A semiconductor heterostructure is a sandwich of or junction between two dissimilar semiconductors with different band gaps (note: a silicon p-n junction is a homo-junction). There is no requirement that the two layers have to be thin enough for tunnelling to take place. 

A semiconductor superlattice is a periodic structure of two or more semiconductors of significantly different band gaps such that multiple quantum wells are formed in the low band gap layers. The layers have to be thin enough to allow carrier transport by tunnelling  to take place. 

Yes; the semiconductor superlattice will have multiple hetero-junctions. 

I think  an Heterojunction refers more to tow materials with different band gap (generally bulk materials)

What I understood from a couple of papers that I read is superlattice is a heterostructure but with multiple quantum wells that have a small barrier thickness in order for carriers to tunnel through the wells. So overall it is more like multiple heterojunctions put together that have very small thicknesses. I could be wrong.

Heterostructure is a name for a structure with different materials.

A layer of AlGaAs on GaAs is a heterostructure, and can be also termed heteroepitaxial structure etc. This is different from a homoepitaxial interface, such as a layer of p-doped GaAs grown over n-doped GaAs.

Superlattice is a heterostructure repeating several times. It doesn't have to be composed of just two different layers although this is by far the most common situation.

To my knowledge these definitions do not require different band gaps of the different layers, but different materials almost always have different band gaps. Bandgap modulation is indeed an important reason to grow heterostructures and superlattices but it isn't the only reason to do so. Strain engineering could be another, and there are several others.

Thanks Lior Kornblum for the answer. I would like to clarify one thing you said "Superlattice is a heterostructure repeating several times." Would that be a "heterojunction" repeating several time as the "heterostrcture" would be the whole superlattice?

Thank you

A semiconductor heterostructure is a sandwich of or junction between two dissimilar semiconductors with different band gaps (note: a silicon p-n junction is a homo-junction). There is no requirement that the two layers have to be thin enough for tunnelling to take place. 

A semiconductor superlattice is a periodic structure of two or more semiconductors of significantly different band gaps such that multiple quantum wells are formed in the low band gap layers. The layers have to be thin enough to allow carrier transport by tunnelling  to take place. 

Yes; the semiconductor superlattice will have multiple hetero-junctions. 

Anas, a heterojucntion is a heterostructure, but often it has the meaning of running a current through the junction.

Heterostructure:  Growing a material on different material. Generally these materials are having different bandgaps and lattice constants. The junction of these two different materials are known as heterojunction. 

Superlattice heterostructure: Growing multiple heterojunctions of two different materials with periodic repetition. But here thickness of the each layer is very thin (generally 1-5 nm, depending upon lattice mismatch). Due to these thin layers carriers can easily tunnel through these though it provides multiple quantum wells. Growing superlattice is one of the common techniques to reduce strain in the (top) epitaxial layer. 

Gourab Thanks for the clarification. 

Good question and good answer. Indeed, we assume that the heterostructure  is the various layers. The point. The Superlattice - is somewhere within a single crystal, but different properties. There can be used, and the concept of the band gap. Note, please, in the first case - is not. That's all. Heterostructure has long been well-known concept in optics - it corresponds to artificially birefringence [M.Born, E.Wolf].

Semiconductor heterostructures are layers of two or more different semiconductors grown coherently with one common structures (Kittle) . Super-lattice is one in which many heterostructres will be there.

How can i make Fe/MoS2/Fe hetro structure with VESTA?. Is there any other tool for this. Thanks in advance

Superlattice is a part of heterostructure. Since it is a periodically repeated in space , mathematically one can always define a translational vector. However, there is no such periodic repetition for heterostructure. So there is no lattice translational vector.

The wave function overlap in superlattice.

Salam,

The superlatice was a multi quantum well structure with thin barrier width(between wells), so there is an overlap between wavfunctions of wells.

From my understanding, the basic difference is in the thickness of the layers with different specific bandgaps that are attached to each other and the number of layers in the structure . For superlattice, the thickness should be thin enough (1-10 nm) where as for heterostructures it can be higher than this range. In superlattice the smaller thickness facilitates the carrier tunneling while in usual heterostructures tunneling is not considered significantly.