鍺錫/鍺異質結構二維電洞氣之Rashba自旋-軌域耦合效應與等效質量

Rashba spin-orbit coupling and effective mass of two-dimensional hole gases in GeSn/Ge heterostructures

戴嘉澤(Chia-Tse Tai)

指導教授 ： 李峻霣

國立臺灣大學/電機資訊學院/電子工程學研究所/碩士(2021年)

https://doi.org/10.6342/NTU202100161

摘要

自旋電子元件因為其低功耗的特性而被視為極具發展性的元件，如自旋電晶體和磁阻式記憶體。透過自旋-軌域耦合效應，我們可以利用外加電場操控電子自旋態，此外，自旋-軌域耦合效應也被利用在自旋量子位元中，藉以達到高速量子計算。在四族材料中，鍺錫因為較大的自旋-軌域耦合效應及較小的等效質量，而被視為具發展潛力的自旋電子材料，然而，迄今尚未有文獻探討關於鍺錫薄膜的量子傳輸性質。
在本論文中，三種無摻雜且錫比例分別為6%、9%及11%的鍺錫/鍺異質結構，經由化學氣相沉積磊晶而成。我們將樣品製作成具閘極之霍爾棒元件，在低溫系統量測其量子傳輸性質，並探討了這些無摻雜鍺錫/鍺異質結構中所形成的二維電洞氣電性以及磁傳輸特性，並首次在無摻雜鍺錫系統中展現高遷移率的二維電洞氣。我們透過Shubnikov-de Haas振盪震幅隨溫度的關係萃取出二維電洞氣的等效電洞質量，並發現等效質量(從0.07 m0到 0.10 m0)隨電洞濃度(從2.7×10^11 cm^-2 到 6.1×10^11 cm^-2)線性增加。我們將等效質量隨電洞濃度上升的趨勢歸因於鍺錫量子井中價帶的非拋物線性，這三種鍺錫/鍺異質結構(錫比例為6%、9%及11%)的非拋物線性因子分別為8.0 eV^-1、4.9 eV^-1及 4.0 eV^-1。等效質量和非拋物線性因子在較高錫比例的鍺錫異質結構中較小，我們認為這起因於高錫濃度所造成的壓縮應變，導致價帶結構中的重電洞能帶有較大的形變且增加了重電洞能帶和輕電洞能帶之間的能量差。
我們亦探討了這三種鍺錫/鍺異質結構中的Rashba自旋-軌域耦合效應。透過量測低溫磁導率隨磁場變化並利用Hikami-Larkin-Nagaoka (HLN)公式擬合實驗數據點，可萃取相位同調時間(phase-coherence time)、自旋鬆弛時間(spin-relaxation time)、自旋進動時間(spin-precession time)、k立方Rashba參數(k-cubic Rashba coefficient)以及自旋能帶分裂能量(spin-splitting energy)。我們驗證了Rashba自旋-軌域耦合效應隨閘極偏壓的可調性，並得到在目前所有四族材料中最大的Rashba自旋-軌域耦合強度。同時，我們也發現Rashba自旋-軌域耦合效應有隨錫比例增加而減弱的趨勢，我們將此歸因於壓縮應變對Rashba自旋-軌域耦合效應的影響。較大的壓縮應變增強了角動量在磊晶成長方向(z)的量子化效應，進而抑制了由自旋-軌域耦合效應產生的等效磁場所造成的在量子井平面(x-y)的量子化效應。最後，我們藉由相位同調時間和溫度的關係，探討在鍺錫/鍺異質結構中二維電洞氣的退相干(de-phasing)機制，實驗結果顯示相位同調時間和溫度倒數成正比，其退相干機制主要為電洞-電洞之間的非彈性散射。

關鍵字

鍺錫/鍺異質結構 ； 二維電洞氣 ； 磁傳輸性質 ； 等效電洞質量 ； Rashba自旋-軌域耦合效應 ； 非拋物線性 ； Shubnikov-de Haas震盪

並列摘要

Spintronic devices such as spin field-effect transistors (FETs) and magneto-resistive random access memory (MRAM) are promising due to their low power consumption for the manipulation of spins. Spin-orbit coupling (SOC) provides a way to control the spin states through electrical gating. In addition, SOC also plays an important role in spin-based quantum computing, which enables fast spin qubit operations. Among group-IV materials, GeSn is a promising candidate for its physical properties such as expected larger SOC effect and smaller effective mass. However, there are few works on the quantum-transport properties of GeSn-based undoped heterostructures.
In this thesis, three undoped GeSn/Ge heterostructures with different Sn fractions of 6%, 9%, and 11% are epitaxially grown by chemical vapor deposition and gated Hall bar devices are fabricated for magneto-transport measurements at cryogenic temperatures. We investigate both the electro- and magneto-transport properties of the undoped GeSn/Ge heterostructures and demonstrate the first two-dimensional hole gas in this material system by gating. Hole effective masses are extracted from the temperature-dependent amplitudes of Shubnikov-de Haas oscillations, and it increases linearly from 0.07 m0 to 0.10 m0 as the carrier density varies from 2.7×10^11 cm^-2 to 6.1×10^11 cm^-2. We attribute the effective mass increment to the non-parabolicity effect on the valence band with the non-parabolicity factor of 8.0 eV^-1, 4.9 eV^-1, and 4.0 eV^-1 for the Ge0.94Sn0.06, Ge0.91Sn0.09, Ge0.89Sn0.11 devices, respectively. Both the hole effective mass and the non-parabolicity factor are smaller in the GeSn/Ge heterostructures with a higher Sn fraction due to the larger compressive strain, which leads to a larger band deformation and energy splitting between the heavy-hole and light-hole bands.
We also studied the Rashba SOC effect in the GeSn/Ge heterostructures. Magneto-conductivity is measured and fitted to the Hikami-Larkin-Nagaoka (HLN) model. Phase-coherence time, spin-relaxation time, spin-precession time, k-cubic Rashba coefficient, and spin-splitting energy are extracted. We demonstrate the tunability of the Rashba SOC strength through gating and the strongest Rashba SOC among all group-IV materials. As the Sn fraction increases, the Rashba SOC strength becomes weaker, which is attributed to the effect of strain. The stronger compressive stain in higher Sn device enhances the quantization of angular momentum along the growth (z) direction instead along the direction of an SOC-induced magnetic field (x-y plane). The de-phasing mechanism is also investigated and the relation between phase-coherence time (τ_ϕ) and temperature (τ_ϕ∝T^(-1)) suggests the dominant de-phasing mechanism is hole-hole scattering.

並列關鍵字

GeSn/Ge heterostructures ； two-dimensional hole gas (2DHG) ； magneto-transport property ； hole effective mass ； Rashba spin-orbit coupling (SOC) ； non-parabolicity ； Shubnikov-de Hass (SdH) oscillations

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