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The lack of useful and cost-efficient group-IV direct band gap light emitters still presents the main bottleneck for complementary metal-oxide semiconductor-compatible short-distance data transmission, single-photon emission, and sensing based on silicon photonics. Germanium, a group-IV element like Si, is already widely used in silicon fabs. While the energy band gap of Ge is intrinsically indirect, we predict that the insertion of Ge-Ge split-[110] interstitials into crystalline Ge can open up a direct band gap transmission path. Here, we calculate from first principles the band structure and optical emission properties of Ge, Sb, and Sn split-[110] interstitials in bulk and low-dimensional Ge at different doping concentrations. Two types of electronic states provide the light-emission enhancement below the direct band gap of Ge: a hybridized L-$\mathrm{\ensuremath{\Gamma}}$ state at the Brillouin zone center and a conduction band of $\mathrm{\ensuremath{\Delta}}$ band character that couples to a raised valence band along the $\mathrm{\ensuremath{\Gamma}}$-X direction. Majority carrier introduced to the system through doping can enhance light emission by saturation of nonradiative paths. Ge-Sn split interstitials in Ge shift the top of the valence band towards the $\mathrm{\ensuremath{\Gamma}}$-X direction and increase the $\mathrm{\ensuremath{\Gamma}}$ character of the L-$\mathrm{\ensuremath{\Gamma}}$ state, which results in a shift to longer emission wavelengths. Key spectral regions for datacom and sensing applications can be covered by applying quantum confinement in defect-enhanced Ge quantum dots for an emission wavelength shift from the midinfrared to the telecom regime.

We present a first-principles method for the calculation of the temperature-dependent relaxation of symmetry-breaking atomic driving forces in photoexcited systems. We calculate the phonon-assisted decay of the photoexcited force on the low-symmetry $E_g$ mode following absorption of an ultrafast pulse in the prototypical group-V semimetals, Bi, Sb and As. The force decay lifetimes for Bi and Sb are of the order of $10$ fs and in good agreement with recent experiments, demonstrating that electron-phonon scattering is the dominant mechanism relaxing the symmetry-breaking forces. Calculations for a range of absorbed photon energies suggest that larger amplitude, symmetry-breaking atomic motion may be induced by choosing a pump photon energy which maximises the product of the initial $E_g$ force and its lifetime. We also find that the high-symmetry $A_{1g}$ force undergoes a partial decay to a non-zero constant on similar timescales, which has not yet been measured in experiments. We observe that the imaginary part of the electron self-energy, averaged over the photoexcited carrier distribution, provides a reasonable estimate for the decay rate of symmetry-breaking forces., 7 pages, 9 figures

We use first-principles electronic structure methods to calculate the electronic thermoelectric properties (i.e. due to electronic transport only) of single-crystalline bulk $n$-type silicon-germanium alloys vs Ge composition, temperature, doping concentration and strain. We find excellent agreement to available experiments for the resistivity, mobility and Seebeck coefficient. These results are combined with the experimental lattice thermal conductivity to calculate the thermoelectric figure of merit $ZT$, finding very good agreement with experiment. We predict that 3% tensile hydrostatic strain enhances the $n$-type $ZT$ by 50% at carrier concentrations of $n=10^{20}$ cm$^{-3}$ and temperature of $T=1200K$. These enhancements occur at different alloy compositions due to different effects: at 50% Ge composition the enhancements are achieved by a strain induced decrease in the Lorenz number, while the power factor remains unchanged. These characteristics are important for highly doped and high temperature materials, in which up to 50% of the heat is carried by electrons. At 70% Ge the increase in $ZT$ is due to a large increase in electrical conductivity produced by populating the high mobility $\Gamma$ conduction band valley, lowered in energy by strain., Comment: 21 pages, 11 figures

Photovoltaics is amongst the most important technologies for renewable energy sources, and plays a key role in the development of a society with a smaller environmental footprint. Key parameters for solar cells are their energy conversion efficiency, their operating lifetime, and the cost of the energy obtained from a photovoltaic system compared to other sources. The optimization of these aspects involves the exploitation of new materials and development of novel solar cell concepts and designs. Both theoretical modeling and characterization of such devices require a comprehensive view including all scales from the atomic to the macroscopic and industrial scale. The different length scales of the electronic and optical degrees of freedoms specifically lead to an intrinsic need for multiscale simulation, which is accentuated in many advanced photovoltaics concepts including nanostructured regions. Therefore, multiscale modeling has found particular interest in the photovoltaics community, as a tool to advance the field beyond its current limits. In this article, we review the field of multiscale techniques applied to photovoltaics, and we discuss opportunities and remaining challenges. © T. Abu Hamed et al., published by EDP Sciences, 2018., European Cooperation in Science and Technology: MP1406, The authors are grateful for the financial support by the COST Action MP1406 “MultiscaleSolar.”

The growth, structural and optical properties, and energy band alignments of tensile-strained germanium (ε-Ge) epilayers heterogeneously integrated on silicon (Si) were demonstrated for the first time. The tunable ε-Ge thin films were achieved using a composite linearly graded InxGa1-xAs/GaAs buffer architecture grown via solid source molecular beam epitaxy. High-resolution X-ray diffraction and micro-Raman spectroscopic analysis confirmed a pseudomorphic ε-Ge epitaxy whereby the degree of strain varied as a function of the In(x)Ga(1-x)As buffer indium alloy composition. Sharp heterointerfaces between each ε-Ge epilayer and the respective In(x)Ga(1-x)As strain template were confirmed by detailed strain analysis using cross-sectional transmission electron microscopy. Low-temperature microphotoluminescence measurements confirmed both direct and indirect bandgap radiative recombination between the Γ and L valleys of Ge to the light-hole valence band, with L-lh bandgaps of 0.68 and 0.65 eV demonstrated for the 0.82 ± 0.06% and 1.11 ± 0.03% strained Ge on Si, respectively. Type-I band alignments and valence band offsets of 0.27 and 0.29 eV for the ε-Ge/In(0.11)Ga(0.89)As (0.82%) and ε-Ge/In(0.17)Ga(0.83)As (1.11%) heterointerfaces, respectively, show promise for ε-Ge carrier confinement in future nanoscale optoelectronic devices. Therefore, the successful heterogeneous integration of tunable tensile-strained Ge on Si paves the way for the design and implementation of novel Ge-based photonic devices on the Si technology platform.

Germanium is an indirect semiconductor which attracts particular interest as an electronics and photonics material due to low indirect-to-direct band separation. In this work we bend the bands of Ge by means of biaxial tensile strain in order to achieve a direct band gap. Strain is applied by growth of Ge on a lattice mismatched InGaAs buffer layer with variable In content. Band structure is studied by photoluminescence and photoreflectance, giving the indirect and direct bands of the material. Obtained experimental energy band values are compared with a $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ simulation. Photoreflectance spectra are also simulated and compared with the experiment. The obtained results indicate direct band structure obtained for a Ge sample with $1.94%$ strain applied, with preferable $\mathrm{\ensuremath{\Gamma}}$ valley to heavy hole transition.

In this work we study Ge structures grown on silicon substrates. We use photoluminescence and photoreflectance to determine both direct and indirect gap of Ge under tensile strain. The strain is induced by growing the Ge on an InGaAs buffer layer with variable In content. The band energy levels are modeled by a 30 band k·p model based on first principles calculations. Characterization techniques show very good agreement with the calculated energy values.

We present a systematic study of the impact of strain on off-state leakage current, using experimental data and ab-initio calculations. We developed new models to account for the impact of strain on band-to-band tunneling and trap-assisted tunneling in silicon. We observe that the strain can dramatically increase the leakage current, depending on the type of tunneling involved. We predict that 1% compressive strain can increase the band-to-band tunneling and Shockley Read Hall leakage currents by over 5 and 3 times, respectively.

In this work we study Ge transistor structures grown on silicon substrate. We use photoluminescence to determine the band gap of Ge under tensile strain. The strain is induced by growing Ge on an InGaAs buffer layer with variable In content. The band energy levels are modeled using a 30 band k·p model based on first principles calculations. Photoluminescence measurements show a reasonable correspondence with calculated values of the band energies.

Tunable tensile-strained germanium (epsilon-Ge) thin films on GaAs and heterogeneously integrated on silicon (Si) have been demonstrated using graded III-V buffer architectures grown by molecular beam epitaxy (MBE). epsilon-Ge epilayers with tunable strain from 0% to 1.95% on GaAs and 0% to 1.11% on Si were realized utilizing MBE. The detailed structural, morphological, band alignment and optical properties of these highly tensile-strained Ge materials were characterized to establish a pathway for wavelength-tunable laser emission from 1.55 μm to 2.1 μm. High-resolution X-ray analysis confirmed pseudomorphic epsilon-Ge epitaxy in which the amount of strain varied linearly as a function of indium alloy composition in the InxGa1-xAs buffer. Cross-sectional transmission electron microscopic analysis demonstrated a sharp heterointerface between the epsilon-Ge and the InxGa1-xAs layer and confirmed the strain state of the epsilon-Ge epilayer. Lowtemperature micro-photoluminescence measurements confirmed both direct and indirect bandgap radiative recombination between the Γ and L valleys of Ge to the light-hole valence band, with L-lh bandgaps of 0.68 eV and 0.65 eV demonstrated for the 0.82% and 1.11% epsilon-Ge on Si, respectively. The highly epsilon-Ge exhibited a direct bandgap, and wavelength-tunable emission was observed for all samples on both GaAs and Si. Successful heterogeneous integration of tunable epsilon-Ge quantum wells on Si paves the way for the implementation of monolithic heterogeneous devices on Si.

The authors compared the influence of laser thermal annealing (LTA) and rapid thermal annealing (RTA) on dopant activation and electrical performance of phosphorus and arsenic doped n+/p junction. High carrier concentration above 1020 cm−3 as well as an I ON /I OFF ratio of approximately 105 and ideality factor (n) approximately 1.2–1.5 was achieved with LTA. However RTA revealed very high I ON /I OFF ratio approximately 107, and n close to 1. Non ideal behavior in LTA diodes is attributed to existence of deep level defects in the junction, contributing to leakage current. Meanwhile ideal behavior of RTA diodes is due to removal of defects in the junction during the high thermal budget.

We studied the optical properties of a strain-induced direct-band-gap Ge quantum well embedded in InGaAs. We showed that the band offsets depend on the electronegativity of the layer in contact with Ge, leading to different types of optical transitions in the heterostructure. When group-V atoms compose the interfaces, only electrons are confined in Ge, whereas both carriers are confined when the interface consists of group-III atoms. The different carrier confinement results in different emission dynamics behavior. This study provides a solution to obtain efficient light emission from Ge. DOI: 10.1103/PhysRevLett.110.177404

A first-principles method is applied to find the intra and intervalley n-type carrier scattering rates for substitutional carbon in silicon. The method builds on a previously developed first-principles approach with the introduction of an interpolation technique to determine the intravalley scattering rates. Intravalley scattering is found to be the dominant alloy scattering process in Si1-xCx, followed by g-type intervalley scattering. Mobility calculations show that alloy scattering due to substitutional C alone cannot account for the experimentally observed degradation of the mobility. We show that the incorporation of additional charged impurity scattering due to electrically active interstitial C complexes models this residual resistivity well.

First-principles electronic structure methods are used to predict the piezoresistance of n-type Si 1−x Ge x at various alloy compositions and strain configurations. We report very large gauge factors, G = dρ/d∊/ρ, where ρ is resistivity and ∊ is strain: for compositions x ≃ 0.90 under uniaxial strain in the 〈111〉 direction, G > 500. These gauge factors are over three times larger than the best values for single crystalline bulk Si. This large change in resistance due to strain is explained by the change in the occupancy of the higher-conductance L valley relative to the lower-conductance Δ valley, coupled to a change in inter-valley alloy and phonon scattering.

We use first-principles electronic structure methods to show that the piezoresistive strain gauge factor of single-crystalline bulk $n$-type silicon-germanium alloys at carefully controlled composition can reach values of $G=500$, three times larger than that of silicon, the most sensitive such material used in industry today. At cryogenic temperatures of 4 K we find gauge factors of $G=135\phantom{\rule{0.16em}{0ex}}000$, 13 times larger than that observed in Si whiskers. The improved piezoresistance is achieved by tuning the scattering of carriers between different ($\ensuremath{\Delta}$ and $L$) conduction band valleys by controlling the alloy composition and strain configuration.

First-principles electronic structure methods are used to predict the mobility of n-type carrier scattering in strained SiGe. We consider the effects of strain on the electron-phonon deformation potentials and the alloy scattering parameters. We calculate the electron-phonon matrix elements and fit them up to second order in strain. We find, as expected, that the main effect of strain on mobility comes from the breaking of the degeneracy of the six Δ and L valleys, and the choice of transport direction. The non-linear effects on the electron-phonon coupling of the Δ valley due to shear strain are found to reduce the mobility of Si-like SiGe by 50% per % strain. We find increases in mobility between 2 and 11 times that of unstrained SiGe for certain fixed Ge compositions, which should enhance the thermoelectric figure of merit in the same order, and could be important for piezoresistive applications.

First-principles electronic structure methods are used to predict the rate of n-type carrier scattering due to phonons in highly-strained Ge. We show that strains achievable in nanoscale structures, where Ge becomes a direct bandgap semiconductor, cause the phonon-limited mobility to be enhanced by hundreds of times that of unstrained Ge, and over a thousand times that of Si. This makes highly tensile strained Ge a most promising material for the construction of channels in CMOS devices, as well as for Si-based photonic applications. Biaxial (001) strain achieves mobility enhancements of 100 to 1000 with strains over 2%. Low temperature mobility can be increased by even larger factors. Second order terms in the deformation potential of the Gamma valley are found to be important in this mobility enhancement. Although they are modified by shifts in the conduction band valleys, which are caused by carrier quantum confinement, these mobility enhancements persist in strained nanostructures down to sizes of 20 nm.

First-principles electronic structure methods are used to predict the rate of n-type carrier scattering due to phonons in highly-strained Ge. We show that strains achievable in nanoscale structures, where Ge becomes a direct band-gap semiconductor, cause the phonon-limited mobility to be enhanced by hundreds of times that of unstrained Ge, and over a thousand times that of Si.

The role of reduced dimensionality and of the surface on electron-phonon (e-ph) coupling in silicon nanowires is determined from first principles. Surface termination and chemistry is found to have a relatively small influence, whereas reduced dimensionality fundamentally alters the behavior of deformation potentials. As a consequence, electron coupling to "breathing modes" emerges that cannot be described by conventional treatments of e-ph coupling. The consequences for physical properties such as scattering lengths and mobilities are significant: the mobilities for [110] grown wires are 6 times larger than those for [100] wires, an effect that cannot be predicted without the form we find for Si nanowire deformation potentials., to appear in Nano Letters

First-principles electronic structure methods are used to find the rates of inelastic intravalley and intervalley $n$-type carrier scattering in ${\text{Si}}_{1\ensuremath{-}x}{\text{Ge}}_{x}$ alloys. Scattering parameters for all relevant $\ensuremath{\Delta}$ and $L$ intra- and intervalley scattering are calculated. The short-wavelength acoustic and the optical phonon modes in the alloy are computed using the random mass approximation, with interatomic forces calculated in the virtual crystal approximation using density functional perturbation theory. Optical phonon and intervalley scattering matrix elements are calculated from these modes of the disordered alloy. It is found that alloy disorder has only a small effect on the overall inelastic intervalley scattering rate at room temperature. Intravalley acoustic scattering rates are calculated within the deformation potential approximation. The acoustic deformation potentials are found directly and the range of validity of the deformation potential approximation verified in long-wavelength frozen phonon calculations. Details of the calculation of elastic alloy scattering rates presented in an earlier paper are also given. Elastic alloy disorder scattering is found to dominate over inelastic scattering, except for almost pure silicon $(x\ensuremath{\approx}0)$ or almost pure germanium $(x\ensuremath{\approx}1)$, where acoustic phonon scattering is predominant. The $n$-type carrier mobility, calculated from the total (elastic plus inelastic) scattering rate, using the Boltzmann transport equation in the relaxation time approximation, is in excellent agreement with experiments on bulk, unstrained alloys.

The $p$-type carrier scattering rate due to alloy disorder in ${\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{Ge}}_{x}$ alloys is obtained from first principles. The required alloy scattering matrix elements are calculated from the energy splitting of the valence bands, which arise when one average host atom is replaced by a Ge or Si atom in supercells containing up to 128 atoms. Alloy scattering within the valence bands is found to be characterized by a single scattering parameter. The hole mobility is calculated from the scattering rate using the Boltzmann transport equation in the relaxation time approximation. The results are in good agreement with experiments on bulk, unstrained alloys.

First-principles electronic structure methods are used to find the rates of intravalley and intervalley n-type carrier scattering due to alloy disorder in Si(1-x)Ge(x) alloys. The required alloy scattering matrix elements are calculated from the energy splitting of nearly degenerate Bloch states which arises when one average host atom is replaced by a Ge or Si atom in supercells containing up to 128 atoms. Scattering parameters for all relevant Delta and L intravalley and intervalley alloy scattering are calculated. Atomic relaxation is found to have a substantial effect on the scattering parameters. f-type intervalley scattering between Delta valleys is found to be comparable to other scattering channels. The n-type carrier mobility, calculated from the scattering rate using the Boltzmann transport equation in the relaxation time approximation, is in excellent agreement with experiments on bulk, unstrained alloys.

We review the theoretical description of spin-orbit scattering and electron spin resonance in carbon nanotubes. Particular emphasis is laid on the effects of electron-electron interactions. The spin-orbit coupling is derived, and the resulting ESR spectrum is analyzed both using the effective low-energy field theory and numerical studies of finite-size Hubbard chains and two-leg Hubbard ladders. For single-wall tubes, the field theoretical description predicts a double peak spectrum linked to the existence of spin-charge separation. The numerical analysis basically confirms this picture, but also predicts additional features in finite-size samples., 19 pages, 4 figures, invited review article for special issue in J. Phys. Cond. Mat., published version