Memristor: Modelling and Applications Amit Kulkarni Nguyen Hoang

Content What is memristor? Prediction of memristor Mathematical equations Physical Implementation Pinched hysteresis loop SPICE model Write circuit Read circuit Challenges and Applications Summary 10-01-2012 Chalmers university of Technology DAT175 Topics in Electronic System Design

What is memristor? Two terminal passive electrical component Memorize the charge flow Change the resistance Symbol: 10-01-2012 Chalmers university of Technology DAT175 Topics in Electronic System Design

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 10-01-2012 Chalmers university of Technology DAT175 Topics in Electronic System Design

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. 10-01-2012 Chalmers university of Technology DAT175 Topics in Electronic System Design

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) 10-01-2012 Chalmers university of Technology DAT175 Topics in Electronic System Design

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). 10-01-2012 Chalmers university of Technology DAT175 Topics in Electronic System Design

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 10-01-2012 Chalmers university of Technology DAT175 Topics in Electronic System Design

SPICE model State equation:  10-01-2012 Chalmers university of Technology DAT175 Topics in Electronic System Design

SPICE model (1) Port equation:  10-01-2012 Chalmers university of Technology DAT175 Topics in Electronic System Design

SPICE model (2) Full model: 10-01-2012 Chalmers university of Technology DAT175 Topics in Electronic System Design

Write circuit Decision levels Circuit 10-01-2012 Chalmers university of Technology DAT175 Topics in Electronic System Design

Write circuit(1) Write logic – 1 Write logic – 0 Write 0 from 0, or 1 from 1? 10-01-2012 Chalmers university of Technology DAT175 Topics in Electronic System Design

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? 10-01-2012 Chalmers university of Technology DAT175 Topics in Electronic System Design

Write circuit(3) Applying to ideal case Where is max() 10-01-2012 Chalmers university of Technology DAT175 Topics in Electronic System Design

Read circuit  State perturbation may occur! IEEE/ACM International Conference 2009 (from HP) IEEE/ISCAS International Symposium 2011  State perturbation may occur! 10-01-2012 Chalmers university of Technology DAT175 Topics in Electronic System Design

Read circuit (1) State perturbation: State level changes while applying voltage for reading Memristor is charge-dependent How to avoid/reduce? Complementary-charge circuit 10-01-2012 Chalmers university of Technology DAT175 Topics in Electronic System Design

Read circuit (2) Influence of complementary charge on state stability 10-01-2012 Chalmers university of Technology DAT175 Topics in Electronic System Design

Read circuit (3) 500 reading operations: 500,000 times 10,000 times Δx = 0.0001 10,000 times Δx = 0.005 10-01-2012 Chalmers university of Technology DAT175 Topics in Electronic System Design

Read circuit (4) Outputs of logic 0 and 1: 10-01-2012 Chalmers university of Technology DAT175 Topics in Electronic System Design

Challenges of the research Control state stability For write and read circuits For other applications 10-01-2012 Chalmers university of Technology DAT175 Topics in Electronic System Design

Applications Non-volatile memory Crossbar switch LUT Up to 100Gbits/cm² Crossbar switch LUT 10-01-2012 Chalmers university of Technology DAT175 Topics in Electronic System Design

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 10-01-2012 Chalmers university of Technology DAT175 Topics in Electronic System Design

Thank you for your attention! 10-01-2012 Chalmers university of Technology DAT175 Topics in Electronic System Design