Institute for the Theory of Advanced Materials in Information Technology James R. Chelikowsky, University of Texas at Austin, DMR 0551195

Workshop on Materials Theory

The Institute for the Theory of Advanced Materials in Information Technology held a workshop on materials theory and related topics on October 20-22, 2005. The workshop was held in the Institute of Computational Engineering and Sciences on the campus of the University of Texas at Austin. Approximately 50 scientists from the US, Europe and Israel attended the meeting. The proceedings were published in physica status solidi as indicated on the right.

The hope of using carbon nanotubes as elements of electronic devices has advanced considerably toward becoming reality with recent demonstrations of CNT field-effect transistors (CNT-FETs). The issue of Schottky barrier formation at carbon nanotube contacts with metal leads is of crucial importance for nanotube-based electronic devices. Through first-principles total energy and electronic structure calculations within density functional theory, we have established that the junction between the metal covered part and the bare part of the CNT is responsible for the formation of a p-type Schottky barrier of ~0.4 eV, in excellent agreement with experiment. The figure shows metal-induced gap states, typical of Schottky barrier behavior for the (8,0) semi-conducting nanotube (orange atoms) in contact with a Pd metal ring (blue atoms).

Institute for the Theory of Advanced Materials in Information Technology

James R. Chelikowsky, University of Texas at Austin, DMR 0551195 Schottky barrier formation at a carbon nanotube – metal junction

Institute for the Theory of Advanced Materials in Information Technology James R. Chelikowsky, University of Texas at Austin, DMR 0551195

Doping nanocrystals and self-purification

The properties of impurities in nanostructures can be very different from the precursor materials, sometimes even leading to novel phenomena. This usually is due to quantum confinement effects and to the reduced size of the system. In pure semiconductor nanocrystals, the most remarkable change is in their energy gap, that is blue-shifted from the bulk value as the size of the nanocrystal decreases. This leads to the possibility of tuning the band gap of the material in order to satisfy specific needs, providing a wide spread of applications such as solar cells, electroluminescent devices, and possible electronic devices. Bulk semiconductors need to be doped to build functional devices. In order to develop functional devices with semiconductor nanocrystals, they should also be doped. However, the doping process is difficult and not well understood within the nano-size regime. In particular, nanocrystals are thought to “self-purify” as dopants may easily diffuse to the surface of a nanocrystal. We have discovered that doping may also be energetically unfavorable as the size of the nanocrystal decreases. This is illustrated for Mn doped CdSe nanocrystals (top right) where the relative energy to create to insert the Mn atom increases dramatically for small nanocrystals (bottom right.)

Charge density plot of the impurity d levels in a Mn-doped CdSe nanocrystal with 1.7nm diameter.

Institute for the Theory of Advanced Materials in Information Technology

James R. Chelikowsky, University of Texas at Austin, DMR 0551195

Efficient diagonalization methods for the Kohn-Sham equation

Background. The Kohn-Sham equation is typically solved by iterative diagonalization of the associated Hamiltonian matrix. This is in effect a functional iteration for solving a nonlinear eigenvalue problem, combined with a ‘mixing’ technique for improving convergence of the nonlinear self-consistent field (SCF) loop. Many elaborate methods have been used for solving the Kohn-Sham eigenvalue problem. These methods often focus on the diagonalization of matrices. This perspective de-emphasizes the nonlinear nature of the problem and tends to narrow the scope of methods that can be utilized.

New Approach. We have recently implemented a technique which exploits the nonlinear nature of the self-consistent field iteration. The method solves the original nonlinear Kohn-Sham equation directly by a form of nonlinear subspace iteration. It distinguishes itself from previous methods by not focusing on the intermediate linearized Kohn-Sham eigenvalue problems. Instead, it replaces diagonalization by a polynomial filtering step applied to each basis vector of the subspace being computed. Low degree Chebyshev polynomials are used for filtering as illustrated in the figure. The method reaches convergence within a similar number of self consistent field (SCF) iterations as eigensolver-based approaches but each SCF iteration is much less expensive. The numerical tests show a typical speed-up by an order of magnitude over standard diagonalization-based approaches. This new technique enabled calculations for a number of challenging problems, which heretofore could not be attempted.

Results. The left table below compares the Chebyshev filtering approach with an approach based on ARPACK using one processor for an Si525H276 cluster. The right table shows two recent calculations for larger and more challenging systems performed with moderate resources, namely, 48 and 24 SGI Altix (1.6Ghz Itanium) processors respectively.

Institute for the Theory of Advanced Materials in Information Technology

James R. Chelikowsky, University of Texas at Austin, DMR 0551195

Spin transition in complex oxides under pressure

Fe-Mg oxides may undergo a high spin (HS) to low spin (LS) transition under pressure (23-135 GPa). Previous first principles methods have failed to describe this phenomenon. Using a new rotationally invariant formulation of density functional theory (LDA+U), we were able to describe successfully this transition in the low solute concentration for the oxide: magnesiowüstite (Mw), (Mg1-xFex)O, (x < 0.2). We show that the HS/LS transition goes through an insulating (semiconducting) intermediate mixed spins state without discontinuous changes in properties, as seen experimentally. These encouraging results open for exploration by first principles a new class of spin related phenomena.

FeO

O O

O

O

O

A. HS Maj

FeO

O O

O

O

O

A. HS Maj

FeO

O O

O

O

O

C. LS Maj

FeO

O O

O

O

O

C. LS Maj

FeO

O O

O

O

O

B. HS Min

FeO

O O

O

O

O

B. HS Min-2%

-3%

-2%

-3%

-2%

-3%

D. ∆Voct

Charge densities around a ferrous iron in magnesiowüstite. Isosurface charge densitieswith ρ = 0.3 e/Å3 for majority (A) and minority HS (B), and majority/minority LS (C). Polyhedral volume collapse across the spin transition (D). Six caps surrounding the ferrous ion belong to oxygens.