多面體變異在三元鹵化物及黃銅礦結構化合物對二階非線性光學性質影響之理論與實驗研究

Abstract

鈣鈦礦結構之三元鹵化物是新興的紅外線非線性光學材料， 它同時有鈣鈦礦晶體結構變異的有趣議題，也有優良的紅外線非線性光學特性。 除了傳統以陰、陽離子半徑 所定義的結構變異參數，高史密斯變形因數；本論文也提出了體心陽離子偏移量、面心陰離子偏移量以及 (自立方變成菱方)晶胞角度偏移量等三個新的結構參數，同時以第一原理計算方法、晶體合成和實驗方法進行系統化的 分析與探討各結構參數對三元鹵化物非線性光學的影響與相關性。從計算與實驗分析結果顯示， 菱方晶系的三元鹵化物晶體隨著結構參數的變化同時造成相當大的二階非線性光學係數的變化； 電子能態計算結果顯示這系列的晶體具有直接能隙， 但並非在倒格子空間的原(伽瑪)點上，而是在倒格子空間的對角點上點上；計算能隙值雖較低於實驗值， 而菱方晶系的三元鹵化物晶體具有較大的計算能隙值，此趨勢與實驗值一致。\\ 本論文進一步成長並分析另一屬黃銅礦結構的紅外線非線性光學材料，銀鎵硫、銀鎵硒、銀鎵硫硒； 這是陰、陽離子互為四配位四面體離子團內結構的一類晶體，本論文同樣以第一原理計算方法、晶體成長 和實驗方法進行系統化的分析與探討陰離子取代、各結構參數對銀鎵硫、銀鎵硒、銀鎵硫硒非線性光學 的影響與相關性。發現陰離子取代，以接近線性比例改變了晶體的能隙、非線性係數與紅外線吸收的截止波長。\\ 由於本論文所使用的第一原理計算方法以及開發附屬計算工具均成功地 探討了前述兩類結構的紅外線非線性光學材料，因此，將此理論方法推展至 寬能隙黃銅礦結構與相關結構的三元氮化物晶體進行系統化的分析；二價的第一位陽離子、四價的第二位陽離子與 氮離子互為四配位四面體離子團內結構，因合成與晶體成長不易，目前可比較、參考的數據、文獻有限，但第一原理計算方法 以及所開發附屬計算工具顯示這類三元氮化物晶體具有不同但寬廣的能隙值(約從三個電子伏特到六個電子伏特)， 實驗值會大於前述的計算值，又兼具非零二階非線性光學係數， 可期待此材料在可見光與紫外線非線性光學方面的應用。\\

Microstructures, electronic structures, linear- and nonlinear-optical properties of the crystals with two main polyhedron categories are examined in this study by using both the first principles calculation and the experimental methods. The studied crystals include the rhombohedral ternary halides (ABX$_3$ (A=Cs, Rb, B=Ge, X=Cl, Br, I)), the wide-bandgap ternary nitrides($A^{II}B^{IV}N_2$ ($A^{II}=Be, Mg$, $B^{IV}=C, Si, Ge$)), and chalcopyrite AgGaS$_2$, AgGaSe$_2$, and AgGa(S$_x$Se$_{1-x}$)$_2$. \\ First, one of the most important parts, systematic studies based on first-principles calculations of second-order optical susceptibilities as well as the dielectric function for CsGeX$_3$ (X=Cl, Br, and I; CGX) are presented. The relation between structural properties and the optoelectronic responses are examined. The structural factors, $\Delta \alpha$, $d_{Ge}$, $d_X$ are proposed to describe the degree of distortion from an ideal perovskite structure. $\Delta \alpha$ and $d_{Ge}$ increase when the halide anions are changed from Cl to I; while halide anion displacement, $d_X$, decreases. The structural distortion effect on these rhombohedral CGX crystals is analyzed via the first-principles calculations. The dielectric function and the second harmonic generation (SHG) response coefficient also increase with increasing $\Delta \alpha$ and $d_{Ge}$. The direct bandgaps, $E_G$, of CsGeX$_3$ all occur at the $R$-point, $\Delta E_R$. The experimental bandgaps of CGX crystals become smaller, i.e. $E^{CGC}_G$(3.67eV)$>E^{CGB}_G$(2.32eV)$>E^{CGI}_G$(1.53eV), as the $\Delta \alpha$ and $d_{Ge}$ increase, i.e. $d^{CGC}_{Ge}<d^{CGB}_{Ge}<d^{CGI}_{Ge}$. Partial density of states (PDOS) analysis revealed that the valence band maximun (VBM) and conduction band minimum (CBM) are mainly contributed from the p-orbitals of Germanium. The calculated magnitudes of $\chi^{(2)}_{ijk}$ are close to some reported experimental values near the band gap. \\ Second, the nonlinear optical (NLO) property of hydrated rubidium germanium chloride (HRGC), RbGeCl$_3\cdot x$(H$_2$O), is identified. Infrared absorption data support structural evidence that HRGC contain co-ordinated water molecules with strong hydrogen bond. The infrared spectrum indicated HRGC is transparent in most of the infrared region with only little influnce from water. Calculations based on density functional theory shows that the band gap of the RbGeCl$_3$ (RGC) crystal is at least 3.84eV, which is larger than that of the infrared (IR) NLO crystal CsGeCl$_3$. Single crystals of HRGC, sized up to 3 $\times$ 2 $\times$ 1 cm$^3$, were grown in aqueous solution by a slow dehydrate technique. The synthetic, structural, and optical properties of an off-centrosymmetric IR nonlinear optical (NLO) RbGeCl$_3\cdot x$(H$_2$O) crystal were investigated experimentally. Powder second harmonic generation (PSHG) measurement indicates that the crystal structure of HRGC becomes off-centrosymmetric. Precise X-ray diffraction measurements showed that [100] family diffraction peaks split slightly. Unlike the RGC crystal structure whose space group is P2$_1\bar m$, the HRGC crystal loses the inversion symmetry. Comparisons with known NLO material KH$_2$PO$_4$ (KDP), indicate that HRGC's NLO susceptibility, $\chi^{(2)}$, is about one third of that for KDP. The absorption edge of HRGC occured at 310nm ($\approx$4.0 eV), which indicates NLO HRGC crystal can have larger laser damage threshold. According to the $FTIR$ measurement, HRGC has a transparent region from 0.31 to 30 $\mu$m, thus it can be applied to wider optical spectrum from ultraviolet, visible, to mid-IR. \\ Third, both tetragonal and orthorhombic ternary nitrides $A^{II}B^{IV}N_2$ ($A^{II}$=Be, Mg; $B^{IV}$=C, Si, Ge) are studied by using the first principles calculation, and are compared to the available experimental results. This study reveals the electronic properties, linear and second-order nonlinear optical ($NLO$) properties of the ternary nitrides compounds with chalcopyrite structure performed using the Linear Augmented Slater-Type Orbitals (LASTO) method. The linear and second-order optical susceptibilities as functions of frequency are presented. Specifically, we study the relation between the structural properties and the optical responses. Our electronic band structure and projected density of states (PDOS) analysis reveal that these chalcopyrite $A^{II}B^{IV}N_2$ compounds are direct (with band extrema located at the $\Gamma$-point) and their band gaps are wide [from 2.68eV ($BeGeN_2$) to 4.24eV($MgCN_2$)]. Our PDOS analysis also shows that the effective masses of highest valence band are heavy in $MgSiN_2$ and $MgGeN_2$, which are different from other $A^{II}B^{IV}N_2$ compounds. Our calcultions show this new category of wide-bandgap ternary nitrides have potential applications in optoelectronics. \\ Finally, the lattice parameters, electronic structures, optical and bulk properties of tetragonal nonlinear optical crystals, AgGa(S$_x$Se$_{1-x}$)$_2$ (x=0.0, 0.25, 0.5, 0.75, and 1.0), have been analyzed theoretically with first-principle calculation and measured experimentally in each composition. Our calculation results indicate that in these compounds, their electronic band gaps, optical properties, and bulk moduli are linearly dependent, which are compatible with the experimental measurements. We also find the proportionally mixed electronic contributions from sulfur and selenium at band edges via the partial density of state (PDOS) analysis of . The linear-dependent relationship of their electronic properties can be considered as the cell-volume-effect. Furthermore, the cell parameters, bond length between metal ion and \textit{S} or \textit{Se}, band gap values, and nonlinear optical (NLO) susceptibilities are also found linearly dependent on the compositions and the related cell volumes.\\