二矽化鈷薄膜中量子干涉效應之研究

Abstract

二矽化鈷是在半導體工業中常見的矽化物之一。它的晶格結構與矽非常相似，因此易於在矽基板上形成良好的二矽化鈷磊晶層，並擁有低電阻率與長的彈性平均自由徑。它也是極少數擁有超導性的矽化物之一。在這篇研究中，我們探討電子在二矽化鈷薄膜中的傳輸特性。其中最讓我們感興趣的是，在低溫時的量子干涉校應(反弱局域效應)，以及它所牽涉到的相位同調時間與超導漲落效應。

我們使用固相磊晶的方式來製備二矽化鈷薄膜。基本的製程是先蒸鍍一層鈷薄膜於矽基板上，接著進行高溫退火使鈷原子擴散後形成二矽化鈷。為了瞭解不同無序程度對電子傳輸特性的影響，我們改變薄膜厚度(53 或 25 奈米)以及矽基板方向(<100>或<111>)，並於不同溫度與磁場中，以精密電阻橋量測樣品的電阻變化。它們的低溫(4 K)電阻率介於2.2到5μΩ∙cm之間。其磁電阻(+/- 1 Tesla)在高磁場區會呈現近似拋物線的正磁電阻曲線，我們可以從中分析出載子的平均自由徑，其值約介於50到130奈米。另外，樣品厚度越薄則超導轉變溫度越低，其值約介於1.2到1.5 K之間。

在4到20 K之間，低磁場範圍(+/- 0.2 Tesla)的磁電阻曲線，會在零磁場處呈現明顯的凹陷(dip)。這正是反弱局域效應的特徵，並且表明了此材料有強的自旋軌道偶合。我們利用二維弱局域效應的磁電阻公式並加入超導漲落的貢獻來分析此現象，並藉此得到不同溫度下的相位相干長度L_φ以及超導漲落效應的強度參數β。其中，L_φ長度比一般導體的要長許多，可以超過一微米。而β值會比它的理論預測值要低一些，這可以歸因於強的自旋軌道偶合，它會使虛庫柏電子對(virtual Cooper pair)的自旋匹配更容易被破壞。另外，將相位相干長度L_φ轉換為退相干率(1/τ_φ)之後，我們發現彈性平均自由徑較短的樣品，其1/τ_φ值通常較高。且1/τ_φ在低溫及高溫區分別有趨近1/τ_φ~T^1以及1/τ_φ~T^3的情形。低溫區1/τ_φ~T^1的來源主要是二維的電子-電子散射(1/τ_ee)。經由強無序的極限來推估1/τ_ee的散射強度(A_ee)理論值之後，我們發現理論值和實驗值都落在1×〖10〗^9 Hz/T^3的量級。1/τ_φ~T^3的結果則符合電子-聲子散射理論的乾淨極限之溫度相依關係。其散射強度的理論值和實驗值都落在1×〖10〗^7 Hz/T的量級。此結果對二矽化鈷來說實屬合理，因為其彈性平均自由徑會比其聲子波長長許多，以致於以電子-聲子散射的角度來看，確實是趨近於乾淨極限的理論模型。

相較於以前文獻中的分析方式，我們發現在分析磁電阻時無法忽略超導漲落效應的貢獻。而強自旋軌道偶合的來源也還不明確，但它和樣品的無序度則沒有明顯的相依關係。我們希望這些實驗結果能對於二矽化鈷未來的應用有所幫助。

Cobalt disilicide (CoSi_2) is a kind of common silicides in semiconductor industry. The crystal structure of CoSi_2 is very similar to silicon, so it's ready to grow good epitaxial layers on silicon substrates and the resulting CoSi_2 possesses low resistivity and long elastic mean free path (l_e). It also one of the very few silicides which have superconductivity. In this study, we investigate the electronic transport properties in the CoSi_2 layers. One of the most interested issues for us is the quantum interference effects (e.g. weak anti-localization effect), the related phase coherent length and superconducting (SC) fluctuation effect at low temperatures.

The CoSi_2 layers are made by the method of solid phase epitaxy. Briefly speaking, we deposit patterned cobalt films on pure silicon substrates, and then perform a high-temperature annaeling to drive cobalt diffusion and form CoSi_2 layers. To understand the effect of disorderness on the electrical transport in CoSi_2, we have made samples of different thicknesses (53 and 25 nm) on the substrates of different crystal orientations (Si<100> and Si<111>) and measured them with a low-noise AC resistance bridge at variable temperatures and magnetic fields. The resistivities at 4 Kelvin are between 2.2 and 5 μΩ⋅cm. The magneto-resistances (MRs) within +/- 1 Tesla are positive and show parabolic shape in the high-field region (0.2 - 1 Tesla). From these data, we can extract the carrier mobilities and l_e's which range from 50 to 130 nm. Besides, the thinner the CoSi2 layers, the lower the superconducting transition temperatures (Tc). Their Tc's locate between 1.2 and 1.5 K.

As the temperature is between 4 K and 20 K, the low-field (+/- 0.2 Tesla) MRs reveal clear sharp dips at zero field. The dips are just the signature of weak anti-localization (WAL) and indicate strong spin-orbit coupling (SOC) in this material. We utilize the well established theory of two-dimentional (2D) WAL effect and SC fluctuation to analyze the data and hence extract phase coherent lengths L_φ and the strength parameter β of SC fluctuation at different temperatures. After the analysis, we found that the L_φ can be longer than one micron which is much longer than those in normal conductors. The β is smaller than the theoretical value. This result can be attributed to the strong SOC which induces spin mismatch on the virtual Cooper pairs more quickly. After the L_φ is transformed into dephasing rate (1/τ_φ), we found a rough trend that the samples of shorter le's show higher dephasing rates. Furthermore, 1/τ_φ has two distinct temperature dependences in low-T and high-T regimes, that is, 1/τ_φ~T^1 and 1/τ_φ~T^3, respectively. In the low-T regime, the origin of 1/τ_φ~T^1 is mainly due to electron-electron (e-e) scattering (1/τ_ee) in 2D systems. With the theoretical estimation of e-e scattering strength Aee in the dirty limit, we found that the theoretical Aee is close to the experimental one extracted from 1/τ_φ and both lie in the order of magnitude of 1×〖10〗^9 Hz/T. The temperature dependence of 1/τ_φ~T^3 at higher temperatures fits the theoretical description of electron-phonon scattering (e-ph) rate in the clean limit. The theoretical and experimental e-ph scattering strength A_ep's are both in the order of magnitude of 1×〖10〗^7Hz/T^3. This result is reasonable for our samples because the le is much longer than the phonon wavelength such that the e-ph scattering in CoSi_2 actually corresponds to the model of clean limit.

Comparing to analysis method in the literature, we have found that the curve-fitting of our MRs can not be well done if we do not include the SC fluctuation effect. Another unclear point is the strong SOC in this material. From our result, the SOC strength seems no dependence on the disorderness (i.e. l_e). We hope our study can help to develop more future applications with CoSi_2.