Improving Tolerance to Variations in Memristor-Based Applications Using Parallel Memristors

Abstract

Memristors are being explored for a wide variety of applications such as neuromorphic computing, memory and digital logic. However, they suffer from process variations like any other nanodevice, which in turn impacts their applicability. The effect of process variations, specifically variation in thickness, is highly non-linear on memristors; the effect is greater near the lower memristance region (near M <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$_{\rm on}$</tex><mathgraphic fileref="rajendran-ieq1-2308189.gif" graphicformat="GIF"/></formula> ) than in the higher memristance region (near M <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$_{\rm off}$</tex> <mathgraphic fileref="rajendran-ieq2-2308189.gif" graphicformat="GIF"/></formula> ). Due to this non-linear effect, many applications do not use the lower memristance values. Consequently, the application's functionality and performance is affected. In this work, we propose a technique called parallel memristors. In this technique, instead of using a single memristor, the application uses several memristors connected in parallel. Each memristor in this parallel structure is programmed to a higher memristance value to tolerate variations. Since many memristors are connected in parallel, the effective memristance value can be near the M <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$_{\rm on}$ </tex><mathgraphic fileref="rajendran-ieq3-2308189.gif" graphicformat="GIF"/></formula> value, thereby achieving high-speed operation. We evaluate the parallel memristor technique in two different applications—memristor-based threshold logic and memristor-based memory. We also perform various optimizations to tradeoff between variation tolerance, power, delay, and area.