對矽基量子點量子位元裝置電荷穩定性之有效分析

Efficient Evaluation of the Charge Stability in Silicon-based Quantum Dot Qubit Devices

羅鈺凱(Yu-Kai Lo)

指導教授 ： 管希聖

國立臺灣大學/理學院/物理學研究所/碩士(2020年)

https://doi.org/10.6342/NTU202000568

摘要

低溫電子裝置的快速開發具有相當成本，一部分源自於其冗長而昂貴的實驗環境設置。其中，低溫奈米結構的有效建模與模擬能夠輔助，甚至取代實驗進行，大幅降低其測試成本，因而成為產業需要的重點技術之一。為了將模型套用到新穎架購，最直覺的做法便是將既有的傳統元件建模方法進行延伸。然而，低溫奈米元件通常牽涉到低維度與量子現象，其與傳統模型的巨觀物理並沒有直接相容，導致建模上的困難。其中，以傳統電晶體所構成的量子計算架購為例，其模型必須能準確解釋其電荷穩定性，以及奈米結構區域與其餘巨觀結構之量子相關性。以元件構成的角度來看，其中又以電荷穩定性尤為重要，畢竟若是無法掌握電荷分布，其餘對載子特性的討論都沒有意義。現今已有多個針對此類裝置的建模方案，但都無法全面地掌握所有重要物理特性。在本作品中，我基於現有的方案提出了一個新方法，並探討處理低溫奈米結構建模時的諸多考量。作為驗證，我將新模型應用在近期重要的裝置實驗上，並重現了一部分對於量子計算來說相當關鍵的元件特性。

關鍵字

電荷穩定性圖 ； 低溫物理學 ； 有限元素方法 ； 混合模型 ； 側向量子點 ； 自洽場方法 ； 半導體裝置建模

並列摘要

Efficient modeling of cryogenic nano-structures has long being demanded due to its utility in rapid device development, which is critical to cut manufacturing cost from the expensive, lengthy setup of low-temperature experiments. To adapt to the novel architectures, one would naturally try to extend the existing standard modeling methods which have been reliable in describing conventional devices. But there are, however, some daunting bottlenecks which would generally emerge when multiple scales of physical phenomenons are involved. For instance, in the context of modeling quantum computing devices based on conventional transistor architectures, it is crucial that a model could accurately resolve the charge stability of the device, and the quantum correlations sourced from the nano-structure region and its coupling to the macroscopic environment. Among the requirements, the charge stability is the most important in a formative point of view: If there is no charge loaded, nothing else can be done. While there have been several approaches to this problem, some of the commonly taken ones are shown to suffer from the inability to address all the relevant physics. In this work, I propose a new procedure based on previous approaches to deal with the downsides, and study several essential aspects of cryogenic semiconductor device modeling. To justify this new procedure, I have applied it to model a chosen notable work, and have reproduced some key characteristics that are considered pivotal to a promising qubit device.

並列關鍵字

Charge stability diagram ； Cryogenics ； Finite element method ； Hybrid model ； Lateral quantum dot ； Self-Consistent field method ； Semiconductor device modeling

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