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Multiple Scattering description of Ballistic Electron Emission Miscroscope for materials used in spin injection

Final Report Summary - MS-BEEM (Multiple Scattering description of Ballistic Electron Emission Miscroscope for materials used in spin injection)

The basic idea of this project was to provide a suitable theoretical description of Ballistic Energy Electron Microscopy (BEEM) within the multiple scattering framework, and a code for users. BEEM is based on Scanning Tunnelling Microscopy(STM) and consists in the injection of electrons from the nanometer sized STM tip across a tunnelling gap into a thin metal layer (base) that forms with a semiconductor substrate (collector) a Schottky barrier. A small part of these electrons will travel ballistically (i.e. encountering only elastic scattering by the atoms of the multilayer). At the interface metal/semiconductor, the Schottky barrier will only allow a fraction of them to pass (those with higher energy) and be detected as the BEEM current. Being of excellent spatial resolution (~ 1 nm), it therefore allows to study the spatial dependence of transport in buried interfaces such as those used to study spin injection and has rapidly become a key tool for these studies.

However, proper quantitative studies of transport in these semiconductor heterostructures necessitate a clear understanding of the underlying physical processes at the atomic level (including the influence of defects both in the tip and at interfaces) and a complete control of the electron current. Actual theoretical models to describe BEEM, and therefore help reach this deep understanding, are based on electronic structure or Green's function methods. This is the case of the one developed recently at the host organisation. In particular, these models do not take properly into account the shape, size of the tip and possible defects in it, or defects at the interfaces, although there is clear experimental evidence that these parameters strongly affect the properties on the electron current. To take this effect into account and have a true real space description of BEEM, the present project proposes to develop a Real Space (RS) MS approach. Multiple scattering is a very powerful tool used in many fields of science such as nuclear/particle physics, acoustics, medical physics, atomic physics, geophysics, etc. It is based on the description on the interaction of a wave with a collection of obstacles, and has two key ingredients: the propagator Go of the wave in the absence of obstacles, and the transition operator T which describes the effect of the obstacle on the incident wave. In the case of BEEM, the wave will be that of the electrons carrying the spin and propagating through the magnetic multilayer as the result of the current injection through the STM tip, and the obstacles will be all the atoms they encounter before being collected. Among the various blends of MS (including reciprocal space ones), the framework of the scattering path operator T (I -Go T)^{-1} is particularly interesting both for its physical transparency and its flexibility. So, the present project aims at developing within this framework a more powerful and flexible description of the BEEM, in conjunction with new heterostructures that could eventually lead to a complete control of the spin injection.

We can summarize the main ideas of this project as:

• Objective 1: Development of a scattering path operator scheme to describe BEEM. This includes full potential MS theory (because of the extremely low kinetic energy of the ballistic electrons) as well as MS partitioned theory which allows sort of a natural partitioning of the problem tip + substrate into separate subsystems, and a spin-polarized description. It also involves a precise description of electron-phonon interaction which is crucial for the resistance of the electron current to have the right behavior of Ohm's law macroscopically

• Objective 2: Coding of the corresponding theory and implementation into the MsSpec package developed at the Institut de Physique de Rennes (IPR) by D. Sébilleau and his international coworkers.

• Objective 3: Interface between full-potential electronic structure codes and MsSpec to take properly into account the band structure effects in the description of the scattering process (computation of the T matrices from the electronic structure codes).

• Objective 4: Implementation of the code for GPU cards (Graphical Processing Unit). This means not only standard parallelization for multi-processor architecture, but also for multiple graphical card architecture. This is necessary in view of the important number of atoms required for practical calculations.

• Objective 5: Application to experiments performed at the IPR on heterostructures produced locally, or in collaboration with the joint CNRS and industrial company Thalès research unit. Application to molecular-based systems for spintronics, namely metal/organic molecules/semiconductor, which are studied at the IPR by the group involved in the functionalisation of surfaces in conjunction with the Institut des Sciences Chimiques de Rennes are considered.

Not all the objectives have been reached, although the greatest part of the project has been completed. The theoretical description of BEEM within multiple scattering theory has been done, and a journal article has been started to be written (a brief account of it will appear in the summer 2017 in a book on multiple scattering published by Springer Verlag (Multiple Scattering Theory for Spectroscopies - A Guide to Multiple Scattering Computer Codes), co-edited by D. Sébilleau, K. Hatada and H. Ebert. Objective 1 has been completely achieved. Objective 2 has been partially achieved. The coding is not finished yet, mainly because the MsSpec code into which the present BEEM code has to be incorporated is under heavy rewriting in order to describe spectroscopies involving several electrons and to better blend within the ASE framework which is becoming sort of a reference framework for electronic structure codes. So, most of the subroutine of the BEEM are ready, but waiting for the new version of MsSpec to be ready in order to be incorporated. Objective 3 has been completely achieved. An interface with VASP, which despite being a commercial code is the most used electronic structure code in the world, has been written and tested. It has been published in Computer Physics Communications (ES2MS code) and it is one of the cornerstones of the present project, whose usefulness can be recognized for many other spectroscopies. Extension of ES2MS to the Gaussian code (another very popular electronic structure code, but dedicated to molecules) is underway, and plans have already been made to extend it also to the SPR-KKR code. Objective 4 is not completely achieved. First, it cannot be achieved as long as the new version of MsSpec is not available. Then, the CAPS company who was involved into this project has collapsed, which delayed the work on this objective. However, some experts on GPU have been working on this with us and preliminary tests of the multiple scattering formalism on GPUs have been carried out extensively. The results are extremely encouraging and show a substantial gain in computing time. Likewise, objective 5 has been partially fulfilled. Despite that fact that the code is not ready yet, we have managed to tackle successfully the most difficult part of the comparison to the experiment: reproduce the correct behaviour of the Schottky barrier with the VASP electronic structure code.