Quantum Dots of All Hues : A Modern Marvel

Quantum Dots of All Hues : A Modern Marvel

Reading Time: 8 minutes

Quantum dots are fluorescent nanocrystalline semiconductors that seem to magically change colour with size. The Nerd Druid investigates this 21st century marvel.


Alexei Ekimov discovered quantum dots in a glass matrix in 1981. Four years later, in 1985, Louis Brus discovered quantum dots in colloidal solutions. Their discovery is now at the heart of nanotechnology.

What are quantum dots?

Quantum dots are extremely small semiconducting crystallites. You could fit anywhere between 10-50 atoms along the diameter of a typical quantum dot. The entire structure contains hundred to thousands of atoms.

How big are quantum dots?

Image of size comparison of a standard football, an average human hair, and a typical quantum dot. Lengths are in nanometers. The football is about 20 cm in diameter, the human hair is about 80 μm in diameter, and the two quantum dots (indicated by the yellow circles in the inset of the rightmost image) are approximately 2.5 nm in diameter.
Size comparison of a standard football, an average human hair, and a typical quantum dot. Lengths are in nanometers. The football is about 20 cm in diameter, the human hair is about 80 μm in diameter, and the two quantum dots (indicated by the yellow circles in the inset of the rightmost image) are approximately 2.5 nm in diameter. Image credit : S Pitchaimuthu, Swansea University.

The image above is another excellent way of comparing the size of quantum dots with everyday objects. The one on the very left is a standard football, while the image at the center is that of a human hair. The football is about 20 cm in diameter; the hair is about 80 μm (= 0.08 mm) in diameter. The inset of the rightmost image shows two quantum dots cirlced in yellow; each of them is about 2.5 nm in diameter1. That is about the width of DNA. You could fit about 30000 quantum dots side by side along the width of a human hair, and 80 million quantum dots side by side along the diameter of a football.

What do quantum dots do?

Quantum dots fluoresce; shine light on them and they will glow. In addition to being photoluminescent, quantum dots are also electroluminescent. Pass electric current through them and they glow; put them in a high electric field and they glow.

Image of quantum dots with vivid colours with gradually stepping emission from violet to deep red. These have been manufactured on a large scale at PlasmaChem GmbH.
Quantum dots with vivid colours with gradually stepping emission from violet to deep red. These have been manufactured on a large scale at PlasmaChem GmbH. Image credit : Antipoff/PlasmaChem

Photoluminescence & electroluminescence in everyday life

Why, though, is that so awesome? Plenty of everyday items are photoluminescent and electroluminescent. For instance, your home fluorescent lamp is photoluminescent; electricity passing through the mercury vapour inside the tube causes it to fluoresce and emit ultraviolet radiation. Thankfully, the white layer of phosphor material coating the inner surface of the tube absorbs this UV light and fluoresces, emitting visible light2. Similarly, your car dashboard dials and your calculator backlight are electroluminescent.

Photograph of thirty Fluorescent lamps with reflections giving the impression of many more lamps, in Shinbashi, Tokyo, Japan.
Thirty Fluorescent lamps with reflections giving the impression of many more lamps, in Shinbashi, Tokyo, Japan. Image credit : Oimax (Flickr)
Photograph of 1966 Dodge Charger dashboard, showing electroluminescent dials.
1966 Dodge Charger dashboard, showing electroluminescent dials. Image credit : Jonathan Gibbs (FastbackJon)
Animation of LCD, both unlit and with electroluminescent backlight switched on.
Animation of LCD, both unlit and with electroluminescent backlight switched on. Image credit : Grimlock

Quantum dots produce colour

No, the reason why quantum dots are awesome is their colour-producing capability. Take a look at the image of those coloured bottles above; each contains colloidal quantum dots and have been irradiated with UV light. You can see the entire VIBGYOR there; from left, Violet, Indigo/Blue, Blue/Cyan, Green, Yellow, Orange, Red, and, er, Red again! VIBGYORR, very pirate-y, savvy3?

But LCDs and LEDs also produce colour

It is not impossible to have coloured fluorescent lamps. With the invention of the blue LED (light-emitting diode) in the 1990s, we now have LED lamps of all colours. LCD (liquid crystal display) screens on televisions, computers, and mobile phones are nowadays capable of creating millions of colours. Organic LED screens and their evolved cousins, the AMOLED screens, have made it possible to have ultraHD TV, computer and mobiles.

Why quantum dots, then?

Quantum dots can produce any colour

Take a magnifying glass and peer into the screen you are reading this on. If you don’t have one, use a drop of water. You’ll see that the pixels on the screens have three colours : red, blue, and green. Combinations of this RGB trio make up most of the colours we perceive. This is because our eyes also only have three types of colour-detecting cone cells, and these are sensitive in the red, green, and blue channels.

Red, Green, and Blue LEDs

LEDs are bulk semiconductors. The problem with them is that you can’t quite use the same material to make different colours. For instance, you can use AlGaAs (aluminium gallium arsenide) or GaAsP (gallium arsenide phosphide)4 to fabricate red LEDs. However, if you want a blue LED, you’d need to use InGaN (indium gallium nitride). You’ll not be able to make red LEDs out of InGaN, or green ones out of AlGaAs. That is how light-emitting semiconductors work.

Quantum dot colour depends on their size

Quantum dots are very different in that respect. You can tune their colour at will by simply changing their sizes! Larger quantum dots (5-6 nm) emit orange and red light. Medium sized ones (3 nm) emit green light, while smaller ones (2 nm) emit blue light. The ones in Swansea experiment, those circled in yellow in the earlier image, are about 2.5 nm in diameter and emit blue-green light. These technicolour quantum dots can all be fabricated from the same material.

Graph of quantum dots : size and colour. Different sized quantum dots made of the same material are being irradiated by blue light. As you increase their sizes, the quantum dots fluoresce with colours of longer wavelengths. The smaller ones emit The smaller ones emit blue, blue-green, and green light, while the larger ones emit orange and red light.
Quantum dots : size and colour. Different sized quantum dots made of the same material are being irradiated by blue light. As you increase their sizes, the quantum dots fluoresce with colours of longer wavelengths. The smaller ones emit The smaller ones emit blue, blue-green, and green light, while the larger ones emit orange and red light. Image credit : Nanosys Inc.

An Amazing Technicolour Dreamcoat

If you think about it, this is quite remarkable. For LEDs, the only true colours you get are red, green, and blue5; the colour step-size for them are the differences in frequency between red and green, and that between green and blue. With quantum dots, however, the colours they emit is dependent on their sizes, which in turn is dependent on how many atoms they have. Thus, the colour step size here is devastatingly smaller than LEDs–take out one atom, or put one in, and you get a different frequency. Thus, a different colour. Voila! Human eyes are quite incapable of distinguishing that fine a colour step-size. To us, then, quantum dots can indeed produce any colour.

How do quantum dots produce so many colours?

Why is that? Aren’t quantum dots semiconductors too?

Yes, they are. However, unlike bulk semiconductor diodes, quantum dots do not have Avogadro’s number level of atoms6. In fact, the smallness of quantum dots means that quantum effects begin to make their presence felt.

Atoms & semiconductors

Atomic energy levels

Electrons is an atom are arranged according to their energies. Those with lower energies inhabit lower energy levels–or shells–and stay closer to the central nucleus, while those with higher energies live in higher shells. Now, shine light on a group of atoms. Some of the photons you fire will interact with the atoms. If the energy is correct, electrons might absorb the photon, gain energy, and jump to a higher shell. Pretty soon, however, that energised electron will want to fall back to the energy level it came from. It will do so by emitting a photon of its own. The energy of the photon emitted will be exactly equal to the energy difference between the two energy levels. If this happens fast, within nanoseconds, then this is fluorescence.

Schematic of fluorescence. An electron absorbs a high-energy photon and jumps to an excited state. After a series of vibrational transitions where no photon is emitted, the electron fluoresces back down to its ground state, emitting a photon. The emitted photon has a lower energy and longer wavelength (green) than the incident photon (blue).
An electron absorbs a high-energy photon and jumps to an excited state. After a series of vibrational transitions where no photon is emitted, the electron fluoresces back down to its ground state, emitting a photon. The emitted photon has a lower energy and longer wavelength (green) than the incident photon (blue). Image credit : Jacobkhed.

Semiconductor energy bands

A similar thing happens with light emitting diodes. However, since LEDs are semiconductors, they don’t have the discrete energy levels that atoms have. Instead, their energy levels form two separate continuum bands. An electron from the lower valence band absorbs energy and jumps up to the higher conduction band. In LEDs, it soon jumps back down, emitting a photon. The energy of the photon emitted is the sum of the energy of the band gap and the excitation energy of the electron :

E = Eband-gap + Eexcitation

In the image below, the brown double arrow shows the band gap. LEDs made of a particular material have a fixed band gap value, and thus can only emit light of a certain colour.

Schematic of the splitting of energy levels in quantum dots due to the quantum confinement effect, semiconductor band gap increases with decrease in size of the nanocrystal.
Splitting of energy levels in quantum dots due to the quantum confinement effect, semiconductor band gap increases with decrease in size of the nanocrystal. Image credit : Sigma-Aldrich / Merck.

Quantum dot confinement energy

Particle in a box

Contrast this with quantum dots. Since they are so small, electrons are trapped within them. Quantum mechanical effects kick in, and the energy levels of the electron are like that a particle trapped in a box7. This confinement has its own energy, and adds to the total energy of the fluorescent photon.

Efluorescence = Eband-gap + Econfinement + Eexcitation

It is this Econfinement that makes the quantum dot into a technicolour marvel. You see, according to quantum mechanics, the energy of a particle in a box depends on how large the box is. More particularly, the energy goes as the inverse square of the dimension of the box; decrease the box size by 2, and your energy will multiply by 4.

Electron in a quantum dot box

For an electron in a quantum dot, the quantum dot itself is its box. The inverse square law implies that smaller dots have higher Econfinement, and vice verse. You can see that in the energy level schematic above. As the size of the quantum dot decreases (red > green > blue), the energy gap increases (blue double arrow > green double arrow > red double arrow).

You can increase or decrease this gap by changing the size of the box, that is, the quantum dot. Theoretically, you can change it in steps of a single atom, that is, by a few tenths of a nanometers. The corresponding change in Efluorescence will be extremely fine, and virtually undetectable by human eyes.

Practicality

Of course, technology limits the amount of fine-tuning you can do. For instance, you can’t manually pick up an atom and deposit it within a quantum dot crystal, or pick one out of it. Yet. Everything depends on your crystal deposition process, what materials you use, what conditions you are working in, and how good you are. Still, modern quantum dots are good enough to have the highest true colour resolution among all others.

That is the magic of a quantum dot.

Is that all?

Er, no. That is just the tip of the iceberg as far as quantum dots are concerned. They have tons of other uses other than being fancy screens. Solar panels made out of quantum dots are more efficient than their non-QD counterparts. Also, biomedical applications of quantum dots have picked up steam recently. Turns out quantum dots are brilliant at imaging inside the body, and are being used as such. Also, they make superb organic dyes, and are a 21st century extension of William Perkin’s dream.

Quantum dots aren’t universally fantastic, though. To manufacture them, you need to use compounds of heavy metals that are incredibly toxic to humans, other animals, and the environment. This severely limits their in vivo use. To counter that, a group of Indian-Welsh scientists have very recently teamed up to fabricate quantum dots from the extract of tea leaves. Not only does this decrease the overall toxicity, these tea-powered British Popeye quantum dots seem to be devastatingly effective at invading and killing lung cancer cells.

More on this in the next edition of The Nerd Druid Investigates!, Quantum Dots from Tea Leaves Kill Lung Cancer Cells! In the meantime, here’s a picture of Tintin and Snowy drinking tea.

Tintin and Snowy drinking tea in The Blue Lotus, while a shadowy figure looms outside the window.
Tintin and Snowy drinking tea in The Blue Lotus, while a shadowy figure looms outside the window. Image credit : Hergé.

 

References

Papers

  1. Bawendi, Moungi G. & Steigerwald, Michael L. & Brus, Louis E. : The Quantum Mechanics of Larger Semiconductor Clusters (“Quantum Dots”), Annual Reviews of Physical Chemistry (1990)
  2. Reimann, Stephanie M. & Manninen, Matti : Electronic structure of quantum dots, Reviews of Modern Physics (2002)
  3. Yoffe, A.D. : Semiconductor quantum dots and related systems: Electronic, optical, luminescence and related properties of low dimensional systems, Advances in Physics (2010)
  4. Dey, Samrat et al. : The confinement energy of quantum dots, arXiv (2012)

Other resources

  1. Quantum Dots | Sigma-Aldrich
  2. Quantum Dots | Brus group, Columbia University
  3. Nanotechnology Timeline, National Nanotechnology Initiative
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Footnotes

  1. It is easy to see how. Use the black bars at the bottom as scale. The football scale is 4 cm, the football is five times that. The hair scale is 4 μm, the hair is twice as wide. The quantum dots are half their scale size.
  2. If you are confused as to why a phosphor material is fluorescing, you are not alone. Phosphorescence and fluorescence are both photoluminescent phenomena; the difference lies in their comparative timescales of operation. A fluorescent material will immediately re-emit any absorbed radiation, while a phosphorescent material will do so slowly. Unfortunately, phosphors can both fluoresce and phosphoresce, though I’m not sure if that is a word.
  3. When Isaac Newton demonstrated and classified the visible spectrum, he named the colours violet, indigo, blue, green and the rest. The colour he called blue is basically what we call cyan nowadays, while his indigo is today’s blue; the naming possibly motivated by the novel burgeoning indigo trade in Europe in the seventeenth century.
  4. If those sound like Al Gas and Gasp, you are not alone.
  5. Though there are LEDs nowadays that produce some intermediates too.
  6. 1023. Microelectronics is fabricated out of extremely small diodes which may contain millimoles or micromoles of material. That comes to 1020 or 1017, still astronomically large compared to quantum dots, which have a mere 105.
  7. A very small particle, trapped within a very small box. Not an actual box, but rather walls due to electromagnetic potentials.

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