Ohm's Law Still Applies...

1.5 nm wide nanowire

5 January 2012 — Moore’s Law, the cornerstone rule of the semiconductor industry, may get a reprieve from its predicted demise, according to a group of scientists in Australia and the United States. Their unexpected findings show that a well-understood law of classical physics—and a pillar of electrical engineering—holds for some objects that are just four atoms wide, a size where quantum effects should rule instead.

Michelle Simmons and her colleagues at the University of New South Wales, in Australia, together with collaborators at the University of Melbourne and Purdue University, in Indiana, have built low-resistance silicon wires that show that Ohm’s Law works at the atomic level. Ohm’s Law, an empirical rule discovered by the German physicist Georg Ohm in 1827, says that the current through a conductor is directly proportional to the potential difference across the conductor. Introducing the concept of resistance, the law is a mainstay of circuit theory and is taught to high school and college students in physics and engineering classes.

At least... I tried to!

[Opinion] Nanotechnology will utilize quantum mechanics in initial design concept, even in conventional circuits where your I-Pad apps are concerned as consumer demand drives chips to do more, and faster.

IEEE: Ohm’s Law Survives at the Atomic Scale

The Amazing Story of Quantum Mechanics