Category: Electronics

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
Semiconductors : Junction Diodes and Transistors

Semiconductors : Junction Diodes and Transistors

Reading Time: 8 minutes

Semiconductors are at the heart of modern human civilization. Every word I type using this laptop is an implicit thank you to the incredible versatility and utility of semiconductors, as well as to the wonderful ingenuity of the scientists and engineers who have harnessed the potential of these magical materials to their fullest.

The following is part I of a brief overview of the physics of semiconductors. This is meant to be a starter pack, so to say. For deeper understanding, I suggest that you read a good textbook.

In this article, The Nerd Druid will talk about intrinsic and extrinsic semiconductors, p-n junctions, p-n junction diodes, and bipolar junction transistors and their applications.

Insulators and conductors

Let’s begin with sodium. Sodium is a metal. This means that it is a good conductor of heat and electricity. However, since sodium is very reactive, it isn’t very smart to use it to conduct electricity. Household wires are usually made of copper, which does a fine job of conducting current.

Image of sodium metal
Sodium metal

In comparison, nonmetallic elements and most compounds are poor conductors. Diamond, an allotrope of the nonmetal carbon, is a very good insulator. Ironically, graphite, another carbon allotrope, is a very good conductor. Graphene–atomic monolayers of graphite–is even better at this conduction business. 1 Air is good insulator, and it takes a huge voltage to pass electrons through air. Happens regularly around thunderstorms. Water is a decent conductor, since it has a lot of free protons (H+ cations) that carry the current.

Image of forked lightning. Extremely high potential differences between the Earth and thunderstorm clouds breaks down the insulation of air, forming forked lightning.
Forked lightning. Extremely high potential differences between the Earth and thunderstorm clouds breaks down the insulation of air, forming forked lightning.

Most natural materials found on Earth are either insulators or conductors.

Semiconductors

Intrinsic semiconductors

Some elements and compounds, however, do not identify themselves as either. Elements such as silicon and germanium, and binary compounds such as gallium arsenide and silicon carbide are semiconductors. When heated, semiconductors begin to conduct electricity. This behaviour is quite the opposite of conductors, where resistance increases with increasing temperature. These are intrinsic semiconductors.

Atomic orbitals

Before we proceed, a quick review of atomic orbitals might be helpful. A more detailed overview can be found here.

Electrons are arranged within atoms in orbitals. The energy of the electrons residing in them groups orbitals together in shells. Shells further away from the nucleus have higher energy than those closer to the nucleus. The most commonly encountered orbitals are s, p, and d. Each orbital can have at max 2 electrons.

Consider silicon. A neutral silicon atom has 14 electrons. These are arranged thus : 1s22s22p63s23p23d0. The first shell of silicon has 2 electrons (lowest energy) residing in the filled s-type orbital (1s). The second shell has 8 electrons (higher energy), 2 in the 2s and six in the 2p. The third shell has the remaining 4 electrons (highest energy); 2 in 3s and 2 is 3p. The 3d orbitals are completely vacant.

Image of silicon electronic configuration
Silicon electronic configuration

Extrinsic semiconductors

The behaviour of intrinsic semiconductors can be altered by adding small amounts of another element. For instance, silicon semiconductors can be thus doped using boron or phosphorus. Boron is trivalent, meaning it has three electrons in its outer shell (1s22s22p63s23p1); phosphorus is pentavalent, meaning it has five electrons in its outer shell (1s22s22p63s23p3). Since silicon has only four, phosphorus doped silicon has extra electrons which are free to move about. Similarly, boron doped silicon has fewer electrons, the absent electrons leaving behind holes, which are also free to hop about. The former is a n-type semiconductor, where electrons are the charge carriers 2. The latter is a p-type semiconductor, where the holes are the charge carriers 3 These extrinsic semiconductors are far more conductive than their undoped counterparts.

p-n junction

A single wafer of semiconductor can also be doped in two different ways; the boundary between the p-type and n-type regions form a p-n junction. When electrodes are attached to the two sides, this becomes the basic building block of all semiconducting electronic devices.

Depletion region

When a p-n junction is fabricated, there are more holes on the p-side and more electrons on the n-side. Immediately, holes and electrons begin migrating across the junction 4. This sets up a diffusion current pointing from the p-side to the n-side.

As holes diffuse over to the n-side, they leave behind negative bound ions. Similarly, diffusing electrons leave behind positive bound ions. Once on the n-side, the holes recombine with the electrons there and disappear. The electrons emulate this behaviour on the p-side. Soon enough, a region forms around the junction which has very few charge carriers. This is the depletion region.

Image showing formation of the depletion region in a p-n junction semiconductor
Formation of the depletion region in a p-n junction semiconductor

The cations and anions left behind set up an electric field pointing from the n-side to the p-side, thus opposing the diffusion current. Once a sufficient number of electrons and holes have diffused, this opposing field is strong enough to stop the diffusion current altogether, and set up its own drift current pointing from the n-side to the p-side.

p-n junction diode

Connect the p-n semiconductor to electrodes. This makes it a p-n junction diode. There are two ways this can be done.

Forward bias

In the first scenario, connect the anode (+ve electrode) to the p-side, and the cathode (-ve electrode) to the n-side. This is the forward bias condition.

The anode will inject holes into the p-side, while the cathode will inject electrons into the n-side. This will push and squeeze the depletion region so that it is narrow enough for electrons and holes to jump across. Once this happens, a current flows across the p-n semiconductor.

Illustration of forward bias in a diode. As the forward bias voltage increases, the deplection region gets narrower and finally collapses
As the forward bias voltage increases, the depletion region gets narrower and finally collapses. This allows current to flow through the diode.

Energetically speaking, the depletion region creates an energy barrier. In forward bias, if the voltage is not high enough, electrons and holes will not have sufficient energy to surmount the depletion barrier. Which is why the current-voltage graph of a p-n junction diode shows a knee in forward bias. The voltage above which the diode turns on is called the cut-in or the forward voltage (VF).

Reverse bias

In the second scenario, reverse the polarity 5. Connect the anode to the n-side and the cathode to the p-side. They will inject holes and electrons as before, though this time this will lead to greater recombinations and will serve to further widen the depletion region.

Illustration of reverse bias in a diode. Reverse bias widens the depletion region, making it almost impossible for current to flow through the diode.
Reverse bias widens the depletion region, making it almost impossible for current to flow through the diode.

Energetically, the reverse voltage will raise the height of the depletion region potential barrier. In this reverse bias state, the diode does not let current pass. Well, not unless the voltage is high enough so that the current flows in the opposite direction as before. That is breakdown. But we don’t want that to happen.

Transistors

Diodes are electronic valves; they allow current to pass in one direction. As such, they are very useful in circuits. However, they can be made much more useful if two p-n junction semiconductors are attached end-to-end in series, creating three separate zones. Attach electrodes to these three zones and you have a bipolar junction transistor (BJT).

There are two ways to do this; you either get a p-n-p transistor or an n-p-n transistor. The middle zone is called the base, and the ones on the two ends are called the collector and the emitter. Now, connect electrodes to each of these regions and apply potentials.

Image of an n-p-n transistor, with n-type collector and emitter, and p-type base.
An n-p-n transistor, with n-type collector and emitter, and p-type base.

Of course, BJTs are not the only type of transistor around. Field effect transistors work in a slightly different fashion. I’ll not be discussing FETs here.

Modes of operation : Switch and amplifier

The transistor can operate in four modes. One can control this by tuning the base voltage VB, the emitter voltage VE and the collector voltage VC. In what follows, I shall use an n-p-n transistor to illustrate the mechanism. You can convert this into a p-n-p by merely flipping the “>” signs and reversing the current.

Saturation mode : VB > VC , VB > VE

Recall that the transistor is n-p-n, so that the base is p and the emitter and collector are n. Thus, VBE > 0 and VBC > 0 imply that both the base-emitter (BE) and base-collector (BC) junctions are in forward bias mode. This setup behaves like a closed circuit; current flows freely between the collector and the emitter. For n-p-n, the collector current IC points from the collector to the emitter. Electrons, the majority carriers in n-p-n, are emitted by the emitter and collected by the collector 6.

The transistor is now ON.

Cut-off mode : VB < VC , VB < VE

The signs are reversed; VBE < 0 and VBC < 0. Both the BE and BC junctions are reverse biased. No current flows in the transistor, and it behaves like an open circuit.

The transistor is now OFF.

By reversing the voltages, one can thus use the transistor as a switch.

Forward active mode : VC > VB > VE

Here, VBE > 0 but VBC < 0; the BE junction is forward biased, while the BC junction is reverse biased. In this mode, the transistor acts as an amplifier–a small input base current IB gives rise to a very large output collector current IC.

IC = β IE

where β is large, usually 100.

Image of a transistor in forward active mode, acting as an amplifier. The n-type emitter emits electrons, a majority of which reach the collector due to the large potential difference between C and E.
A transistor in forward active mode, acting as an amplifier. The n-type emitter emits electrons, a majority of which reach the collector due to the large potential difference between C and E.
Reverse active mode : VC < VB < VE

This is basically the same as forward active, except β is much smaller. This mode is seldom used in practice.

Schematic of the four modes of a transistor; saturation (ON), cutoff (OFF), forward active (amplifier), and reverse active.
The four modes of a transistor; saturation (ON), cutoff (OFF), forward active (amplifier), and reverse active.

Applications

Transistors are the basic building blocks of computers and modern electronics, and have wide-ranging applications.

As a switch

Keep the transistor in switch mode and assign labels to the states of the switch; 0 for OFF, 1 for ON. The transistor now functions as a bit, the fundamental unit of classical computing.

You can string a few transistor switches together and form logic gates. These follow Boolean algebra, and allow you to perform OR, AND and NOT operations. More complex combinations of transistors give NOR, NAND, and XOR gates.

Bits and logic gates can be used together to implement a series of instructions. This implementation of an algorithm is a computer program.

Finally, by connecting transistors together in certain ways, it is possible to make it stay either in the saturation or the cut-off states until a new input has been applied. Such flip-flops can either be in 0 or 1 states, and thus can store bits. These are the building blocks of computer memory.

As an amplifier

Hearing aids are wonderful applications of transistor amplifiers. The microphone converts sounds into electrical current. It then feeds this into the base of a transistor which is operating in the active mode. The collector current, greatly amplified, feeds into a loudspeaker. Prof Calculus (in moon rocket mode) would greatly approve.

A panel from the tintin book Destination Moon, showing Professor Calculus and Captain Haddock
Professor Calculus and Captain Haddock, from Destination Moon.

References and Further Reading

  1. All About Circuits
  2. ExplainThatStuff
  3. SparkFun