Enhancement of Thermoelectric Performance by using nano-structures
Koji Miyazaki
Department of Mechanical and Control Engineering
Kyushu Institute of Technology
Sensui-cho 1-1, Tobata-ku, Kitakyushu 804-8550 Japan

Abstract
Thermoelectricity is the direct conversion of thermal energy to electrical energy.

The performanceof thermoelectric materials is characterized by the dimensionless figure-of-merit, ZT, which isdefined as ZT=S2T/, where S is the Seebeck coefficient,  is the electrical conductivity, T is the is the thermal conductivity.

Here, we made a porous thin film of

Bi0.4Te3Sb1.6 with extremely low thermal conductivity. The measured enhanced figure of merit of
1.8 at room temperature

The reduction in thermal conductivity was rationalized using a model forthe full distribution of the phonon mean free path in the film.

The heat conduction of nano-structured materials is currently receiving the greatest attention in
the thermoelectric energy conversion. Semiconductor nanowires1, semiconductors with embedded
nanostructures2, and semiconductor superlattices3,4 are under intense investigation for the promise of
enabling practical systems with significantly higher efficiencies for the conversion of heat toelectrical power.

In this study, we fabricated Bi0.4Te3.0Sb1.6 nano-porous thin films on anodized

5

porous alumina by a flash deposition method6, and measured their thermoelectric properties. The
in-plane electrical conductivity and Seebeck coefficient are measured, and the cross-plane thermal
conductivity was measured by a pico-second thermoreflectance method7, at room temperature.
Furthermore, we calculated phonon MFPs and a normalized cumulative thermal conductivity byusing the kinetic theory (L=CvgL/3), where C is the specific heat used Debye model, vg is groupvelocity, L is the phonon MFP used impurity scattering and umlkapp scattering. The reduction intherml conductivity was rationalized using the model of the full distribution of the phonon mean free(a)(b)

Fig.1 Porous thin film of Bi0.4Te3.0Sb1.6(b) SEM image(a) Bi0.4Te3.0Sb1.6 thin film on porous alumina substrate

Table 1 Thermoelectric properties of Bi0.4Te3.0Sb1.6
Porous thin filmThin Film6

BulkSeebeck Coefficient, V198252200Electrical Conductivity, S/cm

398550800

Thermal Conductivity, W/(m･K)

0.25

1.0

2.3

ZT at 300K

1.8

1.00.6path.
We made a porous thin film o f bismuth antimony telluride (Bi0.4Te3Sb1.6) on porous alumina
substrate as shown in Fig.1.

The thickness of the Bi0.4Te3Sb1.6 film was 100 nm while that of theporous alumina was 1 m. The average diameter of the holes was 20 nm, and the average pitch of
the hexagonally arranged holes was 50 nm. The packing density was 78%.

The thermoelectric properties of the porous Bi0.4Te3Sb1.6 thin film were measured at room
temperature, and are compared with parameters for typical Bi0.4Te3Sb1.6 thin films in Table 1. The
in-plane electrical conductivity  of the porous film was measured at room temperature by afour-point probe method with the accuracy of ±3%. The measured value is proportional to thepacking density of the material, which can be explained by the conventional model related to thediffusive transport of electrons. The mean free path of electrons is roughly calculated to be 30nm.
The in-plane Seebeck coefficient S was also measured at room temperature with accuracy of ±5%.
One end of the thin film is connected to a heat sink and the other end to a heater. The Seebeckcoefficient is determined as the ratio of the potential difference (V) along the films to thetemperature difference (T). The thermal conductivity of the sample was 0.25 W/(m·K), which
was measured by the picosecond thermoreflectance method with a fitting error of 0.05W/(m·K)
assuming the specific heat of bulk Bi0.4Te3Sb1.6.7 Although the cross-plane thermal conductivity of
the film was determined in the present study, the in-plane thermal conductivity is considered to be in
the same order as that of the cross-plane. Cross-plain and in-plain thermal conductivities ofnanostructured materials are usually both reduced by strong phonon scattering.8,9 The measured
thermal conductivity is in the same order as the theoretical minimum value because long-range
phonon transport is suppressed by the porous structure.
A model using a full distribution was employed to describe the phonon mean free path in theporous thin film.10The lattice thermal conductivity is expressed as13 L   Cvg Ld ,(1)where  is the angular frequency, C is the specific heat per unit frequency by using Debye model, vg
is the group velocity by using a sinusoidal model, and L is the effective phonon MFP which can bedivided into terms of impurity/alloy scattering and umklapp scattering:Cumulative thermal conductivity, W/(m·K)

1.6
1.2

Bi2Te30.8

Sb2Te30.4
0.0010

10

123

410
10
10
Cutoff mean free path, nm

10510

6

Fig.2 Cumulative thermal conductivity of Bi2Te3 and Sb2Te31   L
1 , T  .
L1 , T   Limpurity  umklapp (2)Impurity scattering is calculated using impurity scattering Limpurity-1=A14/vs, where vs is the soundvelocity, A1 is a fitting parameter which may also be estimated from other properties. For umklapp
scattering, we use Lumklapp-1=B12Texp(-B2/T)/vs, where B1 and B2 are fitting parameters. We findfitting parameters of Bi2Te3 are A1= 1.3 x 10-42 s3, B1=1.1 x 10-18 s/K, and B2= 120 K and of Sb2Te3
A1= 1.2 x 10-41 s3, B1=4.4 x 10-19 s/K, and B2= 120 K. The distribution function L for the thermal
conductivity per unit mean free path was calculated. The cumulative thermal conductivity (l)calculated by phonons with a mean free path between 0 and l: (l )    L dLl(3)0where l is the cutoff mean free path, was plotted. The cumulative thermal conductivities of Bi2Te3and Sb2Te3 as a function of the mean free path are depicted in Fig.2. When the cutoff mean freepath is greater than 100 m, the cumulative thermal conductivities of Bi2Te3 and Sb2Te3 reachapproximately that of a single crystal. The cumulative thermal conductivity is reduced as the cutoff
mean free path decreases. The experimental result 0.25 W/(m·K) thermal conductivity is fairly
similar to the calculated value 0.155 W/(m·K) for the model at a cutoff mean free path of 50 nm.
Here, the cutoff mean free path was assumed according to the average pore spacing.

Thesignificant reduction of the thermal conductivity is caused by significant scattering of long-range
phonons by the pores in the thin film.

In conclusions, nano-porous thin film is proposed as the nano-structure to enhance theperformance of thermoelectricity.

By making nano-porous structure with the size between electron

and phonon mean free path (MFP), it is possible to decrease phonon transport more than electrontransport.

Acknowledgement
This work was supported by the New Energy and Industrial Technology Development Organization(NEDO).

The authors wish to thank Dr. Saburo Tanaka for discussion of mean free pathcalculations, Prof. Chihaya Adachi and Dr. Shuzo Hirata for making nano-porous alumina, and Dr.
Kazuko Ishikawa for thermal conductivity measurements.

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