US20080037706A1 - Device and method for performing X-ray analysis - Google Patents

Device and method for performing X-ray analysis Download PDF

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US20080037706A1
US20080037706A1 US11/501,309 US50130906A US2008037706A1 US 20080037706 A1 US20080037706 A1 US 20080037706A1 US 50130906 A US50130906 A US 50130906A US 2008037706 A1 US2008037706 A1 US 2008037706A1
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energy
filter
max
rays
equal
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Gustaaf Christian Simon Brons
Petronella Emerentiana Hegeman
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Malvern Panalytical BV
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Panalytical BV
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Assigned to PANALYTICAL B.V. reassignment PANALYTICAL B.V. ASSIGNMENT OF ASSIGNORS INTEREST (SEE DOCUMENT FOR DETAILS). Assignors: BRONS, GUSTAAF C.S., HEGEMAN, PETRONELLA E.
Publication of US20080037706A1 publication Critical patent/US20080037706A1/en
Priority to US12/110,035 priority patent/US7949092B2/en
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N23/00Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00
    • G01N23/22Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00 by measuring secondary emission from the material
    • G01N23/223Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00 by measuring secondary emission from the material by irradiating the sample with X-rays or gamma-rays and by measuring X-ray fluorescence
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2223/00Investigating materials by wave or particle radiation
    • G01N2223/07Investigating materials by wave or particle radiation secondary emission
    • G01N2223/076X-ray fluorescence
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2223/00Investigating materials by wave or particle radiation
    • G01N2223/10Different kinds of radiation or particles
    • G01N2223/101Different kinds of radiation or particles electromagnetic radiation
    • G01N2223/1016X-ray
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2223/00Investigating materials by wave or particle radiation
    • G01N2223/20Sources of radiation
    • G01N2223/204Sources of radiation source created from radiated target
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2223/00Investigating materials by wave or particle radiation
    • G01N2223/30Accessories, mechanical or electrical features
    • G01N2223/313Accessories, mechanical or electrical features filters, rotating filter disc
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2223/00Investigating materials by wave or particle radiation
    • G01N2223/30Accessories, mechanical or electrical features
    • G01N2223/316Accessories, mechanical or electrical features collimators

Definitions

  • the invention relates to a device for performing X-ray analysis, more particularly analysis of X-ray fluorescence originating from a relatively small irradiated region of a sample.
  • X-ray fluorescence (XRF) spectrometry is generally applied for the purpose of identifying and determining concentrations of elements in specimens of materials, be it in solid, liquid or powder form.
  • micro-region a relatively small region of a sample for analysis.
  • the desired dimensions of the micro-region to be irradiated lie, as an indication, in the order of magnitude of several tens of to several thousand square micrometres.
  • surrounding electronics in this way remain practically non-irradiated, and the risk of possible damage due to the effect of X-rays can be avoided.
  • the invention has for its object to provide a device of the type stated in the preamble which fulfils this wish.
  • the device comprises for this purpose an X-ray tube and at least one capillary lens for focusing the X-rays in a micro-region at a location for a sample for analysis, in addition to a detector for detecting X-ray fluorescence from the sample, wherein the device further comprises at least one energy-dependent filter placed in the optical path between the X-ray tube and the sample location, wherein the filter is adapted to block in considerable measure X-rays with an energy which is equal to or lower than a predetermined energy value, this such that the dimensions of the micro-region are substantially bounded within predetermined permissible values.
  • the invention is based on the insight that the dimensions of the irradiated region at the sample location are energy-dependent: at lower energies the irradiated region is larger.
  • the dimensions of the irradiated region can be bounded within predetermined permissible values by applying an energy-dependent filter placed in the optical path between the X-ray tube and the sample location.
  • the setting of the threshold value of the filter determines the realized dimensions of the irradiated region.
  • the device according to the invention has the further advantage that diffraction peaks occurring at an energy which is equal to or lower than the predetermined energy value of the filter are eliminated. This implies a significant improvement in the reliability of the outcome of the X-ray analysis.
  • the filter comprises aluminium.
  • the thickness of the filter is preferably smaller than or equal to 300 micrometres.
  • the thickness of the filter must provide an optimum between the desired transmission characteristics of the filter and the intensity per energy value required at the position of the sample location.
  • the X-ray tube is adapted to generate an X-ray beam with a microfocus.
  • Suitable low-power microfocus tubes are obtainable in the field.
  • the filter is placed in the optical path between the X-ray tube and the capillary lens.
  • the capillary lens is a polycapillary lens.
  • a polycapillary lens is highly suitable for focusing the filtered X-ray beam of the microfocus tube on the sample location.
  • the invention also relates to a method for performing X-ray analysis using a device according to the invention, comprising the steps of:
  • step b) selecting a filter which is adapted to block in considerable measure X-rays with an energy which is equal to or lower than a predetermined energy value, wherein the energy value is chosen to be substantially equal to the energy determined in step b).
  • a suitable filter can be selected for any application.
  • step c) of the method comprises the following steps of:
  • FIG. 1 shows a diagram of a preferred embodiment of the device according to the invention
  • FIG. 2A shows in a graph the relation between the spot size (curve A) and the transmission of a filter suitable for the invention (curve B) plotted against the energy of the X-rays;
  • FIG. 2B illustrates in a graph the relation between the transmission and the spot size.
  • FIG. 1 shows schematically the most important components of device 1 according to the invention in their mutual interrelation.
  • Device 1 is generally intended for analysis of materials using XRF spectrometry.
  • Device 1 comprises an X-ray tube 2 , an energy-dependent filter 3 , a capillary lens 4 , a sample location 5 and an X-ray detector 6 .
  • X-ray tube 2 is preferably adapted to generate an X-ray beam R from a microfocus.
  • a microfocus is understood to mean a focus on the anode with dimensions in the order of several tens to about 100 micrometres (L+W)/2, this also being referred to in the technical field as “focal spot size”.
  • Such an X-ray tube is commercially available and is referred to in the field as a microfocus tube.
  • An example of a suitable microfocus tube is “Series 5000 Packaged X-ray tubes”, marketed by Oxford Instruments, X-ray Technology established in Scotts Valley Calif., United States of America.
  • Filter 3 is placed in the optical path between X-ray tube 2 and capillary lens 4 .
  • Filter 3 is adapted to block in considerable measure X-rays from beam R with an energy which is equal to or lower than a predetermined energy value.
  • the predetermined energy value depends on the desired dimensions for setting the region to be irradiated, this being illustrated on the basis of FIGS. 2A and 2B .
  • Material with a K-absorption edge which is less than or equal to 2 keV results in a smooth transmission curve for the filter. Different materials meet this requirement, including aluminium, silicon, carbon.
  • the thickness of the filter lies in the range up to 300 micrometres, preferably in the range of 50 to 200 micrometres. The thickness of the filter must be chosen as optimum between the desired transmission characteristics on the one hand and the energy efficiency of the X-ray tube on the other.
  • the X-ray beam passing through filter 3 is designated RF.
  • FIG. 2A shows two curves in one graph: curve A illustrates the spot size S of the X-rays at different energies and curve B shows the transmission characteristic T of a filter suitable for the invention.
  • curve A illustrates the spot size associated with the irradiated region, or micro-region, on the sample is plotted on the left on the vertical axis and expressed in micrometre Full Width Half Max (FWHM).
  • FWHM micrometre Full Width Half Max
  • the energy of the X-rays expressed in kilo-electron volts is shown on the horizontal axis.
  • Curve A clearly shows the trend that the spot size decreases as the energies increase.
  • curve B the percentage transmission of the filter is shown on the vertical axis.
  • Filter 3 is here an aluminium filter with a thickness of 200 micrometres.
  • FIG. 2B shows a graph with curve C therein which illustrates schematically the resulting spot size of microfocus tube 2 on a sample 5 for analysis after applying the filter 3 as described with reference to FIG. 2A .
  • the horizontal axis shows the dimensions of spot size S on the sample expressed in micrometre Full Width Half Max (FWHM).
  • the vertical axis shows the percentage transmission T of filter 3 .
  • a suitable filter can be selected for a device according to the invention for any intended application.
  • a first step in the desired maximum dimensions S max for the micro-region are determined.
  • the spot size S max is determined at 35 micrometre FWHM.
  • E max of the X-rays associated with the desired maximum dimensions S max for the micro-region is determined.
  • This E max can be directly derived from curve A which shows the relation between these two quantities.
  • E max has the value 6.7 keV.
  • a filter is selected which is adapted to block in considerable measure X-rays with an energy which is equal to or lower than E max , in this numerical example 6.7 keV.
  • the transmission characteristic is subsequently determined for one or more filters of differing thickness of the selected filter material.
  • curve B is determined for an aluminium filter of a thickness of 200 micrometres.
  • the permissible transmission for X-rays with an energy E max has to be determined.
  • the permissible transmission for 6.7 keV is approximately 1%.
  • the aluminium filter of 200 micrometre thickness is found to readily satisfy this criterion.
  • Capillary lens 4 focuses the beam R F as a beam R F+L on the sample location 5 .
  • Lens 4 can be both a polycapillary and a monocapillary lens. Diverse suitable capillary lenses are commercially available.
  • device 1 irradiates a relatively small region (micro-region) of a sample at sample location 5 .
  • the dimensions of the irradiated micro-region can be derived directly from dimensions of the spot size in micrometre FWHM.
  • the following relation known in the field can be used for this purpose:
  • 6*sigma shows the so-called footprint, i.e. the dimensions of the region on the sample within which 99.7% of the X-radiation is incident.
  • the spot size between approximately 20 and 25 FWHM results in a footprint of between 50 and 60 micrometres respectively.
  • Dimensions of the irradiated region, or micro-region, in the order of magnitude of 50 ⁇ 50 micrometres are therefore feasible with the embodiment described herein. This makes device 1 particularly suitable for analysis of the composition of so-called wafers in the semiconductor industry.
  • the device according to the invention has the further important advantage that the diffraction peaks, which occur at energy values falling within the energy range largely blocked by the filter, are generally eliminated.
  • Detector 6 is adapted to detect X-ray fluorescence F coming from the irradiated region in the sample. Diverse suitable X-ray detectors are commercially available.
  • device 1 is described in the context of Energy Dispersive (ED) XRF. It will however be apparent to a skilled person in the field that the invention is not limited thereto, but is also very readily applicable in the case of Wavelength Dispersive (WD) XRF.
  • ED Energy Dispersive
  • WD Wavelength Dispersive
  • FIG. 1 an analyzer crystal (not shown) must then for instance be placed in the optical path between sample location 5 and detector 6 .
  • the invention is expressly not limited to the described and shown embodiment.
  • the combination of a standard X-ray tube with a capillary lens can particularly also be envisaged, even though this is energetically less efficient.

Abstract

The invention relates to a device for performing X-ray analysis. Device 1 comprises an X-ray tube 2 and at least one capillary lens 4 for focusing the X-rays in a micro-region at a location 5 for a sample for analysis. Device 1 further comprises a detector 6 for detecting X-ray fluorescence from the sample. Device 1 further comprises at least one energy-dependent filter 3 placed between the X-ray tube 2 and the capillary lens 4. The filter 3 is adapted to substantially block X-rays with an energy which is lower than a predetermined threshold value.

Description

  • The invention relates to a device for performing X-ray analysis, more particularly analysis of X-ray fluorescence originating from a relatively small irradiated region of a sample.
  • X-ray fluorescence (XRF) spectrometry is generally applied for the purpose of identifying and determining concentrations of elements in specimens of materials, be it in solid, liquid or powder form.
  • There is a wish in different technical fields to irradiate only a relatively small region (micro-region) of a sample for analysis. The desired dimensions of the micro-region to be irradiated lie, as an indication, in the order of magnitude of several tens of to several thousand square micrometres. Particularly in the semiconductor industry, where semi-manufactures are usually analyzed, surrounding electronics in this way remain practically non-irradiated, and the risk of possible damage due to the effect of X-rays can be avoided.
  • The invention has for its object to provide a device of the type stated in the preamble which fulfils this wish.
  • The device according to the invention comprises for this purpose an X-ray tube and at least one capillary lens for focusing the X-rays in a micro-region at a location for a sample for analysis, in addition to a detector for detecting X-ray fluorescence from the sample, wherein the device further comprises at least one energy-dependent filter placed in the optical path between the X-ray tube and the sample location, wherein the filter is adapted to block in considerable measure X-rays with an energy which is equal to or lower than a predetermined energy value, this such that the dimensions of the micro-region are substantially bounded within predetermined permissible values.
  • The X-ray tube and the capillary lens together generate an X-ray beam in a micro-region at the sample location. The invention is based on the insight that the dimensions of the irradiated region at the sample location are energy-dependent: at lower energies the irradiated region is larger. The dimensions of the irradiated region can be bounded within predetermined permissible values by applying an energy-dependent filter placed in the optical path between the X-ray tube and the sample location. The setting of the threshold value of the filter determines the realized dimensions of the irradiated region. The device according to the invention has the further advantage that diffraction peaks occurring at an energy which is equal to or lower than the predetermined energy value of the filter are eliminated. This implies a significant improvement in the reliability of the outcome of the X-ray analysis.
  • In a first preferred embodiment the filter comprises aluminium. The thickness of the filter is preferably smaller than or equal to 300 micrometres. The thickness of the filter must provide an optimum between the desired transmission characteristics of the filter and the intensity per energy value required at the position of the sample location.
  • In a further preferred embodiment the X-ray tube is adapted to generate an X-ray beam with a microfocus. Suitable low-power microfocus tubes are obtainable in the field.
  • In a practical preferred embodiment the filter is placed in the optical path between the X-ray tube and the capillary lens.
  • According to yet another preferred embodiment, the capillary lens is a polycapillary lens. A polycapillary lens is highly suitable for focusing the filtered X-ray beam of the microfocus tube on the sample location.
  • The invention also relates to a method for performing X-ray analysis using a device according to the invention, comprising the steps of:
  • a) determining the desired maximum dimensions for the micro-region;
  • b) determining the energy of the X-rays associated with the desired maximum dimensions for the micro-region;
  • c) selecting a filter which is adapted to block in considerable measure X-rays with an energy which is equal to or lower than a predetermined energy value, wherein the energy value is chosen to be substantially equal to the energy determined in step b).
  • Using the method according to the invention a suitable filter can be selected for any application.
  • According to a preferred embodiment, step c) of the method comprises the following steps of:
  • 1) selecting filter material that is suitable for blocking in considerable measure X-rays with an energy which is equal to or lower than the energy determined in step b);
  • 2) determining the transmission characteristic in a number of filters with differing thickness of the selected filter material; and
  • 3) selecting a thickness for the filter material associated with a predetermined value for the permissible transmission of X-rays with an energy equal to the energy determined in step b).
  • The invention will be described further on the basis of the drawings, in which:
  • FIG. 1 shows a diagram of a preferred embodiment of the device according to the invention;
  • FIG. 2A shows in a graph the relation between the spot size (curve A) and the transmission of a filter suitable for the invention (curve B) plotted against the energy of the X-rays; and
  • FIG. 2B illustrates in a graph the relation between the transmission and the spot size.
  • FIG. 1 shows schematically the most important components of device 1 according to the invention in their mutual interrelation. Device 1 is generally intended for analysis of materials using XRF spectrometry.
  • Device 1 comprises an X-ray tube 2, an energy-dependent filter 3, a capillary lens 4, a sample location 5 and an X-ray detector 6.
  • X-ray tube 2 is preferably adapted to generate an X-ray beam R from a microfocus. In the context of this invention a microfocus is understood to mean a focus on the anode with dimensions in the order of several tens to about 100 micrometres (L+W)/2, this also being referred to in the technical field as “focal spot size”. Such an X-ray tube is commercially available and is referred to in the field as a microfocus tube. An example of a suitable microfocus tube is “Series 5000 Packaged X-ray tubes”, marketed by Oxford Instruments, X-ray Technology established in Scotts Valley Calif., United States of America.
  • Filter 3 is placed in the optical path between X-ray tube 2 and capillary lens 4. Filter 3 is adapted to block in considerable measure X-rays from beam R with an energy which is equal to or lower than a predetermined energy value. The predetermined energy value depends on the desired dimensions for setting the region to be irradiated, this being illustrated on the basis of FIGS. 2A and 2B. Material with a K-absorption edge which is less than or equal to 2 keV results in a smooth transmission curve for the filter. Different materials meet this requirement, including aluminium, silicon, carbon. The thickness of the filter lies in the range up to 300 micrometres, preferably in the range of 50 to 200 micrometres. The thickness of the filter must be chosen as optimum between the desired transmission characteristics on the one hand and the energy efficiency of the X-ray tube on the other. The X-ray beam passing through filter 3 is designated RF.
  • FIG. 2A shows two curves in one graph: curve A illustrates the spot size S of the X-rays at different energies and curve B shows the transmission characteristic T of a filter suitable for the invention. For the purpose of curve A the spot size associated with the irradiated region, or micro-region, on the sample is plotted on the left on the vertical axis and expressed in micrometre Full Width Half Max (FWHM). The energy of the X-rays expressed in kilo-electron volts is shown on the horizontal axis. Curve A clearly shows the trend that the spot size decreases as the energies increase. For the purpose of curve B the percentage transmission of the filter is shown on the vertical axis.
  • The graphs show measurements on device 1 according to the invention in the described preferred embodiment. Filter 3 is here an aluminium filter with a thickness of 200 micrometres.
  • FIG. 2B shows a graph with curve C therein which illustrates schematically the resulting spot size of microfocus tube 2 on a sample 5 for analysis after applying the filter 3 as described with reference to FIG. 2A. The horizontal axis shows the dimensions of spot size S on the sample expressed in micrometre Full Width Half Max (FWHM). The vertical axis shows the percentage transmission T of filter 3.
  • From curve C can clearly be seen the trend that a minimization of the spot size can be achieved in a device according to the invention. In the preferred embodiment of device 1 can be seen that filter 3 transmits the most X-rays at a spot size of between approximately 20 and 25 FWHM.
  • By means of the method according to the invention a suitable filter can be selected for a device according to the invention for any intended application.
  • The method steps are described and elucidated below by means of a numerical example.
  • In a first step in the desired maximum dimensions Smax for the micro-region are determined. In the context of the numerical example the spot size Smax is determined at 35 micrometre FWHM.
  • In a second step the energy Emax of the X-rays associated with the desired maximum dimensions Smax for the micro-region is determined. This Emax can be directly derived from curve A which shows the relation between these two quantities. In the chosen numerical example Emax has the value 6.7 keV.
  • In a third step a filter is selected which is adapted to block in considerable measure X-rays with an energy which is equal to or lower than Emax, in this numerical example 6.7 keV.
  • The selection of a suitable filter is carried out according to the invention on the basis of the following steps.
  • A choice must first be made for a filter material that is suitable for blocking in considerable measure X-rays with an energy which is equal to or lower than Emax, in this numerical example 6.7 keV. In this example a choice has been made for aluminium.
  • The transmission characteristic is subsequently determined for one or more filters of differing thickness of the selected filter material. In this example curve B is determined for an aluminium filter of a thickness of 200 micrometres.
  • In order to select a suitable thickness for the filter, the permissible transmission for X-rays with an energy Emax has to be determined. In this numerical example the permissible transmission for 6.7 keV is approximately 1%. The aluminium filter of 200 micrometre thickness is found to readily satisfy this criterion.
  • It is noted for the sake of completeness that the relation between spot size S and energy E also depends on the capillary 4. Curves A and C must therefore be determined separately for each configuration of device 1.
  • Capillary lens 4 focuses the beam RF as a beam RF+L on the sample location 5. Lens 4 can be both a polycapillary and a monocapillary lens. Diverse suitable capillary lenses are commercially available.
  • During operation device 1 irradiates a relatively small region (micro-region) of a sample at sample location 5. The dimensions of the irradiated micro-region can be derived directly from dimensions of the spot size in micrometre FWHM. The following relation known in the field can be used for this purpose:

  • FWHM/2.36=sigma
  • wherein 6*sigma shows the so-called footprint, i.e. the dimensions of the region on the sample within which 99.7% of the X-radiation is incident.
  • The spot size between approximately 20 and 25 FWHM results in a footprint of between 50 and 60 micrometres respectively. Dimensions of the irradiated region, or micro-region, in the order of magnitude of 50×50 micrometres are therefore feasible with the embodiment described herein. This makes device 1 particularly suitable for analysis of the composition of so-called wafers in the semiconductor industry.
  • The device according to the invention has the further important advantage that the diffraction peaks, which occur at energy values falling within the energy range largely blocked by the filter, are generally eliminated. In the shown and described preferred embodiment of device 1 the diffraction peak occurring in a sample Si(100), which is normally visible at 5.5 keV, is for instance eliminated.
  • Detector 6 is adapted to detect X-ray fluorescence F coming from the irradiated region in the sample. Diverse suitable X-ray detectors are commercially available.
  • It is noted that device 1 is described in the context of Energy Dispersive (ED) XRF. It will however be apparent to a skilled person in the field that the invention is not limited thereto, but is also very readily applicable in the case of Wavelength Dispersive (WD) XRF. In FIG. 1 an analyzer crystal (not shown) must then for instance be placed in the optical path between sample location 5 and detector 6.
  • Finally, the invention is expressly not limited to the described and shown embodiment. In addition to the described combination of a microfocus tube with a polycapillary lens, the combination of a standard X-ray tube with a capillary lens can particularly also be envisaged, even though this is energetically less efficient.
  • The invention therefore extends generally to any embodiment falling within the scope of the appended claims, as seen in the light of the foregoing description and drawings.

Claims (8)

1. Device (1) for performing X-ray analysis, comprising an X-ray tube (2) and at least one capillary lens (4) for focusing the X-rays in a microregion at a location (5) for a sample for analysis, in addition to a detector (6) for detecting X-ray fluorescence from the sample, wherein the device further comprises at least one energy-dependent filter (3) placed in the optical path between the X-ray tube and the location (5), wherein the filter is adapted to block in considerable measure X-rays with an energy which is equal to or lower than a predetermined energy value (Emax), this such that the dimensions of the micro-region (Smax) are substantially bounded within predetermined permissible values.
2. Device as claimed in claim 1, wherein the filter (3) comprises aluminum.
3. Device as claimed in claim 1, wherein the thickness of the filter (3) is smaller than or equal to 300 micrometres.
4. Device as claimed in claim 1, wherein the filter (3) is placed in the optical path between the X-ray tube (2) and the capillary lens (4).
5. Device as claimed in claim 1, wherein the X-ray tube (2) is a microfocus tube.
6. Device as claimed in claim 1, wherein the capillary lens (4) is a polycapillary lens.
7. Method for performing X-ray analysis using a device (1) as claimed in claim 1, comprising the steps of:
a) determining the desired maximum dimensions (Smax) for the micro-region;
b) determining the energy (Emax) of the X-rays associated with the desired maximum dimensions (Smax) for the micro-region;
c) selecting a filter (3) which is adapted to block in considerable measure X-rays with an energy which is equal to or lower than a predetermined energy value, wherein the energy value is chosen to be substantially equal to the energy (Emax) determined in step b).
8. Method as claimed in claim 7, wherein step c) comprises of:
1. selecting filter material that is suitable for blocking in considerable measure X-rays with an energy which is equal to or lower than the energy (Emax) determined in step b);
2. determining the transmission characteristic (curve B) in a number of filters with differing thickness of the selected filter material; and
3. selecting a thickness for the filter material associated with a predetermined value for the permissible transmission of X-rays with an energy equal to the energy (Emax) determined in step b).
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