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

Abstract

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.

Figures (3)

• Figure 1: (a) One-dimensional LDOS at vanishing transverse wave-vector ($p=0$) calculated with the envelope function approximation. The potential seen by electrons is marked by the white line, and corresponds to the CBM in the semiconductor and to the vacuum level $E_\mathrm{vac}$ in the vacuum. The LDOS shows that electron wavefunctions have a planewave structure both in vacuum for all energies and in the semiconductor for energies higher than the bulk CBM. For energies lower than the bulk CBM in the BBR, there is still a continuum of states but two resonant states appear at 2.4 and 3.0 eV. (b) 1D DOS at $p=0$, obtained by integration of the LDOS over $z <0$. The DOS is fitted with the sum of two Lorentzian functions of the form $A_1/[(E-E_1)^2 +(\Gamma_1 /2)^2] + A_2/[(E-E_2)^2 +(\Gamma_2 /2)^2]$. The fitted energy and spectral width of the resonances are $E_1 = 2.4$ eV, $E_2 = 3.0$ eV, $\Gamma_1 = 37.7$ meV and $\Gamma_2 = 28.2$ meV. The corresponding lifetimes are $\tau_1 = \hbar /\Gamma_1 = 17.5$ fs and $\tau_2 = 23.4$ fs. (c) 1D DOS conditioned to $z < 0$ as a function of the transverse wavevector $p$ (i.e. $\mathrm{DOS}|_{z<0} (p,E) = \int_{-L}^0 \mathrm{LDOS}(p,z,E) \, \mathrm{d}z / L$). The solid line corresponds to the dispersion relation in vacuum ($E = E_\mathrm{vac} + \hbar^2 p^2 / 2 m_0$). The dashed lines correspond to approximated dispersion relations for the two resonant states ($E \approx E_n + \hbar^2 p^2 / 2 m_e$) and the dashed dotted line corresponds to that of the bulk CBM $E = V_c(-\infty) + \hbar^2 p^2 / 2 m_e$.
• Figure 2: Schematic of the photoemission processes for a p-type semiconductor in NEA, for near band gap excitation. The blue arrows schematize above band gap excitation, while the orange ones picture below band gap excitation and absorption in the BBR.
• Figure 3: EDCs and DEDCs on GaN for near band gap excitation, from 2.85 to 4.13 eV. The vacuum level is at about 1.5 eV above the Fermi level ($E_\mathrm{F}$), meaning that NEA is achieved. For photon energies $h\nu >$ 3.4 eV, the $\Gamma$ contribution from electrons accumulated in the bulk CBM, appears at identical position in all curves (blue shaded area). Additional contributions at lower energy than $\Gamma$ are marked by the two gray-shaded area in the DEDC. The positions of the calculated resonant states are indicated by dashed red lines.