Arguably the most important milestone in the development of modern computing was the invention of the complementary metal-oxide-semiconductor (CMOS) transistor as a replacement to Vacuum Tubes.  This sprung a "silicon revolution" that resulted in the empirically proven Moore's Law, which essentially states that with the trajectory of transistor miniaturization, processing power and transistors per chip will effectively double every two years.  As researchers continue to follow this path, the future of the transistor is beginning to come into question. The physical limitations of miniaturization are beginning to influence the most sacred law in computer chip development, and researchers are beginning to look into what may replace the CMOS transistor, as it once did to the Vacuum Tube.
The physical limitation of transistor scalability begins with an examination of the allowable distance between discrete components on a chip. In order for gates to remain discretized, there must be a measurably thick oxide between each gate -- this is referred to as "Gate Oxide Thickness."  To maintain the current trajectory of Moore's Law, the thickness of the oxide must decrease; the issue arises when this thickness begins to approach a length on the order of only a few atoms.  The effect of small gate lengths is a notable increase in, what formerly was one of silicon's greatest benefits, leakage currents.  In order to be effective in computing, a transistor must be capable of holding defined voltages for reliable lengths of time; with increased leakage, however, this reliability becomes a liability. To combat this, the voltage supplied must be scaled inversely alongside the changing transistor sizes.  This can be defined, through basic equations of electromagnetism, to be proportionally related to the effective capacitance of the transistor - but with a decrease in capacitance there is an increase in thermal noise, as defined by Nyquist.  As a result of increased thermal noise, the likelihood of bit-flipping within a transistor increases, decreasing the overall reliability of the CMOS transistors. 
A hot topic in research today is finding what may replace the transistor. The future of quantum computing, which utilizes known phenomenon such as tunneling to transport electrons, currently receives a lot of hype as a potential replacement. There are, however, other suggestions that may be worth considering as well: restructuring of conductive polymers, magnetostatic nanodevices, ballistic transport (i.e. zero resistance).  Other suggestions refer to begin to use materials with higher dielectric constants as the inter-gate oxides, which may help to combat another issue in scalability, parasitic capacitance. [1,3]
This is not the first time that Moore's Law has come into question. As early as 1975, Moore himself altered the growth rate to fit growing trends.  Thus far, each problem that has been faced research has been able to overcome without having to entirely revamp the physics and underlying principles of computing; with the current trend, however, this may not be as readily fixed. To combat the miniaturization limits, it is necessary to experiment with new technologies, and attempt to find the "next transistor."
© Evan Lee. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
 S. E. Thompson and S. Parthasarathy, "Moore's Law: The Future of SI Microelectronics," Materials Today 9, No. 6, 20 (2006).
 "Excerpts From a Conversation with Gordon Moore: Moore's Law," Intel Corporation, 306959-001US, March 2005.
 M. Schulz, "The End of the Road For Silicon?" Nature 399, 729 (1999).
 L. B. Kish, "End of Moore's Law: Thermal (Noise) Death of Integration in Micro and Nano Electronics," Phys. Lett. A. 305 144 (2002).
 N. Z. Haron and S. Hamdioui, "Why is CMOS Scaling Coming to an End?" Proc. 3rd Intl. Design and Test Workshop, p. 98 (2008).