1. HP Labs, 1501 Page Mill Road, Palo Alto, California 94304, USA

Correspondence to: R. Stanley Williams¹ Correspondence and requests for materials should be addressed to R.S.W. (Email: stan.williams@hp.com).

Abstract

Anyone who ever took an electronics laboratory class will be familiar with the fundamental passive circuit elements: the resistor, the capacitor and the inductor. However, in 1971 Leon Chua reasoned from symmetry arguments that there should be a fourth fundamental element, which he called a memristor (short for memory resistor)¹. Although he showed that such an element has many interesting and valuable circuit properties, until now no one has presented either a useful physical model or an example of a memristor. Here we show, using a simple analytical example, that memristance arises naturally in nanoscale systems in which solid-state electronic and ionic transport are coupled under an external bias voltage. These results serve as the foundation for understanding a wide range of hysteretic current–voltage behaviour observed in many nanoscale electronic devices^{2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19} that involve the motion of charged atomic or molecular species, in particular certain titanium dioxide cross-point switches^{20, 21, 22}.

1. HP Labs, 1501 Page Mill Road, Palo Alto, California 94304, USA

Correspondence to: R. Stanley Williams¹ Correspondence and requests for materials should be addressed to R.S.W. (Email: stan.williams@hp.com).