Wire length scaling

A second application of current interest in which widely separated length scales come into play is fabrication of modulated foils or wires with layer thickness of a few nanometers or less [156]. In this application, the aspect ratio of layer thickness, which may be of nearly atomic dimensions, to workpiece size, is enormous, and the current distribution must be uniform on the entire range of scales between the two. Optimal conditions for these structures require control by local mechanisms to suppress instability and produce layer by layer growth. Epitaxially deposited single crystals with modulated composition on these scales can be described as superlattices. Moffat, in a report on Cu-Ni superlattices, briefly reviews the constraints operating on their fabrication by electrodeposition [157]. 

Nano-structures comments on an example of extreme microstructure In a chapter entitled Materials in Extreme States , Cahn (2001) dedicated several comments to the extreme microstructures and summed up principles and technology of nano-structured materials. Historical remarks were cited starting from the early recognition that working at the nano-scale is truly different from traditional material science. The chemical behaviour and electronic structure change when dimensions are comparable to the length scale of electronic wave functions. Quantum effects do become important at this scale, as predicted by Lifshitz and Kosevich (1953). As for their nomenclature, notice that a piece of semiconductor which is very small in one, two- or three-dimensions, that is a confined structure, is called a quantum well, a quantum wire or a quantum dot, respectively. 

Assuming that the electron density in each wire varies slowly on the length scale of kp1 (except for unimportant regions very close to the boundaries), we use the WKB wave function... 

Figure 3.5.13 (A) Equilibrium times for diffusion on macroscopic (1 mm) and nanoscopic (10 nm) length scales. (B) Illustration of ionic and electronic wiring, with hierarchical porosity as Li+ distribution network and a carbon second-phase e- distribution network. Reprinted from [58] with permission, copyright 2007 John Wiley Sons.

The possibility of tuning spontaneous polarizationj illustrated in Fig. 4.42a, b. As seen from Fig. 4.42a, spontaneous polarization Ps(T,R) increases with the decrease of wire radius for a fixed surface tension coefficient x. For p, = 10 N/m, EuTiOs nanowire of radius 2 lattice constants (1 7c. r O.4 nm) is predicted to be ferroelectric at temperatures lower than 300 K. The wire of radius 4 lattice constants is predicted to be ferroelectric at temperatures lower than 100 K (Fig. 4.42b). For p = 10 N/m and wire radius of 2-4 lattice constants ( 0.8-1.6 nm), the spontaneous polarization reaches the values of 0.1-0.5 C/m at temperatures lower than 100 K. Note, that LGD phenomenology predicts higher enhancement of P3 (T, R) for nanowires with radius R = I lattice constant, but the continuous approach is not quantitatively correct for such small sizes. There is an inherent limitation of the LGD continuous approach that does not allow us to explore all length scales. 

Some of the critical length scales of circuits that can now be fabricated, such as the diameter of the wires and the interwire separation distance (or pitch), are more commonly associated with biological macromolecules, such as proteins, mRNA oligonucleotides, and so on, than with electronics circuitry. In fact, one unique application of nanoscale molecule-electronics circuitry, and perhaps the... 

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