Deriving Insights from Computation: Molecular Electronics to Self-trapped Excitons
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Deriving Insights from Computation: Molecular Electronics to Self-trapped Excitons
Steven G. Louie Physics Department, UC Berkeley and MSD, LBNL
Electron Transport:
Self-trapped Excitons:
Supported by: NSF and DOE
J.-H. Choi Y.-W. SonJ. Neaton J. Ihm (Korea)K. Khoo M. Cohen
S. Ismail-Beigi (Yale)O1
Si1
Si2
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Molecular Electronics
Present approach: Ab initio scattering-state method
Other ab initio approaches:NEGF methods -- (e.g., TRANSIESTA, Guo, et al., …)Lippman-Schwinger -- (e.g., di Ventra & Lang, …)Master equation -- (e.g., Gebauer & Car, …)
(Electron transport through single molecules,atomic wires, …)
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Example of a Molecular Electronic Device
(For a review, see Reed & Chen, 2000)
Chen, et al (1999); Rawlett, et al (2002)
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Some fundamental issues
• Open system: infinitely large and aperiodic
• Out of equilibrium: Chemical potential ill-defined across molecule
• Nanometer length scales: atomic details of contact and self-consistent electronic structure are important
µL µR
Current
R
LVscf = Vpp + VHa + Vxc
Self-consistent potential
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Theoretical framework
• Compute bias-dependent transmission coefficients t
• Current from transmission of states T(E,V)
• Formalism for an open, infinite system out of equilibrium capturing the atomic-scale details of the molecular junction • Two-terminal geometry with semi-infinite leads
R leadConductor
rt
L lead
i
€
I(V)=2e
hT(E,V)
μR
μL
∫dE
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First-principles Scattering-State Approach to Molecular Electronic Devices
Choi, Cohen & Louie (2004)
€
I(V)=2e
hT(E,V)
μR
μL
∫dE
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Closer look at a scattering state
Example state propagating from left to right with energy E
where, e.g.,
Transmission matrix
Incident L lead stateTransmitted R lead state &
evanescent waves
Reflected L lead state &evanescent waves
Conductor C state
R leadConductor
r t
L lead
i
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Conductance of Pt-H2 junction
[1] R.H.M. Smit et al., Nature 419, 906 (2002)
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
Conductance (2e2/h)
Num
ber
of C
ount
s
Pt• Conductance of single H2 molecule has been interpreted by break-junction measurements to be close to 1 G0 = 2e2/h
• Single channel
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Pd-H2 junction: Reduced conductance
Pd
Increasing H2 conc. x
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
PdHx PdHx
1 2 3 4 5 1 2 3 4 5 1 2 3 4 5
Cou
nts
Conductance (2e2/h)Conductance (2e2/h) Conductance (2e2/h)
Similar experiments with Pd nanojunctions yields about 0.3-0.5 G0, a factor of two or three less than Pt.
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Modeling the junction
H—H?
[111]
Tip—H?
Break junction
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Transmission spectra
Resonances Plateau
Khoo, Neaton & Louie (2005)
G=1.01G0
G=0.35G0
EF Pt
PdResonances
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Physical picture
EF
Pt
E
Pt case
Pd casePd
E
EF
• Junction states are band-like
• Scattering is minimal over a range of energies
• Junction states are resonant
• Scattering is large and energy dependent
JunctionMetal
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Local electronic structure
Pt Pd
Tra
nsm
issi
on (
2e2/h
)
H2
Tip atom
Bulk atom
Pt
Loca
l den
sity
of
stat
es
H2
Tip atom
Bulk atom
Pd
Khoo, Neaton and Louie (2005)
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Local electronic structure
H2
Tip atom
Bulk atom
H2
Tip atom
Bulk atom
Pt Pd
Pt Pd
Loca
l den
sity
of
stat
esT
rans
mis
sion
(2e
2/h
)
Band-like
Localized
Khoo, Neaton and Louie (2005)
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Conductance of H2 nanojunctions
Pd / H2 Pt / H2
Experiment 0.3 - 0.6G0 1.0G0
Our work
(G0 = 2e2/h)
0.35G0 (Pd)
0.14G0 (PdH)
1.01G0
H2 nanojunction conductanceStrongly lead-dependent: Tip atoms play a key roleClosed-shell molecule is a good conductor!Transport properties of small molecules are strongly affected by lead
Our calculations characterize conduction in the junction and explain experiment
Khoo, Neaton & Louie (2005)
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Negative Differential Resistance and Lead Geometry Effects
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Son, Choi, Ihm, Cohen and Louie (2004)
Calculated I-V Curve of a Tour Molecular Junction
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unoccupiedoccupied
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Dominant transmitting state
L U
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L U
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Potential Drop across Molecular Junction
Potential at 0.6 A above molecularplane
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Forces in the Photo-Excited State: Self-trapped Exciton
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Forces in Excited State
• For many systems, photo-induced structural changes are important
– differences between absorption and luminescence– self-trapped excitons– molecular/defect conformation changes– photo-induced desorption
• Need excited-state forces– structural relaxation– luminescence study– molecular dynamics, etc.
• GW+BSE approach gives accurate forces in photo-excited state
Ismail-Beigi & Louie, Phys. Rev. Lett. 90, 076401 (2003)
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Excited-state Forces
ES = E0 + ΩS
∂RES = ∂RE0 + ∂RΩS
E0 & ∂RE0 : DFT
ΩS : GW+BSE
Ismail-Beigi & Louie, Phys. Rev. Lett. 90, 076401 (2003).
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Verification on molecules
Ismail-Beigi & Louie, Phys. Rev. Lett. 90, 076401 (2003).
Excited-state force methodology
• Proof of principle: tests on molecules
- CO and NH3
• GW-BSE force method works well
• Forces allow us to efficiently find excited-state energy minima
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SiO2 (-quartz): optical properties
• Oxygen• Silicon
[1] Ismail-Beigi & Louie (2004)[2] Philipp, Sol. State. Comm. 4 (1966)
[1]
Emission at ~ 3 eV!
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Self-trapped exciton (STE) in SiO2 (-quartz)
Triplet STE has ≈ ms and ~ 6 eV Stokes shift [1]
[1] e.g. Itoh, Tanimura, & Itoh, J. Phys. C 21 (1988).
1. Start with 18 atom bulk
cell
2. Randomly displace
atoms by ±0.02 Å
3. Relax triplet exciton state4. Repeat steps 2&3: same
final config.
Ismail-Beigi & Louie (2005)
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Structural Distortion from Self-Trapped Exciton in SiO2
Final configuration: Broken Si-O bond Hole on oxygen Electron on silicon Si in planar sp2 configuration
Ismail-Beigi & Louie (2005)
• Oxygen• Silicon
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Self-Trap Exciton Geometry
Bond (Å)
Bulk Defect
Si1-O1 1.60 1.97 (+23%)
Si2-O1 1.60 1.68 (+5%)
Si1-Oother 1.60 1.66 (+4%)
Angles Bulk Defect
O1-Si1-Oother 109o ≈ 85o
Oother-Si1-Oother 109o ≈ 120o
O1
Si1
Si2
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Atomic rearrangement for STE
No activation barrier!
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Electron-Hole Wavefunction of Self-Trapped Exciton in SiO2
Hole probability distributionwith electron any where in the crystal
Electron probability distribution given the hole is in the colored box
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Electron & Hole Distributions of Self-Trapped Exciton in SiO2
Final configuration: Broken Si-O bond Hole on oxygen (brown) Electron on silicon (green) Si in planar sp2 configuration
Ismail-Beigi & Louie, PRL (2005)
• Oxygen
• Silicon QuickTime™ and aGIF decompressor
are needed to see this picture.
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Constrained DFT Calculations
Constrained LSDA: DFT with excited occupations
Problems:
• Relaxes back to ideal bulk from random initial displacements: excited-state energy surface incorrectly has a barrier.
• Large initial distortion needed for STE [1,2]
• Predicted Stokes shift and STE luminescence energy are very poor to correlate with experiments
[1] Song et al., Nucl. Instr. Meth. Phys. Res. B 166-167, 451 (2000).[2] Van Ginhoven and Jonsson, J. Chem. Phys. 118, 6582 (2003).
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STE in SiO2: Comparison to Experiment
Luminescence freq.: T (eV)
Stokes shift (eV)
Luminescence Pol || z (*)
Expt. [1-6]2.6, 2.74, 2.75, 2.8
6.2-6.40.48, 0.65,
0.70
GW+BSE 2.85 6.37 0.72
CLSDA (forced)
4.12 2.14 ----
1. Tanimura et al., Phys. Rev. Lett. 51, 423 (1983).
2. Tanimura et al., Phys. Rev. B 34, 2933 (1986).3. Itoh et al., J. Phys. C 21, 4693 (1988).4. Itoh et al., Phys. Rev. B 39, 11183 (1989).5. Joosen et al., Appl. Phys. Lett. 61, 2260
(1992).6. Kalceff & Phillips, Phys. Rev. B 52, 3122
(1996).
(*)
€
Pol =Iz − Ixy
Iz + Ixy
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Summary
First-principles calculations may be used to gain insightsinto new and old problems
• Electron transport through single molecule can exhibitdramatic negative differential resistance. (Chargerearrangement mechanism discovered.)
• Self-trapped exciton in SiO2 => broken-bond geometryand huge Stokes shifts.
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