An In Intro troduction to to Computational Nan anoscience Lin - - PowerPoint PPT Presentation
An In Intro troduction to to Computational Nan anoscience Lin in-Wang Wang ng Material Sc Science Div ivision Lawrence Berk rkeley Natio tional Lab US S Department t of of Ene nerg rgy Offic ffice of of Sc Scie ience What
Contact: linwang wang, lwwang@lbl.gov
An In Intro troduction to to Computational Nan anoscience
Lin in-Wang Wang ng Material Sc Science Div ivision Lawrence Berk rkeley Natio tional Lab US S Department t of
nerg rgy Offic ffice of
Scie ience
n we do
it ?
Contact: linwang wang, lwwang@lbl.gov
Making ne new soli
tate te mate terials
rystal com
lloys
Impurity and nd dop
fying th the siz ize and nd shape of
the mate terial
2 2 B
x xB
1
Contact: linwang wang, lwwang@lbl.gov
Nanostructure as a ne new mate terial Defi finiti tion: Nanostr tructure is is an n assembly of
nanometer scale “building blocks”. Why na nano nometer scale: This is is is th the scale le when th the properties of these “building blocks” become different fro from bulk lk. siz ize Ele lectron Wavefuncti tion Nanostructure Bot
re in in na nano nometers
Contact: linwang wang, lwwang@lbl.gov
Com
tional challenge
initio meth thod ato toms mol
na nanostr tructures bul ulk siz ize 1-100 100 ato toms 1000 1000-10^6 10^6 ato toms In Infi finite (1 (1-10 atom toms in in a unit nit cell ll) method Ab ini initio method
ffective mass meth thod Challenge for for com
tional na nanoscience. Ab ini initio ele lements ts and nd re reli liability New meth thodology and nd algo lgorithm Even lar larger Su Supercomputer (E (ES!)
3
Contact: linwang wang, lwwang@lbl.gov
Number of atoms Accuracy
GW/BSE, Coupled Cluster Empirical Pseudopotential Non-selfconsistent LDA Time dependent DFT Direct LDA
101
102
103
104 105 106
Contact: linwang wang, lwwang@lbl.gov
Ab ini initio dens nsity fun functional calc lculations
2
i i i
N i i ,.., 1
2
N i i
Se Selfconsistency N ele lectron N wave fun functions Density Functional
Contact: linwang wang, lwwang@lbl.gov
Two tas tasks for for a hybrid na nano no com
thod
2
i i i
so
ill have th the Hamiltonian. (2) (2) To
the sing ingle part rticle Hamiltonian (Schroedinger’s equation), to get the physical properties. (We want ab ini initi tio re reli liability, but t no not t a full full ab ini initi tio calculation) (Not the usual PDE, many eigen states, don’t want and ne need to to solv
ll of
them) (1) (1) To
get t th the pote
V(r (r) [o [or r th the charge dens nsity (r) (r)]
Contact: linwang wang, lwwang@lbl.gov
Charge patc tching meth thod Se Selfconsistent LDA ca calculation of
a singl ingle gra graphite sheet Non
quality pote
for na nanotube Get t info information fro from small syste tem ab in initi itio calc., th then n ge gene nerate th the charge dens nsities for for lar large syste tems
Contact: linwang wang, lwwang@lbl.gov
Charge patc tching: fre free stan tanding quantu tum dots
In In675
675P652
LDA quality calc lculations (e (eig igen ene nergy err rror ~ 20 meV) CBM VBM 64 pro rocessors (IB (IBM SP SP3) for for ~ 1 hou
r Total charge density motifs
Contact: linwang wang, lwwang@lbl.gov
Pla lanewave expansion of
the wavefunction
q iqr
Fast t Fou
ransformation betw tween re real space (r) (r) an and Fou
(q).
2
i i i
Contact: linwang wang, lwwang@lbl.gov
Fol
Spectr trum Meth thod
i i i
i ref i i ref
2 2
N
2
i i i
Contact: linwang wang, lwwang@lbl.gov
NERSC NERSC: Nati ational Ene nerg rgy Research Sci Scientific Com
nter Hop
Cray XE6 machine, 150,0 ,000 com
.3 Peta tafl flops
Contact: linwang wang, lwwang@lbl.gov
Examples of
new pro roperties
and gap gap inc increase CdSe quantum dot
Single ele lectr tron effe ffects ts
trans nsport t (C (Cou
blo lockade).
roperties, surface effe ffects and nd no no dis islocations
Contact: linwang wang, lwwang@lbl.gov
Fre ree stan tanding quantum dots
CdSe quantum dot
TEM im image
nthesised
Inte terior atom toms are re in in bulk lk cry rystal stru tructure
Surface atom toms are re passivated
iamete ter ~ 20-100 A
few th thou
toms, beyond ab ini initi tio meth thod
Contact: linwang wang, lwwang@lbl.gov
CdSe qua uantum dots
as biol iological tags tags
tically mor
table th than dye mole
n have multi ltiple colo
Contact: linwang wang, lwwang@lbl.gov
Qua uantum dot
avefunctions Cro ross secti tion ele lectron wavefunctions
Contact: linwang wang, lwwang@lbl.gov
CdSe quantum dot
results
Contact: linwang wang, lwwang@lbl.gov
CdTe na nano nowire Exp: Calc:
Contact: linwang wang, lwwang@lbl.gov
Quantum dot and wire calculations for semiconductor materials IV-IV: Si III-V: GaAs, InAs, InP, GaN, AlN, InN II-VI: CdSe, CdS, CdTe, ZnSe, ZnS, ZnTe, ZnO
Contact: linwang wang, lwwang@lbl.gov
Pola
rods
Cd CdSe qua quantum rod rods The elec lectron wav avefunctio ions of f a a qua quantum ro rods
Contact: linwang wang, lwwang@lbl.gov
Pola
rods (co (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
2.0 1.8 1.6 1.4 1.2 1.0 Aspect Ratio
Energy (eV)
Stoc Stock shif shift t (m (meV) As Aspect t ratio tio of
the qu quantum rod
Calc. Expt.
0.6 0.4 0.2 0.0 Polarization 10 8 6 4 2 Aspect ratio
Calc: Expt:
Contact: linwang wang, lwwang@lbl.gov (a) CBM (xz-plane) (c) CBM (b) VBM (xz-plane) (d) VBM d=5.18 nm [111] x y
Quantum wir ire ele lectronic state tates
Contact: linwang wang, lwwang@lbl.gov
(1) CB1 (3) CB3 (2) CB2 (4) VB1 (6) VB3 (5) VB2
L=9.9nm D=2nm
CdSe quantum dot: arrow shape
Contact: linwang wang, lwwang@lbl.gov
VB VB-1 VB VB-2 VB VB-3 VB VB-4 Diff ifferent Bloc loch state tate characte ters for for th the VB state tates
Contact: linwang wang, lwwang@lbl.gov
CdSe tetrapod electronic states
Contact: linwang wang, lwwang@lbl.gov
Cor
CBM VBM CdSe CdSe/CdS CdSe/CdTe
Contact: linwang wang, lwwang@lbl.gov
So Solar cell ll usin ing stab table, abundant, and nd env
nign mat Zn ZnO/ZnS cor
ire
Band gap lowers down further from superlattices. The absorption length is similar to bulk Si, thus similar among f material for solar cell.
23% th theoretical effic fficiency for for sola
ll
Contact: linwang wang, lwwang@lbl.gov
CdSe cor
inside CdS S na nano norode Hydrodynamic stra train pro rofi file (re (relaxed using ing VFF) 0.02 .02
0.00 .00 0.01 .01
Contact: linwang wang, lwwang@lbl.gov
Wit ithout cor
Wit ith cor
The effe ffect t of
the CdSe Se cor
to ele lectr tron and nd hole
Gre reen: ele lectr tron, re red: hole
Contact: linwang wang, lwwang@lbl.gov
Effe ffect of
urface dip ipole mom
Cd te term rminated surfa rface Cd and nd Se Se te term rminate ted surf rface
Contact: linwang wang, lwwang@lbl.gov
The shift ift of
Contact: linwang wang, lwwang@lbl.gov
How to calculate an exciton in nanosystem?
Mat aterial A Mat aterial B el elect ctron ho hole
What t is is th the bind inding ene nergy of
the inte interface exciton ? The approach: G GW+BSE Approximation: GW LDA+C (for (for bulk lk shor
t ra rang nge effe ffect) P(r) (r) (su
(surface imag age po potentia ial, for for lon long ran range effe ffe
BSE SE CI I calculation CBM VBM
Contact: linwang wang, lwwang@lbl.gov
) ( ) ( ) ( ) ( ) ( 2 1
2
r r r V r P r V
c c c v C LDA
) ( ) ( ) ( ) ( ) ( 2 1
2
r r r V r P r V
v v v c C LDA
Natu tural l band nd alig ignment 0. 0.28 eV 0. 0.54 eV
A selfc lfconsistent t calculati tion fo for r a bou
iton
' '
'
bulk r r
2 ) ( ) (
C V V C
Contact: linwang wang, lwwang@lbl.gov
CdSe/CdTe Nanorods
Exciton binding energy: 0.4 to 0.25 eV Exciton radiative recombination life time: ~1 µs Correlation effect: < 1 meV for ground exciton state
34 34
10 nm nm
CdTe CdSe
Contact: linwang wang, lwwang@lbl.gov
CdSe quantum dot
rray, con
Sn2S6 mole
Tal alapin, et.al t.al, Sci Science (20 (2005 05); Kov
t.al, Sc Science (20 (2009).
Contact: linwang wang, lwwang@lbl.gov
What t cause th the ele lectron tra trans nsport ? ? (1) (1) Min ini-band bulk lk lik like tra trans nsport: (2) (2) Thermo acti tivati tion, ov
r th the barr rrier (l (like th the Sc Schott ttky barr rrier) (3) (3) Phon
isted hop
(e (e.g .g., described by Marcus th theor
ΔE
Contact: linwang wang, lwwang@lbl.gov
Sn Sn2S6 atom tomic attac ttachment t to to CdSe surfa rfaces Fla lat surfa rface calculati tion for for th the mole
ttachment
Contact: linwang wang, lwwang@lbl.gov
Div ivide-and-conquer scheme to to ge get t th the charge dens nsity
Contact: linwang wang, lwwang@lbl.gov
CB CBM
CBM+1 The ele lectron cou
tween th the tw two
tates
Natom Size D (nm) V (coupling
meV)
468 2.5 4.1 1051 3.4 1.4 1916 4.3 0.37 3193 5.1 0.14
2V 2V
Contact: linwang wang, lwwang@lbl.gov
Calculating th the re re-organization ene nergy
Natom Size D (nm) λ (re-org. energy, meV) V (coupling meV, type I) 468 2.5 145 4.1 1051 3.4 62 1.4 1916 4.3 32 0.37 3193 5.1 23 0.14
(1) The λ >> >> V, , so
the wave fun function will ill be loc localized, it it is is no not t mini ini-band tra transport (2) th the barr rrier heig ight ΔE can n be ~ 2 eV. . It It cannot t be ov
therm rmally excited tra trans nsport. (3) (3) Must be phon
trans nsport ΔE CBM LDOS
Contact: linwang wang, lwwang@lbl.gov
E(Q (QD2)-E(QD1) (e (eV) Hop
rate te fro from QD1 to to QD2 (1/p (1/ps)
31 3193 93 QD QD 46 468 8 QD QD 1051 1051 1916 1916
So Solid line line: Marcus th theor
Dashed line line: quantum tre treatment t of
Atta ttachment typ type I
The hop
rate te
Contact: linwang wang, lwwang@lbl.gov
Situation (QD cubic array, size=4.3nm) Type-I attachment Mobility μ (cm2/V/S) No QD size fluctuation, no connection fluctuation 8.22 x10-2 5% QD size fluctuation, no connection fluctuation 4.80 x 10-2 5% QD size fluctuation, uniform connection fluctuation 1.02 x 10-2 Experiment, size=4.5nm 3 x 10-2
Carrier mob
ty of
the QD arr rray in in small carr rrier dens nsity lim limit
Contact: linwang wang, lwwang@lbl.gov
Why are quantum mechanical calculations so expensive?
If the size of the system is N: N coefficients to describe one wavefunction i = 1,…, M wavefunctions , M is proportional to N. Orthogonalization: M2 wavefunction pairs
each with N coefficients: N*M2, i.e N3 scaling.
r d r r
j i 3 *
) ( ) (
The rep repeated ca calc lculation of f the these orth rthogonal l wavefunctions make the the co computation ex expensive, , O(N (N3). ). For lar large syste tems, , an an O(N (N) met ethod is is crit critical
Contact: linwang wang, lwwang@lbl.gov
F F
Total = ΣF {
}
Phy Phys. . Re Rev.
B 77 77, , 16 1651 5113 13 (2 (200 008); ; J.
Phys: : Co Cond
att. . 20 20, , 29 2942 4203 03 (2 (200 008)
ρ(r (r)
LS3DF: 1D Example
Contact: linwang wang, lwwang@lbl.gov
(i,j,k) Fragment (2x1) Interior area Artificial surface passivation Buffer area Bou
ffects are re (ne (nearly) cancelled ou
t betw tween th the fra fragm gments
Total = ΣF {
F F
}
F F
k j i
, , 111 122 212 221 112 121 211 222
Similar procedure extends to 2 and 3D
Contact: linwang wang, lwwang@lbl.gov
A example of
the glob global syste tem and nd th the fra fragments ts
Contact: linwang wang, lwwang@lbl.gov
Schematics for LS3DF calculation
Contact: linwang wang, lwwang@lbl.gov
No
lfconsiste tent t pro roblem for for th the glob global syste tem
Contact: linwang wang, lwwang@lbl.gov
Cro Cross ove ver wit with dir direct LDA LDA met ethod [PE [PEtot] t] is s 50 500 0 ato atoms. Si Simil ilar to to oth ther O(N O(N) meth ethods.
Operation counts
(x (x1012
12)
Contact: linwang wang, lwwang@lbl.gov
ZnTeO alloy weak scaling calculations
irst lar large scale ru run n on
ranklin at t NERSC: 135 Tflop flops/s, 40% effic fficiency
Subsequent ru runs ns on
Intre trepid at t ALCF: 224 Tflop flops/s, 40% effic fficiency
inal ru runs ns on
Jagu guar XT5 at t NCCS: 442 Tflop flops/s, 33% effic fficiency
No Note: Ecut cut = = 60 60Ryd wit with d state states, up up to to 36 36864 ato atoms
Perf rformance [ [ Tflop flop/s]
50 100 150 200 250 300 350 400 450 500 50,000 100,000 150,000 200,000 TFlop/s . Cores
LS3DF
Jaguar Intrepid Franklin
Number of
Contact: linwang wang, lwwang@lbl.gov
A mor
tail example of
the Zn ZnO na nano norod syste tem
Num Num ato atom: 27 2776 Num Num ele elect ctron: 24 24220 Rea eal spac space gri rid: 72 720x 0x300x300 Fra ragment div divid idin ing grid rid: 18 18x6x6
Contact: linwang wang, lwwang@lbl.gov
Con
Fir irst t pri rinciple calculation New algo lgorithm methodology Large scale supercomputer Mil illions atom tom na nanostr tructures + +