QUANTUM DOTS
Quantum Confinement
Gopal Ramalingam1, Poopathy Kathirgamanathan 2, Ganesan Ravi3, Thangavel
Elangovan4, Bojarajan Arjun kumar 5, Nadarajah Manivannan6, Kasinathan Kaviyarasu7
1,5
Deapartment of Nanoscience and Technology, Alagappa University, karaikudi- 630003,
Tamil Nadu. email:
2
Department of Chemical and Materials Engineering, Brunel University London, Uxbridge,
UB8PH, UK
3
Deapartment of Physics, Alagappa University, karaikudi-630 003, Tamil Nadu
4
Department of Energy Science, Periyar University, Salem -636 011, Tamil Nadu, India
6
Design, Brunel University London, Uxbridge UB8 3PH, UK.
7
UNESCO-UNISA Africa Chair in Nanoscience's/Nanotechnology Laboratories, College of
Graduate Studies, University of South Africa (UNISA), Muckleneuk Ridge, P O Box 392,
Pretoria, South Africa.
7
Nanosciences African network (NANOAFNET), Materials Research Group (MRG), iThemba
LABS-National Research Foundation (NRF), 1 Old Faure Road, 7129, P O Box722, Somerset
West, Western Cape Province, South Africa
Abstract
Quantum Confinement is the spatial confinement of electron-hole pairs (excitons) in
one or more dimensions within a material and also electronic energy levels are discrete.
It is due to the confinement of the electronic wave function to the physical dimensions of
the particles. Furthermore this can be divided in to three ways: 1D confinement (free
carrier in a plane) -Quantum Wells, 2D confinement (carriers are free to move down) -
Quantum Wire and 3D-confinement (carriers are confined in all directions) are
discussed in details. In addition the formation mechanism of exciton, quantum
confinement behaviour of strong, moderate and week confinement have been discussed
below.
Keywords: Quantum dots; Energy level; Exciton; Confinement; Bohr radius;
1. Introduction of Quantum confinement
The term ‘quantum confinement’ is mainly deals with energy of confined
electrons (electrons or electron-hole). The energy levels of electrons will not remain
continuous as in the case of bulk materials compare to the nanocrystal. Moreover,
obtains the confined electron wave functions, they become a discrete set of energy levels
as shown in the figure 1. Such kinds of effects appear when the dimensions of the
potential approach nearly to de Broglie wavelength of electrons and resulting in the
changes or discreteing levels of energy. The effects are defined as quantum confinement
and consequently, for nano-crystals are often called quantum dots (QDs). Furthermore,
this quantum dot effect influence into the nanomaterial properties such as electrical,
optical as well as mechanical behavior of material . It is due to the peculiar nature in
nano material possess higher energy electrons than the bulk material’s. Depending on
the QDs size, confined electrons have higher energy than the electrons in bulk materials.
1
, The semiconductor nanomaterials exhibit fascinating properties when reducing their
dimensionality from 2D to 1D or 1D to 0D. Perhaps, the quantum confinement effect
occurs when reducing the size and shape of nanomaterials is less than 100-10nm or even
lesser. These changes due to discrete set of elelctron energy level and that lead to size
confinement [1-3] figure 1&2.
To know more about quantum confinement it is necessary to understand the
phenomenon of quantum dots (QDs). QDs are the new class of materials in which
quantum confinement effects can be evident. QDs are very tiny semiconductor crystals in
the order of nanometer size and also molecules are tightly confined electrons or electron-
hole pairs called “excitons” (explained in the next section) in all three dimensions. QDs
are a subatomic group in the family of nanomaterials, which comprises metals,
insulators, semiconductors, and organic materials. It’s well known, the quantum
confinement occurs only in semiconductors quantum dots and because of their tunable
bandgap nature than zero band gap in metals respectively. As mentioned before the
peculiar tunable band gap properties QD are composed only group such as II-VI, III-V,
and IV-VI based materials. The optical, electrical and bandgap are tunable with respect
to changes in particle size that leads to different multiple application.
The main discussion is that, how bandgap can be tuned with respect to size? For
that we need to understand the formation of discrete energy levels and the formation of
excitons.
2. Formation of discrete energy level
To understand or recall the formation of discrete energy level, when atoms are
brought together in a bulk material the number of energy states increases substantially
to form nearly continuous bands of states. And also decreasing trend was occurred in the
amount of atoms in material and energy states were delocalized with confinement
nature. Furthermore, electron-hole pairs converting spatially confined nature when the
particle towards natural de-Broglie wavelength of electrons in the conduction band. As a
result the energy difference between energy bands is increased with decreasing in
particle size dimension as shown in the figure 3.
Particle behaves like a free particle when the dimensions of the confining
structure are very large in comparison to the de Broglie wavelength. On this stage, the
energy states are continuous and the bandgap is comes to its original position and
another energy spectrum does not remain continuous and becomes discrete in nature
when the dimensions of confining structure are decreased towards nanoscale. Therefore,
the bandgap exhibits size dependence properties, and eventually causes a blue shift in
the emitted light as the particle’s size is decreased. However, this effect demonstrates the
consequences of confining the electrons and electron-hole pair (or the excitons) within a
dimension which approaches the critical quantum limit, often termed as the Bohr
exciton radius.
In this view, a quantum dot confines in all the three dimensions; a quantum wire
(nanowire) confines in two dimensions; and a quantum well confines only in one
dimension. The corresponding structures are also termed as zero dimensional (0D), one
dimensional (1D), and two dimensional (2D) potential wells, respectively, with regard to
the number of dimensions in which the confined particle has freedom of movement. The
below figure 4 shows the overview of quantum confinement in nanostructures.
2
Quantum Confinement
Gopal Ramalingam1, Poopathy Kathirgamanathan 2, Ganesan Ravi3, Thangavel
Elangovan4, Bojarajan Arjun kumar 5, Nadarajah Manivannan6, Kasinathan Kaviyarasu7
1,5
Deapartment of Nanoscience and Technology, Alagappa University, karaikudi- 630003,
Tamil Nadu. email:
2
Department of Chemical and Materials Engineering, Brunel University London, Uxbridge,
UB8PH, UK
3
Deapartment of Physics, Alagappa University, karaikudi-630 003, Tamil Nadu
4
Department of Energy Science, Periyar University, Salem -636 011, Tamil Nadu, India
6
Design, Brunel University London, Uxbridge UB8 3PH, UK.
7
UNESCO-UNISA Africa Chair in Nanoscience's/Nanotechnology Laboratories, College of
Graduate Studies, University of South Africa (UNISA), Muckleneuk Ridge, P O Box 392,
Pretoria, South Africa.
7
Nanosciences African network (NANOAFNET), Materials Research Group (MRG), iThemba
LABS-National Research Foundation (NRF), 1 Old Faure Road, 7129, P O Box722, Somerset
West, Western Cape Province, South Africa
Abstract
Quantum Confinement is the spatial confinement of electron-hole pairs (excitons) in
one or more dimensions within a material and also electronic energy levels are discrete.
It is due to the confinement of the electronic wave function to the physical dimensions of
the particles. Furthermore this can be divided in to three ways: 1D confinement (free
carrier in a plane) -Quantum Wells, 2D confinement (carriers are free to move down) -
Quantum Wire and 3D-confinement (carriers are confined in all directions) are
discussed in details. In addition the formation mechanism of exciton, quantum
confinement behaviour of strong, moderate and week confinement have been discussed
below.
Keywords: Quantum dots; Energy level; Exciton; Confinement; Bohr radius;
1. Introduction of Quantum confinement
The term ‘quantum confinement’ is mainly deals with energy of confined
electrons (electrons or electron-hole). The energy levels of electrons will not remain
continuous as in the case of bulk materials compare to the nanocrystal. Moreover,
obtains the confined electron wave functions, they become a discrete set of energy levels
as shown in the figure 1. Such kinds of effects appear when the dimensions of the
potential approach nearly to de Broglie wavelength of electrons and resulting in the
changes or discreteing levels of energy. The effects are defined as quantum confinement
and consequently, for nano-crystals are often called quantum dots (QDs). Furthermore,
this quantum dot effect influence into the nanomaterial properties such as electrical,
optical as well as mechanical behavior of material . It is due to the peculiar nature in
nano material possess higher energy electrons than the bulk material’s. Depending on
the QDs size, confined electrons have higher energy than the electrons in bulk materials.
1
, The semiconductor nanomaterials exhibit fascinating properties when reducing their
dimensionality from 2D to 1D or 1D to 0D. Perhaps, the quantum confinement effect
occurs when reducing the size and shape of nanomaterials is less than 100-10nm or even
lesser. These changes due to discrete set of elelctron energy level and that lead to size
confinement [1-3] figure 1&2.
To know more about quantum confinement it is necessary to understand the
phenomenon of quantum dots (QDs). QDs are the new class of materials in which
quantum confinement effects can be evident. QDs are very tiny semiconductor crystals in
the order of nanometer size and also molecules are tightly confined electrons or electron-
hole pairs called “excitons” (explained in the next section) in all three dimensions. QDs
are a subatomic group in the family of nanomaterials, which comprises metals,
insulators, semiconductors, and organic materials. It’s well known, the quantum
confinement occurs only in semiconductors quantum dots and because of their tunable
bandgap nature than zero band gap in metals respectively. As mentioned before the
peculiar tunable band gap properties QD are composed only group such as II-VI, III-V,
and IV-VI based materials. The optical, electrical and bandgap are tunable with respect
to changes in particle size that leads to different multiple application.
The main discussion is that, how bandgap can be tuned with respect to size? For
that we need to understand the formation of discrete energy levels and the formation of
excitons.
2. Formation of discrete energy level
To understand or recall the formation of discrete energy level, when atoms are
brought together in a bulk material the number of energy states increases substantially
to form nearly continuous bands of states. And also decreasing trend was occurred in the
amount of atoms in material and energy states were delocalized with confinement
nature. Furthermore, electron-hole pairs converting spatially confined nature when the
particle towards natural de-Broglie wavelength of electrons in the conduction band. As a
result the energy difference between energy bands is increased with decreasing in
particle size dimension as shown in the figure 3.
Particle behaves like a free particle when the dimensions of the confining
structure are very large in comparison to the de Broglie wavelength. On this stage, the
energy states are continuous and the bandgap is comes to its original position and
another energy spectrum does not remain continuous and becomes discrete in nature
when the dimensions of confining structure are decreased towards nanoscale. Therefore,
the bandgap exhibits size dependence properties, and eventually causes a blue shift in
the emitted light as the particle’s size is decreased. However, this effect demonstrates the
consequences of confining the electrons and electron-hole pair (or the excitons) within a
dimension which approaches the critical quantum limit, often termed as the Bohr
exciton radius.
In this view, a quantum dot confines in all the three dimensions; a quantum wire
(nanowire) confines in two dimensions; and a quantum well confines only in one
dimension. The corresponding structures are also termed as zero dimensional (0D), one
dimensional (1D), and two dimensional (2D) potential wells, respectively, with regard to
the number of dimensions in which the confined particle has freedom of movement. The
below figure 4 shows the overview of quantum confinement in nanostructures.
2
