Computational Nanoscience at NERSC Lin-Wang Wang Computational - PowerPoint PPT Presentation

Computational Nanoscience at NERSC Lin-Wang Wang Computational Research Division Lawrence Berkeley National Lab US Department of Energy Office of Science • What can we do ? • How do we do it ? • Examples Contact: linwang wang, lwwang@lbl.gov

Material as a mark of civilization Bronze age Stone age Semiconductor Nanostructure information age age Nanoscience is a material science: Nano size building block Assemble them into device Contact: linwang wang, lwwang@lbl.gov

Making new solid state materials A 2 B • New crystal compounds 2 A − x B • Alloys 1 x • Impurity and doping • Modifying the size and shape of the material Contact: linwang wang, lwwang@lbl.gov

Nanostructure as a new material Definition: Nanostructure is an assembly of nanometer scale “building blocks”. Why nanometer scale: This is the scale when the properties of these “building blocks” become different from bulk. size Electron Wavefunction Nanostructure Both are in nanometers Contact: linwang wang, lwwang@lbl.gov

Examples of new properties • Band gap increase CdSe quantum dot • Single electron effects on transport (Coulomb blockade). • Mechanical properties, surface effects and no dislocations Contact: linwang wang, lwwang@lbl.gov

Theoretical Challenge Three corner stones of modern science: Theoretical analysis Computational simulation Experiment atoms nanostructures bulks molecules analytical sol. Analytical statistics, band structure. solution special funct. expansion Feynman diagram Numerical Nanostructures are often complex systems: solution need atomistic, realistic, numerical simulations. Contact: linwang wang, lwwang@lbl.gov

Computational challenge atoms nanostructures bulk molecules Infinite 1-100 1000-10^6 (1-10 atoms size atoms atoms in a unit cell) • Ab initio method Challenge for Ab initio method • Effective mass computational method method nanoscience. 3 O ( N ) Ab initio New methodology Even larger elements and algorithm Supercomputer and reliability (ES!) Contact: linwang wang, lwwang@lbl.gov

Ab initio electronic structure calculations All the material science problems are solved ! ----- Schroedinger, 1930’s 1 1 Z ∑ ∑ ∑ − ∇ + + Ψ = Ψ 2 { } ( r ,.. r ) E ( r ,.. r ) i 1 N 1 N − − 2 | r r | | r R | i i , j i , R i j i N Ψ N ( r 1 r ,.. ) Linear equation, but extremely large dimension: 2 Density functional theory and local density approximation ----- W. Kohn’s 1997 Nobel prize 1 1 ∑ 2 N − ∇ + ρ + ψ = ψ 2 { V ( r , [ ( r )]) } ( r ) E ( r ) i i i − 2 | r R | R ∑ ρ = ψ 2 ( r ) | ( r ) | ψ ( r ) : single electron wave function i i i Contact: linwang wang, lwwang@lbl.gov

Ab initio density functional calculations 1 − ∇ + ψ = ψ 2 { V ( r )} ( r ) E ( r ) i i i 2 ψ { } Selfconsistency = i i 1 ,.., N N electron N wave functions N ∑ ρ = ψ 2 ( r ) | ( r ) | i i Density Functional V ( r ) Contact: linwang wang, lwwang@lbl.gov

Two tasks for a hybrid nano computation method [or the charge density ρ (r) ] (1) To get the potential V(r) so we will have the Hamiltonian. (We want ab initio reliability, but not a full ab initio calculation) (2) To solve the single particle Hamiltonian (Schroedinger’s equation), to get the physical properties. 1 − ∇ + ψ = ψ 2 { V ( r )} ( r ) E ( r ) i i i 2 (Not the usual PDE, many eigen states, don’t want and need to solve all of them) Contact: linwang wang, lwwang@lbl.gov

Charge patching method Non-selfconsistent LDA Selfconsistent LDA quality potential for calculation of a single nanotube graphite sheet Get information from small system ab initio calc., then generate the charge densities for large systems Contact: linwang wang, lwwang@lbl.gov

Motif based charge patching method ρ ρ ( LDA ) motif graphite = ∑ ρ ρ − patch aligned ( r ) ( r R ) nanotube motif R Error: 1%, ~20 meV eigen energy error. Contact: linwang wang, lwwang@lbl.gov

Charge patching: free standing quantum dots In 675 P 652 LDA quality calculations (eigen energy error ~ 20 meV) 64 processors (IBM SP3) for ~ 1 hour Total charge density CBM VBM motifs Contact: linwang wang, lwwang@lbl.gov

The accuracy for the small Si quantum dot Contact: linwang wang, lwwang@lbl.gov

Folded Spectrum Method 1 − ∇ + ψ = ψ 2 { V ( r )} ( r ) E ( r ) i i i 2 ψ = ε ψ − ε ψ = ε − ε ψ H 2 2 ( H ) ( ) i i i ref i i ref i N Contact: linwang wang, lwwang@lbl.gov

Planewave expansion of the wavefunction 1 − ∇ + ψ = ψ 2 { V ( r )} ( r ) E ( r ) i i i 2 ∑ ψ = iqr ( r ) C ( q ) e q Fast Fourier Transformation between real space ψ (r) and Fourier space C(q). Contact: linwang wang, lwwang@lbl.gov

A parallel Fast Fourier Transformation code • Specially designed for PW elec. structure calculation. • Work load balance • Memory balance • Minimum communication Time for one FFT (sec) 576x576x576 FFT 0.3 2 8 8 0.03 x 2 8 8 x 2 8 8 EPM calc. 128x128x128 0.003 Contact: linwang wang, lwwang@lbl.gov

NERSC NERSC: National Energy Research Scientific Computing Center memory processor 6000 IBM SP3 processors, total peak speed: ~ 5 Tflop Contact: linwang wang, lwwang@lbl.gov

Free standing quantum dots CdSe quantum dot TEM image • Chemically synthesised • Interior atoms are in bulk crystal structure • Surface atoms are passivated • Diameter ~ 20-100 A • A few thousand atoms, beyond ab initio method Contact: linwang wang, lwwang@lbl.gov

Quantum dot wavefunctions Cross section electron wavefunctions Contact: linwang wang, lwwang@lbl.gov

CdSe quantum dot results Contact: linwang wang, lwwang@lbl.gov

CdSe quantum dots as biological tags • Optically more stable than dye molecules • Can have multiple colors Contact: linwang wang, lwwang@lbl.gov

Photoluminescence intermittency of CdSe QD Contact: linwang wang, lwwang@lbl.gov

Auger effect in CdSe quantum dot Auger life times Exp. Calc. Cooling ~0.2-0.5ps >0.5ps 2 exciton->1 exc. ~2.7 ps ~2. ps τ τ / − > − > 2 eh 1 eh 3 eh 1 eh 2.7 2.4 Contact: linwang wang, lwwang@lbl.gov

Polarization of CdSe quantum rods CdSe quantum rods The electron wavefunctions of a quantum rods Contact: linwang wang, lwwang@lbl.gov

Polarization of quantum rods (continued) Calc. Expt. 100 40 1.30 Stock shift (meV) 30 80 1.25 20 60 1.20 10 40 1.15 0 Energy (eV) 2 4 6 8 10 1.2 1.6 2.0 2.4 2.8 Aspect ratio of the quantum rods 1.10 -1.10 -1.15 -1.20 0.6 -1.25 Polarization 0.4 -1.30 Calc: Expt: -1.35 0.2 -1.40 0.0 -1.45 1.0 1.2 1.4 1.6 1.8 2.0 0 2 4 6 8 10 Aspect Ratio Aspect ratio Contact: linwang wang, lwwang@lbl.gov

Quantum wire electronic states (c) CBM [111] (a) CBM (xz-plane) x y (d) VBM (b) VBM (xz-plane) d=5.18 nm Contact: linwang wang, lwwang@lbl.gov

InP quantum rods and wires (111) direction rods and wires -3.0 -3.0 (b) (a) -3.1 -3.1 1 π -3.2 -3.2 -3.3 -3.3 -3.4 -3.4 4 σ -3.5 -3.5 3 σ Energy level (eV) -3.6 -3.6 2 σ 1 σ -3.7 -3.7 -6.0 -6.0 1 σ 2 σ -6.1 -6.1 3 σ -6.2 -6.2 4 σ -6.3 -6.3 5 σ -6.4 -6.4 -6.5 -6.5 0.0 .1 .2 .3 .4 .5 1 2 3 4 5 6 k z Aspect ratio Rods Wire Contact: linwang wang, lwwang@lbl.gov

InP wires / InP dots Contact: linwang wang, lwwang@lbl.gov

GaN (111) and (112) quantum wires (WZ) (111) GaN wire (112) GaN wire CB1 CB2 Contact: linwang wang, lwwang@lbl.gov

CdSe quantum dot: arrow shape (1) CB 1 (2) CB 2 (3) CB 3 L=9.9nm D=2nm (5) VB 2 (4) VB 1 (6) VB 3 Contact: linwang wang, lwwang@lbl.gov

Different Bloch state characters for the VB states VB-1 VB-2 VB-4 VB-3 Contact: linwang wang, lwwang@lbl.gov

CdSe tetrapod electronic states Contact: linwang wang, lwwang@lbl.gov

CdSe/CdTe tetrapod with one CdTe arm Electron state Hole state Contact: linwang wang, lwwang@lbl.gov

CdSe/CdS/CdSe quantum rod VBM CBM Band alignment of bulk CdSe/CdS CdSe CdS 7.470eV 7.177eV CB CB 6.423eV VB 6.155eV Contact: linwang wang, lwwang@lbl.gov

Anticrossing (coupling) states under electric field 2.270 2.265 CB2 2.260 Energy (eV) ∆ ~ 10 meV 2.255 2.250 CB1 (a) C B 1 2.245 4x10 -6 2.240 0 10 20 30 40 50 60 70 2x10 -6 Electric field (meV/10nm) 0x10 0 (b) C B 2 6 double layers of CdS: ∆ =10 meV 4x10 -6 3 double layers of CdS: ∆ =30 meV 2x10 -6 Contact: linwang wang, lwwang@lbl.gov 0x10 0 0 2 4 6 8 10

Core/shell quantum dots CdSe CdSe/CdS CdSe/CdTe CBM VBM Contact: linwang wang, lwwang@lbl.gov

Effects of stacking faults Contact: linwang wang, lwwang@lbl.gov

Self-assembled quantum dot AFM image • Formed by themselves during MBE growth • Strain between the dot and the substrate • Size range ~ 100-500 A, ~ a million atoms InAs on GaAs substrate • No dislocations, or surface defects • Can be used for single electron device Contact: linwang wang, lwwang@lbl.gov