Energy band diagram of a system of Silicon Quantum dots

Question

Suppose that we have a system of Silicon nanoparticles embedded in ZnO dielectric matrix. i'm thinking about how to construct the energy band structure of this system , suppose that we already have all the values of electron affinity, work function and energy bandgap of c-Si and ZnO. So i will align the Fermi level of c-Si and ZnO first, and repeat the process to get a periodic pattern for the energy band of the whole system. c-Si and ZnO used in this case are all intrinsic so there are little carriers in the system at equilibrium.
My question is will there be a field at the interface of c-Si and ZnO in the energy band structure like in the case of p-n junction ? In p-n junction there is diffusion of minor carriers (e into p side and hole into n side) which results in the recombination of e and holes at the interface and thus there is a depletion region with a lot of charged ions, so there is a field at the interface of p-n junction. In c-Si and ZnO the situation is different, there's no charged ions at the interface and thus no field. But i'm quite confused, should the energy band be abrupt at the interface, like in metal-metal contact ?

I am trying drawing the detail of the energy band diagram, there is a lot of things i don't know about this, so please give me some ideas on what i should take note of ? (band offset, quantum effects etc. )

Answer 1

Yes, there will be electric field and yes, the energy band will be abrupt at the interface. In general case both effects exist at the contact for any materials (even for metal-metal contact).

The height of the step at the interface is equal to the difference of the electron affinities. It can be zero e.g. for p-n junction when the materials on both sides are the same. The parameter one should look for is called VBO (valence band offset).

From the abstract of this article:

...the energy band alignment and interfacial microstructure of ZnO/Si heterojunction are investigated by x-ray photoelectron spectroscopy. The valence band offset (VBO) is determined to be
3.15±0.15 eV and conduction band offset is −0.90±0.15 eV

The distribution of carriers near to the interface is inhomogeneous and produces the electric field that aligns the Fermi level. For narrow quantum wells (or quantum dots) this effect is usually negligible (the Fermi level in QW is the same as in the barrier bulk).

If the nanoparticles are large enough this effect will take place though. One should compare the size of the particle to the Debye length (screening length, $L_D$). If the concentration of carriers is very low then $L_D$ goes to infinity and there is no field at all. Probably this is your case.