Improved modelling of the Pockels effect may help advance optoelectronic technology

The use of light signals to connect electronic components is a key element of today’s data communication technologies, because of the speed and efficiency that only optical devices can guarantee. Photonic integrated circuits, that use photons instead of electrons to encode and transmit information, are found in many computing technologies. Most are currently based on silicon – a good solution because it is already used for electronic circuits, but with a limited bandwidth. An excellent alternative is tetragonal barium titanate (BTO), a ferroelectric perovskite that can be grown on top of silicon and has much better optoelectronics properties. But since this material is quite new in the field of applied optoelectronics, a better comprehension of its quantum properties is needed in order to further optimize it. A new article by MARVEL scientists published in Physical Review B presents a new computational framework to simulate the optoelectronics behavior of this material, and potentially of other promising ones. 

The study is the result of a collaboration between academia and industry, funded by the Swiss innovation agency Innosuisse. The Swiss startup Lumiphase, that produces BTO-based devices, turned to scientists from Mathieu Luisier’s lab at ETH Zurich, who collaborated with Nicola Marzari’s group at EPFL Lausanne to simulate the material and help optimize it. 

The key challenge for the researchers was to accurately simulate the physical phenomenon at play: the Pockels effect - a change in the refractive index of the material in the presence of an electric field. “In an optoelectronic transceiver, you build an interferometer with two arms,” explains first author Virginie de Mestral, from the Luisier lab. “On one arm you just let the light go through. On the other arm, which is integrated onto a BTO thin-film, you modulate the refractive index by applying an electric field, and so you change the phase of the electromagnetic wave. When you recombine the waves from the two arms you create interference patterns that can be used to encode 1s and 0s”.

The current computational models used to study Pockels effects are based on density-functional perturbation theory (DFPT), a method that describes the response of atomistics systems to external perturbations. DFPT for Pockels relies on the use of a specific exchange-correlation functional called LDA. But finding the right functional for calculating Pockels effects in a material like BTO is difficult and limits the accuracy of the calculations.  The authors wanted to devise a method that would be independent of a specific functional and would bypass DFPT entirely, relying only on standard Density Functional Theory. 

An efficient way to do it was to use finite differences, a numerical technique to solve differential equations. De Mestral explains that the AiiDA open-source infrastructure was essential for this. “We needed a lot of finite differences calculations,” she says. “Doing them by hands could work for one material, but we wanted a method that could be applied to different materials and be useful in the industry. AiiDA enabled us to automatize finite differences calculations”. 

Another problem the scientists had to deal with was how to get rid of a phenomenon that shows up when simulating BTO: the occurrence of imaginary phonon frequencies. In essence, it is a sign that the simulated material is not dynamically stable. This typically happens in ferroelectric materials that change phase at different temperatures. 

The solution to stabilize these phonon modes was to create a supercell (a cell that describes the same crystal as the unit cell, but with a larger volume) and induce some off-centering of the titanium atoms inside of it. “In doing so we are better representing reality, because this is what is actually measured with X-rays, and the imaginary phonon frequencies turn real and positive,” says de Mestral. 

The results were validated by comparing them to existing experimental results, and to previous calculations based on DFPT. The results proved comparable, but not perfectly overlapping. “One reason is that we don’t have access to the exact crystal structures used in previous calculations,” says de Mestral. “Another reason is that in the industry we work with thin films, but in DFT we have bulk materials that are defect-free. In addition, no piezoelectric contribution to the Pockels effect was included”. 

An important result explained in the paper addresses the correlation between the titanium off-centering and the Pockels coefficient of the material. “The higher the coefficient is, the smaller the device can be, which is essential in industrial applications,” says de Mestral “We noticed that the Pockels coefficient increases dramatically when the titanium off-centering is smaller, which means that we are closer to a high-symmetry material”. 

In the future, the group would like to also study how the Pockels effect depends on the frequency of the applied electric field. “It is quite a lot of work that has not been done yet because the frequencies we’re interested in are quite low, and to obtain what we want we need to move ions, not only electrons”, says de Mestral.