METHOD AND SYSTEM FOR DETERMINING THE POSITION OF A RADIATION SOURCE

Abstract

The present invention refers to a method for determining a position of a divergent radiation source (1), comprising Irradiating a pixel detector (2) with a predetermined intensity distribution of radiation with wavelength λ originated from the radiation source (1), wherein the pixel detector (2) comprises a plurality of pixels with pixel coordinates (x.sub.i, y.sub.i, z.sub.i); Detecting, for each of the plurality of pixels, an intensity of the incident radiation (10); Determining, for each of the plurality of pixels, an incidence direction of the incident radiation using information on an orientation of an internal periodic structure at the pixel and the predetermined intensity distribution, wavelength λ and the detected intensity; and Determining the position (x.sub.p, y.sub.p, z.sub.p) of the radiation source (1) using the pixel coordinates (x.sub.i, y.sub.i, z.sub.i) and the incidence direction for each of the plurality of pixels. The invention further refers to a system, a computer-related product and a sample (8) for performing such method and to the use of a pixel detector (2) for determining a position of a divergent radiation source (1)

Claims

1. Method for determining a position of a divergent radiation source, comprising: irradiating a pixel detector with a predetermined intensity distribution of radiation with wavelength λ originated from the radiation source, wherein the pixel detector comprises a plurality of pixels with pixel coordinates (x.sub.i, y.sub.i, z.sub.i); detecting, for each of the plurality of pixels, an intensity of the incident radiation; determining, for each of the plurality of pixels, an incidence direction of the incident radiation using information on an orientation of an internal periodic structure at the pixel and the predetermined intensity distribution, wavelength λ and the detected intensity; and determining the position (x.sub.p, y.sub.p, z.sub.p) of the radiation source using the pixel coordinates (x.sub.i, y.sub.i, z.sub.i) and the incidence direction for each of the plurality of pixels.

2. Method according to claim 1, further comprising: the detected intensity at each of the plurality of pixels depends on the incident intensity distribution and the orientation of the internal periodic structure at the pixel and wavelength λ.

3. Method according to claim 1, further comprising: determining, for each of the plurality of pixels, a polar component φ.sub.i and/or an azimuthal component θi of an angle of incidence of the incident radiation using the information on an orientation of an internal periodic structure at the pixel and the predetermined intensity distribution, wavelength λ and the detected intensity.

4. Method according to claim 1, further comprising: determining, for each of the plurality of pixels, an orientation of an internal periodic structure by: comparing the detected intensity with a simulated intensity, wherein the simulated intensity depends on an assumed orientation of an internal periodic structure and an assumed radiation source position or measuring the orientation of an internal periodic structure in an independent measurement; determining, for each of the plurality of pixels, an incidence direction and the position (x.sub.p, y.sub.p, z.sub.p) of the radiation source by: comparing the detected intensity with a simulated intensity, wherein the simulated intensity depends on the determined orientation of an internal periodic structure and an assumed radiation source position of the incident radiation.

5. Method according to claim 1, characterized in that: the assumed orientation of an internal periodic structure at each of the plurality of pixels corresponds to manufacturer specifications on the orientation of an internal periodic structure; and the determined orientation of an internal periodic structure at each of the plurality of pixels considers manufacturing uncertainties.

6. Method according to claim 1, characterized in that: the radiation source comprises a spatial extension that is small compared to the dimensions of the detector and quasi-isotropically emits radiation in a predetermined solid angle, and the predetermined intensity distribution is isotropic at each of the plurality of pixels.

7. Method according to claim 1, characterized in that: the pixel detector comprises a detector surface, divided into a plurality of pixels with pixel coordinates (x.sub.i, y.sub.i, z.sub.i), and a detector volume, divided into a plurality of voxels corresponding to the plurality of pixels, wherein each voxel comprises a material with a fixed orientation of an internal periodic structure.

8. Method according to claim 1, characterized in that: the pixel detector comprises a detector surface, divided into a plurality of pixels with pixel coordinates (x.sub.i, y.sub.i, z.sub.i), and a detector volume, divided into a plurality of voxels corresponding to the plurality of pixels and comprising a single crystalline material.

9. Method according to claim 1, characterized in that: the divergent radiation source is a sample region reflecting or deflecting an incident beam of a primary radiation.

10. Method according to claim 9, characterized in that: the sample region comprises a polycrystalline or amorphous sample volume that is configured for quasi-isotropically reflecting or deflecting the primary radiation.

11. System for determining the position of a divergent radiation source, comprising: a divergent radiation source; a pixel detector with a plurality of pixels with pixel coordinates (x.sub.i, y.sub.i, z.sub.i); and a control unit configured for performing a method according to claim 1.

12. System according to claim 11, characterized in that: the pixel detector is hybrid pixel detector, comprising a sensor with a detector surface, divided into a plurality of pixels with pixel coordinates (x.sub.i, y.sub.i, z.sub.i), and a detector volume, divided into a plurality of voxels corresponding to the plurality of pixels, wherein each voxel comprises a material with fixed orientation of an internal periodic structure, and an electronics chip with a plurality of amplification pixels, each corresponding to one of the plurality of pixels.

13. Sample for a system according to claim 11, the system further comprising a primary radiation source, wherein the divergent radiation source is a calibration region of a sample; wherein the calibration region comprises a polycrystalline or amorphous material; and wherein the calibration region is configured for quasi-isotropically reflecting or deflecting an incident beam of primary radiation.

14. A computer readable medium comprising program instructions, wherein when executed in a control unit of a system according to claim 11 the program instructions are operable to perform the method for determining.

15. Use of a pixel detector for determining a position of a divergent radiation source, wherein the pixel detector comprises a detector surface, divided into a plurality of pixels with pixel coordinates (x.sub.i, y.sub.i, z.sub.i), and a detector volume, divided into a plurality of voxels corresponding to the plurality of pixels, wherein each voxel comprises a material with fixed orientation of an internal periodic structure at each of the plurality of voxels; wherein the pixel detector is irradiated with radiation originated from the radiation source; wherein the radiation has a predetermined intensity distribution and a wavelength λ and wherein an intensity of the incident radiation is detected for each of the plurality of pixels; wherein for each of the plurality of pixels an incidence direction of the incident radiation is determined using information on the orientation of the internal periodic structure at the pixel and the predetermined intensity distribution, wavelength λ and the detected intensity; and wherein the position (x.sub.p, y.sub.p, z.sub.p) of the radiation source is determined using the pixel coordinates (x.sub.i, y.sub.i, z.sub.i) and the incidence direction for each of the plurality of pixels.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0040] The features of the invention become apparent to those skilled in the art by the detailed description of exemplary embodiments with reference to the attached drawings in which:

[0041] FIG. 1 shows a schematic illustration of a system according to an embodiment,

[0042] FIG. 2 shows (A) a schematic illustration of a detector channeling effect of electron waves incident on a single crystalline detector and (B) the angular dependence of backscattered intensity,

[0043] FIG. 3 shows a schematic illustration of the principle of determining the radiation source position according to the present invention,

[0044] FIG. 4 shows a schematic illustration of detected intensity pattern modulated by a detector channeling pattern (DCP),

[0045] FIG. 5 shows the comparison of the negative of (a) a measured and (b) a simulated detector channeling pattern, and

[0046] FIG. 6 shows a measured EBSD pattern superimposed with a detector channeling pattern and a simulated EBSD pattern and a simulated detector channeling pattern.

DETAILED DESCRIPTION OF THE INVENTION

[0047] Referring to FIG. 1, an exemplary embodiment of a system according to the invention is shown, the system being integrated in a scanning electron microscope (SEM) as an apparatus for electron backscatter diffraction. The SEM comprises an electron source 7 as primary radiation source that radiates a sample 8 with a focused electron beam 9 as primary radiation. The electron beam 9 is focused on a region of a sample 8 and is diffracted by the sample in this region. Thereby, the sample region becomes a divergent radiation source 1 for backscattered electrons 10 that are incident on a detector surface 4 of sensor 3.

[0048] The backscattered electrons produce a diffraction pattern as a predetermined intensity distribution on the detector surface 4, wherein the intensity can be modulated by sample 8 dependent of the inner structure of the sample. Through the detector surface 4, the electrons enter a detector volume 5, wherein the electrons interact with the detector material in producing electron-hole pairs. The electron hole pairs lead to a current that is detected and amplified by an electronics chip 6 that is affixed to the sensor 3. The sensor 3 and electronics chip 6 together constitute detector 2.

[0049] FIG. 2 (A) shows a schematic illustration of the detector channeling effect that is the physical effect underlying the method according to the invention. The latter effect results e.g. if backscattered electrons 10, as shown in FIG. 1, are irradiated on a detector surface 4, as shown in FIG. 1, comprising a crystalline structure with multiple crystal lattice planes 11.

[0050] As shown in FIG. 2 (A), the electrons 10 emitted from the radiation source 1 (in FIG. 1 the spot where the electron beam 9 from the SEM 7 hits the sample 8) travel towards the detector plane 4 that is made from a silicon wafer cut in (111) orientation. The electrons impinge on each pixel 4a of detector surface 4 at a specific incidence direction, e.g. given by the polar component φ.sub.i of the angle of incidence of the incident radiation with respect to the surface normal of the detector surface 4 and the azimuth component θ.sub.i of the angle of incidence of the incident radiation with respect to the surface plane of the detector surface 4.

[0051] The penetration depth of the incident radiation 10 into the silicon detector volume 5 is determined by multiple electron reflections at the silicon crystal lattice planes 11 within the detector volume 5 and changes near the Bragg angle, because of the preferential excitation of Bloch waves that are localized either on lattice planes or exactly between them (cf. D. C. Joy et al. J. Appl. Phys. 53 R 81 (1982)). Since the incident radiation 10 penetrates to various depth into the detector volume 5, the excitation of electron-hole pairs in the silicon voxel, i.e. the intensity detected at this pixel, is changed as a function of the incidence direction, as shown in FIG. 2. Because the electrons can go less deep when there is a large backscattered signal, the detected intensity pattern modulated by the detector channeling effect is negatively proportional to the backscattered intensity as shown in FIG. 2 (B).

[0052] The detector channeling effect thus provides a one-to-one relationship between pixel position (x.sub.i, y.sub.i) on detector surface 4 and the incidence direction of the incident radiation and thus the radiation source position (x.sub.SOURCE, y.sub.SOURCE, z.sub.SOURCE). As shown in FIG. 3, planar detector surface 4 with area elements dA.sub.n is reacting to diffraction effects of incident radiation from the source 1 in the area element dA.sub.n. Each area element dA.sub.n at a specific position (x.sub.n, y.sub.n) on the detector is showing an intensity which is related to the direction from the radiation source 1 to the area element dA.sub.n and vice versa. A triangulation procedure involving the intensities from all area elements dA.sub.n; i.e. from all pixels, of the detector 2 thus allows to pinpoint the position of source 1.

[0053] An exemplary detected intensity pattern solely modulated by the detector channeling effect, i.e. a pure detector diffraction pattern, is shown in FIG. 4. The shown 2D intensity pattern is visible in the detector response even in total absence of diffraction effects from sample 8. The observed patterns further have the negative intensity distribution relative to what is usually observed for backscattered electrons from a crystal. Thus, these patterns are interpreted as electron channeling patterns formed not by the sample 8 but in the crystalline detector volume 5 instead. A pattern as shown in FIG. 4 will be obtained by detecting an incident radiation from an amorphous sample 8 as divergent radiation source 1 of deflected or reflected primary radiation with a single-crystalline detector made from a silicon wafer cut in (111) orientation.

[0054] Crystallographically, the detector channeling pattern gives crystal lattice directions (“zone axes”) as crossing points of the center lines of the Kikuchi bands seen in the pattern. The angles between all lattice directions are known for the detector structure used and thus provide the calibration reference values. In order to find the absolute coordinates of the source point mathematically, one can (a) determine the two-dimensional position (x.sub.i, y.sub.i) of the crossing points (zone axes) in the measured pattern image and (b) assign the respective three-dimensional lattice direction [u.sub.iv.sub.iw.sub.i] to each of these points. In addition, from the detector crystal calibration described above, one obtains the three-dimensional crystallographic direction of the fixed detector surface normal direction [u.sub.Nv.sub.Nw.sub.N], while the respective two-dimensional projection point (x.sub.N, y.sub.N) of this direction is changing in dependence on the actual source point position and needs to be identified in the measured pattern image. Measured in absolute units of the detector coordinate system, this (x.sub.N, y.sub.N) then directly provides the two-dimensional coordinates of the source point (X.sub.SOURCE, Y.sub.SOURCE) because, by definition of the gnomonic projection, the surface normal of the planar detector is going through the source point of the projection. The remaining z-component Z.sub.SOURCE of the source point can be obtained by calculating right-angled triangle(s), with the 90° angle between the experimentally measured 2D vector(s) (x.sub.i−x.sub.N, y.sub.i−y.sub.N) and the surface normal. The 2D vector(s) (x.sub.i−x.sub.N, y.sub.i−y.sub.N) in the detector plane subtend the known angle(s) α.sub.i between [u.sub.iv.sub.iw.sub.i] and [u.sub.Nv.sub.Nw.sub.N] as viewed from the source point. Thus, Z.sub.SOURCE is given as the length of the adjacent leg (along [u.sub.Nv.sub.Nw.sub.N]) of the theoretically known angle α.sub.i between [u.sub.Nv.sub.Nw.sub.N] and [u.sub.iv.sub.iw.sub.i] at the source point, where the opposite leg is measured experimentally as d.sub.i=|(x.sub.i−x.sub.N, y.sub.i−y.sub.N)|, i.e. Z.sub.SOURCE=d.sub.i/tan(α.sub.i). While it appears that a single measurement [u.sub.iv.sub.iw.sub.i] and [u.sub.Nv.sub.Nw.sub.N] can be used to roughly estimate Z.sub.SOURCE, the accuracy of the Z.sub.SOURCE value depends on the method used to identify the corresponding (x.sub.i, y.sub.i) and (x.sub.N, y.sub.N) in the pattern image. The precision of the method can be estimated from the statistical variation of the values of z.sub.SOURCE in dependence on the various measured d.sub.i. Alternatively, in order to use the complete information present in the pattern (i.e. beyond identifying discrete point coordinates) and to achieve the highest accuracy, one can apply a quantitative comparison between the complete measured 2D pattern and a simulated pattern with the source point coordinates (X.sub.SOURCE, Y.sub.SOURCE, Z.sub.SOURCE) as parameters like described below. It is stressed again, that in order to identify (directly or implicitly) the direction of the reference zone axes, one needs to measure a 2D information as the collective information of the plurality of pixels relative to each other. The intensity of a single pixel does not suffice to assign a direction to that pixel.

[0055] FIG. 5 shows a calibration of the inverted detected intensity pattern (left side) solely modulated by the detector channeling effect by comparison with a simulation for a detected intensity pattern (right side) that was produced using the dynamical theory of electron diffraction (cf. A. Winkelmann et al. Ultramicroscopy 107, 414 (2007)). The 3D parameters of the electron source (X.sub.SOURCE, Y.sub.SOURCE, Z.sub.SOURCE) and the internal orientation of the silicon crystal structure with respect to the detector surface plane are input to the simulation and a best-fit optimization procedure gives the 3D parameters of the electron source (X.sub.SOURCE, Y.sub.SOURCE, Z.sub.SOURCE). The internal orientation of the silicon crystal structure relative to the edges of the detector is be described by Euler angles (φ.sub.1,Φ,φ.sub.2) that describe a rotation sequence around moving ZXZ-axes in the Bunge convention.

[0056] The fixed detector crystal orientation is estimated as the mean orientation determined from a series of measurements which consist in moving the 12 keV electron beam 9 in a regular two-dimensional grid over the surface of a sample 8 that shows no backscattering diffraction pattern. The calibration procedure for each measured pattern involves the quantitative comparison of the measured pattern with theoretical simulations depending on the radiation source 1 position and the internal orientation of the silicon crystal structure with respect to the detector surface 4. In a 10×10 map with approximately 10 μm step size on the sample 8, the best fit orientation was determined by the optimization of the normalized cross-correlation coefficient r relative to simulated Kikuchi data for silicon. For the dynamical electron diffraction simulations and the best-fit optimizations, the software ESPRIT DynamicS by Bruker Nano, Berlin, was applied.

[0057] In a first calibration step, both the 3D parameters of the sample 8 as electron source (X.sub.SOURCE, Y.sub.SOURCE, Z.sub.SOURCE) and the internal orientation of the silicon crystal structure in detector volume 5 with respect to the detector surface 4 plane were parameters left to vary in the optimization procedure. As the crystalline detector volume is from a commercial quality silicon wafer cut in (111) orientation, a fixed despite unknown orientation for the crystalline detector volume 5 was assumed in the simulation. Using the software MTEX (cf. F. Bachmann et al. Solid State Phenom. 160, 63 (2010)) this fixed orientation was approximated as the mean orientation from all the measurements in the map and resulted in Euler angles of (φ.sub.1=179.95°, Φ=54.53°, φ.sub.2=45.15°,). This corresponds to a misorientation angle of 0.24° away from an ideal (111) surface, which is compatible with the manufacturing uncertainties. In a second determination step, the detector crystal orientation was then fixed in the simulations at the determined mean crystal orientation obtained in the first run in order to obtain the final best-fit radiation source 1 position values. The best-fit coordinates with a cross-correlation coefficient of r=0.71 of the electron source were (x.sub.P, y.sub.P, z.sub.P)=(6313 μm, 5753 μm, 6416 μm) in the coordinate system of FIG. 3.

[0058] In an alternate embodiment of the method according to the invention, a EBSD pattern superimposed with a detector channeling pattern is measured and used to determined the radiation source position and therewith the sample orientation by comparison with either a simulated EBSD pattern or a simulated detector channeling pattern, as shown in FIG. 6. According to this embodiment, the underlying watermark due to the detector channeling effect is used to calibrate an experimental Kikuchi pattern without using any other information than the pattern itself and the instrumentally fixed crystal orientation of detector volume 5.

[0059] Therefore FIG. 6 shows a Kikuchi pattern measurement at 25 keV using a silicon sample covered by 10 nm of nanocrystalline HfO.sub.2, which for Kikuchi pattern formation can be considered amorphous. The crystal orientation in the detector volume 5 was assumed at the values of (179.95, 54.53, 45.15) as determined above. The panels in the top row of FIG. 6 show the measured pattern (left) and an inverted copy (right) of that pattern. The lower panel shows on the right side the best-fit simulation for the radiation source 1 position from the negative of the total experimental pattern. The radiation source 1 position, i.e. the projection center, was determined with a best fit r-value of 0.38 at (x.sub.P, y.sub.P, z.sub.P)=(6305 μm, 6888 μm, 6388 μm). This corresponds to viewing angles on the detector screen of 95.2 degrees horizontally and 95.5 degrees vertically.

[0060] It is instructive to observe that the cross-correlation approach is stable enough to detect the local minimum of r when the simulated pattern registers with that part of the pattern structure that is connected only to the detector diffraction. Finally, the orientation of the measured sample region is obtained by fitting the original measurement in the top left panels of FIG. 6 assuming the projection center determined in the previous step from the inverted pattern in the top right panel. The result is shown in the bottom left panel of FIG. 6 and corresponds to an orientation of (φ.sub.1=179.95°, Φ=19.93°, φ.sub.2=215.59°). The orientation was determined with a best fit r-value of r=0.43, again showing a selective minimum, but now for the structure corresponding to the sample orientation. In the optimization procedure using two different patterns mixed in one image, it is useful that one pattern is a negative since this should tend to stabilize the optimization procedure that looks for a maximum of the cross-correlation coefficient, in contrast to a minimum that would be reached for the negative pattern.

[0061] It could be envisaged to combine both optimizations in a simultaneous fit procedure. In the example experiment related to FIG. 6, the relative mixture of sample 8 and detector volume 5 diffraction was tuned to about 50% each by adjusting the energy of the electron beam 9 and the thickness of the covering HfO.sub.2 film. In a conventional experiment involving high-quality crystalline surfaces, the pattern contribution due to the detector channeling effect is on the order of parts of a percent. However, as the detector diffraction contribution is in principle known, the extraction of this contribution from a measured Kikuchi pattern should be possible by image processing techniques like template matching or similar approaches.

[0062] The pixel detector used in the method according to the embodiment described above comprises a sensor 3 with a detector surface 4, divided into a plurality of pixels or pixel surfaces 4a with pixel coordinates (xi, yi, zi), and a detector volume 5, divided into a plurality of voxels or pixel volumes 5a corresponding to the plurality of pixels 4a. Each voxel 5a comprises a crystalline material with fixed crystal orientation. The pixel detector further comprises an electronics chip 6 with a plurality of amplification pixels 6a, each corresponding to one of the plurality of pixels 4a.

[0063] In the case of the pixel detector 2 used in the exemplarily methods as described above, the sensor 3 and the electronics chip 6 are independent, wherein the sensor 3 comprises 300 μm of silicon. The detector 2 consists of arrays of individual independent counters. Each pixel 4a of the sensor 3 has its own amplification pixel 6a in the electronics chip 6. Sensor 3 and electronics chip 6 are composed of 256×256 square pixels 4a, each 55 μm*55 μm in size, covering a global surface of around 1.4 cm*1.4 cm. Each pixel of the sensor 3 is electrically and mechanically connected, through solder bumps, to the corresponding pixel of the CMOS ASIC electronics chip 6.

[0064] Each pixel 6a of the electronics is basically composed of a charge sensitive amplifier, a discriminator, and a 14-bit counter. Each amplification pixel basically 6a comprises a sensor with bias voltage, solder bumps, preamplifier, threshold, discriminator, threshold adjustment and counter. The basic operating principle is as follows: when incident radiation hits a pixel 4a of sensor 3 a cloud of charges (electron-hole pairs) is generated within the material of the sensor 3. The quantity of generated charge is proportional to the total energy deposited within the sensor 3 by the incident radiation. The charges, drifting under the effect of the electric field applied to the sensor 3, are collected by the solder bump and transferred to the ASIC electronic chip 6. The signal from the sensor 3 is amplified by the shaping preamplifier and then compared, by the discriminator, with a threshold value. If the signal is greater than the specified threshold value, the discriminator generates a logic signal whose width is proportional to the time for which the voltage at the output of the preamplifier is above the threshold. The global threshold set for the chip 6 can be adjusted individually for each pixel, in order to compensate for small differences between pixels. An equalization of the matrix is typically performed in order to have a more uniform response within the global detector area. If the threshold level is set above the intrinsic noise of the device, it is possible to operate in noise-free conditions.

REFERENCE SIGNS

[0065] 1 divergent radiation source [0066] 2 pixel detector [0067] 3 sensor [0068] 4 detector surface [0069] 4a pixel surface [0070] 5 detector volume [0071] 5a pixel volume [0072] 6 electronics chip [0073] 6a amplification pixel [0074] 7 primary radiation source [0075] 8 sample [0076] 9 primary radiation [0077] 10 predetermined intensity distribution/incident radiation/backscattered electrons [0078] 11 crystal lattice planes