Generally there are three known ways in which a band gap can be created in carbon.
1. Via functionalization. However functionalization is a chemical reaction that changes the underlying material properties.
2. Creation of allotropes that have tunable band gaps like fullerenes & tetrahedral amorphous carbon(Tac or diamond like carbon).Fullerenes are hard to obtain in large quantities and Tac can't be patterned. Meaning it has to be first deposited & then post processing steps need to be applied. Unlike other forms of carbon(eg glassy) this introduces complexities in manufacturing.
3. Creating quantum dots.Quantum dots are few atom structures(a 2nm qd will only contain about 28 carbon atoms,possibly less) and therefore their energy levels are discretized and different from bulk crystal structures. For this reason they are also called artificial atoms.
While QDs offer a simple strategy to tune band gaps in any element/semiconducting compound its hard to actually use these materials in bulk.
Carbon offers more possibilities for tuning its band gap. And one of the most exciting ones is creating nano composites of quantum dots & carbon nanotubes. In such a composite the qds are semiconducting particles whose size determines the band gap. While cnts provide a shell to the underlying qd core.
Literature suggests that band gap can be tuned from 1.6-2.3 ev this is enough for use in optoelectronic components. But since nano carbon have excellent thermal conductivity & current carrying capacity these structures can also be used in power electronics. Any material with a band gap of over 2ev should show some degree of transparency implying the possibility of their use in transparent conducting applications (tac is already a contender in this particular segment but it'll be good to have more options)
Key factors that make this possible
1.Graphitic sheets including graphene are not completely planar. They fold along the edges to minimize energy of the dangling bonds. Unless they have been passivated with hydrogen for example.
2.Graphene fragments can be cut off from graphene sheet in any direction & they will stabilize themselves by folding along the edges. Such structures are called graphene nano ribbons.
3. GNRs have a band gap. Smaller the structure ,larger the gap. The behave similarly to quantum dots & at small enough sizes they can be called artificial atoms.
4. Such structures are common in the universe with one major difference. They are hydrogenated & no folding is necessary to minimize surface energy. These structures are called Polycyclic Aromatic Hydrocarbons or P.A.H. They are known to be fluorescent & semiconducting.
5. CNT can act as nano reaction chamber in which nano carbon can grow.The diameter of carbon nanotube is between 1-10nm (but other geometries also exist) and they can grow in length of upto centimeters. Consequently semiconducting carbon dots(or gnr or quantum cylinders or quantum rings or even chains) can be placed inside CNT.
6. CNT acts as a shell & preserves the underlying core,also provides an encapsulation to structure quantum dots(which is one of the major limiting factors in their use). These structures can be patterned obviating the need for post processing steps.
With this structure we have miniaturized cathode ray tubes. CNT maintains a "vacuum inside" their tubes so that these particles can independently function(as nano fluorescent lamps for example).Operational temperatures are limited by stability of the shell in an oxidative atmosphere 400-500c should not be a problem. But higher than that & the system will break(unless it is in a vacuum,beyond the reach of oxygen).
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