1. Arithmetic Operations within Memristor-Based Analog Memory
Mika Laiho, Eero Lehtonen
Microelectronics Laboratory, University of Turku

2. 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

3. 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

4. Memristor Without programming threshold With 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

5. 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,

6. Modeling Memristor The time derivative of the state variable W
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

7. Simulated Memristor Characteristics
Device simulation based on SPICE model

8. Simulated Memristor Characteristics
Device simulation based on SPICE model

9. Memristor Analog Memory/Computing Circuit
VSSR

10. Memory/Computing Circuit SimulationV1 CT
Vin
Imem W Ir
Circuit simulation based on SPICE model

11. Processing as Summation
Programming phase
Monitoring phase
gm1 = gm4 + gm5.

12. Processing as Invertor

13. Processing as Universal Addition

14. 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

15. 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