Ron Neale returns to The Memory Guy blog to discuss a “Universal Law” about memory elements and selectors that was presented by CEA Leti at the IEEE’s 2019 IEDM conference last December.
At IEDM 2019 D. Alfaro Robayo et al presented a paper titled: Reliability and Variability of 1S1R OxRAM-OTS for High Density Crossbar Integration that had a rather interesting claim of a “Universal Law”. It is possible that some links to the past might help to provide an explanation for this law. The law states that the resistance of each component of a memory cell is the same for a given programming current, even if the memory and threshold switch selector, are made from significantly different materials. In the paper’s example the memory is an HfO ReRAM and the threshold switch is a chalcogenide-based composition.
Early work on chalcogenide-based phase change memory (PCM) and threshold switches provided models for their operation. The CNP model for PCM memory operation that I referred to in an earlier post, explained that the post-threshold switching conducting state, prior to any crystallization, has the electrical characteristics of a constant current density filament, i.e. constant voltage (Vc) for increasing and decreasing current. This state’s I-V characteristic was also observed in chalcogenide threshold switches or selectors without crystallization.
In the CNP model the post-threshold switching conducting filament is so hot that, soon after it is established, crystals start to grow in the lower-temperature region around it. As the annulus of crystals grows and bridges the inter-electrode gap this annulus takes current away from the filament. This has the effect of reducing the size of the filament, facilitating the further growth of crystals radially inwards towards the higher-temperature filament. The process continues until, finally, the filament is extinguished and all of the applied current flows in the cylindrical crystal annulus. The important point is that all of this growth occurs at a constant filament voltage, and this means that the final resistance will be approximately equal to Vc/I. The memory programmed resistance becomes a linear function of current, i.e. a straight line.
The above figure illustrates voltage as a function of time for a chalcogenide-based threshold switch “TS”, and a PCM element. In this diagram, the constant voltages for the conducting states of the PCM (Vcm) and the threshold switch (Vct) were almost identical, in the range ~0.5V to 1 V. The important point in relation to the “Universal law” is that threshold switches of a similar composition (with some doping additions) also had an I-V characteristic with the same constant voltage in the conducting state, the signature of a constant current density filament.
This would mean that, for two chalcogenide-based devices in series in a memory cell, the conducting-state resistance of the threshold switch would always be the same as the final programmed resistance of the PCM. The Alfaro Robayo paper’s “Universal Law” is always obeyed, even if the devices were measured or programmed separately with the same currents.
A trailing edge on the programming pulse would guarantee that the core region would be filled in and the “Universal Law” even more accurately obeyed. This is because as the tiny remnant of the molten column conducting the holding current (Ih) is finally extinguished that amorphous material is likely to be quenched into its high resistance amorphous state. If that happens there will be a small error in the value of the final resistance when compared with anticipated Vc/Ip.
(Note while the constant voltage was clear on the early device I-V characteristics, the significantly smaller process geometries of modern devices cause the resistance of the electrodes to become important as it is added as a significant series resistance in the I-V characteristics. Despite this change, extrapolation of the combined characteristics to zero current indicate a constant voltage value. Furthermore some modern PCM devices have one electrode consisting of crystallized memory material which acts as a massive nucleus for the crystal growth for the SET state of the memory, with the growing crystal of the SET state tracking a reducing-in-size hotspot, as the SET current is reduced, to make contact with the second electrode. There is no obvious reason why that type of device should follow the Universal Law in the manner of the CNP model described in the earlier paragraphs of this article).
The IEDM 2019 paper’s observation of this same “Universal Law” for a chalcogenide-based threshold switch in series with an OxRAM HfO memory element might suggest that a constant current density mechanism, or some other effect, is at work in the HfO, with a very similar Vc.
The common factor between the two different memory types is that HfO has a group VI element from the periodic table, as do the chalcogenide glasses in PCM. This might tempt one to suggest the soft dielectric breakdown of HfO is the same as is observed in the chalcogenide glasses, resulting in the same constant voltage, constant current density conducting state. This theory is supported, in part, by the fact that the pre-switching current of HfO is very similar to that of the chalcogenides, and that both are caused by Poole-Frenkel emission followed by Tunnelling/Schottky field emission. (For pure HfO, Schottky field emission would require voltages an order of magnitude higher than the 2 volts available in a modern memory cell without some degree of field localisation).
Even if that premise is accepted, to match the CNP model would also require conducting crystals or other conducting material to grow around the filament, with the added need for the voltages to be the same, as required by the “Universal Law”. The melting point of HfO is above 2,000 degrees C so it is unlikely that a molten column forms the conducting state.
If the “Universal Law” requires a constant current density filament, one way that it could be achieved would be something that I will characterise as an inverse CNP (i-CNP) effect. In this model the non-volatile conducting state grows radially outwards, illustrated in the figure above, rather than growing radially inwards around the conducting column. An important difference between CNP and i-CNP is that, with i-CNP, the constant current density appears as the end point of the programming operation. The form of the I-V characteristics immediately after threshold switching is not important.
In this figure (a) and (b) illustrate two possible options for the memory’s condition after it has been Formed and Reset. In (a) the tip of the Formed conducting column is shown with the material between it and the electrode returned to a nearly-pure HfO composition, while in (b) the column has remnants of enriched and conducting HfO left behind after Forming and Reset.
The i-CNP model starts with the initial breakdown of the region between the electrode and the Reset region that may be caused by either of two mechanisms as illustrated in (c) and (d). This could be the action shown in (c), where the breakdown follows the creation of a single region of enriched HfO by electromigration after dielectric breakdown from conduction along grain boundaries in the HfO which has crystallized after Reset. The alternative, as illustrated in (d), is that the material breaks down along a percolation path formed by the enriched debris.
However it is formed, from that point forward with the continuous application of the programming current, the enriched conducting column of HfO (with many oxygen vacancies), expands radially, pushing ahead of it a cylindrical annulus of oxygen-enriched material, as illustrated in (c) and (d).
At some point the current density (J) in the now-conducting region of a single or multiple filaments reaches a minimum value (Jm) where the radial growth ceases. This minimum value is always the same irrespective of the programming current (Ip), and creates a conducting filament with a resistance value of Vc/Ip. When a memory element and selector are stacked the added external series resistance will be the same.
The conducting state could be established in either of two ways: thermal gradient or electromigration. A conical shape to the tip or surface of the Hf-enriched volume, or multiple filaments or nano-dendrites, would tend to favour a purely electromigration-driven process and a more simple link to that as the cause.
If my version of the i-CNP model is correct it does not answer the question: “Why are the constant voltages the same, or very close to each other?” This is an essential requirement for obtaining the same resistance values and fulfilling the requirements of a “Universal Law”.
The original HfO films on the memory stack are of the order 10nm thick and the voltage across the device in its conducting state appears to be of the order 1 volt. If we make an allowance for a reduction in effective thickness as a result of Forming by the enriched layer, then a voltage in the same range as the chalcogenide does not appear to be unreasonable.
For the moment, until further experimental evidence is available, a better option might be to consider the same values of the voltage a matter of good fortune.
Contact or junction effect.
Using that idea of a single conducting column or multiple nano-dendrites growing to bridge the inter electrode gap there might be a more highly-speculative explanation which could lead to a clamping voltage of the order 0.5V on the HfO memory device during act of programming.
As the conducting column or nano-dendrites reach the electrode a constant voltage contact barrier of some type is formed. This would mean that as more filaments grow, or as a single one expands, the I-V characteristics tend to move towards a certain current – the programming current Ip – with a constant contact voltage, meeting the Vc/Ip requirement of the universal law.
Such a model makes it unnecessary to know the conducting state immediately after switching, other than the fact that it must provide a sufficient current density to allow the growth of the conducting column or nano-dendrites by driving out the oxygen.
Again, for the “Universal Law” to apply, the resistance of the conducting state of the chalcogenide threshold switch, as the other memory cell component, will be defined by the constant voltage of its conducting state and by the programming current. The key requirement is for the conducting voltages of both devices in the memory cell be very close to each other, something that is not intuitively obvious, unless, that is, the threshold switching and post-switching conduction mechanisms are the same in HfO as they are in the chalcogenides.
Clearly a lot more experimental evidence is needed to confirm the true Universal nature of the common resistance observations.
Reliability and Variability of 1S1R OxRAM-OTS for High Density Crossbar Integration, D. Alfaro Robayo et al, Proceedings of IEDM 2019
A Model for an Amorphous Semiconductor Memory Device, M H Cohen, R G Neale & A Paskin, Journal of Non-crystalline Solids, 8 -10, 1972, 885-891
2 thoughts on “Observations on the “Universal Law” for NV Memory Cells”
Thanks a lot Ron Neale for your interest to our work! Glad to see you noticed this “universal law” we reported in the paper. I was curious to see the OTS behavior in the famous R(Iprog) trend, and it finally matches and follows the same trend than RRAM devices (in a dynamic way). I personally found it very interesting and we are honored to have your opinion on that point.
We are currently working in this direction in order to understand more what happens, also analyzing your inputs, and we hope to provide some insights in the future.
Gabriel, thank you for your appreciative comment. As I am sure you are aware if you are going to pursue the true nature “Universal Law” then I think the key variables will be the variation of programmed resistance with thickness for HfO, as well as other oxide memory types and chalcogenide based PCMs. While for selectors the variation of conduction voltage with thickness (t) will be the key variable, after the voltage contribution from the series resistance of conductors is removed. With current as a third variable in all cases.
If the two logic states of HfO memory are the result of the modulation of the tip of a Formed permanent filament then perhaps the variation of programmed resistance with deposited film thickness (t) will not be large, assuming the resistance of the permanent Formed (Rf) part of the programmed device is low. If it is not, then the simple equation for programmed state resistance will have to have a variable added as some function of thickness (t) to the series resistance term,
i.e. Rp = Vc/Ip + (Rf (t) + Rseries).
With Vc the result of the constant current density minimum when the act of programming ceases.
I wish you and your colleagues every success with your work and perhaps look forward to some new enlightenment at IEDM 2020. Irrespective of the results in terms of the Universal Law, your work will add some important design variables for other possible applications, non memory, of your devices!
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