Nanophysics built into the properties of bulk matter

Even if we can describe the size scale of 1 mm - 10 nm as one of "classical scaling", before distinctly size-related anomalies are strongly apparent, a nanotechnologist must appreciate that many properties of bulk condensed matter already require concepts of nanophysics for their understanding. This might seem obvious, in that atoms themselves are completely nanophysical in their structure and behavior!

Beyond this, however, the basic modern understanding of semiconductors, involving energy bands, forbidden gaps, and effective masses m for free electrons and free holes, is based on nanophysics in the form of Schrodinger's equation as applied to a periodic structure.

Periodicity, a repeated unit cell of dimensions a,b,c (in three dimensions) profoundly alters the way an electron (or a "hole", which is the inherently positively charged absence of an electron) moves in a solid. As we will discuss more completely below, ranges (bands) of energy of the free carrier exist for which the carrier will pass through the periodic solid with no scattering at all, much in the same way that an electromagnetic wave will propagate without attenuation in the passband of a transmission line. In energy ranges between the allowed bands, gaps appear, where no moving carriers are possible, in analogy to the lack of signal transmission in the stopband frequency range of a transmission line.

So, the "classical" range of scaling as mentioned above is one in which the consequences of periodicity for the motions of electrons and holes (wildly "non-classical", if referred to Newton's Laws, for example) are unchanged. In practice, the properties of a regular array of 100 atoms on a side, a nanocrystal containing only a million atoms, is still large enough to be accurately described by the methods of solid state physics. If the material is crystalline, the properties of a sample of 106 atoms are likely to be an approximate guide to the properties of a bulk sample. To extrapolate the bulk properties from a 100-atom-per-side simulation may not be too far off.

It is probably clear that a basic understanding of the ideas, and also the fabrication methods, of semiconductor physics is likely to be a useful tool for the scientist or engineer who will work in nanotechnology. Almost all devices in the Micro-electromechanical Systems (MEMS) category, including accelerometers, related angular rotation sensors, and more, are presently fabricated using the semiconductor micro-technology.

The second, and more challenging question, for the nanotechnologist, is to understand and hopefully to exploit those changes in physical behavior that occur at the end of the classical scaling range. The "end of the scaling" is the size scale of atoms and molecules, where nanophysics is the proven conceptual replacement of the laws of classical physics. Modern physics, which includes quantum mechanics as a description of matter on a nanometer scale, is a fully developed and proven subject whose application to real situations is limited only by modeling and computational competence.

In the modern era, simulations and approximate solutions increasingly facilitate the application of nanophysics to almost any problem of interest. Many central problems are already (adequately, or more than adequately) solved in the extensive literatures of theoretical chemistry, biophysics, condensed matter physics and semiconductor device physics. The practical problem is to find the relevant work, and, frequently, to convert the notation and units systems to apply the results to the problem at hand.

It is worth saying that information has no inherent (i.e., zero) size. The density of information that can be stored is limited only by the coding element, be it a bead on an abacus, a magnetized region on a hard disk, a charge on a CMOS capacitor, a nanoscale indentation on a plastic recording surface, the presence or absence of a particular atom at a specified location, or the presence of an "up" or "down" electronic or nuclear spin (magnetic moment) on a density of atoms in condensed matter, (0.1 nm)"3 = 1030/m3 = 1024/cm3. If these coding elements are on a surface, then the limiting density is (0.1 nm)~2 = 102O/m2, or 6.45 x 1016/m2.

1.2 Moore's Law

The principal limitation may be the physical size of the reading element, which historically would be a coil of wire (solenoid) in the case of the magnetic bit. The limiting density of information in the presently advancing technology of magnetic computer hard disk drives is about 100Gb/in2, or 10n/in2. It appears that non-magnetic technologies, perhaps based on arrays of AFM tips writing onto a plastic film such as polymethylmethacrylate (PMMA), may eventually overtake the magnetic technology.

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