Quantum Dots - Paper Example

Quantum dots are semiconductor structures that contain a tiny droplet of free electrons. According to Coe-Sullivan (2009), the dimensions of typical quantum dots range from nanometers to a few microns. The history of these semiconductors dates back to 1988 when the first low dimensional structure QW (Quantum Wells) was developed. It was followed by quantum wire in which quantum dots were subsequently developed (Paul and Brazis 2017). Recently, quantum dots have captured the attention of scholars from various disciplines. The structures are used in transistors, solar cells (Jasim 2015), diode lasers, and second-harmonic generation (Xin et al. 2015). Due to their highly tunable properties, quantum dots have also drawn further attention from the field of quantum computing and medical imaging.

Quantum dots (QDs) is, therefore, an area of interest in the field of nanotechnology. It is where manipulation of matter on atomic, molecular, and super-molecular scale has widened the scope and application of quantum dots. The properties of quantum dots have drawn the attention of researchers for more than three decades and continue to take the centre stage in the field of nanotechnology. It is in this context that the current paper draws its inspiration in which a review of the application of the quantum dots is provided. To achieve the required objectives, the author will also review the perspectives and future applications of quantum dots.

The definition of quantum dots is premised on the size of their properties. For instance, they are small semiconductors that are few nanometers in size (Prasad 2008). The size of the QDs is so small that their optical and electronic properties are different from that of large particles. With these properties, QDs have recently become central to the theme of nanotechnology. The ever expanding applicability of the quantum dots is hinged on their optical properties. The principle behind their dimension is that it is sufficiently small to enable what is referred in the world of physics as quantum confinement (Lyon et al. 2013). The aspect of quantum confinement is exhibited in all the three dimensions of QDs. The structural component of the quantum dots has baffled experts in the field of nanophysics. The phenomenon of quantum confinement is defined as the change of electronic and optical properties due to their sufficiently small size. Typically, the size of the quantum dots is said to be less than 10 nanometers (Wu and Li 2007). As such, the size of the band-gap tends to increase as the size of the nanostructure decreases. The process results in what is referred to as exciton. It is a process where electrons and holes are squeezed into a dimension that is of critical quantum measurement. The phenomenon is observed in fluorescence. In semiconductors, for instance, light absorption results in the exciton of electrons from the valence and the conduction of the band (Zhu et al. 2008). Generally, a hole is created in the process. The electron and the hole can recombine to form what is referred to as exciton. When the exciton recombines, the electron goes back into ground state. During the process, the exciton energy is emitted as light. The emission is what is referred to as fluorescence.

A simplified model is provided by Van Driel (2005) in Figure 1 below. According to Van Driel (2005), the energy of the emitted proton is the total sum of the band gap energy. It is exhibited between the highest occupied level and the lowest unoccupied energy level. The energy is also contained in the confinement energies of the hole and the excited electron, including the bound energy of the exciton. The development is illustrated in the figure below:

Figure 1

Confinement energy and quantum dots

Source: Van Driel (2005)

The confinement energy depends on the size of the quantum dots. As such, absorption and fluorescence emission can be tuned by manipulating the size of the quantum dot during its synthesis. It is observed that the larger the dot, the lower the energy absorption onset and the fluorescence spectrum. On the other hand, smaller dots are said to absorb more energy.

Recent research in nanotechnology suggests that the shape of the quantum dots is also a factor of coloration. However, there is no enough information to substantiate these new findings. In addition, studies, such as those conducted by Kobayashi et al. (2007), Cho et al. (2009), and Caruge et al. (2008) reveal that the lifetime of fluorescence is dependent on the size of the quantum dot itself. Larger dots are characterised by more space with high energy levels. The properties make it possible for the electron-hole pair to be trapped. It explains why electron-hole pairs characterised by larger dots have longer lifespan. The property is illustrated in the figure below:

Figure 2

Fluorescence spectra of CdTe quantum dots in different sizes

Source: Van Driel (2005).

The figure above shows that different sized quantum dots generate light of varying colours. The development is as a result of quantum confinement. Quantum dots are used to improve fluorescence quantum yield by using shells with larger band-gap semiconductor material around them. According to Lee et al. (2000), the improvement is attributed to limited accessibility of electrons and hole towards non-radiative surface. Other studies, such as those conducted by Luker and Luker (2008) and Murray et al. (2000), suggest that the improvement is attributed to reduced auger recombination.

In the initial exploration, researchers fabricated quantum dots through the use of electron beam lithography, a phenomenon referred in physics as chemical vapour deposition (CVD). Recently, however, quantum dots have become standalone semiconductors that are fabricated in solution through colloidal process.

To this end, the structure of quantum dots exhibits unique semiconductor and optical properties. The properties are tunable as a function in relation to the physical size and composition of the quantum dots. The link is illustrated in Figure 3 below:

Figure 3

An example of size-dependent fluorescence spectra for quantum dots

Source: Paul and Brazis (2017).

From the diagram above, it is clear that the properties present characteristics that are intermediate between bulk semiconductor materials and molecule. To this end, one can conclude that a general property of quantum dots is that the optical emission can be tuned by manipulating its diameter. For instance, dots derived from cadmium selenide (CdSe) have the ability to change their particle size. For example, CdSe can be adjusted to form fluoresce from blue to red. The property is of critical importance in that it suggests the possibility of more efficient properties, such as light emitting diodes (LEDs), displays, and lasers. The same is also true in its applicability in the field of construction, especially with regards to improved transistors, quantum computing, and image application (Paul and Brazis 2017).

Quantum dots are useful due to their semiconducting abilities. The significance is especially evident when it comes to their interaction with photons, such as light. As such, it is critical to explore band theory in semiconductors.

Bandgap Theory in Semiconductors

According to the band theory of semiconductors, the aspect of discrete energy band is critical in the understanding of quantum dots. The same is true for semiconductor band gap. The band gap is a key property in semiconducting materials. It explains why quantum dots, as semiconducting materials, interact with light energy (Belkin et al. 2015). The phenomenon is explained in the context of electrons transitioning from one state of energy to another. For example, absorption of quantised energy leads to the transition of electron to a higher energy state. During light emission, electron transition to a lower state of energy leads to the release of a proton. The development is attributed to various kinds of energy levels in the electron within which an atom occupies. In this case, the levels with the lowest energy are first occupied before the higher states of energy are filled (Johnson 2015).

Large atoms tend to come together and form a solid. During the process, discrete energy levels begin to interact and form a continuous band of energy. As atoms combine, energy bands are slightly shifted as a result of interaction with the surrounding atoms. The process results in increased number of larger atoms. In the long run, the differences between various levels are so small such that continuous bands of energy levels are formed. Electrons can occupy these bands of energy (Paul and Brazis 2017). The development is illustrated in Figure 4 below:

Figure 4

Band structures of individual atoms combine together to forms bands

Source: Paul and Brazis (2017).

The combination illustrated above increases the number of atoms. During the process, energy levels at the atomic orbital blend together to form continuous bands of energy states.

Quantum Dot Behaviour

The physical behaviour of quantum dots can be understood using the concepts of bulk semiconductor bandgap and quantum confinement. For example, when the semiconductor is sufficiently large, such as when it is more than 1 mm, the quantum confinement has no significant effect. Instead, there will be what is referred to as semiconductor bandgap behaviour (Paul and Brazis 2017). However, quantum confinement becomes more significant when the crystal is the size of a nanometre. The phenomenon is clearly expressed when the crystal is smaller than twice the exciton Bohr radius of the particle. It can be calculated using the formula shown below. In the formula, ab denotes the Bohr radius (0.053 nm), m mass, m the reduced mass, and er is the relative permittivity.

The literature explored so far, especially the studies by Van Driel (2005), Davies (2008), and Paul and Brazis (2017), show that values for the exciton Bohr radius for semiconductors employed in the quantum dots are between 5.6 nm in CdS and 40.0 nm for PbS. The effectiveness of the bandgap of the quantum particles is achieved by the bulk of the semiconductor bandgap, which is added to the quantum confinement energy. In this case, the Eg is the bulk of the semiconductor bandgap and the mass of the particle.

In the equation above, a is the radius of the quantum dot. The Ry* is used to incorporate the additional effect of the exciton energy. The energy is defined as the Coulomb attraction between the negatively charged electron and the positively charged hole. In this case, q is the electron charge while e0 is the permittivity of free space. As the particle increases in size, it reaches the bulk semiconductor state with energy bands separated by the bandgap energy. To this end, the illustration of the quantum dot bandgap reveals that the gap energy is influenced by the physical size of the of the quantum dot (Davies 2008). Considering that the radius of the quantum dots is below the exciton Bohr radius, the quantum confinement energy increases in size. During the process, the quantum confinement dominates over the bulk semiconductor bandgap. As the crystal increases in size, the value approaches the bulk semiconductor bandgap. The development is illustrated in the figure below:

Figure 5

Change in energy levels as a function of particle size

Source: Paul and Brazis (2017).

To this end, it can be deduced that the tuning of the bandgap quantum dot can be realised by combining a selected semiconductor material and controlling its physical size. The change in bandgap in several semiconductors mostly employed in quantum dots is illustrated in the figure below:

Figure 6

Quantum dot bandgap energy as a function of crystal radius and semiconducting material

Source: Winiarz et a...