以第一原理計算研究碳矽奈米管的光學性質

Abstract

中文摘要 碳矽塊材為硬度高的材料之一,其元件適合於高壓高頻環境下工作。這些性質是源自於量子效應,我們猜測其奈米結構可能有更新的现象,此論文的目的是用第一原理去了解其光學性質。單層的碳矽奈米管分成zigzag, armchair, chiral，可視為石墨狀的單層碳矽平面捲繞而成。我們運用密度泛函理論中的局域密度近似研究其能帶結構和光學介電函數，並且用此理論預測出穩定的原子結構。發現碳矽奈米管除了極小的(3,0)(4,0)是金屬外，其餘都是半導體。更進一步地說，zigzag型式碳矽管的能隙會隨著其直徑變小而趨近於零。但當直徑大於20 Å時，碳矽管能隙則趨向於單層碳矽平面的能隙。再者，當電場平行於管軸時，介電函數虛部的頻譜約在3eV會出現明顯的尖峰。所有的碳矽管在高能量範圍(6eV以上)會出現較寬的信號。然而，對於小直徑的碳矽管像是(4,2)(4,4)的光譜，會不同於大管徑的光譜。當電場垂直管軸時，除了(4,4)(3,0)(4,0)外，其餘的碳矽管分別在3eV和6eV會有信號產生並且其強度約是電場平行於管軸時的一半。 接著我們研究其碳矽管及單層碳矽平面和2H,4H,6H和3C塊材的非線性光學的性質，方法也是基於密度泛函理論中的局域密度近似。爾後發現zigzag和chiral 的碳矽管有比碳矽塊材大約十倍的非線性光學係數，且比氮硼奈米管大約十三倍。此現象或許使碳矽管成為光電材料的另選擇。在低維度下的材料考慮多體效應可修正其光譜圖，因此我們基於激發子所產生的影響而刊出初步的結果。

Abstract Silicon carbide in bulk form is one of the hardest material materials and is suitable for electronic devices operated in extreme environments. Silicon carbide with its wide band gap, high thermal conductivity, and radiation resistance, is important for usage in high-temperature, high-pressure environments. It is reasonable to predict that the novel properties of bulk SiC due to quantum size e ects would also reflect in silicon carbide nanostrctures. The band structure and optical dielectric function of single-walled zigzag, armchair, and chiral silicon carbide nanotubes (SiC-NTs) as well as the single honeycomb SiC sheet have been calculated within density-functional theory in the local-density approximation. The underlying atomic structure of the SiC-NTs is determined theoretically. These findings indicate that all the SiC nanotubes are semiconductors, except the ultrasmall (3,0) and (4,0) zigzag tubes which are metallic. Moreover, the energy band gap of the zigzag SiC-NTs which is direct, may be reduced from that of the SiC sheet to zero by reducing the diameter, and the band gap for all the SiC nanotubes with a diameter larger than 20 A is almost independent of diameter. For the electric field parallel to the tube axis (E

z), the epsilon for all the SiC-NTs with a moderate diameter (say, D > 8 A) in the low-energy region(0-6 eV) consists of a single distinct peak at ~3 eV. However, for the small diameter SiC nanotubes such as the (4,2),(4,4) SiC-NTs, the epsilon spectrum does deviate markedly from this general behavior. In the high-energy region(from 6 eV upwards), the epsilon for all the SiC-NTs exhibit a broad peak centered at ~7 eV. For E perpendicular to z, the epsilon spectrum of all the SiC-NTs except the (4,4), (3,0) and (4,0) nanotubes, in the low energy region also consists of a pronounced peak at around 3 eV while in the high-energy region is roughly made up of a broad hump starting from 6 eV. The magnitude of the peaks is in general about one-half of the magnitude of the corresponding ones for E

z, showing a moderate optical anisotropy in the SiC-NTs. Subsequently, the second-order nonlinear optical susceptibility (chi^(2)_(abc)) and linear electro-optical coefficient (r_(abc)) of a large number of single-walled zigzag, armchair and chiral SiC nanotubes (SiC-NTs) as well as bulk SiC polytypes (2H-, 4H-, 6H- and 3C-SiC) and single graphitic SiC sheet have been calculated from first-principles. The calculations are also based on local density approximation. It is found that both the zigzag and chiral SiC-NTs exhibit large second-order nonlinear optical behavior with the chi^(2)_(abc) and r_(abc) coefficients being up to ten-times larger than that of bulk SiC polytypes, and also being up to thirteen-times larger than the counterparts of the corresponding BNNTs. Furthermore, the phenomena indicate that SiC-NTs are promising materials for nonlinear optical and opto-electric applications. Many body effects modify the optical properties of low dimensional systems. Therefore, we demonstrate preliminary results of the silicon carbide bulk and SiC-NTs(3,3)(5,5), which are based on Green's function approach and electron-hole interaction effects. Excitonic effects modify the optical spectra of SiC-NTs(3,3)(5,5). The epsilon_z for SiC-NTs(3,3) exhibit a sharp peak centered at 2.05 eV and 5.25 eV, and the epsilon_z for SiC-NTs(5,5) exhibit a sharp peak centered at 1.05 eV and 2.95 eV. These large many-body effects will dominate the optical responses, and explain the discrepancies between theories and experiments.