We study a two-particle lattice Schrödinger operator describing two identical fermions on the one-dimensional lattice Z with a nearest-neighbor interaction of strength λ ∈ R. The Hamiltonian acts in the antisymmetric subspace ℓ 2 , a (Z 2 ). Using the direct-integral decomposition with respect to the total quasi-momentum k ∈ T := (−π, π], we reduce the spectral problem to a family of fiber operators H λ (k) acting in the odd relative-coordinate space ℓ 2 , odd (Z). For every k ∈ (−π, π), the fiber Hamiltonian is represented as a one-dimensional discrete Schrödinger operator, equivalently, as a Jacobi operator with a finite-range boundary perturbation, and its essential spectrum is σ ess H λ ( k ) = [4 − 4 cos k/2, 4 + 4 cos k/2]. We give a complete description of the spectral transition at both edges of the essential spectrum. For each k ∈ (−π, π), the operator H λ (k) has a unique simple eigenvalue outside the essential spectrum if and only if |λ| > 2 cos k /2. This eigenvalue is given explicitly by E(k, λ) = 4 + λ + 4 cos 2 k/2 / λ, and the corresponding eigenfunction is obtained in explicit form in the relative coordinate. For |λ| < 2 cos k/2, there is no eigenvalue outside the essential spectrum. The critical threshold transition is also analyzed for each k ∈ (−π, π). At the critical coupling |λ| = 2 cos k/2, the discrete eigenvalue merges with the corresponding edge of the essential spectrum and gives rise to a threshold resonance. The corresponding threshold equation admits a nonzero bounded odd solution belonging to ℓ ∞,odd (Z) \ ℓ 2,odd (Z), showing that the spectral threshold is a resonance rather than an eigenvalue. We further establish the strong-coupling and threshold asymptotics of the discrete spectrum. In particular, in the strong-coupling regime the eigenfunction becomes localized at the interaction sites, whereas at the critical coupling it converges pointwise to the corresponding threshold resonant solution. The exceptional fiber k = π, for which the relative hopping vanishes and the essential spectrum collapses to the point {4}, is treated separately.
The paper presents the results of a comprehensive study on a dual-barrier silicon photodiode structure, Au–SiO 2 ·nSi–Au, featuring back-to-back rectifying metal-semiconductor junctions operating in both photodiode and photovoltaic modes. The peak spectral photosensitivity is observed at λ ≈ 0.85 – 0.90 µm, and the incorporation of the SiO 2 layer broadens the spectral response by 20 – 30 % via barrier and tunneling carrier transport mechanisms. The short-circuit photocurrent (I sc ) increases from 0.30 to 0.50 µA at low illumination levels and saturates at 0.65 – 0.67 µA for Φ ≥ 400 – 500 lx; the open-circuit voltage is V oc = 0.065 – 0.067 V. At an applied voltage of 6 V, the photocurrent reaches approximately 20 µA, while in the range of 0.02 – 0.10 V, the ideality factor is n = 1.7, indicating the contribution of generation-recombination processes and tunneling. The transient response is characterized by a rise time of t r = 88.7 ns, a fall time of t f = 109.2 ns, a carrier lifetime of τ = 56.3 ns, and an overall response time of t resp ≈ 10 −7 s. Under reverse bias from 0 to 6 V, the space charge region (SCR) width increases from 0.72 to 1.95 µm, and the maximum electric field strength rises from 2.2·10 4 to 6.0·10 4 V/cm. The aggregate of the obtained parameters demonstrates that the proposed structure is promising for high-speed near-infrared (NIR) photodetector applications.
We compare and disentangle measurement protocol from material physics of isotypic (n-SiC/n-Si) and anisotypic (n-SiC/p-Si) heterojunctions grown by high-temperature chemical vapour deposition (endotaxy), using Kelvin probe force microscopy (KPFM), scanning tunnelling spectroscopy (STS), precision electrical measurements with a Keithley 2450 SourceMeter, and an integral charge-storage test on a 0.1 F supercapacitor. Two-wire probing shows an enhanced low-bias current in the isotypic structures; four-wire Kelvin sensing, which reduces the voltage-drop contribution of external leads and contacts (but does not by itself average current over the device area, eliminate a local Schottky contact, or prove a specific transport mechanism), collapses this current to a much lower, bulk/interface-limited level. The observation is consistent with a parallel contribution from interface-assisted transport at the high density of interface states measured by KPFM/STS (D it up to (4.8 ± 0.3) × 10 12 cm −2 eV −1 ); we treat trap-assisted tunnelling (TAT) as the leading mechanistic hypothesis rather than an established fact, since the present dataset does not by itself discriminate TAT from Schottky/Poole–Frenkel emission, barrier inhomogeneity, or current crowding. Anisotypic junctions show a genuine diode-like I–V characteristic and an operationally defined open-circuit voltage V oc ≈ 1.2 V. Under the specified 14 C activity and load, the anisotypic device reaches a substantially higher terminal voltage on the 0.1 F capacitor than the isotypic device after 30 min (0.25 V versus 0.05 V, E ani /E iso ≈ 25). Based on in situ KPFM/STS mapping (spatial resolution 30 nm, threshold activation delay t a = 2.3±0.5 s, stretched-exponential relaxation τ = 35 ± 2 s, β = 0.65 ± 0.05) and a critical, manufacturer-documentation-based reassessment of what four-wire Kelvin sensing, generator polarity, and output-off protocols do and do not establish, we propose a measurement-and-interpretation protocol for SiC/Si (and, by extension, other wide-bandgap) heterojunction metrology, and illustrate its necessity with three worked examples (a SiC Schottky diode, an InGaN/GaN LED, and a 63 Ni–Si betavoltaic cell) in which a plausible but methodologically naive measurement yields a materially wrong physical conclusion.
Direct solar-to-hydrogen conversion via photovoltaic-driven water splitting is a promising strategy for sustainable fuel production. In this work, an integrated water-splitting system combining a high-voltage dyesensitized solar cell (DSSC) module with bifunctional FeCoNiPt electrocatalysts was developed. The Nb-doped TiO2 electron transport layers were synthesized by a hydrothermal method and employed as photoanodes for DSSC fabrication. The module consisted of three DSSCs connected in series, generated sufficient photopotential to drive overall water electrolysis. The DSSCs exhibited stable photovoltaic performance under AM 1.5G illumination and reduced light intensities. The electrocatalytic electrodes were fabricated from earthabundant FeCoNiPt alloy nanoparticle deposited on nickel foam and used to construct the electrolyzer. The integrated system achieved an estimated solar-to-hydrogen (STH) efficiency of approximately 6.5%, over a broad range of illumination intensities from 100 to 1000 W/m2 . These results demonstrate an effective strategy for self-powered solar hydrogen production using high-voltage DSSC modules and low-platinum bifunctional electrocatalysts.
We study a translation-invariant two-channel Hamiltonian on the two-dimensional lattice Z 2 describing two identical spinless bosons with no direct boson–boson interaction, coupled through an on-site association/dissociation term of strength γ ∈ R to a structureless molecular channel of fixed scalar internal energy E 0 ∈ R. The model is a 2 × 2 block operator matrix; it is translation invariant and admits a fiber decomposition over the total quasi-momentum k ∈ T 2 , whose fibers H γ (k) act on C ⊕ L 2,e (T 2 ). The perturbation distinguishing H γ (k) from the free operator has rank at most two, so the essential spectrum of each fiber is [ϵ min (k), ϵ max (k)], equal to [0, 16] at k = 0, independently of E 0 and γ. For the distinguished fiber H γ (0), we determine the discrete spectrum completely and uniformly in the coupling: when γ = 0, the channels decouple and the only discrete eigenvalue is the bare molecular level E 0 , present exactly when E 0 ∈/ [0, 16]; whereas for every γ ̸= 0 and every E 0 ∈ R, the operator has exactly two simple discrete eigenvalues, one strictly below and one strictly above the two-boson continuum [0, 16]. In two dimensions, the logarithmic singularity of the lattice Green’s function at the spectral edges makes both bound states appear for arbitrarily weak coupling, the binding energies being exponentially small when E 0 lies inside the continuum and only algebraically small (up to a logarithm) when E 0 sits at a band edge. The model is a rigorous lattice realization of Feshbach-induced binding produced by interchannel coupling alone.
