Post on 22-Feb-2016
description
Thermoelectric properties of ultra-thin Bi2Te3 films
Jesse Maassen and Mark Lundstrom
Network for Computational Nanotechnology,Electrical and Computer Engineering,
Purdue University,West Lafayette, IN USA
DARPA-TI meeting, August 15, 2012
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Motivation• In recent years, much research has focused energy-related science and technology,
in particular thermoelectrics.
• Some of the best known thermoelectric materials happen to be topological insulators (e.g., Bi2Te3).
• Work has appeared showing that TI surface states in ultra-thin films (<10 nm) can lead to enhanced thermoelectric properties.
ZT ~ 2P. Ghaemi, R.S.K. Mong and J. Moore, Phys. Rev. Lett. 105, 166603 (2010).
ZT ~ 7F. Zahid and R. Lake, Appl. Phys. Lett. 97, 212102 (2010).
The work presented here reproduces and expands these results.
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Figure-of-merit
IeIQ
T1 T2ΔT = T1 – T2
ΔV = V1 – V2V1 V2
G : Electrical conductanceS : Seebeck coefficientke : Electronic thermal conductance kl : Lattice thermal conductance
Material properties€
ZT = S2GTke + kl
Thermoelectricfigure-of-merit :
€
S = −ΔV ΔT (open circuit, zero electrical current)
€
ke = IQ ΔT (open circuit, zero electrical current)
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Thermoelectric transport coefficients
€
σ = σ ' ε( )dε∫ Conductivity
€
S = − kBq
⎛ ⎝ ⎜
⎞ ⎠ ⎟ε − EFkBT
⎡ ⎣ ⎢
⎤ ⎦ ⎥∫ σ ' ε( )σ
dε Seebeck
€
κ0 = T kBq ⎛ ⎝ ⎜
⎞ ⎠ ⎟2ε − EFkBT
⎡ ⎣ ⎢
⎤ ⎦ ⎥2
∫ σ ' ε( ) dε Electronic thermal conductivity (zero field)
€
κe = κ 0 − S2σ T Electronic thermal conductivity (zero current)
€
ZT = S2σ Tκ e +κ l
Differential conductivity/conductance is the central quantity for thermoelectric calculations.
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Conductance / conductivity in the Landauer picture
Scattering
Band structure
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G' ε( ) = 2q2
hM ε( ) −∂f0
∂ε ⎡ ⎣ ⎢
⎤ ⎦ ⎥dε
€
G = 2q2
hT ε( ) M ε( )∫ −∂f0
∂ε ⎡ ⎣ ⎢
⎤ ⎦ ⎥dε
€
G = G' ε( )dε∫
T = 1 (ballistic)
CONDUCTANCE€
σ ' ε( ) = 2q2
hλ ε( )
M ε( )A
−∂f0∂ε
⎡ ⎣ ⎢
⎤ ⎦ ⎥
€
σ =LAG = L
A2q2
hT ε( ) M ε( )∫ −∂f0
∂ε ⎡ ⎣ ⎢
⎤ ⎦ ⎥dε
€
σ = σ ' ε( )dε∫
T = λ / L (diffusive)
CONDUCTIVITY
Conductance (conductivity) is better suited to describe ballistic (diffusive) transport.
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kx kyE(k)
€
Ek = h2m∗ kx
2 + ky2( )
Number of conducting channels• How do we calculate the # of
conducting channels (modes)?
• Let’s consider a simple example: 2D film with parabolic Ek.
E
kx
M(E,ky)
0 1 2
E
ky
1
0 0
M(E,ky)
Transport
EM
(E)
€
M E( )Ly
= 12π
M E,ky( )dkyBZ∫
€
2m∗E π h
€
M E( )∝ vx ⋅D E( )
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Ultra-thin Bi2Te3 films
1 QL
0.74 nm
2 QL
1.76 nm
3 QL
2.77 nm
4 QL
3.79 nm
5 QL
4.81 nm
6 QL
5.82 nm
: A site: B site: C site
c-axis
1 quintuple layerTe1
BiTe2
Te1Bi
Experimental bulk lattice parametersare assumed: ab-axis = 4.38 Å
c-axis = 30.49 Å
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Band structure
Computed using density functional theory (DFT), with the VASP simulation package.
• Band gap exists only for 1QL and 2QL.
• For QL>2, surface state close the gap.
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Distribution of modes• Modes corresponds to the
number of quantum conducting channels.
• Analytical model by Moore [PRL 105, 166603 (2010)], only well describes the conduction band.
• Scaling factor disprepancy with the result of Zahid & Lake [APL 97, 212102 (2010)].
• 1QL, 2QL, 3QL are different, but QL>4 are very similar.
• Sharp increase in modes at the valence edge only with 1QL.
€
MW
= 1π
E 2 − Δ2
hvD
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Why sharp increase with 1QL?Answer comes from analyzing the k-resolved modes.
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Seebeck coefficient• Large positive
Seebeck with 1 QL.
• Max. Seebeck with 1 QL, the result of a larger band gap.
• Seebeck decreases with increasing film thickness.
ΔEbulkΔE1QL
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S ∝ ΔEkBT
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Power factor
• 1 QL : maximum PF is 6-7x larger than others.
• Large PF results from enhanced conduction near the VB edge.
• Demonstration of TE enhancement through band structure.
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PF = S2GNumerator of ZT :
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Figure-of-merit
• 1 QL : potential ZT 4x larger than bulk.
• QL > 2 leads to low ZT, due to small (or zero) band gap.
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ZT = S2GT
κ e + κ l
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Conclusions / future work
• Electronic enhancement of ZT with 1 QL, due to the shape of the VB.
• Strict constraint on thickness, enhancement only predicted for 1 QL.
• Future work:– Impact of scattering on TE parameters.– Predict lattice thermal conductivity (phonon transport).– Study thin films of Bi2Se3, Sb2Te3 and MoS2.