Isotope and temperature shifts of direct and indirect band gaps in diamond-type semiconductors

Spectroscopic signatures of nonpolarons: the case of diamond

Polarons are quasi-particles made from electrons interacting with vibrations in crystal lattices. They derive their name from the strong electron-vibration polar interactions in ionic systems, that induce spectroscopic and optical signatures of such quasi-particles. In this paper, we focus on diamond, a non-polar crystal with inversion symmetry which nevertheless shows interesting signatures stemming from electron-vibration interactions, better denoted "nonpolaron" signatures in this case. The (non)polaronic effects are produced by short-range crystal fields, while long-range quadrupoles only have a small influence. The corresponding many-body spectral function has a characteristic energy dependence, showing a plateau structure that is similar to but distinct from the satellites observed in the polar Fröhlich case. We determine the temperature-dependent spectral function of diamond by two methods: the standard Dyson-Migdal approach, which calculates electron-phonon interactions within the lowest-order expansion of the self-energy, and the cumulant expansion, which includes higher orders of electron-phonon interactions. The latter corrects the nonpolaron energies and broadening, providing a more realistic spectral function, which we examine in detail for both conduction and valence band edges.

Anomalous boron isotope effects on electronic structure and lattice dynamics of CuB2O4

Copper metaborate had a unique crystal structure and exhibited noteworthy magnetic phase transitions at 21 and 10 K.

Coupling First-Principles Calculations of Electron-Electron and Electron-Phonon Scattering, and Applications to Carbon-Based Nanostructures

We report first-principles calculations of electronic gaps, lifetimes, and photoelectron spectra of a series of molecules, performed by efficiently combining the computation of electron-electron and electron-phonon self-energies. The dielectric matrix is represented in terms of dielectric eigenpotentials, utilized for both the calculation of G₀ W₀ quasi-particle energies and the diagonalization of the dynamical matrix; virtual electronic states are never explicitly computed and all self-energies are evaluated over the full frequency spectrum. Our formulation enables electronic structure calculations at the many-body perturbation theory level, inclusive of electron-phonon coupling, for systems with hundreds of electrons.

Isotope engineering of van der Waals interactions in hexagonal boron nitride

Hexagonal boron nitride is a model lamellar compound where weak, non-local van der Waals interactions ensure the vertical stacking of two-dimensional honeycomb lattices made of strongly bound boron and nitrogen atoms. We study the isotope engineering of lamellar compounds by synthesizing hexagonal boron nitride crystals with nearly pure boron isotopes (¹⁰B and ¹¹B) compared to those with the natural distribution of boron (20 at% ¹⁰B and 80 at% ¹¹B). On the one hand, as with standard semiconductors, both the phonon energy and electronic bandgap varied with the boron isotope mass, the latter due to the quantum effect of zero-point renormalization. On the other hand, temperature-dependent experiments focusing on the shear and breathing motions of adjacent layers revealed the specificity of isotope engineering in a layered material, with a modification of the van der Waals interactions upon isotope purification. The electron density distribution is more diffuse between adjacent layers in ¹⁰BN than in ¹¹BN crystals. Our results open perspectives in understanding and controlling van der Waals bonding in layered materials.

Nonadiabatic Kohn Anomaly in Heavily Boron-Doped Diamond

We report evidence of a nonadiabatic Kohn anomaly in boron-doped diamond, using a joint theoretical and experimental analysis of the phonon dispersion relations. We demonstrate that standard calculations of phonons using density-functional perturbation theory are unable to reproduce the dispersion relations of the high-energy phonons measured by high-resolution inelastic x-ray scattering. On the contrary, by taking into account nonadiabatic effects within a many-body field-theoretic framework, we obtain excellent agreement with our experimental data. This result indicates a breakdown of the Born-Oppenheimer approximation in the phonon dispersion relations of boron-doped diamond.

Nuclear Quantum Effects on Aqueous Electron Attachment and Redox Properties

Nuclear quantum effects (NQEs) on the reduction and oxidation properties of small aqueous species (CO₂, HO₂, and O₂) are quantified and rationalized by first-principles molecular dynamics and thermodynamic integration. Vertical electron attachment, or electron affinity, and detachment energies (VEA and VDE) are strongly affected by NQEs, decreasing in absolute value by 0.3 eV going from a classical to a quantum description of the nuclei. The effect is attributed to NQEs that lessen the solvent response upon oxidation/reduction. The reduction of solvent reorganization energy is expected to be general for small solutes in water. In the thermodynamic integral that yields the free energy of oxidation/reduction, these large changes enter with opposite sign, and only a small net effect (0.1 eV) remains. This is not obvious for CO₂, where the integrand is strongly influenced by NQEs due to the onset of interaction of the reduced orbital with the conduction band of the liquid during thermodynamic integration. We conclude that NQEs might not have to be included in the computation of redox potentials, unless high accuracy is needed, but are important for VEA and VDE calculations.

Ab initio Electronic Structure of Liquid Water

Self-consistent GW calculations with efficient vertex corrections are employed to determine the electronic structure of liquid water. Nuclear quantum effects are taken into account through ab initio path-integral molecular dynamics simulations. We reveal a sizable band-gap renormalization of up to 0.7 eV due to hydrogen-bond quantum fluctuations. Our calculations lead to a band gap of 8.9 eV, in accord with the experimental estimate. We further resolve the ambiguities in the band-edge positions of liquid water. The valence-band maximum and the conduction-band minimum are found at -9.4 and -0.5  eV with respect to the vacuum level, respectively.

Temperature dependence of the electronic structure of semiconductors and insulators

The renormalization of electronic eigenenergies due to electron-phonon coupling (temperature dependence and zero-point motion effect) is sizable in many materials with light atoms. This effect, often neglected in ab initio calculations, can be computed using the perturbation-based Allen-Heine-Cardona theory in the adiabatic or non-adiabatic harmonic approximation. After a short description of the recent progresses in this field and a brief overview of the theory, we focus on the issue of phonon wavevector sampling convergence, until now poorly understood. Indeed, the renormalization is obtained numerically through a slowly converging q-point integration. For non-zero Born effective charges, we show that a divergence appears in the electron-phonon matrix elements at q → Γ, leading to a divergence of the adiabatic renormalization at band extrema. This problem is exacerbated by the slow convergence of Born effective charges with electronic wavevector sampling, which leaves residual Born effective charges in ab initio calculations on materials that are physically devoid of such charges. Here, we propose a solution that improves this convergence. However, for materials where Born effective charges are physically non-zero, the divergence of the renormalization indicates a breakdown of the adiabatic harmonic approximation, which we assess here by switching to the non-adiabatic harmonic approximation. Also, we study the convergence behavior of the renormalization and develop reliable extrapolation schemes to obtain the converged results. Finally, the adiabatic and non-adiabatic theories, with corrections for the slow Born effective charge convergence problem (and the associated divergence) are applied to the study of five semiconductors and insulators: α-AlN, β-AlN, BN, diamond, and silicon. For these five materials, we present the zero-point renormalization, temperature dependence, phonon-induced lifetime broadening, and the renormalized electronic band structure.

Path-integral simulation of solids

The path-integral formulation of the statistical mechanics of quantum many-body systems is described, with the purpose of introducing practical techniques for the simulation of solids. Monte Carlo and molecular dynamics methods for distinguishable quantum particles are presented, with particular attention to the isothermal-isobaric ensemble. Applications of these computational techniques to different types of solids are reviewed, including noble-gas solids (helium and heavier elements), group-IV materials (diamond and elemental semiconductors), and molecular solids (with emphasis on hydrogen and ice). Structural, vibrational, and thermodynamic properties of these materials are discussed. Applications also include point defects in solids (structure and diffusion), as well as nuclear quantum effects in solid surfaces and adsorbates. Different phenomena are discussed, as solid-to-solid and orientational phase transitions, rates of quantum processes, classical-to-quantum crossover, and various finite-temperature anharmonic effects (thermal expansion, isotopic effects, electron-phonon interactions). Nuclear quantum effects are most remarkable in the presence of light atoms, so that especial emphasis is laid on solids containing hydrogen as a constituent element or as an impurity.

Effect of the quantum zero-point atomic motion on the optical and electronic properties of diamond and trans-polyacetylene

The quantum zero-point motion of the carbon atoms is shown to induce strong effects on the optical and electronic properties of diamond and trans-polyacetylene, a conjugated polymer. By using an ab initio approach, we interpret the subgap states experimentally observed in diamond in terms of entangled electron-phonon states. These states also appear in trans-polyacetylene causing the formation of strong structures in the band structure that even call into question the accuracy of the band theory. This imposes a critical revision of the results obtained for carbon-based nanostructures by assuming the atoms frozen in their equilibrium positions.

Electron-phonon renormalization of the direct band gap of diamond

We calculate from first principles the temperature-dependent renormalization of the direct band gap of diamond arising from electron-phonon interactions. The calculated temperature dependence is in good agreement with spectroscopic ellipsometry measurements, and the zero-point renormalization of the band gap is found to be as large as 0.6 eV. We also calculate the temperature-dependent broadening of the direct absorption edge and find good agreement with experiment. Our work calls for a critical revision of the band structures of other carbon-based materials calculated by neglecting electron-phonon interactions.

Photoluminescence of isotopically purified silicon: how sharp are bound exciton transitions?

We report the first high resolution photoluminescence studies of isotopically pure Si (99.896% (28)Si). New information is obtained on isotopic effects on the indirect band gap energy, phonon energies, and phonon broadenings, which is in good agreement with calculations and previous results obtained in Ge and diamond. Remarkably, the linewidths of the no-phonon boron and phosphorus bound exciton transitions in the (28)Si sample are much narrower than in natural Si and are not well resolved at our maximum instrumental resolution of approximately 0.014 cm(-1). The removal of the dominant broadening resulting from isotopic randomness in natural Si reveals new fine structure in the boron bound exciton luminescence.

Isotopic mass and lattice constant: X-ray standing wave measurements

The molecular volume of crystals depends on their isotopic masses. This influence originates from the zero-point motion and the resulting small differences in lattice constants. This effect was measured with high precision by using an x-ray standing wave. The standing wave is generated during Bragg reflection and thus is in phase with the planes of the substrate crystal, which is covered with a homoepitaxial film that has a different isotopic composition than the substrate. The positions of the surface planes of the film with respect to the substrate planes are revealed by the photoelectrons excited by the maxima of the standing wave. For germanium-76 on natural germanium(111), a difference in lattice constant of -1.1 x 10(-5) and -2.5 x 10(-5) at 300 and 54 kelvin, respectively, was found. The results are in good agreement with theoretical predictions.