MIMETIS - Objectifs

Mapping electric, magnetic and strain fields at the nanometer scale by electron holography

Electron holography is a powerful technique for measuring the phase of the electron wave and can be used to study the local electric and magnetic fields within and around materials at the nanoscale in a fully quantitative way.

When the fast electrons are interacting in a TEM with any electrostatic or magnetic fields within a thin specimen and possibly with stray fields around it, the associated electron wave is phase shifted. This phase shift can be quantitatively measured thanks to the Aharonov - Bohm equation (Eq. 1) :

Where V is the electrostatic potential, A_z the components of the magnetic vector potential along the beam direction z, C_E a constant dependent of the electron beam energy.

This equation can be rewritten (Eq. 2):

where B is the component of the magnetic induction perpendicular to both x and y.

The holography experiment in a TEM consists in interfering a reference electron beam (ref.) that has passed through the vaccuum with the electron beam (2) that has been phase shifted after interacting with an object and/or the electromagnetic fields surrounding it. This is achieved thanks to a biprism located in the column. The overlap between these two beams results in an interference pattern (the hologram) from which the phase shift of the electron beam (2) can be measured by Fourier analysis.

Projection of the electrostatic and /or magnetic fields within and around the materials under study can then be achieved following Eq.2 allowing their quantitative measurements at the nanometer scale.

Electron microscopes have not in general been optimized for electron holography and only few of them are able to perform EH experiments with sufficient spatial resolution and good sensitivity in phase shift measurements. The I2TEM instrument used within the MIMETIS project has been designed for performing lectron holography experiments and provide significantly improved performances. The position of biprisms can be optimized and the capability of using various multiple biprisms configurations provide flexibility concerning field of view and spatial resolution whilst eliminating artifacts from Fresnel fringes. This drastically improves EH and particularly the dark-field electron holography (see below) which in addition would benefit from specific positions for objective apertures in Lorentz mode.

In addition to studies at remanence, such electron holography can be performed under the application of various external stimuli (magnetic field, electrostatic potential, temperature, stress, electrical currents) thanks to the use of dedicated holders for in-situ experiments that are available within the MIMETIS project. This requires particular sample preparation processes that is also achievable in the MIMETIS project using the dedicated FIB Helios.

Thanks to these advanced instruments MIMETIS aims at studying the local changes of electrostatic and magnetic fields in and around nanomaterials and devices when they are submitted external stimuli. From the analysis of these fields variations, MIMETIS aims at extracting the evolution of fondamental values (charge density changes, magnetisation) the nanomaterials are experienced.

Example of charges measurements from Electric field mapping

A electrically charged nanomaterial or device is radiating around it an electric field that can easely be calculated using the Gauss law.

As this electric field can be quantitatively measured by EH we recently showed that EH can therefore be used to determine and and map the density of charges in any materials with a sensitivity of about 1 electron.

This method has been successfully applied for measuring charges in insulating MgO nanocube (see figures) but also to investigated the variation of carriers in carbon nanotubes as a function of the electrical potential they have been brought in-situ up to the value where a cold field emmision occurs.

Electric field generated by an electrically charged MgO nanocube.

(a) Holographic setup,

(b) Amplified cosinus contour map (13×) of the reconstructed phase of a charged MgO particle

(c) False color representation of the reconstructed phase with contours (every 0.3 rad).

Reference

Counting elementary charges on nanoparticles by electron holography

C. GATEL, A. LUBK, G. POZZI, E. SNOECK, and M.J. HŸTCH

Phys. Rev. Lett. 111, 025501 (2013)

http://dx.doi.org/10.1103/PhysRevLett.111.025501

Observing charge on nanoparticles. (a) Holographic setup, (b) amplified cosinus contour map (13×) of the reconstructed phase of a charged MgO particle and (c) false color representation of the reconstructed phase with contours (every 0.3 rad).

Example of Magnetic field mapping for determing the magnetic domain wall configuration

Equation 2 shows that EH gives quantitative access to the components of the magnetic induction projected in the plane parrallel to the electron beam direction. The analysis of the local magnetic configurations in various magnetic nanostructures allows to determine the structure of domain walls (see figure as exemple) and also to quantify the local induction and magnetization. These results are generally comforted by micromagnetic simulations.

Reference:

Magnetic Mapping Using Electron Holography

E. Snoeck and C. Gatel

in Transmission Electron Microscopy in Micro-nanoelectronics ed. A. Claverie,

Editeur : ISTE Ltd and John Wiley & Sons Inc (18 décembre 2012)

Transverse DW and hybrid magnetic state in 55 and 85 nm Ni nanocylinders.

(a) and (d) Amplitude image of 55 and 85 nm nanocylinders, respectively.

(b) and (e) Experimental magnetic phase shift and corresponding induction field lines.

(c) and (f) Magnetic phase shift and corresponding induction field lines calculated from micromagnetic simulation.

The difference of isophase contour is the same for the experiment and simulation, showing the quantitative agreement, and is set to 0.6 and 0.3 rad for 55 and 85 nm, respectively.

The color bars on the right give the amplitude of the phase shift in radian.

The dashed lines are a guide for the eye to position the wires. The arrows on the scheme represent a simplified view of the magnetization within the wire.

Dark-field electron holography

In 2009, the CEMES researchers has shown that strain fields can also be measured by electron holography and develop a new method for strain mapping: i.e. the dark-field electron holography. Compared to "classical" electron holography, the dark-field electron holography method consists on realizing the interferences between two diffracted beams that are coming from two regions of different strain states one being stated as reference (fully relaxed) crystal, the other being the strained regions that wanted to be analyzed. The phase shift between the two diffracted beams carries the so-called "geometric phase" that allows recovering the deformation of the strained area compared to the reference one. Combining the geometric phases of two non-collinear diffracted beams permit the quantitative mapping of the the strain within the whole region on interest over field of view as large as few microns, with nanometer resolution and strain sensitivity better that 0.1%.

Dark-field electron holography for strain mapping is a major breakthrough, particularly for applications in the microelectronics industry where strained silicon has become an integral part of device technology.

Reference:

Nanoscale holographic interferometry for strain measurements in electronic devices

M. Hÿtch, F. Houdellier, F. Hüe and E. Snoeck

Nature, 453, 1086-1089 (June 2008) DOI: 10.1038/nature07049

Example of strain field mapping by dark field electron holography in a strained semiconducting devices

Cartography of the strain induced in a Si substrate by the growth of SiGe islands

In situ : dynamical behaviours under external stimulis

The above experiments can be performed in the remanent state but also under the in-situ application of an external stimuli in order to investigate in magnetic materials for example the local hysteris loops, the domain wall (DW) nucleation field and propagation field, the DWpinnning, devices working regime. The Figure below illustrates the magnetic fields generated in front of the pole of a Hard Disk Drive (HDD) writer as a function of an applied electrical current studied in situ by EH in a TEM.

Upper row: Experimental images of the magnetic flux generated by the write pole for applied currents of 0 mA, +10 mA and +60 mA,

Bottom row: Experimental images of the magnetic flux due to the shield which remains constant

The video beside shows the magnetic reversal observed in-situ in a TEM in an Heusler alloy (Ni2MnGa) presenting a perpendicular magnetic anisotropy (PMA). Lorentz Microscopy have demonstrated that the Domain Wall closed loops can form periodic lattices of magnetic bubbles with an inner up (down) magnetization and an outer down (up) magnetization at room temperature of nanometer size (approx. 100 nm).

Within the MIMETIS framework we are developping new form of in situ experiment by means of :

New sample holders

The MiMETIS project helped us in gaining a wide range of sample holders dedicated to in situ measurements. It thus actually possible to apply various stimuli onto a sample during its observation : applying locally an electric bias using a piezoelectric probe, applying a local stress, injecting current with a various temperature range, applying purely in-plane magnetic fields or indenting a sample to observe its deformation.

New TEM techniques and image treatment

Along with the addition of extra dimensions to the TEM images (relative to the stimuli in consideration) we have to develop various way of analysing such complex dataset. We therefore developped some new form of holography (publication under process, to appear soon here) to add an extra dynamical sensitivity within the classical pseudo-static measurements. Moreover manipulating at the same time the microscope and the stimuli require the use of advanced driving scripts that are developped in the lab.

Original sample holder developments

All in situ approaches reaquire samples that are adapted to the stimuli under study (e.g. contact pads for current injection). We thus designed new forms of TEM sample to be able to preserve the main characteristics of a TEM sample (a thickness below 100 nm being the most mandatory) to the needs of the desired stimuli (e.g. a free space for approaching a tip). All these design are made with the available nanofabrication processes : FIB conjointly with various lithography steps in cleanroom facilities.

New sample holder preparation

Last but not least we develop our own vision of what an ideal sample holder for in situ experiment could be. These developments take in consideration the lab knowledge and the existing sample holder for developping a new generation of sample holder that may become new standards for the future of in situ TEM

Dimensions walkthrough of an in-situ experiment :

meter : the I²TEM microscope with its sample holder loaded

centimeter : an home-made sample holder with a chipset ready to be loaded

millimeter : a connexion established with the sample holder and a sample

micrometer : the connection pads linking to the nanostructure of interest on an electron transparent area (blue square)

nanometer : the nanotructure under observation (TEM image - permalloy stripe where a current is injected to move domain walls - spin-torque process)

Développement en parallèle d’expérimentations MET et MEB sur des MEM

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