Quantum dot

A quantum dot (engl. Dot quantum , QD) is a nanoscopic structure of the material, usually made of semiconductor material (eg. B. InGaAs , CdSe or Ga In P / InP ). Charge carriers ( electrons , holes ) in a quantum dot are so limited in their mobility in all three spatial directions that their energy can no longer assume continuous , but only discrete values (see order of magnitude / spectrum). Quantum dots behave similarly to atoms , but their shape, size or the number of electrons in them can be influenced. This allows the electronic and optical properties of quantum dots to be tailored. Typically, their own atomic order of magnitude is about 10 ⁴ atoms. If it is possible to arrange several individual quantum dots in close proximity to each other so that charge carriers (especially electrons) can “jump” from one to the next quantum dot via tunneling processes, one speaks of quantum dot molecules .

Commercially available, wet-chemically produced quantum dots in solution

Methods of manufacture

Quantum dot (idealized) with wetting layer ( InAs / GaAs )

• Wet chemical methods (e.g. cadmium selenide , zinc oxide ): The so-called nanoparticles are present as colloidal particles in a solvent. The actual quantum dot is surrounded by further layers to improve the optical properties, water solubility or biocompatibility .
• Molecular beam epitaxy : self-organized quantum dots are formed from thin layers (a few nanometers or less than 5 atomic layers) at interfaces between different semiconductor layers, for example by the Volmer-Weber or the Stranski-Krastanov method. The cause of the self-organization lies in the tension in the quantum dot layer caused by the different lattice constants of the substrate and quantum dot material. The ECS theory ( equilibrium crystal shape ) of thermodynamics makes the prediction that a macroscopic inclusion with a fixed volume 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, small elevations, so-called islands, form from the quantum dot layer. This process also reduces the tension within the islands. This is another driving force behind the agglomeration .
• Lithography : the quantum dot is 'written' on a substrate by means of electron beams , atomic force microscope or the like and then 'exposed' by a suitable etching process ( wet / dry etching ). The resulting mesas can now be left free-standing or, in order to improve the electronic or optical properties, be enclosed again by a suitable semiconductor material by growing a further layer. During the structuring process, the quantum dot can also be provided with electrical leads. The disadvantage of this method is the accumulation of lattice defects caused by the etching , which leads to deteriorated electronic and thus also optical properties of the quantum dot.
• In electrostatically defined quantum dots , the three-dimensional confinement of the charge carriers is achieved through a combination of epitaxial and lithographic methods: at the interface between two layers of epitaxially grown semiconductor material (e.g. GaAs on AlGaAs), a quantum well , the movement, forms due to the different band structure of electrons is confined to the interface. In order to restrict them in the remaining two dimensions, microscopic electrodes are applied to the system (e.g. lithographically). By applying a suitable voltage to the electrodes, a potential minimum is generated in the quantum well, in which individual electrons can be captured at low temperatures (25 mK). Electrostatically defined quantum dots differ in several ways from colloidal or epitaxially grown quantum dots: they are larger (approx. 10 ⁵ to 10 ⁶ atoms; diameter of 100 to 1000 nm in the quantum well level), they can only have either positively or negatively charged charge carriers capture, the inclusion is weaker, which is why they can only be examined at very low temperatures. Single or multiple coupled quantum dots can be produced deterministically, the material used can be produced stress-free and with a very low defect density and the electrodes allow direct electronic manipulation of the trapped charge carriers.

Magnitude

The size of the quantum dot is in the range of the De Broglie wavelength of the electron , because this is where the quantum properties come to light . The de Broglie wavelength of an electron is:

${\displaystyle \lambda ={\frac {h}{\sqrt {2\,m_{e}^{*}\,E}}}}$

with E at room temperature:

${\displaystyle E=k_{\mathrm {B} }\cdot T=1{,}38\cdot 10^{-23}{\frac {\mathrm {J} }{\mathrm {K} }}\cdot 300\,\mathrm {K} =4{,}14\cdot 10^{-21}\mathrm {J} }$

This results in:

${\displaystyle \lambda ={\frac {6{,}626\cdot 10^{-34}\,\mathrm {Js} }{\sqrt {2\cdot 9{,}109\cdot 10^{-31}\,\mathrm {kg} \cdot 4{,}14\cdot 10^{-21}\,\mathrm {J} }}}\approx 7{,}6\,\mathrm {nm} }$

This value is an approximation, since the formula concerns the substance-specific effective electron mass and thus the wavelength is also material-dependent.

For holes , the greater mass with these quantum dot sizes results in a weaker confinement. This means that the line-like energy structure ( density of states 0D) is not as pronounced.

The quantum dot forms a potential well that represents a quantum mechanical confinement, i.e. H. causes a stronger localization of the wave function .

spectrum

Due to the previously determined size of the quantum dot, atom-like states are formed. The transition from the classic band model of semiconductor physics to the quantized energy levels of low-dimensional solids is continuous and depends on the strength of the confinement or confinement of the wave function of the charge carrier in the quantum dot or, more precisely, its wave function.

The spectrum of a quantum dot is now defined by the energy emitted when the charge carriers recombine . As expected, this should be a line spectrum for atom-like quantized states . Now the dipole oscillation , which leads to a spectral line, has to be understood as a damped harmonic oscillator with finite damping. With the Fourier transformation of the envelope from the spatial space into the frequency space , a Lorentz curve is obtained , the width of which depends on the damping constant. It is said that the spectral lines are 'Lorentz broadened', which corresponds to a homogeneous line broadening .

According to the Fourier analysis (F), the damped harmonic oscillation process leads to a Lorentz broadened line in the frequency space

A quantum dot ensemble, i.e. several quantum dots, has a Gaussian curve as a common spectrum . This reflects the Gaussian size distribution of the quantum dots around a statistically frequent value that was favored by the growth process. The Gaussian emission spectrum is the hallmark of inhomogeneous line broadening : Quantum dots of identical size from an ensemble each emit homogeneously broadened spectra of the same wavelength. However, the different size classes of the quantum dots emit at slightly different wavelengths. The superposition of these spectral Lorentz curves of different wavelengths leads to the Gaussian distribution.

Line broadening mechanisms

One differentiates between homogeneous

• Lorentz broadening
• Energy time blur
• Charge carrier - exciton interaction (especially with type II quantum dots)
• Charged quantum dots

and inhomogeneous broadening mechanisms , the latter mainly due to the presence of several quantum dots in the sample as expected (see: spectrum of a quantum dot ensemble ).

use

Due to their controllable optical and electronic properties, quantum dots are of interest for many applications

• Dye for markers in fluorescence microscopy and flow cytometry
• LEDs , displays , in particular for optimizing the background lighting of liquid crystal displays
• Quantum dot laser
• Single photon source
• Quantum computing
• Quantum dot spin valve
• Image sensors for digital cameras
• One-electron transistor
• Quantum dot solar cell

literature

• Dieter Bimberg : The Zoo of Quantum Dots Physics Journal , August / September 2006, p. 43ff.
• Peter Michler (Ed.): Single Semiconductor Quantum Dots. Springer 2009, ISBN 978-3540874454
• Peter Michler (Ed.): Quantum Dots for Quantum Information Technologies. Springer 2017, ISBN 978-3-319-56378-7

Web links

Commons : quantum dots  - collection of images, videos and audio files

Wiktionary: quantum dot  - explanations of meanings, word origins, synonyms, translations

• Mark Rossi: Charge carrier relaxation and recombination mechanisms in semiconductor quantum dots. Diploma thesis, University of Stuttgart, December 2002. - The second chapter is interesting here. (PDF file; 3.02 MB)
• heise.de - Kevin Bullis: Fantastic color games ; TechnologyReview article dated June 29, 2006 on quantum dot LEDs
• heise.de - Prachi Patel-Predd: Screens made of colored quantum dots ; TechnologyReview article from December 17, 2008 on colored quantum dots screens

Individual evidence

1. ↑ R. Hanson et al. : Spins in few-electron quantum dots . In: Reviews of Modern Physics . 79, 2007, p. 1217. arxiv : cond-mat / 0610433 . doi : 10.1103 / RevModPhys.79.1217 .
2. ↑ D. Loss and DP DiVincenzo, "Quantum computation with quantum dots", Phys. Rev. A 57 , p120 (1998) ; on arXiv.org in Jan. 1997
3. ↑ Quantum dots: Technical applications of the "artificial atoms". In: World of Physics. Retrieved January 13, 2017 . 
4. ↑ DaNa2.0 - data and knowledge on nanomaterials: Quantum dots material info . Retrieved January 13, 2017 . 
5. ↑ Quantum Dot Displays. In: Compendium of Infotip Service GmbH. Retrieved January 13, 2017 . 
6. ↑ Sascha Steinhoff: InVisage Quantum: Revolutionary image sensor to replace CMOS and CCD . In: c't digital photography . November 23, 2015 ( heise.de [accessed January 13, 2017]).