矽鍺低維度材料熱傳性質之非平衡分子動力學模擬研究

An Investigation of the Lattice Thermal Transport Phenomenon in Low-Dimensional Si/Ge via the Molecular Dynamics Simulation

張泰鳴(Tai-Ming Chang)

指導教授 ： 黃美嬌

國立臺灣大學/工學院/機械工程學研究所/博士(2010年)

https://doi.org/10.6342/NTU.2010.01028

摘要

近年來因低維度材料的低熱傳導係數能改善熱電元件的效率，所以受到廣泛的研究。在過去的理論與實驗中皆發現薄膜、奈米線、超晶格、量子點超晶格等低維度材料之晶格熱傳導係數能低於塊材1~2個數量級；然而對於複雜的奈米結構以理論分析或是在實驗製程上皆不易進行。因此本論文企圖建立以非平衡分子動力學(NEMD)模擬方法來計算低維度材料的熱傳性質，其中先以單晶矽薄膜進行模擬，藉此整理並建立合理的模擬方法，而後再對複雜的矽鍺量子點異質結構進行模擬，觀察量子點對熱傳性質之影響。模擬中，矽、鍺原子的作用力採用兼具二體與三體勢能的Stillinger-Weber勢能函數。
在薄膜的模擬過程中，由於MD的溫度計算屬古典力學之方法，若模擬溫度比材料的Debye溫度來得低並不適用，因此需要對模擬溫度進行量子修正。在過去的文獻中皆以Debye模型或塊材的聲子態密度進行修正，而本論文採用平衡分子動力學(EMD)模擬得到的薄膜聲子態密度來做修正。此外，在有限模擬尺寸的薄膜平面下會失去長波長聲子的貢獻，稱為數值有限尺寸效應；為了得到無窮域的結果，本論文模擬了數個不同平面長度的薄膜，並藉由前人研究中的外插技巧來求得無窮域薄膜的結果。從模擬結果來看，當MD模擬溫度在室溫附近時必須進行量子修正，且以本論文所提出以薄膜態密度進行修正最為合理，與理論聲子波茲曼方程式在某一表面粗糙度下的預測結果相當一致。
至於矽鍺異質結構的模擬，首先比較NEMD常用的兩種熱傳模擬方式：控制熱流量法與控制溫度法，從模擬過程中發現在異質結構中因介面的影響而需相當長的熱傳穩態時間與取樣平均步數，而結果顯示控制溫度法能有較好的收斂情形。接著為了瞭解量子點對熱傳的影響，本論文模擬三種異質結構：矽/鍺量子點/鍺、矽/鍺量子點/矽異質結構與矽鍺量子點超晶格。由前兩種的模擬結果顯示，嵌入的量子點反而可減緩異質結構介面處的聲頻不匹配(acoustic mismatch)；然而若濕潤層存在時，熱傳導係數可能因量子點佔有相當大的鍺材料比例，或濕潤層與量子點之間有波的破壞性干涉而下降。而量子點超晶格的模擬結果顯示，在多個介面的影響下熱傳導係數只隨著量子點密度增加而降低，此結果在定性上甚至定量上與實驗量測結果相當一致。

關鍵字

薄膜 ； 超晶格 ； 量子點 ； 晶格熱傳導係數 ； 態密度 ； 非平衡分子動力學

並列摘要

The low-dimensional structures have been widely investigated because of their low thermal conductivities for improving the efficiency of thermoelectric materials. Past theoretical and experimental studies found that the lattice thermal conductivity of thin-film, nanowire, superlattice, quantum dot (QD) superlattice etc., can further reduce 1~ 2 order of magnitude to their bulk counter parts. Nonetheless, it’s much difficult to analyze or fabricate the complicated nanostructures through the theoretical model or the experiment. Hence, in this thesis we attempt to establish the NEMD simulation to calculate the thermal properties of low-dimensional materials. We first arrange and build a reasonable procedure of NEMD approach by employing the simulation of single crystal of the silicon thin film, and further simulate the QD heterostructures to observe the influence on thermal properties of QD. The Stillinger-Weber potential which contains two-body and three-body interactions is adopted for silicon and germanium in the simulation.
In the simulation of thin film, since the calculation of temperature in MD belongs to classical mechanics, it’s necessary to make the quantum correction of temperature when lower than Debye temperature. Most of investigations made the correction by using the Debye or bulk DOS. In this thesis, however, we adopt the thin film DOS via EMD simulation. Besides, the so-called finite-size-effect is caused by absence of phonons with long wave lengths in the finite size of in-plane thin film. To obtain the results of infinite domain, samples of various lengths are simulated and an extrapolation technique is employed. The investigation shows the thermal conductivities should be corrected when simulated temperature is close to room temperature. Moreover, the corrected results by the thin-film DOS presented in this thesis are reasonable and agree excellently with the theoretical predictions having a similar surface roughness based on the phonon Boltzmann equation.
As for simulation of Si/Ge heterostructures, two commonly used methods, control heat flux and control temperature, are compared first for producing the heat transfer in the NEMD simulation. It is found that the longer simulation time is required to attain the steady state and to take the time average because of the existence of interface. Besides, the use of control temperature method has the better convergence. Next, to clarify QD phenomenon, we employed three heterostructures, a Si/Ge QD/Ge heterostructure, a Si/Ge QD/Si heterostructure, and a QD superlattice in this thesis. From the simulation results of former two heterostructures, we found that acoustic mismatch can be alleviated by the QDs embedded inside. However, the existence of the wetting layer may create an additional interface and cause the destruction of phonon transport by wave interference. The large Ge concentration of QD may also lead to reduction the effective thermal conductivity because the low thermal conductivity of Ge material. Since many interfaces are existed in the QD superlattices, the effective thermal conductivity only decreases with the increasing QD density, and it qualitatively and quantitatively agree with the experimental measurements.

並列關鍵字

Thin-film ； Superlattice ； Quantum dot ； Lattice thermal conductivity ； Density of states ； Non-equilibrium molecular dynamics

參考文獻

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