本研究探討了摻磷矽樣品經過不同退火時間後的二次諧波產生（Second Harmonic Generation, SHG）特性。我們選擇了兩種類型的摻磷矽樣品進行比較：一種是經過離子注入(ion-implanted)技術摻磷的Si(111)樣品，另一種是通過原位摻雜(in-situ doping)技術摻磷的Si(100)樣品。每種樣品分別在不同的退火時間下進行處理，以研究退火過程對材料非線性光學特性的影響。
在實驗中，我們使用二次諧波產生技術對兩種樣品進行光學測量，包括非線性極化強度 P^((2))與電場 E^((2ω)) 的計算公式。通過設置多種參數，如振幅、相位、基底和表面態的非線性係數，我們確定了材料的二階非線性系數 χ^((2))。實驗結果顯示，不同退火時間對兩種樣品的二次諧波強度均有顯著影響。具體而言，經過離子注入摻磷的Si(111)樣品利用傳統的傅立葉分析方法，接著我們以其作為SBHM模擬中，各個數值(a_1 、a_2 、a_3 、a_4 、a_b 、a_sd)的基礎，去模擬分析不同退火條件下原位摻雜的Si(100)樣品。
我們的數據擬合結果基於理論模型，考慮了材料的非線性極化強度及其電場分量，從而揭示了摻磷濃度和退火時間對材料非線性光學響應的影響機制。這些發現不僅有助於理解摻雜和熱處理對矽材料光學特性的調控作用，還對於設計和優化矽基光電子器件具有重要參考價值。通過這項研究，我們展示了不同退火時間下摻磷矽樣品的SHG特性，透過SBHM分析方式來分析離子佈值經退火後的品質分析，證實由於傳統傅立葉分析，特別對於尚未完成結晶之破壞。藉由此結果，可以進一步利用SBHM來分析CVD成長 in-situ doping Si 超薄膜之結構變遷。這此作除了發展一套可以分析超薄膜的退火分析之實驗方式與機制，更可以從SBHM的結果了解超薄膜結構之鍵結形式。

This study thoroughly investigates the Second Harmonic Generation (SHG) characteristics of phosphorus-doped silicon samples following various annealing durations. The research focuses on comparing two types of phosphorus-doped silicon samples: one doped using the ion-implantation technique on Si(111) and the other doped using in-situ doping on Si(100). The samples were subjected to different annealing times to examine the impact of the annealing process on the nonlinear optical properties of the materials.
In the experiments, we used SHG techniques for optical measurements on both types of samples, including the calculation formulas for the nonlinear polarization intensity P^((2))and the electric field E^((2ω)). By setting multiple parameters such as amplitude, phase, and the nonlinear coefficients of bulk and surface states, we determined the second-order nonlinear coefficients χ^((2)) of the materials. The experimental results showed that different annealing times had significant effects on the SHG intensity of both types of samples. Specifically, for the ion-implanted phosphorus-doped Si(111) samples, we used the traditional Fourier analysis method as the basis for the SBHM simulation, analyzing various parameters(a_1 、a_2 、a_3 、a_4 、a_b 、a_sd) under different annealing conditions for the in-situ doped Si(100) samples.
The data fitting results, based on a theoretical model that considers the nonlinear polarization intensity and its corresponding electric field components, provided a detailed understanding of the influence mechanisms of phosphorus concentration and annealing time on the nonlinear optical response of the materials. These findings are crucial for comprehending how doping and thermal treatments regulate the optical properties of silicon materials. Additionally, they serve as an important reference for the design and optimization of silicon-based optoelectronic devices. The study highlights the effectiveness of the SBHM model in analyzing these complex interactions within the materials, thereby contributing to the development of advanced models for predicting and controlling material properties.
Moreover, the research demonstrates the critical role of SHG as a sensitive and non-destructive optical technique for probing the internal structures and properties of doped silicon. By comparing the SHG responses of the two types of samples, the study provides a clearer picture of how different doping techniques and annealing processes influence the nonlinear optical characteristics of silicon. For instance, the ion-implanted samples exhibited distinct SHG patterns compared to the in-situ doped samples, reflecting the differences in how phosphorus atoms integrate into the silicon lattice during the doping process. These differences are further influenced by the annealing conditions, which can cause changes in the crystal structure, defect density, and overall material quality.
The insights gained from this study not only advance the understanding of the relationship between doping, annealing, and nonlinear optical properties in silicon but also open up new avenues for the application of SHG in material science. The ability to accurately measure and analyze SHG responses under varying conditions allows researchers to fine-tune the doping and annealing processes to achieve desired optical properties, which is critical for the development of next-generation silicon-based photonic devices. Additionally, the study underscores the potential of combining traditional analysis methods with advanced models like SBHM to achieve a more comprehensive understanding of complex material behaviors.
Through this extensive research, we demonstrated the SHG characteristics of phosphorus-doped silicon samples under different annealing times and performed an in-depth analysis of their underlying mechanisms. These findings offer valuable insights for future material design and applications, particularly in the field of silicon-based optoelectronics. The study's approach and results provide a strong foundation for further exploration into the nonlinear optical properties of doped semiconductors, paving the way for more efficient and effective material engineering strategies in the industry.

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