1. Memristor: Modelling and Applications
Amit Kulkarni Nguyen Hoang

2. Content What is memristor? Prediction of memristor
Mathematical equations
Physical Implementation
Pinched hysteresis loop
SPICE model
Write circuit
Read circuit
Challenges and Applications
Summary
Chalmers university of Technology DAT175 Topics in Electronic System Design

3. What is memristor? Two terminal passive electrical component
Memorize the charge flow
Change the resistance
Symbol:
Chalmers university of Technology DAT175 Topics in Electronic System Design

4. Leon Chua’s prediction of existence of Memristor
About 200 years ago 3 passive elements RLC.
Transistor can also expressed as Thevnin’s equivalent circuit and hence it is not a fundamental element.
1960s: Leon Chua - expert in non linear circuit theory based on math provable basis.
Based on non linear circuit theory, found something missing from basic circuit equations by generalizing the non linear systems
He called it memristor because it has resistance with memory.
1971- Published the paper: Memristor the missing ckt element.
People wondered which physical element can couple the charge and flux in ckt element.
Memristor is a passive (cannot induce net energy into ckt that they are connect to) element with state. The state(memroy) is expressed in terms of one or more state variables related to each other forming state equations.
Dr.Leon O. Chua University of California, Berkeley
Chalmers university of Technology DAT175 Topics in Electronic System Design

5. Mathematical equations of memristor
‘w’ is a state variable
Eqn1>Resistance “R(w,i)” is dependent on the state and the time.
Full equation of state?? Define function of i(t)
Eqn2>shows how the state varies w.r.t time
Any model showing the dependent on the state and that state evolving w.r.t time can represent the memristor.
Chalmers university of Technology DAT175 Topics in Electronic System Design

6. Physical implementation
Tio2 is the semiconductor with auto doped. TiO2-x remove one oxygen atom from it and that creates ‘n’ type doping, the vacancy that has created by the oxygen is positively charged. The vacancy is very slightly mobile, apply the electric field across the memristor to drag them towards left
Dr. R. Stanley Williams
HP Labs(Quantum science)
Chalmers university of Technology DAT175 Topics in Electronic System Design

7. State equations of implemented memristor
Small voltages produces enormous amount of electric field in nanoscale devices.
This produces non linearities in ionic transport. These non linearities are significant at the thin film edges. This causes the boundary region gradually decreases to zero. The whole phenomenon is modelled by the function f(x).
Chalmers university of Technology DAT175 Topics in Electronic System Design

8. Pinched hysteresis loop
Also called as bow-tie curve.
Memristor connected to a AC voltage source of A=1v and f=1Hz and 0.5Hz
Area of the lobes decreases with increase in frequency and attains linearity thus exhibiting the resistance property.
For high frequency, the time given to evolve the state(w) is low hence the boundary change is less hence resistance is still high.
Thus the area of the lobes is decreased.
Courtesy: Massimiliano Di Ventra, Yuriy V. Pershin, and Leon O. Chua. Publication: Circuit Elements With Memory: Memristors,Memcapacitors, andMeminductors
Chalmers university of Technology DAT175 Topics in Electronic System Design

9. SPICE model State equation: 
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10. SPICE model (1) Port equation: 
Chalmers university of Technology DAT175 Topics in Electronic System Design

11. SPICE model (2) Full model:
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12. Write circuit Decision levels Circuit
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13. Write circuit(1) Write logic – 1 Write logic – 0
Write 0 from 0, or 1 from 1?
Chalmers university of Technology DAT175 Topics in Electronic System Design

14. Write circuit(2) Express flux in terms of state variable Ideal case:
logic-1 at level 1
logic-0 at level 0
Where is the max(), defining the boundary?
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15. Write circuit(3) Applying to ideal case Where is max()
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16. Read circuit  State perturbation may occur! IEEE/ACM International
Conference 2009
(from HP) IEEE/ISCAS
International Symposium 2011
 State perturbation may occur!
Chalmers university of Technology DAT175 Topics in Electronic System Design

17. Read circuit (1) State perturbation:
State level changes while applying voltage for reading
Memristor is charge-dependent
How to avoid/reduce?
Complementary-charge
circuit
Chalmers university of Technology DAT175 Topics in Electronic System Design

18. Read circuit (2) Influence of complementary charge on state stability
Chalmers university of Technology DAT175 Topics in Electronic System Design

19. Read circuit (3) 500 reading operations: 500,000 times 10,000 times
Δx =
10,000 times
Δx = 0.005
Chalmers university of Technology DAT175 Topics in Electronic System Design

20. Read circuit (4) Outputs of logic 0 and 1:
Chalmers university of Technology DAT175 Topics in Electronic System Design

21. Challenges of the research
Control state stability
For write and read circuits
For other applications
Chalmers university of Technology DAT175 Topics in Electronic System Design

22. Applications Non-volatile memory Crossbar switch LUT
Up to 100Gbits/cm²
Crossbar switch
LUT
Chalmers university of Technology DAT175 Topics in Electronic System Design

23. Summary
Memristor can remember amount of charge goes through it via its varied resistance
SPICE model is available for circuit-level research
Read-write circuits are available
Challenge in applications: state stability
Vast of applications
Chalmers university of Technology DAT175 Topics in Electronic System Design

24. Thank you for your attention!
Chalmers university of Technology DAT175 Topics in Electronic System Design