We discuss a model for the on-site matrix elements of the sp3d5s* tight-binding hamiltonian of a strained diamond or zinc-blende crystal or nanostructure. This model features on-site, off-diagonal couplings between the s, p and d orbitals, and is able to reproduce the effects of arbitrary strains on the band energies and effective masses in the full Brillouin zone. It introduces only a few additional parameters and is free from any ambiguities that might arise from the definition of the macroscopic strains as a function of the atomic positions. We apply this model to silicon, germanium and their alloys as an illustration. In particular, we make a detailed comparison of tight-binding and ab initio data on strained Si, Ge and SiGe.
We present a comprehensive theory of the circularly polarized luminescence and its dependence on strain in spin-polarized Si and Ge. Symmetries of wavefunctions and interactions are used to derive concise ratios between intensities of the right and left circularly polarized luminescence for each of the dominant phonon-assisted optical transitions. These ratios are then used to explain the circular polarization degrees of the luminescence peaks in the spectra of biaxially-strained Si and Ge, and of relaxed ${\rm{Si}}_{1-x}{\rm{Ge}}_{x}$ alloys. The spectra are numerically calculated by a combin…
Germanium-Tin is emerging as a material exhibiting excellent photonic properties. Here we demonstrate optical initialization and readout of spins in this intriguing group IV semiconductor alloy and report on spin quantum beats between Zeeman-split levels under an external magnetic field. Our optical experiments reveal robust spin orientation in a wide temperature range and a persistent spin lifetime that approaches the ns regime at room temperature. Besides important insights into nonradiative recombination pathways, our findings disclose a rich spin physics in novel epitaxial structures direc…
We present ab initio calculations of the electronic and optical properties of hexagonal SiGe alloys in the lonsdaleite structure. Lattice constants and electronic band structures in excellent agreement with experiment are obtained using density-functional theory. Hexagonal Si has an indirect band gap, while hexagonal Ge has a pseudo-direct gap, i.e. the optical transitions at the minimum direct band gap are very weak. The pseudo-direct character of pure hexagonal Ge is efficiently lifted by alloying. Already for a small admixture of Si, symmetry reduction enhances the oscillator strength of th…
A Fe89.15Cr10.75 alloy in a heavily strained (by cold rolling) and strain-relaxed states was studied by means of the conversion electrons Mössbauer spectroscopy (CEMS). Analysis of the spectra in terms of a two-shell model revealed significant differences between the studied samples, in particular, in values of the hyperfine field, a distribution of Cr atoms within the first two neighbor-shells, the latter was expressed in terms of the short-range order parameters, and in the magnetic texture.
Enhancement of the electronic thermoelectric properties of bulk strained silicon-germanium alloys using the scattering relaxation times from first principles
The electronic energy band structure of strained and unstrained Si, Ge and SiGe alloys is examined in this work using thirty-level k.p analysis. The energy bands are at first obtained with ab initio calculations based on the Local-Density-Approximation of Density-Functional Theory, including a GW correction and relativistic effects. The so-calculated band structure is then used to extract the unknown k.p fitting parameters with a conjugate-gradient optimization procedure. In a similar manner, the results of ab initio calculations for strained materials are used to fit the unknown deformation p…
Theoretical studies have shown that new physical properties such as tunable gap openings or quantum spinHall effects could be expected from group-IV graphene analogs (silicene, germanene, stanene). While therehave been numerous studies of growth of such Si, Ge, Sn monolayers, the demonstration of their hexagonalorganization has been often based on postgrowth characterization, and their analogy to graphene has remainedcontroversial. Our real-time scanning tunneling microscopy (STM) observation during Ge deposition on Ag(111)in the 380--430 K temperature range reveals that Ag atoms are involved …
We extend the previous 30-band $k$$\cdot$$p$ model effectively employed for relaxed Ge$_{1-x}$Sn$_{x}$ alloy to the case of strained Ge$_{1-x}$Sn$_{x}$ alloy. The strain-relevant parameters for the 30-band $k$$\cdot$$p$ model are obtained by using linear interpolation between the values of single crystal of Ge and Sn that are from literatures and optimizations. We specially investigate the dependence of band-gap at $L$-valley and $Γ$-valley with different Sn composition under uniaxial and biaxial strain along [100], [110] and [111] directions. The good agreement between our theoretical predict…
High-entropy alloys (HEAs) are solid solutions of multiple elements with equal atomic ratios which present an innovative pathway for de novo alloy engineering. While there exist extensive studies to ascertain the important structural aspects governing their mechanical behaviors, elucidating the underlying deformation mechanisms still remains a challenge. Using atomistic simulations, we probe the particle rearrangements in a yielding, model HEA system to understand the structural origin of its plasticity. We find the plastic deformation is initiated by irreversible topological fluctuations whic…
Using first-principles calculations, we show that the conduction and valence band energies and their deformation potentials exhibit a non-negligible compositional bowing in strained ternary semiconductor alloys such as InGaAs. The electronic structure of these compounds has been calculated within the framework of local density approximation and hybrid functional approach for large cubic supercells and special quasi-random structures, which represent two kinds of model structures for random alloys. We find that the predicted bowing effect for the band energy deformation potentials is rather ins…
We demonstrate the crossover from indirect- to direct band gap in tensile-strained germanium by temperature-dependent photoluminescence. The samples are strained microbridges that enhance a biaxial strain of 0.16% up to 3.6% uniaxial tensile strain. Cooling the bridges to 20 K increases the uniaxial strain up to a maximum of 5.4%. Temperature-dependent photoluminescence reveals the crossover to a fundamental direct band gap to occur between 4.0% and 4.5%. Our data are in good agreement with new theoretical computations that predict a strong bowing of the band parameters with strain.
Phase separation in strained and strain-free samples of Fe84.85Cr15.15 induced by an isothermal annealing at 402 deg C up to 3888 h was studied by means of the Mossbauer spectroscopy. The measured Fe-site spectra were analyzed with two different procedures viz. a hyperfine field distribution and a two-shell superposition methods. Information relevant to the kinetics of the separation process, concentration of Cr in Fe-rich phase, short-range ordering and magnetic texture was obtained based on values of spectral parameters. In particular, the following quantities pertinent to the kinetics were …
The mechanisms of stability or instability in the strained alloy film growth are of intense current interest to both theorists and experimentalists. We consider dislocation-free, coherent, growing alloy films which could exhibit a morphological instability without nucleation. We investigate such strained films by developing a nonequilibrium, continuum model and by performing a linear stability analysis. The couplings of film-substrate misfit strain, compositional stress, deposition rate, and growth temperature determine the stability of film morphology as well as the surface spinodal decomposi…
We used molecular dynamics (MD) simulations to investigate the mechanical properties of cubic zinc blende (ZB) Si0.5Ge0.5 alloy nanowire (NW). Tersoff potential is employed to elucidate the effect of nanowire size, crystal orientations, and temperature on the material properties. We found that the reduction in the cross-sectional area results in lower ultimate tensile strength and Youngs modulus of this alloy which can be attributed to the increased surface to volume ratio. The [111] oriented Si0.5Ge0.5 NW exhibits the highest fracture strength compared to other crystal orientations but [110] …
We propose that the driving force of an ultrafast crystalline-to-amorphous transition in phase-change memory alloys are strained bonds existing in the (metastable) crystalline phase. For the prototypical example of GST, we demonstrate that upon breaking of long Ge-Te bond by photoexcitation Ge ion shot from an octahedral crystalline to a tetrahedral amorphous position by the uncompensated force of strained short bonds. Subsequent lattice relaxation stabilizes the tetrahedral surroundings of the Ge atoms and ensures the long-term stability of the optically induced phase.
Ultrarelativistic charged particles are predicted to emit hard electromagnetic radiation of undulator type while being channeled in a crystal with periodically bent crystallographic planes. The recently proposed crystalline undulator with the bending amplitude smaller than the distance between the bent planes and the bending period shorter than the period of channeling oscillations is far superior to what was proposed previously. In the same time, it is more challenging from the technical point of view because its bending period has to be in the sub-micron range. It is shown that a mixed cryst…
Structure-Dependent Chemical Order Modification in Strained Alloy Nanoparticles
Guangdong Technion – Israel Institute of Technology（广东以色列理工学院）；Universidad de Castilla-La Mancha（卡斯蒂利亚-拉曼恰大学）；Aristotle University of Thessaloniki（塞萨洛尼基亚里士多德大学）
Germanium and silicon-germanium alloys have found entry into Si technology thanks to their compatibility with Si processing and their ability to tailor electronic properties by strain and band-gap engineering. Germanium's potential to extend Si functionalities, as exemplified by lasing action of strained-Ge on Si substrates, has brought the material back to attention. Yet despite these advances, non-radiative transitions, induced by crystal defects originating from the Ge/Si interface, continue to be a serious bottleneck. Here we demonstrate the drastic emission enhancement achieved via contro…
Lonsdaleite germanium has a direct band gap, but it is not an efficient light emitter due to the vanishing oscillator strength of electronic transitions at the fundamental gap. Transitions involving the second lowest conduction band are instead at least three orders of magnitude stronger. The inversion of the two lowest conduction bands would therefore make hexagonal germanium ideal for optoelectronic applications. In this work, we investigate the possibility to achieve this band inversion by applying strain. To this end we perform ab initio calculations of the electronic band structure and op…
A continuum dynamical model is developed to determine the morphological and compositional instabilities on the free surface of heteroepitaxial alloy films in the absence of growth. We use linear stability analysis to study the early nonequilibrium processes of surface evolution, and calculate the stability conditions and diagrams for different cases of material parameters. There are two key considerations in our treatment: the coupling between top free surface of the film and the bulk phase underneath, and the dependence of both Young's and shear elastic moduli on local composition. The combin…
Efficient and cost-effective Si-compatible lasers are a long standing wish of the optoelectronic industry. In principle, there are two options. For many applications, lasers based on III-V compounds provide compelling solutions, even if the integration is complex and therefore costly. However, where low costs and also high integration density are crucial, group-IV-based lasers - made of Ge and GeSn, for example - could be an alternative, provided their performance can be improved. Such progresses will come with better materials but also with the development of a profounder understanding of the…
Germanium is a strong candidate as a laser source for silicon photonics. It is widely accepted that the band structure of germanium can be altered by tensile strain so as to reduce the energy difference between its direct and indirect band gaps. However, the conventional deformation potential model most widely adopted to describe this transformation happens to have been investigated only up to 1 % uniaxially loaded strains. In this work, we use a micro-bridge geometry to uniaxially stress germanium along [100] up to $\varepsilon_{100}$=3.3 % longitudinal strain and then perform electro-absorpt…
We demonstrate room-temperature electroluminescence (EL) from light-emitting diodes (LED) on highly strained germanium (Ge) membranes. An external stressor technique was employed to introduce a 0.76% bi-axial tensile strain in the active region of a vertical PN junction. Electrical measurements show an on-off ratio increase of one order of magnitude in membrane LEDs compared to bulk. The EL spectrum from the 0.76% strained Ge LED shows a 100nm redshift of the center wavelength because of the strain-induced direct band gap reduction. Finally, using tight-binding and FDTD simulations, we discuss…
Corrosion is a major concern for many industries, as corrosive environments can induce structural and morphological changes that lead to material dissolution and accelerate material failure. The progression of corrosion depends on nanoscale morphology, stress, and defects present. Experimentally monitoring this complex interplay is challenging. Here we implement in situ Bragg coherent X-ray diffraction imaging (BCDI) to probe the dissolution of a Co-Fe alloy microcrystal exposed to hydrochloric acid (HCl). By measuring five Bragg reflections from a single isolated microcrystal at ambient condi…
The lifting of the two-fold degeneracy of the conduction valleys in a strained silicon quantum well is critical for spin quantum computing. Here, we obtain an accurate measurement of the splitting of the valley states in the low-field region of interest, using the microwave spectroscopy technique of electron valley resonance (EVR). We compare our results with conventional methods, observing a linear magnetic field dependence of the valley splitting, and a strong low-field suppression, consistent with recent theory. The resonance linewidth shows a marked enhancement above $T\simeq 300$ mK.
GeSn alloys are the most promising semiconductors for light emitters entirely based on group IV elements. Alloys containing more than 8 at.% Sn have fundamental direct band-gaps, similar to conventional III-V semiconductors and thus can be employed for light emitting devices. Here, we report on GeSn microdisk lasers encapsulated with a SiNx stressor layer to produce tensile strain. A 300nm GeSn layer with 5.4 at.% Sn, which is an indirect band-gap semiconductor as-grown with a compressive strain of -0.32 %, is transformed via tensile strain engineering into a truly direct band-gap semiconducto…
The precise knowledge of the atomic order in monocrystalline alloys is fundamental to understand and predict their physical properties. With this perspective, we utilized laser-assisted atom probe tomography to investigate the three-dimensional distribution of atoms in non-equilibrium epitaxial Sn-rich group IV SiGeSn ternary semiconductors. Different atom probe statistical analysis tools including frequency distribution analysis, partial radial distribution functions, and nearest neighbor analysis were employed in order to evaluate and compare the behavior of the three elements to their spati…
The incorporation of bismuth (Bi) in GaAs results in a large reduction of the band gap energy (E$_g$) accompanied with a large increase in the spin-orbit splitting energy ($\bigtriangleup_{SO}$), leading to the condition that $\bigtriangleup_{SO} > E_g$ which is anticipated to reduce so-called CHSH Auger recombination losses whereby the energy and momentum of a recombining electron-hole pair is given to a second hole which is excited into the spin-orbit band. We theoretically investigate the electronic structure of experimentally grown GaBi$_x$As$_{1-x}$ samples on (100) GaAs substrates by dir…
We have synthesized 20 nm thick films of tetragonally strained interstitial Fe-Co-B alloys epitaxially grown on Au55Cu45 buffer layer. The strained axis is perpendicular to the film plane and the corresponding lattice constant c is enlarged with respect to the in-plane lattice parameter a. By adding the interstitial boron with different concentrations 0, 4, and 10 at.% we were able to stabilize the tetragonal strain in 20 nm Fe-Co films with different c/a ratios of 1.013, 1.034 and 1.02, respectively. Using ferromagnetic resonance (FMR) and x-ray magnetic circular dichroism (XMCD) we found tha…
We theoretically investigate the impact of the defect-limited carrier lifetime on the performance of germanium (Ge) light sources, specifically LEDs and lasers. For Ge LEDs, we show that improving the material quality can offer even greater enhancements than techniques such as tensile strain, the leading approach for enhancing Ge light emission. Even for Ge that is so heavily strained that it becomes a direct bandgap semiconductor, the ~1 ns defect-limited carrier lifetime of typical epitaxial Ge limits the LED internal quantum efficiency to less than 10%. In contrast, if the epitaxial Ge carr…
Rare earth free alloys are in focus of permanent magnet research since the accessibility of the elements needed for nowadays conventional magnets is limited. Tetragonally strained iron-cobalt (Fe-Co) has attracted large interest as promising candidate due to theoretical calculations. In experiments, however, the applied strain quickly relaxes with increasing film thickness and hampers stabilization of a strong magnetocrystalline anisotropy. In our study we show that already 2 at% of carbon substantially reduce the lattice relaxation leading to the formation of a spontaneously strained phase wi…
We propose a simple and effective approach to construct the empirical tight-binding parameters of ternary alloys in the virtual crystal approximation. This combines a new, compact formulation of the strain parameters and a linear interpolation of the hamiltonians of binary materials strained to the alloy equilibrium lattice parameter. We show that it is possible to obtain a perfect description of the bandgap bowing of ternary alloys in the InGaAsSb family of materials. Furthermore, this approach is in a good agreement with supercell calculations using the same set of parameters. This scheme op…
We calculate the electronic structure of germanium-tin (Ge$_{1-x}$Sn$_{x}$) binary alloys for $0 \leq x \leq 1$ using density functional theory (DFT). Relaxed alloys with semiconducting or semimetallic behaviour as a function of Sn composition $x$ are identified, and the impact of epitaxial strain is included by constraining supercell lattice constants perpendicular to the [001] growth direction to the lattice constants of Ge, zinc telluride (ZnTe), or cadmium telluride (CdTe) substrates. It is found that application of 1% tensile strain reduces the Sn composition required to bring the (positi…
Thermodynamics and kinetics of Li, Na, and Mg storage in Ge is studied ab initio. The most stable configurations can consist of tetrahedral, substitutional, or a combination of the two types of sites. In the dilute limit, Li, Na prefer interstitial, while Mg prefers substitutional sites. At higher concentrations of Li, Na, and Mg, there is a combination of interstitial and substitutional sites. This is an important finding, as previous ab initio studies of alloying type electrode materials ignored substitutional sites. Insertion energies computed at dilute concentration (x = 1/64) show that Na…
In this study we numerically calculate the spatial profile of mechanical strain on self-assembled germanium (Ge) quantum dots (QDs) grown on a silicon (Si) substrate. Although the topic has been exhaustively studied, interesting features have not been explained or even mentioned in the literature yet. We studied the effect of the cap layer considering two cases: capped QDs (where a Si cap is present above the Ge QDs) and uncapped QDs (where no Si is present above the Ge QDs). We observed that Ge in the capped QDs is more strained compared with the the uncapped QDs. This expected effect is attr…
Severe lattice distortion is suggested for high entropy alloys (HEAs), however, evidence for such effect so far is lacking, and the nature of distortion is yet to be understood. Here, we reveal the distortion in an fcc HEA, Al0.1CrFeCoNi, by direct imaging using electron nanodiffraction. Information about crystal symmetry, lattice strain and atomic distortion are data-mined and mapped from many (~10^4) diffraction patterns. Application to the HEA reveals two embodiments of distortion, nm-sized mosaic blocks of paracrystals and strained nano-clusters. Their interaction gives rise to fractal str…
Some issues that arise when modeling elastic energy for binary alloys are discussed within the context of a Keating model and density functional calculations. The Keating model is based on atomistic modeling of elastic interactions in binary alloy using harmonic springs with species dependent equilibrium lengths. It is demonstrated that the continuum limit for the strain field are the usual equations of linear elasticity for alloys and that they correctly capture the coarse-grained displacement field. In addition, it is established that Euler-Lagrange equation of the continuum limit of the ela…
We investigate the strain-rate-dependent mechanical behavior and deformation mechanisms of a refractory high entropy alloy, Ti29Zr24Nb23Hf24 (at.%), with a single-phase body-centered cubic (BCC) structure. High-temperature compression tests were conducted at temperatures from 700 to 1100°C at strain rates ranging from 10-3 to 10 s-1. A sudden stress drop after yield point was observed at higher temperatures and lower strain rates with the Zener-Holloman parameter, lnZ, in the range of 17.2-20.7. Such a softening behavior can be related to the interaction of dislocations with short-range cluste…
The dynamics of phase field crystal (PFC) modeling is derived from dynamical density functional theory (DDFT), for both single-component and binary systems. The derivation is based on a truncation up to the three-point direct correlation functions in DDFT, and the lowest order approximation using scale analysis. The complete amplitude equation formalism for binary PFC is developed to describe the coupled dynamics of slowly varying complex amplitudes of structural profile, zeroth-mode average atomic density, and system concentration field. Effects of noise (corresponding to stochastic amplitude…
We introduce an off-lattice model with continuous particle distances and pair-potential interactions which allows for the efficient simulation of strained heteroepitaxial growth by means of kinetic Monte Carlo (KMC) simulations. We discuss in detail the application of our model to the simulation of three important strain relaxation mechanisms: First, the formation of misfit dislocations in strained adsorbate films is investigated. We find a power-law misfit dependence of the critical layer thickness, in agreement with various experimental studies. Second, we study the self-assembled island for…
Effect of cold rolling strain on the microstructural evolution in equimolar MoNbTaTiZr refractory complex concentrated alloy: Comprehensive characterization
Disentangling Strain and Ti3+ Contributions to the Anomalous Hall Effect in Epitaxial RuO2 Films
University of Minnesota−Twin Cities（明尼苏达大学双城分校）；Hankuk University of Foreign Studies（韩国外国语大学）；Kyung Hee University（庆熙大学）；Temple University（天普大学）；Diamond Light Source Ltd.（钻石光源有限公司）；Pacific Northwest National Laboratory（太平洋西北国家实验室）
The performance of strained silicon as the channel material for transistors has plateaued. Motivated by increasing charge-carrier mobility within the device channel to improve transistor performance, germanium (Ge) is considered as an attractive option as a silicon replacement due to its highest p-type mobility in all of the known semiconductor materials and being compatible with today's conventional CMOS manufacturing process. However, the intrinsically high carrier mobility of Ge becomes significantly degraded because Ge's native oxide is unstable and readily decomposes into several GexOy su…
Silicon crystallized in the usual cubic (diamond) lattice structure has dominated the electronics industry for more than half a century. However, cubic silicon (Si), germanium (Ge) and SiGe-alloys are all indirect bandgap semiconductors that cannot emit light efficiently. Accordingly, achieving efficient light emission from group-IV materials has been a holy grail in silicon technology for decades and, despite tremendous efforts, it has remained elusive. Here, we demonstrate efficient light emission from direct bandgap hexagonal Ge and SiGe alloys. We measure a subnanosecond, temperature-insen…
We present a theoretical analysis and optimisation of the properties and performance of mid-infrared semiconductor lasers based on the dilute bismide alloy In$_{x}$Ga$_{1-x}$As$_{1-y}$Bi$_{y}$, grown on conventional (001) InP substrates. The ability to independently vary the epitaxial strain and emission wavelength in this quaternary alloy provides significant scope for band structure engineering. Our calculations demonstrate that structures based on compressively strained In$_{x}$Ga$_{1-x}$As$_{1-y}$Bi$_{y}$ quantum wells (QWs) can readily achieve emission wavelengths in the 3 -- 5 $μ$m range…
Silicon-Germanium (Si$_{1-x}$Ge$_x$) layers are commonly used as stressors in the gate of MOSFET devices. They are expected to introduce a beneficial stress in the drift and channel regions to enhance the electron mobility. When reducing the gate lateral size, one of the major issues is the stress relaxation which results in a significant decrease in the electron mobility. We report a new morphological evolution of a strained epitaxial SiGe nanolayer on a silicon gate (mesa) driven by strain inhomogeneity due to finite-size effects. Unlike the self-induced instability of strained films, this e…
Germanium-based alloys hold great promise for future spintronics applications, due to their potential for integration with conventional Si-based electronics. Mn5Ge3 exhibits strong ferromagnetism up to the Curie temperature Tc~295K. We use Point Contact Andreev Reflection (PCAR) spectroscopy to measure the spin polarization of Mn5Ge3 epilayers grown by solid phase epitaxy on Ge(111). In addition, we calculate the spin polarization of bulk Mn5Ge3 in the diffusive and ballistic regimes using density-functional theory. The measured spin polarization, Pc=43+/-5% is compared to our theoretical esti…
