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Arithmetic Operations within Memristor-Based Analog Memory

Mika Laiho, Eero LehtonenMicroelectronics Laboratory, University of Turku

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Key Points

Be able to program the memristor to the reference resistance using the cyclincally programming scheme

Computing capability, such as addition, both on negative and positive analog conductance, is demonstrated

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Digital Memory verse Analog Memory

Digital memory (1-bit information depending on ON/OFF state, including SRAM, DRAM, PCRAM, MRAM, Flash, etc.)

Analog memory (many intermediate states between ON/OFF states)

Memoristor can be used for both digital and analog memory

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Memristor

Without programming threshold– Linearly programmed with charge flowing through

the device– AC readout for memory application– Pose high requirements on R/W cycles

With programming threshold – Nonlinear programmed with charge flowing

through the device– DC readout possible

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Memristor With Programming Threshold

Bipolar reversible and nonvolatile switching of nanoscale TiO2-x devices

J. J. Yang et al., Memristor switching mechanism for metal/oxide/metal nanodevices, Nature Nanotechnology, 2008, 3, 429-433

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Modeling Memristor

The window function

The time derivative of the state variable W

The current through the memristor

• ᵅ and ᵝ are fitting constants that are used to characterize the ON state• ᵡ and ᵞ are the fitting constants used to characterize the net electronic barrier when the memristor is switched OFF• a, b, p and q are constants depending on the physical properties of the memristor• w is the state variable of the memristor

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Simulated Memristor Characteristics

Device simulation based on SPICE model

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Simulated Memristor Characteristics

Device simulation based on SPICE model

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Memristor Analog Memory/Computing Circuit

VSSR

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Memory/Computing Circuit Simulation

V1

Vin

Imem

Ir

CT

W

Circuit simulation based on SPICE model

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Processing as Summation

Monitoring phase Programming phase

gm1 = gm4 + gm5.

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Processing as Invertor

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Processing as Universal Addition

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Conclusions

Memristors could be used as analog memories and for computing

A two-memristor configuration was proposed to be used as a memory element so that addition operations of both positive and negative numbers could be performed

Further study on performing multiplication and division is expected

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Limitations

Control circuits for programming the memristors is too complicated increasing design complexity

Many sequences are required leading to slow programming

The programming time is unpredictable