低維孔隙結構對熱電優值影響之研究

Abstract

本論文旨在探討奈米線線寬、孔隙密度及孔隙間距高寬比對多孔矽奈米線徑向熱電優值之影響。輻射傳輸方程式將被用來同時描述電子和聲子於介質中的運動行為，並佐以鬆弛時間近似的假設來簡化能量載子之間複雜的碰撞機制。當載子運動至材料內任一界面時，採用彈性鏡面式散射直接對其動量造成改變來反映出界面阻力將成為尺寸效應下傳輸係數變化的關鍵因素。研究結果顯示，於散射相依的區間中，多孔奈米線的熱電優值將會隨著孔隙間距高寬比增加而出現週期性震盪遞減的行為，此時載子的紐森數、孔隙密度以及孔隙間距高寬比三者被用來綜合判斷孔隙界面是否有效地被散射所利用。當奈米線線寬為10奈米，孔隙間距高寬比介於0.72及1.38之間時，運動於孔隙間的能量載子彼此破壞其入射時的狀態而呈現出較窄的能量分佈，這使得熱電優值在此區間不降反升；當孔隙間距高寬比介於1.38及2.13之間時，孔隙間的載子能夠持續地保持入射時的本徵態來提高其返回原材料入射邊界的機率，這會降低材料能量傳遞的能力而使熱電優值再度下滑。於本文研究中所發現到多孔奈米線的徑向熱電優值將隨著孔隙參數變化而產生震盪的行為，此結果可以用來給予低維孔隙結構應用於熱電製程時之結構性參數最佳化上的建議。

The purpose of this study is to investigate the effects of wire thickness、pore density and interpore aspect ratio on the radial thermoelectric figure-of-merit in porous nanowire systems, which incorporate the description of electrons and phonons transport behaviors into radiative equations due to their ballistic nature. Constant relaxation time approximation and elastic specular scattering on the boundaries are utilized to simplify the complicated collision mechanisms for carrier-carrier and carrier-boundary interactions. Although the nanoporous matrix is a connected system where perfect confinement cannot take place, we show how the difference in the magnitude of carrier-boundary scattering give the possibility to obtain relative high thermoelectric figure-of-merit. These results suggest that carefully choosing a set of parameters composed of Knudsen number、pore density and interpore aspect ratio will be very crucial to optimize thermoelectric processes in low-dimensional porous structures, and it could be advantageous for power generation or cooling applications in the near future.