How does surface electronic properties (i.e band structure, electron affinity and Ionization energy) vary from bulk to nano domain (i.e quantum well, nanorod etc.) and can we get any information of 2DEG formation using XPS or UPS.
In order to answer Your question may it is a good idea to first of all to have a look at some XPS reviews after famous XPS researhcers - Tougard, Fujimori, ..... Or find some lectures in XPS, devoted material characterization with XPS technique - there are a lot of them. Please, don't take my answer as something as "push out".
XPS and UPS only probe to ca. 10 nm. So, if your junction between the two films you're studying are really thin then maybe you can find some information. However, if the films are thick then either spectroscopic method will not work.
Later try to read some book, for example: J.F. Watts and J. Wolstenholme, An Introduction to Surface Analysis by XPS and AES, 2003, J. Wiley & Sons, UK.
in a nutshell these become quantized :) For example, in a thin metal film (2D material) one observes an electron confinement in the direction, perpendicular to the film surface, and the energy levels become quantized. In the quantum wires/nanowires (1D objects) quantization occurs in both directions perpendicular to the rod, and in quantum dots (0D) the quantization of energy levels occurs in all directions of electron momentum. This quantization phenomena may be interpreted both as emergence of distinct energy levels instead of a continuous band, or as a formation of an energy gap. See, for example, this paper about quantization in graphene nanoribbons (remarkeably graphene itself is already a 2DEG material, and is studied by XPS here):
Concerning the probing depth of XPS, I'd like to correct David a little bit - conventional core-level XPS (hv = 40 - 1500 eV) only probes to 1-2 nm deep, which is due to a strong interaction of (photo)electrons with the media. In order to go deeper one typically has to go very high kinetic energies of photoelectrons, hence high photon energies. Therefore, you may want to look up some articles on HAXPES, which stands for HArd X-ray PhotoElectron Spectroscopy. However, an opposite approach is also applicable for enhancing the probing depth of photoemission, when one works at very low photoelectron energies. A very elegant experiment was performed by a group of J. Wells, where they have probed the core levels of a buried 2DEG (so-called delta-layer) in silicon using very low kinetic energies of photoelectrons:
This group has also performed some studies of the delta-layer in silicon using resonant enhancement of signal via coupling of the wavefunctions of the surface and the buried layer interface.