Charged particle microscope with improved spectroscopic functionality
09812287 · 2017-11-07
Assignee
Inventors
- Cornelis Sander Kooijman (Veldhoven, NL)
- Thijs Thomas Withaar (Eindhoven, NL)
- Gerard Nicolaas Anne van Veen (Waalre, NL)
Cpc classification
H01J37/285
ELECTRICITY
G01N23/223
PHYSICS
H01J37/244
ELECTRICITY
G01N23/2257
PHYSICS
G01N23/2252
PHYSICS
International classification
H01J37/244
ELECTRICITY
G01N23/223
PHYSICS
H01J37/285
ELECTRICITY
Abstract
An improved spectroscopic analysis apparatus and method are disclosed, comprising directing a beam of radiation onto a measurement location on a specimen, thereby causing a flux of X-rays to emanate from this location; examining the X-ray flux using a detector arrangement, thus acquiring a spectrum; choosing a set of different measurement directions originating from the location; recording outputs from the detector arrangement for different measurement directions; adopting a spectral model that is a convoluted mix of terms B and L.sub.p, where B is the Bremsstrahlung background spectrum and L.sub.p comprises spectral lines corresponding to the specimen composition at the measurement location; and then automatically deconvolving the set of measurements on the basis of the spectral model to calculate L.sub.p to determine the chemical composition of the specimen at the measurement location. The method includes corrections for differential X-ray absorption within the specimen along the different measurement directions.
Claims
1. A method of examining a specimen using a spectroscopic apparatus, comprising the following steps: providing the specimen on a specimen holder; directing a focused input beam of radiation onto a location P on the specimen, thereby producing an interaction that causes a flux of X-rays to emanate from said location; examining said flux using a detector arrangement, thus accruing a measured spectrum for said location; choosing a set of different measurement directions d={dn} that originate from P, where n is a member of an integer sequence; recording an output On of said detector arrangement for different values of dn, thus compiling a measurement set M={(On, dn)}; adopting a spectral model On′ for On that is a convoluted mix of terms B(dn) and Lp, where: B(dn) is a substantially continuous spectral component associated with Bremsstrahlung; L.sub.P is a substantially discrete spectral component associated with the composition of the specimen at location P; automatically deconvolving the measurement set M on the basis of said spectral model On′ and distill Lp therefrom, wherein spectral model On′ is expressed in the form:
O.sub.n′=A(dn)*R(dn)
R(dn)=[Lp+B(dn)] in which A(dn) is an absorption function, accounting for the dependence of x-ray absorption as a function of the path length within the specimen, * is a mathematical convolution and R(dn) is a radiation function comprising the types of x-ray emitted from the specimen.
2. The method according to claim 1, wherein said deconvolution comprises, for each value of n, computationally determining a minimum divergence:
min div(O.sub.n∥O.sub.n′)=min div(O.sub.n∥A(d.sub.n)*[L.sub.p+B(d.sub.n)]) between O.sub.n and O.sub.n′, wherein one solves for L.sub.p while applying constraints on A(d.sub.n).
3. The method according to claim 1, wherein A(d.sub.n) is modelled according to:
4. The method according to claim 1, wherein: said detector arrangement comprises a plurality of sub-detectors {S.sub.n} that are angularly distributed about said specimen holder, whereby each sub-detector S.sub.n registers X-rays emanating along associated direction d.sub.n to yield associated output value O.sub.n; and the measurement set M is compiled by simultaneously acquiring its component data pairs (O.sub.n, d.sub.n).
5. The method according to claim 1, wherein: said detector arrangement comprises a unitary detector and an associated adjustment mechanism that allows said detector to be selectively aligned along different directions d.sub.n in the set d; and the measurement set M is compiled by sequentially acquiring its component data pairs (O.sub.n, d.sub.n).
6. The method according to claim 5, wherein said adjustment mechanism is selected from the group comprising: means for angularly moving the unitary detector relative to the specimen; and a tiltable specimen holder for adjusting an angular orientation of the specimen relative to the unitary detector, and combinations hereof.
7. The method according to claim 1, wherein said directing, examining and deconvolving steps are automatically repeated for a series of successive locations on the specimen.
8. The method according to claim 1, wherein said spectrum is selected from the group comprising an EDX spectrum, a PIXE spectrum and an XRF spectrum.
9. A spectroscopic apparatus, comprising: a specimen holder, for holding a specimen; a source, for producing an input beam of radiation; an illuminator, for directing said beam so as to irradiate the specimen; a detector arrangement, for detecting a flux of X-rays emanating from the specimen in response to said irradiation; a computer processor, programmed to perform at least one automated procedure in the apparatus, wherein said computer processor programmed to perform the following steps: choose a set of different measurement directions d={d.sub.n} that originate from P, where n is a member of an integer sequence; record an output On of said detector arrangement for different values of d.sub.n, thus compiling a measurement set M={(On, d.sub.n)}; adopt a spectral model On′ for On that is a convoluted mix of terms B and L.sub.p, where: B is a substantially continuous spectral component associated with Bremsstrahlung; and L.sub.P is a substantially discrete spectral component associated with the composition of the specimen at location P; and deconvolve the measurement set M on the basis of said spectral model On′ and distill L.sub.P therefrom, wherein spectral model On′ is expressed in the form:
On′=A(dn)*R(dn)
R(dn)=[Lp+B(dn)] in which A(d.sub.n) is an absorption function, accounting for the dependence of x-ray absorption as a function of the path length within the specimen, * is a mathematical convolution and R(d) is a radiation function comprising the types of x-ray emitted from the specimen.
10. The spectroscopic apparatus according to claim 9, wherein; said input beam comprises charged particles; and said apparatus is a charged-particle microscope.
11. The spectroscopic apparatus according to claim 9, wherein; said detector arrangement comprises a plurality of sub-detectors {S.sub.n} that are angularly distributed about said specimen holder.
12. The spectroscopic apparatus of claim 11, wherein each sub-detector S.sub.n registers X-rays emanating along associated direction d.sub.n to yield associated output value O.sub.n; and the computer processor is programmed to compile the measurement set M by simultaneously acquiring its component data pairs (O.sub.n, d.sub.n).
13. The spectroscopic apparatus of claim 11, wherein the sub-detectors {S.sub.n} are segments of a larger unitary detector.
14. The spectroscopic apparatus of claim 11, wherein the sub-detectors {S.sub.n} are discrete detectors.
15. The spectroscopic apparatus according to claim 9, wherein; said detector arrangement comprises a unitary detector and an associated adjustment mechanism that allows said detector to be selectively aligned along different directions d.sub.n in the set d; and the computer processor is programmed to compile the measurement set M by sequentially acquiring its component data pairs (O.sub.n, d.sub.n).
16. The spectroscopic apparatus according to claim 15, wherein said adjustment mechanism comprises an actuator for angularly moving the unitary detector relative to the specimen.
17. The spectroscopic apparatus according to claim 15, wherein said adjustment mechanism comprises an actuator for adjusting an angular orientation of the specimen relative to a fixed unitary detector.
18. The spectroscopic apparatus according to claim 9, wherein said detector arrangement comprises one or more of: an EDX detector; a PIXE detector; and an XRF detector, and combinations hereof.
19. The spectroscopic apparatus according to claim 9, wherein the computer processor is further programmed to automatically repeat on a series of locations on the specimen, the steps of: choose a set of different measurement directions d={d.sub.n} that originate from P, where n is a member of an integer sequence; record an output O.sub.n of said detector arrangement for different values of d.sub.n, thus compiling a measurement set M={(O.sub.n, d.sub.n)}; adopt a spectral model O.sub.n′ for O.sub.n that is a convoluted mix of terms B and L.sub.p, where: B is a substantially continuous spectral component associated with Bremsstrahlung; L.sub.p is a substantially discrete spectral component associated with the composition of the specimen at location P; and deconvolve the measurement set M on the basis of said spectral model O.sub.n′ and distill L.sub.p therefrom, on a series of locations on the specimen.
Description
(1) The invention will now be elucidated in more detail on the basis of exemplary embodiments and the accompanying schematic drawings, in which:
(2)
(3)
(4)
(5) In the Figures, where pertinent, corresponding parts may be indicated using corresponding reference symbols.
EMBODIMENT 1
(6) One intuitive way to consider the non-linear deconvolution task at hand is to formulate it using so-called Bayesian statistics.
(7) One first defines a number of probabilities that will be used throughout the elucidation below, whereby the following shorthand notation is introduced:
(8) A(d.sub.n) may be written as A.sub.n;
(9) R(d.sub.n) may be written as R.sub.n;
(10) B(d.sub.n) may be written as B.sub.n.
(11) One can then set forth the following:
(12) Pr(R.sub.n|O.sub.n) is the probability of distilling the spectral components R.sub.n given the recorded output values O.sub.n. The spectral components R.sub.n comprise Bremsstrahlung components B.sub.n and discrete (characteristic line) spectral component L.sub.p. Pr(R.sub.n) is the prior probability associated with the spectral components R.sub.n, representing available knowledge about the structure to be reconstructed. Pr(O.sub.n) is the probability associated with the acquired spectra; however, this is essentially a constant, given that the spectra O.sub.n are actually observed/measured values.
Using Bayes' rule one now obtains:
(13)
In the Bayesian framework, the current problem can be expressed as the following maximization task: =argmax.sub.R.sub.
in which one needs to enforce the positivity of the reconstructed variable R.sub.n. This is necessary in order to obtain a physically meaningful solution. More commonly, one will use the so called log-likelihood function to simplify the calculations: =argmin.sub.R.sub.
As regards its statistical nature, the data recording (detection) process in the current invention is well represented by a Poisson process; given the nature of charged-particle and X-ray detectors, one can assume that each element of the recorded spectra O.sub.n is formed by the realization of independent Poisson processes. This leads to:
(14)
wherein it should be noted that “x” is not the linear Cartesian coordinate X, but is instead an algebraic denotation of (three-dimensional) position.
To recover the spectral components R.sub.n, one needs to minimize the criterion:
(15)
Given that the Σ.sub.xΔΩlog (O.sub.n(x)!) term does not contain any variables, the criterion can be redefined as:
J((R.sub.n|O.sub.n))=Σ.sub.xΔΩ((A.sub.n*R.sub.n)(x))−O.sub.n(x).Math.log((A.sub.n*R.sub.n)(x)) (6)
It is important to note that this criterion is related to Kullback-Leibler generalized I-divergence IDIV(O.sub.n∥R.sub.n). This can be seen from the definition of I-divergence:
(16)
from which one can obtain:
IDIV(O.sub.n∥R.sub.n)=J((R.sub.n|O.sub.n))−Σ.sub.xΔΩO.sub.n(x).Math.log(O.sub.n(x)) (8)
The second term in (8) is a constant with regard to minimization and, hence, minimizing J((R.sub.n|O.sub.n)) is equivalent to minimizing IDIV(O.sub.n∥R.sub.n).
Reference is now made to the following journal article: [1] H. Lantéri, M. Roche, C. Aime, “Penalized maximum likelihood image restoration with positivity constraints: multiplicative algorithms, Inverse Problems,” vol. 18, pp. 1397-1419, 2002,
in which it was shown that a positivity-constrained minimization problem of the type (2) above can be solved using the following iterative scheme:
(17)
This algorithm is also known as the Maximum-Likelihood Expectation Maximization algorithm, which is further described, for example, in the following references: [2] L. Shepp, Y. Vardi, “Maximum-Likelihood reconstruction for emission tomography,” IEEE Transactions on Medical Imaging, MI-5, pp. 16-22, 1982. [3] Richardson, William Hadley. “Bayesian-Based Iterative Method of Image Restoration”, JOSA 62 (1), pp 55-59, 1972.
Convergence in expression (9) can be accelerated by using the exponent q as follows:
(18)
Typically, q ∈ [1, 1.5] and, in addition to acceleration, it can act as a regularizing factor. In the current case, the iterative algorithm needs to be sequentially used for all values A.sub.n associated with the different measurements. Convergence can be assessed empirically or based on other criteria, such as the relative change in the variables.
If one needs to recover or adjust the values of A.sub.n, one can use alternate minimization of R.sub.n and A.sub.n. One then obtains the following algorithm:
(19)
One can choose to have more iterations for the variables A.sub.n or R.sub.n at each cycle; such a choice can be determined based on experience/experimentation. For example, if it is generally noticed that R.sub.n tends to converge faster, then more iterations can be spent searching for the different values A.sub.n.
If prior knowledge about the variables A.sub.n or R.sub.n is available, it can be incorporated into the Bayesian formulation using a combination of conditional Pr(.|.) and joint probabilities Pr(.,.) as follows:
(20)
It follows that the minimization problem (2) is then modified as follows:
{circumflex over (V)}=argmax.sub.V≧0{Pr(V,K.sub.n|O.sub.n)} (13)
and the log-likelihood criterion to be minimized then becomes
(21)
While the first term is the data term that ensures that one fits the observations, the second and third terms are known as regularization terms that use knowledge and assumptions about the variables to limit the space of solutions and reduce the effects of noise. The criterion J(R.sub.n,A.sub.n|O.sub.n) can be minimized using the Maximum Likelihood Expectation Maximization approach. Optimization can be also carried using a variety of other convex and non-convex methods, as set forth, for example, in the following reference: [4] William H. Press, Saul A. Teukolsky, William T. Vetterling, Brian P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, Second Edition (1992).
(22) For completeness, it is noted that the approach set out in the current Embodiment can be regarded as a hybrid/variant of the so-called Richardson-Lucey Algorithm (RLA). The RLA is a known mathematical technique that can be applied to solve a variety of problems. For example, it was used by NASA scientists in an attempt to computationally improve blurred imagery from the original (i.e. uncorrected) Hubble Space Telescope.
EMBODIMENT 2
(23)
(24) The particle-optical column 1 comprises an electron source 9 (such as a Schottky emitter), lenses 11, 13 to focus the electron beam C onto the specimen S, and a deflection unit F (to perform beam deflection/scanning of the beam C). The apparatus M further comprises a controller/computer processing apparatus E for controlling inter alia the deflection unit F, lenses 11 and 13, X-ray detector arrangement D (=individual detectors D1+D2+D3+D4), and electron detector D′, and displaying information gathered from the X-ray detector arrangement D/electron detector D′ on a display unit 27.
(25) The items D, D′ are chosen from a variety of possible detector types that can be used to examine different types of “stimulated” output radiation flux emanating from the specimen S in response to irradiation by the input beam C. In the apparatus depicted here, the following detector choices have been made: In detector arrangement D, each of the individual sub-detectors D1, D2, D3, D4 is a silicon drift detector (SDD) that is used to detect a flux of X-rays emanating from the specimen S; alternatively, a Silicon Lithium (Si(Li)) detector, for example, could be used for this purpose. As here depicted, there are four sub-detectors D1-D4, though one could just as easily choose a different number of sub-detectors. Alternatively/supplementally, one could elect to detect X-rays using a movable unitary detector, and/or a stationary unitary detector in combination with a variety of different tilts of the specimen holder H. Detector D′ is a segmented electron detector, comprising a plurality of independent detection segments (e.g. quadrants) disposed about a central aperture 23 (allowing passage of the beam C). Such a detector can, for example, be used to investigate (the angular dependence of) a flux of output (secondary or backscattered) electrons emerging from the specimen S.
As a supplement to the depicted X-ray detector arrangement D and electron detector D′, one could, if desired, also elect to detect other types of output radiation emanating from the specimen S, such as cathodoluminescence, for instance. One could also elect to use a different type of electron detector D′, such as a boron-doped solid state detector, for instance.
(26) By scanning the input beam C over the specimen S, output radiation—generally comprising, a flux of X-rays, infrared/visible/ultraviolet light, secondary electrons and backscattered (BS) electrons—emanates from the specimen S. Since such output radiation is position-sensitive (due to said scanning motion), the information obtained from the X-ray detector arrangement D/electron detector D′ will also be position-dependent. This fact allows the output of: Electron detector D′ to be used to produce an electron image of (part of) the specimen S, which image is basically a map of an output of detector D′ as a function of scan-path position on the specimen S. One or more of sub-detectors D1, D2, D3, D4 to be used to yield a position-dependent EDX spectrum of (part of) the specimen S.
(27) The signals from items D, D′ pass along control lines (buses) E′, are processed by the controller E, and displayed on display unit 27. Such processing may include operations such as combining, integrating, subtracting, false colouring, edge enhancing, and other processing known to the skilled artisan. In addition, automated recognition processes (e.g. as used for particle analysis) may be included in such processing.
(28) It should be noted that many refinements and alternatives of such a set-up will be known to the skilled artisan, including, but not limited to: The use of dual beams—for example an electron beam C for imaging and an ion beam for machining (or, in some cases, imaging) the specimen S; The use of a controlled environment at the specimen S—for example, maintaining a pressure of several mbar (as used in a so-called Environmental SEM) or by admitting gases, such as etching or precursor gases,
etc.
(29) Turning now to
EMBODIMENT 3
(30)
(31) The specimen S is held on a (rod-like) specimen holder H that seats into a cradle A′ (such as the FEI CompuStage) connected to a positioning device (stage, actuator) A; this cradle A′ can typically be moved/positioned in X, Y, Z, and can also often be rotated about X and/or Y (see the depicted Cartesian coordinate system). Such positioning allows different parts of the specimen S to be irradiated/imaged/inspected by the electron beam traveling along axis C′, and also allows the specimen S to be tilted as part of a tomographic measurement series (sinogram acquisition), for example; in principle, it also allows scanning motion to be performed, as an alternative to beam scanning.
(32) The (focused) electron beam C traveling along axis C′ will interact with the specimen S in such a manner as to cause various types of “stimulated” radiation flux to emanate from the specimen S, including (for example) secondary electrons, backscattered electrons, X-rays and optical radiation (cathodoluminescence). If desired (as is the case in the current invention), one or more of these radiation types can be detected; in the current case, each of the sub-detectors D1, D2, D3, D4 is an EDX detector—such as an SDD or Si(Li) detector, for example—which together comprise a detector arrangement D, and which (individually or in groups) allow an EDX spectrum to be acquired, in much the same way as in Embodiment 2 above (SEM). However, in addition, one can study electrons that traverse (pass through) the specimen S, emerge (emanate) from it and continue to propagate (substantially, though generally with some deflection/scattering) along axis C′. Such a transmitted electron flux enters an imaging system (combined objective/projection lens) 24, which will generally comprise a variety of electrostatic/magnetic lenses, deflectors, correctors (such as stigmators), etc. In normal (non-scanning) TEM mode, this imaging system 24 can focus the transmitted electron flux onto a fluorescent screen 26, which, if desired, can be retracted/withdrawn (as schematically indicated by arrows 26′) so as to get it out of the way of axis C′. An image (or diffractogram) of (part of) the specimen S will be formed by imaging system 24 on screen 26, and this may be viewed through viewing port 28 located in a suitable part of a wall of enclosure V. The retraction mechanism for screen 26 may, for example, be mechanical and/or electrical in nature, and is not depicted here.
(33) As an alternative to viewing an image on screen 26, one can instead make use of the fact that the depth of focus of the electron flux emerging from imaging system 24 is generally quite large (e.g. of the order of 1 meter). Consequently, various other types of analysis apparatus can be used downstream of screen 26, such as: TEM camera 30. At camera 30, the electron flux can form a static image (or diffractogram) that can be processed by controller E and displayed on a display device (not depicted), such as a flat panel display, for example. When not required, camera 30 can be retracted/withdrawn (as schematically indicated by arrows 30′) so as to get it out of the way of axis C′. STEM recorder 32. An output from recorder 32 can be recorded as a function of (X,Y) scanning position of the beam C on the specimen S, and an image can be constructed that is a “map” of output from recorder 32 as a function of X,Y. Recorder 32 can comprise a single pixel with a diameter of e.g. 20 mm, as opposed to the matrix of pixels characteristically present in camera 30. Moreover, recorder 32 will generally have a much higher acquisition rate (e.g. 10.sup.6 points per second) than camera 30 (e.g. 10.sup.2 images per second). Once again, when not required, recorder 32 can be retracted/withdrawn (as schematically indicated by arrows 32′) so as to get it out of the way of axis C′ (although such retraction would not be a necessity in the case of a donut-shaped annular dark field recorder 32, for example; in such a recorder, a central hole would allow beam passage when the recorder was not in use). As an alternative to imaging using camera 30 or recorder 32, one can also invoke spectroscopic apparatus 34, which could be an EELS module, for example (EELS=Electron Energy-Loss Spectroscopy).
It should be noted that the order/position of items 30, 32 and 34 is not strict, and many possible variations are conceivable. For example, spectroscopic apparatus 34 can also be integrated into the imaging system 24.
(34) Note that the controller (computer processor) E (which may have a unitary or composite structure, as desired) is connected to various illustrated components via control lines (buses) E′. This controller E can provide a variety of functions, such as synchronizing actions, providing setpoints, processing signals, performing calculations, and displaying messages/information on a display device (not depicted). The skilled artisan will understand that the interior of the enclosure V does not have to be kept at a strict vacuum; for example, in a so-called “Environmental TEM/STEM”, a background atmosphere of a given gas is deliberately introduced/maintained within the enclosure V. The skilled artisan will also understand that, in practice, it may be advantageous to confine the volume of enclosure V so that, where possible, it essentially hugs the axis C′, taking the form of a small tube (e.g. of the order of 1 cm in diameter) through which the employed electron beam passes, but widening out to accommodate structures such as the source 4, specimen holder H, screen 26, camera 30, recorder 32, spectroscopic apparatus 34, etc.
(35) As depicted in