Optical properties of excited silicon and germanium at low temperatures

Part I of this thesis deals with 3 topics concerning the luminescence from bound multi-exciton complexes in Si. Part II presents a model for the decay of electron-hole droplets in pure and doped Ge.

Part I.

We present high resolution photoluminescence data for Si doped With Al, Ga, and In. We observe emission lines due to recombination of electron-hole pairs in bound excitons and satellite lines which have been interpreted in terms of complexes of several excitons bound to an impurity. The bound exciton luminescence in Si:Ga and Si:Al consists of three emission lines due to transitions from the ground state and two low lying excited states. In Si:Ga, we observe a second triplet of emission lines which precisely mirror the triplet due to the bound exciton. This second triplet is interpreted as due to decay of a two exciton complex into the bound exciton. The observation of the second complete triplet in Si:Ga conclusively demonstrates that more than one exciton will bind to an impurity. Similar results are found for Si:Al. The energy of the lines show that the second exciton is less tightly bound than the first in Si:Ga. Other lines are observed at lower energies. The assumption of ground state to ground-state transitions for the lower energy lines is shown to produce a complicated dependence of binding energy of the last exciton on the number of excitons in a complex. No line attributable to the decay of a two exciton complex is observed in Si:In.

We present measurements of the bound exciton lifetimes for the four common acceptors in Si and for the first two bound multi-exciton complexes in Si:Ga and Si:Al. These results are shown to be in agreement with a calculation by Osbourn and Smith of Auger transition rates for acceptor bound excitons in Si. Kinetics determine the relative populations of complexes of various sizes and work functions, at temperatures which do not allow them to thermalize with respect to one another. It is shown that kinetic limitations may make it impossible to form two-exciton complexes in Si:In from a gas of free excitons.

We present direct thermodynamic measurements of the work functions of bound multi-exciton complexes in Al, B, P and Li doped Si. We find that in general the work functions are smaller than previously believed. These data remove one obstacle to the bound multi-exciton complex picture which has been the need to explain the very large apparent work functions for the larger complexes obtained by assuming that some of the observed lines are ground-state to ground-state transitions. None of the measured work functions exceed that of the electron-hole liquid.

Part II.

A new model for the decay of electron-hole-droplets in Ge is presented. The model is based on the existence of a cloud of droplets within the crystal and incorporates exciton flow among the drops in the cloud and the diffusion of excitons away from the cloud. It is able to fit the experimental luminescence decays for pure Ge at different temperatures and pump powers while retaining physically reasonable parameters for the drops. It predicts the shrinkage of the cloud at higher temperatures which has been verified by spatially and temporally resolved infrared absorption experiments. The model also accounts for the nearly exponential decay of electron-hole-droplets in lightly doped Ge at higher temperatures.

Extracting material response from simple mechanical tests on hardening-softening-hardening viscoplastic solids

Compliant foams are usually characterized by a wide range of desirable mechanical properties. These properties include viscoelasticity at different temperatures, energy absorption, recoverability under cyclic loading, impact resistance, and thermal, electrical, acoustic and radiation-resistance. Some foams contain nano-sized features and are used in small-scale devices. This implies that the characteristic dimensions of foams span multiple length scales, rendering modeling their mechanical properties difficult. Continuum mechanics-based models capture some salient experimental features like the linear elastic regime, followed by non-linear plateau stress regime. However, they lack mesostructural physical details. This makes them incapable of accurately predicting local peaks in stress and strain distributions, which significantly affect the deformation paths. Atomistic methods are capable of capturing the physical origins of deformation at smaller scales, but suffer from impractical computational intensity. Capturing deformation at the so-called meso-scale, which is capable of describing the phenomenon at a continuum level, but with some physical insights, requires developing new theoretical approaches.

A fundamental question that motivates the modeling of foams is ‘how to extract the intrinsic material response from simple mechanical test data, such as stress vs. strain response?’ A 3D model was developed to simulate the mechanical response of foam-type materials. The novelty of this model includes unique features such as the hardening-softening-hardening material response, strain rate-dependence, and plastically compressible solids with plastic non-normality. Suggestive links from atomistic simulations of foams were borrowed to formulate a physically informed hardening material input function. Motivated by a model that qualitatively captured the response of foam-type vertically aligned carbon nanotube (VACNT) pillars under uniaxial compression [2011,“Analysis of Uniaxial Compression of Vertically Aligned Carbon Nanotubes,” J. Mech.Phys. Solids, 59, pp. 2227–2237, Erratum 60, 1753–1756 (2012)], the property space exploration was advanced to three types of simple mechanical tests: 1) uniaxial compression, 2) uniaxial tension, and 3) nanoindentation with a conical and a flat-punch tip. The simulations attempt to explain some of the salient features in experimental data, like
1) The initial linear elastic response.
2) One or more nonlinear instabilities, yielding, and hardening.

The model-inherent relationships between the material properties and the overall stress-strain behavior were validated against the available experimental data. The material properties include the gradient in stiffness along the height, plastic and elastic compressibility, and hardening. Each of these tests was evaluated in terms of their efficiency in extracting material properties. The uniaxial simulation results proved to be a combination of structural and material influences. Out of all deformation paths, flat-punch indentation proved to be superior since it is the most sensitive in capturing the material properties.

On Ultrafast Time-Domain TeraHertz Spectroscopy in the Condensed Phase: Linear Spectroscopic Measurements of Hydrogen-Bond Dynamics of Astrochemical Ice Analogs and Nonlinear TeraHertz Kerr Effect Measurements of Vibrational Quantum Beats

Much of the chemistry that affects life on planet Earth occurs in the condensed phase. The TeraHertz (THz) or far-infrared (far-IR) region of the electromagnetic spectrum (from 0.1 THz to 10 THz, 3 cm^-1 to 300 cm^-1, or 3000 μm to 30 μm) has been shown to provide unique possibilities in the study of condensed-phase processes. The goal of this work is to expand the possibilities available in the THz region and undertake new investigations of fundamental interest to chemistry. Since we are fundamentally interested in condensed-phase processes, this thesis focuses on two areas where THz spectroscopy can provide new understanding: astrochemistry and solvation science. To advance these fields, we had to develop new instrumentation that would enable the experiments necessary to answer new questions in either astrochemistry or solvation science. We first developed a new experimental setup capable of studying astrochemical ice analogs in both the TeraHertz (THz), or far-Infrared (far-IR), region (0.3 - 7.5 THz; 10 - 250 cm^-1) and the mid-IR (400 - 4000 cm^-1). The importance of astrochemical ices lies in their key role in the formation of complex organic molecules, such as amino acids and sugars in space. Thus, the instruments are capable of performing variety of spectroscopic studies that can provide especially relevant laboratory data to support astronomical observations from telescopes such as the Herschel Space Telescope, the Stratospheric Observatory for Infrared Astronomy (SOFIA), and the Atacama Large Millimeter Array (ALMA). The experimental apparatus uses a THz time-domain spectrometer, with a 1750/875 nm plasma source and a GaP detector crystal, to cover the bandwidth mentioned above with ~10 GHz (~0.3 cm^-1) resolution.

Using the above instrumentation, experimental spectra of astrochemical ice analogs of water and carbon dioxide in pure, mixed, and layered ices were collected at different temperatures under high vacuum conditions with the goal of investigating the structure of the ice. We tentatively observe a new feature in both amorphous solid water and crystalline water at 33 cm^-1 (1 THz). In addition, our studies of mixed and layered ices show how it is possible to identify the location of carbon dioxide as it segregates within the ice by observing its effect on the THz spectrum of water ice. The THz spectra of mixed and layered ices are further analyzed by fitting their spectra features to those of pure amorphous solid water and crystalline water ice to quantify the effects of temperature changes on structure. From the results of this work, it appears that THz spectroscopy is potentially well suited to study thermal transformations within the ice.

To advance the study of liquids with THz spectroscopy, we developed a new ultrafast nonlinear THz spectroscopic technique: heterodyne-detected, ultrafast THz Kerr effect (TKE) spectroscopy. We implemented a heterodyne-detection scheme into a TKE spectrometer that uses a stilbazoiumbased THz emitter, 4-N,N-dimethylamino-4-N-methyl-stilbazolium 2,4,6-trimethylbenzenesulfonate (DSTMS), and high numerical aperture optics which generates THz electric field in excess of 300 kV/cm, in the sample. This allows us to report the first measurement of quantum beats at terahertz (THz) frequencies that result from vibrational coherences initiated by the nonlinear, dipolar interaction of a broadband, high-energy, (sub)picosecond THz pulse with the sample. Our instrument improves on both the frequency coverage, and sensitivity previously reported; it also ensures a backgroundless measurement of the THz Kerr effect in pure liquids. For liquid diiodomethane, we observe a quantum beat at 3.66 THz (122 cm^-1), in exact agreement with the fundamental transition frequency of the υ4 vibration of the molecule. This result provides new insight into dipolar vs. Raman selection rules at terahertz frequencies.

To conclude we discuss future directions for the nonlinear THz spectroscopy in the Blake lab. We report the first results from an experiment using a plasma-based THz source for nonlinear spectroscopy that has the potential to enable nonlinear THz spectra with a sub-100 fs temporal resolution, and how the optics involved in the plasma mechanism can enable THz pulse shaping. Finally, we discuss how a single-shot THz detection scheme could improve the acquisition of THz data and how such a scheme could be implemented in the Blake lab. The instruments developed herein will hopefully remain a part of the groups core competencies and serve as building blocks for the next generation of THz instrumentation that pushes the frontiers of both chemistry and the scientific enterprise as a whole.

I. Electron spin relaxation studies of manganese(II) complexes in acetonitrile. II. Nuclear spin relaxation studies of bromine in tetrabromomanganese(II) in acetonitrile

Magnetic resonance techniques have given us a powerful means for investigating dynamical processes in gases, liquids and solids. Dynamical effects manifest themselves in both resonance line shifts and linewidths, and, accordingly, require detailed analyses to extract desired information. The success of a magnetic resonance experiment depends critically on relaxation mechanisms to maintain thermal equilibrium between spin states. Consequently, there must be an interaction between the excited spin states and their immediate molecular environment which promote changes in spin orientation while excess magnetic energy is coupled into other degrees of freedom by non-radiative processes. This is well known as spin-lattice relaxation. Certain dynamical processes cause fluctuations in the spin state energy levels leading to spin-spin relaxation and, here again, the environment at the molecular level plays a significant role in the magnitude of interaction. Relatively few electron spin relaxation studies of solutions have been conducted and the present work is addressed toward the extension of our knowledge in this area and the retrieval of dynamical information from line shape analyses on a time scale comparable to diffusion controlled phenomena.

Specifically, the electron spin relaxation of three Mn⁺²3d⁵ complexes, Mn(CH₃CN)₆⁺², MnCl₄^-2 in acetonitrile has been studied in considerable detail. The effective spin Hamiltonian constants were carefully evaluated under a wide range of experimental conditions. Resonance widths of these Mn⁺² complexes were studied in the presence of various excess ligand ions and as a function of concentration, viscosity, temperature and frequency (X-band, ~9.5 Ԍ Hz and K-band, ~35 Ԍ Hz).

A number of interesting conclusions were drawn from these studies. For the Et₄NCl-₄^-2 system several relaxation mechanisms leading to resonance broadening were observed. One source appears to arise through spin-orbit interactions caused by modulation of the ligand field resulting from transient distortions of the complex imparted by solvent fluctuations in the immediate surroundings of the paramagnetic ion. An additional spin relaxation was assigned to the formation of ion pairs [Et₄N⁺…MnCl₄^-2] and it was possible to estimate the dissociation constant for this specie in acetonitrile.

The Bu₄NBr-MnBr₄^-2 study was considerably more interesting. As in the former case, solvent fluctuations and ion-pairing of the paramagnetic complex [Bu₄N⁺…MnBr₄^-2] provide significant relaxation for the electronic spin system. Most interesting, without doubt, is the onset of a new relaxation mechanism leading to resonance broadening which is best interpreted as chemical exchange. Thus, assuming that resonance widths were simply governed by electron spin state lifetimes, we were able to extract dynamical information from an interaction in which the initial and final states are the same

MnBr₄^-2 + Br^- = MnBr₄^-2 + Br^-.

The bimolecular rate constants were obtained at six different temperatures and their magnitudes suggested that the exchange is probably diffusion controlled with essentially a zero energy of activation. The most important source of spin relaxation in this system stems directly from dipolar interactions between the manganese 3d⁵ electrons. Moreover, the dipolar broadening is strongly frequency dependent indicating a deviation between the transverse and longitudinal relaxation times. We are led to the conclusion that the 3d⁵ spin states of ion-paired MnBr₄^-2 are significantly correlated so that dynamical processes are also entering the picture. It was possible to estimate the correlation time, ^Td, characterizing this dynamical process.

In Part II we study nuclear magnetic relaxation of bromine ions in the MnBr4-2-Bu4NBr-acetonitrile system. Essentially we monitor the 79Br and 81Br linewidths in response to the [MnBr4-2]/[Br-] ratio with the express purpose of supporting our contention that exchange is occurring between "free" bromine ions in the solvent and bromine in the first coordination sphere of the paramagnetic anion. The complexity of the system elicited a two-part study: (1) the linewidth behavior of Bu4NBr in anhydrous CH3CN in the absence of MnBr4-2 and (2) in the presence of MnBr4-2. It was concluded in study (1) that dynamical association, Bu4NBr k1= Bu4N+ + Br-, was modulating field-gradient interactions at frequencies high enough to provide an estimation of the unimolecular rate constant, k1. A comparison of the two isotopic bromine linewidth-mole fraction results led to the conclusion that quadrupole interactions provided the dominant relaxation mechanism. In study (2) the "residual" bromine linewidths for both 79Br and 81Br are clearly controlled by quadrupole interactions which appear to be modulated by very rapid dynamical processes other than molecular reorientation. We conclude that the "residual" linewidth has its origin in chemical exchange and that bromine nuclei exchange rapidly between a "free" solvated ion and the paramagnetic complex, MnBr4-2.

Polaron hopping in olivine phosphates studied by nuclear resonant scattering

Valence fluctuations of Fe²⁺ and Fe³⁺ were studied in a solid solution of Li_xFePO₄ by nuclear resonant forward scattering of synchrotron x rays while the sample was heated in a diamond-anvil pressure cell. The spectra acquired at different temperatures and pressures were analyzed for the frequencies of valence changes using the Blume-Tjon model of a system with a fluctuating Hamil- tonian. These frequencies were analyzed to obtain activation energies and an activation volume for polaron hopping. There was a large suppression of hopping frequency with pressure, giving an anomalously large activation volume. This large, positive value is typical of ion diffusion, which indicates correlated motions of polarons, and Li⁺ ions that alter the dynamics of both.

In a parallel study of Na_xFePO₄, the interplay between sodium ordering and electron mobility was investigated using a combination of synchrotron x-ray diffraction and nuclear resonant scattering. Conventional Mossbauer spectra were collected while the sample was heated in a resistive furnace. An analysis of the temperature evolution of the spectral shapes was used to identify the onset of fast electron hopping and determine the polaron hopping rate. Synchrotron x-ray diffraction measurements were carried out in the same temperature range. Reitveld analysis of the diffraction patterns was used to determine the temperature of sodium redistribution on the lattice. The diffraction analysis also provides new information about the phase stability of the system. The temperature evolution of the iron site occupancies from the Mossbauer measurements, combined with the synchrotron diffraction results give strong evidence for a relationship between the onset of fast electron dynamics and the redistribution of sodium in the lattice.

Measurements of activation barriers for polaron hopping gave fundamental insights about the correlation between electronic carriers and mobile ions. This work established that polaron-ion interactions can alter the local dynamics of electron and ion transport. These types of coupled processes may be common in many materials used for battery electrodes, and new details concerning the influence of polaron-ion interactions on the charge dynamics are relevant to optimizing their electrochemical performance.