Arithmetic Operations within
Memristor-Based Analog Memory
Mika Laiho, Eero Lehtonen
Microelectronics 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 current through the memristor
The time derivative of the state variable W
The window function
• 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
CT
Vin
Imem
W
Ir
Circuit simulation based on SPICE model
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Processing as Summation
Programming phase
Monitoring 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

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