Introduction

Quantum wires, wells, and dots are semiconductor crystals whose size, in one, two, and three dimensions respectively, are limited to atomic sizes; a few nanometers. Q-dot, a three dimensional midget, is a sphere with a radius of few nm that can confine an electron in zero-dimension; hence the name "dot". The other nano crystals, Q-wires and Q-wells, are equally limited in size, and can confine electrons in one and two dimensions. What makes Q-crystals interesting, both for their science as well as their application, is that their physical properties are effectively controlled by their nano-dimensional size.

In the case of Q-dots, the dimensional of the semiconductor controls both its electric and photoelectric properties. This has been shown to lead to novel applications in optoelectronics including fluorescence, lasing, nonlinear optical effects, and other optoelectronic application such as ultra-fast switching.

It was in early 1980s that the first quantum dots were successfully made in a research laboratory. About five years earlier Leo Ascii et al. had demonstrated one dimensional confinement in quantum well structures. In less than a decade Aleksey Ekimov et al. obtained evidence for three dimensional confinement in quantum dots. The trick was to grow a semiconductor crystal of atomic dimensions. The construction of Q-dots took two separate paths. In one method the dot is constructed using lithography techniques of microchip manufacturing; creating one Q-dot at a time. In the second method chemical processes are used to grow Q-dots in bulk.

Two of the primary applications of Q-dots are in optoelectronics and in fluorescence tagging techniques. Both of these applications are thanks to the confinement of electron in the semiconductor material. Below, we will first discuss these two applications and then examine the basics of the underlying science of quantum confinement.

Optoelectronic Applications

The semiconductor material Gallium-Arsenide (GaAs) is a compound semiconductor made of gallium (Ga) and arsenic (As). It has a band-gap of 1.43 eV, can be combined with impurities to create number of variations in its semiconductor properties, and is very efficient in absorption/emission of light. It is therefore very much favored in optoelectronic applications (this is in contrast with silicone based semiconductors - with a band gap of 1.1 eV - that are commonly used in electronic applications). Addition of impurities such as aluminum (Al) and phosphorous (P) to GaAs allows for creation of regions with higher or lower electron or hole densities. Fabrication of light emitting semiconductors uses lithography to create layers of these materials in a design that converts electric energy supplied to its electrodes into light. In the case of semiconductor lasers, such as the ones used in CD players, presence of impurities in the semiconductor creates energy levels between the semiconductors energy bands. These energy levels then play a similar role in making lasing transitions possible.

A typical laser diode has dimensions of few to one hundred micrometers (see pages on Quantum Application). Therefore optical lithography can be successfully used to create such structures. In the case of Q-dot diode lasers that require engineering at the level of afew nanometers, optical lithography cannot provide necessary resolution.

One of the methods of obtaining higher resolution is to employ shorter wavelengths by using X-ray or particle beams (electrons or ions, for example). In one method of Q-dots fabrication a layer of only a few nm in thickness (of say GaAs), is deposited on a bulk semiconductor material (AlGaAs). This layer is covered with another bulk layer of the semiconductor (say AlGaAs ) thus creating a Q-well. Then through a series of steps involving electron beam etching and chemical removal using solvents a Q-dot is created on a tower of bulk semiconductor. By using a mask this process can be repeated over and over to fabricate an array of Q-dot. An alternative to particle beam removal is to deposit gates and electrodes, in nm scale of course, to use electric fields to confine electrons in the Q-well to nm by nm areas and thus create regions of Q-dots on the Q-well layer. One advantage of this technique is that by controlling the gate potentials one could affect the Q-dot's size.

Arrays of Q-dot lasers are far more efficient than standard heterojunction diode lasers. But the primary advantage of Q-well and Q-dot lasers is that by adjusting dimensions the output wavelength can be controlled in a range that is not possible using bulk materials only.

Fluorescence Tagging Applications

By far the most common application of Q-dots is in fluorescence tagging, where they replace molecular dyes. These range from biological to environmental applications. In these applications when the tagging substance is irradiated with light it absorbs the light and then re-emits it at a different wavelength. The emission spectrum then is the tell-tale sign for the presence of the tagging substance. For example, injecting a tagging substance into a particular biological cell makes it possible to identify that cell amid other cells from its fluorescence.

There are several reasons that make Q-dots more advantageous to molecular competition. The first of these is that Q-dots can absorb a wide band of light for their excitation, but they emit in a very narrow band. In contrast, most molecular dyes can absorb only a very narrow band of wavelength, so most of the illuminating light is not used. Also, these molecules emit is a much wider band of wavelengths. As a result, to distinguish separate features one needs to use very different molecular dyes, each with its own required excitation wavelengths. In the case of Q-dots their emission wavelength depends on their size. So, Q-dots made of the same semiconductor material, but of different sizes all can be excited by the same light source, but then they emit distinctly different wavelengths.

Another feature of Q-dots that makes them a good candidate for tagging purposes is that their tagging property is controlable - with proper chemistry these objects can be attached to "molecules with a purpose". This is in contrast to traditionally used molecular tags have well defined binding characteristics. As a result a particular molecular tag may or may not bind with a given molecule or surface. Since Q-dots have a surface that could bind with a variety of molecules, they could be prepared (funtionalized) so as to attach to well defined targets, even at the molecular level.

A third feature of Q-dots that makes them desirable for tagging is due to their nonlinear optical behavior. Through freqency-doubling nonlinear optical materials can absorb two photons of longer wavelength and create a single photon of lower wavelength. But most optical materials have a small non-linearity. Q-dots are made with large nonlinear properties that have allowed researchers to employ them for deep noninvasive imaging. This is done by focusing long wavelength laser light that is not absorbed by tissue beneath the skin of a rat injected with Q-dots in the tail blood vessels. As the dots reach the focal point of the illuminating laser they frequency-double the laser radiation (absorb two of the long wavelength photons simultaneously) and emit light well into the visible. This "fluorescence" allows the imaging of the blood vessels/tumors without opening the tissue.

One of the drawbacks of Q-dots for medical applications is that their safe use in biological environments is not well understood. Many of the substances, such as arsenic, used in manufacturing semiconductors are toxic. Even though the Q-dots can be made with a "protective coating", the long term integrity of the coating and its overall effect on biological environments it is not well understood at this time. However, the high sensitivity of Q-dots as fluorescent tags often require such small quantities for use in most applications that the issue of safety may not be a major concern.

Manufacturing of Q-dots for fluorescence is very different than their production for optoelectronics applications. Q-dots used for tagging are prepared from nucleation in oxides or by thermodynamically controlled precipitation in a vapor phase. These dots are manufactured in a colloidal suspension that could then be made into other forms, such as thin films or coatings. One common nanocrystal Q-dot is made of a core of cadmium sellenide (CdSe), few nanometers in diameter, followed by a shell of ZnS. Because the core surface is not perfectly uniform, dangling bond at this surface tend to quench optical transitions. The shell's "protective" layer therefore enhances the fluorescence by more than an order of magnitude. In addition, this coating happens to also increase the broad-band absorption characteristic of the Q-dot.

Science of Quantum Dots

To understand how Q-dots are different from bulk semiconductors we need to employ the help of quantum mechanics (quantum physics- see the pages on Introduction to Quantum Theory). In the description of quantum mechanics electron in the semiconductor crystal has a wavelike representation. The wavelength of this wave, l, is inversely proportional to electron's momentum, p. Also, according to Heisenberg's Uncertainty Principle position, x, and momentum p of the electron are correlated in that confinement of electron in a space xmin results in a maximum possible energy for the electron. Based on this uncertainty principle we can write:

dE = (h / 4p dx)/2m

In the above h is Planck's constant and m is the electron mass. Fortunately, in the semiconductor the electron's mass is reduced to an effective value, called the effective mass, to around 10% of its value in free space. Because of this, room-temperature confinement of electron can take place in nm size crystals. But to examine the effects of this confinement we need to restore to a model description of a trapped particle in the quantum world.

One model describing confinement of electron to a Q-dot is that of a particle trapped inside a box. In this model quantum mechanics predicts quantized energy levels similar to the simpler one-dimensional case. Another model describing this confinement is based on the electron-hole attraction, or the energy quantization of exciton.

In the study of Q-wires and Q-wells the one-dimensional and two-dimensional potential well models could be applied to predict energy levels due to the confinement. In the case of Q-dots the exciton model is a more realistic one. When an electron is promoted to the conduction band in bulk semiconductor material a hole is created in the valence band. The absence of negative charge in the valence band makes the hole's effective charge to be positive, thus attracting the electron. This pair form a hydrogenic atom that is relatively loosely bound. In the Q-dot where the size of the nanocrystal is comparable to the effective Bohr radius of the exciton, then the binding is stronger. Below is a list of effective Bohr radii for different nanocrystals

Material Bohr Radius (nm)
CdSe 6
PbS 20
InAs 34
PbSe 46

 

In contrast, the Bohr radius for hydrogen atom is about 0.05 nm. Notice that the difference in the Bohr radii in different materials is solely due to the effective mass of the electron in that material. This difference is also exhibited in the hydrogenic energy levels. These values are given by:

 

E = - 13.6 m/ ( e2 . n2) eV , where n =1,2,...

In the above equation m is the ratio of the effective electron mass in the bulk material to its value in vacuum and e is the ratio of the bulk material's permittivity to that in free space.

 

Last Modified January 17, 2006 malekis@union.edu

Quantum Dots

2300 nm (IR) - 350 nm (UV) emission of Q-dots illuminated with a single light source. For further details see Evident Technologies

This photograph shows double tagging of mitochondria and microtubules in NIH 3T3 cells. See the Photo Gallery at QuantumDot Corporation.

Reference to original article:

A.I.Ekimov, et al. "Quantum size effect in three dimensional microscopic semiconductor crystals" JETP Lett. 34, 345 (1981)

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