探討高熱導率材料的超長聲子平均自由徑

Investigation of Ultra-Long Phonon Mean Free Paths in a High Thermal Conductivity Material

周廷翰(Ting-Han Chou)

指導教授 ： 孫啟光

國立臺灣大學/電機資訊學院/光電工程學研究所/碩士(2019年)

https://doi.org/10.6342/NTU201900045

摘要

熱管理(thermal management)是現代電子元件所面臨的重大挑戰，高熱導率材料可以用來耗散電子元件產生的廢熱已達到增進元件效能與延長元件使用週期的目的，由於非金屬結晶固體擁有優越的高熱導率，了解這些晶體的熱傳導特性引起了學術研究上與實際應用上的極大興趣。在室溫下晶體的熱傳主要是由兆赫(THz)頻段的聲學聲子所主宰，這些帶熱聲子的平均自由徑(mean free path)與傳播時的散射機制是熱傳上最為重要同時也是最少被了解的資訊，過去許多研究試圖通過各種技術去實驗量測或是理論計算聲子的平均自由徑來解釋固體導熱的物理根本，然而高熱導率材料的聲子平均自由徑(尤其在兆赫頻段)還從未被準確量測過，因此，本研究的目的在於釐清一個帶熱聲子(兆赫聲學聲子)在高熱導率晶體裡能傳播多長的距離，並且了解哪些聲子散射機制會在傳播過程中發生並限制了聲子平均自由徑。這份研究的價值並不僅限於了解熱傳的物理根本與開發熱管理元件，還可以延伸到同調聲子的應用像是高解析度超音波顯微術、原子層介面量測技術、與高溫聲學孤立子之探討。
在此論文中，我們使用先進的光學激發-偵測(pump-probe)系統與特殊的樣品結構來直接地量測室溫下1-1.4 THz聲學聲子的平均自由徑，我們藉由比較不同溫度下量測到的聲學衰減以消除晶格缺陷散射與介面散射這些外來因素，並獲得氮化鎵晶體(GaN)的本質聲子平均自由徑長達3.5-5.2微米，此聲子平均自由徑只有考慮聲學聲子與熱聲子之間的交互作用，這些結果不僅給出了關鍵證據來證明高熱導率晶體具有微米等級的聲子平均自由徑，我們更證明了第一原理計算可以用來準確預測兆赫聲子的平均自由徑。根據第一原理計算，我們很驚訝地發現了對於氮化鎵晶體來說，1 THz聲學聲子傳播主要是由一個聲學聲子與兩個光學聲子之間的交互作用所主宰，這對於過去所有的同調聲子研究是一個完全出乎意料的結果。我們將這個發現歸因於氮化鎵晶體的特殊聲子色散關係，我們認為此交互作用可以在其他具有相似聲子特性的晶體內發現，並預期具有更高熱導率的晶體可以展現更長的聲子平均自由徑，此外，藉由比較碲化鉛晶體(PbTe)的非彈性X光散射量測結果，我們建立了兆赫聲學聲子的平均自由徑與晶體熱導率之間的正向關係。

關鍵字

高熱導率材料 ； 兆赫聲學 ； 聲子平均自由徑 ； 聲子間交互作用 ； 氮化鎵

並列摘要

Thermal management is a major challenge for the modern electronic devices. High thermal conductivity materials are needed for heat dissipation to improve device performance and extend device lifetime. Since non-metallic crystalline solids possess exceptional high thermal conductivity, studying thermal transport properties in these crystals intrigue the great interests from both academic researches and practical applications. At room temperature, thermal transport in crystalline solids is dominated by acoustic phonons in THz frequency range. Mean free paths (MFP) and scattering mechanisms of these heat-carrying phonons are the most important but the least understood factors to thermal transport. Previous studies attempt to measure and calculate the phonon MFPs to explain the origin of solid’s thermal conductivity. However, the phonon MFPs (especially in THz range) in high thermal conductivity materials has yet been accurately measured. Thus, the goal of this work is to solve a fundamental issue of how long can a heat-carrying phonon (THz acoustic phonon) propagate in high thermal conductivity crystals and what scattering mechanisms will occur during the propagation and limit the phonon MFP. The impact of this study is not limited to thermal transport researches and thermal management applications, but can be extended to coherent phonon applications such as high-resolution ultrasonic imaging, atomically-thin interface probing technique, and acoustic solitons at higher temperature.
In this thesis, we use an advanced optical pump-probe system and an unique sample structure to directly measure the MFPs of acoustic phonons at 1-1.4 THz at room temperature. To eliminate the extrinsic factors of scattering by lattice imperfection and interface roughness, we compare the measure acoustic attenuation at different temperature and obtain the intrinsic phonon MFPs of 3.5-5.2 µm in GaN, which are only associated with interactions with thermal phonons. Our results not only give a critical experimental evidence of micrometer-long phonon MFPs in high thermal conductivity crystals, we further prove that first-principles calculations can accurately predict THz phonon MFPs. According to first-principles calculations, we surprisingly find the interactions between one acoustic phonon and two optical phonons provide a dominant scattering channel to 1 THz acoustic phonon transport in GaN. This result is totally unexpected for the previous coherent phonon researches. We attribute this finding to the special phonon dispersion in GaN. This interaction is considered to occur in other crystals with similar phonon properties and the higher thermal conductivity crystals are expected to exhibit the longer phonon MFPs. Furthermore, by comparing with inelastic x-ray scattering measurements on PbTe, we establish a positive correlation between THz acoustic phonon MFPs and thermal conductivity.

並列關鍵字

high thermal conductivity ； THz acoustics ； phonon mean free path ； phonon-phonon interactions ； Gallium Nitride

參考文獻

1. P. Ball, Feeling the heat. Nature, 492, 174-176 (2012).

2. M.M. Waldrop, More than moore. Nature, 530, 144-147 (2016).

3. A.S. Shehabi, Sarah ; Sartor, Dale ; Brown, Richard ; Herrlin, Magnus ; Koomey, Jonathan ; Masanet, Eric R ; Horner, Nathaniel ; Azevedo , Inês ; Lintner, William., United States Data Center Energy Usage Report. (2016).

4. G.A. Slack, Nonmetallic crystals with high thermal conductivity. Journal of Physics and Chemistry of Solids, 34, 321-335 (1973).

5. J. Callaway, Model for Lattice Thermal Conductivity at Low Temperatures. Physical Review, 113, 1046-1051 (1959).