Simplified description of dynamics in neuromorphic resonant tunneling diodes.

Abstract

[eng] ABSTRACT In this article, the standard theoretical model accounting for a double barrier quantum well resonant tunneling diode (RTD) connected to a direct current source of voltage is simplified by representing its current-voltage characteristic with an analytically approachable, anti-symmetric N-shaped function. The time and variables involved are also transformed to reduce the number of parameters in the model. Responses observed in previous, more physically accurate studies are reproduced, including slow-fast dynamics, excitability, and bistability, relevant for spiking signal processing. A simple expression for the refractory time of the excitable response is derived and shown to be in good agreement with numerical simulations. In particular, the refractory time is found to be directly proportional to the circuit's intrinsic inductance. The presence or absence of bistability in the dependence of the parameters is also discussed thoroughly. The results of this work can serve as a guideline in prospective endeavors to design and fabricate RTD-based neuromorphic circuits for power and time-efficient execution of neural network algorithms. Nanoscale resonant tunneling diodes have a potential application as fundamental units (i.e., nodes) in spiking neuromorphic processors given their locally negative differential conductance, small size, and high frequency. In prior theoretical studies,1-3 a resonant tunneling diode connected to DC voltage has been demonstrated as a class-2 excitable spike generator (i.e., excitability is achieved when the circuit is biased in proximity to an Andronov-Hopf bifurcation4). In these works, the non-ohmic current-voltage characteristic is represented by Schulman's formula5 that, while physically accurate, is also analytically complex. Here, a more simple, anti-symmetric, N-shaped current-voltage characteristic, made by a linear function minus a sigmoid, is used instead. This, together with the normalization of the time and variables involved in the equations, provides a simplified model with a reduced number of parameters that reproduces most of the typical responses reported in the works mentioned above. The simplified model also allows for an approachable description of the equilibrium solutions and their transitions in terms of the parameters on the analytical, numerical, and geometrical basis. In particular, the model may or may not exhibit a coexistence of fixed-value response with self-oscillations (i.e., bistability), which represents a hindrance for the purpose of excitable spike generation. Based on an adiabatic approximation and slow-fast dynamics, an analytically simple expression for the refractory time (i.e., the duration of the excitable spike) is integrated. This expression is shown to be directly proportional to the circuit's intrinsic inductance and is in good agreement with numerical simulations.