熱在半導體或絕緣材料中主要是經由聲子來傳遞，本文使用聲子輻射熱傳方程式，模擬在微小尺寸下一維板狀鑽石薄膜內之暫態熱傳現象。探討以往學者為簡化問題，採用不同假設所造成的影響，並研究鑽石薄膜內的雜質濃度、薄膜厚度與溫度條件對熱傳現象所造成的效應。 由研究結果發現，使用假設聲子在每一頻率下皆可達平衡狀態的簡化平衡條件，在溫度預估上會造成嚴重誤差，如當薄膜厚度為0.10 mm溫度條件為77.0 K時，溫度誤差約為22%，但其對於熱通量的影響非常小，此結果說明了聲子在某些頻率下會有非平衡狀態發生，簡化平衡條件是個不好的假設。若為了便於計算，使用不隨頻率改變的特徵鬆弛時間取代隨頻率變化的鬆弛時間，會導致聲子平均自由路徑遠大於實際值，因此在溫度與熱通量的預估上皆會產生誤差，當薄膜厚度為0.10 mm溫度條件為77.0 K時，溫度誤差約為50%熱通量誤差約為16%。 以往在使用聲子輻射熱傳方程式時，大都假設薄膜被金屬物質包覆，因此薄膜邊界可視為黑體邊界條件，但電子元件主要是由半導體或絕緣材料構成，在邊界上會有反射的現象發生，本研究證明當薄膜厚度為0.1 mm，溫度條件為300.0 K，邊界反射率r=0.8時，若一昧使用黑體邊界條件，會造成溫度誤差約為57%，熱通量誤差約為356%。由研究結果得知，薄膜厚度的減小與雜質濃度的降低皆會使穿透傳遞的現象越趨明顯，造成邊界上的溫度差愈大；而溫度的增加會使聲子的平均自由路徑變短，在相同厚度的薄膜中，聲子發生碰撞的機會大幅增加，其熱傳較偏向巨觀的擴散現象。 Heat transport in semiconductor and dielectric materials is mainly by phonons. The transient heat conduction in microscale diamond films is investigated by using the equation of phonon radiative transfer (EPRT). The accuracy of using the simplified condition of equilibrium on the heat transfer characteristics are studied. These results show that using the simplified condition of equilibrium produces large errors in temperature distribution. It produces an error of about 22% in temperature, when the film thickness is 0.1 mm. This means the nonequilibrium condition does occur at some frequencies, and the simplified condition of equilibrium is not a good assumption. On the other hand, using the dominant frequency relation to replace the real relaxation time causes the calculated phonon mean free paths to be much larger than actual mean free paths. This causes errors of 50% in temperature and 16% in heat flux, when the film thickness is 0.1 mm. Effects of boundary reflection on the heat transfer characteristics are also investigated. The net heat flux across the film decreases as the boundary reflectivity increases. For a reflectivity of 0.8, the net heat flux is only 22 percent of the corresponding black surface case. Effects of impurity concentration, film thickness and boundary temperature on the heat transfer characteristics are also investigated. The results show that if we reduce the film thickness or the impurity concentration, the phonon transport becomes more ballistic and the temperature jumps at boundaries become larger. Increasing the film temperature, the mean free path becomes smaller and the phonon transport becomes more diffusive.
