Hong Jiang ( 蒋 鸿）College of Chemistry, Peking University

Shenzhen, Dec 20, 2012

Email: h.jiang@pku.edu.cn

Homepage: www.chem.pku.edu.cn/jianghgroup

Towards Rational Design of Solar Materials:

Electronic Band Structures from the GW

Perspective

Outline Challenges in materials for solar energy conversion

Electronic band structure from first-principles

GW for solar energy conversion materials

Conclusions

R. M. Navarro Yerga et al. (2009)

Solar energy: the power for the futureDirect exploitation of solar energy

Solar electricity (photovoltaic cell)

Solar fuels (photo-catalysis)

N. S. Lewis, Nature (2001)

Particulate photocatalysts

Photoelectrochemical cells

Grand challenges for materials right band gap

right band edge positions

easy electron-hole separation

efficient charge transfer in bulk and

across the solid/solution interface

chemical stability

• • • • • •

Maeda and Domen

JPCC (2007)

Routes towards new solar materialssensitization of TiO2

Doping of TiO2

Organic materials

New inorganic materials

Nanostructured materials

• • • • • •

infinite possibilities rational design!!!

P. V. Kamat JPCC (2007)

Maeda and Domen (2007)

Fundamental scientific issues

Electronic band structures of complicated materials

Excited states (e.g. e/h-phonon coupling) of extended

systems

electron/hole transfer in bulk (effects of defects)

e/h transfer at solid/solution interface

Catalysis on solid/solution interface

• • • • • •

R. J. D. Miller and R. Memming (2008)

What can first-principles modeling do now?

Detailed structural and energetic properties (e.g. TiO2 surface,

defects)

Electronic band structures (e.g. Egap)

Band edge position (w.r.t. vacuum)

Level alignment at solid/molecule interface

Basic band parameters

electron/hole semi-classical dynamics

quantum size effects

• • • • • •

bulk* *e

2 2

h

2nc

2

1 1 1.8

2g gE m

eE

R Rm

GW method : the first-principles

approach for electronic band structure

Yu and Cardona, Fundamentals of Semiconductors (2003)

+

-

hv

-- -

-

hv

--- -

-

-

-- -+

hv

PES IPS absorption

vacuum

IEg

NiO

DFT band gap problem

Perdew & Levy (1983); Godby & Sham (1988)

Cohen, Mori-Sanchez, Yang, Chem. Rev. 112, 289

(2012)

KS HOMO-LUMO Gap Egap even with exact Exc

But for all explicit density functionals, e.g. LDA/GGA, xc=0

Band Gap from hybrid-functionals

2 NL GKS GKS GKSext H xc

1

2 i i iV V V

NLxc

( , ')( , ')

( , ')xcEV

r r

r rr r

GKS GKSgap VBM CBM E

M. Marsman et al. (2008)

Hybrid-functionals approach generalized Kohn-Sham (GKS)

approach

Cohen, Mori-Sanzhez, and Yang (2008)

Garcia-Lastra et al. Phys. Rev. B 80, 245427 (2009)

Quasi-particle equation (courtesy of Dr. R. I. Gomez-Abal ）

H. Jiang, Acta Phys.-Chim. Sin. 26, 1017(2010)

G0W0 and GW0 approximation

“best G best W” G0W

0, partial SC GW0

Implementation: FHI-gap(Green-functions with Augmented Planewaves)

Based on full-potential linearized augmented planewaves (FP-LAPW)

Currently interfaced with WIEN2k (P. Blaha et al. (2001))

G0W0, GW0@LDA/GGA(+U)

Spin-polarization magnetic systems

Further developments FP (FHI-PKU)-GAP H. Jiang ， R. I. Gomez-Abal, et al. submitted to Comput. Phys. Comm. (2012)

GW: the state of the art

H. Jiang, Acta Phys.-Chim. Sin. 26, 1017(2010) H. Jiang et al. PRL 102, 126403(2009)

Transition metal dichalcogenides (TMDC)

Jiang, H., J. Chem. Phys , 134, 204705 (2011)

Jiang, H., J. Phys. Chem. C 116, 7664 (2012).

H. Wang, F. Wu and H. Jiang, J. Phys. Chem. C 115, 16180 (2011)

ATaO3 (A=Li, Na, K)

All have photocatalytic activity for pure

water-splitting under UV radiation

strongly influenced by excess alkali

and NiO cocatalyst

La-doped NaTaO3+NiO: QE=56%,

pure water, UV light (the current

record)Using data from Kata and Kudo, JPCB (2001)

Hu et al. APL (2009)

ATaO3 ： Band GapsPm-3m Pbnm

R3ch

H. Wang, F. Wu and H. Jiang, J. Phys. Chem. C, 115, 16180, (2011)

c-ATaO3 o-NaTaO3 r-LiTaO3

The ionic model for the band gap

a cpol VBpo

a cM M C

ag l B

c 1

2E EI WE A We V V

aA

cI

aMV

cMV

apolE

cpolE

VBW

CBW

gE

P. A. Cox, The Electronic Structure and Chemistry of Solids (1987)

R3ch

Pbnm

Cubic LiTaO3: Change of volume

Change of crystal structures: Pm-3m R3c R3chPm-3m

x = 0.0 1.0180

180

O-Ta-O =

Ta-O-Ta=

169

144

O-Ta-O =

Ta-O-Ta=

CB

VBVBM

CBM

F

vac

I

crucial for interface properties:

band offsets in semiconductor hetero-junctions

Photo-catalytic reaction: suitable alignment between the VB/CB edges

with the redox potentials of relevant reactions

CB

VBVBM

CBM

F

vacV

I

Graetzel, Nature (2001)

IP of extended systems from first-principles

IP from KS orbital energies:

•exact Kohn-Sham

•LDA/GGA - HOMO very poor approximation !!!

HOMOI CB

VBVBM

CBM

F

vac

I

0V

V

VBM

core

(KS) (slab) (slab)vac VBM

(KS) (slab) (slab) (bulk) (bulk)vac ref VBM ref

I V

I V

GW correction: GW-VBM scheme

( VBM) (KS) bulkVBMGWGWI I

(KS)gE

( )gGWE

( )VBMGW

(KS)I

Vvac

TMDC: absolute band positions

Jiang, H., J. Phys. Chem. C 116, 7664

(2012).

electronic band structure extremely important for solar-energy

conversion materials;

GW : the method of choice for electronic band structures, promising

for solar energy conversion

ATaO3: accurate for A=Na and K, but overestimates for A=Li new

physics; crystal structures have significant influences on electronic

band structures in LiTaO3, mainly via Madelung potentials and band

widths; Internal distortion of TaO6 stronger influences on Egap than

inter-TaO6 distortion

Absolute band positions from first-principles: quasi-particle

corrections necessary, but may not be enough for some materials

AcknowledgementsCoworkers: Huihui Wang, Feng Wu, Yuchen Shen

Funding: NSFC

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