Nanometers Micrometers Millimeters

A nanometer, 10~9m, is about ten times the size of the smallest atoms, such as hydrogen and carbon, while a micron is barely larger than the wavelength of visible light, thus invisible to the human eye. A millimeter, the size of a pinhead, is roughly the smallest size available in present day machines. The range of scales from millimeters to nanometers is one million, which is also about the range of scales in present day mechanical technology, from the largest skyscrapers to the smallest conventional mechanical machine parts. The vast opportunity for making new machines, spanning almost six orders of magnitude from 1 mm to lnm, is one take on Richard Feynman's famous statement [4]: "there is plenty of room at the bottom". If L is taken as a typical length, 0.1 nm for an atom, perhaps 2 m for a human, this scale range in L would be 2 x 1010. If the same scale range were to apply to an area, 0.1 nm by 0.1 nm vs 2 m x 2 m, the scale range for area L2 is 4 x 1020. Since a volume I3 is enclosed by sides I, we can see that the number of atoms of size 0.1 nm in a (2 m)3 volume is about 8xl030. Recalling that Avogadro's number NA= 6.022 x 1023 is the number of atoms in a gram-mole, supposing that the atoms were 12C, molar mass 12 g; then the mass enclosed in the (2 m)3 volume would be 15.9 x 104kg, corresponding to a density 1.99 x 104kg/m3 (19.9 g/cc). (This is about 20 times the density of water, and higher than the densities of elemental carbon in its diamond and graphitic forms (which have densities 3.51 and 2.25 g/cc, respectively) because the equivalent size L of a carbon atom in these elemental forms slightly exceeds 0.1 nm.)

A primary working tool of the nanotechnologist is facility in scaling the magnitudes of various properties of interest, as the length scale L shrinks, e.g., from 1 mm to 1 nm.

Clearly, the number of atoms in a device scales as L3. If a transistor on a micron scale contains 1012 atoms, then on a nanometer scale, L'/L = 10~3 it will contain 1000 atoms, likely too few to preserve its function!

Normally, we will think of scaling as an isotropic scale reduction in three dimensions. However, scaling can be thought of usefully when applied only to one or two dimensions, scaling a cube to a two-dimensional (2D) sheet of thickness a or to a one-dimensional (ID) tube or "nanowire" of cross sectional area a2. The term "zero-dimensional" is used to describe an object small in all three dimensions, having volume a3. In electronics, a zero-dimensional object (a nanometer sized cube a3 of semiconductor) is called a "quantum dot" (QD) or "artificial atom" because its electron states are few, sharply separated in energy, and thus resemble the electronic states of an atom.

As we will see, a quantum dot also typically has so small a radius a, with correspondingly small electrical capacitance C = 4it££0a (where ££0 is the dielectric con stant of the medium in which the QD is immersed), that the electrical charging energy l/ = Q2/2C is "large". (In many situations, a "large" energy is one that exceeds the thermal excitation energy, kBT, for T = 300 K, basically room temperature. Here T is the absolute Kelvin temperature, and feB is Boltzmann's constant, 1.38 x 10~23 J/K.) In this situation, a change in the charge Q on the QD by even one electron charge e, may effectively, by the "large" change in U, switch off the possibility of the QD being part of the path of flow for an external current.

This is the basic idea of the "single electron transistor". The role of the quantum dot or QD in this application resembles the role of the grid in the vacuum triode, but only one extra electron change of charge on the "grid" turns the device off. To make a device of this sort work at room temperature requires that the QD be tiny, only a few nm in size.

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