What Is Density Functional Theory and How Does It Work? | Synopsys

Density Functional Theory

What is Density Functional Theory (DFT)?

Density functional theory (DFT) is a quantum-mechanical atomistic simulation method to compute a wide variety of properties of almost any kind of atomic system: molecules, crystals, surfaces, and even electronic devices when combined with non-equilibrium Green's functions (NEGF).

DFT belongs to the family of first principles (ab initio) methods, so named because they can predict material properties for unknown systems without any experimental input. Among these, DFT has earned popularity due to the relatively low computational effort required.

The DFT approach is widely applied in organic and inorganic chemistry, materials sciences like metallurgy or ceramics, and for electronic materials, to just name a few areas.

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A very brief historical background

The ground-breaking developments of quantum mechanics in the early 20th century finally provided the answer to many outstanding questions about the nature and properties of the atom. Applying these principles to more complicated systems such as molecules and solid-state materials proved more difficult, however; even in classical physics there is no general solution to a three-body problem (such as the combined orbital motion of the sun, the moon, and the Earth), and to describe just a water molecule we have to deal with ten electrons and three atomic nuclei.

The success and applicability of DFT lies in some very clever realizations in the mid-1960s by Walter Kohn, Pierre Hohenberg, and Lu Jeu Sham. By not focusing on the individual electrons but instead using the electron density as the fundamental variable to solve for, and furthermore reformulating the many-body problem as an equivalent single-particle problem, density functional theory was born.

Over the following decades the method was turned into a practical tool by many contributors, and through the use of powerful numerical computers, DFT became an indispensable tool for materials science, chemistry, and many other fields. Relatively straightforward additions of the spin degree of freedom have enabled the description of magnetic systems, and on top of that, relativistic effects and even superconductivity can be treated.

What problems does DFT solve?

Atomistic modeling in general, and DFT calculations in particular, provide significant value to researchers and scientists working with chemicals, electronic materials, etc., in two distinct ways:

  1. Since it can handle essentially any element in the periodic table in any kind of atomic arrangement, without the need for experimental input parameters, DFT has strong predictive power, even for completely new molecules or materials. In this way, atomistic simulations can reduce development time and cost by down-selection of promising material candidates prior to going into the lab and dealing with expensive and possibly hazardous chemicals with unknown properties and behavior. Using high-performance computer (HPC) clusters, a single person can screen hundreds or even thousands of materials in parallel, vastly outnumbering the number of experiments a human can perform at the same time.
  2. Second, DFT calculations are used to help understand how materials and devices behave and operate under different conditions. A trained DFT user can correlate measurement data with simulation results to draw conclusions about the physical origin of certain effects observed in the material or device, but which cannot readily be explained with simple models. Such insight is crucial in order to fully exploit the effects and material in question, and even more so in order to, for instance, scale down device dimensions or optimize material choices or process conditions.

Thus, thanks to its predictive capabilities and atomistic quantum-mechanical nature, DFT is a crucial tool for technology pathfinding, to explore novel materials and exotic physical phenomena, years prior to a first test device being manufactured or even before new material has been fully characterized experimentally!

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How does DFT fit in the Synopsys product portfolio?

The QuantumATK atomistic modeling platform from Synopsys is one of the most modern and versatile materials simulation codes on the market. It can be used to compute electronic, thermal, mechanical, optical, magnetic, ferroelectric, thermoelectric and many other properties of complex molecules, amorphous and crystalline materials, interfaces, and even atomistic devices. The code is also designed to be efficient, versatile and robust, but also easy-to-use and suitable to new users, offering both a NanoLab graphical user interface and Python scripting for more experienced users to automate tasks and create advanced workflows and data analysis.

QuantumATK can also be connected to TCAD tools and DTCO flows to support the use of new materials in process simulations and novel device architectures. Through specially designed application-centric modules, engineers with limited background in the theory of DFT can still take advantage of atomistic modeling, by focusing on the important design parameters as input, while the expert system within the software takes care of tuning the numerical and computational parameters to obtain accurate and fast results.

Going beyond DFT

Keep in mind that QuantumATK is more than just a DFT code! It comprises force fields and semiempirical models as well, and the synergy obtained by these models co-existing in the same code environment makes it possible to solve unique problems, such as combining a classical potential for phonons with a DFT model for the electrons in thermal or electron transport simulations or use machine learning to fit accurate force-fields for new materials.

Moreover, QuantumATK is developed with the ambition to provide as realistic physical results as possible, in complex materials and under many different circumstances. This requires a simulation engine that can handle DFT calculations for very large systems, and we are constantly adding new models that aim to provide more accurate results faster. The LCAO-HSE model is capable of providing accurate band alignments between different materials, e.g. in a high-k metal gate stack (HKMG), even in systems with 3000+ atoms, and the NEGF method is able to describe electron transport (with phonon scattering included, if desired) of complex atomic-scale devices.

Learn more about how QuantumATK performs accurate and reliable Density Functional Theory (DFT) simulations in semiconductor physics/device technologies.