Hierarchical Structuring of Black Silicon Wafers by Ion-Flow-Stimulated Roughening Transition: Fundamentals and Applications for Photovoltaics

Ion-flow-stimulated roughening transition is a phenomenon that may prove useful in the hierarchical structuring of nanostructures. In this work, we have investigated theoretically and experimentally the surface texturing of single-crystal and multi-crystalline silicon wafers irradiated using ion-beam flows. In contrast to previous studies, ions had relatively low energies, whereas flow densities were high enough to induce a quasi-liquid state in the upper silicon layers. The resulting surface modifications reduced the wafer light reflectance to values characteristic of black silicon, widely used in solar energetics. Features of nanostructures on different faces of silicon single crystals were studied numerically based on the mesoscopic Monte Carlo model. We established that the formation of nano-pyramids, ridges, and twisting dune-like structures is due to the stimulated roughening transition effect. The aforementioned variety of modified surface morphologies arises due to the fact that the effects of stimulated surface diffusion of atoms and re-deposition of free atoms on the wafer surface from the near-surface region are manifested to different degrees on different Si faces. It is these two factors that determine the selection of the allowable "trajectories" (evolution paths) of the thermodynamic system along which its Helmholtz free energy, F, decreases, concomitant with an increase in the surface area of the wafer and the corresponding changes in its internal energy, U (dU>0), and entropy, S (dS>0), so that dF=dU - TdS<0, where T is the absolute temperature. The basic theoretical concepts developed were confirmed in experimental studies, the results of which showed that our method could produce, abundantly, black silicon wafers in an environmentally friendly manner compared to traditional chemical etching.

Electrostatic image force energy for charges in three-layer structures: exact formulas and their approximations

The problem of image force energyW(Z) in three-layer plane structures, whereZis the coordinate perpendicular to the layers, has been reconsidered. In the classical electrostatic limit, where the dielectric permittivitiesɛ_iof all structure components (i= 1, 2, 3) are constants, the exact general dependencesW(Z) were obtained for each layer and anyɛ_i-combination in terms of the Lerch transcendent function. For certain combinations ofɛ_i, an ion adsorption minimum was found to arise in one of the covers far from the interlayer. Some other combinations ofɛ_ican lead to the appearance of a potential barrier, which does not permit a free charge existing in the cover to approach the interlayer, although it will be attracted to the interlayer in the close vicinity of the latter. For symmetric structures (ɛ₁=ɛ₃), the asymptotic behavior ofW(Z→∞)was shown to beZ-2rather thanZ-1, as it takes place in the two-layer case. Simple approximate analytical formulas that describeW(Z) and possess high accuracy for arbitrary relationships among theɛ_i-constants were proposed.

Orientation of adsorbed polar molecules (dipoles) in external electrostatic field

A model is proposed in the framework of classical electrostatics to describe the behavior of an adsorbed polar molecule near the plane interface between two insulators under the action of an external electrostatic field. The molecule is considered as a permanent point dipole that polarizes the interface and interacts with it through electrostatic image forces. The latter and the applied field try to reorient the dipole in a competitive manner. The system behavior turns out to be rather complicated: it may show a bistable character with a hysteresis (a switch). Such a switch can serve as an element in a memory network made of adsorbed molecules.

Electric dipole image forces in three-layer systems: The classical electrostatic model

General exact analytical expressions have been derived for the image force energy W_i(Z, φ) of a point dipole in a classical three-layer system composed of dispersionless media with arbitrary constant dielectric permittivities ε_i. Here, i = 1-3 is the layer number, and Z and φ are the dipole coordinate and orientation angle, respectively. It was found that the long-range asymptotics W_i(Z→∞,φ) in both covers (i = 1, 3) are reached unexpectedly far from the interlayer (i = 2). Another specific feature of the solution consists in that the interference of the fields created by polarization charges emerging at both interfaces leads to the appearance of a constant contribution inside the interlayer with a non-standard dependence on the dipole orientation angle φ. It was shown that by changing the dielectric constants of the structure components, one can realize two peculiar regimes of the W_i(Z, φ) behavior in the covers; namely, there arises either a potential barrier preventing adsorption or a well far from the interface, both being of a totally electrostatic origin, i.e., without involving the Pauli exchange repulsion, which is taken into account in the conventional theories of physical adsorption. The results obtained provide a fresh insight into the physics of adsorption in physical electronics, chemical physics, and electrochemistry.

Quasiparticle conductance-voltage characteristics for break junctions involving d-wave superconductors: charge-density-wave effects

Quasiparticle tunnel conductance-voltage characteristics (CVCs), [Formula: see text], were calculated for break junctions (BJs) made up of layered d-wave superconductors partially gapped by charge-density waves (CDWs). The current is assumed to flow in the ab-plane of electrodes. The influence of CDWs is analyzed by comparing the resulting CVCs with CVCs calculated for BJs made up of pure d-wave superconductors with relevant parameters. The main CDW-effects were found to be the appearance of new CVC peculiarities and the loss of CVC symmetry with respect to the V-sign. Tunnel directionality was shown to be one of the key factors in the formation of [Formula: see text] dependences. In particular, the orientation of electrodes with respect to the current channel becomes very important. As a result, [Formula: see text] can acquire a large variety of forms similar to those for tunnel junctions between superconductors with s-wave, d-wave, and mixed symmetry of their order parameters. The diversity of peculiarities is especially striking at finite temperatures. In the case of BJs made up of pure d-wave superconductors, the resulting CVC can include a two-peak gap-driven structure. The results were compared with the experimental BJ data for a number of high-T _c oxides. It was shown that the large variety of the observed current-voltage characteristics can be interpreted in the framework of our approach. Thus, quasiparticle tunnel currents in the ab-plane can be used as an additional mean to detect CDWs competing with superconductivity in cuprates or other layered superconductors.

Influence of the spatially inhomogeneous gap distribution on the quasiparticle current in c-axis junctions involving d-wave superconductors with charge density waves

The quasiparticle tunnel current J(V) between the superconducting ab-planes along the c-axis and the corresponding conductance [Formula: see text] were calculated for symmetric junctions composed of disordered d-wave layered superconductors partially gapped by charge density waves (CDWs). Here, V is the voltage. Both the checkerboard and unidirectional CDWs were considered. It was shown that the spatial spread of the CDW-pairing strength substantially smears the peculiarities of G(V) appropriate to uniform superconductors. The resulting curves G(V) become very similar to those observed for a number of cuprates in intrinsic junctions, e.g. mesas. In particular, the influence of CDWs may explain the peak-dip-hump structures frequently found for high-T c oxides.

The phase diagram for coexisting d-wave superconductivity and charge-density waves: cuprates and beyond

Phase diagrams of d-wave superconductivity characterized by an order parameter Δ coexisting with charge-density waves (CDWs) characterized by an order parameter Σ were constructed for the two-dimensional Fermi surface (FS) appropriate to, e.g., cuprates. CDWs were considered as an origin of the pseudogap appearing at antinodal FS sections of the d(x2-y2) superconductor. Two types of the Σ-reentrance were found: with the temperature, T, and with the opening of the CDW sector, 2α. The angular plots in the momentum space for the resulting gap profile over the FS ('gap roses') were obtained. The gap patterns are rather involved, giving insight into the difficulties of the interpretation of photoemission spectra. It was shown that the Σ-Δ coexistence region exists even for the complete dielectric gapping due to the distinction between the superconducting and CDW order parameter symmetries. The checkerboard and unidirectional CDW configurations were examined, and both the phase diagrams and the behavior with T and α of the order parameters were found to differ. A more general case with a non-zero mismatch angle β between the superconducting lobes and the CDW sectors was analyzed, the case β = π/4 corresponding to the d(xy) symmetry of the superconducting order parameter. The phase diagrams were found to be sensitive to β-variations, showing that internal strains and external pressure can drastically affect the behavior of Σ(T) and Δ(T).

Mechanical stability of proteins

A number of experiments and experimentally based simulations showed that beta-proteins are mechanically more stable than alpha-proteins. However, the theory that might explain this evidence is still lacking. In this paper we have developed a simple elastic theory, which allows to estimate critical forces for stretching both kinds of proteins. It has been shown that unfolding of beta-proteins does really require notably higher forces as compared to the stretching of alpha-proteins.

Excess nonspecific Coulomb ion adsorption at the metal electrode/electrolyte solution interface: role of the surface layer

Excess ion adsorption gamma induced by the polarization image forces in the system of a metal electrode/symmetric electrolyte solution separated by an insulating interlayer has been calculated. The adopted theoretical scheme involves the Coulomb Green's function in a three-layer system with sharp interfaces and specular reflection at them. The influence of the spatial dispersion of the dielectric permittivities epsilon(i)(k) in all the three media on the image force energy W(im) and the adsorption gamma has been analyzed, where k is the wave vector. A comparison with the classical model, where epsilon(i)=const, has been carried out. It has been shown that both the Debye-Hückel ion screening and the spatial dispersion of the solvent contribution epsilon(solv)(k) to the overall dielectric function epsilon(el)(k) of the electrolyte solution lead to the qualitative difference with the results for the classical model. In particular, in a wide range of ion concentrations n0 a thin interlayer L > or = 5-10 angstroms effectively screens out the attractive influence of the metallic electrode, so that the net Coulomb adsorption may become repulsive. The approach and the results obtained qualitatively describe two physically different situations. Specifically, the introduced interlayer corresponds either to the dense near-electrode (inner) electrolyte layer or to the intentionally deposited control coating of arbitrary thickness.