518 | Nature | Vol 585 | 24 September 2020
Article
Third-order nanocircuit elements for
neuromorphic engineering
Suhas Kumar^1 ✉, R. Stanley Williams^2 & Ziwen Wang^3Current hardware approaches to biomimetic or neuromorphic artificial intelligence
rely on elaborate transistor circuits to simulate biological functions. However, these
can instead be more faithfully emulated by higher-order circuit elements that
naturally express neuromorphic nonlinear dynamics^1 –^4. Generating neuromorphic
action potentials in a circuit element theoretically requires a minimum of third-order
complexity (for example, three dynamical electrophysical processes)^5 , but there have
been few examples of second-order neuromorphic elements, and no previous
demonstration of any isolated third-order element^6 –^8. Using both experiments and
modelling, here we show how multiple electrophysical processes—including Mott
transition dynamics—form a nanoscale third-order circuit element. We demonstrate
simple transistorless networks of third-order elements that perform Boolean
operations and find analogue solutions to a computationally hard graph-partitioning
problem. This work paves a way towards very compact and densely functional
neuromorphic computing primitives, and energy-efficient validation of
neuroscientific models.The exponential growth of both the volume of data and also the
demand for computing, coupled with performance saturation of
transistor-based computing systems, has fuelled interest in alterna-
tive computing primitives^9. Neuromorphic, neuron-like or biomimetic
computing may yield dramatic performance improvements over digital
computation in the rapidly growing areas of identification and clas-
sification of information buried within massive datasets, and solving
computationally hard problems such as viral genome sequencing.
However, the efficient hardware implementation of brain-inspired
and neural network algorithms is still a major challenge^9 ,^10. Commu-
nication and processing of data via neuromorphic dynamics is a key
goal for brain-inspired computers^11 , but a single electronic component
that can mimic a neuron does not exist. Periodic spiking requires only
second-order complexity, but full neuromorphic action-potential func-
tionality (including phasic and periodic spiking, bursting, self-sustained
oscillations, chaos and sub/super-threshold active dynamics) requires
a minimum of third-order complexity (three state variables or equiva-
lent)^5. There have been few successful second-order elements (exhibit-
ing only periodic spiking and oscillations)^3 ,^8 ,^12 , and the efforts aimed
at achieving extended neuromorphic properties used circuits with
multiple elements^13 ,^14. There have been no previous demonstrations
of an isolated third-order electronic element, neuromorphic or oth-
erwise. Digital transistor-based chips attempt to simulate the com-
plex equations representing the rich nonlinear dynamics of neurons,
thereby making them complicated, bulky and energy-inefficient^15.
The design and realization of higher-order electronic elements will
enable extremely efficient implementations of neuromorphic arti-
ficial intelligence. Such realizations may also provide a platform on
which to explore models of higher-order brain functions (for example,
psychiatric conditions), which are currently impeded by computing
bottlenecks^16 ,^17.
Here we fabricated sub-100-nm components, each of which incor-
porated a NbO 2 volatile Mott memristive switch, an internal parallel
capacitor defined by the metal contacts sandwiching a dielectric, and
an internal series resistor defined by an electrode interface (Fig. 1a–c,
Supplementary Figs. 2–4). The quasistatic current–voltage behav-
iour (Fig. 1d) of the element measured by sourcing a current consists
of an S-type negative differential resistance (NDR) at lower currents,
followed by a box-shaped hysteresis at higher currents. The NDR is
known to originate from a positive feedback mechanism in which Joule
heating is enhanced by the super-linear thermally activated transport
of NbO 218 –^20. The box-shaped hysteresis in quasistatic measurements
has been observed recently and attributed to a Mott transition, but
other mechanisms such as local temperature redistribution have also
been suggested^20 –^22. Although interesting nonlinear phenomena have
been reported in materials exhibiting a Mott transition (such as chaos
driven by thermal noise)^3 , the unique dynamics associated with the Mott
transition itself have not been previously characterized, and as we will
show here, the transition contributes an additional state variable that
can be harnessed to produce neuromorphic functions.
The hysteresis may have different causes in various components,
and so we performed additional physical measurements to determine
its origins in our element. Cross-sectional transmission electron micro-
graphs and electron-diffraction patterns within the active as-grown
amorphous NbO2+δ (over-oxidized NbO 2 ) layer of an element that had
been operated once past the hysteresis exhibited crystallized NbO 2
within a 10-nm region near the centre of the structure (Fig. 1e, f, Sup-
plementary Figs. 5–7). The crystallization temperature is close to the
local temperature expected at the power level of the Mott transi-
tion^18 ,^20 ,^23 , and so we infer that Joule heating in a localized active region
forms the ordered structure. Material surrounding the active region
had a higher oxygen concentration and was probably not Mott active^24.https://doi.org/10.1038/s41586-020-2735-5
Received: 28 January 2020
Accepted: 3 August 2020
Published online: 23 September 2020
Check for updates(^1) Hewlett Packard Labs, Palo Alto, CA, USA. (^2) Texas A&M University, College Station, TX, USA. (^3) Stanford University, Stanford, CA, USA. ✉e-mail: [email protected]