Because the electrons are confined to a much smaller space than in a (practically infinite) crystal (or other macroscopic solid state object). Intuitively, we can see from quantum mechanics that this confinement leads to a shift in the energy levels, which therefore can affect the band gap. - Think of the particle in a box usual example from quantum mechanics: when you squeeze the box and make its length smaller, the energy levels of solutions to the Schrödinger equation will shift.

When you come from a potential which is period in all three dimensions, and then take away the periodicity in one (nanowire e.g.), two (graphene e.g.), or even three dimensions (quantum dot e.g.), you can see that this will have an effect on the energy levels (band structure more precisely) and therefore the difference between the highest occupied level and the lowest unoccupied level (or band of levels) may shift, thus changing the band gap when we make the transition from "infinite" solid to nano-scale material.

Because the electrons are confined to a much smaller space than in a (practically infinite) crystal (or other macroscopic solid state object). Intuitively, we can see from quantum mechanics that this confinement leads to a shift in the energy levels, which therefore can affect the band gap. - Think of the particle in a box usual example from quantum mechanics: when you squeeze the box and make its length smaller, the energy levels of solutions to the Schrödinger equation will shift.

When you come from a potential which is period in all three dimensions, and then take away the periodicity in one (nanowire e.g.), two (graphene e.g.), or even three dimensions (quantum dot e.g.), you can see that this will have an effect on the energy levels (band structure more precisely) and therefore the difference between the highest occupied level and the lowest unoccupied level (or band of levels) may shift, thus changing the band gap when we make the transition from "infinite" solid to nano-scale material.

The band gap will become broader, due to the nano-size effect.

When the material size decreases to nanolevel, its bandgap automatically increases, so high energy is required to eject the electron from valance to conduction band.

All the properties of materials are structure dependent. Boundaries between the crystallites play a vital role in changing of these properties. This is similar to the situation as same material might have different optical, electrical and magnetic behavior in particle, bulk or thin film form. It seems very difficult that a grain or particle approaches to the atomic dimensions. So, a particle will surely consist of number of crystallites. The size and number of crystallites in a particle or grain always predict the number boudaries present in it. The greater the number of boundaries will significantly effect the properties of material.

The answer is in the concept of origin of band gap.

I agree with Ralph Scheicher

In addition to explaination by RALP, i like to add this.

Specifically, if you talk about nanoparticles of seminconductor, you can see significant change in the energy gap(band gap) for the particles sizes, those are less than bohr exciton diameter of that semiconducting system.

Any way, while chopping a micron sized particle to (i) say 100nm and then, (ii) to 10snm, the surface effects are dominating in (i), and size effect is dominated in (ii).

According to electronic structure, there is transistion of band (in BULK) those transform to descreate energy levels (in NANO). As said earlier , at Nano level, energy eigen values can be obtained by way of solving "particle in box " QM problem. Finally, energy gap shows 1/R(sqaure) depdendence - If R is radius of the particle.

I am not agree with the confinement of particle description. Because, this is completely a different situation in case of materials. While as the description of confinement of particles working well for gaseous environment. The electron gas concept however for materials have not similarity with it. The energy band gap concept in materials have not any concern with the energy of that particle system. The broken symmetries at the surfaces related with the un-complete and broken shell spheres. In case of nano size particles, the surface area significantly increased. Because of this greater surface area, the broken symmetries are also increased. These broken symmetries at surfaces intercepts and find the greater number of free carriers due to greater broken shells. For electrical conduction mechanism, it is well known that electrical conduction is totally a surface phenomenon which supports my this argument that "The number of free carriers increased in the system with the increase of surface area". Hence, due to this reason the bandgap of a material also changes with the decrease or increase of surface area i.e from micro to nano or vice versa.

Fine explanation by Ralph. The origin of band structure and quantum approach lead to change in band gap.

Murtaza Saleem has a point: for "nano-sized" materials, surface effects become increasingly important compared to bulk effects (simply seen from the ratio of surface to volume for a sphere with radius R: 4piR*R / (4piR*R*R/3) so proportional to 1/R, meaning it becomes larger for smaller R).

But still, in addition to those very important surface effects, there is real change in the bulk band structure due to the removal of periodicity in one or more dimensions. The associated curved bands in the corresponding directions in reciprocal space become "flat" (dispersion-free) and that *can* (but does not *need* to necessarily) alter the band gap (if the affected band was giving rise to the states at the valence or conductance band edge).

Well, the band gap of material ll get increased when its size reduced to nano. In the case of ZnO, dopant such as Fe , Mn into ZnO sometimes reduces the bandgap value of the ZnO by increasing the dopant concentration even though its in the scale of nano . Why So?

the band gap value decrease with the increase in dopant concentration can be because of two effects. firstly, the addition of dopant can cause an increase in density of states in valence band. or secondly it can also create localized states within the forbidden gap it self. Both of these effects thus decrease the band gap

I think confinement is the main reason. However, it depends on the kind of material, the actual morphology dimension (1D, 2D, or 3D islands would behave differently), interface with substrate or vacuum etc. It is not possible to give a general answer. The best general answer it is that the band gap depends on the boundary conditions...

I totally agree with Ralph, band gap change lead to surface effect and extraordinary properties of nano materials. @Kumuthini: dopant may affect in 2 different way: Donor (ie. As doped in Ge) or Acceptor (In doped in Ge).

Donors add a band between Valence and Conduction band and near to Conduction band. At temperatures higher than 0K, donor electrons can be excited and migrate to added band.

at T>0K :

-------x-----x------- Ec (Conduction band)

---x--o--x--o--x---- Ed (Donor band) As have 5 electron at Valence band

----x---x---x---x--- Ev (Valence band) Ge have 4 electron at Valence band

It called N-Type semiconductor, carriers are holes

Acceptors add a band between Valence and Conduction band and near to Valence band. At temperatures higher than 0K, Valence electrons can be excited and migrate to added band.

at T>0K :

--------------------- Ec (Conduction band)

---x--x--x--x--x---- Ea (Acceptor band) In have 3 electron at Valence band

----x---x---o---x--- Ev (Valence band) Ge have 4 electron at Valence band

It called P-Type semiconductor, carriers are electrons

There is the blue shift of the exciton energy as a result of the

quantum-confined effect. Thus, this effect determines dimension of the band gap. I agree with a Ralph Scheicher' comment.

Reply to Kumuthini Rajendran is following : In the case of ZnO doped by magnetic impurities such as Fe , Mn and other reduction of band gap may be caused by the formation of solid solutions. Besides, there is the magnetic polaron effect. As a result, exciton energy is reduced. Which is the method of the determination of band gap you use ? It will allow more correctly to understand your question.

Yu. Gnatenko @: Sir i used the plot of photon energy versus (αɦν)2 to evaluate bandgap values of Fe doped ZnO nanoparticles from UV-Vis Absorption spectra. In this, for certain doping concentration of Fe the bandgap value increases and it decreases , further increasing the Fe concentration.

Kumuthini Rajendran @ : Method for the determination of the semiconductors band gap by approximation of the absorption edge is the bar and widespread. However, the accuracy this method, even in the case of single crystals, is insufficient. It due to the fact that the slope of the absorption edge is strongly dependent on the presence of intrinsic defects in the crystal: the more defects, the slope is less. Therefore, the presence of defects in the crystal can lead to deformation of the energy bands, as well as to an additional but intrinsic absorption. Therefore, for the same semiconductor compound can be obtained different values of the band gap. In the case of nanostructured semiconductor films there is a significant amount of their intrinsic defects. Therefore, to obtain the relative change in the band gap for diiferent samples they must have the same optical and crystalline quality. In this connection, it is also to carry out structural measurements. For a system of ZnO: Fe, in the case that your films have a fairly good optical quality, you mentioned the changes of the band gap can be attributed to the following factors. At low concentrations of iron (can not be more than 1-2%) increase in the band gap due to the quantum size effect. At high concentrations, can form a substitutional solid solution ZnFeO, for which the band gap should decrease as compared to the undoped ZnO. In this case, we have two competing mechanisms: an increase in the band gap as a result of the quantum size effect and a decrease as a consequence the formation of a solid solution of substitution.

What is difference between band gap , optical band gap and mobility gap ?

is there any characterizations other than UV-Vis spec for determining band gap of a material

By measuring resistivity as a function of temperature, band gap of a material can be determined.