2. Memristors
L.O. Chua, “Memristor – The Missing Circuit Element,” IEEE Trans., 1971
( , )v M x i i
( , )
dx
f x i
dt
Resistor
v R i
Capacitor
q C v
Inductor
L i
Memristor
M q
3. Memristors are Real!
• 2008 Hewlett Packard
D.B. Strukov et al, “The missing memristor found,” Nature, 2008
2
( ) 1 ( )v ON
OFF
R
M q R q t
D
RON
ROFF
Voltage [V]
Current[mA]
5. Memristors are the Next Memory
• Dense
• Fast
• Nonvolatile
• Low power
• High endurance
6. Not Just Memory
• Logic circuits
• Analog circuits
• Neuromorphic systems
• Sensors
• New architectures
7. Why Use Memristors in Logic?
Integrating memristors
with standard logic
Logic within the
memory
Memristor layer
CMOS
layer
Beyond Moore
Save die area
More logic on die
Beyond Von-Neumann
Flexible
Save power, BW
9. Memristor Ratioed Logic (MRL)
• Voltage as logical state
• Memristors only as computational elements
S. Kvatinsky “MRL – Memristor Ratioed Logic,” CNNA 2012
ORAND
IN1
IN1
IN2IN2
OUT OUT
Hello, I am Shahar Kvatinsky and I’ve got the difficult assignment of separating you from lunch. I will talk today about logic design with memristors.
Messages:Passive elements, varying resistance – memristance1971 – chua – symmetryChanges due to current or flux1976 – memristive systems – internal state variable – equations (M, ohm)Basically – need to know – memory resistor, hysteresisMemristors are passive elements with varying resistance, also known as a memristance. These devices were conceived theoretically by Prof. Leon Chua in 1971 for symmetry reasons, comparing the three known electronic circuit fundamental elements – the resistor, the capacitor, and the inductor.Changes in the memristance depend upon the history of the device, namely, the total charge which passes through it, or, alternatively, the total flux in the device.The theory of memristors was extended to memristive systems by Chua and Steve Kang in 1976,adding an internal state variable connecting the memristance and the history of the device. The equations define a memristive system, M is the memristance of the memristor, its unit is Ohm, and it is depended in the current and the state variable x.Basically – all you need to understand for this talk is that a memristor is a resistor that changes its resistance according to its current. In other words, it is a resistor with hysteresis in its I-V curve.
Messages – 2008, HPLinear model – equation - RON, ROFFLater we’ll see not practicalIn 2008, Hewlett-Packard announced the fabrication of a working memristor. A linear ion drift model was proposed for describing the behavior of this memristor.The memristance of a linear ion drift memristor is shown here <CLICK>. where ROFF and RON are, respectively, the maximum and minimum resistance of the memristor.We will see later in this talk that this model is not practical for logic.Comment: µv is the average ion mobility, D is the memristor physical thickness, and q(t) is the total charge passing through the memristor. The linear ion drift model is the most commonly used memristor model, although practical memristors exhibit highly non-linear behavior.X = w/D
I will focus on memory and logic in this talkMemristors hold promise for use in diverse applications such as memory, logic, analog circuits, and neuromorphic systems. Different applications require different characteristics from the memristor. Understanding the desired characteristics for different applications can therefore assist device physicists in targeting the required behavior when fabricating memristive devices, potentially optimizing these devices for different applications. In this presentation, the desired characteristics for different applications are discussed from the viewpoint of the electronic circuit design process.
CMOS logic is good, so why bother with memristor logic?First reason – if the memristor-based memory is there, we can do logic in the same price! We can break the conventional Von Neuman architecture to new architecture for calculation inside the memory. It can be done in parallel and in a dynamic manner.Second reason – we can use memristor-based logic as a redundant logic layer for backup or fixing soft errors for example and to save die area – ECC, Die area, etc.And the last reason – it is fun and interesting, after all I am in the academia…
Before we begin with the logic gates themselves, let’s define the polarity of a memristor. The polarity is represented by the thick line in the memristor symbol. When current is getting inside the thick line, the resistance of the memristor is decreased and when current is flowing outside the thick line the resistance is increased.IntoOut of
In this logic family, the memristors are not used as a memory device, but as a computational element and as a variable resistor.This logic family consists two memristors per gate, implementing OR and AND logic gates. The difference between the gates is the polarity of the memristorsMemristor characteristic does not matterInitial state of memristors do not matter
Initial state of memristors does not importantCases 2 and 3 are symmetrical!
Before we begin with the logic gates themselves, let’s define the polarity of a memristor. The polarity is represented by the thick line in the memristor symbol. When current is getting inside the thick line, the resistance of the memristor is decreased and when current is flowing outside the thick line the resistance is increased.IntoOut of
An animation of the process.Important things to note:Command flush – penalty for utilization & powerMultiple units of memory to hold all requestsCache – If we decided to lose it the switch could be made earlier (smaller penalty) but at the cost of more switches
An animation of the process.Important things to note:Command flush – penalty for utilization & powerMultiple units of memory to hold all requestsCache – If we decided to lose it the switch could be made earlier (smaller penalty) but at the cost of more switches
An animation of the process.Important things to note:Command flush – penalty for utilization & powerMultiple units of memory to hold all requestsCache – If we decided to lose it the switch could be made earlier (smaller penalty) but at the cost of more switches
Before we begin with the logic gates themselves, let’s define the polarity of a memristor. The polarity is represented by the thick line in the memristor symbol. When current is getting inside the thick line, the resistance of the memristor is decreased and when current is flowing outside the thick line the resistance is increased.IntoOut of
Before we begin with the logic gates themselves, let’s define the polarity of a memristor. The polarity is represented by the thick line in the memristor symbol. When current is getting inside the thick line, the resistance of the memristor is decreased and when current is flowing outside the thick line the resistance is increased.IntoOut of
