We use first-principles electronic-structure theory to determine the intra- and intervalley electron-alloy scattering parameters in -type Ge−Sn alloys. These parameters are used to determine the alloy scattering contributions to the -type electron mobility of Ge−Sn at 300 and 15K using a first iteration of the Boltzmann transport equation in the relaxation-time approximation. For unstrained Ge−Sn, we find that an Sn concentration of at least 13.5% is needed to achieve an electron mobility greater than that of Ge. Our results show that the mobility of Ge−Sn can be over 25 times that of Ge, or 105cm2/(Vs). At 15K, incorporation of less than 6% Sn into Ge quadruples its mobility, which suggests that Ge−Sn has potential applications as a high-mobility 2D electron gas. Applying biaxial tensile strain to Ge−Sn further increases the mobility and achieves this improvement at lower Sn content than in unstrained Ge−Sn. Published by the American Physical Society 2025

GeSn has emerged as a promising material for spintronics due to its long spin-lifetime, compatibility with silicon technology, high mobility and tunable electronic properties. Of particular interest is the transition from an indirect to a direct band gap with increasing Sn content, which enhances optical properties, electron transport and we find also affects spin transport behaviour, which is critical for spintronics applications. We use first-principles electronic-structure theory to determine the spin-flip electron-alloy scattering parameters in n-type GeSn alloys. We also calculate the previously undetermined intervalley electron spin-phonon scattering parameters between the L and Γ valleys. These parameters are used to determine the electron-alloy and electron-phonon scattering contributions to the n-type spin-relaxation of GeSn, as a function of alloy content and temperature. As in the case of phonon scattering, alloy scattering reduces the spin-relaxation time. However, switching the spin transport from the typical L valley of Ge to the Γ valley by sufficient addition of Sn, the relaxation time can be substantially increased. For unstrained, room temperature GeSn, we find a Sn concentration of at least 10% is required to achieve a spin-relaxation time greater than Ge, with 17% Sn needed to increase the spin-relaxation time from the nanosecond range to the microsecond range. At low temperatures (30K), adding 10% Sn can increase the spin-relaxation time from 10^-7s to 0.1s. Applying biaxial tensile strain to GeSn further increases the spin-relaxation time and at a lower Sn content than in unstrained GeSn.

In recent years, computational approaches which couple density functional theory (DFT)-based description of the electron–phonon and phonon–phonon scattering rates with the Boltzmann transport equation have been shown to obtain the electron and thermal transport characteristics of many 3D and 2D semiconductors in excellent agreement with experimental measurements. At the same time, progress in the DFT-based description of the electron–phonon scattering has also allowed to describe the non-equilibrium relaxation dynamics of hot or photo-excited electrons in several materials, in very good agreement with time-resolved spectroscopy experiments. In the latter case, as the time-resolved spectroscopy techniques provide the possibility to monitor transient material characteristics evolving on the femtosecond and attosecond time scales, the time evolution of photo-excited, nonthermal carrier distributions has to be described. Similarly, reliable theoretical approaches are needed to describe the transient transport properties of devices involving high energy carriers. In this review, we aim to discuss recent progress in coupling the ab initio description of materials, especially that of the electron–phonon scattering, with the time-dependent approaches describing the time evolution of the out-of-equilibrium carrier distributions, in the context of time-resolved spectroscopy experiments as well as in the context of transport simulations. We point out the computational limitations common to all numerical approaches, which describe time propagation of strongly out-of-equilibrium carrier distributions in 3D materials, and discuss the methods used to overcome them.

We report on electroluminescence spectroscopy experiments demonstrating room-temperature light emission from heavily alloyed SiGe quantum dots, for which the light emission properties are enhanced by incorporated split-[110] self-interstitials. The quantum dots are formed during molecular beam epitaxy deposition of Si0.6Ge0.4 alloys on n-doped silicon-on-insulator substrates. To create the split-[110] self-interstitials the quantum dots were co-implantated in-situ using Si and Ge ions. The hybrid emitters were further embedded into the intrinsic region of a p-i-n diode structure to enable electrical pumping. Similar to previous theoretical results on unstrained Ge-based quantum dots containing these defects, radiative direct transitions are possible for these SiGe light emitters. However, in SiGe dots these transitions are not at the Brillouin zone center. Instead, first-principles calculations indicate that the presence of the split-[110] self-interstitial defect in strained and unstrained SiGe can lead to optically direct transitions in momentum space in the X-direction of the Brillouin zone.

Efficient p‐ and n‐type in situ doping of compressively strained germanium tin (Ge1‐xSnx) semiconductor epilayers, grown by chemical vapor deposition on a standard Si(001) substrate, is demonstrated. Materials characterization results reveal unusual impact of dopants manifesting via a pronounced reduction of Sn content in the epilayer, accompanied by an enhancement of the growth rate, due to increasing p‐type doping concentration. Furthermore, the opposite behavior for n‐type doping is observed, resulting in a less pronounced increase of Sn concentration and no effect on growth rate. Nevertheless, a very high density of electrically active holes up to ≈4 × 1020 cm−3 is obtained in p‐type doped Ge1‐xSnx epilayer resulting in the lowest resistivity of 0.15 mΩ cm among all in situ doped epitaxial and strained group‐IV semiconductors. Also, the metal‐to‐insulator transition in Ge1‐xSnx is experimentally demonstrated for doping levels above 1 × 1017 cm−3, which is substantially lower than in any group‐IV semiconductor, and theoretically predict it to be as low as ≈1 × 1017 cm−3. The findings enabled by the doping regime explored in this work can open novel prospects to engineer low resistivity contacts and charge current injection in applications covering next‐generation transistors, qubits, diodes, electrically driven light sources, sensors and hybrid quantum devices.

Strain is commonly used in metal-oxide-semiconductor technologies to boost on-state performance. This booster has been in production for at least a decade. Despite this, a systematic study of the impact of strain on off-state leakage current has been lacking. In this work we use experimental data and ab-initio calculations to refine existing models to account for the impact of strain on band-to-band tunnelling and trap-assisted tunnelling in silicon. We observe that the strain may dramatically increase the leakage current, depending on the type of tunnelling involved. For band-to-band and trap-assisted tunnelling, low uniaxial strains of 0.1% (or 180 MPa) can increase the leakage current by 60% and 10% compared to the unstrained case, respectively. Using our models, we predict that compressive strain on the order of 1% (or 2 GPa) can increase the leakage current by 150 times. Conversely, tensile strain may diminish or at most double the leakage current in all observed cases. Though detrimental in conventional inversion-mode MOSFETs, these processes may be used to boost the performance of Tunnel Field Effect Transistors, where on-state current is defined by band-to-band tunnelling.

We investigate experimentally and using first-principles theory the generation of phonons and the relaxation of carriers on picosecond timescales across the Brillouin zone of photo-excited Ge by inter-valley electron–phonon scattering. The phonons generated are typical of those generated in semiconductor devices, contributing to the accumulation of heat within the material. We simulate the time-evolution of phonon populations, based on first-principles band structure and electron–phonon and phonon–phonon matrix elements, and compare them to data from time-resolved x-ray diffuse scattering experiments, performed at the Linac Coherent Light Source x-ray free-electron laser facility, following photo-excitation by a 50 fs near-infrared optical pulse. We show that the intensity of the non-thermal x-ray diffuse scattering signal, which is observed to grow substantially near the L-point of the Brillouin zone over 3–5 ps, is due to phonons generated by scattering of carriers between the Δ and L valleys. These phonons have low group velocities, resulting in a heat bottleneck. With the inclusion of phonon decay through 3-phonon processes, the simulations also account for other non-thermal features observed in the x-ray diffuse scattering intensity, which are due to anharmonic phonon–phonon scattering of the phonons initially generated by electron–phonon scattering.

Quantum phases of solid-state electron systems look poised to sustain exotic phenomena and a very rich spin physics. We propose a practical silicon-based architecture that spontaneously sustains topological properties, while being fully compatible with the high-volume manufacturing capabilities of modern microelectronic foundries. Here we show how Ge1-xSnx alloys, an emerging group IV semiconductor, can be engineered into junctions that demonstrate a broken gap alignment. We predict such basic building block undergo a quantum phase transition that can elegantly accommodate the existence of gate-controlled chiral edge states directly on Si. This will enable tantalizing prospects for designing integrated circuits hosting quantum spin hall insulators and advanced topological functionalities.

As forward-looking electron devices increasingly adopt high-mobility low-band-gap materials, such as germanium (Ge), questions remain regarding the feasibility of strain engineering in low-band-gap systems. Particularly, the Ge L- Gamma valley separation (similar to 150 meV) can be overcome by introducing a high degree of tensile strain ( epsilon >= 1.5%). It is therefore essential to understand the nature of highly strained Ge transport, wherein multivalley electron conduction becomes a possibility. Here, we report on the competitiveness between L- and Gamma-valley transport in highly tensile-strained (epsilon similar to 1.6%) Ge/In0.24Ga0.76As heterostructures. Temperature-dependent magnetotransport analysis reveals two contributing carrier populations, identified as lower- and higher-mobility L- and Gamma-valley electrons (in Ge), using temperature-dependent Boltzmann transport modeling. Coupling this interpretation with electron-cyclotron-resonance studies, the effectivemass (m*) of the higher-mobility Gamma-valley electrons is probed, revealing m*=(0.049 +/- 0.007)me. Moreover, a comparison of empirical and theoretical m* indicates that these electrons reside primarily in the first-two quantum sublevels of the Ge Gamma valley. Consequently, our results provide an insight into the strain-dependent carrier dynamics of Ge, offering alternative pathways toward efficacious strain engineering.

Strain and band gap engineered epitaxial germanium (epsilon-Ge) quantum-well (QW) laser structures were investigated on GaAs substrates theoretically and experimentally for the first time. In this design, we exploit the ability of an InGaAs layer to simultaneously provide tensile strain in Ge (0.7-1.96%) and sufficient optical and carrier confinement. The direct band-to-band gain, threshold current density (Jth), and loss mechanisms that dominate in the epsilon-Ge QW laser structure were calculated using firstprinciples-based 30-band k.p electronic structure theory, at injected carrier concentrations from 3 x 10(18) to 9 x 10(19) cm(-3). The higher strain in the epsilon-Ge QW increases the gain at higher wavelengths; however, a decreasing thickness is required by higher strain due to critical layer thickness for avoiding strain relaxation. In addition, we predict that a J(th) of 300 A/cm(2) can be reduced to <10 A/cm(2) by increasing strain from 0.2% to 1.96% in epsilon-Ge lasing media. The measured room-temperature photoluminescence spectroscopy demonstrated direct band gap optical emission, from the conduction band at the G-valley to heavy-hole (0.6609 eV) from 1.6% tensile-strained Ge/In0.24Ga0.76As heterostructure grown by molecular beam epitaxy, is in agreement with the value calculated using 30-band k.p theory. The detailed plan-view transmission electron microscopic (TEM) analysis of 0.7% and 1.2% tensile-strained epsilon-Ge/InGaAs structures exhibited well-controlled dislocations within each epsilon-Ge layer. The measured dislocation density is below 4 x 10(6) cm(-2) for the 1.2% epsilon-Ge layer, which is an upper bound, suggesting the superior epsilon-Ge material quality. Structural analysis of the experimentally realistic 1.95% biaxially strained In0.28Ga0.72As/13 nm epsilon-Ge/In0.28Ga0.72As QW structure demonstrated a strained Ge/ In0.28Ga0.72As heterointerface with minimal relaxation using X-ray and cross-sectional TEM analysis. Therefore, our monolithic integration of a strained Ge QW laser structure on GaAs and ultimately the transfer of the process to the Si substrate via an InGa(Al)As/III-V buffer architecture would provide a significant step toward photonic technology based on strained Ge on a Si platform.

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 investigate from first-principles theory and experiment the generation of phonons on picosecond timescales and the relaxation of carriers in multiple conduction band valleys of photo-excited Ge by inter-valley electron-phonon scattering. We provide a full description of the phonon and electron relaxation dynamics without adjustable parameters. Simulations of the time-evolution of phonon populations, based on first-principles band structure and electron-phonon and phonon-phonon matrix elements, are compared with data from time-resolved x-ray diffuse scattering experiments, performed at the LCLS x-ray free-electron laser facility, which measures the diffuse scattering intensity following photo-excitation by a 50 fs near-infrared optical pulse. Comparing calculations and measurements show that the intensity of the non-thermal x-ray diffuse scattering signal, that is observed to grow substantially near the L-point of the Brillouin zone over 3-5 ps, is due to phonons generated by scattering of carriers between the $Δ$ and L valleys. Non-thermal phonon populations throughout the Brillouin zone are observed and simulated from first principles without adjustable parameters for times up to 10 ps. With inclusion of phonon decay through 3-phonon processes, the simulations also account for other non-thermal features observed in the x-ray diffuse scattering intensity, which are due to anharmonic phonon-phonon scattering of the phonons initially generated by electron-phonon scattering.

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 experiments. We predict that 3% tensile hydrostatic strain enhances the n-type ZT by 50% at carrier concentrations of n=1020cm−3 and a 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 the electrical conductivity produced by populating the high mobility Γ conduction band valley, lowered in energy by strain.

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 Bi, Sb, and As. The force decay lifetimes for Bi and Sb are of the order of 10 fs and in agreement with recent experiments, demonstrating that electron-phonon scattering is the primary 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 maximizes the product of the initial E_{g} force and its lifetime. The high-symmetry A_{1g} force undergoes a partial decay to a nonzero constant on similar timescales, which has not yet been measured in experiments. The average imaginary part of the electron self-energy over the photoexcited carrier distribution provides a crude indication of the decay rate of symmetry-breaking forces.

Germanium is an indirect semiconductor which attracts a 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 bandgap. 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 k·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 Г-valley to heavy hole transition.

We calculate the uniaxial and dilatation acoustic deformation potentials, $\Xi^{\text{L}}_{u}$ and $\Xi^{\text{L}}_{d}$, of the conduction band L valleys of PbTe from first principles, using the local density approximation (LDA) and hybrid functional (HSE03) exchange-correlation functionals. We find that the choice of a functional does not substantially affect the effective band masses and deformation potentials as long as a physically correct representation of the conduction band states near the band gap has been obtained. Fitting of the electron-phonon matrix elements obtained in density functional perturbation theory (DFPT) with the LDA excluding spin orbit interaction (SOI) gives $\Xi^{\text{L}}_u = 7.0$~eV and $\Xi^{\text{L}}_d = 0.4$~eV. Computing the relative shifts of the L valleys induced by strain with the HSE03 functional including SOI gives $\Xi^{\text{L}}_u = 5.5$~eV and $\Xi^{\text{L}}_d = 0.8$~eV, in good agreement with the DFPT values. Our calculated values of $\Xi^{\text{L}}_u$ agree fairly well with experiment ($\sim 3-4.5$~eV). The computed values of $\Xi^{\text{L}}_d$ are substantially smaller than those obtained by fitting electronic transport measurements ($\sim 17-22$~eV), indicating that intravalley acoustic phonon scattering in PbTe is much weaker than previously thought.

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 systemcompared 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.

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.

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.

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.