# What I do

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I am currently a postdoctoral researcher in Aalto University, Finland. I work with Prof. Tomi Laurila and Prof. Tapio Ala-Nissilä between the Department of Electrical Engineering and Automation and the Centre of Excellence in Computational Nanoscience (COMP) on the modeling of the interaction between organic molecules and carbon-based sensors in electrochemical detection processes. Throughout the sections below I summarize the main lines of research that I am or have been involved with.

I obtained my PhD in solid-state physics in August 2013 at the Photonics Theory Group at the Tyndall National Institute, Cork, Ireland, where I started in April 2009. My thesis supervisors were Prof. Eoin O'Reilly and Dr. Stefan Schulz. Broadly speaking, my research focused on the properties of strained crystals, more precisely tetrahedrally bonded compounds, such as the III-V. Materials in the III-V category include technologically important semiconductors such as GaAs or the group-III nitrides.

## Contents

This page contains brief information about the different topics I am or have been working on. There is always more information available from the different published papers and, when I have the time, I usually write a longer page here on the Wiki. These more in-depth resources are available as links from the different sections below. I try to keep this as up to date as time allows, at least to give an overview of current research themes. For that reason, I usually promote new items, or research lines where there was a recent development, to the top of the list.

## Computational discovery of new piezoelectric materials

Enhancement of the piezoelectricity of ScAlN with increasing Sc content, taken from our paper.

Check out our paper on piezoelectric properties of ScAlN alloys.

The availability of new piezoelectric materials compatible with silicon chip integration for micro-electromechanical systems (MEMS) application is a highly attractive prospect. These new materials will help to bridge the gap between mechanical and electronic devices, making MEMS increasingly small and efficient. AlN is today's industry's standard and research is intensifying worldwide on AlN derivatives such as ScAlN. One of my research interests is to apply different computational techniques to discover new piezoelectric materials with enhanced piezoelectric coefficients. We have started with the exhaustive characterization of ScAlN, already published, and initial screening of another system on which I am currently working. Hopefully I will be able to secure funding to intensify and expand my activities in that direction if a current project proposal is successful.

## Material tensors

Also check out the MattPy and Projected tensors pages.

As part of my work on elasticity and piezoelectricity I have done some work on rotation and projection of material tensors building on previous work by Moakher and Norris.[1] I have released a collection of Python routines, that I named MattPy, whose main functionality is to automatize the optimized projection of triclinic material tensors onto a higher symmetry tensor including the rotational degrees of freedom. It also has some other utilities such as general tensor rotations, conversion between Voigt and Cartesian forms, etc. It works with elastic (stiffness) tensors and piezoelectric tensors (both "e" and "d" forms). Now I need to improve a bit the documentation and update the implementation paper. At the moment some useful expressions can be found on this wiki (Projected tensors page) and further info is available on the original implementation, which currently only has an archaic (and deprecated) version of the projection code (in Mathematica language). This paper can be found on the arXiv and I am hoping to carry out a major update as soon as possible. However, the amount of time that I have available to work on this project is very limited so progress is expected to be slow. The last version of both code and (incomplete) documentation are publicly available on GitHub.

## Orbital-free DFT

Linear scaling of orbital-free DFT compared to the superlinear scaling of Kohn-Sham DFT. See our paper, Ref. [2], for the details.

For further details, check out the local tutorial on how to run GPAW OFDFT calculations and visit the GPAW website.

Orbital-free density functional theory (DFT) has been around since before the celebrated seminal papers by Hohenberg & Kohn[3] and Kohn & Sham.[4] The early work by Thomas,[5] Fermi[6] and Dirac,[7] which predates the papers by Hohenberg-Kohn-Sham by about 35 years, already aimed at simplifying the electronic structure problem by expressing the total energy of the system as a functional of the density: $C_\text{TF} \int \text{d}\textbf{r} \, n^{5/3} (\textbf{r})$ for the Thomas-Fermi kinetic energy and $C_\text{x} \int \text{d}\textbf{r} \, n^{4/3} (\textbf{r})$ for the Dirac exchange. The Dirac exchange is still used in local density approximations (LDAs) to the exchange energy in present day electronic structure codes. In contrast, the Thomas-Fermi functional is a poor approximation of the kinetic energy of a system of interacting electrons, failing to predict critical properties such as chemical bonding between atoms. Indeed, DFT did not gain widespread attention until the introduction of the Kohn-Sham single particle ansatz, which enables a reasonably accurate determination of kinetic energies and leads to satisfactory description of many properties of matter, such as atomic shell structure. The ever increasing computational power and development of efficient iterative codes have popularized Kohn-Sham DFT to the point that nowadays it is arguably the most widely used electronic structure method.

Nevertheless, Kohn-Sham DFT comes with its own set of shortcomings, one of which is the super-linear (usually cubic) scaling with system size (see figure to the right). One is then tempted to look back towards the orbital-free formulation of DFT, which offers linear scaling with system size, and hope that the accuracy can be improved this time around. However, to the intrinsic problem of finding accurate orbital-free functionals, one has to add the difficulty to achieve convergence of the self-consistency cycle in orbital-free DFT calculations.

In Olga Lopez-Acevedo's group, we have been working on using the projector-augmented wave (PAW) formalism[8] to improve the convergence capabilities of orbital-free DFT compared to what was previously available. We have implemented[2] the orbital-free DFT method in GPAW, an open source collaborative electronic structure code.[9] Any kinetic density functional available from the LibXC library[10] (including future developments), also an open-source effort, can be used with the new GPAW module. This bet for widely-available open-source codes opens the door to increased collaboration among the community and maximum flexibility. We have also worked on a systematic assessment[11] of a parametrized orbital-free kinetic energy functional made possible by the new implementation, and continue working on further development of orbital-free DFT.

## Amorphous carbon (a-C)

Atomic model of an a-C surface generated as part of my work, using density functional theory. See our publication for details.

Check out our amorphous carbon paper.

Amorphous carbon (commonly abbreviated as a-C) is a versatile material with multiple applications in industry and research. There is growing interest in a-C and more particularly high-density a-C, also known as tetrahedral amorphous carbon (ta-C), as coating for use in biological applications. ta-C is biocompatible, corrosion resistant, withstands bacterial adhesion, and can be integrated with CMOS technology. All these qualities make it an ideal candidate to be used as electrode coating for the electrochemical detection of biomolecules, such as the neurotransmitters dopamine and glutamate. The work in Tomi Laurila's group at the Department of Electrical Engineering and Automation in Aalto University aims at the experimental measurement and characterization of these processes. My job is to study the link between the experimental observations and the processes taking place at the atomic scale, for which I resort to different computational methods. Browse below for more detailed information on our different lines of work.

### Amorphous carbon surfaces

More info coming soon. In the mean time, check out this and this papers.

## Group-III nitrides

Check out the group-III nitrides page.

Group-III nitrides are material compounds of nitrogen (N) and the elements in the first column of the p-element block of the periodic table (technically, group IIIB): boron (B), aluminium (Al), gallium (Ga), indium (In) and thallium (Tl). The compounds AlN, GaN, InN and their alloys are technologically important semiconductors with multiple applications in optoelectronics, in particular incorporated in LEDs for light production. Much of my work during my PhD at the Tyndall National Institute has focused on the study of some of the properties of these materials. The main lines of research are summarized below, with links to more detailed information.

### Built-in field control in group-III nitrides

Check out the field control page. For related papers check J. Appl. Phys. 109, 084110 (2011) and Phys. Stat. Sol. C 9, 838 (2012).

Schematic diagram of the carrier separation occurring in a GaN/AlN quantum dot, induced by the strong built-in electrostatic field.

When grown in the hexagonal wurtzite phase, nitrides present permanent spontaneous polarization along the [0001] direction. The high lattice mismatch between the binaries (14% between InN and AlN) leads to additional strain-induced (piezoelectric) polarization when heterostructures are grown. In quantum wells and quantum dots, the polarization difference between dot or well and the barrier around it gives interfacial charge accumulation, similar to what happens in a capacitor, from which very strong electric fields of the order of MV/cm arise. This causes a strong spatial separation of the carriers (figure on the left), hence diminishing the wave function overlap and the recombination rate, among other issues. Polarization matching or field control is a means of reducing the intrinsic built-in field in nitride-based devices, such as InGaN light-emitting diodes. During my time in Tyndall, we worked on optimizing combinations of compositions in active layer and barriers that allow a minimization of the built-in electrostatic fields in nitride nanostructures. Go to the field control page to learn more about this.

## Undergraduate studies in La Laguna

Before starting my PhD, I undertook undergraduate studies in Physical Sciences (Licenciado en Física) at Universidad de La Laguna, in the Canary Islands, Spain, from October 2003 until January 2009. During my final year I was involved in a short research project under the supervision of Prof. Santiago Brouard on continuous measurement in quantum mechanics (see the Split operator method page for the method we used to solve the stochastic Schrödinger equation). I was also involved in setting up a "quantum eraser" class experiment with a Mach-Zehnder interferometer under the supervision of Prof. Rafael Sala.

## References

1. M. Moakher and A. N. Norris. The closest elastic tensor of arbitrary symmetry to an elasticity tensor of lower symmetry. J. Elasticity 85, 215 (2006).
2. J. Lehtomäki, I. Makkonen, M. A. Caro, A. Harju, and O. Lopez-Acevedo. Orbital-free density functional theory implementation with the projector augmented-wave method. J. Chem. Phys. 141, 234102 (2014).
3. P. Hohenberg and W. Kohn. Inhomogeneous Electron Gas. Phys. Rev. 136, B864 (1964).
4. W. Kohn and L. J. Sham. Self-Consistent Equations Including Exchange and Correlation Effects. Phys. Rev. 140, A1133 (1965).
5. L. H. Thomas. The calculation of atomic fields. Math. Proc. Cambridge Philos. Soc. 23, 542 (1927).
6. E. Fermi. Un metodo statistico per la determinazione di alcune priorietà dell'atomo. Rend. Accad. Naz. Lincei 6, 32 (1927).
7. P. A. M. Dirac. Note on exchange phenomena in the Thomas atom. Proc. Cambridge Philos. Soc. 26, 376 (1930).
8. P. E. Blöchl. Projector augmented-wave method. Phys. Rev. B 50, 17953 (1994).
9. J. Enkovaara, C. Rostgaard, J. J. Mortensen,J. Chen, M. Dułak, L. Ferrighi, J. Gavnholt, C. Glinsvad, V. Haikola, H. A. Hansen, H. H. Kristoffersen, M. Kuisma, A. H. Larsen, L. Lehtovaara, M. Ljungberg, O. Lopez-Acevedo, P. G. Moses, J. Ojanen, T. Olsen, V. Petzold, N. A. Romero, J. Stausholm-Møller, M. Strange, G. A. Tritsaris, M. Vanin, M. Walter, B. Hammer, H. Häkkinen, G. K. H. Madsen, R. M. Nieminen, J. K. Nørskov, M. Puska, T. T. Rantala, J. Schiøtz, K. S. Thygesen, and K. W. Jacobsen. Electronic structure calculations with GPAW: a real-space implementation of the projector augmented-wave method. J. Phys.: Condens. Matter 22, 253202 (2010).
10. M. A. L. Marques, M. J. T. Oliveira, and T. Burnus. Libxc: A library of exchange and correlation functionals for density functional theory. Comp. Phys. Comm. 183, 2272 (2012).
11. L. A. Espinosa Leal, A. Karpenko, M. A. Caro, and O. Lopez-Acevedo. Optimizing a parametrized Thomas-Fermi-Dirac-Weizsäcker functional for atoms. Phys. Chem. Chem. Phys. (accepted), DOI:10.1039/C5CP01211B (2015).