back-focal-plane of an objective lens of the polarized Raman spectrometric apparatus.

7. The method according to claim 1, comprising moving the polycrystalline material by a computer-controlled sample stage to facilitate the illumination of the multiple locations.

8. The method according to claim 1, wherein the illuminating and collecting are executed one location after the other.

9. The method according to claim 1, wherein the illuminating comprises scanning a spot from one location of the multiple location to another location of the multiple locations.

10. The method according to claim 1, wherein the determining, by the computer, the average dimension of the grains comprises: determining a variance of the Raman amplitudes of the Raman peaks; determining a mean of the Raman amplitudes of the Raman peaks; and determining the average dimension of the grains by multiplying a dimension of the spot by a ratio between the variance of the Raman amplitudes of the Raman peaks and a square of the mean of the Raman amplitudes of the Raman peaks.

11. The method according to claim 1, comprising performing a calibration step using a reference polycrystalline material of known grain dimension to determine a mapping between mapping between values of the distribution of Raman amplitudes of Raman peaks to values of the average dimension of the grains.

12. A polarized Raman spectrometric system for defining parameters of a polycrystalline material, the polarized Raman spectrometric system comprising: a polarized Raman spectrometric apparatus that is configured to: illuminate multiple locations of the polycrystalline material by multiple spots; wherein the polycrystalline material comprises grains; collect radiation emitted from the multiple spots; and generate a plurality of signals from the multiple locations of the polycrystalline material; a computer that is configured to: determine, based on the plurality of signals, Raman peaks of the multiple locations; determine, using a peak fitting algorithm, a distribution of Raman amplitudes of the Raman peaks; and determine an average dimension of the grains based on the distribution of Raman amplitudes of the Raman peaks.

13. The polarized Raman spectrometric system according to claim 12, wherein the polarized Raman spectrometric apparatus is configured to illuminate and collect without cross-talk between the multiple spots.

14. The polarized Raman spectrometric system according to claim 12, wherein the multiple spots have sub-micron dimensions.

15. The polarized Raman spectrometric system according to claim 12, wherein dimensions of the grains are smaller than an optical resolution of the polarized Raman spectrometric apparatus.

16. The polarized Raman spectrometric system according to claim 2, wherein the Raman spectrometric apparatus is configured to adjust dimensions of the multiple spots by adjusting a numerical aperture (NA) of the polarized Raman spectrometric apparatus.

17. The polarized Raman spectrometric system according to claim 16, wherein the Raman spectrometric apparatus is configured to adjust the NA using a variable aperture that is positioned at a back-focal-plane of an objective lens of the polarized Raman spectrometric apparatus.

18. The polarized Raman spectrometric system according to claim 12, comprising a computer-controlled sample stage that is configured to move the polycrystalline material to facilitate the illumination of the multiple locations.

19. The polarized Raman spectrometric system according to claim 12, wherein the Raman spectrometric apparatus is configured to illuminate and collect one location after the other.

20. The polarized Raman spectrometric system according to claim 12, wherein the Raman spectrometric apparatus is configured to scan a spot from one location of the multiple location to another location of the multiple locations.

21. The polarized Raman spectrometric system according to claim 12, wherein the computer is configured to determine the average dimension of the grains by: determining a variance of the Raman amplitudes of the Raman peaks; determining a mean of the Raman amplitudes of the Raman peaks; and determining the average dimension of the grains by multiplying a dimension of the spot by a ratio between the variance of the Raman amplitudes of the Raman peaks and a square of the mean of the Raman amplitudes of the Raman peaks.

22. The polarized Raman spectrometric system according to claim 12, comprising performing a calibration step using a reference polycrystalline material of known grain dimension to determine a mapping between mapping between values of the distribution of Raman amplitudes of Raman peaks to values of the average dimension of the grains.

Description

BRIEF DESCRIPTION OF THE FIGURES

(1) Disclosed embodiments will be understood and appreciated more fully from the following detailed description taken in conjunction with the appended figures. The drawings included and described herein are schematic and are not limiting the scope of the disclosure. It is also noted that in the drawings, the size of some elements may be exaggerated and, therefore, not drawn to scale for illustrative purposes. The dimensions and the relative dimensions do not necessarily correspond to actual reductions to practice of the disclosure.

(2) FIGS. 1A&B illustrate Raman imaging's for large-scale grains.

(3) FIGS. 2A-D illustrate the principles behind the system and method used for probing the average grain dimensions according to some embodiments of the present invention.

(4) FIG. 3 is a schematic diagram of a computerized method for probing the average grain dimensions according to some embodiments of the present invention.

(5) FIGS. 4A-D illustrate a Polarized Raman Spectrometric apparatus for taking single-shot spatially-resolved Raman measurements at a set of sample points on a sample in accordance with some embodiments of the present invention.

(6) FIG. 5 is a schematic diagram of a computerized method for probing the average grain dimensions by taking single-shot spatially-resolved Raman measurements at a set of sample points on a sample according to some embodiments of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

(7) In the following description, various aspects of the present application will be described. For purposes of explanation, specific configurations and details are set forth in order to provide a thorough understanding of the present application. However, it will also be apparent to one skilled in the art that the present application may be practiced without the specific details presented herein. Furthermore, well-known features may be omitted or simplified in order not to obscure the present application.

(8) The term comprising, used in the claims, is open ended and means the elements recited, or their equivalent in structure or function, plus any other element or elements which are not recited. It should not be interpreted as being restricted to the means listed thereafter; it does not exclude other elements or steps. It needs to be interpreted as specifying the presence of the stated features, integers, steps or components as referred to, but does not preclude the presence or addition of one or more other features, integers, steps or components, or groups thereof. Thus, the scope of the expression a system comprising x and z should not be limited to systems consisting only of components x and z. Also, the scope of the expression a method comprising the steps x and z should not be limited to methods consisting only of these steps.

(9) As used herein, the term and/or includes any and all combinations of one or more of the associated listed items. Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the specification and relevant art and should not be interpreted in an idealized or overly formal sense unless expressly so defined herein. Well-known functions or constructions may not be described in detail for brevity and/or clarity.

(10) It will be understood that when an element is referred to as being on, attached to, connected to, coupled with, contacting, etc., another element, it can be directly on, attached to, connected to, coupled with or contacting the other element or intervening elements may also be present. In contrast, when an element is referred to as being, for example, directly on, directly attached to, directly connected to, directly coupled with or directly contacting another element, there are no intervening elements present. It will also be appreciated by those of skill in the art that references to a structure or feature that is disposed adjacent another feature may have portions that overlap or underlie the adjacent feature.

(11) FIGS. 1A&B illustrate Raman imaging's for large-scale grains, grains larger than 1 m. The figures illustrate a polycrystalline material comprised of multiple regions, each structured as a crystal domain, but with varying orientations (crystal orientation is depicted as the direction of lines inside the grain region).

(12) As seen in the figures, when the grains are large enough to be optically resolved, a polarized Raman image can be taken, to provide direct mapping of the grains orientation. The Raman signal can be tuned to be highly sensitive to the crystal orientation by correct choice of the illumination and collection polarizations.

(13) However, it is almost always the case that grain dimensions are significantly smaller than the optical resolution, hindering such a direct method.

(14) Thus, the present invention provides a polarized Raman Spectroscopic system and method for resolving and defining parameters of grains smaller than 1 m.

(15) The polarized Raman Spectroscopic system, in accordance with some embodiments of the present invention, is comprised of a polarized Raman Spectrometric apparatus, a computer-controlled sample stage for positioning a sample at different locations, and a computer comprising a processor and an associated memory.

(16) The polarized Raman Spectrometric apparatus comprises a light source for generating a light beam, a detection unit including a spectrometer, and an optical system comprised of multiple lenses including an objective lens.

(17) In accordance with some embodiments of the present invention, the apparatus further comprises multiple polarizers for polarizing the illuminating light beam and the detected beam.

(18) In accordance with some embodiments of the present invention, in order to collect signals at multiple locations on the sample, either the sample stage is translated along the X-Y axes to position the sample at multiple locations, or the point illumination is scanned across the sample.

(19) FIGS. 2A-D illustrate the principles behind the system and method used for probing the average grain dimensions according to some embodiments of the present invention.

(20) FIGS. 2A-B illustrate a case of large-grains, namely, grain dimensions that are comparable to the illumination spot size 202. In this case, at each measurement location, a small number of grains, e.g., grains within darker regions 204A-D, contributes to the measured signal 206. As seen in FIG. 2B, the Raman signal varies significantly since the grains dimensions are comparable to the illumination spot size 202, and thus, the measurement averages over a small number of grain orientations.

(21) FIGS. 2C&D illustrate a case of small grains, namely, grains that are much smaller than the illumination spot size 208. In this case, each measurement averages over many grain orientations in regions 210A-D. Consequently, the Raman signal 208 shows small variations around its average value, and the grain dimensions can be deduced from the signal variance.

(22) FIG. 3 is a schematic diagram of a computerized method 300 using a processor and associated memory for probing the average grain dimensions according to some embodiments of the present invention.

(23) In accordance with some embodiments of the present invention, the method 300 is based on a point illumination which is scanned across the sample measuring one point at a time with a relatively high resolution and no cross-talk between measurements

(24) The method 300 comprises the following steps:

(25) Step 302Providing a Raman spectrometry system. In accordance with some embodiments of the present invention, the Raman Spectrometric System is provided with a high numerical (NA) aperture optical system to allow efficient collection of the Raman signal from multiple positions.

(26) Step 304Running high-resolution polarized Raman measurements at a set of points at any spatial distribution on a sample, getting Raman peaks at these points, and using standard peak-fitting algorithms to provide a distribution of Raman amplitudes.

(27) Step 306Determining the intensity of the Raman peaks related to the material of the tested sample.

(28) Step 308Calculating the standard deviation of the distribution of Raman amplitudes.

(29) Step 310Deriving the average grain size from the standard deviation of the distribution of Raman amplitudes.

(30) By standard statistical considerations, an estimation for the average grain dimensions is given by

(31) $\begin{array}{cc}\frac{\mathrm{Variance}\mathrm{of}\mathrm{Raman}\mathrm{signal}}{{\left(\mathrm{mean}\mathrm{Raman}\mathrm{signal}\right)}^2}~\frac{\mathrm{grain}\mathrm{size}}{\mathrm{spot}\mathrm{size}}& \mathrm{equation}1\end{array}$

(32) For a given crystal type, the Raman intensity is given by the Raman selection rule as follows:
I=|e.sub.s.sup.T.Math..Math.e.sub.i|.sup.2equation 2
where the exact value of the proportionality factor depends on the assumption of a completely random grain orientations and of the distribution of Raman intensities induced by it.

(33) is the so-called Raman Tensor associated with each vibration mode, and e.sub.i,s are the incident and scattered electric field polarizations. For each grain in a polycrystalline material, the Raman tensor is rotated accfording to it's orientation.

(34) If the orientation is represented by a rotation matrix , the intensity from an ensemble of grains can be determined as follow:
I=.sup.gI.sup.g|e.sub.s.sup.T.Math.().Math.e.sub.i|.sup.2equation 3
where I.sub.g is the intensity of the illumination spot at the corresponding grain. By performing the summation, the spatial distribution of the spot and the orientational distribution of the grains can be related to a distribution of the observed intensity, and so to a concrete relation between the observed relative variance and grain size.

(35) It should be noted that corrections to this estimator can be obtained by a one-time calibrationa sample with well-known grain size can be measured, and the proportionality constant between the Raman signal variance and grain size can be accurately obtained, accounting for any uncertainties in the illumination spot shape or other system parameters.

(36) In accordance with some embodiments of the present invention, the following are several specific system aspects which are essential to this method: Numerical aperture (NA): (a) a high numerical aperture is essential in order to allow efficient collection of the Raman signal at short acquisition times. In the current context, the high-NA also leads to small spot size, as dictated by diffraction:

(37) $\begin{array}{cc}\mathrm{Spot}\mathrm{size}~\frac{}{NA},& \mathrm{equation}4\end{array}$ where is the wavelength. Consequently, high-NA allows characterization of smaller grain sizes. It should be noted that equation 4 is simplified for clarityfor Raman metrology the illumination and collection wavelengths are slightly different, and the illumination and collection NA may be different. (b) Controlling the illumination NA and\or collection NA impact the measured spot size, i.e., it is possible to vary the number of grains inside the spot, and consequently affect the grain statistics. Specifically, measurements can be taken at a set of distinct values of NA (illumination and\or collection) where for each configuration the spot size can be calculated and the grain size can be deduced from equation 1. This approach presents an alternative to the discussed method of scanning the spot over different locations and may be advantageous in cases when the measured structure resides in a small area, preventing such scanning approach. In accordance with some embodiments of the present invention, such method may be implemented by placing a variable aperture at the back-focal-plane of the objective (at illumination and\or collection paths) and controlled electronically. Another implementation of direct benefit for this measurement is the use of multi-wavelength Raman spectroscopy. By using a set of different excitation wavelength, it is possible to change the spot size (see Eq. 2). Thus, using a set of measurements with different spot sizes, for instance, controlled by the excitation wavelength, it is possible to analyze how Raman signal varies with different grain statistics, and deduce the average grain size. An additional implementation which can improve throughput and performance is angle resolved Raman Spectroscopy. By controlling the illumination angle-of-incidence, and separating the collected signal coming from different scattering angles, multiple views of the same spot are recorded and can be combined to gather more information from a single measurement and thus reduce the number of required measurements and improve the measurement stability.

(38) In accordance with some embodiments of the present invention, an optical arrangement of special benefit in this method is the use of single-shot spatially-resolved Raman imaging. This approach involves the following: An illumination spot shaped so as to project an elongated line on the sample. This can be achieved by the addition of a line-spot element such as a cylindrical lens, a holographic optical element, micro-lens array or others. The line spot element is aligned so that the elongated direction points along the spectrometer slit direction, or close to this direction. Consequently, the measured signal on a 2-D sensor, such as a spectrometer charge coupled device (CCD), involves a set of Raman spectra, corresponding to different locations along the illuminated spot. the 2D image on the spectrometer CCD is registered. Each CCD line holds the Raman spectrum corresponding to a different location on the sample.

(39) In accordance with some embodiments of the present invention, such implementation enables the acquisition of Raman spectra from multiple positions in a single measurement, not requiring any motion of the sample or scanning the illumination point across the sample, and grain dimensions may be derived from the statistical distribution of these different Raman spectra.

(40) Such implementation is illustrated in FIGS. 4 and 5.

(41) FIGS. 4A-D illustrate a Polarized Raman Spectrometric apparatus 400 for taking single-shot spatially-resolved Raman measurements at a set of sample points on a sample in accordance with some embodiments of the present invention.

(42) Raman Spectrometric system 400 comprises a light source 402, a detection unit including a spectrometer 404, an optical system 406 configured as light directing arrangement for directing light from the light source 402 towards a sample 408 and directing the returned light from the sample 408 to the spectrometer 404, and single or multiple polarizers (not seen in the figure) for polarizing the illuminating light beam and the detected beam.

(43) The optical system 406 comprises a line-spot element 210, beam splitter 412, objective lens unit 414 (one or more lenses) and focusing lens 416.

(44) The spectrometer 404 generates spectral data of light incident thereon, and the output of the spectrometer 404 is transferable to a computer via wired or wireless communication, e.g., via Wi-Fi or Bluetooth, or a combination thereof.

(45) FIG. 4A is a schematic illustration of an illumination path in the Raman Spectrometric system 400 according to some embodiments of the present invention. Seen in the figure, a laser beam 420 generated via light source 402 is passed through line-spot element 410, which creates an elongated line-spot 422 on the sample 408.

(46) The line-spot element 410 may be selected from a cylindrical lens, a holographic optical element, a micro-lens array or any other suitable optical component.

(47) As seen in FIG. 4A, line-spot element 410 creates beam divergence in one axis to form an elongated line-spot 422 on the sample 408 while leaving the beam 420 unaffected in the other axis. Beam splitter 412 reflects the beam towards the objective lens unit 414, which focuses it on the sample 408. As seen in the figure, due to the beam divergence in one axis, elongated line-spot 422 is created on the sample 408.

(48) FIG. 4B is a schematic illustration of a collection path according to some embodiments of the present invention. Seen in the figure, light emerging from the sample 408 passes through objective lens unit 414 and beam splitter 412 and focused by a focusing lens 416 onto the spectrometer slit 430 of spectrometer 404. In this layout, the line-shaped points 422 on sample 408 is imaged onto the spectrometer slit 430, e.g., line-shaped points 432, which is used to schematically demonstrate this imaging layout. Spectrometer 404 is illustrated in FIG. 4C, and the sample 408, is illustrated in FIG. 4D. Seen in FIG. 4C, the line-shaped points 432 on the spectrometer slit 430 are spectrally resolved, to create a 2D image 436 on the CCD 438. Image 436 is hence directly related to the line-shaped points 422 on the sample 408.

(49) In accordance with some embodiments of the present invention, the 2D image 436 yields the position-dependence spectra, e.g., one axis corresponds to the wavelength and the other axis to the position on the sample.

(50) The measured sample 408, is illustrated in FIG. 4D. As seen in the figure, different parts of the line-shaped points 432 are imaged to different lines of the CCD 438, where they can be separately read and analyzed.

(51) FIG. 5 is a schematic diagram of a computerized method 500 for probing the average grain dimensions by taking single-shot spatially-resolved Raman measurements at a set of sample points on a sample according to some embodiments of the present invention.

(52) Method 500 comprises the following steps:

(53) Step 502Providing a Raman Spectrometric System including the Raman Spectroscopic apparatus of FIGS. 4A-D. In accordance with some embodiments of the present invention, the Raman Spectrometric apparatus is provided with a high numerical (NA) aperture optical system to allow efficient collection of the Raman signal from multiple positions in a single measurement and in a relatively short acquisition time.

(54) Using such implementation, Raman spectra from multiple positions can be acquired in a single measurement, not requiring any motion of the measurement spot or sample, and grain dimensions are derived from the statistical distribution of these different Raman spectra.

(55) Step 504Using the Raman spectroscopic system to form an elongated line-shaped points on a sample.

(56) The line-shaped points are aligned along the spectrometer slit direction, or close to this direction. Consequently, the measured signal on the spectrometer CCD involves a set of Raman spectra, corresponding to different locations along the illuminated spot.

(57) Step 506Running high-resolution polarized Raman measurements to generate a 2D image of lines that are directly related to the line-shaped points on the sample and getting Raman peaks at these point. In accordance with some embodiments of the present invention, there is no need to map an image of the probed region, but rather take measurements at sample points. The measurements should be close enough together as to represent a localized measurement where the average grain dimensions are stationary.

(58) Step 508Registering the 2D image on the spectrometer CCD.

(59) Contrary to standard Raman measurements, in this layout the 2D image on the spectrometer CCD is registered, and each CCD line holds the Raman spectrum corresponding to a different location on the sample.

(60) Step 510Transferring the data from the CCD to a computer via wired or wireless communication.

(61) Step 512Using standard peak-fitting algorithms to provide a distribution of Raman amplitudes.

(62) Step 514Determining the intensity of the Raman peaks related to the material of the tested sample.

(63) Step 516Calculating the standard deviation of the distribution of Raman amplitudes.

(64) Step 518Deriving the average grain size from the standard deviation of the distribution of Raman amplitudes

(65) Statistical Accuracy:

(66) In accordance with some embodiments of the present invention, the accuracy of the estimated grain size using the present system and method is dictated by the size of the measured statistical ensemble, i.e., the more measurement points acquired, the better is the statistical analysis and the more accurate is the estimated grain size. However, the size of the required statistical ensemble for a specific degree of convergence depends on the grain size, i.e., larger grains lead to larger statistical ensemble. Such dependence can lead to measurement instabilities, as the measurement performance may vary with respect to sample characteristics.

(67) Additionally, the measured variance is also influenced by measurement errors such as photon shot noise and other noise sources. Such noise sources should either be made negligible relative to the grain-related variance (e.g., by controlling the acquisition time per position), or properly taken into account in the analysis.

(68) In accordance with some embodiments of the present invention, such errors may be mitigated by analyzing the collected signal and noise during measurement, and estimating the statistical validity during data collection. This way, standard statistical tests may be applied to the data and dictate whether additional measurements are required. Such approach may also serve to improve the measurement throughput, as acquisitions are only taken when needed, rather than wasted in situations where statistics are satisfactory.

(69) Such approach, and its variations, enables the following: Non-contact, non-destructive measurements, Small spot (<1-few microns), allowing measurement of small regions, Potentially fast measurements: while Raman metrology is significantly slower than standard optical scatterometry methods (e.g. ellipsometry, reflectometry), it can be made significantly faster than x-ray or TEM based methods. By a correct choice of laser sources and high-efficiency optical layout and spectrometer, the Raman metrology may become efficientas specific acquisition times greatly depend on the measured material and its Raman cross section, expected measurement times may be of tens of seconds or few minutes.

(70) It should be noted that the material under consideration has to be a Raman-active material that provides a distinct peak (or a set of peaks) in the Raman spectrum, and the Raman signal can be tuned to be highly sensitive to the crystal orientation by tuning the illumination and collection polarizations.