Quantum Dot


In this region, electron energy levels cannot exist in any form. The bandgap is a quantum mechanical phenomenon, and is the energy difference that is usually on the order of about one electron volt for most semiconductors. The bandgap separates the valence band from the more energetic conduction band, making it difficult for electrons to jump to the conduction band. In a regular semiconductor crystal, the bandgap is fixed owing to continuous energy states. In a quantum dot crystal, the bandgap is size dependent and can be altered to produce a range of energies between the valence and conduction band. Quantum mechanics dictates that the bandgap of a quantum dot will always be larger in magnitude.


For our purposes, this band contains the energy levels that are above the bandgap and higher. Because the bandgap is always much larger than the distance between energy levels, not many electrons can jump the bandgap and cross into the conduction band from the valence band. The very small number of electrons naturally occupying the conduction band is due primarily to thermal collisions.

Electrons can also be stimulated to cross the bandgap if they absorb radiation with energy greater than or equal to the bandgap energy. This fact, and their subsequent emission of radiation as the electrons fall back down to the valence band, is the basis for the utility of quantum dots.


The set of physical conditions where energy levels are separated by such a small amount of energy that for some processes, they may be treated as if they were not separated by any energy amount at all. This type of model works well for semiconductor crystals with large numbers of atoms and physical dimensions much great than 10 nanometers. The most important repercussion of approximating energy levels as continuous is that under those conditions, the bandgap of a material may be treated as fixed and unchangeable.


The set of physical conditions where energy levels are separated by enough energy that the addition or subtraction of one atom or electron to the crystal will measurably change the energy of the bandgap. This type of model works well for semiconductor crystals with a small number of atoms and physical dimensions on the order of 10 nanometers.

It is when a semiconductor crystal has discrete states that it can be defined as a quantum dot, and this is when it takes on useful and interesting properties. This is because adding or subtracting an atom is a process that is relatively easy to engineer, and with far reaching consequences- the crystal emits at a different (and specifiable, to within limits) wavelength. This specification and tunability would be impossible with a traditional semiconductor with continuous energy levels, because one atom is insignificant given the size of such a bulk semiconductor, which is many orders of magnitude larger in number of atoms than a quantum dot. This largeness of traditional semiconductors makes the change in bandgap so small, upon changing one atom, that it is impossible to measure or use gainfully- resulting in a fixed bandgap.


The electrons of all materials may only have certain allowable energies as shown by quantum mechanics. It is customary to describe each of these allowed energies as occurring at 'energy levels,'with the understanding that electrons can only exist at an energy level and not in between them. For example, a hypothetical electron may exist with 2 units of energy, or 3 units of energy, but not with 2.730459 units of energy.

Quantum mechanics additionally dictates that only 2 electrons can exist at any one energy level (Pauli Exclusion Principle). The result is that in any crystal, electrons will start filling the lowest energy levels first, and continue to fill levels with higher energies until no more electrons remain without energy levels.

The more atoms that are in a crystal, the smaller the distance between energy levels. The distance between levels never becomes zero- there is always some finite distance between energy levels, no matter how small. However, if the dimensions of a semiconductor crystal become much larger than the Exciton Bohr Radius of the material, then the distance between energy levels in the crystal becomes very small, and it is then convenient for our purposes to describe the energy levels as continuous, i.e. treating them as if they had no difference between them.


An exciton is the term used to describe the electron-hole pair created when an electron leaves the valence band and enters the conduction band. Excitons have a natural physical separation between the electron and the hole that varies from substance to substance; this average distance is called the Exciton Bohr Radius. In a large semiconductor crystal, the Exciton Bohr Radius is small compared to the crystal, and the exciton is free to wander throughout the crystal. In a quantum dot, the Exciton Bohr Radius is on the order of the physical dimension of the dot or smaller, and the exciton is confined. This second set of conditions is called quantum confinement, which is synonymous with having discrete, rather than continuous energy levels.


This is the natural physical separation in a crystal between an electron in the conduction band and the hole it leaves behind in the valence band. The size of this radius controls how large a crystal must be before its energy bands can be treated as continuous. Therefore, the Exciton Bohr Radius can rightly be said to define whether a crystal can be called a semiconductor quantum dot, or simply a bulk semiconductor.


It is convenient to describe the absence of an electron in a valence band energy state as a 'hole.' Holes can be treated as positively charged, and arise when a negatively charged electron jumps to the conduction band. The combination of the electron and the hole together is called an exciton.


The set of conditions under which a crystal is on the order of or smaller than the Exciton Bohr Radius of its constituent compound. Under quantum confinement, energy levels may be treated as discrete. By definition, quantum dots are in a state of quantum confinement.


There are many acceptable definitions. For our purposes, a quantum dot is defined as:

1. A crystal of semiconductor compound (eg. CdSe, PbS) with a diameter on the order of the compound's Exciton Bohr Radius. Quantum dots have a range of useful electrical and optical properties that diverge in character from those of bulk material. Quantum dots are between 2 and 10 nanometers wide (10 and 50 atoms).
2. A novel kind of semiconductor that can be molded into a variety of new and useful forms and made into many devices that surpass the operating capacities of traditional semiconductors.
3. An electromagnetic radiation emitter with an easily tunable bandgap.


A material with electrical properties resembling those partially of insulators and partially of conductors. The application of external stimuli such as heat or voltage can radically alter the conductivity of a semiconductor. Semiconductors, especially Silicon and Germanium, are the cornerstone of the modern electronics industry.


The dimensions of a quantum dot are measured in nanometers (typically between 2 and 10). For reference, 1 million quantum dots lined up end to end is about one fifth of an inch long.


This band contains all the electrons from the one with the lowest energy, to the one with energy just on the lower edge of the bandgap. Since electrons tend to occupy energy states with the lowest energy possible, the valence band's energy levels are usually almost completely full.