Quantum dot

A quantum dot ( engl. quantum dot, QD ) is a nanoscopic material structure, usually made of semiconductor material (eg, InGaAs, CdSe or GaInP / InP). Charge carriers (electrons, holes) in a quantum dot are so far limited in their mobility in all three spatial directions, that their energy is no longer continuous, but only discrete values ​​can assume (see scale / spectrum). Quantum dots thus behave similarly to atoms, but can their shape, size or the number of electrons are affected in them. This electronic and optical properties of quantum dots to tailor. Typically their own atomic scale is about 104 atoms. If it is possible to arrange another several individual quantum dots in close proximity, so that charge carriers (mainly electrons) via tunneling processes can hop from one to the next quantum dot, one speaks of quantum dot molecules.

Methods for the preparation of

• Wet chemical methods ( eg cadmium selenide, zinc oxide ): The so-called nanoparticles are present in a solvent as colloidal particles. The actual quantum dot is surrounded by further layers to improve the optical properties, water solubility, or biocompatibility.
• Molecular self-assembled quantum dots are formed from thin layers ( a few nanometers or less than 5 atomic layers ) at the interface between different semiconductor layers, for example by the Volmer -Weber or Stranski - Krastanov method. The reason for the self-organization is the damage caused by the different lattice constants of substrate and quantum dot material stresses the quantum dot layer. ECS theory ( equilibrium crystal shape - equilibrium crystal form ) of Thermodynamics makes the prediction that a fixed volume of macroscopic inclusion in thermodynamic equilibrium takes the form that minimizes the surface free energy ( Ostwald ripening ). This leads to the fact that from a certain layer thickness of the quantum dot layer small elevations, so-called islands that form. The tension within the islands is reduced by this operation. This represents a further driver of agglomeration

• Lithography: the quantum dot is ' written ' using the electron beam, scanning force microscope or the like to a substrate, followed by a suitable etching method ( Nass-/Trockenätzen ) ' exposed .' The resulting mesas can now left free -standing or to improve the electronic or optical properties are again of a suitable semiconductor material, by growing a further layer enclosed. During the patterning process, the quantum dot can also be provided with electrical leads. The disadvantage of this method is that the etching caused by accumulation of lattice defects, leading to deterioration in the electronic and hence optical properties of the quantum dot.
• In electro- statically defined quantum dots of the three-dimensional confinement of the charge carriers is achieved by a combination of epitaxial and lithographic methods: at the interface between two layers of epitaxially grown semiconductor material ( for example, GaAs on AlGaAs ) formed due to the different band structure, a quantum well, the movement of the electron limited to the interface. In order to ( for example lithographically ) applied microscopic electrodes on the system now limit in the remaining two dimensions. By applying suitable voltage to the electrodes, a potential well is generated in the quantum well, in which individual electron at low temperatures ( 25 mK) can be captured. Electrostatically defined quantum dots differ in several respects from colloidal or epitaxially grown quantum dots: they are larger (about 105 to 106 atoms; diameter of 100 to 1000 nm in the quantum well plane), they can only either positive or negative capture charged carriers the inclusion is weaker, so they can be studied only at very low temperatures. Single or multiple coupled quantum dots can be made ​​deterministic, the material used may be made without tension and with a very low defect density and the electrodes allow the direct electronic manipulation of trapped charge carriers.

Magnitude

The size of the quantum dot is in the range of the de Broglie wavelength of the electron, because here come the quantum properties of a-days. The de Broglie wavelength of an electron, is:

With E at room temperature:

This results in:

This value is an approximation because it is in the formula is the substance-specific electron effective mass, and thus the wavelength is dependent on the material.

For holes is due to the higher mass of these quantum dot sizes a weaker confinement. That is, the line-like energy structure ( density of states 0D) is not as pronounced.

The quantum dot forming a potential well, which is a quantum-mechanical confinement, i.e., causes a greater localization of the wave function.

Spectrum

Due to the previously determined size of the quantum dot is atom -like states form. The transition from classical band model of semiconductor physics to the quantized energy levels of low-dimensional solids is continuous and ( confinement English) on the strength of the inclusion or limitation of the wave function of the in- quantum-dot charge carrier, or more precisely, its wave function dependent.

The spectrum of a quantum dot is now defined in terms of the energy emitted upon recombination of the charge carriers. As expected, this should be a line spectrum with a similar atomic quantized states. Now the Dipolschwingung, which leads to a spectral line, but be understood as a damped harmonic oscillator with finite attenuation needs. Of the Fourier transform of the envelope of the spatial domain to the frequency domain to obtain a Lorentz curve, the width of which depends on the attenuation constant. We say that the spectral lines are ' lorentzverbreitert ', which corresponds to a homogeneous line broadening.

A quantum dot ensemble, ie multiple quantum dots, has as a common spectrum, a Gaussian curve. This reflects the Gaussian size distribution of the quantum dots to a statistically frequently occurring value, which was favored by the growth process. The Gaussian emission spectrum is the mark of an inhomogeneous line broadening: quantum dots with identical size of an ensemble each emitting homogeneously broadened spectra of the same wavelength. However, the different size classes of the quantum dots emit light at different wavelengths. The superposition of these spectral Lorentz curves of different wavelengths leads to the Gaussian distribution.

Line broadening mechanisms

A distinction into homogeneous

• Lorentz broadening
• Energy - time uncertainty
• Carrier - exciton interaction (especially with type II quantum dots )
• Charged quantum dots

And inhomogeneous broadening mechanisms, with the latter than expected comes about mainly by the presence of multiple quantum dots in the sample (see spectrum of a quantum dot ensembles).

Use

Quantum dots are interesting because of their optical and electronic properties can be influenced.

• Markers in biology
• Use in LEDs, displays
• Quantum dot laser
• A photon source
• Quantum computing
• Photonic crystal
• Quantum-dot spin valve
• Image sensors for digital cameras, see Rolling shutter effect
• Single -electron transistor