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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
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”
Elias Assmann (TU Vienna) LaVO3 |SrTiO3 for solar cells WIEN2013@PSU 3 / 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”
Elias Assmann (TU Vienna) LaVO3 |SrTiO3 for solar cells WIEN2013@PSU 3 / 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”
Elias Assmann (TU Vienna) LaVO3 |SrTiO3 for solar cells WIEN2013@PSU 3 / 15
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
Elias Assmann (TU Vienna) LaVO3 |SrTiO3 for solar cells WIEN2013@PSU 4 / 15
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
Elias Assmann (TU Vienna) LaVO3 |SrTiO3 for solar cells WIEN2013@PSU 4 / 15
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
Elias Assmann (TU Vienna) LaVO3 |SrTiO3 for solar cells WIEN2013@PSU 5 / 15
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
Elias Assmann (TU Vienna) LaVO3 |SrTiO3 for solar cells WIEN2013@PSU 6 / 15
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)
Elias Assmann (TU Vienna) LaVO3 |SrTiO3 for solar cells WIEN2013@PSU 7 / 15
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)
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
Elias Assmann (TU Vienna) LaVO3 |SrTiO3 for solar cells WIEN2013@PSU 7 / 15
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)
É DFT: n- and p-interface conducting
É both interfaces occur byperiodic boundary conditions
Elias Assmann (TU Vienna) LaVO3 |SrTiO3 for solar cells WIEN2013@PSU 7 / 15
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
Elias Assmann (TU Vienna) LaVO3 |SrTiO3 for solar cells WIEN2013@PSU 8 / 15
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
Elias Assmann (TU Vienna) LaVO3 |SrTiO3 for solar cells WIEN2013@PSU 9 / 15
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
Elias Assmann (TU Vienna) LaVO3 |SrTiO3 for solar cells WIEN2013@PSU 10 / 15
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)]
Elias Assmann (TU Vienna) LaVO3 |SrTiO3 for solar cells WIEN2013@PSU 11 / 15
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)
Elias Assmann (TU Vienna) LaVO3 |SrTiO3 for solar cells WIEN2013@PSU 12 / 15
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)
Elias Assmann (TU Vienna) LaVO3 |SrTiO3 for solar cells WIEN2013@PSU 12 / 15
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)
Elias Assmann (TU Vienna) LaVO3 |SrTiO3 for solar cells WIEN2013@PSU 12 / 15
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)
Elias Assmann (TU Vienna) LaVO3 |SrTiO3 for solar cells WIEN2013@PSU 13 / 15
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
Elias Assmann (TU Vienna) LaVO3 |SrTiO3 for solar cells WIEN2013@PSU 14 / 15
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
Elias Assmann (TU Vienna) LaVO3 |SrTiO3 for solar cells WIEN2013@PSU 15 / 15
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
Elias Assmann (TU Vienna) LaVO3 |SrTiO3 for solar cells WIEN2013@PSU 15 / 15
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
Elias Assmann (TU Vienna) LaVO3 |SrTiO3 for solar cells WIEN2013@PSU 1 / 3
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
Elias Assmann (TU Vienna) LaVO3 |SrTiO3 for solar cells WIEN2013@PSU 2 / 3