12-07-2013, 01:53 PM
Memristor based multilevel memory
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INTRODUCTION
History
For nearly 150 years, the known fundamental passive circuit elements were limited to the capacitor (discovered in 1745), the resistor (1827), and the inductor (1831). Then, in a brilliant but underappreciated 1971 paper, Leon Chua, a professor of electrical engineering at the University of California, Berkeley, predicted the existence of a fourth fundamental device, which he called a memristor. He proved that memristor behavior could not be duplicated by any circuit built using only the other three elements, which is why the memristor is truly fundamental.
Memristor is a contraction of “memory resistor,” because that is exactly its function to remember its history. A memristor is a two-terminal device whose resistance depends on the magnitude and polarity of the voltage applied to it and the length of time that voltage has been applied. When you turn off the voltage, the memristor remembers it’s most recent resistance until the next time you turn it on, whether that happens a day later or a year later.
Chua discovered a missing link in the pair wise mathematical equations that relate the four circuit quantities-charge, current, voltage, and magnetic flux-to one another. These can be related in six ways. Two are connected through the basic physical laws of electricity and magnetism, and three are related by the known circuit elements: resistors connect voltage and current, inductors connect flux and current, and capacitors connect voltage and charge. But one equation is missing from this group: the relationship between charge moving through a circuit and the magnetic flux surrounded by that circuit.
Working
If a positive voltage is applied to the top electrode of the device, it will repel the (also positive)oxygen vacancies in the TiO2-xlayer down into the pure TiO2 layer. That turns the TiO2 layer into TiO2- x and makes it conductive, thus turning the device on. A negative voltage has the opposite effect: the vacancies are attracted upward and back out of the TiO2, and thus the thick- ness of the TiO2 layer increases and the device turns off.
The oxygen deficiencies in the TiO2-x manifest as “bubbles” of oxygen vacancies scattered throughout the upper layer. A positive voltage on the switch repels the (positive)oxygen deficiencies in the metallic upper TiO2- x layer, sending them into the insulating TiO2layer below. That causes the boundary between the two materials to move down, increasing the percentage of conducting TiO2- x and thus the conductivity of the entire switch. The more positive voltage is applied, the more conductive the cube becomes.
Bow Ties:
Leon Chua’s original graph of the hypothetical memristor’s behavior is shown at top right; the graph of R. Stanley William’s experimental results are shown below. The loops map the switching behavior of the device: it begins with a high resistance, and as the voltage increases, the current slowly increases. As charge flows through the device, the resistance drops, and the current increases more rapidly with increasing voltage until the maximum is reached. Then, as the voltage decreases, the current decreases but more slowly, because charge is flowing through the device and the resistance is still dropping. The result is an on-switching loop. When the voltage turns negative, the resistance of the device increases, resulting in an off-switching loop.
Resonant Tunnelling Diode Memristor
1994, F. A. Buot and A. K. Rajagopal demonstrated that a 'bow-tie' current-voltage (I-V) characteristics occurs in AlAs/GaAs/AlAs quantum-well diodes containing special doping design of the spacer layers in the source and drain regions, in agreement with the published experimental results This 'bow-tie' current-voltage (I-V) characteristic is sine qua non of a memristor although the term memristor is not explicitly mentioned in their papers. No magnetic interaction is involved in the analysis of the 'bow-tie' I-V characteristics.
3-Terminal Memristor
Although the memristor is defined in terms of a 2-terminal circuit element, there was an implementation of a 3-terminal device called a memistor developed by Bernard Widrow in 1960.Memistors formed basic components of a neural network architecture called ADALINE developed by Widrow and Ted Hoff the memistor was described as follows:
Like the transistor, the memistor is a 3-terminal element. The conductance between two of the terminals is controlled by the time integral of the current in the third, rather than its instantaneous value as in the transistor.
Array Based Multilevel Memory of Memristor
The proposed method has the operating point of the memristor be maintained its desired location (or resistance value) utilizing a set of pre-determined multiple resistance levels. Fig.2.4.1 shows the basic idea of the proposed method, where the resistance array to be referenced and the memristor to be programmed (tuned) are shown.
The goal is to have the memristor keep any of the resistance level selected from the resistance array. If a predetermined magnitude of the current pulse Is (t) is applied to the resistance array, different levels of voltages V k will appear at each node of the resistance array. The same current pulse is (t) is also applied to the memristor.
Advantages
When you turn off the voltage, the memristor remembers its most recent resistance until the next time you turn it on, whether that happens a day later or a year later. This freezing property suits memristors brilliantly for computer memory. The ability to indefinitely store resistance values means that a memristor can be used as a nonvolatile memory. That might not sound like very much, but go ahead and pop the battery out of your laptop, right now—no saving, no quitting, nothing. You’d lose your work, of course. But if your laptop were built using a memory based on memristors, when you popped the battery back in, your screen would return to life with everything exactly as you left it: no lengthy reboot, no half-dozen auto-recovered files.
disadvantages
Despite many favorable features, memristors have several weaknesses in practice. One weakness comes from the nonlinearity in the Ø vs. q curve which makes it difficult to determine the proper pulse width for achieving a desired resistance value.
If the nonlinearity is spatially variant in the die of a chip which is common in the fabrication process, the difficulty could be very serious. Another difficulty comes from the property of the memristor which integrates any kind of signals including noise that appeared at the memristor and results in the memristors being perturbed from its original pre-set values.
Thus, the resistance can be interpreted as the slope at an operating point on the Ø-q curve. If the Ø-q curve is nonlinear, the resistance will vary with the operating point. For instance, if the Ø-q curve is the nonlinear function Shown in Fig. 3.2.1, its small-signal resistance can be obtained by re-plotting it as a function of Øq in the R vs .Ø plane as in Fig. 3.2.2.Since the flux Ø is obtained by integrating the voltage, the resistance of the memristor can be controlled by applying a voltage signal across the memristor.
CONCLUSION
The reference resistance array-based multilevel memristor memory is proposed in this paper. The idea has been implemented with two circuits namely the write-in and the read-out circuits. Simulation of the write-in circuit shows that the memristors memorize the desired discrete resistance levels regardless of their characteristic differences. In read-out simulation, contents of the memristors move toward their original values from the deviated ones whenever the read-out processing is performed.
The proposed multilevel idea of the memristor together with its intrinsic feature of small size should make the memristor to be a powerful memory device. Also, if the number of multilevel of memory is increased, the memristor could be an ideal element for synaptic weight implementation since the synaptic multiplication can be performed simply by Ohm’s law
V=IR in the memristor.