New computational framework provides better understanding of defects in semiconductor materials

All materials contain inherent defects. These are not always harmful, since they can be used to engineer and introduce certain properties into a material. However, it is crucial to understand how they function and how they affect the material’s properties.

To understand and model defects in different materials, researchers’ standard calculations are usually based on zero Kelvin, minus 273 degrees Celsius, the theoretically lowest possible temperature at which all atoms and molecules are completely stationary. But for materials intended for use in real-world products and everyday applications, it is essential to know how they behave at ordinary temperatures.

Researchers at Chalmers University of Technology have now demonstrated a significantly more effective framework for calculating the properties of defects while accounting for different temperature effects, enabling results that are much closer to reality. The findings are presented in an article published in npj Computational Materials.

Defects affect the performance and function of materials

Professor Julia Wiktor at the Department of Physics and Astronomy leads the research group behind the study. Their work focuses on studying and modelling new materials using advanced computer simulations and machine learning.

“We usually model materials as perfect crystals where every atom occupies a fixed position in a lattice, but real materials are not so perfect. An atom may be missing, there may be an extra atom between lattice sites, or two atoms may have swapped places. We need to understand these imperfections because they affect the performance and function of materials,” says Professor Julia Wiktor.

Tracking defects across different temperatures

The materials the research group typically investigates are mainly within solar cell technology, but this time they used a broader set of benchmark systems to test whether the method could be applied to other material classes and emerging technologies.

“We modelled defects in the materials by studying a missing atom in the crystal structure and observing how temperature affects the behaviour of this point defect. This is something that most models and simulations based on 0 Kelvin fail to capture, and it is an important step towards understanding how different materials actually behave under real operating conditions. Our results match experimental observations, but unlike experiments we do not just obtain an initial and a final measurement – we can follow the defect throughout the entire temperature range,” says doctoral student Tobias Hainer.

The position determines the impact of the defect

Defects can often introduce new energy levels into materials. A semiconductor, for example, has a so-called band gap, meaning an energy interval without available electronic states, and defects can introduce different levels within this gap. If a level lies deep within the band gap, this is in most cases undesirable for applications. But if it lies closer to the edge of the band gap, it can be engineered to tune the semiconductor’s electrical properties.

“The position of a defect level is highly significant when designing applications based on a material. If at zero Kelvin we predict that the defect lies near the edge, we may believe it to be harmless or even beneficial, but if at another temperature it shifts deeper into the gap it may become harmful, or vice versa. The position is therefore crucial,” explains Tobias Hainer.

Temperature matters in modelling

The research group can now demonstrate a more efficient way of carrying out calculations at temperatures above 0 Kelvin, in a manner that is practically feasible for many different types of materials and without excessive computational cost.

“The most important aspect we investigated is how these energy levels associated with a missing atom change with temperature, and we found quite significant shifts in several materials, both quantitatively and qualitatively. These changes would be missed in a model based on zero Kelvin. We have therefore shown that temperature really does matter in modelling and is necessary in order to describe these systems correctly,” says Julia Wiktor.

Machine learning enabled the calculations

The study is part of broader efforts at the Department of Physics and Astronomy to use machine learning to make materials modelling more accurate and computationally efficient, an area in which Julia Wiktor’s group collaborates with Professor Paul Erhart’s group.

“The fact that we can now draw these conclusions is closely linked to developments in machine learning. Ten years ago, we probably would not have been able to do this on such a scale, because the calculations are extensive and time-consuming. It is exciting that these new developments make it possible to carry out studies like this in a comprehensive way,” says Julia Wiktor.

“The main hope is that the method will be useful for researchers dealing with concrete material problems where the behaviour of defects or their importance is unknown, allowing them either to collaborate with us or to use the method themselves.”

About the research:

• The article Thermal Stabilization of Defect Charge States and Finite-Temperature Charge Transition Levels was published in npj Computational Materials and is written by Tobias Hainer, Ethan Berger, Esmée Berger, Olof Hildeberg, Paul Erhart and Julia Wiktor.

• The project acknowledges funding from the Swedish Strategic Research Foundation, the Swedish Energy Agency, the Swedish Research Council, the European Research Council, and the Knut and Alice Wallenberg Foundation. The computations were enabled by resources provided by the National Academic Infrastructure for Supercomputing in Sweden (NAISS) at C3SE, PDC, and NSC, partially funded by the Swedish Research Council