The serendipitously discovered solution-liquid-solid (SLS) mechanism has been refined into a nearly general synthetic method for semiconductor nanowires. Purposeful control of diameters and diameter distributions is achieved. The synthesis proceeds by a solution-based catalyzed-growth mechanism in which nanometer-scale metallic droplets catalyze the decomposition of metallo-organic precursors and crystalline nanowire growth. Related growth methods proceeding by the analogous vapor-liquid-solid (VLS) and supercritical fluid-liquid-solid (SFLS) mechanisms are known, and the relative attributes of the methods are compared. In short, the VLS method is most general and appears to afford nanowires of the best crystalline quality. The SLS method appears to be advantageous for producing the smallest nanowire diameters and for variation and control of surface ligation. The SFLS method may represent an ideal compromise. Recent results for SLS growth are summarized.
Originating from a broken spatial inversion symmetry, ferroelectricity is a functionality of materials with an electric dipole that can be switched by external electric fields. Spontaneous polarization is a crucial ferroelectric property, and its amplitude is determined by the strength of polar structural distortions. Density functional theory (DFT) is one of the most widely used theoretical methods to study ferroelectric properties, yet it is limited by the levels of approximations in electron exchange-correlation. On the one hand, the local density approximation (LDA) is considered to be more accurate for the conventional perovskite ferroelectrics such as $\mathrm{BaTi}{\mathrm{O}}_{3}$ and $\mathrm{PbTi}{\mathrm{O}}_{3}$ than the generalized gradient approximation (GGA), which suffers from the so-called super-tetragonality error. On the other hand, GGA is more suitable for hydrogen-bonded ferroelectrics than LDA, which largely overestimates the strength of hydrogen bonding in general. We show here that the recently developed general-purpose strongly constrained and appropriately normed (SCAN) meta-GGA functional significantly improves over the traditional LDA/GGA for structural, electric, and energetic properties of diversely bonded ferroelectric materials with a comparable computational effort and thus enhances largely the predictive power of DFT in studies of ferroelectric materials. We also address the observed system-dependent performances of LDA and GGA for ferroelectrics from a chemical bonding point of view.
A gedanken density is not a real one but one imagined in the construction of density functional approximations. The uniform electron gas is the original gedanken density, but we will be concerned here with two others: (1) the groundstate density of one electron in the presence of a nonuniform periodic potential , in which the reduced density gradient s = |∇n| /[2(3π2)1/3n4/3diverges almost everywhere as the volume tends to infinity. This density was used in the construction [1] of a generalized gradient approximation (GGA): To satisfy the general Lieb-Oxford lower bound [2] on the exchangecorrelation energy for all possible densities, the exchange enhancement factor Fx ≡ eapprox x /eunif x in the large-s limit for a spin-unpolarized density must be less than or equal to 1.804. (2) a two-electron spherical ground-state density in which s takes the same arbitrary positive value wherever the density is non-zero [3]. This density can be used to show that, to satisfy the tight Lieb-Oxford bound on the exchange energy of a two-electron density for every possible such density, Fx for such a density (and probably for every density) must be less than 1.174. The local spin density approximation (LSDA) for exchange (Fx = 1) satisfies this tight bound, but standard GGA’s and meta-GGA’s do not. A talk by Jianwei Sun will present what may be the first beyond-LSDA approximation to satisfy this strong new constraint.
In Table III, the MGGA lattice constant for NaCl should be 5.60 Å, and the MGGA mean absolute error should be reduced to 0.043 Å, which is now less than the GGA error.For further tests of the PKZB meta-GGA and eight other density functionals, see [1].
By extrapolating the energies of nonrelativistic atoms and their ions with up to 3000 electrons within Kohn-Sham density functional theory, we find that the ionization potential remains finite and increases across a row of the periodic table, even as Z → ∞. The local density approximation for the exchange contribution becomes more accurate (or even exact) in this limit. Extended Thomas-Fermi theory matches the shell average of both the ionization potential and density change.
Density-functional approximations for the exchange-correlation energy Exc[n] of a many-electron ground state are highly developed and widely useful. When a paramagnetic current jp(r) is present, Vignale and Rasolt have extended the Kohn-Sham theorems and presented an additive correction valid to second order in the gauge-invariant vorticity nu=Delta x (jp/n):Exc[n, jp]=Exc[n, jp=0] + DeltaE(VR)(xc)[n, nu]. Apart from spin-polarization effects, their correction is unambiguous for a generalized gradient approximation (GGA). But for a meta-GGA (MGGA), one needs to know how to go back from the orbital kinetic energy density tau([n, jp];r) to tau([n,0];r); we show how to do this here. Numerical tests on the degeneracies for open-shell atoms show that current-density corrections reduce the error of GGA from 2 to 1 kcal/mol, and of MGGA from 5 to 2 kcal/mol.
While members of the 2D semiconducting transition metal dichalcogenide (TMD) family MX<sub>2</sub> (M = {Mo, W}, X = {S, Se}) are promising for device applications, stacked layer (vertical) heterojunctions exhibit features that make them inappropriate for light-emitting applications. Such vertical heterojunctions exhibit type II, rather than the preferred type I band alignment. Using density functional theory calculations, we identify the pseudo-binary and quaternary alloy composition range for which band alignment is type I. While broad regions of composition space lead to type I band alignment, most light-emitting devices require direct bandgaps. We demonstrate that by taking advantage of alloying and/or twisting between layers, a wide range of type I, direct bandgap stacked layer (vertical) heterojunctions are achievable. These results and the underlying method developed here provide new opportunities for TMD vertical heterojunction device optimization and opens the door to new classes of TMD vertical heterojunction device applications.
