Quantum Dots

If you read popular science articles, you probably have come across the term “quantum dot.” It pops up everywhere – “quantum dots” for drug delivery, “quantum dots” for multicolored display, “quantum dot lasers” – the list seems endless. So, what is a quantum dot? Roughly speaking, it is a tiny structure made of a solid material. It is so tiny (typically consisting of 1,000 -10,000 atoms) that an electron inside it is severely restricted in its movement. Now, when an electron’s motion is so severely constrained, its kinetic energy can assume only certain allowed values that are determined by the size and shape of the dot, as well as the material making up the dot.

Gallium arsenide (GaAs) is a popular material out of which quantum dots can be made, because the effective mass of an electron and the shape of the crystal correlate at room temperature to form desirable properties. Note that 1 nanometer = 10^-9 meter, which is roughly 100,000 times smaller than the thickness of human hair. Since atoms in GaAs are spaced approximately 0.5 nm apart, a quantum dot contains about 25,000 atoms.

One important property of quantum dots is their exceptionally large surface-to-volume ratios. In the case of a cube of edge W, this ratio is 6/W; in the case of a sphere of diameter D, the ratio is 6/D.  The ratio increases as the dimension of the dot (W or D) becomes smaller. For a basketball of diameter 0.1 m, the ratio is 60 m^-1, but for a quantum dot of diameter 10 nanometers (10^-8 m), the ratio is 6×10⁸ m^-1, which is ten million times larger. The large surface-to-volume ratio of the quantum dot is used in chemical and biological sensors. The sensing activity typically takes place only on the surface and not in the interior; therefore it pays to have a large surface-to-volume ratio. It may be beneficial to replace a large sensing particle with several tiny particles or quantum dots.

To understand this even better, note that the volume of the basketball is 10²¹ times larger than that of the quantum dot we just described, so the basketball can be broken up into 10²¹quantum dots. The combined surface area of all these dots is 10⁷ times larger than that of the basketball. Therefore, breaking up the basketball into quantum dots, results in a sensor that is ten million times more effective. That is why quantum dots are so important in applications such as sensing, targeted drug delivery, and catalysis – all of which require a large surface-to-volume ratio.

Quantum dots are also useful in multi-colored displays (see Figure 1). They emit light when an electron inside the dot undergoes a transition from a higher energy (excited) state to a lower energy (ground) state. The color of the emitted light depends on the difference in the energies of the final and initial states as well as the size of the dot. Therefore, quantum dots of different sizes will emit different colored light. This is the basis of multicolored display.

Fabricating quantum dots with good control over size, material purity, and placement on a given surface is not an easy task. Two approaches are common: the “top-down approach” where a large piece of material is chiseled down to a small quantum dot using the process of lithography and etching. A slight variation of this approach is electrostatic delineation of quantum dots where metal pads are placed on a thin layer of material as shown in Figure 2. A negative potential is applied to the pads, which drives away the electrons from underneath, leaving a small puddle of electrons in the center; these form a quantum dot.

The second approach is “bottom up” and is known as self-assembly. Here, spontaneous congregation of atoms into structures of well defined size (of a few nanometers) and shape form quantum dots.

Directed self assembly is a refinement of the process, where the spontaneous congregation is allowed to proceed on a patterned substrate that offers preferred sites for nucleation of quantum dots. This is also referred to as template-based self assembly since the patterned substrate acts as a template for spatially ordering the quantum dots.

Fig. 3 shows as example where a material was deposited on a porous ceramic film containing a quasi-periodic array of pores. The deposited atoms congregated on the island between the pores to form a spatially ordered array of pyramidal quantum dots.

Fig. 3 shows as example where a material was deposited on a porous ceramic film containing a quasi-periodic array of pores. The deposited atoms congregated on the island between the pores to form a spatially ordered array of pyramidal quantum dots.

Quantum dots are fascinating entities that are increasingly making their way into a large assortment of commercial and defense related products. Rapid advancements are being made in perfecting the synthesis methods and one can expect to see quantum dots permeate the marketplace within the next decade or so.