The extensive photo response on metal/n-Si clarified by the zero-gap with inter-band phonon scatterings

UVA to NIR with multi-directional photo responses have been found on metal (Au)/n-Si device. A reasonable explanation has not been found in various physical models of Si-devices for the phenomena. We approached a zero-gap at X (reciprocal point) in two conduction bands of Si to analysis the optical response with the inter-band phonon scatterings. The calculation of the quantum efficiency between X-$Γ$ and X-W successfully simulated the sensitivities in visible region (1.1 to 2.0 eV), the carrier density profile well fitted the response in NIR (0.6 to 1.0 eV). Filling up the zero-gap by doping electrons ($\sim 10^{18}$/cm$^3$) at around X, a lower limit of 0.6 eV arose in the measurement below Si-band gap of 1.17 eV. Indirect/direct transitions of inter conduction bands: X-W, X-K and $Γ$-L in the 1st Brillouin Zone/Van Hove singularity at L point, synchronizing with phonon scattering, gave a variety of directional photo-responses. The carrier scattering model for the inter bands (X-W, X-K and $Γ$-L) were consistent with the directional dependence of photo-currents under UVA (3.4 eV) and Visible (3.06 eV) excitations. Band to band scatterings assisted to extend the available optical range and increase its variety of directional responses. Utilizing this principle, a new frontier will be opened in the photo-conversion system by using indirect-transition semiconductors and thus, it will be released from those band gaps and directivity limitations.

💡 Research Summary

The paper reports an unusually broad photo‑response of Au/n‑Si devices, extending from the ultraviolet (≈350 nm) through the visible to the near‑infrared (≈2100 nm). Conventional explanations based on Schottky barrier photodiodes fail: the extracted barrier height (≈0.45 eV) does not match literature values (≈0.8 eV), and significant photocurrent is observed well below the Si indirect band‑gap (1.17 eV). To resolve this, the authors focus on the silicon band structure in the first Brillouin zone, emphasizing a “zero‑gap” at the X point where two conduction bands (designated X₁ along Γ‑X and Xᵤ along X‑W/K) intersect. Because the energy separation is essentially zero, indirect inter‑band transitions become possible when assisted by phonon scattering.

Four processes are considered: (I) direct transitions at the Van Hove singularity of the L point (Γ‑L direction), responsible for the UV‑visible response around 3.4–3.5 eV; (II) a similar Van Hove singularity at X (excluded because its gap exceeds the experimental photon energy); (III) the X₁ → Xᵤ indirect transition, which can absorb photons from ≈0.8 eV up to ≈2.7 eV; and (IV) n‑type doping (~10¹⁸ cm⁻³) that pre‑populates the lower X₁ band, effectively “filling” the zero‑gap and enabling sub‑1 eV response without phonon assistance.

The authors calculate quantum efficiency (QE) by combining the transition probability (proportional to a constant oscillator strength and the coupling density of states, DOS₍CV₎) with carrier mobility μ (derived from effective mass and electric field). DOS₍CV₎ and μ are evaluated at specific k‑points (e.g., k ≈ 2.0 π/a at X) using known silicon parameters; regions where the effective mass diverges are excluded. The photocurrent is then expressed as I = q · μ · n · E, where n is proportional to DOS₍CV₎.

Calculated QE curves show that process I predicts a peak near 3.5 eV, larger than the measured values, while process III reproduces the experimental trend from 1.0 to 2.7 eV remarkably well. The inclusion of process IV yields a modest QE below 1.0 eV, matching the observed low‑energy tail down to 0.6 eV. The agreement validates the hypothesis that the X‑point zero‑gap, together with phonon‑assisted inter‑band scattering, governs the broadband response.

Experimentally, the Au electrodes form self‑organized nanostructures (thickness 10–30 nm, aspect ratio 10–100) that support surface plasmons. These plasmonic features act as optical waveguides, coupling incident light into the silicon and providing multiple propagation directions. Photocurrent measurements under top, reverse (through the substrate), and diagonal illumination reveal distinct angular dependencies, with about a 50 % reduction for in‑plane illumination at 0°/180°. This multi‑directional behavior is attributed to the combination of plasmonic field enhancement at metal edges and the anisotropic nature of the X‑point transitions (different k‑vectors for X₁ and Xᵤ).

In conclusion, the study demonstrates that indirect inter‑band transitions enabled by a zero‑gap at the X point, assisted by phonon scattering and modulated by doping, can extend silicon‑based photodetectors well beyond the conventional indirect band‑gap limit. The work suggests a new design paradigm for broadband photoconversion: exploiting indirect‑transition semiconductors, engineering carrier populations at critical k‑points, and integrating plasmonic metal nanostructures to control directionality. Future research directions include tailoring phonon spectra, optimizing doping concentrations, and designing resonant plasmonic geometries to further boost efficiency, potentially applying the concept to other indirect‑gap materials such as germanium or silicon carbide.