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

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

Apr 06, 2023 356 likes •833 views

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,

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SLIDE 1

Contact: linwang wang, lwwang@lbl.gov

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
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SLIDE 2

Contact: linwang wang, lwwang@lbl.gov

Material as a mark of civilization Bronze age Stone age Semiconductor information age Nanostructure age Nanoscience is a material science: Nano size building block Assemble them into device

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SLIDE 3

Contact: linwang wang, lwwang@lbl.gov

Making new solid state materials

  • New crystal compounds

2 2B

A

x xB

A −

1

  • Alloys
  • Impurity and doping
  • Modifying the size and shape of the material
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SLIDE 4

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

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SLIDE 5

Contact: linwang wang, lwwang@lbl.gov

Examples of new properties

  • Band gap increase

CdSe quantum dot

  • Single electron effects
  • n transport (Coulomb

blockade).

  • Mechanical properties,

surface effects and no dislocations

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SLIDE 6

Contact: linwang wang, lwwang@lbl.gov

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

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SLIDE 7

Contact: linwang wang, lwwang@lbl.gov

Computational challenge atoms molecules nanostructures bulk Infinite (1-10 atoms in a unit cell) 1-100 atoms 1000-10^6 atoms size

  • Ab initio method

Ab initio method

  • Effective mass

method New methodology and algorithm

) (

3

N O

Challenge for computational nanoscience. method Ab initio elements and reliability Even larger Supercomputer (ES!)

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SLIDE 8

Contact: linwang wang, lwwang@lbl.gov

Ab initio electronic structure calculations All the material science problems are solved !

  • ---- Schroedinger, 1930’s

) ,.. ( ) ,.. ( } | | | | 1 2 1 {

1 1 , , 2 N N R i i j i j i i i

r r E r r R r Z r r Ψ = Ψ − + − + ∇ −

∑ ∑ ∑

) ,.. (

2 1 r

r Ψ

N

N

Linear equation, but extremely large dimension: Density functional theory and local density approximation

  • ---- W. Kohn’s 1997 Nobel prize

) ( ) ( } | | 1 )]) ( [ , ( 2 1 {

2

r E r R r r r V

i i i R

ψ ψ ρ = − + + ∇ −

∑

2

| ) ( | ) ( r r

i i

∑

= ψ ρ

) (r

i

ψ

: single electron wave function 2

N

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SLIDE 9

Contact: linwang wang, lwwang@lbl.gov

Ab initio density functional calculations

) ( ) ( )} ( 2 1 {

2

r E r r V

i i i

ψ ψ = + ∇ −

N i i ,.., 1

} {

=

ψ

2

| ) ( | ) ( r r

N i i

∑

= ψ ρ

Selfconsistency N electron N wave functions Density Functional

) (r V

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SLIDE 10

Contact: linwang wang, lwwang@lbl.gov

Two tasks for a hybrid nano computation method (1) To get the potential V(r) [or the charge density ρ (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.

) ( ) ( )} ( 2 1 {

2

r E r r V

i i i

ψ ψ = + ∇ −

(Not the usual PDE, many eigen states, don’t want and need to solve all of them)

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SLIDE 11

Contact: linwang wang, lwwang@lbl.gov

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

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SLIDE 12

Contact: linwang wang, lwwang@lbl.gov

Motif based charge patching method

) ( LDA

graphite

ρ

motif

ρ

) ( ) ( R r r

R aligned motif patch nanotube

− =∑ ρ ρ

Error: 1%, ~20 meV eigen energy error.

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SLIDE 13

Contact: linwang wang, lwwang@lbl.gov

Charge patching: free standing quantum dots In675P652 LDA quality calculations (eigen energy error ~ 20 meV) CBM 64 processors (IBM SP3) for ~ 1 hour Total charge density motifs VBM

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SLIDE 14

Contact: linwang wang, lwwang@lbl.gov

The accuracy for the small Si quantum dot

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SLIDE 15

Contact: linwang wang, lwwang@lbl.gov

Folded Spectrum Method

) ( ) ( )} ( 2 1 {

2

r E r r V

i i i

ψ ψ = + ∇ −

i i i

H ψ ε ψ =

i ref i i ref

H ψ ε ε ψ ε

2 2

) ( ) ( − = −

N

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SLIDE 16

Contact: linwang wang, lwwang@lbl.gov

Planewave expansion of the wavefunction

) ( ) ( )} ( 2 1 {

2

r E r r V

i i i

ψ ψ = + ∇ −

∑

=

q iqr

e q C r ) ( ) ( ψ

Fast Fourier Transformation between real space ψ(r) and Fourier space C(q).

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SLIDE 17

Contact: linwang wang, lwwang@lbl.gov

A parallel Fast Fourier Transformation code

Time for one FFT (sec)

0.3 0.03 0.003 128x128x128 2 8 8 x 2 8 8 x 2 8 8 576x576x576 EPM calc.

  • Specially designed for PW elec.

structure calculation.

  • Work load balance
  • Memory balance
  • Minimum communication

FFT

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SLIDE 18

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

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SLIDE 19

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
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SLIDE 20

Contact: linwang wang, lwwang@lbl.gov

Quantum dot wavefunctions Cross section electron wavefunctions

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SLIDE 21

Contact: linwang wang, lwwang@lbl.gov

CdSe quantum dot results

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SLIDE 22

Contact: linwang wang, lwwang@lbl.gov

CdSe quantum dots as biological tags

  • Optically more stable than dye molecules
  • Can have multiple colors
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SLIDE 23

Contact: linwang wang, lwwang@lbl.gov

Photoluminescence intermittency of CdSe QD

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SLIDE 24

Contact: linwang wang, lwwang@lbl.gov

Auger effect in CdSe quantum dot

eh eh eh eh 1 3 1 2

/

> − > −

τ τ

Auger life times Exp. Calc. Cooling ~0.2-0.5ps >0.5ps 2 exciton->1 exc. ~2.7 ps ~2. ps 2.7 2.4

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SLIDE 25

Contact: linwang wang, lwwang@lbl.gov

Polarization of CdSe quantum rods

CdSe quantum rods The electron wavefunctions of a quantum rods

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SLIDE 26

Contact: linwang wang, lwwang@lbl.gov

Polarization of quantum rods (continued)

40 30 20 10 2.8 2.4 2.0 1.6 1.2 100 80 60 40 10 8 6 4 2

1.30 1.25 1.20 1.15 1.10

  • 1.45
  • 1.40
  • 1.35
  • 1.30
  • 1.25
  • 1.20
  • 1.15
  • 1.10

2.0 1.8 1.6 1.4 1.2 1.0 Aspect Ratio

Energy (eV)

Stock shift (meV) Aspect ratio of the quantum rods

Calc. Expt.

0.6 0.4 0.2 0.0 Polarization 10 8 6 4 2 Aspect ratio

Calc: Expt:

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SLIDE 27

Contact: linwang wang, lwwang@lbl.gov

Quantum wire electronic states

(a) CBM (xz-plane) (c) CBM (b) VBM (xz-plane) (d) VBM d=5.18 nm [111] x y

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SLIDE 28

Contact: linwang wang, lwwang@lbl.gov

InP quantum rods and wires

Energy level (eV)

  • 3.7
  • 3.6
  • 3.5
  • 3.4
  • 3.3
  • 3.2
  • 3.1
  • 3.0

Aspect ratio

1 2 3 4 5 6

  • 6.5
  • 6.4
  • 6.3
  • 6.2
  • 6.1
  • 6.0

1σ 2σ 4σ 3σ 1π 1σ 2σ 3σ 4σ 5σ

  • 3.7
  • 3.6
  • 3.5
  • 3.4
  • 3.3
  • 3.2
  • 3.1
  • 3.0

kz

0.0 .1 .2 .3 .4 .5

  • 6.5
  • 6.4
  • 6.3
  • 6.2
  • 6.1
  • 6.0

(a) (b)

Rods Wire (111) direction rods and wires

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SLIDE 29

Contact: linwang wang, lwwang@lbl.gov

InP wires / InP dots

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SLIDE 30

Contact: linwang wang, lwwang@lbl.gov

GaN (111) and (112) quantum wires (WZ)

(111) GaN wire (112) GaN wire CB1 CB2

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SLIDE 31

Contact: linwang wang, lwwang@lbl.gov

CdSe quantum dot: arrow shape (1) CB1 (3) CB3 (2) CB2 (4) VB1 (6) VB3 (5) VB2

L=9.9nm D=2nm

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SLIDE 32

Contact: linwang wang, lwwang@lbl.gov

Different Bloch state characters for the VB states VB-1 VB-2 VB-4 VB-3

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SLIDE 33

Contact: linwang wang, lwwang@lbl.gov

CdSe tetrapod electronic states

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SLIDE 34

Contact: linwang wang, lwwang@lbl.gov

CdSe/CdTe tetrapod with one CdTe arm Electron state Hole state

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SLIDE 35

Contact: linwang wang, lwwang@lbl.gov

CdSe/CdS/CdSe quantum rod

CB VB 7.177eV 6.423eV 7.470eV 6.155eV

Band alignment of bulk CdSe/CdS VBM CBM CdS CdSe

CB

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SLIDE 36

Contact: linwang wang, lwwang@lbl.gov

Anticrossing (coupling) states under electric field

0x10 0 2x10 -6 4x10 -6 2 4 6 8 10 0x10 0 2x10 -6 4x10 -6

(a) C B 1 (b) C B 2

10 20 30 40 50 60 70

Energy (eV)

2.240 2.245 2.250 2.255 2.260 2.265 2.270

∆~10 meV

CB1 CB2 Electric field (meV/10nm)

6 double layers of CdS: ∆=10 meV 3 double layers of CdS: ∆=30 meV

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SLIDE 37

Contact: linwang wang, lwwang@lbl.gov

Core/shell quantum dots CdSe/CdS CdSe/CdTe CdSe CBM VBM

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SLIDE 38

Contact: linwang wang, lwwang@lbl.gov

Effects of stacking faults

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SLIDE 39

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

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SLIDE 40

Contact: linwang wang, lwwang@lbl.gov

Electronic states in embedded InAs quantum dot

e3 e2 e1 e0 e3 e5 e4 e6 e7

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SLIDE 41

Contact: linwang wang, lwwang@lbl.gov

Hole states in embedded InAs quantum dots

70h/200b InAs QD ψ2(h0)+ψ2(h1)+ψ2(h2) Angle Side Green: 10% Blue: 25% Top

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SLIDE 42

Contact: linwang wang, lwwang@lbl.gov

Energy levels, comparison with experiment

0 GaAs CBM InAs 1ML Wetting

  • 60 meV

e0 e1,2 e3,4,5 h0 h1 h2 0 GaAs VBM 82 meV 249 (235) 1.044 eV (1.098) e6,7 59 (50) 59 (48) 55 2 (2) 8

  • 228 (280)

168 (180)

Black: Calculation Red: Petrof, UCSB Blue: Schmidt, PRB 54, 11346 (96) green: Itskevich, PRB 58, R4250(98)

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SLIDE 43

Contact: linwang wang, lwwang@lbl.gov

Hole localization in InGaN alloy

In In In In N N N

N Ga In

8 . 2 .

32768 atom random cell

hole Blue Laser from InGaN

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SLIDE 44

Contact: linwang wang, lwwang@lbl.gov

Impurity level calculation of GaAs:N N As Ga

2047 2048

) (

1 N

a

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SLIDE 45

Contact: linwang wang, lwwang@lbl.gov

2 million atom GaAlAs alloy wavefunction

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SLIDE 46

Contact: linwang wang, lwwang@lbl.gov

Conclusion First principle calculation New algorithm methodology Large scale supercomputer + + Millions atom nanostructures