First-principles combinatorial design of transition temperatures in multicomponent systems: the case of Mn in GaAs

First-Principles Atomistic Thermodynamics and Configurational Entropy

In most applications, functional materials operate at finite temperatures and are in contact with a reservoir of atoms or molecules (gas, liquid, or solid). In order to understand the properties of materials at realistic conditions, statistical effects associated with configurational sampling and particle exchange at finite temperatures must consequently be taken into account. In this contribution, we discuss the main concepts behind equilibrium statistical mechanics. We demonstrate how these concepts can be used to predict the behavior of materials at realistic temperatures and pressures within the framework of atomistic thermodynamics. We also introduce and discuss methods for calculating phase diagrams of bulk materials and surfaces as well as point defect concentrations. In particular, we describe approaches for calculating the configurational density of states, which requires the evaluation of the energies of a large number of configurations. The cluster expansion method is therefore also discussed as a numerically efficient approach for evaluating these energies.

Optimizing molecular properties using a relative index of thermodynamic stability and global optimization techniques

We devised a global optimization (GO) strategy for optimizing molecular properties with respect to both geometry and chemical composition. A relative index of thermodynamic stability (RITS) is introduced to allow meaningful energy comparisons between different chemical species. We use the RITS by itself, or in combination with another calculated property, to create an objective function F to be minimized. Including the RITS in the definition of F ensures that the solutions have some degree of thermodynamic stability. We illustrate how the GO strategy works with three test applications, with F calculated in the framework of Kohn-Sham Density Functional Theory (KS-DFT) with the Perdew-Burke-Ernzerhof exchange-correlation. First, we searched the composition and configuration space of CmHnNpOq (m = 0-4, n = 0-10, p = 0-2, q = 0-2, and 2 ≤ m + n + p + q ≤ 12) for stable molecules. The GO discovered familiar molecules like N2, CO2, acetic acid, acetonitrile, ethane, and many others, after a small number (5000) of KS-DFT energy evaluations. Second, we carried out a GO of the geometry of CumSnn (+) (m = 1, 2 and n = 9-12). A single GO run produced the same low-energy structures found in an earlier study where each CumSnn (+) species had been optimized separately. Finally, we searched bimetallic clusters AmBn (3 ≤ m + n ≤ 6, A,B= Li, Na, Al, Cu, Ag, In, Sn, Pb) for species and configurations having a low RITS and large highest occupied Molecular Orbital (MO) to lowest unoccupied MO energy gap (Eg). We found seven bimetallic clusters with Eg > 1.5 eV.

Thermoelectricity in transition metal compounds: the role of spin disorder

At room temperature and above, most magnetic materials adopt a spin-disordered (paramagnetic) state whose electronic properties can differ significantly from their low-temperature, spin-ordered counterparts.

Smooth heuristic optimization on a complex chemical subspace

In the present work, several heuristic reordering algorithms for deterministic optimization on a combinatorial chemical compound space are evaluated for performance and efficiency.

Genetic design of enhanced valley splitting towards a spin qubit in silicon

The long spin coherence time and microelectronics compatibility of Si makes it an attractive material for realizing solid-state qubits. Unfortunately, the orbital (valley) degeneracy of the conduction band of bulk Si makes it difficult to isolate individual two-level spin-1/2 states, limiting their development. This degeneracy is lifted within Si quantum wells clad between Ge-Si alloy barrier layers, but the magnitude of the valley splittings achieved so far is small--of the order of 1 meV or less--degrading the fidelity of information stored within such a qubit. Here we combine an atomistic pseudopotential theory with a genetic search algorithm to optimize the structure of layered-Ge/Si-clad Si quantum wells to improve this splitting. We identify an optimal sequence of multiple Ge/Si barrier layers that more effectively isolates the electron ground state of a Si quantum well and increases the valley splitting by an order of magnitude, to ~9 meV.

Discrete Optimization of Electronic Hyperpolarizabilities in a Chemical Subspace

We introduce a general optimization algorithm based on an interpolation of property values on a hypercube. Each vertex of the hypercube represents a molecule, while the interior of the interpolation represents a virtual superposition ("alchemical" mutation) of molecules. The resultant algorithm is similar to branch-and-bound/tree-search methods. We apply the algorithm to the optimization of the first electronic hyperpolarizability for several tolane libraries. The search includes structural and conformational information. Geometries were optimized using the AM1 Hamiltonian, and first hyperpolarizabilities were computed using the INDO/S method. Even for small libraries, a significant improvement of the hyperpolarizability, up to a factor of ca. 4, was achieved. The algorithm was validated for efficiency and reproduced known experimental results. The algorithm converges to a local optimum at a computational cost on the order of the logarithm of the library size, making large libraries accessible. For larger libraries, the improvement was accomplished by performing electronic structure calculations on less than 0.01% of the compounds in the larger libraries. Alternation of electron donating and accepting groups in the tolane scaffold was found to produce candidates with large hyperpolarizabilities consistently.

A complete representation of structure-property relationships in crystals

Whereas structure-property relationships have long guided the discovery and optimization of novel materials, formal quantitative methods to identify such relationships in crystalline systems are beginning to emerge. Among them is cluster expansion, which has been successfully used to parametrize the configurational dependence of important scalar physical properties such as bandgaps, Curie temperatures, equation-of-state parameters and densities of states. However, cluster expansion is currently unable to handle anisotropic properties, a key distinguishing feature of crystalline systems central to the design of modern epitaxial structures and devices. Here, I introduce a tensorial cluster expansion enabling the prediction of fundamental tensor-valued material properties such as elasticity, piezoelectricity, dielectric constants, optoelectric coupling, anisotropic diffusion coefficients, surface energy and stress. As an application, I develop predictive ab initio models of anisotropic properties relevant to the design and optimization of III-V semiconductor epitaxial optoelectronic devices.

Atomic control of conductivity versus ferromagnetism in wide-gap oxides via selective doping: V, Nb, Ta in anatase TiO2

We identify two general types of electronic behaviors for transition-metal impurities that introduce excess electrons in oxides. (i) The dopants introduce resonant states inside the host conduction band and produce free electrons; (ii) the dopants introduce a deep gap state that carries a magnetic moment. By combining electronic structure calculations, thermodynamic simulations, and percolation theory, we quantify these behaviors for the case of column V-B dopants in anatase TiO2. Showing behavior (i), Nb and Ta dopants can convert the insulator TiO2 into a transparent conductor. Showing behavior (ii), V dopants could convert nonmagnetic TiO2 into a ferromagnet. Whether a dopant shows behavior (i) or (ii) is encoded in its atomic d orbital energy.

Finding the atomic configuration with a required physical property in multi-atom structures

In many problems in molecular and solid state structures one seeks to determine the energy-minimizing decoration of sites with different atom types. In other problems, one is interested in finding a decoration with a target physical property (e.g. alloy band gap) within a certain range. In both cases, the sheer size of the configurational space can be horrendous. We present two approaches which identify either the minimum-energy configuration or configurations with a target property for a fixed underlying Bravais lattice. We compare their efficiency at locating the deepest minimum energy configuration of face centered cubic Au-Pd alloy. We show that a global-search genetic-algorithm approach with diversity-enhancing constraints and reciprocal-space mating can efficiently find the global optimum, whereas the local-search virtual-atom approach presented here is more efficient at finding structures with a target property.

Design rules to achieve high-T(C) ferromagnetism in (Ga, Mn)As alloys

The Curie temperature T(C) of ferromagnetic semiconductor alloys depends not only on the alloy composition, but also on the spatial configuration of the magnetic impurities. Here we use a set of first-principle-calculated Curie temperatures to uncover-via a statistical, 'data mining' approach-the rules that govern the dependence of T(C) on the configuration of Mn substitutional impurities in GaAs. We find that T(C) is lowered (raised) when the average number of first (third and fourth) nearest-neighbour Mn pairs increases, suggesting simple atom-by-atom strategies to achieve high T(C) in (Ga, Mn)As alloys.