oxide heterostructures for solar cells · oxide heterostructures for solar cells elias assmann...

Oxide Heterostructures for Solar CellsElias Assmann

Institute of Solid State Physics, Vienna University of Technology

WIEN2013@PSU, Aug 14

É LaVO3|SrTiO3 proposed as photovoltaic absorber.

Phys. Rev. Lett. 110, 078701 (2013)

1 large intrinsic electric field

2 conducting interface(s)

3 direct gap of 1.1eV

4 flexible multijunction design

É Outlook: dynamical mean-field theoryfor correlated heterostructures

Prototype Heterostructure: LaAlO3|SrTiO3

É cubic perovskites [room temp]

É wide-gap band insulators

two types of interfaces [(001) direction]:

p-typeÉ (AlO2) – |SrO

É insulating

n-type

É (LaO)+|TiO2É conducting: insulator + insulator = metal

É interesting features, e.g., two-dimensional electron gas, superconducting

Elias Assmann (TU Vienna) LaVO3 |SrTiO3 for solar cells WIEN2013@PSU 2 / 15

Polarized Layers in LaAlO3|SrTiO3

adapted from N. Nakagawa et al., Nature Mat. 5, 204 (2006)

Formal valences:

É Sr2+Ti4+O6–3

É neutral SrO, TiO2 layers

É La3+Al3+O6–3

É alternatingly charged (LaO)+, (AlO2) – layers

Plate capacitor model: large internal electric field (∼ 1ε47V/unit cell),

potential gradient

⇒ “polarization catastrophe”


Avoiding the polarization catastrophe

adapted from N. Nakagawa et al., Nature Mat. 5, 204 (2006)

É Electronic reconstruction electron doped n-interface,

hole doped p-interface

É experimental support:critical thickness

É problem: why is thep-interface insulating?

É Oxygen vacanciesÉ O2– vacancy contributes 2 holes

É Ionic reconstructionÉ structural relaxation in DFT


Bulk SrTiO3 and LaVO3

SrTiO3

É (almost) cubic Perovskite

É TiO6 octahedra

É d0 band insulator

LaVO3

É distorted Perovskite (VO6 octahedra)

É d2 Mott insulator

É band gap: 1.1eV

É AF-C spin, AF-G orbital order


LaVO3|SrTiO3

Computational method: GGA + UV = 3eV, UTi = 9.8eV

É spin order: AF-C

É orbital order: AF-G (dxz | dyz)

É multi-layer vs. thin-film


1: Potential gradient & 2: Conducting interface(s)

p

V4 V dxy-states

Vb (↑)Va (↓)

V3 V dxy-states

V2 V dxy-states

n

V1 V dxy-states

-2 -1 0 1 2

Ti

E [eV]

V dxy-statesTi

density-functional theory (GGA+U):

É layer-resolved density of states:band shift = potential gradient

É ∼ 0.3eV/u.c. = 0.08eV/Å

É core-level energy E1s(z)



p

V4 V dxy-states

Vb (↑)Va (↓)

V3 V dxy-states

V2 V dxy-states

n

V1 V dxy-states

-2 -1 0 1 2

Ti

E [eV]

V dxy-statesTi



É ∼ 0.3eV/u.c. = 0.08eV/Å


SrT

iO3

LaV

O3

(LaO

)+(V

O 2)-

TiO 2

SrO

n-I

F

p-I

F

p-I

F

layer

E1

s [e

V]

0.0

0.4

0.8

1.2

-5 -4 -3 -2 -1 1 2 3 4



p

V4 V dxy-states

Vb (↑)Va (↓)

V3 V dxy-states

V2 V dxy-states

n

V1 V dxy-states

-2 -1 0 1 2

Ti

E [eV]

V dxy-statesTi



É ∼ 0.3eV/u.c. = 0.08eV/Å


É DFT: n- and p-interface conducting

É both interfaces occur byperiodic boundary conditions


3: Strong absorption across solar spectrum

É band gap 1.1eV is in the optimal range for efficiency

É Shockley-Queisser limit

É optical absorption of LaVO3 compares favorably to e.g. GaAs, CdTe


4: Flexible gap grading

p

Fe

gap ~ 2.2 eV

FeO

n

V

gap ~ 1.1 eV

V

-2 -1 0 1 2 3

STO

E [eV]

Ti

É heterostructures grown bypulsed laser deposition (PLD)

⇒ layer-by-layer band gap grading

É e.g., for a tandem cell, combineLaVO3 and LaFeO3 (gap: 2.2eV)

É gradient, conducting interfaces persist


Summary: Solar Cells

. . .

(MO2)-

(M'O2)-

(MO2)-

(M'O2)-

SrTiO3substrate

LaMO3,gap: Δ

(LaO)+conductingn-type layer

(TiO2)0

(SrO)0

E*

LaM'O3,Δ' > Δ

(LaO)+

(LaO)+

conductingp-type layer

(LaO)+1 large intrinsic electric field

2 conducting interface(s)

3 LaVO3: direct gap 1.1eV

4 combine oxides for multijunction cell

É experimental realization in progress(R. Claessen & J. Pflaum, Würzburg)

É EA, P. Blaha, R. Laskowski, K. Held, S. Okamoto, and G. Sangiovanni,PRL 110, 078701 (2013)

É synopsis in APS Physics

É popular-level coverage in various media


Dynamical mean field theory (DMFT) in 1 slide

tDMFT

U

U

U

UU

U U

UU

Σ

U

lattice problem 7−→ impurity problem

É 1 interacting site in a “bath” of non-interacting electrons

É non-local correlations neglected: (k, ω) 7→ imp(ω)

É self-consistency: Gimp = Gloc

[Georges et al., RMP (1996); Kotliar & Vollhardt, Phys. Today (2004)]


DMFT with Inequivalent Atoms

É Nneq nonequivalent correlated atomsNd d-Bands per atomN := Nat ·Nd dimensional space

É Local Green function (big N×N matrix)

G(ω) =∑

k

1

(ω+ μ)−HDFT(k)− (ω)

É Weiss field (small Nd ×Nd-matrix for each atom i)

G−1i

(ω) =h

G(ω)�

�

atom iloc

i−1+ i(ω)

É impurity solver: self-energy matrix with Nneq independent entries

CT-QMC code w2dynamics, Parragh et al. PRB (2012)


Low-Energy Model for LDA+DMFT

⇒

Maximally-Localized Wannier Functions

wmR = V(2π)3

∫

BZ

dke−ik·R∑

nUnm(k)ψnk

unitary U(k) minimize spread ⟨Δr2⟩.

wannier90: Mostofi et al., CPC (2008)

Wien2Wannier: Kunes et al., CPC (2010)

woptic: Wissgott et al., PRB (2012)


Outlook: DMFT

-3 -2 -1 0 1 2 3 4 5 6

A(ω

)

ω [eV]

Ti

V

É DMFT for inequivalent atomsÉ independent i(ω) coupled in G(ω)

paramagnetic insulator

É construct minimal model (MLWF)É Wien2Wannier, wannier90

É optical properties(d-d transitions dominate!)É woptic

É structural optimization with DMFTÉ charge self consistency


Big Thanks to . . .

Peter BlahaTU Vienna

Karsten HeldTU Vienna

Robert LaskowskiTU Vienna

Satoshi OkamotoOak Ridge National Lab

Giorgio SangiovanniUni Würzburg

Experiment (Würzburg):É Ralph ClaessenÉ Jens Pflaum

Thank you for listening


M-O-M bond angle (M = V, Ti)

Lattice distortion in the heterostructure:

155

160

165

170

175

-5 -4 -3 -2 -1 0 1 2 3 4

layer

(a)(b)(c)(d)

bulk


LaVO3 absorption: Details

0

10

20

30

40

0 1 2 3 4

α [µ

m-1

]

ℏω [eV]

STO|LVO (xx)STO|LVO (zz)bulk LaVO3 (xx)bulk LaVO3 (zz)

É Absorption: I(x) ∼ e−αx

É Lattice distortion:α(ω) αij(ω)

for comparison, plot

α =1

3

∑

ij

αij

back


Heterostructure DOS for different sizesb

ulk

LV

O totalV

2 layers

3 layers

-8 -6 -4 -2 0 2 4 6 8

4 layers

E [eV]

Critical thickness: 4 layers LaVO3


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