How to extract the surface potential profile from the ARPES signature of a 2DEG

Electron gases (2DEG) confined in the quantum well (QW) of a semiconductor surface exhibit electronic properties with essentially two-dimensional (2D) character and quantized energies, directly observable by angle resolved photoemission spectroscopy (ARPES). Here, we present a simple formalism to extract the surface potential from the in-plane dispersion of the 2DEG and analytically derive the ARPES intensity in the damped free electron final state approximation. We find that the out-of-plane modulation of ARPES spectral weight explicitly encodes the shape and the bulk extent of the electronic wave function. Damping of the photoemission final state however leads to an underestimation of the wave function's bulk penetration. Our method provides a novel and universal way to deduce elusive information about the surface electronic structure from photon energy dependent ARPES measurements.