Dedicated to Stanford R. Ovshinsky on the occasion of his 90th birthday
Phase change materials are characterized by a unique property combination which encompasses a pronounced property contrast between the amorphous and crystalline state, as well as rapid crystallization. This property portfolio is ideally suited for data storage applications. In this paper, the understanding of the relationship between the properties of phase change materials and their mechanism of chemical bonding will be reviewed in an attempt to provide a generic explanation for many of the unconventional properties of phase change materials.
Already as early as 1968, Dr. Stanford Ovshinsky published one of his scientific breakthroughs 1. In this year, ‘Stan’ as his friends call him, reported the reversible electronic switching of a certain chalcogenide (Ge10Si12As30Te48) and suggested that this principle could be used for electronic data storage. A little later, he and his coworkers also demonstrated that similar chalcogenides could be used for rewritable optical data storage, where storage was achieved by the phase transformation from the amorphous to the crystalline state 2. While it took another two decades to optimize these compounds to realize commercial applications 3–6, the research by Dr. Ovshinsky paved the way for these storage media. In hindsight, it is not only impressive to see the vision that has characterized Stan's work throughout the years. It is also noteworthy that he has always tried to advance both novel applications as well as a fundamental understanding of the unique properties of chalcogenides. I still vividly remember the first time I met Stan at the European Phase Change and Optical Storage Symposium (E\PCOS) below Mount Säntis in Switzerland in 2001 7. In this workshop he did not only discuss the application potential of phase change materials in advanced rewritable optical storage media, but also raised the question, how the remarkable properties of this unique class of materials have to be related to an unconventional bonding mechanism.
In this review, I will attempt to summarize our understanding of the relationship between the exceptional properties of phase change materials and the underlying bonding mechanisms. In a first attempt to do so, in Fig. 1 a map is displayed which shows a larger number of different chalcogenides. The position of a given compound in this map is determined by the ionicity and the hybridization of the s- and p-electrons of the constituting elements as described in more detail in Ref. 8. The black symbols denote different chalcogenides.
Looking at Fig. 1 it becomes clear that the different compounds are grouped into distinct bands for tellurides, selenides, sulphides and oxides (not visible in this map). The tellurides are characterized by the smallest ionicity difference of the constituents and small average s–p hybridization. In this map, colour has been used to mark those chalcogenides which have particularly interesting electronic properties. Green symbols depict those compounds such as GeTe, Ge2Sb2Te5 or Ge8Sb2Te11, that have the characteristic properties of phase change materials, i.e. possess a pronounced difference of optical properties between the amorphous and crystalline state and crystallize rapidly 8, 9. These green points agglomerate in the lower left corner of the map, i.e. for materials with small ionicity difference and low s–p hybridization. In this part of the map, most of the compounds are tellurides. Nevertheless, there are even other interesting electronic properties that can be found for compounds in the close vicinity of phase change materials. Orange circles denote materials with thermoelectric properties. Such alloys hence have interesting transport properties, i.e. a markedly better conduction for charge as compared to heat 10. Blue circles depict superconductors, which includes materials such as GeTe and SnTe. Conventional superconductivity requires the prevalence of a pronounced electron–phonon coupling, which implies that, at least for a number of chalcogenides, this coupling has to be strong. Finally red circles denote topological insulators which also possess unique charge transport properties such as topologically protected surface states. It is remarkable that for chalcogenides, and in particular tellurides, we see such a rich spectrum of attractive electronic properties.
In this paper, an attempt is presented to explain why certain chalcogenides have these striking properties that are the basis for their thermoelectric, superconductor, phase change material or topological insulator behaviour. While the effort is undertaken to explain most of these material properties, the focus will be on an elucidation of the characteristics of phase change materials. In the following, the optical properties and the origin of optical contrast in phase change materials will be discussed. Subsequently rules will be presented, which help to identify those compounds, which have phase change properties, leading to a ‘treasure’ map for phase change materials. In the following paragraph, the relationship between the bonding mechanism in amorphous and crystalline phase change materials and the atomic arrangement will be briefly discussed. Subsequently, recent findings regarding ultrafast transformations between the amorphous and crystalline state will be presented. After that, the transport properties of crystalline compounds will be discussed. In this section, a remarkable sensitivity of the electrical resistivity upon the disorder in the crystalline state will be identified and explained. In the concluding paragraph, an attempt will be presented to relate all properties presented so far to the remarkable bonding in tellurides.
2 From understanding the optical contrast in phase change materials to a ‘treasure map’
From experience we know that solids usually do not change their optical properties such as the reflectivity upon the transformation from the amorphous to the crystalline state. This can be seen also from Fig. 2, which shows two pieces of SiO2, as an example of a typical insulator.
While one of these two samples is amorphous, the second one is crystalline. With our eyes it is impossible to see a difference in the optical properties such as transmittance or reflectance. Even if we would use an optical spectrometer and measure the transmittance, we could hardly detect a difference between the amorphous sample (left side) and the crystalline sample (right side). A similar statement can be made about amorphous and crystalline metals. Again the optical properties, such as the reflectance, hardly differ. This implies that only very few materials could possibly possess a difference in optical properties between the amorphous and crystalline state. Such a claim immediately raises two questions: why are certain solids characterized by a pronounced difference in optical properties between both states? How can we identify (and optimize) solids which are characterized by this unique property?
Figure 3 attempts to provide a first answer. In this viewgraph, the reflectance of a thin film of the phase change material GeSb2Te4 is depicted both for the amorphous and the crystalline state in the infrared regime up to 8000 cm−1 (∼1 eV). Three striking differences are discernible in these spectra. Oscillations in reflectance, which are characteristic for interferences of the IR photons, extend up to higher energies for the amorphous phase.
This demonstrates that the amorphous state has a significantly larger band gap! Furthermore the reflectance for the crystalline state, even in the energy range where oscillations are observed, i.e. below the band gap, is significantly smaller than 1. This implies that an adsorption mechanism must exist below the band gap, such as, e.g. free carrier absorption. Finally the reflectance oscillations for the crystalline state are significantly smaller spaced, i.e. the reflectance minima are more closely spaced in energy. Clearly for this phase change material the properties of the amorphous and the crystalline state are markedly different. Since these oscillations are governed by an interference effect, the refractive index must be significantly higher in the crystalline state 9. Indeed, for all phase change materials we have studied so far 9, a drastic increase of refractive index accompanies the transition from the amorphous to the crystalline state. A careful data analysis has revealed that crystalline phase change materials are characterized by remarkably high refractive indices, indicative for a particularly large electronic polarizability, while the amorphous state shows a rather conventional electronic polarizability. The occurrence of a remarkably high refractive index (or alternatively a particularly large electronic polarizability) appears to be one of the fingerprints of phase change materials.
This finding has to be related to the bonding in crystalline phase change materials. Interesting enough, many phase change materials crystallize in octahedral-like atomic arrangements. Antimony is possibly the simplest material which reveals the characteristic properties of phase change materials as shown recently for thin films of this element 11. Sb has five valence electrons. However, the energy of the two outermost s-states and the three outermost p-states is so different that s–p hybridization can be neglected. Hence antimony mainly utilizes its three valence p-states to form chemical bonds. The atomic arrangement in elementary Sb can be described in a reasonable approximation as a simple cubic structure, where every atom has six nearest neighbours, i.e. an octahedral arrangement. Under these conditions the three p-states are decoupled and can be considered separately. Therefore, in the following we will only focus on the x-direction and the corresponding p-state. An atom has two nearest neighbours in x-direction, as depicted schematically in Fig. 4, but only one p-electron to bond to these two nearest neighbours.
Hence there are two energetically degenerate electronic configurations, as shown on the left and right side of Fig. 4. However, the system can further lower its energy by forming a hybrid from these two configurations.
This is shown in the middle of Fig. 4. Linus Pauling has introduced the term ‘resonance bonding’ to describe the bonding mechanism depicted 12. The same bonding mechanism is also responsible for the electronic configuration in aromatic hydrocarbons such as benzene.
A closer inspection of Fig. 4 already provides evidence why the electronic polarizability of crystalline phase change materials is so high. The electronic configuration depicted in the middle of Fig. 4, the case of ‘resonance bonding’, is very sensitive to the excitation by an external electromagnetic field. Hence ‘resonance bonding’ can account for the high electronic polarizability of crystalline phase change materials. This is not the only fingerprint of this bonding configuration, though. Resonance bonding also leads to high values of the ‘Born effective charge’, which characterizes the coupling between optical phonons and an external electric field. Therefore, an atomic displacement such as the excitation of a transverse optical phonon leads to a pronounced charge rearrangement. Therefore, resonance bonding is also accompanied by a strong coupling between phonons and electronic states. This explains also why certain chalcogenides, such as GeTe and SnTe, have superconducting properties; yet their critical temperatures of <1 K are too small for application purposes.
Each of these ‘fingerprints’ (large electronic polarizability, high Born effective charge, pronounced electron–phonon coupling) can be employed to identify those chalcogenides which utilize ‘resonance bonding’. However, it is also possible to derive some guidelines to identify potential phase change materials based upon trends in elemental composition of different chalcogenides. The electronic configuration depicted in the centre of Fig. 4 is only possible if the different elements in a given phase change material do not differ significantly in terms of their ionicity. If the ionicity difference is too large, the formation of the special form of a covalent bond employed in resonance bonding is unfavourable. Instead, ionic bonds would be utilized. Therefore, the materials which display resonant bonding are characterized by a small difference in ionicity of the different elements. Resonance bonding is also endangered, if significant distortions away from a perfect octahedral arrangement appear. Such distortions, which are frequently attributed to the Peierls effect, remove the degeneracy of the configurations displayed on the right and left hand side of Fig. 4. Therefore, pronounced distortions of the octahedral atomic arrangement also weaken ‘resonance bonding’. Such distortions increase with increasing hybridization of s- and p-states. Both the ionicity as well as the average level of sp-hybridization can be derived from the properties of the constituting elements as discussed in detail in Ref. 8.
This has led to the map displayed in Fig. 1. As expected from the discussion above, phase change materials, which are depicted as green circles, are only found among those chalcogenides, which have a small sp-hybridization and low ionicity. These materials are mostly tellurides, since already for selenides the bonding becomes more ionic and the hybridization between the s- and p-states is more pronounced. This explains the special role of tellurides in phase change memories.
In the amorphous state, resonance bonding is not possible, since the lack of long-range order prevents the formation of degenerate electronic configurations. Instead, in the amorphous state, ordinary covalent bonds are utilized. This immediately explains the difference in electronic polarizability and hence the optical contrast. Nevertheless, they are still ongoing discussions on the detailed atomic arrangement in the amorphous phase of phase change materials such as Ge2Sb2Te5 or GeSb2Te4. At present, they are two different models that have been invoked to explain the properties of the amorphous phase. Kolobov et al. 13 have focused on the atomic arrangement of the germanium atom in the amorphous and crystalline state. From an EXAFS-analysis they have concluded that the atomic arrangement of the germanium atom is octahedral like in the crystalline state, while it is tetrahedral like in the amorphous state. On the contrary, Huang and Robertson 14 present arguments, why the atomic arrangement should be octahedral-like in both the amorphous and the crystalline state. At present, this discussion is still ongoing. Possibly, the majority of atoms in the amorphous phase are indeed octahedrally coordinated, but a small fraction of germanium atoms is tetrahedrally coordinated 15–17. It has been suggested that germanium atoms which have at least one Ge nearest neighbour are particularly prone to participate in a tetrahedral atomic arrangement. Clearly, it would be beneficial if a more coherent picture of the atomic arrangement in the amorphous state could be obtained. Fortunately, in recent years a gradual improvement of the understanding of the atomic positions in the amorphous state is emerging 18.
3 Towards a microscopic understanding of rapid crystallization processes
At the same time, it is important to keep in mind, what are the main challenges for the understanding and optimization of phase change materials for data storage applications. As discussed above, the presence or absence, respectively, of resonance bonding can explain the optical contrast between the amorphous and crystalline state of phase change materials 19. Hence it seems as if this property is already sufficiently well described. At present, crystallization kinetics is another area of intense research in the field of phase change memories. The main motivation comes from the desire to realize electronic memories that can compete in speed with DRAM, but have the added benefit of being non-volatile such as Flash memories 20. Such a phase change memory might help to realize a universal memory, combining the advantages of DRAM and Flash.
Indeed, in recent years, there has been remarkable progress reported in terms of the observed switching speeds of phase change memories. Bruns et al. 21 reported that GeTe can be switched in a few nanoseconds upon application of a low voltage pulse of <1.5 V to a small device cell. In this study, it was shown that the recrystallization time depended strongly on the size of the amorphous bit that had to be crystallized. This is evidence for growth-dominated recrystallization. Already in late 1990s, systematic experiments by researchers at Philips in Eindhoven (Netherlands) had shown that there are two different mechanisms of crystallization that can be distinguished by comparing the contribution of nucleation and crystal growth to recrystallization 22. While in some materials nucleation proceeded very rapidly (nucleation-dominated recrystallization), in others growth was more important (growth-dominated recrystallization). It already had been shown in the past that a first order transition such as the transformation from the amorphous to the crystalline state can be disentangled into growth and nucleation 23. However, the unique challenge posed by phase change materials stems from the fact that nucleation and growth in these storage media proceed on a nanosecond time- and nanometer length-scale. This is a tremendous challenge for experimental investigations so that often either only a high temporal resolution is employed, which can help to establish fundamental limits of transformation speed 24, but sacrifices spatial resolution or alternatively, the experiments are performed at much slower times scales but with nanometer spatial resolution 25. Nevertheless, these studies have confirmed the importance of nucleation and growth for recrystallization. In particular, it could be shown that the main difference between different phase change materials is the nucleation rate. While some materials such as Ge2Sb2Te5 show rapid nucleation, others such as alloys of Ag and In with Sb2Te (AIST) feature slow nucleation and fast growth. At present it seems as if the differences in crystal growth between different materials are smaller than the differences in nucleation. The fast nucleation observed for Ge2Sb2Te5, e.g. can be explained by the low reduced glass transition temperature (Trg = Tg/TM). Materials such as AIST, on the contrary, have a somewhat higher reduced glass transition temperature. As already shown by Turnbull more than 50 years ago 26, the nucleation rate is inversely proportional to the reduced glass transition temperature. Materials such as SiO2 have a rather large Trg of more than 0.8 and hence are good glass formers. Phase change materials, on the contrary, are all bad glass formers to ensure rapid recrystallization 27. Hence they possess high nucleation rates when quenched below the melting temperature.
With the ongoing miniaturization of memory devices, crystal growth is becoming increasingly important, even for materials with high nucleation rates. For decreasing cell sizes, the rate of formation of a critical nucleus decreases while the necessary time to recrystallize a bit simply by crystal growth from the surrounding crystalline matrix decreases. Hence, crystal growth is becoming increasingly important. This has helped to understand recent results such as the data obtained by Bruns et al. They demonstrate that for GeTe the switching speed depends upon the diameter of the amorphous region to be recrystallized 21. Loke et al. 28 have even achieved shorter recrystallization times of <1 ns, establishing DRAM-like switching speeds in phase change materials. As mentioned above, such short recrystallization times for small memory cells are most likely due to very high crystal growth rates. Until recently, it has not been possible to measure the velocity of crystal growth for phase change materials in the relevant temperature range between the glass transition temperature Tg and the melting temperature TM. Orava et al. 29 have used a novel calorimeter to measure ultrafast crystallization processes and could derive the temperature dependence of the growth velocity from these data. Their findings are schematically depicted in Fig. 4, together with data for a well-known glass former (SiO2) and Si.
Obviously the temperature dependence of the crystal growth velocity for the good glass former SiO2 is very different from the data observed for the phase change material Ge2Sb2Te5. While the data for SiO2 can be explained by an Arrhenius behaviour, this is not the case for Ge2Sb2Te5, which shows a temperature dependent activation energy. Angell 30 has introduced the concept of fragility, to differentiate between undercooled liquids with high fragility and materials like SiO2 with low fragility. Materials with a high fragility show a strong temperature dependence of the viscosity at the glass transition temperature as well as a pronounced temperature dependence of the activation energy for viscous flow. Clearly Ge2Sb2Te5 forms a very fragile liquid and has a very high crystal growth velocity. This temperature dependence and the high maximum crystal growth velocity are crucial for fast recrystallization via crystal growth. Such data also help to improve our understanding of glass formation and the nature of the glass state in phase change materials as well as the undercooled liquid state in fragile liquids in general 31.
4 Charge transport in crystalline phase change materials
Already in the introduction it has been mentioned that tellurides have remarkable electronic properties and show superconductivity, thermoelectric properties and the characteristics of topological insulators. For the application of phase change materials in electronic memories understanding the change in resistivity upon crystallization is very important. However, even in metals and ordinary semiconductors such as silicon, a large change in resistivity is observed upon the transformation from the amorphous to the crystalline state. Hence one can wonder, if non-volatile memories employing phase change materials could also be realized with well-known materials such as Si or GaAs, or other compounds on the map in Fig. 1, not marked by green dots. At this point in time, there is no clear answer to this important question. However, from Fig. 5, we can conclude that a non-volatile phase change memory based upon the transformation from amorphous to crystalline Si would most likely be much slower than a comparable device based on Ge2Sb2Te5. In addition, Si and many other conventional semiconductors have rather high melting temperatures, often exceeding 1300 K. This requires high power to melt the corresponding material. In phase change materials, on the contrary, significantly lower melting temperatures are encountered, which help to reduce the power to melt. Most likely the low melting temperatures can be attributed to their pronounced entropy change upon melting 33. Nevertheless, the question whether the selection criteria for phase change materials are different for optical and electronic memories is still open.
There are two other important questions regarding charge transport in phase change materials. In recent years, it has become clear that the resistivity in the amorphous state changes with time. This resistance ‘drift’ to higher resistivities is a major obstacle to realize a multi-level storage concept with phase change materials. While the details of the resistance drift mechanism are not yet fully understood, largely because we are lacking an in-depth understanding and experimental characterization of the responsible electronic defects, this paper will focus on the crystalline state and its charge transport mechanism. At first sight, it is less obvious why an in-depth understanding of the electrical resistivity in the crystalline state is crucial as well. The change of resistance with time is much smaller for this state, so resistance drift is no concern. However, the energy consumption for the transition from the crystalline to the amorphous state is the limiting factor to realize devices which consume less power (‘Green IT’). Identifying crystalline phase change materials with a higher resistivity could help to create Joule's heat more efficiently and hence switch to the amorphous state with less power.
Usually the resistivity of crystalline semiconductors is controlled by doping. However, in crystalline phase change materials, it appears as if the position of the Fermi energy is less controlled by details of the chemical composition, but rather by the inherent tendency of crystalline phase change materials to create vacancies 34, 35. These vacancies pin the Fermi energy in the valence band and lead to p-type conductivity. Interesting enough, the resistance in several crystalline phase change materials shows a pronounced dependence upon annealing temperature. This is displayed in Fig. 6.
This figure shows a transition from non-metallic behaviour, i.e. a negative temperature coefficient of resistivity (TCR) (dρ/dT < 0) to metallic behaviour, with dρ/dT > 0 36. This transition is not caused by a significant change of the carrier concentration. Instead the metal–insulator transition is driven by a change of order upon annealing. The samples which reveal non-metallic behaviour are hence insulating, since they possess a remarkably high level of disorder. Recent DFT calculations confirm this finding and attribute the insulating properties to vacancy clusters which dissolve upon annealing, causing the transition from insulating to metallic behaviour 37. This is rather unusual and implies that tailoring the electrical properties of phase change materials can be accomplished by careful control of the disorder in the crystalline state. In particular, it should be possible to create a crystalline state with a higher electrical resistivity by applying short electrical pulses which are sufficient to crystallize the phase change material but insufficient to produce pronounced order in the crystalline region. This could help to enable more efficient phase change memories.
Tellurides possess a rich spectrum of remarkable and technologically important optical and electronic properties. In phase change memories the remarkable optical contrast between the amorphous and the crystalline state enables rewriteable optical data storage. This optical contrast can be attributed to the presence and disappearance of resonance bonding in the crystalline and the amorphous state, respectively. Resonance bonding can only exist for a subgroup of tellurides, which are characterized by a small ionicity difference of the constituting elements as well as a small hybridization of the valence s- and p-electrons. Hence it is possible to predict, which chalcogenides have the potential to be successfully employed as phase change materials. Resonance bonding leads to several unique material properties such as high electronic polarizabilities and large effective Born charges. The former are responsible for the high reflectivity of crystalline phase change materials, while the latter lead to a pronounced electron–phonon coupling, which is a prerequisite for superconductivity. Hence it is not so surprising that some chalcogenides such as GeTe or SnTe are superconductors.
However, phase change materials are not only characterized by resonance bonding. Another characteristic feature is the occurrence of lattice distortions away from a perfect octahedral atomic arrangement. These distortions are caused by the Peierls effect, an electronic mechanism to lower the energy of the solid 38. These lattice distortions in conjunction with resonance bonding govern most of the properties of phase change materials. The Peierls distortion also affects the phonon modes and leads to a rather anharmonic potential with low phonon frequencies for the transverse optical modes 39. The anharmonicity is a prerequisite for the short lifetime of lattice vibrations which reduce the thermal conductivity and hence enables thermoelectric properties. The low phonon frequencies of the transverse optical phonon modes also lead to a significant increase of the static dielectric constant (ε0) over the (already high) optical dielectric constant (ε∞) via the Lyddane–Sachs–Teller relationship. The high values of the static dielectric constant give rise to very efficient screening of the electrons and hence very small electronic correlations. This is a prerequisite to see disorder induced localization as compared to localization induced by pronounced electron correlations. Therefore the combination of efficient electronic screening, p-bonding, vacancies and lattice distortions in the crystalline state is responsible for the charge carrier localization observed. This phenomenon is only observed in a subgroup of tellurides with particularly high disorder 36.
What is missing so far is an atomistic concept which links the rapid crystallization to the bonding in phase change materials. While it has become clear in recent years that phase change materials are bad glass formers which form fragile liquids, it is not yet clear, which underlying characteristics are responsible for fast recrystallization.
In summary, we can conclude that in the last decades chalcogenides have enabled a range of new applications which utilize their remarkable material properties. By now we understand most of these properties and are about to understand the remaining mysteries. Hopefully this will further improve the application potential of this unique material class.
In the past decade I had the pleasure to work with a group of highly motivated and talented Ph.D. students and post-Docs in the phase change group at RWTH Aachen. The present manuscript describes data and conclusions obtained by working with this group. Financial support by the Deutsche Forschungsgemeinschaft through the SFB 917 (‘Nanoswitches’) is gratefully acknowledged.
Matthias Wuttig is a Full Professor of Physics at the University of Technology, Aachen, Germany since 1997 and JARA-Professor at Research Center Jülich. He is speaker of the strategy board (since 2009) and was Dean of the Faculty of Science, Mathematics and Computer Sciences (2006–2008). He leads the Research Group: Physics of Novel Materials, which characterizes and investigates novel materials with unique optical and electronic properties. Recently this research has been focused on the explanation of the unique property portfolio of phase-change materials.