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 =S2GT

ke + 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 = TkBq

⎛

⎝ ⎜

⎞

⎠ ⎟

2ε − EFkBT

⎡

⎣ ⎢

⎤

⎦ ⎥

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∫ σ ' ε( ) dε Electronic thermal conductivity (zero field)

€

κe = κ 0 − S2σ T Electronic thermal conductivity (zero current)

€

ZT =S2σ T

κ 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

€

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 =L

AG =

L

A

2q2

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 =h

2m∗ kx2 + ky

2( )

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

=1

2πM E,ky( )dky

BZ

∫

€

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.

€

M

W=

1

π

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

€

S ∝ΔE

kBT

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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.

€

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.