鋅-氧化矽複合物之熱電勢的展透行為研究

Abstract

數十年來，展透理論已經被廣泛的運用在各種自然現象當中。例如，森林大火、疾病的傳染以及電子傳輸效應。而在金屬-絕緣體複合物中，其導電率所具有的展透行為，也已經被討論了許多年之久。當金屬體積比大於臨界體積比時，電阻率將遵循一個簡單的power law。而就另一方面而言，熱電勢的展透行為也已經有理論的討論。1991年，Bergman和Levy認為熱電勢的展透行為與導電率以及熱導率的比值有關，以我們所量測的系統為例，當導電率比值遠大於熱導率比值時，其臨界行為可以一簡單的熱電勢power law所表示。

我們在4He降溫系統下，架設了一個可以量測熱電勢的樣品座。並藉由量測一系列不同成分體積比的Znx(SiO2)1-x之電阻率以及熱電勢，來研究其展透行為。而由我們實驗的結果得知，熱電勢的臨界體積比介於0.261與0.265間，與電阻率的臨界體積比(0.262±0.003)約略相等，且此值介於三維臨界體積與二維臨界體積的最小值之間，符合1980年，H. Kesten所證明。

Percolation theory in natural phenomena has been known for several decades. Typical examples include forest blaze, contagious disease and the properties of electrical-transport, etc. In particular, the percolation behavior of electrical conductivity in the metal-insulator composites, has long been of great interest. In a sample with the metal volume fraction larger than the critical volume fraction, i.e., the resistivity is given by a simple power law. The thermoelectric power in a metal-insulator composite has also been discussed. In 1991, Bergman and Levy proposed that the behavior of thermoelectric power should depend on electrical and thermal conductivity ratios of the two constituent components. For x>xc and electrical ratios bigger than thermal conductivity ratios (which is pertinent to our case), the thermopower is also given by a simple power law.

We have set up a system which can measure thermoelectric powers at low temperatures in a 4He variable temperature cryostat. By measuring thermoelectric powers and resistivities of a series of Znx(SiO2)1-x composites, we have studied the percolation behavior of thermoelectric power and resistivity. According to our experimental result, the critical volume fraction for the thermoelectric power is 0.261-0.265, which is close to the critical volume fraction for resistivity (0.262 ±0.003). This value lies between the three-dimensioned critical volume fraction and the two-dimensioned critical volume fraction minimum, onfirming that, as theoretically by H. Kesten, 1980.