本文針對提升超導性的手法，提出物理學模型，來擴展McMillan關於耦合強度等於2的結果。本文研究通過調整聲子頻率、載子數或壓力，來增加超導臨界溫度的策略。特別是，我們展示了與聲子頻率、載子數或壓力對應的臨界耦合常數，其決定了超導溫度變化的趨勢是上升還是下降。本文解釋了弱耦合和強耦合超導體之間相反行為的原因，且與文獻研究一致。本文還展示了載子數效應和壓力效應中觀察到的「穹頂」現象。此外，本文藉由臨界耦合常數，系統性地將超導體分為三個類別：弱耦合、中等耦合和強耦合。本文發現，弱耦合超導和強耦合超導的增強策略是完全相反的，但都不可避免地將超導性帶入中等耦合性。最後，我們提出了用於進一步增加中等耦合超導體臨界溫度的一般性方法：Zigzag方法。

藉由此物理學模型的指引，本研究以粉末燒結法製備多元高熵氧化物塊材，研究其低溫電性質。設計成份由前述超導理論指引，據此選用高德拜溫度、多電子元素、小原子元素且多元高熵化配方，製備含多元的高熵氧化物塊材，分為兩個系列，稱為DCC、DCCC系列，共計16種氧化物。兩系列化合物皆是由鉍-鍶-鈣-銅-氧系統比例出發，DCC選用碳化鈦、磷酸鋁、氮化硼、矽、氟化鈉、銅、氧化釔、氧化鉍等元素；DCCC較DCC增加氧化鑭、鈮、碳酸鋰、硫化鎢。兩系列粉末皆以銅作為變量，量測其在800、850℃大氣燒結48小時後的電性。低溫電阻率量測結果皆呈現半導體行為，電阻隨銅含量增加而下降。聲速量測發現，電阻率的大小與聲速有相關性，電阻率越小、聲速越大。

In this study, we propose a phenomenological model to extend McMillan's results on a coupling strength equal to 2. We investigate possible strategies to enhance superconductivity by tuning the phonon frequency, carrier number, or pressure. In particular, we show that the critical coupling constants corresponding to the phonon frequency, carrier number, or pressure determine whether the variation of the critical temperature is positive or negative. These observations explain the contrasting behavior between weak and strong coupling superconductors and are consistent with experimental observations. We also demonstrate the dome observed in the carrier number effect and pressure effect. Additionally, these critical coupling constants systematically separate superconductivity into three regions: weak, intermediate, and strong coupling. We find that the enhancement strategies for weak and strong coupling regions are opposite, but both inevitably bring superconductivity into the intermediate coupling region. Finally, we propose general zigzag methods for intermediate coupling superconductors to further enhance the critical temperature.
Using this physical model as a guide, the experiments prepared multi-component high-entropy oxide bulk materials through powder sintering and studied their low-temperature electrical properties. The composition was designed based on superconductivity theory, selecting high-Debye temperature, multi-electron elements, and a mixture of diverse elements to prepare high-entropy oxide bulk materials, divided into two series, totaling 16 oxide materials. Both series of compounds started with the bismuth-strontium-calcium-copper-oxygen system, referred to as the DCC and DCCC series. DCC included elements such as titanium carbide, aluminum phosphate, boron nitride, silicon, sodium fluoride, copper, yttrium oxide, and bismuth oxide, while DCCC, in addition to DCC elements, added lanthanum oxide, niobium, and lithium carbonate. Copper content was varied in both series, and their electrical properties were measured after sintering in the atmosphere at 800℃ and 850℃ for 48 hours. The low-temperature electrical resistivity measurements showed semiconductor behavior, with resistance decreasing as the copper content increased.

第一章 前言 19
第二章 文獻回顧 21
2.1 超導物理現象 21
2.1.1 超導發現的歷史進程 21
2.1.2 高溫超導與近年超導的發展 24
2.1.3 Type I、Type II超導與理論的關係 25
2.2 超導材料的介紹 27
2.2.1 元素超導 27
2.2.1 合金超導 28
2.2.2 金屬化合物超導 29
2.2.3 碳基超導和有機超導 30
2.2.4 銅氧化物超導 32
2.2.5 鐵基超導 33
2.2.6 二硼化鎂 34
2.2.7 富氫超導 35
2.2.8 鎳基超導 39
2.2.9 高熵合金與高熵合金超導 40
2.2.10 高熵氧化物超導的研究 44
2.3 文獻上改變Tc的研究 46
2.3.1 同位素效應 46
2.3.2 聲子頻率 49
2.3.3 壓力 53
2.3.4 單位晶包大小 61
2.3.5 銅氧面數量 63
2.3.6 氫摻雜 64
2.3.7 異質載子摻雜 68
2.3.8 閘控偏壓 70
2.3.9 多元元數 73
2.3.10 膜厚 74
2.4 統整增加超導性方法的分類與分析 77
2.5 超導理論 79
2.5.1 BCS理論 79
2.5.2 BCS修正理論 80
2.5.3 BCS的理論上限？ 83
2.5.4 超導密度泛函理論 84
2.5.5 超導性對一般態電導的影響 86
2.5.6 超導趨勢與相關變數的關係 87
2.5.7 超導趨勢在不同超導材料中的差異、穹頂現象 88
第三章 超導性的臨界耦合常數理論建模 89
3.1 理論建模 89
3.1.1 理論分析 89
3.1.2 超導電聲交互作用 93
3.1.3 超導與聲子頻率Ω的關係 94
3.1.4 超導與載子數Z的關係 96
3.1.5 超導與壓力P的關係 98
第四章 超導性的臨界耦合常數理論分析 100
4.1 穹頂的成因 100
4.2 臨界溫度Tc與聲子頻率Ω的關係 102
4.3 臨界溫度Tc與載子數量Z的關係 104
4.4 臨界溫度Tc與壓力效應P的關係 106
4.5 提高臨界溫度Tc的策略 108
第五章 DCC高熵氧化物製備與電性研究 113
5.1 研究規劃 113
5.1.1 高熵氧化物材料作為尋找常溫超導之優勢 113
5.1.2 DCC高熵氧化物配方設計理念 116
5.1.3 研究過程 121
5.1.4 電性分析 121
5.1.5 材料分析 121
5.2 DCC系列電性量測研究 122
5.2.1 DCC6 122
5.2.2 DCC7 123
5.2.3 DCC8 124
5.2.4 DCC9 125
5.2.5 DCC10 126
5.2.6 DCC11 128
5.2.7 DCC12 130
5.2.8 DCC13 132
5.2.9 DCC14 134
5.2.10 DCC電阻表 136
5.3 SEM電子顯微鏡量測 140
5.4 DCC聲速量測 141
5.5 DCC系列研究討論 143
第六章 DCCC高熵氧化物製備與電性研究 145
6.1 研究規劃 145
6.1.1 DCCC高熵氧化物配方設計理念 145
6.1.2 研究過程 146
6.1.3 電性分析 146
6.1.4 材料分析 146
6.2 DCCC系列電性量測研究 148
6.2.1 DCCC6 148
6.2.2 DCCC7 149
6.2.3 DCCC8 150
6.2.4 DCCC9 151
6.2.5 DCCC10 152
6.2.6 DCCC11 153
6.2.7 DCCC12 154
6.2.8 DCCC13 155
6.2.9 DCCC14 156
6.2.10 DCCC電阻表 157
6.3 SEM-EDS電子顯微鏡量測 160
6.4 DCCC聲速量測 161
6.5 DCCC系列研究討論 162
6.6 未來建議研究方向 163
第七章 結論 166
第八章 本研究的貢獻 168
第九章 附表 170
9.1 DCC7-EDS 170
9.2 DCC12-EDS 171
9.1 DCCC7-EDS 172
9.2 DCCC12-EDS 173
9.3 DCC與DCCC EDS比較 174
第十章 參考文獻 175

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