Observation of quasi bound states in open quantum wells of cesiated p-doped GaN surfaces

The electron density of states in the open quantum well formed by the downward band bending region at the surface of cesiated p-type GaN is investigated. We theoretically predict the existence of metastable resonant states in this non confining potential with an intrinsic lifetime around 20 fs. Their experimental observation requires access to the empty conduction band of the cesiated semiconductor, which is possible with near-band gap photoemission spectroscopy. The energy distribution of the photoemitted electrons shows contributions coming from electrons accumulated into the resonant states at energies which agree with calculations.

💡 Research Summary

In this work the authors investigate the electronic density of states associated with the downward band‑bending region that forms at the surface of cesiated p‑type GaN. Because the Fermi level is pinned mid‑gap while the cesium monolayer creates a negative electron affinity (NEA) condition, the surface potential consists of a triangular well that is open toward vacuum. The authors ask whether such an “open quantum well” can support any quasi‑bound electronic states despite the fact that electrons can tunnel out into vacuum.

To answer this, they develop a Green‑function based open‑system formalism for the effective‑mass Schrödinger equation. The potential profile is obtained by solving Poisson’s equation for Mg‑doped GaN (≈10²⁰ cm⁻³) and by adding a thin (0.3 nm) triangular barrier representing the Cs layer (height ≈5 eV). By evaluating the local density of states (LDOS) as the imaginary part of the Green’s function, they find a continuous background of states in the band‑bending region but also two pronounced local maxima at 2.4 eV and 3.0 eV above the Fermi level (p = 0). Lorentzian fits give full‑widths of 37.7 meV and 28.2 meV, corresponding to lifetimes of roughly 18 fs and 23 fs. These are interpreted as metastable resonant states in which electrons undergo many reflections inside the triangular well before leaking into vacuum, analogous to leaky Fabry‑Pérot modes or quasinormal modes in photonics. The calculations also show that the resonances persist even without the Cs barrier, indicating that the thin barrier merely provides a convenient NEA surface rather than being essential for the formation of the states.

Experimentally, the authors prepare a 200‑nm‑thick p‑GaN layer (Mg ≈5×10¹⁹ cm⁻³, surface overdoping ≈10²⁰ cm⁻³) on an n‑GaN buffer, clean it chemically, anneal it, and deposit a full Cs monolayer under ultra‑high vacuum. The NEA condition is verified by the observed vacuum level ≈1.5 eV above EF. Photoemission spectra are recorded using a UV lamp with narrow‑band filters (bandwidth ≈10 nm) for photon energies ranging from 2.85 eV to 4.13 eV. An energy analyzer with 50 meV resolution collects the emitted electrons, and both the raw energy distribution curves (EDCs) and their numerical derivatives (DED Cs) are analyzed.

For photon energies above the GaN band gap (3.4 eV), a bulk‑conduction‑band minimum (CBM) contribution (labelled Γ) appears as a broad positive feature in the EDC and a corresponding negative dip in the DED C. Below the band gap, bulk absorption is absent; only surface‑proximate absorption (process (i) in the schematic) and Franz‑Keldysh absorption in the strong field of the band‑bending region (process (ii)) can generate electrons. In this regime the low‑energy “S” peak associated with surface absorption is always present. Importantly, two additional features (labelled (1) and (2) in the DED C) emerge as the photon energy is increased. Feature (1) is visible for all photon energies but becomes clear around 3.26 eV; feature (2) appears only above ≈3.26 eV and merges into the Γ shoulder for higher energies. The energies of these two features match the theoretically predicted resonant states at 2.4 eV and 3.0 eV above EF, confirming the existence of the quasi‑bound states.

The paper thus demonstrates three key points: (i) an open quantum well at a semiconductor surface can host localized resonances despite the lack of true confinement; (ii) a Green’s‑function open‑system approach can quantitatively predict both the resonance energies and their sub‑femtosecond lifetimes; (iii) low‑energy photoemission under NEA conditions provides a sensitive probe of such surface resonances, separating them from bulk contributions. The findings have implications for the design of high‑efficiency photocathodes, for understanding surface electron dynamics, and for broader studies of open quantum systems where leaky modes play a functional role.