Low-Power Microwave Relaxation Oscillators Based on Phase-Change Oxides for Neuromorphic Computing

Neuro-inspired computing architectures are one of the leading candidates to solve complex, large-scale associative learning problems. In addition to the widely studied spiking neural network architecture, other neuro-inspired architectures, such as the oscillatory neural network, can be used to solve such special purpose computing problems. In both cases, voltage- or current-controlled relaxation oscillators are considered a minimal representation of neurons for hardware implementations. For an oscillatory neural-network architecture, such oscillators should demonstrate synchronization and coupling dynamics to achieve collective learning behavior, in addition to desirable individual characteristics such as scaling, power, and performance. To this end, we propose the use of nanoscale, epitaxial heterostructures of phase-change oxides and oxides with metallic conductivity as the fundamental unit of a low-power, tunable electrical oscillator capable of operating in the microwave regime. We perform simulations to show that an optimized heterostructure design with low thermal boundary resistance can result in an operation frequency of up to 3 GHz and a power consumption as low as 15 fJ/cycle with rich coupling dynamics between the oscillators on a 100-nm channel. This study provides an alternative device design of tunable relaxation oscillators for neuromorphic computing applications.

Figure 1

Oscillatory neural network circuit and implementations. (a) Circuit of a four-oscillator ONN with capacitor coupling, (b) Schematic of pattern matching ONN implementation. Each pixel is interpreted as a current input to the corresponding oscillator. The synchronized phase relationship is analyzed and compared to the memorized pattern. A degree of match (DOM) is introduced to adjust the matching accuracy; (c) Schematic of vertex coloring ONN implementation. Adjacent graphs are computed as coupled oscillators. All oscillators are synchronized at certain phases, which are related to different colors.

Figure 2

Device structure, circuit diagram, and comparison with other oscillators. (a) Schematic of the typical ${\mathrm{VO}}_2$ electrical oscillator, where the ${\mathrm{VO}}_2$ channel is connected in series to a known resistor and the Joule heating in the series resistor adds to the extraneous power consumption. (b) Schematic of the proposed ${\mathrm{VO}}_2$-based bilayer electrical oscillator with ${\mathrm{SrRuO}}_3$ as the second layer. The bilayer is connected in parallel to a capacitor and a current source is used to inject current into the device. (c) Schematic of the circuit diagram for the proposed oscillator device. (d) Comparison of the proposed ${\mathrm{VO}}_2$ relaxation oscillator with competing oscillators.

Figure 3

Operation mechanism of the bilayer oscillator. (a) Time-dependent variation of voltage and temperature of the MIT device for the highest achievable oscillation frequency of 3 GHz; the capacitance used is C = 1 pF. The different operating critical points within an oscillation are noted as A, B, C, and D and are discussed in (b). The inset shows the power spectrum of the voltage oscillations that shows a dominant frequency of 3 GHz. (b) Simulated voltage-current (V-I) curve of the oscillatory cycle during the sustained oscillations in the device. The four stages of operation of the oscillator are charging, heating, discharging, and cooling. The stages are represented in a clockwise manner with the lettering scheme used in the V-I curve corresponding to each stage described in (a). The stages are separated by four critical points: A, B, C, and D. A and C represent the onset of the charging and discharging of the capacitor, respectively, while B and D represent the onset of heating and cooling, respectively.

Figure 4

Tunability of the bilayer oscillator. (a) Current-Capacitance phase diagram of the operating regimes of MIT-based electrical oscillator. Region IV depicts fully sustained oscillations with a frequency range from 0 to 3 GHz, time evolution of the voltage across the MIT device after the current is applied is characterized by: I, no oscillation; II, one oscillation; III, damped oscillations; IV, sustained oscillations; (b) The effects of the resistances of metallic oxide and the MIT layer on the oscillator operation. The dominant parameters controlling the oscillation frequency in region A are R_M and R_H, and in region B are R_L and R_H. (C = 1000 fF, I = 0.2 mA) (c) Frequency tunability by current and capacitance, C = 100, 1000, and 10 000 fF; current ranges from I_min to I_max.

Figure 5

Synchronization characteristics of coupled bilayer oscillators. (a) Schematic of the circuit diagram for two bilayer electrical oscillators connected in series for the synchronization studies. (b) The phase diagram of the synchronization characteristics between the two oscillators for different driving phases (difference in drive current) and coupling strengths (coupling capacitance). One can notice the formation of the Arnold's tongue demonstrating the region where synchronization can be easily achieved and the oscillations lock in the same frequency even if they started with different frequencies. (c) Simulated voltage oscillations for two oscillators synchronizing or remaining out of sync with each other. The depicted time span is 10 to 15 ns. The inset shows the power spectrum of the oscillations for the two oscillators, which are locked in different frequencies when out of sync. (d) Phase maps for different I₁ and C_i combinations corresponding to (c) from 10 to 50 ns.

Figure 6

The temperature-dependent resistivity of ${\mathrm{VO}}_2$. We use different transition temperatures for heating and cooling cycles as expected for a first-order phase transition. The resistance-temperature relationship used in the simulation is shown here.

Figure 7

Temperature profile for the cross section of the channel. The channel dimensions are length = 1 μm, width = 1 μm, thickness of ${\mathrm{VO}}_2$ = 30 nm, and thickness of ${\mathrm{SrRuO}}_3$ = 20 nm (V = 1.5 V, t = 10 ns).

Figure 8

Capacitor and current tunability and power spectrum near the highest frequency region. (a) Frequency tuned by capacitance at fixed I₀ = 2 mA. (b) Frequency tuned by current at fixed C = 100 fF.