Law of Large Numbers System Design

Abstract

To date we have relied on the "Law of Large Numbers" below the device level to guarantee deterministic device behavior (e.g. dopant ratios, transition timing, electron state storage). However, at the nanoscale, we hope to build devices with small numbers of atoms or molecules (e.g. wires which are 3-10 atoms wide, diodes built from 1-10 molecules), and we hope to store state with small numbers of electrons (e.g. 10's). If we are to build devices at these scales, we will no longer be able to rely on the "Law of Large Numbers" below the device level. We must, instead, employ the "Law of Large Numbers" above the device level in order to obtain predictable behavior from atomic-scale phenomena which are statistical in nature. At the same time, the "Law of Large Numbers" can also help us by providing statistical differentiation at scales smaller than those we can pattern directly or economically using lithography. In this chapter, we examine various applications of the "Law of Large Numbers" above the device level to build reliable and controllable systems from nanoscale devices and processes that only have statistically predictable behavior.