Regular pulsing induced by noise in a monolithic semiconductor neuron Alexander S. Samardak1, Alain Nogaret1, Stephen Taylor1, Natalia B. Janson2, Alexander G. Balanov3, Ian Farrer4, David A. Ritchie4 1 Department of Physics, University of Bath, Bath BA2 7AY, UK 2 Department of Mathematics, University of Loughborough, Loughborough LE11 3TU, UK 3 Department of Physics, University of Loughborough, Loughborough LE11 3TU, UK 4 Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, UK Abstract. We report on the stochastic dynamics of a semiconductor neuron that uses the non-linear conductances of modulation doped semiconductors to compute electrical spikes. This GaAs-based neuron has pn wires which propagate and delay electrical pulses and a soma which sums and regenerates pulses through the positive feedback of a quantum tunnel amplifier vertically integrated with the wire. The neuron exhibits the property of excitability: it responds with a spike to a perturbation that exceeds a certain threshold value, and remains silent if the perturbation is small. When exciting the neuron with a sub-threshold periodic signal, a superimposed random noise is shown to enhance the coherence of the output pulse train. We perform a systematic study of stochastic resonance and coherence resonance as a function of excitation parameters and analyze output spectra using statistical tools. Keywords: artificial neuron, stochastic resonance, coherence resonance. PACS: 81.05.Ea, 85.30.De, 85.30.Mn dendrite at regular intervals along the axon to apply pulses and to probe the neuron response. The top n- In this paper, we study the stochastic dynamics of a type layer was etched prior to the evaporation of AuZn "semiconductor neuron". This GaAs-based device p-type contacts. Care was taken to avoid the top n- mimics the structure of a real neuron with its pn wires type contact diffusing into the p-type layer and thus acting as artificial nerve fibres and its tunnel amplifier shorting the pn junction. To this end the Ohmic contact acting as the decision centre of the neuron. The axon used was PdGe. This was alloyed at 210˚C giving a and dendrites propagate and delay electrical pulses diffusion length into the n-layer of about 20nm which while the soma regenerates pulses through the positive is less than the width of the n-type layer. After this feedback of a quantum tunnelling amplifier vertically process we observe rectification in the current – integrated with the pn wire. The neuron is excitable in voltage characteristics across the p-and n-contacts. that an above threshold signal is regenerated by tunnelling amplification prior to being transmitted into the axon. The neurons structure, shown in Fig.1, was fabricated from GaAs layers grown by MBE. The GaAs multilayer consists of a pn junction grown on FIGURE 1. The semiconductor neuron has dendrites, a top of a p+n+ tunnel layer. The three dendrites, axon soma and a 6mm long axon. The blown up picture shows the free standing pn-wire which carries electrical impulses. The and soma were fabricated by means of optical inset depicts the I-V characteristics of pn wires doped lithography and reactive ion etching. p-type and n- p=n=5×1016cm-3 (J1) and 5×1017cm-3 (J2) respectively. type Ohmic contacts were diffused at the end of each CREDIT LINE (BELOW) TO BE INSERTED ON THE FIRST PAGE OF EACH PAPER CP1199, 29th International Conference on the Physics of Semiconductors, edited by M. J. Caldas and N. Studart 2009 American Institute of Physics 978-0-7354-0736-7/09/$25.00 Downloaded 12 Aug 2010 to Redistribution subject to AIP license or copyright; see http://proceedings.aip.org/about/rights_permissions

To fabricate the soma the p+n+ tunnel layers were specifically to non-linear systems, where the output is etched away yielding free standing pn wires. At the not proportional to the input. soma, insulated tunnel layers give a small area pillar which applies positive feedback to the pn wire. The insert in Fig.1 shows that the wire is free standing and there are supporting bridges along the wire. The soma is biased between a contact made to the bottom p+ layer and another contact made on the top n-layer. We have applied short pulses and a random noise to the dendrites and measured the output Vout with the axon's contacts using a multifunctional DAQ card. Our neuron is subjected to input signals that reach two different dendrites: a sinusoidal signal and random noise. The sine amplitude remains constant while the amplitude of noise is being changed from 0 to 1V. The noise applied is a broadband signal containing a flat spectrum of frequencies like a white noise, but with non-zero mean. The tunnel amplifier (the soma) is in series with an inductance 10mH and a variable resistor and is biased by a dc voltage of 0.31V. This biases the soma near the peak of the current-voltage characteristic of the tunneling amplifier. At the peak, the soma is in a pre- firing state. A weak input signal can shift the tunnel FIGURE 2. Neuron response (top curve) to an input diode working point to the negative differential signal combining random noise (noisy signal) and sub-threshold sinusoidal signal (15 kHz). For clarity the noise resistance (NDR) region where the soma oscillates and periodic signal values are shown on different scales. with a frequency about 30 kHz and an amplitude of 200mV. In other words, we choose a very low Our neurons are a good example of a non-linear regeneration threshold, since a small perturbation will system, firing only when the electrical potential across induce positive feedback on the transmission line. a tunnel junction reaches a critical threshold. In such a The temporal dependences of both input signals, system, a weak input which fails to reach the threshold and the output signal, measured on the axon at 350um can be lifted above it by the injection of noise. from soma, are shown in Fig.2. If we only apply a If one applies only noise to the non-linear system periodic signal with sub-threshold amplitude of 0.2V without periodic perturbation, then we observe another without noise (Vn=0V) or with only a very faint noise, remarkable phenomenon called coherence resonance the soma is not activated. As a result, one only sees a (CR). CR is a phenomenon whereby noise alone residual signal response to the sine input. With generates a highly coherent response when applied to increasing noise, the neuron fires with increasing an excitable system. Under these conditions, the regularity up to a noise amplitude of Vn=0.59V. The coherence of output pulse trains depends non- latter is the "optimal" noise intensity at which the monotonically on noise intensity. spiking of the neuron is closest to being periodic. This The present results show that the neuron has corresponds to the most regular oscillations of this dynamic response analogue to biological neuron which neuron. At larger values of noise, the signal from the makes it suitable as a simulation tool for complex neuron appears more smeared out. This means the networks and for making powerful associative decrease of regularity in the neuron response. memories based on spiking networks. The observed phenomenon is called stochastic resonance and can be interpreted as the amplification of a weak sub-threshold periodic signal by noise, or the unmasking of the periodic signal contaminated by strong noise by means of a nonlinear device, which is This research is supported by the Leverhulme Trust the neuron in our case. Stochastic resonance applies (F/0035/1 N) and EPSRC (UK). Downloaded 12 Aug 2010 to Redistribution subject to AIP license or copyright; see http://proceedings.aip.org/about/rights_permissions

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