The short answer is yes. The theory for this, due to Peierls, Wannier, Slater, Luttinger, and Luttinger & Kohn, is referred to as the Envelope Function Theory. It is best described in the PhD thesis of Johan Peter Cuypers, Scattering of Electrons at Heterostructure Interfaces, the link to which I attach below.

http://repository.tue.nl/386541

Dear Behnam Farid;

Great thank for your precious help.

You are most welcome Kebbab.

I agree with Mr Behnam, the theory works well. I would here a word of caution is You need to take care of temperature and nice bonding.

In theory you can do anything. I'm afraid that for this particular task, theory usually doesn't work well when compared to experimental results.

Even if you can assume a Schottky model, there are numerous pitfalls. Unfortunately, the Schottky model doesn't work in many (most?) cases. In practice there are many other effects occurring at interfaces that can cause the bands to considerably deviate from the Schottky prediction. Reaction between the two materials, polarized chemical bonds, the so called metal induced gap states (MIGS) and many follow up acronyms are common examples for the so called Fermi level pinning (FLP) phenomenon, which basically means "things are going very Schottky here"

Fifty-some years ago people (I think Volker Heine was the first) have coined the S-factor which empirically tried to quantify how far away a system is from the Schottky limit (S=0) to a complete FLP (S=1, sometimes referred to as the Bardeen limit).

The introduction of metal gate / high-k dielectrics to the 45nm node (Intel, 2007), preceded by about a decade of intensive research, has brought renewed interest to these problems, this time at the metal-insulator interface perspective (as part of MOS devices), which isn't much different than metal-semiconductor contacts.

The only instances where I saw successful theoretical explanations to these phenomena was in cases where there were some experimental results and then theory was used to try to rationalize the mechanisms of FLP, but I haven't seen much of a theoretical prediction.

@ Lior Kornblum - The problem is in my opinion the one-electron picture used in conjunction with the envelope-function theory. If the starting point is the LDA bandstructure, we know that the  band gaps are generally too small. If on the other hand the starting point is the Hartree-Fock bandstructure. then we have the opposite problem of too large band gaps. The envelope-function theory is on its own sound; it needs however to be implemented within the framework of the many-body theory, taking into account that the self-energy is both energy and momentum dependent (for instance, some work has been done -- if my memory is not failing by Schlüter, Sham, Haydock and Godby -- on the influence of the so-called 'image potential', which is an interaction effect, on the barrier heights). But aside from this, all theoretical calculations related to the 2D electron systems (including those concerning the integer and fractional quantum Hall effects) use tacitly the envelope-function theory -- all of them invariably take account of the envelopes of the single-particle electronic states, and not the full spatial variations of these functions.

You are most welcome Kebbab.

@Behnam Farid, some theoretical approaches may have limited use in very specific experimental conditions - mostly in epitaxial heterointerfaces, whereas most practical cases are not so clean. Even in the almost-ideal case of epitaxial interfaces, can you account for dislocations? what is their electronic contribution? how do you account for intermixing/interdiffusion across the interface?

In many practical cases you would typically encounter a poly-crystalline metal on the semiconductor, with or without preferred orientation or epitaxial relation; there may be a thin oxide at the interface or intentional dopant(s); there may be an intentional or unintentional interface reaction / intermixing, and several other issues that are very hard to predict in advance.

I can give a personal example; I spent the first three years of my PhD trying to understand why the band offsets of Ta on Al2O3 differ from that of Pt and Al. I spent dozens of hours in a dark TEM room until I was able to find a ~2nm layer at the Ta-Al2O3 interface that accounted for the 0.4eV shift in the measured the band offset (see link). Could the envelope function approximation predict that for a poly-crystalline Ta on an amorphous aluminum oxide?

http://journals.aps.org/prb/abstract/10.1103/PhysRevB.84.155317

Theory can go never wrong unless it is not understood fully. Theory is an intelligent observation based conclusion of behaviors. Some time, if the complex behavior is not understood fully, and try to compare with practical results, it is felt that theory does not work. The conditional part of theoretical and practical results need to have identical

@Amipara Manilal, in theory and in a philosophical sense that is true. In reality, for this particular question and topic, things are not so easy. This is due to a combination of the fact that most theories not working very well even for near-ideal practical cases, and mostly due to the inability of existing theories to predict a large range of material/metallurgical behavior possible at such interfaces.

So in a practical sense, can theory predict the band structure at a metal-semiconductor contact, without prior knowledge of the interface structure and chemistry? Very rarely (and for such cases the simple formula of the Schottky model might do a better job than first principles and other fancy approaches).

With that being said, in high-quality epitaxial interfaces between semiconductors there may be a wider window where theory can predict the band structure.

@ Lior Kornblum - The envelope-function theory cannot predict more that one puts into it. The kind of problems you are describing are requiring of first-principles molecular-dynamics simulations (taking full account of e.g. the annealing process), and even then the question arises as to whether the formalism adopted (such as the local-density approximation within the framework of the density-functional theory) is sufficiently accurate for the task. The envelope-function theory as often employed works on the basis of two semi-infinite crystals brought into contact, without  any due consideration regarding the fact that a semi-infinite crystal is not an infinite crystal and that breaking the periodicity in one direction brings about considerable change in the electronic structure and ionic positions in some layer around the surface. Consequently, the envelope-function theory works best when lattice mismatch is minimal, such as in GaAs heterostructures. I emphasise, the envelope-function theory cannot do wonders and consequently has its limitations. In the cases where it is genuinely applicable, it does what is expected from it to do.

Thank you for the reference.

Check for instance:

https://www.researchgate.net/publication/267330419_A_Theoretical_Investigation_on_Decorated_Graphene_NanoribbonSilicon_Schottky_Diode_as_Hydrogen_Sulfide_Gas_Sensor

Conference Paper A Theoretical Investigation on Decorated Graphene Nanoribbon...

Dear all;

Certainly, experiment gives accurate results. But the theoretical approaches are sometimes useful for the guidance of the choice of the suitable materials in a given application. Even if the calculation result is less precise, it lead at least to the nature of the contact (type I, Type II or ohmic). I think that should be sufficient for the choice of materials to be used. The information about the accuracy of the used method can be evaluated when the contact is really made, only the experiment can inquire us of the result.

Cordially.