在本論文中我設計並完成了一根用於測試或表徵超導量子元件的低溫微波探頭。本論文將詳述此量測棒背後設計的物理理念。該量測棒可插入於液態氦桶或商用低溫恆溫器(Cryostat)中，其基本上可操作在1.5 K至室溫的範圍。此外，量測棒具備微波(2 ~ 8 GHz)與電訊號量測的處理能力。在微波量測的部分，我們留下一些連接端口，以便於將來擴展其功能。目前，我們的目標是將此量測棒用於量測特定類型的元件，例如底材為鈮的超導參數放大器。在微波量測的考量下，該量測棒包含一條裝置了50 dB衰減器的微波輸入線，以及與低溫隔離器、大約在4.2 K的低溫高電子遷移率放大器(High electron mobility transistor, HEMT)、室溫下40dB微波放大器集成的微波輸入線。此設計是為了消除輸入訊號的外部環境雜訊，同時避免HEMT引起的回授雜訊。該量測棒可在2 ~ 10 GHz且低至1.5 K的溫度條件下，使用約 -130 dBm的衰減與80 dB的增益執行微波量測。我們詳述了測試結果並討論了雜訊的問題，指出了未來的改進方向。在附錄中，我附上了量測棒各部份的詳細示意圖，以及HEMT的一些初步研究，包括其設計的佈局和開發的製程步驟。

This thesis is devoted to implement a versatile insert for use to test or characterize superconducting quantum devices. This probe can be inserted to liquid helium tank or cryostat, operable from 1.5 K up to room temperature and equipped with microwave (2 - 8 GHz), and electric measurement capabilities. We leave few flexible connection ports to extend its functions in the future. Currently, we aim to use this insert for a specific type of device, namely Nb-based Josephson parametric amplifier. The probe contains a microwave input line added with attenuators of 50 dB, and output line integrated with an isolator followed by a high electron mobilities transistor (HEMT) at around 4.2K and 40 dB microwave amplifier at room temperature. This design is for eliminating external environment noise for input signals, and meanwhile to avoid back noise induced by HEMT. This insert can perform microwave measurement with -130 dBm excitation, 80 dB gain over 2-10 GHz, down to 1.5 K. We describe the detailed testing results, discuss the noise issues, and indicate the improvement directions in the future. In the appendix, I append the detailed schematic diagram of each parts of the insert, and some preliminary studies of HEMT device, including its design layout and fabrication processes developed.

摘要 i
Abstract ii
致謝 iii
目錄 iv
第一章 緒論 1
1.1研究動機 1
1.2論文架構 2
第二章 量測棒設計的考量 4
2.1量測棒的熱傳探討 4
2.1.1量測棒材料的影響-熱傳導 (Thermal conduction) 4
2.1.2輻射熱的阻擋-熱輻射 (Heat radiation) 6
2.1.3量測棒溫控的考量-熱對流 (Heat convection) 8
2.2阻抗匹配的議題 9
2.2.1傳輸線理論 9
2.2.2散射參數 12
2.3元件產生共振腔模態的考量 14
2.3.1波導 (Waveguide) 14
2.3.2矩形共振腔 (Cavity resonator) 18
2.4放大器的雜訊探討 22
2.4.2元件雜訊 24
2.4.3雜訊量測-冷衰減法 25
第三章 量測棒的設計與計算 28
3.1冷卻系統的限制 28
3.2熱傳的限制 29
3.1.4材料的考量-熱傳導 29
3.2.2輻射屏的設置-熱輻射 31
3.2.3溫控的設計-熱對流 32
3.3液態氦的消耗估計 32
3.4 量測棒設計與規格 36
3.5預期規格 42
3.5.1量測系統架構 42
3.5.2量測棒預期規格 44
3.5.3預期元件規格 45
3.6線長與元件造成之影響 46
第四章 微波元件的測試結果 53
4.1微波元件的介紹與量測 53
4.1.1元件介紹 53
4.1.2微波元件的量測 56
4.2 量測小結 62
第五章 總結與未來工作 65
參考文獻 68
附錄一 量測棒工程圖 70
附錄二 高電子遷移率電晶體 85
A2.1 高載子遷移率電晶體 85
A2.2 文獻探討 88
A2.3光罩設計 94
A2.4 樣品製程 96
A2.4.1製程介紹 97
A2.4.2實驗小結 106
附錄的參考文獻 108

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