DETECTION OF MAGNETIZATION INHOMOGENEITIES IN ULTRA-SCALED MAGNETIC NANOWIRES

Abstract

The invention concerns a method for nonperturbative detection of one or more magnetic inhomogeneities resulting from nano-defects in a single longitudinal anisotropic magnetic sample structure having a nanometric cross-sectional dimension. A solid-state lattice with a single spin defect is used for magnetometry assessment of the anisotropic magnetic sample structure to determine quantitative information concerning minor defects and inconsistencies in the sample structure.

Claims

1. Method for nonperturbative detection of one or more magnetic inhomogeneities resulting from nano-defects in a longitudinal magnetic sample structure possessing a shape-induced anisotropy and having a widest nanometric cross-sectional dimension from 1 nm to 500 nm, or from 1 nm to 50 nm comprising: a) movably positioning a sensing surface of a solid-state lattice sensor of diamond material, comprising one single spin defect (NV) in the apex of the solid-state lattice sensor, at a first scanning position in proximity of the magnetic sample structure, b) irradiating the one spin defect (NV) by applying optical radiation (L) and a microwave field continuously or in one or more pulses to the one spin defect (NV) such as to detect a Zeeman shift upon exposure of the irradiated one spin defect to the magnetic field of the magnetic sample structure, c) detecting a photoluminescence (PL) output signal from the solid-state lattice sensor comprising the one spin defect (NV), d) scanning the surface of the magnetic sample structure in performing steps a) to c) at a series of scanning positions over at least a portion of the length of the magnetic sample structure such as to obtain quantitative information on the magnetic field spatial distribution.

2. The method according to claim 1, wherein the spin defect (NV) is a nitrogen-vacancy (NV) point defect in the diamond lattice.

3. The method according to claim 1, wherein the diamond sensor is a monocrystalline diamond sensor.

4. The method according to claim 1, comprising the step of mapping detected inhomogeneities in a magnetization distribution along a scanned portion of the magnetic sample structure.

5. The method according to claim 1, wherein the magnetic field strength at a scanning position is related to an intensity of PL output signal at that scanning position.

6. The method according to claim 5, wherein an optically detected magnetic resonance (ODMR) spectrum is recorded at each of multiple scanning positions.

7. The method according to claim 6, wherein the magnetic field strength is determined on the basis of the separation of resonance peaks in the recorded ODMR spectrum.

8. The method according to claim 7, wherein a detected inhomogeneity in a magnetic field distribution is used to identify and/or to quantify a local inconsistency or defect, such as an inconsistency in geometry, in stoichiometry or in chemical composition, and/or defects in crystallinity or in amorphous characteristics, optionally on the basis of a set of predetermined data.

9. The method according to claim 8, wherein the detected inhomogeneity in the magnetic field distribution is based on a set of predetermined data, and wherein said predetermined data are empirical data, for example data obtained from previous measurements of comparable or substantially the same magnetic sample structures.

10. The method according to claim 1, wherein the sensing surface of the solid-state lattice sensor is positioned no more than 100 nm, or no more than 50 nm, or no more than 20 nm, preferably no more than 10 nm, or no more than 1 nm, from the sample surface.

11. The method according to claim 1, wherein the spin defect is located 100 nm or less, 50 nm or less, 20 nm or less, ideally 10 nm or less, from the sensing surface of the solid-state lattice sensor.

12. The method according to claim 1, wherein the solid-state lattice sensor has a detection sensitivity of no more than 10 ?T/?Hz, or no more than 5 ?T/?Hz, preferably no more than 2.5 ?T/?Hz.

13. The method according to claim 1, wherein the magnetic sample structure is a uniaxial sample structure with a single easy axis and the magnetization is aligned along the single easy axis of the magnetic sample structure.

14. The method according to claim 1, wherein the magnetic sample structure has at least one maximal transversal dimension perpendicular to its main axis of less than 50 nm, or of less than 30 nm, preferably of less than 10 nm.

15. The method according to claim 1, the magnetic sample structure being a ferromagnet, an anti-ferromagnet, a semi-conductor or a paramagnetic sample structure.

16. The method according to claim 1, wherein the magnetic sample structure is a nanowire or nanotube.

17. The method according to claim 1, configured to scan a plurality of nanowires arranged on or embedded in a carrier substrate.

18. The method according to claim 2, comprising the step of mapping detected inhomogeneities in a magnetization distribution along a scanned portion of the magnetic sample structure.

19. The method according to claim 2, wherein the spin defect is located 100 nm or less, 50 nm or less, 20 nm or less, ideally 10 nm or less, from the sensing surface of the solid-state lattice sensor.

20. The method according to claim 13, wherein the magnetic sample structure is a nanowire, a nanotube, or a plurality of nanowires embedded in a carrier substrate.

Description

SHORT DESCRIPTION OF THE DRAWINGS

[0073] Exemplar embodiments of the invention are disclosed in the description and illustrated by the drawings in which:

[0074] FIGS. 1A and 1B are schematic representations of possible embodiments of Nitrogen-vacancy magnetometry (SNVM) set-ups measuring NW arrays, whereby

[0075] FIG. 1A shows the scanning system is operated at constant frequency shift mode, and

[0076] FIG. 1B shows the scanning system operated at constant height mode.

[0077] FIGS. 2A and 2B is a schematic representation of two different section views of a NW with detected defects depicted as cross-hatched areas, FIG. 2A is a side view and FIG. 2B is a top view.

[0078] FIG. 3A is a schematical illustration of different energy levels of negatively charged NV.sup.? centre in diamond, whereby transitions from the ground state or fluorescence bright state m.sub.s=0 to fluorescence dark stages states m.sub.s=+/?1 under continuous microwave excitation are indicated as waved arrows.

[0079] FIG. 3B is an optically detected magnetic resonance spectrum of a single scanning NV.sup.? centre used in this study, with a dc detection sensitivity of 2.3?0.2 ?T/?Hz.

[0080] FIG. 3C shows an SNVM/atomic force microscope (AFM) image of a carrier substrate with six parallel CoFeB NWs in iso-B mode corresponding to the magnetic component of B.sub.NV=0.2 mT.

[0081] FIGS. 3D and 3E show different plots SNVM/AFM images of the same section of carrier substrate as imaged in FIG. 3C in full B mode with a field range from ?1 mT to 1 mT, whereby

[0082] FIG. 3C is a surface plot, and

[0083] FIG. 3E is a contour plot of the same SNVM/AFM image.

EXAMPLES OF EMBODIMENTS OF THE PRESENT INVENTION

[0084] In an embodiment of this invention, the sample under study was an array of CoFeB NWs with cross-section area of ca. 120 nm.sup.2 and 6 nm wire width and a wire length in the millimetre range, as described in S. Dutta et al., Sub-100 nm2 Cobalt Interconnects, in IEEE Electron Device Letters, vol. 39, no. 5, pp. 731-734, May 2018, doi: 10.1109/LED.2018.2821923. The NWs were fabricated through subtractive patterning by borrowing the concept of gate spacers from complementary metal-oxide-semiconductor (CMOS) manufacturing processes. CoFeB is selectively etched on the sidewall of sacrificial SiO.sub.2 lines, thus creating a pathway to achieve ultimate NWs dimension over large area using standard lithographic techniques.

[0085] The amorphous nature of the patterned CoFeB NWs was confirmed by scanning electron microscopy (SEM) and transmission microscopy (TEM) imaging (not shown).

[0086] While the invention was performed on the magnetic NWs described in the previous paragraphs, it will be obvious to the skilled person that the invention is not limited to these specific NWs and that other longitudinal anisotropic magnetic sample structures with nanometre cross-sections are also suitable sample structures.

[0087] FIG. 1A shows a schematic 3D view of NWs arranged on a possible carrier structure 2. The carrier structure 2 may for example be made of silicon on which a layer of SiO.sub.2 is deposited. The carrier structure may comprise a plurality of sacrificial lines 21 which are preferably parallel to each other, two of such lines 21 are depicted in FIGS. 1A and 1B. The NWs 1 are etched on the side walls of these sacrificial lines 21.

[0088] Other arrangements of NWs are possible and the invention is not limited to any particular kind of arrangement of NWs on a carrier substrate. NWs may also be embedded into a carrier substrate, or embedded inside a matrix layer, which may be disposed on a carrier substrate.

[0089] The dimensions of the patterned NWs were determined by cross-section scanning transmission electron microscopy (STEM). The width of the NWs was 6 nm?0.5 nm, the cross-sectional area of the NW was 120?5 nm.sup.2. The sacrificial SiO2 lines 21 were less than 500 4 nm in width. The sacrificial lines with the lateral NWs were arranged in parallel such that the carrier substrate contained between 3000 and 5000 NWs per millimetre (mm) cross-sectional width. It is important that the sacrificial lines 21 are non-magnetic to avoid interference with the magnetic field of the NWs 1 arranged on the lines.

[0090] The in-plane magnetization of individual NW on the above-described NW array was assessed. The NW arrays exhibited an in-plane magnetization along each wire as observed by the hysteresis loops measured by vibrating sample magnetometry (data not shown).

[0091] The magnetization loops on a millimetre wide carrier structure with approximately 4000 NWs of the similar length arranged in parallel, uniformly distributed over the area were measured and analysed using First Order Reversal Curves (FORC).

[0092] The FORC method is a known statistical approach to study the switching processes in an assembly of magnetic entities ranging from nm to bulk sizes.

[0093] These analyses revealed a rather narrow distributions of both switching and interaction fields in the NW array and suggested that the NWs are rather magnetic uniform having similar individual switching fields, whereas the detected tight interaction field distribution centred in zero demonstrated nearly no magnetic interactions between the wires.

[0094] The measurements failed to detect the presence of any nonuniformities or nano-defects in individual NWs.

[0095] Nonuniformities were however detected by the method presented by this invention. Schematics of possible experimental setups of this invention are shown in FIGS. 1A and 1B. The solid lattice probe, in the present case a diamond probe with a diamond tip 5 comprises a single NV.sup.? defect NV, which is positioned at a distance d.sub.NV from the surface of NW array.

[0096] Magnetic imaging was performed with a commercial SNVM (the Qnami ProteusQ, Qnami AG) operating under ambient conditions. A commercial diamond tip hosting a single NV.sup.? defect at its apex (Qnami, Quantilever MX) has an integrated quartz tuning fork to allow frequency modulation-based AFM (FM-AFM) and is scanned above the NW array. Other control methods or modes, such as amplitude-modulation AFM (AM-AFM) or contact mode AFM, are also suited and may be used to control the AFM scan. The invention is not particularly limited to any specific AFM control method.

[0097] The orientation of the NV.sup.? centre was characterized by the polar angle ?.sub.NV and the azimuthal angle ?.sub.NV, which were determined to be ?.sub.NV=57.1??2.5? and ?.sub.NV=270.3??0.9? respectively.

[0098] In one aspect of the invention, as depicted in FIG. 1A, the scan of the sample or the NW array is performed at a constant frequency shift ode, also called a constant force mode. The movement of the NV.sup.? defect contained in the diamond tip 5 of the probe across the NW array during the scan is shown as a dashed line M. In this mode a predefined area is scanned by following the surface topography of the sample or the NW array, whereby the frequency shift of the tuning fork is the same as its predefined level. The predefined level is the feedback signal in the z-feedback of the scanning probe system. In other words, the distance d.sub.NV between the NV.sup.? defect and the surface of the sample or the NW array is maintained constant.

[0099] In an alternative aspect of this invention, the scan of sample or the NW array is performed at constant height mode. In this mode the NV defect follows the dashed line M shown in FIG. 1B during the scan. The movement of the NV.sup.? defect across the sample structure or the array is plane parallel to the average slope of the sample surface but not lower than the highest point in the predefined scan area. This mode does not require a z-feedback. It may be performed as an open loop.

[0100] FIGS. 2A and 2B schematically depicts a section of a NW with nano-defects 10 giving rise to inconsistencies in local magnetizations. Two different section views are shown together with the Cartesian coordinator defined in FIGS. 1A and 1B. The defect 10 has a width 8d along the NW direction. The NW height h.sub.NW and width ?.sub.NW define the cross-section area of the NWs. The defect area 10 has a higher or lower local magnetization compared to the defect-free area of the NW. The shape of the defects is random and in most cases is irregular. The shape of the defect is not confined to any specific type of geometrical shape. The present method permits to determine the size and approximate shape of the defects, but not the exact contours of the nano-defects in the NWs.

[0101] The ground state of negatively charged NV.sup.? defect in the diamond tip 5 of the probe is a spin triplet state, consisting of the magnetic sublevels |m.sub.s=0 and |m.sub.s=+1 as depicted in FIG. 3A, where m.sub.s refers to the magnetic quantum number along the NV.sup.? quantization axis. The transition from fluorescence bright state m.sub.s=0 to fluorescence dark states m.sub.s=+/?1 under continuous microwave excitation can be probed by optically detected magnetic resonance (ODMR) spectrum shown in FIG. 3B.

[0102] In the absence of an external magnetic field, the states |m.sub.s=+1 are degenerated and exhibit a splitting of D.sub.0=2.87 GHz from |m.sub.s=0. When an external magnetic field is applied along the NV.sup.? axis, it induces a Zeeman splitting proportional to 2?.sub.NVB.sub.NV of the sublevels |m.sub.s=+1, where ?.sub.NV=28 GHz/T is the gyromagnetic ratio, and B.sub.NV is the detected magnetic field projected on the NV.sup.? quantization axis. In this study, the NV.sup.? spin was initialized with 515 nm green laser L, shown in FIGS. 1A and 1B, and its red photoluminescence PL signal was optically read out via the confocal microscope module. This setup enables optical detection of ODMR of NV.sup.? defects after initialization into the fluorescent bright |m.sub.s=0 ground state.

[0103] A near-field microwave, placed at a distance of no more than 0.5 mm, preferably no more than 0.1 mm to the NV.sup.? centre in the sensor tip of the probe, drives the ground state spin population resonantly with either of the |m.sub.s=0 to |m.sub.s=+1 transitions to populate the less fluorescent |m.sub.s=+1 ground states. As shown in FIG. 3B, which is a diagram of the integrated PL signals over the frequency sweep of the near-field microwave, the shift in population resulted in a significant drop in NV fluorescence, with an ODMR contrast of around 24%.

[0104] The microwave frequency f.sub.MW difference between the two optically detected ODMR resonance dips, as shown in the diagram of FIG. 3B, thus yields a direct quantitative measure of B.sub.NV in a self-calibrated manner, via the simple relation of ??=2?.sub.NVB.sub.NV, where ?.sub.NV=g.sub.e.Math.?.sub.B/h?28 MHz.Math.mT.sup.?1 is the reduced NV gyromagnetic ratio. By fitting the ODMR spectrum, a dc magnetic sensitivity of 2.3?0.2 ?T/?Hz has been confirmed.

[0105] A bias field B.sub.b of approximately 1 mT was applied along the NV defect axis to determine the sign of the measured magnetic fields. Due to the tip-sample interaction, the tuning fork frequency shift (?f=5 Hz for all the measurements in this study) was used as the z-feedback during the scanning in order to ensure a constant tip-sample distance z.sub.NV. The distance between the NV.sup.? centre sensor and the sample surface was calibrated to be z.sub.NV=59.7?1.8 nm through a calibration process above the edges of a uniformly magnetized ferromagnetic strip.

[0106] The NV.sup.? centre to-sample (or NV.sup.? fly height) distance calibration between the NV.sup.? spin sensor tip and the sample surface was inferred by mapping the stray magnetic field generated above the upward (downwards) edge of a uniformly magnetized ferromagnetic thin film strip, made of for example CoFeB. In this calibration step the NV.sup.? defect carried by the diamond tip integrated in a quartz tuning-fork sensor, operating in shear force mode, flew at a distance d above the ultrathin perpendicularly magnetized calibration sample with a defined thickness. The calibrations were performed in both up-step and down-step sides of a very wide CoFeB strip (20 ?m wide along x direction, and 200 ?m long along y direction). The measured B.sub.NV profile was recorded while scanning the NV.sup.? defect across the two edges of 20 ?m wide [Ta/CoFeB (?1 nm)/MgO/Ta] calibration strip. The distance d was then extracted by fitting the experimental data, using a known method described in T. Hingant, et al. Phys. Rev. Applied 4, 014003 (2015), https://doi.org/10.1103/PhysRevApplied.4.014003.

[0107] A preliminary quick characterization of a magnetic field distribution is also possible by imaging iso-magnetic field contours that are resonant to a specific microwave frequency f.sub.MW, hereinafter referred to as iso-B mode, which may have a pixel dwell time of no more than 20 ms. SVNM images in iso-B mode of sample NWs are shown in FIG. 3C.

[0108] In this imaging mode, the NV.sup.? defect PL intensity was monitored while scanning the magnetic sample and applying a microwave field with a fixed frequency f.sub.iso. The PL image exhibits dark contours when the electron spin transition is in resonance with the chosen microwave frequency.

[0109] In FIGS. 3C, 3D, and 3E the roman numbers I to VI shown underneath the images indicate the positions of six NWs on the array.

[0110] The iso-B mode image shown in FIG. 3C corresponds to the magnetic component of B.sub.NV=0.2 mT. The grey scale indicates the PL output signal in kilo counts per second (kcps) The dark, primarily rounded contours along and around the length of the six NWs correspond to the same magnetic field of 0.2 mT measured along the NV.sup.? axis.

[0111] In the iso-B PL image shown in FIG. 3C, dark lines can be seen along the CoFeB NWs. These lines are a result of the plasmonic quenching effect. The plasmonic quenching effect is known in the art. On top of the dark line in FIG. 3C, round-shaped ring features can be discerned along the NWs. These ring features may be positioned at either side of the NW or may be centred at or close to the main axis of the NW at two different orientations of the sample, respectively. The ring feature is related to the NV.sup.? orientation with respect to the NW spatial orientations.

[0112] To determine the full magnetic field B.sub.NV distribution, an ODMR spectrum can for example be recorded at each position or pixel during the scan to deliver a complete scan of the magnetic field, hereinafter called full-B mode. In this study, a pixel integration time of 4.5 seconds was used in all the full-B mode images to ensure a reasonable signal to noise ratio, as shown in FIGS. 3D and 3E depicting full B-mode SNVM/AFM images of sample NWs. However, this imaging time is relatively long and may not be suitable or desirable for all applications.

[0113] FIGS. 3D and 3E show a full-B scan of the same area scanned in iso-B mode of FIG. 3C. The images correspond to an area size of 2 ?m?2 ?m. The magnetic field range scanned was ?1 mT to 1 mT. In this plot, the density and shape of local stray magnetic fields in the scanned range are indicated in different intensities of grey shades.

[0114] Figure D is a surface plot of the imaged area with the greyscale indicating the magnetization of a scanned pixel.

[0115] FIG. 3E corresponds to the same image shown is a contour plot.

[0116] The SNVM measurements performed in this study were repeated using several different single-NV.sup.? tips with different NV.sup.? orientations. In addition, sample orientation with respect to the NV.sup.? tip was also varied between different experiments. The results of these different set ups are consistent throughout.

[0117] The unexpected observations in SNVM/AFM results detecting magnetic stray fields caused by nano-defects in the structure of the NWs were subsequently confirmed by numerical analysis of SNVM image simulations as part of which the geometry of the CoFeB NWs was modelled according to morphology data based on TEM images (not shown).

[0118] The TEM measurements performed as part of the study indicated that defects might be present in the wires. However, the expected defects were in the range of 10 nm to 100 nm in width along the NW.

[0119] Based on the state of the art, defects in this range were up to today not expected affect the magnetic field of a NW. These simulations confirm that the detected magnetic inhomogeneities measured in SNVM/AFM are linked to nano-defects, such as geometric inconsistencies and chemical inhomogeneities in the NWs.

[0120] This invention arrived at the new insight that state-of-the-art nanowires may indeed contain a plurality of nano-defects and that these nano-defects cause weak magnetic stray fields, which can be measured by SNVM. Local changes in magnetic field can for example be due to an inconsistent NW geometry, such as roughness, interruptions, edges, and shape deformations, and defectivity, such as local crystallinity changes, point defects and amorphous regions.

[0121] Clearly, as a general principle, the combination of increased NWs density on an NW array and low intensity of local stray magnetic field caused by such nano-defects in individual NWs add to the complexity of mapping defects within an NW array.

[0122] Behind this background it is remarkable that by using the present method it was possible to detect a relative high density of weak magnetic inhomogeneities in the measured NWs. The magnetic inhomogeneities of the wires could be detected in full-B modes, as well as in iso-B modes. The results of these studies provided quantitative information on the associated magnetic field distribution.

[0123] Moreover, qualitative information concerning the nature of the defects causing the magnetic inhomogeneities, could also be determined on the basis of numerical analysis and modelling. It could be shown that simulation data can be used to interpret the SNVM measurements to arrive at a quantitative and/or a qualitative characterisation of the defects or inconsistencies.

[0124] The combination between the experimental SNVM data and simulation SNVM images adds to the unprecedented capability of the present invention to determine weak variations of magnetic properties in ultra-scaled magnetic devices.

[0125] Up to now subtle magnetic defects in magnetic longitudinal nanostructures have so far gone largely undetected. The present invention shows a clear pathway for the quantitative analysis of novel magnetic materials for spintronic devices at aggressively scaled dimensions.

[0126] It should be understood, that various changes and modifications to the presently embodiment described herein will be apparent to those skilled in the art. Such changes and modifications may be made without departing from the present invention. To the extent that these embodiments and modifications do not depart from the scope of the claims, it is intended that they are also included in the invention disclosed herein.