A memristive spiking neuron with firing rate coding

Abstract

Perception, decisions, and sensations are all encoded into trains of action potentials in the brain. The relation between stimulus strength and all-or-nothing spiking of neurons is widely believed to be the basis of this coding. This initiated the development of spiking neuron models; one of today's most powerful conceptual tool for the analysis and emulation of neural dynamics. The success of electronic circuit models and their physical realization within silicon field-effect transistor circuits lead to elegant technical approaches. Recently, the spectrum of electronic devices for neural computing has been extended by memristive devices, mainly used to emulate static synaptic functionality. Their capabilities for emulations of neural activity were recently demonstrated using a memristive neuristor circuit, while a memristive neuron circuit has so far been elusive. Here, a spiking neuron model is experimentally realized in a compact circuit comprising memristive and memcapacitive devices based on the strongly correlated electron material vanadium dioxide (VO2) and on the chemical electromigration cell Ag/TiO2-x /Al. The circuit can emulate dynamical spiking patterns in response to an external stimulus including adaptation, which is at the heart of firing rate coding as first observed by E.D. Adrian in 1926.

Keywords: memristive devices; negative differential resistor; neural coding; neuromorphic systems; spiking neuron.

Figure 1

Response to a stimulation principle: (A) Schematic of a single neuron, which can be divided into three functional parts: Dendrites, collect signals from other neurons; cell body (soma), the central processing unit of a neuron; axon, neuronal output stage. (B) Relationship between firing rate of a neuron and the strength of input stimulation reflecting the response to a stimulation principle as proposed by E. D. Adrian in 1926 (Adrian, , ; Maass and Bishop, 2001).

Figure 2

Circuit scheme used to emulate neuronal functionalities: The circuit consists of an integrator circuit (blue) based on a negative differential resistor and a memcapacitor C_M, as well as on an output branch with a diode D in series with two ohmic resistors R₁ and R₂ (red) which deliver the spikes v_out(t) from the oscillating voltage u(t). Inset: Typical oscillation for a constant input current of 0.25 mA. While the constant voltage source V_B shifts the base voltage to a negative value, the voltage divider with the diode D cause a constant output voltage v_out(t) in an interval (labeld as t_ref) in which u(t) is smaller than the build-in voltage of the diode. The used device parameters of the circuit were R₁ = 47 kΩ, R₂ = 10 kΩ, C_M = C₀ = 0.068 μF, V_B = −3.5 V.

Figure 3

Electrical characteristics of the VO₂ device: (A) Resistance versus temperature characteristic. Inset of (A): X-ray 2θ-ω scan of the VO₂ film on a TiO₂ (001) substrate measured with Cu K_α radiation. The observed peaks correspond to TiO₂ (002) and to VO₂ (40-2)_M1 (insulating phase, space group P2₁/c, a_M1 = 5.743 Å, b_M1 = 4.517 Å, c_M1 = 5.375 Å, and β_M1 = 122.618°) (B) Current voltage characteristic of a lateral VO₂ device together with a schematic sketch of the device structure. In all sub-figures indicating the red arrows the heating cycle and the blue arrows showing the cooling direction.

Figure 4

Experimental realization of a memcapacitor: (A) Schematic drawing of the memcapactitive circuit including a memristive device. (B) Calculated impedance phase φ_RM||C2 between the memristive device and the capacitor C₂ as function of the resistance R_M.

Figure 5

Electrical characteristics of the memristive device: (A) Measured I-V curve of an Ag-doped TiO_2-x -based memristive device together with a sketch of the layer sequence of this cell. A current compliance of 0.1 mA has been set. (B) Measured resistance variation of the device by applying 2 ms voltage pulses with an amplitude of 10 V. The dashed red lines show the desired memcapacitive range obtained from Figure 4B. (C) Distribution of the set voltage obtained from 620 identically voltage sweeps using a current compliance of 0.1 mA. The red curve is a Gaussian data fit.

Figure 6

Emulation of fire frequency coding: (A) Circuit layout to emulate firing frequency coding. In contrast to Figure 2 C_M was replaced by a constant capacitance C₀. (B) Recorded spike pattern for different current inputs. (C) Measured oscillation frequencies as function of the input current i(t). I_Θ denotes the threshold value for the spike initiation. Parameters used for the circuit: R₁ = 47 kΩ, R₂ = 10 kΩ, C₀ = 0.068 μF, V_B = −3.5 V.

Figure 7

Emulation of adaptation: (A) Measured spike pattern for a constant current input based on a memcapacitance C_M(t). (B) Layout of the investigated circuit which corresponds to the one depicted in Figure 2. (C) Characteristics of two individual spikes and corresponding phase diagram (D), where the insets show the initial phase of the spikes. Parameters used for the circuit: R₁ = 1MΩ, R₂ = 47kΩ, C₁ = 0.165μF, C₂ = 0.068μF, V_B = −5.5 V.