In this third part of a four-part series, contributor Ron Neale continues his analysis of selector technologies focusing the nature of the mystery of Forming and a number of the many unanswered questions.
From Part 2 of this series it is very clear that only a detailed and accurate description of threshold switching will allow an assessment of what might be possible during the act of Forming, when the threshold voltage of a selector or memory (if the latter is fabricated in its amorphous state) is reduced in some cases by a factor more than 30% from its as-fabricated value. The problem is that there have been numerous attempts to account for the threshold switching mechanism. In Part 3 of this series I will briefly explore some of threshold switching options and search for any which might be used to account for Forming.
Threshold switching: The key.
If understanding what is happening during threshold switching is the key to what might be possible during that single cycle of threshold switching associated with selector Forming, then there is a possible converse connotation: If we really understand what is happening during Forming it may provide a much greater insight into threshold switching itself.
For example, if sufficient power is available during Forming to cause a permanent significant physical change somewhere in the selector device structure, then it is highly likely that there is enough power for more subtle structural changes to account for threshold switching during normal operation after a device has been Formed. Melting is a structural change which satisfies many researchers, but more recently other structural changes have been suggested and those will be explored in the following paragraphs.
In the past there have been many attempts to try and describe threshold switching, all of which have supporters. They can be divided into three groups:
- Mixed thermal electronic
with the electronic group further subdivided into many subsets, combinations, and some fine tuning. Most of the early attempts to describe threshold switching as a purely electronic mechanism really provided nothing more than a good description of the conduction mechanism leading to threshold switching. What they all failed to provide was the common denominator, that is, that one composition or structural feature which is common to all of the possible glass compositions where threshold switching is observed (although a Group VI element, one of the chalcogenides, is always included). The opening paragraphs of the three papers listed below have excellent summaries of the various past approaches to explanations of threshold switching.
- Te-based chalcogenide materials for selector applications, A. Velea, et al, Scientific Reports 7, Article number: 8103 (2017)
- The gradual nature of threshold switching, M. Wimmer and M. Salinga, New Journal of Physics 16 (Nov 2014) 113044 doi:10.1088/1367-2630/16/11/113044
- A unified model of nucleation switching, Nardone, M., Karpov, V. G., Jackson, D. C. S. Applied Physics Letters 94, 103509 (2009)
Thermal models and history.
Many attempts at explaining threshold switching argued against a purely thermal model on the basis of switching time and power. (Often for commercial reasons an all electronic model was viewed as more attractive). Those explanations ignored the effects of localization of current and the expansion of hotspots as the initiator of, and the effect responsible for, threshold switching. Many models based their argument on a requirement for the whole volume of material between the electrodes to rapidly switch with the structure remaining fixed as the voltage approached its threshold switching transition. These models failed to allow for the possibility of recoverable structural changes like localised melting.
In the early days, one of the first serious attempts at a model to account for the post-threshold switching crystallization in PCMs was presented [A model for an Amorphous Semiconductor Memory Device, M H Cohen at al, Journal of Non-Crystalline Solids, 8-10 (1972), 885-891]. Called the CNP model (after the initials of the authors) this work represented the result of threshold switching as a core volume of amorphous material around which crystallization occurred. The CNP model required the core region to be at a temperature higher than the crystallization temperature of the PCM material, to allow for the crystals to grow up a temperature gradient, which is an essential requirement for crystal growth. This model did not answer the chicken-and-egg problem: Was that hot core (possibly molten) essential for the threshold switching transition to the conducting state or was it simply a consequence of power dissipation after some type of electronic switching?
Another part of the CNP model introduced the idea of a percolation path which could be used as the initiator of the conducting state. In this case the origin of the idea of a percolation path was, at the time, used as a means of accounting for a PCM failure mode. It was a failure mode where a PCM device, in what appeared to be its high resistance reset state, would go directly into the conducting state without threshold switching when the voltage applied was increased above the read voltage value. This clearly demonstrated that it was possible to arrive at the full conducting state without the need for threshold switching, but merely by thermal expansion from a hot narrow percolation path region. In the latter parts of this article I want to return that point in relation to Forming.
Later Kroll and Prof Cohen [Theory of electrical instabilities of mixed electronic and thermal origin, D.M.Kroll, M.H.Cohen Journal of Non-Crystalline Solids, Volumes 8–10, June 1972, Pages 544-551] refined the CNP model and provided a more complete mathematical description of the threshold switching as a thermal process, where the method of conduction prior to and after the switching transition from the high-to-low resistance state was almost incidental as long as it could provide an activated rate of change of electrical conductivity leading to the dissipation needed for thermal switching. At the moment the most popular pre-switching conduction mechanism is a Poole Frenkel model with a finely-tuned impact ionization approach.
Moving to the more recent generation of chalcogenide devices, a team at IBM, Zurich [Evidence for thermally-assisted threshold switching behavior in nanoscale phase-change memory cells, Manuel Le Gallo, et al, IBM Research – Zurich, December 2015] offered some very strong experimental evidence for a thermal initiation of threshold switching in PCM material, part of which was evidence that the dissipated power at the moment of threshold switching is constant for a range of increasing applied voltages and, (i.e. shorter delay times) and at elevated temperatures.
The IBM Zurich team appeared to be able to probe what might be described as a thermal “link” which initiates switching and what could also be considered as the end point of the conducting state, i.e. the holding current: the minimum current when the conducting state terminates. The figure to the left is a simple illustration of the growth and collapse of the link.
The figure to the right uses the same curves as were shown in the second chart of Part 2, with an added orange loop superimposed on the centre of the I-V characteristic to illustrate what might be considered as the I-V characteristics of the initiating link.
Can that evidence be transferred to selector material compositions? My view is yes. If not, then it would suggest that there are two threshold switching mechanisms, one for selectors and a separate and different one for PCM in the same general family of chalcogenide-based material compositions.
It would be very interesting to know if the IBM experiments were repeated with un-Formed selector devices: Would Forming occur if the maximum current was limited to just the holding current? This is complicated, but not impossible, and can be achieved using a family of similar devices, because the holding current is not known until the selector has been Formed.
What are the other options for threshold switching and how might they be used to account for Forming?
All glasses crystallize and crystallization occurs in two steps: nucleation followed by crystal growth. Is it possible that homogeneous nuclei which form before crystals start to grow could provide a more conducting percolation path and be metastable, as long as crystal growth is not allowed to proceed, and because of their size they resort back to becoming part of the original amorphous structure?
While homogeneous nucleation is a relatively rare phenomenon under normal conditions, that may not be the case when the material is subjected to thermal excitation in a high electric field. This idea is not new, and the work reported by Nardone, Karpov et al in the paper cited earlier in this post is an example of authors who originated this approach to explain threshold switching.
In this situation these metastable nucleating points might then be able to provide a preferred initial percolation conduction path, which is then thermally linked, to initiate the threshold switching transition. After this initial transition the post-threshold switching hot current carrying conducting column can expand.
If nucleation points are a real possibility to explain threshold switching they do not explain Forming; but might be of some help. If the nucleating points are metastable it would then point to the change in threshold voltage observed after Forming as caused by a structural change of a different type, say a combination of electro-migration and surface reaction. If however the nucleating points are not metastable but a permanent part of a Formed selector device they could be used to account for the effects of Forming.
The nucleation model immediately raises a question with respect to the nature of threshold switching in some PCM devices where there is already available a massive nucleating site in the form of one electrode made of crystallized memory material. Homogeneous metastable nucleation sites might still appear in the remaining amorphous material when it is heated during the switching delay time prior to the switching transition. This will establish the initiating link, and its radial expansion and conduction of current before crystal growth from the large nucleating site of the electrode begins.
Incipient metals to the rescue.
Perhaps one the most exciting explanations from the electronics side which is now finding favour. An explanation of threshold switching and rapid insulator-to-crystal transitions based on a new classification of materials called incipient metals can be found in: Incipient Metals: Functional Materials with a Unique Bonding Mechanism, Wuttig M. et al, Advanced Materials, December 2017.
Incipient metals have a bonding structure which matches that of neither a metal nor an insulator – they are meta-valent. Meta-valency allows this new class of material, when suitably stimulated, to reversibly switch between the insulating and metal states. Many chalcogenide glass compositions can now be classified as incipient metals.
Not only can meta-valency in incipient metals be used to account for rapid insulating-to-crystal transitions, it can also be used to describe the threshold switching in those materials used for selectors where crystallization does not occur. In the latter case it is a matter of degree only requiring a sufficient switching of the metastable bonds to create a conducting state without complete and permanent crystallization.
Meta-valency can also be used to describe annealing. In simple terms it means that some of the bonds which facilitate the metal state hang around when most of the bonding returns to the insulating state or amorphous state. Then slowly over time those bonds revert to the insulating state, reducing the electrical conductivity and adding to the threshold voltage required to bring them, and the rest of the bonds, from the insulating to the conducting state.
In summary meta-valency appears to be able to:
- Provide a description of threshold switching for selectors where crystallization does not occur
- Provide a bonding system which can be part of complete crystallization and then still be available for threshold switching in PCM materials after the material has been reset from the fully crystallized state
- Account for annealing in all of those cases.
Perhaps a new qualification needs to be added to any search for the “Lowest Common Denominator” of a structural feature which would need to be a present in every one of the millions of chalcogenide glass compositions where threshold switching is observed. In the light of incipient metals this search might now need only two classifications: Those compositions which are meta-valent and commercially useful, and the rest.
Does meta-valency play a part in Forming, possibly if some of the bonds can become locked in the metal state?
Recently high-speed x-ray analysis has discovered two liquid states for a memory material one of which only appears for a very short time. Is it possible there could be two amorphous states with different structures for selectors, one insulating and one conducting, that are only obtainable when excited by an electric field at an elevated temperature? Perhaps meta-valency leading to metastability is the solid state way to describe threshold switching. Or perhaps chalcogenide glasses are able to temporarily adopt the electrical conducting structure of the liquid state without becoming molten at elevated temperatures, and under conditions of high electric field.
Does all of today’s work on thermal models help us to understand Forming? It does suggest that high localised power and temperatures are part of threshold switching. While localised melting may or may not occur in some of the newer selector materials, which are claimed to be stable at 400° C, this would limit the options for those devices either to element separation from electrostatic effects, or to localised elevated temperature electro-migration, as the factor contributing to the changes observed after Forming in those devices. (This claim appears in: Tunable Performances in OTS Selectors Thanks to Ge3Se7-As2Te3, A. Verdy et al, 2019 IEEE 11th International Memory Workshop – IMW – Monterey.)
While there are numerous possible ways in which many of the explanations for threshold switching could account for the action of Forming, other than high current density electro-migration or electrostatic effects (with the latter requiring high temperatures and melting), nothing so far offers a perfect match and the common denominator as far as selectors are concerned.
Also many of the attempts at describing the mechanism of threshold switching based structural changes of any kind: bond switching, nucleation, crystallization, or melting, often seem to fail to acknowledge that within the already small volume of a localized hot spot it only needs something just above 0.15 of the volume fraction (15%) to change in order to start to build a conducting percolation path.
In that respect if we accept the idea of an initial 15% volume fraction percolation path as the precursor to threshold switching, irrespective of the physical changes involved, then there are possible element separation Forming implications.
Rather than looking for a common denominator in composition to account for threshold switching and Forming, is it possible to find a common denominator of a different kind based on the need to convert only a little over 15% of the volume of the material to initiate threshold switching which opens the door to a powerful positive feedback process to complete switching and at the same time account for Forming?
The all-purpose model.
An outline of what I will call my all-purpose model is illustrated in the figure below,
which is a cross-section of an asymmetric device with (in this example) electrodes of different types of conducting material, shown in green and brown. In operation, initially as a voltage pulse greater than the threshold voltage is applied, the temperature of the device starts to rise. Somewhere in a local hotspot the active material reaches what I will call a “transition temperature”. The use of that term avoids any prejudices which might favour a particular mechanism.
When for a 3D structure the volume fraction of greater than 0.15 or 15% is converted to the conducting state, percolation paths start to form. The initial part of the percolation path is shown as the continuous black line in part (a) of the graphic with red lines representing material which has transitioned to the conducting state. This has the effect of localising the current which then preferentially accelerates the growth of what might be called the percolation filamentary volume (red filaments within the thin grey lines) as shown in (b), until finally one (or more) conducting percolation path bridges the inter electrode gap, as show in (c).
At that moment there is an inrush of most of the current, (d), which then then results in the rapid heating and expansion of the conducting filament (beige) to accommodate the current of the conducting state.
This is an all-purpose model because the initial transition to the conducting state to form the percolation path can be based on the mechanism of choice: bond switching, homogeneous crystal nuclei, crystallization, melting, or even a mixed mechanism. Such a model might account for why there is such a large number of different mechanisms to describe threshold switching, all of which appear reasonable. Is it because they are underwritten by, and can all be plugged into, this type of percolation model of switching.
This model also simplifies the equation linking threshold voltage (Vt) and temperature (T) over the operating range to something like: Vt = Vx (1 – cT/Tt) where Vx and c are a constants and Tt is the transition temperature. (The melting temperature Tm or crystallization temperature Tc would be options for Tt.) The validity of this formula can be tested on experimental values.
The link to Forming now becomes obvious. As the initial percolation path bridges the inter-electrode gap, and prior to its expansion, it will be subjected to a very large high current density pulse. At that moment, irrespective of the initial transition mechanism, high current density-localised element separation is going to occur; if molten from electrostatic forces or if solid from electro-migration. Such a model would also explain how and why what outwardly appears to be a relatively low current from a single threshold switching event, compared with that required to reset a PCM memory device, is able to bring about the large physical changes which occur at Forming.
In the next, Part 4, of this series I will look at some models of the location of the physical changes which might be used to account for Forming and scaling.