In-memory ferroelectric differentiator

Abstract

Differential calculus is the cornerstone of many disciplines, spanning the breadth of modern mathematics, physics, computer science, and engineering. Its applications are fundamental to theoretical progress and practical solutions. However, the current state of digital differential technology often requires complex implementations, which struggle to meet the extensive demands of the ubiquitous edge computing in the intelligence age. To face these challenges, we propose an in-memory differential computation that capitalizes on the dynamic behavior of ferroelectric domain reversal to efficiently extract information differences. This strategy produces differential information directly within the memory itself, which considerably reduces the volume of data transmission and operational energy consumption. We successfully illustrate the effectiveness of this technique in a variety of tasks, including derivative function solving, the moving object extraction and image discrepancy identification, using an in-memory differentiator constructed with a crossbar array of 1600-unit ferroelectric polymer capacitors. Our research offers an efficient hardware analogue differential computing, which is crucial for accelerating mathematical processing and real-time visual feedback systems.

Fig. 1. Differential method based on micro control unit (MCU) and in-memory differentiator for processing motion images.

a A flowchart of MCU-based motion image processing. Inset shows that differential operations are serially performed by the MCU. b Same as (a) but with an in-memory differentiator. Inset shows that the in-memory differentiator enables both the storage of the previous frame image and the acquisition of the frame difference through ferroelectric domain dynamics.

Fig. 2. Nonlinear ferroelectric domain dynamics and ferroelectric random-access memory (FeRAM) based on passive capacitor crossbar array.

a A sketch of the “trans” molecular structure of polar P(VDF-TrFE) (top panel) and domain orientation under downward electric field (middle panel) and upward electric field (bottom panel) of a P(VDF-TrFE) capacitor. b The multiple polarization versus electric field (P-E) hysteresis loops (up panel) and the corresponding current density versus electric field (J-E) hysteresis loops (bottom panel) of a typical ferroelectric P(VDF-TrFE) capacitor. c Evolution of the permanent polarization (P_r) as a function of the amplitude of the applied electric field. d Evolution of J peak versus the inverse of the square root of the amplitude of the applied electric field for upward domain switching (up panel) and downward domain switching (down panel) respectively. The linear relationship highlighted by the transparent green and blue colors implies a µ value of 0.5 in Eq. (1). e Schematic of a 40 × 40 ferroelectric capacitor array based on P(VDF-TrFE) ferroelectric polymers. The inset shows the structure of a ferroelectric capacitor unit. f The transient current versus electric field (I-E) curves obtained from 200 sampled units of the ferroelectric capacitor crossbar array. g Orientation of the ferroelectric capacitor domains in the crossbar array that was programmed according to the shape of East China Normal University logo. h The evolution of voltage pulse sequences and the transient output currents over time. Arrows indicate the orientation of the ferroelectric domains. The large displacement current peaks involving the polarization reversal only occur when the voltage pulse has a different polarity to that of the ferroelectric domain. Source data are provided as a Source Data file.

Fig. 3. In-memory differential computing for solving mathematical derivative functions.

a A schematic diagram showing how the domain configuration in 14 ferroelectric capacitors stores data with values varying from −7 to 7. Inset shows the function f(x)=−x, where ∆x = 1, a = −4 and b = 4. b A schematic diagram showing how the ferroelectric domains switching calculates the differential value. The upward (downward) domain switching is labeled in blue and red, respectively. c, d The evolution of transient currents (left) and integral charges (right) with time. In the case of (c), as time increases periodically, the number of capacitors with upward domain switching increases monotonically from 1 to 14 in steps of 1 (inset of c). In the case of (d), as time increases periodically, the number of capacitors with upward domain switching increases monotonically from 0 to 7 in steps of 1 and then remains constant at 7, while the number of capacitors with downward domain switching first remains constant at 7 and then decreases monotonically from 7 to 0 in steps of 1 (inset of d). e The parabolic function g(x)=x²-2x + 1. f The evolution of transient currents (left) and integral charges (right) as a function of time. As time increases periodically, the switching of domains computes g(0)-g(−1), g(1)-g(0), g(2)-g(1) and g(3)-g(2), respectively. g By dividing with the ∆x of 1, that is [g(0)-g(−1)]/[0-(−1)] = g’(−0.5), [g(1)-g(0)]/[1-0] = g’(0.5), [g(2)-g(1)]/[2-1] = g’(1.5) and [g(3)-g(2)]/[3-2] = g’(2.5), the domains switching gives the first-order derivative function g’(x) = 2x−2. The experimental measurements are repeated 12 times to exclude randomness. h The evolution of transient currents (left) and integral charges (right) with time. As time increases periodically, the domains switching calculates g’(0.5)-g’(−0.5), g’(1.5)-g’(0.5) and g’(2.5)-g’(1.5), respectively. i By dividing with the ∆x of 1, that is [g’(0.5)-g’(−0.5)]/[0.5-(−0.5)] = g”(0), [g’(1.5)-g’(0.5)]/[1.5-0.5] = g”(1) and [g’(2.5)-g’(1.5)]/[2.5-1.5] = g”(2), the domains switching gives the second-order derivative function g”(x) = 2. The experimental measurements are repeated 12 times to exclude randomness. Source data are provided as a Source Data file.

Fig. 4. In-memory differential computing for motion extraction.

Sketch of the biological frog retina (a) and ferroelectric capacitors as an in-memory differentiator (b) for motion information extraction. c These charts show the process of implementing frame differences using the ferroelectric in-memory differentiator. By inputting images that are encoded by programming domain configurations into the ferroelectric in-memory differentiator, the ferroelectric domain switching signals simultaneously give motion pixels. d Acquisition of frame difference of a basketball shot through the domain switching signals of the ferroelectric in-memory differentiator.

Fig. 5. In situ motion detection system consisting of the ferroelectric in-memory differentiator.

a Sketch of an in situ motion detection system comprising a camera to directly capture natural events and a ferroelectric capacitor crossbar array as the in-memory differentiator to isolate motion information. b The optical image of a 40 × 40 ferroelectric capacitor crossbar array hardware. c A schematic diagram showing how pixels in the image are encoded by voltage pulses and inputted to the ferroelectric capacitor crossbar array. d–g Four typical cases of pixel alteration and the corresponding transient currents. A positive polarization reversal (positive current bulge) is obtained when the white pixel follows a black pixel (d), the polarization reversal (current bulge) is absent when the white pixel follows the same pixel as a previous pixel (e) and when the black pixel follows the same pixel as a previous pixel (f), and a negative polarization reversal (negative current hump) is obtained when the black pixel follows a white pixel (g). Yellow color highlights the current hump. The cases of (d), (e, f) and (g) are defined for white, blue, and black pixels, respectively. h–i Two adjacent frames of images. j–k The compressed and binarized images with 8 × 10 pixels. l–m The moving pixels obtain by ideal computation and experimental ferroelectric domain switching signals. n The transient current response of the ferroelectric capacitor hardware during image (k) processing. Following the rule of (d–g), the ferroelectric domain switching signals in (n) give the motion image (m). Source data are provided as a Source Data file.

Fig. 6. Extraction of image differences between events over a large range of interval.

a A schematic diagram showing how a ferroelectric capacitor array is used to extract image differences. b A schematic diagram showing how a ferroelectric capacitor array is used to identify defective dies on a silicon wafer. c–f A schematic diagram showing how a ferroelectric capacitor array is used to assess the change in track direction. The track direction is to the right (closed switch) in (c) image and it is forward (open switch) in (d) image. If the track direction is changed from right to front, a clear image differences can be obtained using ferroelectric domain switching signals (e). However, if the track direction is always to the right, a clean blue image is then obtained without ferroelectric domain switching signals (f).