Theoretical and experimental studies of second-order nonlinear optical properties for various polyhedron distortions in ternary halides and some chalcopyrite compounds

• Main Authors: Tang, Li-Chuan, 唐立權
• Other Authors: Chang, Chen-Shiung
• Format: Others
• Language: en_US
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/56630959983291752567

博士 === 國立交通大學 === 光電工程系所 === 97 === 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.\\