TUNABLE AMPERE PHASE PLATE FOR CHARGED PARTICLE IMAGING SYSTEMS

Abstract

A phase shifting device for a charged particle imaging system includes means for passing an electric current in a direction that has a nonzero component parallel to at least one section of the imaging beam. Preferably, the electric current is passed parallel along the section of the imaging beam. The amount of phase shift then centrosymmetrically depends on the distance between the electric current axis and the imaging beam axis. The magnetic field produced by the electric current exhibits the same effect on the phase of the beam as a localized charge according to the prior art.

Claims

1. A phase shifting device for an imaging system comprising a charged particle imaging beam, the phase shifting device comprising means for passing an electric current in a direction that has a nonzero component parallel to at least one section of the imaging beam.

2. The phase shifting device according to claim 1, wherein the means for passing an electric current is configured to pass the electric current along the at least one section of the imaging beam in a direction that encloses an angle of at most 45 degrees with that the at least one section of the imaging beam.

3. The phase shifting device according to claim 1, wherein the means for passing an electric current comprises a conductor in the direction of the electric current and leads that are disposed at an angle between 75 and 105 degrees with the imaging beam to supply electric current.

4. The phase shifting device according to claim 3, characterized in that the conductor is axially symmetric around the direction of the electric current.

5. The phase shifting device according to claim 3, wherein at least one of the conductor and the leads is made of a non-ferromagnetic materials.

6. The phase shifting device according to claim 3, wherein the leads are arranged antiparallel to each other.

7. The phase shifting device according to claim 1, wherein the means for passing an electric current comprises a second charged particle beam.

8. The phase shifting device according to claim 1, has further comprising means for heating a conductor that carries the electric current to at least 200° C.

9. The phase shifting device according to claim 1, for comprising means for adjusting a tilt angle between the direction of the electric current and the imaging beam.

10. An imaging system configured to provide a charged particle imaging beam that is coherently split into one first part that interacts with an object to be investigated and one second reference part that does not interact with the object, means for bringing the two parts of the beam to interference after the first part has contacted the object, and a phase shifting device in a path of at least one of the two parts of the beam, wherein the phase shifting device is the phase shifting device according to claim 1.

11. The imaging system according to claim 10, wherein the imaging system is an electron microscope.

12. The phase shifting device according to claim 1, wherein the means for passing an electric current along the at least one section of the imaging beam in a direction that encloses an angle of at most 20 degrees.

13. The phase shifting device according to claim 1, wherein the means for passing an electric current along the at least one section of the imaging beam in a direction that encloses an angle of at most 10 degrees.

Description

EXPLANATION WITH FIGURES

[0028] In the following, the subject-matter of the invention is explained and confirmed experimentally using figures without limiting the scope of the invention. The following is shown:

[0029] FIG. 1: Conductor and leads to pass a current parallel to the electron beam according to the present invention.

[0030] FIG. 2: Holographic view of the phase shift brought about by the hook arm 1.

[0031] FIG. 3: Amplified interferograms showing different phase changes for currents 0 mA (FIG. 3a), 2 mA (FIG. 3b) and 4 mA (FIG. 3c) through the hook arm 1.

[0032] FIG. 4: Theoretical simulation of the interferograms shown in FIG. 3.

[0033] FIG. 5: Line scans through the phase patterns shown in FIG. 3.

[0034] FIG. 6: Theoretical simulation of interferograms with the electron beam tilted by 5° (FIG. 6a), 10° (FIG. 6b) and 15° (FIG. 6c) against the hook arm 1.

[0035] FIG. 7: Some possible shapes for embodiments of phase shifting devices according to the present invention.

[0036] Electron holography is a powerful technique which, in the medium resolution range, is invaluable in the mapping and quantitative investigation of magnetic and electric fields. Here we apply this technique to the study of the magnetic field produced by a vertical wire carrying a constant current, the closure of the electrical circuit being provided by two horizontal wires, whose magnetic field has a negligible effect on the electron optical phase shift, which are connected to an external voltage power supply. In situ experiments with varying currents are reported and compared to the theoretical predictions. It turns out that the phase shift associated to the electrical current has the same form of that produced by elementary charge.

[0037] Let us recall that the earliest attempts to make an electrostatic phase plate were based on the localized electrostatic charging of a thin wire with results judged of great interest but abandoned because the charging proved difficult to control. The same shortcoming is also shared by the recent idea of using the focalized, unscattered electron beam to create a localized spot of charging. According to Glaeser, there is no physical or mathematical (analytical) understanding of the amount of phase shift they produce, and their use is not recommended, as self-charging is something to be avoided rather than something that can be regarded as producing a useful result. We demonstrate that some, if not all, of these shortcomings can be amended and that a device based on our experiment can be profitably used as a tunable phase plate.

[0038] The starting motivation of this work was the high challenge represented by the generation of magnetic fields to study switching processes in magnetic materials in the transmission electron microscope (TEM). As a result of the fact that a current owing parallel to the plane of an untilted TEM specimen produces no net magnetic phase shift, we examine a short nano-fabricated segment of wire that is oriented parallel to the electron beam direction. Different regions of such a wire could in principle be used to apply either in-plane or out-of-plane magnetic fields to closely-adjacent nanomagnets.

[0039] However, we soon realized that the experiment has more profound meaning and implications: in fact, like elementary electrostatic charges and magnetic dipoles, a straight current line is the building block of any electrical circuit, according to the Ampere law. To our knowledge, no electron microscopy study exists regarding the investigation of the magnetic field associated to a linear wire carrying a constant current, as in the past the main focus was on the production of coils for the investigation of the Aharonov-Bohm effect.

[0040] Taking advantage of the new specimen preparation methods using Focused Ion Beam (FIB) and of the fact that electron holography has become a standard technique with modern field emission, aberration corrected, electron microscopes, we have considered under which conditions the experiment was feasible. The results of our work are illustrated in the following.

[0041] A free-standing three dimensional nanoscale circuit was created using focused ion beam (FIB) milling technique. A chemically etched gold wire was sculpted in two orthogonal directions to form a hook shape device in which the central segment 1 (will be called hook arm from now) will be set parallel to the optic axis of the microscope (FIG. 1). At the final step of milling under 7 pA the desired cross section of the hook arm at 200×200 nm.sup.2 was achieved in a length of 2 μm. The hook arm 1 is hanging on the block 3 of Au from which it was machined by a first lead 2a. The second lead 2b is extending out of the top end of the hook arm 1 to the right-hand side. In the experiment, current was fed into the lead 2a through the gold block 3. The return path of the current was out of the lead 2b through another etched Au needle that was brought into contact with the lead 2b (not shown in FIG. 1). Leads 2a and 2b are substantially perpendicular to the hook arm 1, so that they do not interfere with the phase shift effect brought about by the current through the hook arm 1.

[0042] FIB milling was performed in a dual beam system Helios NanoLab 600i workstation operated at 30 kV by Ga+ ions and varying beam currents of 60 nA to 7 pA at different steps on milling procedure.

[0043] The hook and needle were mounted in a NanoFactory scanning tunneling microscopy specimen holder. Applying the piezo-driven STM tip of the holder a metallic contact was made at the end of the hook and tip of the needle. Current-voltage characteristic of the whole device showed an Ohmic contact with a total resistance of 22 ohm. Also by acquiring I-V curve in a blanked beam condition, it was confirmed that the illuminating electron beam has no effect on the contact properties and total resistance of the system.

[0044] Electron holography measurements were carried out to realize, detect and quantitatively measure the phase shift in electron wave. An elliptical probe was formed in a FEI Titan 60-300 TEM equipped with an XFEG field emission gun and two electron biprisms. Observations were performed in the Lorentz mode in a magnetic-field-free environment (with the conventional microscope objective lens switched off). The microscope was operated at 300 kV during the experiment and the upper biprism was used to form an interference region allowing to obtain a holographic field of view with a 2.4 μm width (FIG. 2). The opaque projection of the hook arm 1 is visible in FIG. 2 as a black bar that is running through the center of the image. All phase images where reconstructed from acquired holograms using HoloWorks 5.0 plugin made by Gatan Inc.

[0045] FIG. 3 a-c shows the four times amplified cosine contour maps, (i.e, reporting 1+Cos(4 Δφ) with φ being the phase shift) of the reconstructed holographic images of the region around the hook arm taken at different, constant currents. The opaque projection of the hook arm 1 is shown in each of FIGS. 3 a-c as a slightly wider noise-filled bar running through the center of the image. In FIG. 3 a the phase image giving rise to the shown cosine map had been reconstructed from two holograms recorded when no current was passing through the device. Essentially, the contour map shows no variation in two dimensions across the hook implying that neither magnetic nor electric field are present around the device. In FIG. 3 b the cosine map of the phase shifted electron wave due to the magnetic field around the hook arm is shown when a nominal current as high as 2 mA is passing through this nano-device. Semi-circular rings in this image represent the projected magnetic field around this segment of the device and have been revealed as the phase shift in transmitted electron beam. Indeed, two holograms were acquired when a constant current of 1 mA was passing through the arm segment but at different directions. It was found that currents parallel and anti-parallel to the electron beam will cause a magnetic field of the same power but of opposite sign as expected in principle. Hence, reconstructing two holograms in reverse magnetic field will result in a phase image with a doubled magnetic phase shift in the phase of the electron wave.

[0046] One time increasing of the current will of a factor of 2 results in a magnetic phase shift due to the 4 mA current around the hook arm as illustrated in FIG. 3 c.

[0047] Comparing the amplified cosine contour maps in FIG. 3 b and c, it is obvious that the power of the magnetic field has been raised two times higher when there is a flow of current equivalent to 4 mA with respect to the current of 2 mA, which is in consist-ence with Ampère law and will be discussed more in detail in the next section. In the holographic contour maps, starting from the center and proceeding radially outside, each change from dark to bright and vice versa corresponds to a fixed amount of phase change equal to π. In FIG. 3c, the frequency of those changes has doubled compared with FIG. 3b, indicating that the amount of phase change has also doubled.

[0048] It can be found that there is a considerable difference in size and shape of the rings at the two sides of the hook device. This feature is attributed to the perturbed reference wave. As is well-known in electron holographic observations, the long range electric and magnetic fields that are inevitably present in the electron microscope perturb the reference wave and produce distortions that are visible in holography studies. We will take this effect into account and will discuss it in the next sections. FIGS. 4 a-c report the theoretically simulated magnetic phase shift profiles of the electron wave at the same constant currents as used in FIG. 3 a, b and c (0, 2 and 4 mA, respectively) displayed as 4 times amplified cosine contour maps. The opaque projection of the hook arm 1 was assumed to be running from left to right and is visible as a white bar. As expected there is no phase shift in the profile of 0 mA current.

[0049] However, it can be seen that the phase shift values increase two times when the current rose up from 2 to 4 mA. Also, it is obvious that the phase shifts are unequal at two sides of the hook which shows the relative effect of the perturbed reference wave presence in hologram formation with respect to the position of electron biprism.

[0050] FIGS. 5 a, b, c show line scans of the phase through the middles of FIG. 3 a, b, c, respectively. The scan proceeds along the section line from A to B that is shown in FIG. 3a. The phase difference, measured on the left-hand axis in radians, is drawn over the distance traveled on that section line, measured on the bottom axis in nanometers. In FIG. 5a, with no magnetic field, there is no phase change, so the line scan only shows a flat line. Comparing FIG. 5c with FIG. 5b, it becomes apparent that the phase increases with about double the slope.

[0051] FIG. 6 shows simulations under conditions identical to FIG. 4b, but under the additional assumption that the electron beam has been tilted by 5° (FIG. 6a), 10° (FIG. 6b) or 15° (FIG. 6c). It can be seen that the departure from cylindrical symmetry is acceptable insofar the tilt angle is inferior to 10°. However, an improved version of the phase plate should provide a tilting device for optimal adjustment.

[0052] FIG. 7 shows sketches of shapes for phase shifting devices according to the invention. All these shapes are meant to be mounted with respect to the imaging beam so that the imaging beam runs from top to bottom in the drawing plane along the vertical structure 1. FIG. 7a shows the embodiment that was used for the present proof of concept; its concrete realization is shown in FIG. 1 and was subsequently discussed.

[0053] A first refinement is shown in FIG. 7b. In this embodiment, the leads 2a and 2b are twice as strong as in FIG. 7a. This makes the phase shifting device more resistant to breaks when it is mounted in the electron microscope. At the same time, the stronger leads 2 allow a larger current to be driven through the vertical structure 1. This can be used to heat that vertical structure 1.

[0054] In the embodiment shown in FIG. 7c, the leads 2a, 2b are not perpendicular to the vertical conductor structure 1 and hence also not perpendicular to the imaging beam. The current in the leads 2a, 2b therefore has a vertical component and produces a magnetic field that modifies the main field generated by the vertical conductor structure 1. This is used to fine-tune the field and hence the phase shift.

[0055] FIG. 7d shows an embodiment where the vertical conductor structure 1 is supplied with currents by multiple leads 2a, 2b, while the current is drawn from it on the return path by multiple leads 2c, 2d as well. The additional leads 2b, 2d per direction both provide mechanical stability of the device for mounting and allow for a stronger current to be passed through the vertical structure 1.

[0056] FIG. 7e shows a U-shaped embodiment where the leads 2a and 2b are antiparallel to each other. Advantageously, this embodiment provides the least screening of the beam because it has the smallest cross section. Only the lead 2a and the diameter of the vertical structure 1 contribute to this cross section, while the lead 2b does not.

[0057] In principle, analysis of the interference pattern resulting from the holography observations allows the phase shift of the object wave

[00001]$\begin{array}{cc}\varphi \left(x,y\right)=C_E.Math.{\int }_{-\infty }^{\infty }.Math.V\left(x,y,z\right).Math.\mathrm{dz}=\frac{e}{h}.Math.{\int }_{-\infty }^{\infty }.Math.A_z\left(x,y,z\right).Math.\mathrm{dz}& \left(1\right)\end{array}$

to be recovered quantitatively and non-invasively. In Eq. (1), x and y are directions in the plane of the specimen, normal to the electron beam direction z. The contribution of electrostatic field is given by the first term, where CE is an interaction constant that takes a value of 6.53*10.sup.6 rad V.sup.−1 m.sup.−1 at 300 kV and V(x,y,z) is the electrostatic potential within and around the specimen. The contribution of the magnetic field is given by the second term, where A.sub.z(x,y,z) is the z-component of the magnetic vector potential and e and h are the absolute values of the electron charge and the reduced Planck constant, respectively.

[0058] In order to calculate the phase shift due to the straight section of current-carrying wire, and more generally to a closed loop, the fifth formulation of the Ampere law in terms of the vector potential is very well suited:

[00002]$\begin{array}{cc}A=\frac{{\mu }_0}{4.Math.\pi }.Math.i.Math.\oint \frac{1}{r}.Math.d.Math..Math.l& \left(2\right)\end{array}$

where μ.sub.0=4π*10.sup.−7 Vs/Am is the vacuum permeability, i the current and dl the line element.

[0059] If we consider a closed loop made by two equal wires of length L aligned with the optical axis, one at the origin and the other far away, let us say at (F,0,0), carrying opposite currents, and connected by horizontal straight wires, we can ascertain that, according to equation (1), the contribution to the electron optical phase shift of the horizontal straight wires is identically zero, whereas that due to the vertical wires gives

[00003]$\begin{array}{cc}\phi =-\frac{e}{\hslash }.Math.\frac{{\mu }_0}{4.Math.\pi }.Math.\mathrm{iL}\left(\log \left[{\left(F-x\right)}^2+y^2\right]-\log \left[x^2+y^2\right]\right)& \left(3\right)\end{array}$

[0060] This results from the integration along the optical axis of the vector potential of the straight wire given, for the one at origin (0,0,0), by

[00004]$\begin{array}{cc}{A}_z=\frac{{\mu }_0}{4.Math.\pi }.Math.i.Math.\frac{1}{\sqrt{x^2+y^2+z^2}}.Math.L& \left(4\right)\end{array}$

[0061] Note that this expression for the z component of the vector potential is the same as that of the potential for an elementary charge (Gauss law), and the neutralizing charge or wire at some distance is necessary in order to obtain a finite result, as shown also by Ballossier for the electrostatic case.

[0062] Here, as a result of the fact that the vacuum reference wave is perturbed by the stray field from the wire, rather than retrieving the ideal object wavefunction

ψ(x,y)=exp(i[φ(x,y)]),  (5)

electron holography yields information about a fictitious object whose wavefunction is given by the expression

ψ(x,y)=exp(i[φ(x,y)−φ(x+D cos(θ),y+D sin(θ)])  (6)

where θ is the angle of the biprism axis with respect to the object and D is the interference distance, which is directly proportional to the biprism potential and should not be confused with the interference field (overlap) width, which also depends on the finite diameter of the electron biprism wire. The value of D can be measured by re-cording two interferograms at different biprism potentials and measuring the variation in distance between recognizable features. The fact that an off-axis electron hologram captures the phase difference between an object and a reference wave has the further advantage that the normalizing contribution to the phase shift is removed.

[0063] In general, the problem of removing the effect of a perturbed reference wave from a single recorded electron hologram is unsolved and the only way to access quantitative information from a single phase image is to compare the measured phase shift with a sound physical model of the field under investigation. Alternatively, the effect of the perturbed reference wave can be minimized by increasing the interference distance, for example by using a TEM equipped with two or three biprisms, one of which is in the condenser lens system of the microscope.