Determination of surface structure of Si-rich SiC(001)(3x2)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 experimentsLu, 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

TAADM SDRM

DDRM ADRM

TAADM

SDRM

DDRM

ADRM

ExperimentRossow et al.JVST B16, 2355(1998)

1 2 3 4 5

0.004

x0.5

x0.1

x0.3

Energy [eV]

RA

S

Surface and bulk states contributing to RAS features of TAADMSurface 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 studyTAADM for SiC(001) 3x2: Further Confirmation by Recent X-ray study

ours exp. (Soukiassian PCSI ‘03)PRL 85, 4381 (2000) 2002

d1 = 2.24 2.42d2 = 2.37 2.24d3 = 2.38 2.55z = 0.5 0.15

d1

d2 d3

Investigate most common steps on Si(001)

[001]

[110]

_[110]

DB SB

SA

[Chadi, PRL 59, 1691 (1987)]

Step contributions to RAS

3 eV feature (S) in spectra of vicinal Si(001) step related

DB steps dominate for miscuts larger than 40

good agreement between experiment and theory

r/r

r/r

1 2 3 4 5Energy [eV]

0.002

0.001

(001)-1O

-2O

-4O

-6O

SA

SB

DB

E1 E2

S

S

SA, SB and DB stepsSchmidt, Bechstedt, Bernholc, PRB 63, 045322 (2001)

experiment: difference between flat & stepped surface Jaloviar et al. PRL 82, 791 (1999)

theory

Multigrid method for quantum simulations

Density functional equations solved directly on the gridMultigrid techniques remove instabilities by working on one length scale at a timeConvergence acceleration and automatic preconditioning on all length scalesNon-periodic boundary conditions are as easy as periodicCompact “Mehrstellen” discretizationAllows for efficient massively parallel implementation

Speedup on Cray T3E withnumber 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, 14362 (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(N3) part)•Fully parallel on IBM SP and Cray T3E tested on > 1000 atoms• Forces, geometry optimization

Briggs, Sullivan, Bernholc PRB 54, 14362 (1996).Fattebert, Bernholc, PRB 62, 1713 (2000).Buongiorno Nardelli, Fattebert, Bernholc, PRB 64, 245423 (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 + Al13

More stable C-Al bond length: 2.15 Å Formation energy: -0.7 eV

(8,0)tube + Al13 + NH3

More stable C-Al bond length: 2.11 Å Formation energy of the molecule complex: -1.8 eV

(8,0) tube + Al13 charge goes to the metal cluster transfer of 0.1 e-

(8,0) tube + Al13 + NH3

0.4 e- from NH3 to the cluster and tube. n-type conductivity

+

|

e-

|

+e-

e-

|

Less electrons More electrons

e-

Charge transfer in semiconducting CNT-cluster assembly

|

A simple view on polarizationMacroscopic solid sample:

and includes all boundary charges.

Polarization is well defined but this definition cannot be used in realistic calculations.

samplesample l

llsample

rdrrbeZV

P )(1 )(r

Ionic part:Localized charges,easy to compute

Electronic partCharges usually delocalized

Periodic solid:

celll

lli

ii rdrrV

beZV

rqV

P

)(11 1

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 1994

1) Polarization is a multivalued quantity and its absolute value cannot be computed.

Piezoelectric polarization:

)( )0(ii

i i

xxxPeP

Modern approaches to compute polarization use Berry phase or Wannier function formalisms.

)nonpolar()polar( PPP

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