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The observed impurity induced far-infrared absorption in CsCl : Rb\(^+\) and CsCl : K\(^+\) is compared with a calculated density of acoustic phonon states in CsCl. The absorption due to CsCl : Rb\(^+\) displays a minimum between the acoustic and optic phonon bands. A narrow line is observed in CsCl: K\(^+\) at 85.8 cm\(^{-1}\) which falls in this quasi-phonon gap.
New resonant-mode infrared absorption lines have been observed in NaCl with high concentrations of fluorine impurities. The quadratic concentration dependence of the strength of these lines indicates that they are due to pairs of fluorine impurities. At the resonant frequencies, the motion of some host ions appears to be as important as the motion of the impurities themselves.
The preparation of Bi2Sea single crystals with low free carrier densities allowed an investigation of the lattice vibrations to be carried out from the reflectivity of cleavage planes at nearly normal incidence of the radiation (E ~ c). The experimental results ean be explained with two classical oscillators, whose eigenfrequencies oceur at 92 and 69.5 cm-I. The static dielectric constant was determined to be 100 ± 10 for E ~ c.
The photoconductivity of both undeformed and deformed Te samples has been investigated at liquid He temperature by means of a Fourier spectrometer. Three peaks were usually found in the spectra of undeformed samples at 11, 24 and 46 cm\(^{-1}\). These are shown to be due to three different chemical impurities. The deformed samples are characterized by additional structure at higher frequencies.
We have studied the lowest magnetic excitation of Ni\(_{1-x}\)Co\(_x\)O mixed crystals for 0.94 \(\leq\) x \(\leq\) 1. Together with previous results for 0.02 \(\leq\) x \(\leq\) 0.07 and neutron data for x = 0.14 and x = 0.30, the results are discussed by means of a model, especially the variation of AFMR frequency and preferred spin direction with Co concentration x.
Non-Formal Education
(1989)
We report here that reconstruction on (100), (1lIlA, and (1l1lB CdTe surfaces is either C(2X2), (2X2), and (l X I) or (2X I), (l X I), and (l X I) when they are Cd or Te stabilized, respectively. There is a mixed region between Cd and Te stabilization in which the reflected high-energy electron-diffraction (RHEED) patterns contain characteristics of both Cd- and Te-stabilized surfaces. We have also found that the Cd-to-Te ratio of the x-ray photoelectron intensities of their 3d\(_{3/ 2}\) core levels is about 20% larger for a Cd-stabilized (1lIlA, (1lIlB, or (100) CdTe surface than for a Te-stabilized one. According to a simple model calculation, which was normalized by means of the photoelectron intensity ratio of a Cd-stabilized (lll)A and aTe-stabilized (1l1lB CdTe surface, the experimental data for CdTe surfaces can be explained by a linear dependence of the photoelectron-intensity ratio on the fraction of Cd in the uppermost monatomic layer. This surface composition can be correlated with the surface structure, i.e., the corresponding RHEED patterns. This correlation can in turn be employed to determine Te and Cd evaporation rates. The Te reevaporation rate is increasingly slower for the Te-stabilized (Ill) A, (l1l)B, and (100) surfaces, while the opposite is true for Cd from Cd-stabilized (Ill) A and (Ill)B surfaces. In addition, Te is much more easily evaporated from all the investigated surfaces than is Cd, if the substrate is kept at normal molecular-beam-epitaxy growth temperatures ranging from 2oo·C to 300 ·C.
We report the results of a detailed investigation on the Te-stabilized (2 x 1) and the Cdstabilized c( 2 X 2) surfaces of ( 100) CdTe substrates. The investigation demonstrates for the first time that both laser illumination and, to a greater extent, high-energy electron irradiation increase the Te desorption and reduce the Cd desorption from ( 100) CdTe surfaces. Thus it is possible by choosing the proper growth temperature and photon or electron fluxes to change the surface reconstruction from the normally Te-stabilized to a Cd-stabilized phase.
We report the contactless determination of the conductivity, the mobility and the carrier concentration of II-VI semiconductors by means of the technique of the partially filled waveguide at a microwave frequency of 9 GHz. The samples are CdHgTe epitaxial layers, grown on CdZnTe substrates by molecular beam epitaxy. The conductivity is determined from the transmission coefficient of the sample in the partially filled waveguide. For the analysis of the experimental data, the complex transmission coefficient is calculated by a rigorous multi-mode matching procedure. By varying the conductivity of the sample, we obtain an optimum fit of the calculated data to the experimental results. Comparison with conductivity data determined by the van der Pauw method shows that our method allows to measure the conductivity with good accuracy. The behaviour of the transmission coefficient of the sample is discussed in dependence on the layer conductivity, the layer thickness and the dielectric constant of the substrate. The calculations require to consider in detail the distribution of the electromagnetic fields in the sample region. The usual assumption of a hardly disturbed TE\(_{10}\) mode cannot be used in our case. By applying a magnetic field in extraordinary Voigt configuration. galvanomagnetic measurements have been carried out which yield the mobility and thus the carrier concentration. These results are also in good agreement with van der Pauw transport measurements.
The microwave transmission and reßection is evaluated for stratified lossy dielectric segments partially filling the rectangular waveguide by the method which combines the multimode network theory with the rigorous mode matching procedure. As an example, we investigate in detail the microwave scattering properties of II-VI-epitaxial layer on a lossy dielectric substrate inserted in the rectangular waveguide. The experimental data verify the accuracy and the effectiveness of the present method. Extensive numerical results are presented to establish useful guidelines for the contactless microwave measurement of the conductivity of the epitaxiallayer.
The influence of different CdZnTe substrate treatments prior to II-VI molecular beam epitaxial growth on surface stoichiometry, oxygen, and carbon contamination has been studied using x-ray photoelectron spectroscopy and reflection high energy electron diffraction. Heating the substrate at 300 °C can eliminate oxygen contamination, but cannot completely remove carbon from the surface. Heating at higher temperatures decreases the carbon contamination only slightly, while increasing the Zn-Cd ratio on the surface considerably. The magnitude of the latter effect is surprising and is crucial when one is using lattice matched CdZnTe (Zn 4%) substrates.
We have grown HgTe/CdTe superlattices by molecular beam epitaxy; barrier thicknesses were in the range from 15 to 91 Å and the well thickness was maintained at a constant value of 30 Å. The infrared photoluminescence was investigated by means of Fourier transform infrared spectroscopy in the temperature range from 4.2 to 300 K. All superlattices showed pronounced photoluminescence at temperatures up to 300 K. To gain more detailed insight into the band structure of the HgTe/CdTe superlattices, band structure calculations were performed. The concept of the envelope function approximation was followed. Employing the transfer matrix method, the calculations were completed taking into account an eight band k·p model. An important parameter in these calculations is the natural valence band offset (VBO) between the well and barrier materials. As a general trend, the value for the direct gap decreases with increasing VBO. The experimentally determined energies of the band gap are in reasonable agreement with the values obtained by the theoretical calculations. A comparison between theory and experiment shows that the observed transition energies are closer to calculations employing a large offset (350 meV) as opposed to a small VBO (40 meV).
In the present work we report the results of magneto-transport measurements on some Hg-based li-VI semiconductor epitaxiallayers grown by molecular beam epitaxy. The transport measurement were carried out at temperatures in the range 0.4 - 4.2 K in magnetic fields up to 10.0 T. Further, we point out the necessity of using multicarrier models for data interpretation and show finally some Shubnikov-de-Haas results on sampies with high mobility carners.
We have investigated Cd\(_{1-x}\)Mn\(_x\)Te thin films with Mn concentrations of x=0.12, 0.18, 0.30, 0.52, and 0.70. These single crystal layers were grown by molecular beam epitaxy on [001] CdTe substrates. The real part of the refractive index, n, was determined below the band-gap Eo in the range of 0.5-2.5 eV at T=300 K. The parallel reOectivity was measured near the Brewster angle at the YAG laser wavelength of 1.064 J.Lm (hv= 1.165 eV). Combining these results with the optical pathlength results (nd) of reOection measurements in a Fourier spectrometer we have determined n(x,v) over a wide spectral range by utilizing a three parameter fit. The accuracy of these results for n should improve waveguide designs based on this material.
In this paper, we present results on the first MBE growth of HgSe. The influence of the GaAs substrate temperature as well as the Hg and Se fluxes on the growth and the electrical properties has been investigated. It has been found that the growth rate is very low at substrate temperatures above 120°C. At 120°C and at lower temperatures, the growth rate is appreciably higher. The sticking coefficient of Se seems to depend inversely on the Hg/Se flux ratio. Epitaxial growth could be maintained at 70°C with Hg/Se flux ratios between lOO and ISO, and at 160°C between 280 and 450. The electron mobilities of these HgSe epilayers at room temperature decrease from a maximum value of 8.2 x 10^3 cm2 /V' s with increasing electron concentration. The concentration was found to be between 6xlO^17 and 1.6x10^19 cm- 3 at room temperature. Rocking curves from X-ray diffraction measurements of the better epilayers have a full width at half maximum of 5S0 arc sec.
The molecular beam epitaxially growth of (001) Hg\(_{1-x}\) Cd\(_z\) Te-HgTe superlattices has been systematically investigated. The well width as well as the period were determined directly by X-ray diffraction. This was accomphshed for the well width by exploiting the high reflectivity from HgTe and the low reflectivity from CdTe for the (002) Bragg reflection. Knowing the well and barrier thicknesses we have been able to set an upper limit on the aver~ge composition of the barriers, Xl, by annealing the superlattice and then measuring the composition of the. resultmg alloy. Xb was shown to decrease exponentially with decreasing barrier width. Xb is appreciably smaller m. narrow barriers due to the increased significance of interdiffusion in the Hg\(_{1-x}\)Cd\(_x\) Te/HgTe interface in narrow barriers. The experimentally determined optical absorption coefficient for these superlattices is compared WIth theoretical calculations. The absorption coefficient was determined from transmission and reflection spectra at 300, 77 and 5 K. Using the thickness and composition of the barriers and wells, and an interface width due to interdiffusion, the complex refractive index is calculated and compared with the experimental absorption coefficient. The envelope function method based on an 8 x 8 second order k . p band model was used to calculate the superlattice states. These results when inserted into Kubo's formula, yield the dynamic conductivity for interband transitions. The experimental and theoretical values for the absorption coefficient using no adjustable parameters are in good agreement for most of the investigated superlattices. Furthermore the agreement for the higher energetic interband transitions is much worse if values for the barrier composition, which are appreciably different than the experimentally determined values, are used. The infrared photoluminescence was investigated at temperatures from 4.2 to 300 K. Pronounced photoluminescence was observed for all superlattices in this temperature range.
We report on the growth of the compound semiconductor MgTe as weil as the ternary alloy Cd\(_{l-x}\)Mg, Te by molecular hcam cpitaxy. This is to our knowkdgc thc first time that this material has heen grown by any epitaxial technique. Bulk MgTe, which is hygroscopic, has a band gap of 3.0 eV and crystallizcs usually in thc wurtzite structure. Pseudomorphic films were grown on zincblende Cd Te suhstrates for a MgTe thickness helow a critical layer thickncss of approximately 500 nm. In addition, Cd\(_{l_x}\),Mg\(_x\)Te epilayers were grown with a Mg concentration between 0 and 68%, which corresponds to a band gap betwcen 1.5 and 2.5 eV at room temperature. The crystalline quality of thc layers is comparabk to CdTc thin films as long as they are fully strained. The lauice constant of zincblende MgTe is slightly smaller than that of CdTe, and the lattice mismatch is as low as O.7%. In addition highly n-type CdMgTe layers were fabricatcd by hromine doping. The tunability of the band gap as weil as the rather good laUice match with CdTc makes the matcrial interesting for optoelectronic device applications for the entire visible range.
A semiempirical model is presented that correlates the broadening of the absorption edge with both transitions below the energy gap and with transitions by the Kane band model. This model correctly fits both the absorption and luminescence spectra of narrow-gap (Hg,Cd)Te samples that have been grown by the traveling heater method as well as by molecular-beam epitaxy. The accuracy of the band-gap determination is enhanced by this model.
The surface sublimation of Cd and Te atoms from the zinc blende (111)A CdTe surface has been investigated in detail by reflection high energy electron diffraction and x-ray photoelectron spectroscopy. These experiments verify that Te is much easier to evaporate than Cd. The experimental value for the Te activation energy from a Te stabilized (111)A CdTe surface is 1.41 ±0.1O eV, which is apparently inconsistent with recent theoretical results.
We have investigated oxygen on CdTe substrates by means of x-ray photoelectron spectroscopy (XPS) and reflection high-energy electron diffraction (RHEED). A Te oxide layer that was at least 15 A thick was found on the surface of as-delivered CdTe substrates that were mechanically polished. This oxide is not easily evaporated at temperatures lower than 350°C. Furthermore, heating in air, which further oxidizes the CdTe layer, should be avoided. Etching with HCI acid (15% HCl) for at least 20 s and then rinsing with de-ionized water reduces the Te oxide layer on the surface down to 4% of a monoatomic layer. However, according to XPS measurements of the 0 Is peak, 20%-30% of a monoatomic layer of oxygen remains on the surface, which can be eliminated by heating at temperatures ranging between 300 and 340 cC. The RHEED patterns for a molecular beam epitaxially (MBE)-grown CdTe film on a (lOO) CdTe substrate with approximately one monoatomic layer of oxidized Te on the surface lose the characteristics of the normal RHEED pattems for a MBE-grown CdTe film on an oxygen-free CdTe substrate.
Molecular beam epitaxially grown short period (001) Hg\(_{1_x}\)Cd\(_x\)Te-HgTe superlattices have been systematically investigated. Several narrow well widths were chosen, e.g., 30, 35 and 40 Å, and the barrier widths were varied between 24 and 90 Å for a particular well width. Both the well width and the total period were determined directly by means of x-ray diffraction. The well width was determined by exploiting the high reflectivity from HgTe and the low reflectivity from CdTe for the (002) Bragg reflection. Knowing the well and barrier widths we have been able to set an upper limit on the average Cd concentration of the barriers, \(\overline x_b\), by annealing several superlattices and then measuring the composition of the resulting alloy. \(\overline x_b\) was shown to decrease exponentially with decreasing barrier width. The structure of a very short period superlattice, i.e., 31.4 Å, was also investigated by transmission electron microscopy, corroborating the x-ray diffraction results.
Infrared photoconductor fabricated with HgTe/CdTe superlattice grown by molecular beam epitaxy
(1993)
An infrared photoconductor fabricated with a HgTe/CdTe superlattice grown on a GaAs substrate by molecular beam epitaxy is described here for the first time. The growth procedure, device fabrication, and measurement results are described. The results show that the device has relatively high uniformity and 1000 K black-body detectivity 2.4 X 10\(^9\) cm Hz\(^{1/2}\) W\(^{-1}\) . The photoconductivity decay method was used for determining carrier lifetime of the HgTe/CdTe superlattice, the measured lifetime is 12\(\mu\)s at 77 K, which is the longest lifetime ever reported for HgTe/CdTe superlattices and we believe that the increase of lifetime is mainly due to the reduction of dimensions.
The structural properties of HgSe grown by molecular beam epitaxy (MBE) are investigated for different lattice mismatches to the substrate and various growth conditions. The growth rate is shown to depend strongly on the growth temperature above lOO°C as well as on the Hg/Se flux ratio. It has been found that the crystalline perfection and the electrical properties are mainly determined by the layer thickness, especially for the growth on highly lattice mismatched substrates. Changes in the surface morphology are related to growth parameters. Differences between the electrical behavior of MBE-grown and bulk HgSe are discussed. The electrical properties of HgSe contacts on p-ZnSe are investigated as a function of different annealing procedures.
The selected area epitaxial overgrowth of narrow gap HgTe as well as wide gap CdTe and ZnTe on CdTe/GaAs substrates, which had been structured by dry etching techniques, has been investigated. A plasma etching process using a barrel reactor with CH\(_4\)-CH\(_2\) gases has been employed to prepare stripes with a width of about 1 μm with anisotropic as well as isotropic etching profiles. It has been found, that the selected area HgTe overgrowth takes place with a high local selectivity to the low index planes of the patterned surface. In contrast, the selected area overgrowth of the wide gap CdTe and ZnTe is controlled by anisotropic growth kinetics provided that the substrate temperature is not lower than 220°C and the starting surface consists of well developed low index crystallographic planes.
The sattering characteristics ot the n-VI semiconductors were analyzed by a method which combines the second-order finite-element method with the rigorous mode matching procedure. The method avolds the difficulty of solving the complex transcendental equation introduced in the multimode network method and calculates all the eigenvalues and eigenfunctions simultaneously which are needed for the mode matching treatment in the longitudinal direction. As a result, the whole solution procedure is significantly simplified. A comparison is given between the experimental data and the calculated results obtained with this analysis and tbe network method. Very good agreement has been achieved, the accuracy and efficiency of the present method are thus verified.
This work is investigating the electronic structure of organic thin films. A central question in this respect is the influence of the interaction between the molecules in the condensed phase and the interaction at metal-organic interfaces on the electronic properties. For this purpose the experimental methods Photoelectron Spectroscopy (PES) and Near Edge X-ray Absorption Finestructure Spectroscopy (NEXAFS) were applied with highest energy resolution. In addition, ab initio calculations were performed for the theoretical simulation of NEXFAS spectra. The investigation is mainly focussing on thin, vacuum sublimated films of aromatic model molecules with oxygen-containing functional groups (NTCDA, PTCDA, NDCA, BPDCA and ANQ) and Ag(111) surfaces. Due to their large, delocalised p-systems these molecules have very interesting properties for their application in electronic devices. Due to the high energy resolution of third generation synchrotron sources the vibronic fine structure in the NEXAFS spectra of these large molecules could be resolved for the first time in the condensed phase. A comparison of the data of the different molecules provides interesting insight into the coupling between electronic transition and vibronic excitation. Although for these molecules a variety of different vibronic modes exist, the NEXAFS data show that preferentially only on mode couples to each electronic transition. The high-resolution PES spectra of the molecules NTCDA, PTCDA, NDCA, BPDCA and ANQ show distinct differences thus providing a fingerprint for each investigated substance. A comparative analysis of the spectra enabled us to define the 1s binding energies of all chemically different carbon and oxygen atoms. Additional structures in the spectra can be assigned as shake-up satellites. The five molecules are an ideal model system for the investigation of fundamental aspects of core electron spectroscopy, such as initial and final state effects and satellites, that are influenced by the intra- and intermolecular electron distribution in the ground and core ionized state. An important aspect in this thesis is the spectroscopic investigation of structurally different NTCDA monolayer phases on the Ag(111) surface. Marked differences in the electronic structures of the different phases, that can be assigned to differences in the metal-adsorbate interaction, could be demonstrated by XPS and NEXAFS. The substrate bonding can be characterized as chemisorptive for both, the compressed as well as the relaxed NTCDA monolayer, which can be unambiguously deduced from the analysis of satellite structures in the O 1s and C 1s XPS spectra. These satellites are due to dynamic screening by charge transfer from the substrate. The NEXAFS data show consistently, that the NTCDA LUMO becomes partly occupied upon adsorption. Highly interesting phase transitions into disordered low-temperature phases occur upon cooling to 160 K for both, the compressed and the relaxed NTCDA monolayer. Thereby, the adsorbate-substrate bonding is increased and the NTCDA LUMO becomes completely occupied. This can be observed in the NEXAFS data, where transitions involving LUMO final states are quenched. Simultaneously, the XPS data show a distinctly decreased intensity of unscreened photoemission states due to enhanced charge transfer screening. In addition, a hysteresis behaviour could be demonstrated for the phase transition of the relaxed monolayer by temperature dependent NEXAFS experiments and the hysteresis curve was determined. The hysteresis could be quantified to approx. 20 K. From SPA-LEED experiments the activating energy for the phase transition of the relaxed monolayer upon cooling could be determined to 60 meV. Finally, a NEXAFS investigation of polyethylene samples with different comonomer content is presented. Differences in the absorption spectra between samples with different comonomer content could be unambiguously assigned to the different crystallinities of the samples by heating a highly crystalline sample in situ close to the melting temperature. Ab initio calculations on a model matrix of butane molecules show, that the spectra of crystalline and amorphous polyethylene differ distinctly due to the intermolecular interaction, which can be observed best for resonances with strong Rydberg character. Thus, the differences in the PE spectra can be explained by the superposition of the signatures of crystalline and amorphous moieties, that are mixed according to the respective crystallinity.
The availability of coherent soft x-rays through the nonlinear optical process of high-harmonic generation allows for the monitoring of the fastest events ever observed in the laboratory. The attosecond pulses produced are the fundamental tool for the time-resolved study of electron motion in atoms, molecules, clusters, liquids and solids in the future. However, in order to exploit the full potential of this new tool it is necessary to control the coherent soft x-ray spectra and to enhance the efficiency of conversion from laser light to the soft x-ray region in the harmonic-generation process. This work developed a comprehensive approach towards the optimization of the harmonic generation process. As this process represents a fundamental example of \emph{light}--\emph{matter} interaction there are two ways of controlling it: Shaping the generating laser \emph{light} and designing ideal states of \emph{matter} for the conversion medium. Either of these approaches was closely examined. In addition, going far beyond simply enhancing the conversion process it could be shown that the qualitative spectral response of the process can be modified by shaping the driving laser pulse. This opens the door to a completely new field of research: Optimal quantum control in the attosecond soft x-ray region---the realm of electron dynamics. In the same way as it is possible to control molecular or lattice vibrational dynamics with adaptively shaped femtosecond laser pulses these days, it will now be feasible to perform real-time manipulation of tightly bound electron motion with adaptively shaped attosecond light fields. The last part of this work demonstrated the capability of the herein developed technique of coherent soft-x-ray spectral shaping, where a measured experimental feedback was used to perform a closed-loop optimization of the interaction of shaped soft x-ray light with a sulfur hexafluoride molecule to arrive at different control objectives. For the optimization of the high-harmonic-generation process by engineering the conversion medium, both the gas phase and the liquid phase were explored both in experiment and theory. Molecular media were demonstrated to behave more efficiently than commonly used atomic targets when elliptically polarized driving laser pulses are applied. Theory predicted enhancement of harmonic generation for linearly polarized driving fields when the internuclear distance is increased. Reasons for this are identified as the increased overlap of the returning electron wavefunction due to molecular geometry and the control over the delocalization of the initial electronic state leading to less quantum-mechanical spreading of the electron wavepacket during continuum propagation. A new experimental scheme has been worked out, using the method of molecular wavepacket generation as a tool to enhance the harmonic conversion efficiency in `pump--drive' schemes. The latter was then experimentally implemented in the study of high-harmonic generation from water microdroplets. A transition between the dominant laser--soft-x-ray conversion mechanisms could be observed, identifying plasma-breakdown as the fundamental limit of high-density high-harmonic generation. Harmonics up to the 27th order were observed for optimally laser-prepared water droplets. To control the high-harmonic generation process by the application of shaped laser light fields a laser-pulse shaper based on a deformable membrane mirror was built. Pulse-shape optimization resulted in increased high-harmonic generation efficiency --- but more importantly the qualitative shape of the spectral response could be significantly modified for high-harmonic generation in waveguides. By adaptive optimization employing closed-loop strategies it was possible to selectively generate narrow (single harmonics) and broad bands of harmonic emission. Tunability could be demonstrated both for single harmonic orders and larger regions of several harmonics. Whereas any previous experiment reported to date always produced a plateau of equally intense harmonics, it has been possible to demonstrate ``untypical'' harmonic soft x-ray spectra exhibiting ``switched-off'' harmonic orders. The high degree of controllability paves the way for quantum control experiments in the soft x-ray spectral region. It was also demonstrated that the degree of control over the soft x-ray shape depends on the high-harmonic generation geometry. Experiments performed in the gas jet could not change the relative emission strengths of neighboring harmonic orders. In the waveguide geometry, the relative harmonic yield of neighboring orders could be modified at high contrast ratios. A simulation based solely on the single atom response could not reproduce the experimentally observed contrast ratios, pointing to the importance of propagation (phase matching) effects as a reason for the high degree of controllability observed in capillaries, answering long-standing debates in the field. A prototype experiment was presented demonstrating the versatility of the developed soft x-ray shaping technique for quantum control in this hitherto unexplored wavelength region. Shaped high-harmonic spectra were again used in an adaptive feedback loop experiment to control the gas-phase photodissociation reaction of SF$_6$ molecules. A time-of-flight mass spectrometer was used for the detection of the ionic fragments. The branching ratios of particular fragmentation channels could be varied by optimally shaped soft x-ray light fields. Although in one case only slight changes of the branching ratio were possible, an optimal solution was found, proving the sufficient technical stability of this unique coherent soft-x-ray shaping method for future applications in optimal control. Active shaping of the spectral amplitude in coherent spectral regions of $\sim$10~eV bandwidth was shown to directly correspond to shaping the temporal features of the emerging soft x-ray pulses on sub-femtosecond time scales. This can be understood by the dualism of frequency and time with the Fourier transformation acting as translator. A quantum-mechanical simulation was used to clarify the magnitude of temporal control over the shape of the attosecond pulses produced in the high-harmonic-generation process. In conjunction with the experimental results, the first attosecond time-scale pulse shaper could thus be demonstrated in this work. The availability of femtosecond pulse shapers opened the field of adaptive femtosecond quantum control. The milestone idea of closed-loop feedback control to be implemented experimentally was expressed by Judson and Rabitz in their seminal work titled ``Teaching lasers to control molecules''. This present work extends and turns around this statement. Two fundamentally new achievements can now be added, which are ``Teaching molecules to control laser light conversion'' and ``Teaching lasers to control coherent soft x-ray light''. The original idea thus enabled the leap from femtosecond control of molecular dynamics into the new field of attosecond control of electron motion to be explored in the future. The \emph{closed}-loop approach could really \emph{open} the door towards fascinating new perspectives in science. Coming back to the introduction in order to close the loop, let us reconsider the analogy to the general chemical reaction. Photonic reaction control was presented by designing and engineering effective media (catalysts) and controlling the preparation of educt photons within the shaped laser pulses to selectively produce desired photonic target states in the soft x-ray spectral region. These newly synthesized target states in turn could be shown to be effective in the control of chemical reactions. The next step to be accomplished will be the control of sub-femtosecond time-scale electronic reactions with adaptively controlled coherent soft x-ray photon bunches. To that end a time-of-flight high-energy photoelectron spectrometer has recently been built, which will now allow to directly monitor electronic dynamics in atomic, molecular or solid state systems. Fundamentally new insights and applications of the nonlinear interaction of shaped attosecond soft x-ray pulses with matter can be expected from these experiments.
Summary The nature of the chemical bond is a topic under constant debate. What is known about individual molecular properties and functional groups is often taught and rationalized by explaining Lewis structures, which, in turn, make extensive use of the valence concept. The valence concept distinguishes between electrons, which do not participate in chemical interactions (core electrons) and those, which do (single, double, triple bonds, lone-pair electrons, etc.). Additionally, individual electrons are assigned to atomic centers. The valence concept is of paramount success: It allows the successful planning of chemical syntheses and analyses, it explains the behavior of individual functional groups, and, moreover, it provides the “language” to think of and talk about molecular structure and chemical interactions. The resounding success of the valence concept may be misleading to forget its approximative character. On the other hand, quantum mechanics provide in principle a quantitative description of all chemical phenomena, but there is no discrimination between electrons in quantum mechanics. From the quantum mechanical point of view there are only indistinguishable electrons in the field of the nuclei, i.e., it is impossible to assign a given electron to a particular center or to ascribe a particular purpose to individual electrons. The concept of indistinguishability of micro particles is founded on the Heisenberg uncertainty relation, which states, that wavepackets diverge in the 6N dimensional phase space, such that individual trajectories can not be identified. Hence it is a deep-rooted and approved physical concept. As an introduction to the present work density partitioning schemes were discussed, which divide the total molecular density into chemically meaningful areas. These partitioning schemes are intimately related to either the concepts of bound atoms in a molecule (as in the Atoms In Molecules theory (AIM) according to Bader or as in the Hirshfeld partitioning scheme) or to the concept of chemical structure in the sense of Lewis structures, which divide the total molecular density into core and valence density, where the valence density is split up again into bonding and non-bonding electron densities. Examples are early and recent loge theories, the topological analysis by means of the Electron Localization Function (ELF), and the Natural Bond Orbital (NBO) approach. Of these partitioning schemes, the theories according to Bader (AIM), to Becke and Edgecomb (ELF) and according to Weinhold (NBO and Natural Resonance Theory, NRT), respectively, were reviewed in detail critically. Points of criticism were explicated for each of the mentioned theories. Since theoretically derived electron densities are to be compared to experimentally derived densities, a brief introduction into the theory of X-ray di®raction experiments was given and the multipole formalism was introduced. The procedure of density refinement was briefly discussed. Various suggestions for improvements were developed: One strategy would be the employment of model parameters, which are to a maximum degree mutually orthogonal, with the object of minimizing correlations among the model parameters, e.g., to introduce nodal planes into the radial functions of the multipole model. A further suggestion involves the guidance of the iterative refinement procedure by an extremum principle, which states, that when di®erent solutions to the least squares minimization problem are available with about the same statistical measures of quality and with about the same residual density, then the solution is to prefer, which yields a minimum density at the bond critical point (BCP) and a maximum polarity in terms of the ratio of distances between the BCP and the nuclei. This suggestion is based on the well known fact, that the bond polarity (in terms of the ratio of distances between the BCP and the respective nuclei) is underestimated in the experiment. Another suggestion for including physical constraints is the explicit consideration of the virial theorem, e.g., by evaluating the integration of the Laplacian over the entire atomic basins and comparing this value to zero and to the value obtained from the integration of the electron gradient field over the atomic surface. The next suggestion was to explicitly use the electrostatic theorem of Feynman (often also denoted as Hellmann-Feynman theorem), which states, that the forces onto the nuclei can be calculated from the purely classical electrostatic forces of the electron distribution and the nuclei distribution. For a stationary system, these forces must add to zero. This also provides an internal quality criterion of the density model. This can be performed in an iterative way during the refinement procedure or as a test of the final result. The use of the electrostatic theorem is expected to reduce significantly correlations among static density parameters and parameters describing vibrations, since it is a valuable tool to discriminate between physically reasonable and artificial static electron densities. All of these mentioned suggestions can be applied as internal quality criteria. The last suggestion is based on the idea to initiate the experimental refinement with a set of model parameters, which is, as much as possible close to the final solution. This can be achieved by performing periodic boundary conditions calculations, from which theoretically created files are obtained, which contain the Miller indices (h, k, l) and the respective intensity I. This file is used for a model parameter estimation (refinement), which excludes vibrations. The resulting parameters can be used for the experimental refinement, where, in a first step, the density parameters are fixed to determine the parameters describing vibrations. For a fine tuning, again the electrostatic theorem and the other above mentioned suggestions could be applied. Theoretical predictions should not be biased by the method of computation. Therefore the dependence of the density analyzing tools on the level of calculation (method of calculation/basis set) and on the substituents in complex chemical bonding situations were evaluated in the second part of the present work. A number of compounds containing formal single and double sulfur nitrogen bonds was investigated. For these compounds, experimental data were also available. The calculated data were compared internally and with the experimental results. The internal comparison was drawn with regard to questions of convergency as well as with regard to questions of consistency: The resulting molecular properties from NBO/NRT analyses were found to be very stable, when the geometries were optimized at the respective level of theory. This stability is valid for variations in the methods of calculation as well as for variations in the basis set. Only the individual resonance weights of the contributing Natural Lewis Structures differed considerably depending on the level of calculation and depending on the substituents. However, the deviations were in both cases to a large extent within a limit which preserves the descending order of the leading resonance structure weights. The resulting bond orders, i.e., the total, covalent and ionic bond order from NRT calculations, were not affected by the shift in the resonance weights. The analysis of the bond topological parameters resulted in a discrimination between insensitive parameters and sensitive parameters. The stable parameters do neither depend strongly on the method of calculation nor on the basis set. Only minor variation occurs in the numerical values of these parameters, when the level of calculation is changed or even when other functional groups (H, Me, or tBu) are employed, as long as the methods of calculation do not drop considerably below a standard level. The bond descriptors of the sulfur nitrogen bonds were found to be also stable with respect to the functional groups R = H, R = Me, and R = tBu. Stable parameters are the bond distance, the density at the bond critical point (BCP) and the ratio of distances between the BCP and the nuclei A and B, which varies clearly when considering the formal bond type. For very small basis sets like the 3-21G basis set, this characteristic stability collapses. The sensitive parameters are based on the second derivatives of the density with respect to the coordinates. This is in accordance with the well known fact, that the total second derivative of the density with respect to the coordinates is a strongly oscillating function with positive as well as negative values. A profound deviation has to be anticipated as a consequence of strong oscillations. lambda3, which describes the local charge depletion in the direction of the interaction line, is the most varying parameter. A detailed analysis revealed that the position of the BCP in the rampant edge of the Laplacian distribution is responsible for the sensitivity of the numerical value of lambda3 in formal double bonds. Since the slope of the Laplacian assumes very high values in its rampant edge, a tiny displacement of the BCP leads already to a considerable change in lambda3. This instability is not a failure of the underlying theory, but it yields de facto to a considerable dependence of sensitive bond topological properties on the method of calculation and on the applied basis sets. Since the total second derivative is important to judge on the nature of the bond in the AIM theory (closed shell interactions versus shared interactions), the changes in lambda3 can lead to differing chemical interpretations. The comparison of theoretically derived bond topological properties of various sulfur nitrogen bonds provides the possibility to measure the self consistency of this data set. All data sets clearly exhibit a linear correlation between the bond distances and the density at the BCP on one hand and between the bond distances and the Laplacian values at the BCP on the other hand. These correlations were almost independent of the basis set size. In this context, the linear regression has to be regarded exclusively as a descriptive statistics tool. There is no correlation anticipated a priori. The formal bond type was found to be readily deducible from the theoretically obtained bond topological descriptors of the model systems. In this sense, the bond topological properties are self consistent despite of the numerical sensitivity of the derivatives, as exemplified above. Often, calculations are performed with the experimentally derived equilibrium geometries and not with optimized ones. Applying this approach, the computationally costly geometry optimizations are saved. Following this approach the bond topological properties were calculated using very flexible basis sets and employing the fixed experimental geometry (which, of course, includes the application of tBu groups). Regression coe±cients similar to those from optimized geometries were obtained for correlations between bond distances and the densities at the BCP as well as for the correlation between bond distances and the Laplacian at the BCP, i.e. the approach is valid. However, the data points scattered less and the coe±cient of correlation was clearly increased when geometry optimizations were performed beforehand. The comparison between data obtained from theory and experiment revealed fundamental discrepancies: In the data set of bond topological parameters from the experiment, the behavior of only 2 out of 3 insensitive parameters was comparable to the behavior of the theoretically obtained values, i.e. theoretical and experimental bond distances as well as theoretical and experimental densities at the BCP correlate. From the theoretically obtained data it was easy to deduce the formal bond type from the position of the BCP, since it changed in a systematic manner. The respective experimentally obtained values were almost constant and did not change systematically. For the SN bonds containing compounds, the total second derivative assumes exclusively negative values in the experiment. Due to the different internal behavior, experimentally and theoretically sensitive bond topological values could not be compared directly. The qualitative agreement in the Laplacian distribution, however, was excellent. In the third and last part of this work, the application to chemical systems follows. Formal hypervalent molecules, i.e. molecules where some atoms are considered to hold more than 8 electrons in their valence shell, were investigated. These were compounds containing sulfur nitrogen bonds (H(NtBu)2SMe, H2C{S(NtBu)2(NHtBu)}2, S(NtBu)2 and S(NtBu)3) and a highly coordinated silicon compound. The set of sulfur nitrogen compounds also contained a textbook example for valence expansion, the sulfur triimide. For these molecules, experimental reference values were available from high resolution X-ray experiments. The experimental results were in the case of the sulfur triimide not unique. Furthermore, from the experimental bond topological data no definite conclusion about the formal bonding type could be drawn. The situation of sulfur nitrogen bonds in the above mentioned set of molecules was analyzed in terms of a geometry discussion and by means of a topological analysis. The methyl-substituted isolated molecules served as model compounds. For the interpretation of the bonding situation additional NBO/NRT calculations were preformed for the sulfur nitrogen compounds and an ELF calculation and analysis was performed for the silicon compound. The ELF analysis included not only the presentation and discussion of the ELF-isosurfaces (eta = 0.85), but also the investigation of populations of disynaptic valence basins and the percentage contributions to these populations of the individual atoms when the disynaptic valence basins are split into atomic contributions according to Bader’s partitioning scheme. The question of chemical interest was whether hypervalency is present in the set of molecules or not. In the first case the octet rule would be violated, in the second case Pauling’s verdict would be violated. While the concept of hypervalency is well established in chemistry, the violation of Pauling’s verdict is not. The quantitative numbers of the sensitive bond topological values from theory and experiment were not comparable, since no systematic relationship between the experimentally and theoretically determined sensitive bond descriptors was found. However, the insensitive parameters are in good agreement and the qualitative Laplacian distribution is, with few exceptions, in excellent agreement. The formal bonding type was deduced from experimental and theoretical topological data by considering the number and shape of valence shell charge concentrations in proximity to the sulfur and nitrogen centers. The results from NBO/NRT calculations confirmed the findings. All employed density analyzing tools AIM, ELF and NBO/NRT coincided in describing the bonding situation in the formally hypervalent molecules as highly polar. A comparison and analysis of experimentally and theoretically derived electron densities led consistently to the result, that regarding this set of molecules, hypervalency has to be excluded unequivocally.
Adaptive femtosecond quantum control has proven to be a very successful method in many different scientific fields like physics, chemistry or biology. Numerous quantum systems and in particular molecules undergoing chemical reactions have been controlled using shaped femtosecond laser pulses. This method allows to go beyond simple observation and to obtain active control over quantum--mechanical systems. It uses interference phenomena in the time and/or frequency domain to achieve selectivity. The shaped femtosecond laser pulses employed in this scheme have until recently been purely linearly polarized. Therefore, they only address the scalar properties of light--matter interaction and neglect the vectorial character of both the dipole moment $\vec{\mu}$ and the electric field $\vec{E}(t)$. Especially in the quantum control of chemical reactions the investigated systems ---the molecules--- are three dimensional and exhibit complex spatio--tempo\-ral dynamics. With the help of polarization--shaped laser pulses one is now able to follow these dynamics in both, time and spatial direction, and can therefore reach a new level of control over quantum--mechanical systems. In this work, the generation of polarization--shaped laser pulses has been implemented in an optical setup. It requires no interferometric stability as a result of the identical beam path for both polarization components. Dual--channel spectral interferometry was employed as experimental pulse characterization and a mathematical description of the time--dependent polarization state of these pulses was given. The polarization modulation of the shaped pulses by subsequent optical elements was investigated and some solutions to minimize these modulations were presented. Jones matrix calculus with experimentally calibrated matrices was implemented to account for all polarization distortions from the LCD to the position of the experiment and for full characterization of the generated pulse shapes. Adaptive polarization shaping was demonstrated in a purely optical realization of the learning--loop concept. The learning algorithm was able to find the needed linear polarization in order to maximize second harmonic generation in a nonlinear optical crystal. The closed--loop configuration has proven to be capable to clear up more complicated polarization distortion, which was introduced using a multiple order half--wave plate designed for use at a wavelength of 620~nm. The additional deformation of the spectral phase through dispersion in a 10~cm long SF10 glass rod has also been compensated automatically. After these optical demonstration experiments ultrafast polarization shaping was applied to control a quantum system. Polarization sensitivity was shown in pump--probe measurements of the multiphoton ionization of potassium dimer molecules K$_2$. This sensitivity was exploited in a more general way in a learning--loop experiment with polarization--shaped laser pulses. A qualitatively new level of control was demonstrated using the time--dependent polarization state of laser pulses as an active agent. This polarization control was applicable even in randomly aligned molecules, which is a significant simplification of the experimental setup. In addition to these polarization control experiments, the three dimensional dynamics of molecules were also investigated and controlled. The \textit{cis--trans} photoisomerization of NK88 was studied in the liquid phase by transient absorption spectroscopy. The isomerization reaction efficiency was enhanced as well as reduced using linearly polarized laser pulses at 400~nm shaped in spectral phase and amplitude. This experiment demonstrates the ability to control the large scale motion of complex molecular groups with shaped femtosecond laser pulses. The modification of the molecular geometry can be regarded as a first step towards control of chirality in photochemistry. Especially with the successful demonstration of polarization quantum control, which is required in the theoretical models for the selective conversion of one enantiomer into the other, the way is paved towards coherent control of chirality. Besides these fascinating applications of polarization shaping it should now also be possible to extend the wavelength range of these pulses. Apart from second harmonic generation in order to reach the ultraviolet region intra-pulse difference frequency generation could be an option to open the mid-infrared spectral range for polarization shaping. With these new wavelength regions numerous new perspectives arise for quantum control using polarization--shaped laser pulses. Referring once more to the novel of Edwin A. Abbott presented in the introduction one could say that shaped femtosecond pulses really have left Flatland. Or to put it into the words of the sphere, when it teaches the square about the perception of dimensions: \begin{quote} ``Look yonder [...] in Flatland thou hast lived; of Lineland thou hast received a vision; thou hast soared with me to the heights of Spaceland;'' \hfill Edwin A.~Abbott~\cite{abbott1884}, 1884 \end{quote}
Shadow Mask assisted Molecular Beam Epitaxy (SMMBE) is a technique enabling selected area epitaxy of semiconductor heterostructures through shadow masks. The objective of this work was the development of the SMMBE technique for the reliable fabrication of compound semiconductor nanostructures of high structural and optical quality. In order to accomplish this, technological processes have been developed and optimized. This, in combination with model calculations of the basic kinetic growth processes has enabled the fabrication of high quality quantum structures. A high spatial precision and control of the incidence regions of the molecular beams during the SMMBE process are required for the fabrication of nanostructures. One of the technological developments to this effect, which has substantially enhanced the versatility of SMMBE, is the introduction of a new type of freestanding shadow masks: Growth through such a mask with different incidence angles of the molecular beams is equivalent to employing different mechanical masks, but is much more accurate since the precision of mechanical alignment is limited. A consistent model has been developed, which successfully explains the growth dynamics of molecular beam epitaxy through shadow masks. The redistribution of molecular fluxes under shadow masks may affect the growth rates on selected areas of the substrate drastically. In the case of compound semiconductors, reactions between the constituent species play important roles in controlling the growth rates as a function of the growth parameters. The predictions of the model regarding the growth of II-VI and III-V compounds have been tested experimentally and the dependence of the growth rates on the growth parameters has been verified. Moreover, it has been shown, that selected area epitaxy of II-VI and III-V compounds are governed by different surface kinetics. Coexisting secondary fluxes of both constituent species and the apparent non-existence of surface diffusion are characteristic for SMMBE of II-VI compounds. In contrast, III-V SMMBE is governed by the interplay between secondary group-V flux and the surface migration of group-III adatoms. In addition to the basic surface kinetic processes described by the model, the roles of orientation and strain-dependent growth dynamics, partial shadow, and material deposition on the mask (closure of apertures) have been discussed. The resulting advanced understanding of the growth dynamics (model and basic experiments) in combination with the implementation of technical improvements has enabled the development and application of a number of different processes for the fabrication of both II-VI and III-V nanostructures. In addition to specific material properties, various other phenomena have been exploited, e.g., self-organization. It has been shown that, e.g., single quantum dots and quantum wires can be reliably grown. Investigations performed on the SMMBE nanostructures have demonstrated the high positional and dimensional precision of the SMMBE technique. Bright cathodoluminescence demonstrates that the resulting quantum structures are of high structural and optical quality. In addition to these results, which demonstrate SMMBE as a prospective nanofabrication technique, the limitations of the method have also been discussed, and various approaches to overcome them have been suggested. Moreover, propositions for the fabrication of complex quantum devices by the multiple application of a stationary shadow mask have been put forward. In addition to selected area growth, the shadow masks can assist in etching, doping, and in situ contact definition in nanoscale selected areas. Due to the high precision and control over the dimensions and positions of the grown structures, which at the same time are of excellent chemical, crystal, and optical quality, SMMBE provides an interesting perspective for the fabrication of complex quantum devices from II-VI and III-V semiconductors.