JOURNAL OF MATERIALS SCIENCE LETTERS 7 (q988) 1245-1246

Importance of substrate materials in thin film thermoelectric devices

KUNIHITO KOUMOTO Department of Industrial Chemistry, Faculty of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113, Japan

The development many years ago of thermoelectric semiconductors has recently been resurrected in a flurry of activity once again for high-temperature ther- moelectric energy conversion. One of the research trends in this field seems to be the application of newly developed techniques for the preparat ion of thin films in both crystalline and amorphous states. The ionized- cluster beam (ICB) method and electron cyclotron resonance (ECR) plasma CVD method have been applied to the thin film formation of amorphous FeSi z [1] and boron carbide [2], respectively. The usual vacuum evaporation and sputtering techniques have also been examined for germanium [3].

Thin film materials specifically in the amorphous state are expected to show a higher energy conversion efficiency than in the crystalline state. Thin film devices are also practically useful in developing a power generator of smaller size. "However, the importance of substrate materials appears not to have so far been taken into account, though a thin film is always mounted on a certain substrate.

This short paper reports the calculation of a figure of merit for thermoelectric energy conversion, based on a simple parallel circuit model involving a thermo- electric thin film and a substrate.

For thermoelectric power generation a temperature difference is supposed to be applied to a thin film device with its direction parallel to the film surface, and hence the device in itself would become a parallel circuit. Then, neglecting the effect of interface phenom-

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tog ( P~/& ) Figure 1 Calculated Seebeck coefficient c~ of a thin film device against resistivity ratio of substrate (subscript 1) and film (subscript 2) for various substrate/film thickness ratios SdSz: (1) 1, (2) 10, (3) 10 2, (4) 10 3.

ena for simplicity, the Seebeck coefficient ~ and resis- tance R of this parallel circuit can be written as

Rs~l + RItz - (1)

Rl + R2

1 1 1 - + - - ( 2 )

R Ri R2

where the subscripts 1 and 2 correspond to the sub- strate and thermoelectric thin film, respectively. Put- ting the cross-sectional areas of substrate and film as S~ and Sz, the Seebeck coefficient ~ and resistivity 0 of a device can be expressed as follows, if the lengths of substrate and film are taken to be the same:

(s,/s2)< + (o,/~2).= = (3)

(o,/~) + (s,/&)

(o,/o=)[(s,/$2) + 11o= o = (4)

(o, /o2) + (&/&) Figs 1 and 2 show how the total Seebeck coefficient and resistivity of a thin film device change with the resistivity ratio and the ratio of cross-sectional areas of the substrate and the film. It should be noted from Fig. 1 that the Seebeck coefficient of the substrate tends to contribute significantly to the total Seebeck coef- ficient when S 1/S 2 becomes large, i.e. the thermoelec- tric film becomes thinner. This tendency is enhanced if the resistivity of the substrate is rather low compared to that of the film. The resistivity of an insulating substrate material such as alumina or silica glass usually decreases exponentially with increasing tem- perature [4], so that the Seebeck coefficient measured at elevated temperatures must be carefully evaluated and analysed especially for a device with a thin film~

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unity ,2 ,

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0 1 2 3 ¢ 5 6 7 tog ( P , / & I

Figure 2 Calculated total resistivity Q of a thin film device against resistivity ratio of substrate (subscript 1) and film (subscript 2) for various substrate/film thickness ratios St/$2: (1) 1, (2) 10, (3) 102, (4) 103 .

0261-8028/88 $03.00 + .12 © 1988 Chapman and Hall Ltd. 1245

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- 4 - - , i

I " 0

0

Z ~/" 8,

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0 1 2 3 ~, 5 6

tog 16/P~ )

i !

7 8

®

®

Figure 3 Calculated figure of merit for a thin film device against resistivity ratio of substrate (subscript 1) and film (subscript 2) for various substrate/film thickness ratios S~/S2: (1) 1, (2) 10, (3) 10 ~, (4) 103. The ratios of Seebeck coefficient (cq/e~) and thermal con- ductivity (x~/x2) were fixed for this calculation to be 5 and 0.1, respectively.

Thermoelectric materials are usually evaluated in terms of the following figure of merit, Z, which corre- sponds to the energy conversion efficiency of a Carnot cycle;

z = ~ / e ~ (5)

where ~: is the thermal conductivity [5]. For a thin film device composed of two different materials e and ~ are expressed by Equations 3 and 4, respectively, while is written as [4]

x = Slxl + $2~c 2 (6)

Combining Equations 3, 4 and 6, the figure of merit for a thin film device can be expressed as

z = o---fi = ,t(x + ,t)(~x + l) \ ~ /

= ~ ( x + ,t)(flx + t) \q~---~/

where Z = el/e2, 5 = e,/e2, x = $1/$2, and fl = x~/~c~, c~/~x 2 and e~/0~ x~ are the figures of merit for the film and the substrate, respectively• It can be said that if combinations of the four factors 2, 6, x and/~ could exist to make both terms in [ ] in Equation 7 larger at the same time than unity, a thin film device having a larger figure of merit than either the film material or the substrate material could theoretically be produced• However, unfortunately these combinations can never be found, and the arrangement of the two different materials in a parallel circuit always results in a decrease in the energy conversion efficiency of a thermoelectric material. Examples of the calculation of Z using Equation 7 are shown in Figs 3 and 4.

Equation 7 tells us that utilizing the same materials for both film and substrate is the best way to minimize the decrease in energy conversion efficiency. However, this is nonsense in developing a new device. Thin films prepared by newly developed techniques are still con-

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unity • ®

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0 1 2 3 4 5 6 7 8

tog (P~/P2}

Figure 4 Calcutated figure of merit for a thin film device against resistivity ratio of substrate (subscript 1) and film (subscript 2) for various substrate/film thermal conductivity ratios x~/x,: (I) 10 -2, (2) 10 -~, (3) 1, (4) 10. The ratios of Seebeck coefficient (~t/~2) and thickness (S,/$2) were fixed for this calculation to be 5 and 102, respectively.

sidered to have a high possibility of showing better properties than the bulk materials prepared by con- ventional methods, and so the efforts to discover sophisticated structures and properties suitable for thermoelectric energy conversion should be con- tinued. In this sense, a few suggestions can be drawn from the present study in order to effectively make use of the film properties; (i) the film/substrate thickness ratio should be as large as possible (Fig. 3), (ii) a substrate with a low thermal conductivity ought to be chosen (Fig. 4), and (iii) a substrate having a larger Seebeck coeffÉcient had better be chosen if the candidate materials show similarity in other properties.

Acknowledgement The author expresses his thanks to Professors K. Matsubara and S. Gonda for valuable discussions. This work was supported by a Grant-in-aid for Scien- tific Research in Priority Areas, Japanese Ministry of Education, Science and Culture (No. 62603514).

References 1. K. MATSUBARA, T. KOYANAGI and T. TAKAGI, in

Proceedings of 6th International Conference on Thermoelectric Energy Conversion, Texas, 1986, pp. 1-6.

2. s. GONDA, K. SASAKI and T. I IZUKA, in Report on Energy Conversion Technology (Japanese Ministry of Education, Science and Culture, 1988) pp. 291-296.

3. T. KIMUR A and N. YUGO, ibid. pp. 297-300. 4. W. D. KINGERY, H . K . BOWEN and D. R. UHL-

MANN, "Introduction to Ceramics", 2nd Ed (Wiley, New York, 1975) pp. 636, 908.

5. Y. SUGE (ed.), "Thermoelectric Semiconductors" (Maki Shyoten, Tokyo, 1966).

Received 11 April and accepted 11 July 1988

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