A graphic of a lattice formed by perpendicularly intersecting lines of yellow and green. The yellow lines denote titanium/gold and the green lines denote bismuth selenide.

Memristor demonstrates use in fully analog hardware-based neural network

The crossbar array memristor made of bismuth selenide (Bi2Se3) sandwiched between gold and titanium electrodes is analog tunable, retention stable and regulator-free in circuit

  • A new Bi2Se3 memristor combines long-term data retention with analog tuning—features that typically trade off—without requiring external circuit regulators, a University of Michigan Engineering study says.
  • The device uses a vertical stack of Au/Bi2Se3/Ti where gold filaments extend and retract without bridging electrodes. They enable analog tuning, mimicking the way biological synapses strengthen or weaken.
  • When integrated into an all-hardware reservoir computing network, the memristor successfully controlled a balance lever while using just 7 microwatts, proving its potential in a fully analog all-hardware neural network to enable neuromorphic computing.

As AI processing demands reach the limits of current CMOS technology, neuromorphic computing—hardware and software that mimic the human brain’s structure—can help process information faster and more efficiently. A new memristor made from 2D layers of bismuth selenide (Bi2Se3) combines long-term data retention and analog tuning to enhance AI energy efficiency and processing speed.

The University of Michigan Engineering study, published in ACS Nano, was funded by the National Science Foundation and the Department of Energy. 

The Bi2Se3 memristor demonstrated three technical requirements that no practical memristors had combined up until this point: long-term data retention, analog-style memory states and the ability to operate regulator-free in circuit. In a demonstration, the memristor successfully controlled a balance lever as part of a fully analog, all-hardware reservoir computing network.

“Our work provides a new pathway for making key components for building hardware-based neural networks. The presented memristors can truly work in a way that AI circuit designers will love,” said Xiaogan Liang, a professor of mechanical engineering at U-M and corresponding author of the study. 

Fabricating a scalable memristor crossbar array

Memristors, devices that adjust electrical resistance based on past current or voltage, enable in-memory computing, an essential component of neuromorphic computing. The ability to store and process information in the same device eliminates the bottleneck in conventional computing where data must constantly shuttle between separate memory and processing units.

The memristor properties needed for hardware-based neural networks are typically at odds with one another. The devices with long-term data retention through non-volatile memory require an external current-regulating device to prevent abrupt switching. On the other hand, those with analog-style memory states, meaning continuous tuning rather than binary switching, suffer from poor data retention.

To overcome these challenges, the research team fabricated crossbar arrays of vertically arranged Bi2Se3 memristors on a silicon substrate. Through photolithography, the team first layered 500-nanometer-wide gold (Au) bottom electrodes on top of a 300-nanometer-thick silicon dioxide base. Bi2Se3 flakes made up of a few stacked 2D layers were then grown directly on the gold electrodes through physical vapor deposition. The gold both serves as an electrode and helps control nucleation and grain size of Bi2Se3, ensuring site-specific growth. 

Four horizontal stripes in a 120 nanometer view. From bottom to top: thick orange layer labeled gold, thin red layer labeled bismuth, thin teal layer labeled titanium, thick top layer labeled gold.
Close examination of the new memristor revealed that gold filaments extend from the bottom electrode into the Bi2Se3 layer and retract without bridging to the top titanium electrode. This enables continuous analog tuning that mimics the way synaptic connections in the human brain strengthen or weaken. Credit: Ki et al., 2026.

To complete the vertical stack, titanium (Ti) and additional gold layers were deposited perpendicular to the bottom electrode to make a lattice with a Au/Bi2Se3/Ti sandwich at the points of intersection.

This gold-assisted vapor deposition process is compatible with existing semiconductor manufacturing approaches, demonstrating scalability.

Gold filaments enable precise analog tuning

When testing device performance, the Bi2Se3 memristors demonstrated strong analog conductance tuning of 10%-40%, stable retention with less than 1% loss over 10,000 seconds. The device operated without external current regulators.

An elemental analysis and simulations revealed that tiny finger-like gold filaments extend upwards from the bottom electrode into the Bi2Se3 layer when voltage is applied. These conductive filaments grow and contract without bridging the gap to the top electrode, allowing smooth analog tuning of the device conductance. The lattice structure formed by the crossbar array facilitates in-memory computing by hosting dynamic growth and retraction of gold filaments, which continuously modulates the device resistance.

A graphic of a lattice formed by perpendicularly intersecting lines of yellow and green. The yellow lines denote titanium/gold and the green lines denote bismuth selenide.
A new memristor combines the three technical requirements needed for hard-ware based neural networks: long-term data retention, analog tuning and the ability to operate regulator-free in circuit. The crossbar array creates a stack including a gold (Au) bottom electrode, a bismuth selenide Bi2Se3 active layer and a titanium (Ti) top electrode at each junction. Credit: Ki et al., 2026.

Fully analog, all-hardware balancing control

A graphic of the propeller-driven balance lever. A vertical pole is attached to a horizontal base. At the top of the pole, a long arm extends in both directions, able to swing upwards or downwards like a see-saw. On the right side, a weight hangs from the tip of the arm. On the left side, a propeller sits atop the arm. An arrow points upwards indicating the propeller is driving the arm upwards.
The Bi2Se3 memristor controlled a balance lever in a fully analog, all-hardware reservoir computing network. By bypassing the need for analog-to-digital conversion, the memristor used just 7 microwatts of power while dynamically adjusting propeller speed to maintain a 90 degree angle. Credit: Ki et al., 2026.

To test the device, the researchers incorporated Bi2Se3 memristors into a fully analog all-hardware reservoir computing network that controlled a balance lever. The balance lever resembles a seesaw with a motor and propeller and one end, a dangling weight on the other end and a sensor that tells the system if the lever is tilted. The goal is to dynamically control the propeller to achieve a 90-degree angle. The Bi2Se3 memristors replaced the software that typically serves as the readout layer that determines actionable output. Their memristor succeeded in calculating how much to spin the propeller to achieve a perfect 90 degree angle. The memristor avoided the need for analog-to-digital conversion, achieving ultra low power consumption of about 7 μW, or 7 millionths of a watt. For scale, a household LED light uses about 8 to 12 watts. 

If scaled up, this new memristor could enable neuromorphic computing devices, which would significantly improve AI hardware energy efficiency, processing speed and simplicity for circuit design. 

The device was built in the Lurie Nanofabrication Facility and studied at the Michigan Center for Materials Characterization, both of which are operated and maintained with support from indirect cost allocations in federal grants.

Device fabrication and characterization was supported by the National Science Foundation (ECCS-2331169). Device physics modeling and simulation, and materials characterizations were supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences (FWP 84274) at Pacific Northwest National Laboratory through a subcontract to the University of Michigan.