Determination of surface structure of Si-rich SiC(001)(3x2) Results for the two-adlayer asymmetric dimer model (TAADM) are the only ones that agree with experiments Lu, Schmidt, Briggs, Bernholc, PRL 85, 4381 (2000)] Various models for Si-rich SiC(001)(3x2) are very close in energy, but comparisons between calculated and measured RAS/RDS allows for unambiguous determination of surface structure

Surface and bulk states contributing to RAS features of TAADM Both intradimer and interdimer have to be taken into account to explain the RAS. C B A The asymmetric dimer in top adlayer is responsible for Peak A and B. The dimers in second adlayer is responsible for the dip at 4.2 eV.

TAADM for SiC(001) 3x2: Further Confirmation by Recent X-ray study ours exp. (Soukiassian PCSI ‘03) PRL 85, 4381 (2000)2002 d1 = d2 = d3 =  z = d1 d2d3

Investigate most common steps on Si(001) [Chadi, PRL 59, 1691 (1987)]

Step contributions to RAS  3 eV feature (S) in spectra of vicinal Si(001) step related  D B steps dominate for miscuts larger than 4 0  good agreement between experiment and theory S S S A,S B andD B steps Schmidt, Bechstedt, Bernholc, PRB 63, (2001) experiment: difference between flat & stepped surface Jaloviaret al. PRL82, 791 (1999) theory

Multigrid method for quantum simulations Density functional equations solved directly on the grid Multigrid techniques remove instabilities by working on one length scale at a time Convergence acceleration and automatic preconditioning on all length scales Non-periodic boundary conditions are as easy as periodic Compact “Mehrstellen” discretization Allows for efficient massively parallel implementation Speedup on Cray T3E with number of processors Runs also on IBM SP, Origin 2000 and Linux clusters See E. L. Briggs, D. J. Sullivan and J. Bernholc Phys. Rev. B 54, (96).

Expansion of the DFT total energy in localized, variationally optimized orbitals - – very few orbitals needed, e.g., 3-4 orbitals per carbon atom Same computational cost as in tight-binding models for computing conductances All operations performed on real-space grid with multigrid acceleration – fast convergence rate Main parts scale linearly with the number of atoms Unoccupied orbitals are essential (small O(N 3 ) part) Fully parallel on IBM SP and Cray T3E tested on > 1000 atoms Forces, geometry optimization Briggs, Sullivan, Bernholc PRB 54, (1996). Fattebert, Bernholc, PRB 62, 1713 (2000). Buongiorno Nardelli, Fattebert, Bernholc, PRB 64, (2001). Ab initio O(N)-like quantum transport calculations Shape of an optimized orbital: valence bond function Basis Multigrids

Semiconducting NT-metal cluster assemblies  (8,0)tube + Al 13  More stable  C-Al bond length: 2.15 Å  Formation energy: -0.7 eV  (8,0)tube + Al 13 + NH 3  More stable  C-Al bond length: 2.11 Å  Formation energy of the molecule complex: -1.8 eV

 (8,0) tube + Al 13  charge goes to the metal cluster  transfer of 0.1 e -  (8,0) tube + Al 13 + NH 3  0.4 e - from NH 3 to the cluster and tube.  n-type conductivity + | e-e- | + e-e- e-e- | Less electronsMore electrons e-e- Charge transfer in semiconducting CNT-cluster assembly |

A simple view on polarization Macroscopic solid sample: and includes all boundary charges. Polarization is well defined but this definition cannot be used in realistic calculations. Ionic part: Localized charges, easy to compute Electronic part Charges usually delocalized Periodic solid: Polarization is ill-defined (except for Clausius-Mossotti limit ) Charges are delocalized No surface charges

Computing polarization of a periodic solid 2) Polarization derivatives are well defined and can be computed. Modern theory of polarization R. D. King-Smith & D. Vanderbilt, PRB 1993 R. Resta, RMP ) Polarization is a multivalued quantity and its absolute value cannot be computed. Piezoelectric polarization: Modern approaches to compute polarization use Berry phase or Wannier function formalisms. Spontaneous polarization:

Wannier functions in flat C and BN sheets   Carbon Boron-Nitride No spontaneous polarization in BN sheet due to the presence of the three-fold symmetry axis