Generalized Ellipsometry on Complex Nanostructures and Low-Symmetry Materials

In this thesis, complex anisotropic materials are investigated and characterized by generalized ellipsometry. In recent years, anisotropic materials have gained considerable interest for novel applications in electronic and optoelectronic devices, mostly due to unique properties that originate from reduced crystal symmetry. Examples include white solid-state lighting devices which have become ubiquitous just recently, and the emergence of high-power, high-voltage electronic transistors and switches in all-electric vehicles. The incorporation of single crystalline material with low crystal symmetry into novel device structures requires reconsideration of existing optical characterization approaches. Here, the generalized ellipsometry concept is extended to include applications for materials with monoclinic and triclinic symmetries. A model eigendielectric displacement vector approach is developed, described and utilized to characterize monoclinic materials. Materials are investigated in spectral regions spanning from the far-infrared to the vacuum ultraviolet. Examples are demonstrated for phonon mode determination in cadmium tungstate and yttrium silicate and for band-to-band transitions in gallia (β-Ga2O3) single crystals. Furthermore, the anisotropic optical properties of an emerging class of spatially coherent heterostructure materials with nanostructure dimensions are investigated. The so-called anisotropic effective medium approximation for slanted columnar thin films is extended to the concept of slanted columnar heterostructure thin films as well as core-shell heterostructure thin films. Examples include the determination of band-to-band transitions, phonon modes and oxidation properties of cobalt-oxide core shell structures and gas-liquid-solid distribution during controlled adsorption of organic solvents in silicon slanted columnar thin films. Advisors: Eva Schubert and Mathias Schuber

Anisotropy and Phonon Modes from Analysis of the Dielectric Function Tensor and the Inverse Dielectric Function Tensor of Monoclinic Yttrium Orthosilicate

We determine the frequency dependence of the four independent Cartesian tensor elements of the dielectric function for monoclinic symmetry Y2SiO5 using generalized spectroscopic ellipsometry from 40–1200 cm−1. Three different crystal cuts, each perpendicular to a principle axis, are investigated. We apply our recently described augmentation of lattice anharmonicity onto the eigendielectric displacement vector summation approach [A.Mock et al., Phys. Rev. B 95, 165202 (2017)], and we present and demonstrate the application of an eigendielectric displacement loss vector summation approach with anharmonic broadening. We obtain an excellent match between all measured and model-calculated dielectric function tensor elements and all dielectric loss function tensor elements. We obtain 23 Au and 22 Bu symmetry long-wavelength active transverse and longitudinal optical mode parameters including their eigenvector orientation within the monoclinic lattice. We perform density functional theory calculations and obtain 23 Au symmetry and 22 Bu transverse and longitudinal optical mode parameters and their orientation within the monoclinic lattice. We compare our results from ellipsometry and density functional theory and find excellent agreement. We also determine the static and above reststrahlen spectral range dielectric tensor values and find a recently derived generalization of the Lyddane-Sachs-Teller relation for polar phonons in monoclinic symmetry materials satisfied [M. Schubert, Phys Rev. Lett. 117, 215502 (2016)]

Phonon order and reststrahlen bands of polar vibrations in crystals with monoclinic symmetry

In this Rapid Communication, we present the order of the phonon modes and the appearance of the reststrahlen bands for monoclinic symmetry materials with polar lattice vibrations. Phonon modes occur in associated pairs of transverse and longitudinal optical modes, and pairs either belong to inner or outer phonon modes. Inner modes are nested within outer modes. Outer modes cause polarization-dependent reststrahlen bands. Inner modes cause polarization-independent reststrahlen bands. The directional limiting frequencies within the Born-Huang approach are bound to within outer mode frequency regions not occupied by inner mode pairs. Hence, an unusual phonon mode order can occur where both lower-frequency as well as upper-frequency limits for the directional modes can be both transverse and/or longitudinal modes. We exemplify our findings using experimental data for the recently unraveled case of monoclinic symmetry β-Ga2O3 [Phys. Rev. B 93, 125209 (2016)] and demonstrate excellent agreement with results from density functional theory calculations

Anisotropy, Phonon Modes, and Lattice Anharmonicity from Dielectric Function Tensor Analysis of Monoclinic Cadmium Tungstate

We determine the frequency dependence of four independent Cartesian tensor elements of the dielectric function for CdWO4 using generalized spectroscopic ellipsometry within mid-infrared and far-infrared spectral regions. Different single crystal cuts, (010) and (001), are investigated. From the spectral dependencies of the dielectric function tensor and its inverse we determine all long-wavelength active transverse and longitudinal optic phonon modes with Au and Bu symmetry as well as their eigenvectors within the monoclinic lattice. We thereby demonstrate that such information can be obtained completely without physical model line-shape analysis in materials with monoclinic symmetry. We then augment the effect of lattice anharmonicity onto our recently described dielectric function tensor model approach for materials with monoclinic and triclinic crystal symmetries [M. Schubert et al., Phys. Rev. B 93, 125209 (2016)], and we obtain an excellent match between all measured and modeled dielectric function tensor elements. All phonon mode frequency and broadening parameters are determined in our model approach. We also perform density functional theory phonon mode calculations, and we compare our results obtained from theory, from direct dielectric function tensor analysis, and from model line-shape analysis, and we find excellent agreement between all approaches. We also discuss and present static and above reststrahlen spectral range dielectric constants. Our data for CdWO4 are in excellent agreement with a recently proposed generalization of the Lyddane-Sachs-Teller relation for materials with low crystal symmetry [M. Schubert, Phys. Rev. Lett. 117, 215502 (2016)]

Phonon order and reststrahlen bands of polar vibrations in crystals with monoclinic symmetry

In this Rapid Communication, we present the order of the phonon modes and the appearance of the reststrahlen bands for monoclinic symmetry materials with polar lattice vibrations. Phonon modes occur in associated pairs of transverse and longitudinal optical modes, and pairs either belong to inner or outer phonon modes. Inner modes are nested within outer modes. Outer modes cause polarization-dependent reststrahlen bands. Inner modes cause polarization-independent reststrahlen bands. The directional limiting frequencies within the Born-Huang approach are bound to within outer mode frequency regions not occupied by inner mode pairs. Hence, an unusual phonon mode order can occur where both lower-frequency as well as upper-frequency limits for the directional modes can be both transverse and/or longitudinal modes. We exemplify our findings using experimental data for the recently unraveled case of monoclinic symmetry β-Ga2O3 [Phys. Rev. B 93, 125209 (2016)] and demonstrate excellent agreement with results from density functional theory calculations

Phonon Order and Reststrahlen Bands of Polar Vibrations in Crystals with Monoclinic Symmetry

In this Rapid Communication, we present the order of the phonon modes and the appearance of the reststrahlen bands for monoclinic symmetry materials with polar lattice vibrations. Phonon modes occur in associated pairs of transverse and longitudinal optical modes, and pairs either belong to inner or outer phonon modes. Inner modes are nested within outer modes. Outer modes cause polarization-dependent reststrahlen bands. Inner modes cause polarization-independent reststrahlen bands. The directional limiting frequencies within the Born-Huang approach are bound to within outer mode frequency regions not occupied by inner mode pairs. Hence, an unusual phonon mode order can occur where both lower-frequency as well as upper-frequency limits for the directional modes can be both transverse and/or longitudinal modes. We exemplify our findings using experimental data for the recently unraveled case of monoclinic symmetry β-Ga2O3 [Phys. Rev. B 93, 125209 (2016)] and demonstrate excellent agreement with results from density functional theory calculations

Phonon order and reststrahlen bands of polar vibrations in crystals with monoclinic symmetry

In this Rapid Communication, we present the order of the phonon modes and the appearance of the reststrahlen bands for monoclinic symmetry materials with polar lattice vibrations. Phonon modes occur in associated pairs of transverse and longitudinal optical modes, and pairs either belong to inner or outer phonon modes. Inner modes are nested within outer modes. Outer modes cause polarization-dependent reststrahlen bands. Inner modes cause polarization-independent reststrahlen bands. The directional limiting frequencies within the Born-Huang approach are bound to within outer mode frequency regions not occupied by inner mode pairs. Hence, an unusual phonon mode order can occur where both lower-frequency as well as upper-frequency limits for the directional modes can be both transverse and/or longitudinal modes. We exemplify our findings using experimental data for the recently unraveled case of monoclinic symmetry β-Ga2O3 [Phys. Rev. B 93, 125209 (2016)] and demonstrate excellent agreement with results from density functional theory calculations

Band-to-band transitions, selection rules, effective mass and exciton binding energy parameters in monoclinic \beta-Ga2O3

We employ an eigen polarization model including the description of direction dependent excitonic effects for rendering critical point structures within the dielectric function tensor of monoclinic \beta-Ga2O3 yielding a comprehensive analysis of generalized ellipsometry data obtained from 0.75 eV--9 eV. The eigen polarization model permits complete description of the dielectric response, and we obtain single-electron and excitonic band-to-band transition anisotropic critical point structure model parameters including their polarization eigenvectors within the monoclinic lattice. We compare our experimental analysis with results from density functional theory calculations performed using a recently proposed Gaussian-attenuation-Perdue-Burke-Ernzerhof hybrid density functional, and we present and discuss the order of the fundamental direct band-to-band transitions and their polarization selection rules, the electron and hole effective mass parameters for the three lowest band-to-band transitions, and their exciton binding energy parameters, in excellent agreement with our experimental results. We find that the effective masses for holes are highly anisotropic and correlate with the selection rules for the fundamental band-to-band transitions, where the observed transitions are polarized closely in the direction of the lowest hole effective mass for the valence band participating in the transition

Tunable plasmonic resonances in highly porous nano-bamboo Si-Au superlattice-type thin films

We report on fabrication of spatially-coherent columnar plasmonic nanostructure superlattice-type thin films with high porosity and strong optical anisotropy using glancing angle deposition. Subsequent and repeated depositions of silicon and gold lead to nanometer-dimension subcolumns with controlled lengths. The superlattice-type columns resemble bamboo structures where smaller column sections of gold form junctions sandwiched between larger silicon column sections ("nano-bamboo"). We perform generalized spectroscopic ellipsometry measurements and finite element method computations to elucidate the strongly anisotropic optical properties of the highly-porous nano-bamboo structures. The occurrence of a strongly localized plasmonic mode with displacement pattern reminiscent of a dark quadrupole mode is observed in the vicinity of the gold subcolumns. We demonstrate tuning of this quadrupole-like mode frequency within the near-infrared spectral range by varying the geometry of the nano-bamboo structure. In addition, coupled-plasmon-like and inter-band transition-like modes occur in the visible and ultra-violet spectral regions, respectively. We elucidate an example for the potential use of the nano-bamboo structures as a highly porous plasmonic sensor with optical read out sensitivity to few parts-per-million solvent levels in water

Elevated temperature dependence of the anisotropic visible-to-ultraviolet dielectric function of monoclinic β-Ga2O3

We report on the temperature dependence of the dielectric tensor elements of n-type conductive β-Ga2O3 from 22 °C to 550 °C in the spectral range of 1.5 eV–6.4 eV. We present the temperature dependence of the excitonic and band-to-band transition energy parameters using a previously described eigendielectric summation approach [A. Mock et al., Phys. Rev. B 96, 245205 (2017)]. We utilize a Bose-Einstein analysis of the temperature dependence of the observed transition energies and reveal electron coupling with average phonon temperature in excellent agreement with the average over all longitudinal phonon plasmon coupled modes reported previously [M. Schubert et al., Phys. Rev. B 93, 125209 (2016)]. We also report a linear temperature dependence of the wavelength independent Cauchy expansion coefficient for the anisotropic below-band-gap monoclinic dielectric tensor elements