Reconfigurable Stochastic Neurons Based on Strain Engineered Low Barrier Nanomagnets

Abstract

Stochastic neurons are efficient hardware accelerators for solving a large variety of combinatorial optimization problems. "Binary" stochastic neurons (BSN) are those whose states fluctuate randomly between two levels +1 and -1, with the probability of being in either level determined by an external bias. "Analog" stochastic neurons (ASNs), in contrast, can assume any state between the two levels randomly (hence "analog") and can perform analog signal processing. They may be leveraged for such tasks as temporal sequence learning, processing and prediction. Both BSNs and ASNs can be used to build efficient and scalable neural networks. Both can be implemented with low (potential energy) barrier nanomagnets (LBMs) whose random magnetization orientations encode the binary or analog state variables. The difference between them is that the potential energy barrier in a BSN LBM, albeit low, is much higher than that in an ASN LBM. As a result, a BSN LBM has a clear double well potential profile, which makes its magnetization orientation assume one of two orientations at any time, resulting in the binary behavior. ASN nanomagnets, on the other hand, hardly have any energy barrier at all and hence lack the double well feature. That makes their magnetizations fluctuate in an analog fashion. Hence, one can reconfigure an ASN to a BSN, and vice-versa, by simply raising and lowering the energy barrier. If the LBM is magnetostrictive, then this can be done with local (electrically generated) strain. Such a reconfiguration capability heralds a powerful field programmable architecture for a p-computer, and the energy cost for this type of reconfiguration is miniscule.

Figures (6)

• Figure 1: (a) Potential energy as a function of the in-plane magnetization orientation in a magnetostrictive nanomagnet shaped like an elliptical disk with small eccentricity. (b) Potential energy as a function of the in-plane magnetization orientation when the nanomagnet is subjected to uniaxial stress along the major axis such that the sign of the product of the stress and the magnetostriction is negative. The inset shows the nanomagnet and the magnetization orientation, with $\theta$ being the angle subtended by the magnetization with the nanomagnet's major axis.
• Figure 2: The potential energy profile in a Co nanomagnet shaped like an elliptical disk as function of the angle $\theta$ subtended by the magnetization with the major axis. The results are shown for different stress values. The quantity $E$ is calculated from Equation (1) and $E_{min}$ is the minimum value of $E$. The nanomagnet has major axis = 100 nm, minor axis = 99 nm and thickness = 5 nm.
• Figure 3: Methodology to reconfigure a BSN into an ASN and vice versa. Applying a gate voltage of the right polarity will generate the right type of biaxial strain in the poled piezoelectric region underneath the nanomagnet. This strain will be transferred to the nanomagnet and it will lower the energy barrier in the latter, making its magnetization fluctuate in an analog manner rather than a binary manner. We can build a magnetic tunnel junction (MTJ) on top of the nanomagnet which will act as its soft layer. This MTJ will be a fluctuating resistor that can be transformed from a BSN to an ASN by turning on the gate voltage to generate strain.
• Figure 4: Temporal fluctuations in the magnetization component directed along the major axis of the nanomagnet $\left ( m_y \right )$ at different values of stress. Note that the behavior gradually transitions from BSN to ASN with increasing stress as the energy barrier within the nanomagnet is progressively depressed.
• Figure 5: (a) Gate control over the barrier height (blue dashed line to red solid line) of each individual memory cell to equalize memory retention and hence reduce device-to-device variability in a memory array. (b) Gate control over sections of memory fabric to emulate memory hierarchy in terms of retention time-scales through barrier height modulation (color coded as light to dark red boxes and corresponding barrier heights), e.g. $\sim \mu s$, $\sim s$, $\sim$ years in a single integrated fabric