# Structural Biochemistry/Quantum Dots
## What are Quantum Dots?

Quantum dots are microscopic semiconductor crystals that are made of clusters of cadmium selenide, cadmium sulfide, indium arsenide, or indium phosphide and they radiate colors when are exposed to ultraviolet light. They are typically between two to ten nanometers long in diameter. Their small size allows for the visible emission of photons as they are excited, which produces wavelengths of color that people can see. They are used to visualize and track individual molecules and their movements inside cells. They are also known as “artificial atoms” because their behavior is analogous to that of single atoms. Quantum dots work based on the principle of quantum confinement, which states that when an object is confined to a small space, the object is only able to occupy certain discrete energy levels. This principle is equivalent to how electrons are only able to occupy discrete energy configuration known as orbital’s. In the case of Quantum Dots, electrons are forced to occupy discrete energy levels based on which wave functions "fit" inside the quantum dot. When electrons are excited from their lower energy levels, the transition from a high energy state to a low energy state emits a photon, just like when an electron makes an energy transition in an atomic transition.
This property of quantum dots is useful for one especially important application, to tag molecules or proteins of interest as well as several other uses outside the field of biology. Some examples include applications in memory chips, quantum computation, quantum cryptography, in room-temperature quantum-dot lasers, just to name a few. The basic concepts underlie these artificial atoms include, but not limited to, the magic numbers in the ground state angular momentum, the spin singlet-triplet transition, the generalized Kohn theorem, and their implications, shell structure, single-electron charging, diamond diagram, etc. They are often used more than traditional organic compounds that are used to stain cells and make cells radiate because they are brighter and more versatile.

## One-Electron Systems

The problem of a single ideally two-dimensional electron in a circular dot with zero confinement potential in the presence of an external magnetic field was studied by Landau leading to the term Landau levels. Hybridization of Landau levels with the levels that arise from spatical confinement occurs at low values of the magnetic field (the magnetic length is larger than or comparable to the size of the confinement potential). As magnetic field increases (the magnetic length becomes much smaller than the radius of the confinement potential), free-electron behavior dominates that of spatial confinement. Therefore, a gradual transition from spatial to magnetic quantization that depends on the relative size of the quantum dots as compared to the magnetic length can be observed.

## Basic Properties Found by Experiments

Using single-electron capacitance spectroscopy, gated resonant tunneling devices, conventional capacitance studies of dot arrays, transport spectroscopy, far-infrared (FIR) magneto-spectroscopy, and Raman spectroscopy the electronic properties of quantum dots are found. An oscillatory structure in the measured capacitance was attributed to the discrete energy levels of a quantum dot. In the presence of a perpendicular magnetic field, Zeeman bifurcation of the energy levels of a quantum dot was also observed. This splitting is believed to occur due to the interplay between competing spatial and magnetic quantization.
Capacitance spectroscopy has been widely used to study the density of states of low-dimensional electron systems. The measured capacitance (or the first derivative of the capacitance versus the gate voltage) reveals structures related to the zero-dimensional quantum levels. As a result, fractionally quantized states, similar to the fractional quantum Hall effect in a two-dimensional electron system, are observed.

### Single-Electron Capacitance Spectroscopy

The electronic ground state in a parabolic confinement potential has been observed in an experiment by Ashoori. The method involved in this experiment is known as single-electron capacitance spectroscopy, and allows direct measurement of the energy levels of a ne-electron dot as a function of the magnetic field. The capacitance was measured between an electrode on top of the QD (the gate) and a conducting layer under the dot that is separated from the dot by a thin tunnel barrier. When the dc gate voltage on the top electrode is varied the Fermi level in the bottom electrode can coincide with the Fermi energy of the dot. Electron tunneling through the thin barrier is observed. Charge modulation in the QD induces a capacitance signal on the gate because of its close proximity to the dot. The capacitance as a function of the gate voltage was found to exhibit a series of uniformly spaced peaks, with separation decreasing with increasing electron number. The peaks are results of the addition of single electrons to the QD. The remarkable aspect of the experiment is that they probed the addition spectrum starting with the very first electron in the dot.

### Optical Transtions

The quantum dot structure was created either by etching techniques or field-effect confinement in this experiment. The samples were prepared from modulation-doped AsGaAs/GaAs heterostructures. For the quantum dots, an array of photoresist dots was created by a holographic double exposure. The rectangular 200nm deep grooves were then etched all the way into the active GaAs layer. Quantum dots can also be grown from seed crystals. Like how sugar crystals are grown to make rock candy, quantum dots can be grown layer by layer until the desired size is achieved in a process known as self-assembly. Field-effect confined quantum dots were prepared by starting from a modulation-doped GaAs-heterojunction. Electrons were laterally confined by a gate voltage applied to a NiCr-gate. A strong negative gate voltage depletes the carriers leaving isolated electron islands (quantum dots).

### Quantum-Dot Light-Emitting Device (LED)

Previously, there had been functional problems with the ligands that were attached to the quantum dots. Scientists have instead utilized these ligands to their advantage; They are now used to cover up the spaces in between the quantum dots. This creates a structure in which there are spaces for the quantum dots to fit in. This allows for the use of a single-layered Quantum-dot Light-Emitting Device, enabling scientists to pass current directly through the quantum dots rather than in between them. Scientists are currently pushing for this new technology of Quantum-Dot LEDs to be used in computer and television displays.

## Applications

Quantum dots is a technology which utilizes microscopic semiconductor crystals to label proteins and genes of interest. The crystals are less than a millionth of an inch in diameter and radiate bright colors when exposed to UV light. Different sized dots radiate with different fluorescent colors. Large dots emit a red color, while small dots emit a blue color. The size affects the color of the fluorescence due to the phenomenon of quantum confinement. As the size of the quantum dot decreases, the electron is forced into a tighter and tighter space. This means that the quantized energy levels of the electron get spaced further and further apart, increasing the energy difference between the excited and relaxed electron energy levels. This phenomenon is exemplified in the classical quantum mechanics problem of the infinite potential well. Choice of the quantum dot material also affects the characteristics of the emission spectra. Choosing a semiconductor with a high bandgap, the energy difference between the highest occupied energy level and lowest unoccupied energy level, results in higher energy photons being released (blue shifting). Also, quantum dots tend to be made from direct bandgap materials like GaAs, which results in more efficient energy transitions and less energy wasted as heat.
The dots are more useful than fluorescent markers because there are more variety in colors, and the light emitted from quantum dots are brighter and more versatile. Another advantage is that until flurophores and chromophores, they do not photobleach, meaning that repeated use does not diminish their capacity to function properly. Because quantum dots are made from inorganic materials, they can be functionalized easily with molecules and do not degrade easily, which maybe pose an environmental risk. They can visualize individual molecules or every molecule of a given type. Quantum dots show promise in allowing scientist to quickly analyze thousands of genes and proteins from patients with disease, such as cancer. They can then customize treatments to each patient’s own molecular profile. Quantum dots can also improve the speed, accuracy, and affordability of various diagnostic tests, whether it be HIV or common allergies. They can also give a specific dose of a drug to a certain type of cell. Compared to other fluorescent markers, they are smaller, more specific and allow further insight into the structure and inner working of a cell. Large scale use of quantum dots, however, may be limited due to the unknown hazards of using nanomaterials in living organisms.

## References

"Inside the Cell"