Resonant bonding in crystalline phase-change materials

ARTICLES

Resonant bonding in crystalline phase-change materials KOSTIANTYN SHPORTKO1 , STEPHAN KREMERS1 , MICHAEL WODA1 , DOMINIC LENCER1 , JOHN ROBERTSON2 AND MATTHIAS WUTTIG1,3 * 1

Institute of Physics (IA), RWTH Aachen University, 52056 Aachen, Germany Engineering Department, Cambridge University, Cambridge CB2 1PZ, UK 3 JARA-FIT, RWTH Aachen University, 52056 Aachen, Germany * e-mail: [email protected] 2

Published online: 11 July 2008; doi:10.1038/nmat2226

The identification of materials suitable for non-volatile phase-change memory applications is driven by the need to find materials with tailored properties for different technological applications and the desire to understand the scientific basis for their unique properties. Here, we report the observation of a distinctive and characteristic feature of phase-change materials. Measurements of the dielectric function in the energy range from 0.025 to 3 eV reveal that the optical dielectric constant is 70–200% larger for the crystalline than the amorphous phases. This difference is attributed to a significant change in bonding between the two phases. The optical dielectric constant of the amorphous phases is that expected of a covalent semiconductor, whereas that of the crystalline phases is strongly enhanced by resonant bonding effects. The quantification of these is enabled by measurements of the electronic polarizability. As this bonding in the crystalline state is a unique fingerprint for phase-change materials, a simple scheme to identify and characterize potential phase-change materials emerges.

Phase-change materials are solids characterized by an unconventional combination of properties. The amorphous and crystalline phases of these materials possess significantly different optical properties. At the same time, these alloys can be rapidly switched between both states. Such characteristics are ideally suited for applications in rewritable optical data storage1 . Up to now, three different generations of optical storage media use phasechange materials for rewritable data storage. In compact discs, a 780 nm wavelength laser (1.59 eV) is used to read, write and erase the data. In second- and third-generation products, this wavelength is reduced to increase storage density. In DVDs, a wavelength of 650 nm (1.91 eV) is used, whereas in Blu-ray discs, a wavelength of 405 nm (3.06 eV) is used. As the bandgap of typical phase-change materials is well below 1.5 eV, these optical excitations cause bandto-band transitions2 . A second application is in electronic phase-change memory, which uses the pronounced difference in resistivity between the phases. This is a non-volatile memory that has fast data transfer rates and high storage densities. It could enable phase-change memory to replace flash memory in the future and has the potential to create a ‘universal memory’ that might compete with the speed of dynamic random access memory3–5 . A number of material properties are critical for this application, including the resistance contrast, transition speed between amorphous and crystalline state and material dependence of the switching characteristics. These are again ultimately related to the materials’ electronic states6 . Here, we investigate the dielectric function ε(ω) of each phase by infrared spectroscopy and spectroscopic ellipsometry. The present study focuses on the energy range above the highest phonon frequencies (30 meV) but below the optical gap of typically 0.75 eV.

In this range, the dielectric function ε(ω) is governed by the electronic polarizability of the valence electrons, and probes the chemical bonding of the phase-change materials. This enables us to give an unambiguous interpretation of the difference between the bonding in the amorphous and crystalline state. It shows that the bonding in the crystalline phase is unusual in its large component of resonant bonding. The sample geometry shown in Fig. 1 was used to determine the dielectric function. The reference specimen, shown in Fig. 1a, consists of a glass substrate coated with a 150 nm Au layer, which acts as an almost ideal mirror in our energy range. Films of different stoichiometry were then sputter-deposited on top of this layer, and the reflectance of the samples determined. Phase-change materials such as GeTe, Ge2 Sb2 Te5 , Ge1 Sb2 Te4 , Ge2 Sb2 Te4 , Ge3 Sb4 Te8 , Ge15 Sb85 and Ag5 In6 Sb59 Te30 were used, and compared with conventional sp3 -bonded semiconductors such as AgInTe2 . The sample geometry in Fig. 1b ensures that the measured reflectance spectra are exclusively governed by the dielectric function ε(ω) of the film and its thickness. As the materials investigated are either amorphous or polycrystalline and have no pronounced texture, ε(ω) is isotropic. Our method contrasts with previous studies that focused on higher energies7 or used Fourier-transform infrared spectroscopy (FTIR) in transmittance mode8 , which hinders the separation of changes in thickness and optical properties. Figure 2 shows infrared reflectance measurements for the amorphous and crystalline phases of a typical non-phase-change material, AgInTe2 . The blue curves are the reflectance spectrum of a 0.65 ± 0.01-µm-thick film of as-deposited AgInTe2 , confirmed to be amorphous by X-ray diffraction. The film was annealed for 30 min at 180 ◦ C, which crystallized it to a four-fold-coordinated

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ARTICLES a

b

1.0 Optical bandgap (oscillations decrease)

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Difference in reflectance oscillation frequency due to change of (n × t) on crystallization

2 0.6 R

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Figure 1 Sample cross-section. a, Reference specimen. b, Sample investigated. 1: glass substrate, 2: Au layer, 3: semiconductor layer.

Amplitude decrease from complete reflectance level due to absorption

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Figure 3 Infrared reflectance spectra of a Ge2 Sb1 Te4 film. Blue: amorphous state, red: crystalline state. The solid lines describe the experimental data, whereas the dashed lines denote the simulation results. On crystallization, the thickness decreased from 0.53 to 0.50 µm. The contributions of different phase-change film properties to the reflectance curve are marked.

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Figure 2 Infrared reflectance spectra of an AgInTe2 film with a thickness of 0.65 µm. Blue: amorphous state, red: crystalline state. The solid lines describe the experimental data, whereas the dashed lines denote the simulation results.

chalcopyrite structure. There was no significant change in film thickness. This is consistent with X-ray reflectivity measurements of the density and thickness of thinner films before and after crystallization. The reflectance spectra of both phases closely resemble each other. Both the maxima of the curves and the positions of their minima are very similar. The films are transparent below their bandgap, measured to be 1.38 eV. This is clearly seen in that the reflectance maxima are close to 1 below this energy. The spacing of adjacent maxima depends on the product of refractive index and film thickness, and hence must be similar in both phases. The resulting dielectric function is shown in Supplementary Information, Fig. S1. For energies below 0.75 eV, both curves show no significant absorption and have a similar, constant real part of the dielectric function, ε1 (ω), that is, constant refractive index. This implies that their chemical bonding is very similar, as discussed later. Thus, the small difference in optical properties is not sufficient for rewritable optical storage applications. In addition, AgInTe2 has rather slow crystallization rates (not shown here). Hence, AgInTe2 does not possess phase-change properties9 . A very different behaviour is seen in the reflectance curves of the phase-change alloy Ge2 Sb1 Te4 in Fig. 3. Again, the blue curves are for the as-deposited amorphous state and the red curves for the crystalline film with rocksalt structure10 . The as-deposited film was 0.53 ± 0.01 µm thick, and decreased to 0.50 ± 0.01 µm after crystallization. This 6 ± 3% decrease is consistent with X-ray reflectivity measurements on thinner films. 654

There are three significant differences between the amorphous and crystalline curves. These are also denoted in the figure. First, the interference fringes extend to much higher photon energies for the amorphous than the crystalline phase, owing to the larger bandgap of the amorphous phase7 . Second, the reflectance maxima are lower in the crystalline phase, owing to subgap (Drude-like) absorption by free carriers. Third, and most important, is the pronounced difference in spacing of the reflectance minima. The spacing is about 40% smaller in the crystalline phase, which added to the thickness difference, implies that the refractive index is ∼50% larger in the crystalline phase. This is supported by a detailed analysis of the spectra in Fig. 4a–d, which show both the real and imaginary part of the dielectric function, that is, ε1 and ε2 . The reflectance spectra of all investigated phase-change materials show a similar effect; ε∞ is much larger in their crystalline phase. This is also visible in the two extra measurements shown in the Supplementary Information, and was also noted by MendozaGalvan and Gonzalez-Hernandez8 . As can be seen from Fig. 4a–d, the excess of ε∞ for the crystalline phase is significant and reaches values over 200%. This difference is a generic feature of phasechange materials. Whereas the spectra of the amorphous phases resemble that of amorphous AgInTe2 , the crystalline spectra show a distinct difference. This is clear evidence for a difference in bonding. We consider the origin of this difference. First, we model the observed dielectric function from 0.05 to 3 eV. We can exclude phonon contributions that lie below 0.03 eV. We include a Drude-like term for free carriers plus a single Tauc– Lorentz oscillator, following Jellison11 . ε1 (ω) and ε2 (ω) thereby automatically obey the Kramers–Kronig relationship. We find no contribution from free carriers for the amorphous phases. As their bandgaps are larger than 0.5 eV, the extinction coefficient k is zero below 0.5 eV and ε1 (ω) = n2 , where n is the refractive index. For the crystalline phases, there is a Drudelike absorption. Its contribution can be subtracted out within this model to simplify comparisons. The dielectric functions seen in Fig. 4 show a single peak due to bonding–antibonding transitions. We now analyse the optical dielectric constant ε∞ , that is, the low energy-limit of ε1 in the range studied here, by the nature materials VOL 7 AUGUST 2008 www.nature.com/naturematerials


ARTICLES Ge15Sb85 Ge2Sb1Te4 Ge1Sb2Te4 Ge2Sb2Te4 Ge2Sb2Te5 Ge3Sb4Te8 GeTe AgInSbTe

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Figure 4 Dielectric function ε 1 (ω) and ε 2 (ω) for various materials. a,b, Amorphous phase-change sample. c,d, Crystalline sample including Drude-type contribution. e,f, Crystalline sample with Drude contribution subtracted.

Clausius–Mossotti model12 . If each atom of element i is assigned a polarizability of α i , then

X ε∞ − 1 ρ P nj aj , = ε∞ − 2 3ε0 i n i m i j where ε0 is the permeability of free space, ρ is the density and m i and n i are the atomic weights and densities of element i respectively. A satisfactory fit is found for αGe = 5.07 × 1040 C m2 V−1 , αSb = 7.82 × 1040 C m2 V−1 and αTe = 7.66 × 1040 C m2 V−1 , describing all experimental values for ε∞ within an average of 4%.

This indicates that this model with constant polarizabilities will fit these and similar amorphous compounds. We can also attempt to fit ε∞ for the crystalline phases. We must first subtract out the low-energy Drude contribution from free carriers as shown in Fig. 4e,f. The resulting ε∞ values are compared in Table 1. If both phases have the same atomic polarizabilities, then ε∞ of the crystalline phase should only differ from the value of the amorphous phase owing to the density change. However, this is not the case; the experimental values are severely under-estimated, see Table 2. We also analysed the ε∞ values by a bond polarizability model, following the ideas of Philips and Levine13 . Assuming the



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ARTICLES Table 1 Optical dielectric constants and energy gaps. This table comprises the measured optical dielectric constants ε ∞ of amorphous and crystalline phases of phase-change materials without Drude contribution, and Se, Te (refs 24,25). In addition, on the right-hand side the optical gaps E g are listed. The third column is a measure of resonance bonding in the crystalline state. AIST: Ag5 In6 Sb59 Te30 . ε∞

Ge1 Sb2 Te4 Ge1 Sb1 Te2 GeTe Ge2 Sb2 Te5 Ge15 Sb85 Ge2 Sb1 Te4 Ge3 Sb4 Te8 AIST Te Se

Eg

Amorphous Crystalline

% Amorphous Crystalline % increase decrease

16.6 ± 0.3 14.8 ± 0.4 13.2 ± 0.2 16.0 ± 0.4 26.9 ± 0.7 14.5 ± 0.3 15.6 ± 0.2 19.6 ± 0.5 11 5.7

118 222 152 108 — 106 178 169 204 72

36.2 ± 0.9 47.7 ± 0.8 33.2 ± 0.8 33.3 ± 0.8 — 29.8 ± 1.6 43.4 ± 1.2 52.8 ± 1.5 33.4 9.79

0.76 0.77 0.78 0.77 0.41 0.80 0.79 0.63

0.39 0.20 0.55 0.48 — 0.61 0.24 0.18

49 74 35 29 — 24 70 71

Table 2 Polarizability enhancement in the crystalline phase. Shown here are the calculated optical dielectric constants ε ∞ of amorphous and crystalline phases using the Clausius–Mossotti relationship under the assumption of a constant polarizability for each element in all amorphous and crystalline phases, respectively. Whereas all amorphous materials can be described sufficiently well, no reasonable fit is possible for the crystalline phases. This implies that for the amorphous phases, the knowledge of the stoichiometry is sufficient to predict the optical dielectric constant ε ∞ , whereas this is not the case for the crystalline phases. Amorphous

Crystalline

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Calculated

Error (%)

Calculated

Error (%)

Ge1 Sb2 Te4 Ge1 Sb1 Te2 GeTe Ge2 Sb2 Te5 Ge15 Sb85 Ge2 Sb1 Te4 Ge3 Sb4 Te8

15.7 15.7 12.3 15.7 26.7 13.8 16.5

5.4 6.1 6.8 1.9 0.7 4.8 5.8

22.2 36.4 24.8 24.9

38.7 23.7 25.3 25.2

23.7 26.9

20.5 38.0

atomic coordinations in the amorphous phases follow the 8-N rule, Te = 2, Sb = 3, Ge = 4, then ε∞ of the amorphous phases can be fitted by a sum of constant bond polarizabilities, whereas those of the crystalline phases cannot. This is demonstrated in the Supplementary Information. We will identify the mechanism for this polarizability enhancement in terms of the difference in chemical bonding. As the bonding will have a profound impact on the local atomic arrangement, we will review briefly the structural motifs observed for crystalline and amorphous phase-change materials. Early ideas of the local structure of amorphous semiconducting phases such as the continuous random network model suggested that the local coordination of the amorphous phase followed that of the parent crystalline phase. In phase-change materials, the bonding is different, but how? There have been a number of experiments to determine the local structure of the crystalline and amorphous states of phase-change materials. The amorphous phase was usually the focus of attention. In a first investigation, Taylor and co-workers used the covalent nature of bonding (8-N rule, N being the valence) to discuss the structural order in Gex Sby Te1−x−y glasses with respect to the formation of homo- and hetero-polar bonds14 . Kolobov et al.15 showed by extended X-ray absorption 656

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Figure 5 Schematic diagram demonstrating the origin of resonance bonding for Sb. On the left-hand side, one limiting case for bonding in an undistorted Sb phase is shown. A second limiting case is shown on the right-hand side. The solid can minimize its energy by forming a hybrid wavefunction, which is shown in the middle of this figure. This bonding is described as resonance bonding. The pronounced electron delocalization gives rise to an increased electronic polarizability.

fine-structure (EXAFS) spectroscopy that the local structure of the amorphous and crystalline phase of Ge2 Sb2 Te5 , a prototype material, was considerably different, with the Ge atoms being fourfold-coordinated in the amorphous phase, whereas the Sb and Te sites remain basically octahedral in both phases. Subsequently, Baker et al.16 gave evidence for Ge–Ge bonds in the amorphous phase for this alloy. These authors stressed that the coordination numbers of the different elements in the amorphous phase are generally consistent with the 8-N rule of covalent bonding; Ge = 4, Sb = 3 and Te = 2. This finding has since been confirmed by a simultaneous analysis of X-ray and neutron diffraction data as well as EXAFS data17 . In contrast, the coordination numbers of the crystalline phases are higher than expected from the 8-N rule, and are based on the distorted, six-fold-coordinated A7 rhombohedral structure of GeTe (refs 18,19). The A7 structure is a distorted NaCl structure also adopted by Sb. Consider Sb in the ideal NaCl structure. The Sb atom has a filled valence s-orbital, and its bonding occurs between the p-orbitals which each contain one electron. To first approximation, these form three independent chains of p-states along the x,y and z directions. This leads to a half-filled band with a zero bandgap at the Fermi energy EF . This structure is unstable with respect to a Peierls distortion, which forms alternative shorter and longer bonds along the chain, lowers the free energy and opens up a gap at EF (refs 20,21). Rhombohedral GeTe is isoelectronic to Sb. It possesses the same structure, but exhibits a small amount of polar bonding, which opens up a small gap at EF even for the undistorted chain. The distortion increases the size of this gap. However, the size of the distortion is relatively small; thus, the change of the electronic system is rather small as well. Similar distortions were also found for ternary alloys such as Ge1 Sb2 Te4 (ref. 22). The situation in which a single, half-filled p-band forms two bonds to the left and right (more than allowed by the 8-N rule) was called resonant bonding by Pauling23 . This bonding is schematically shown in Fig. 5, which shows the (001) plane of a hypothetical simple cubic crystal of Sb. In this structure, each Sb atom has six nearest neighbours, but only three p-electrons to facilitate covalent bonding between adjacent Sb atoms. Different limiting cases can be identified as shown on the left- and right-hand side of Fig. 5. In reality, a superposition of these configurations is observed, which is schematically shown in the middle of this figure. This electron configuration has been coined as resonance bonding by Pauling. The pronounced electron delocalization, which characterizes resonant bonding, leads to a significantly increased electronic polarizability. This phenomenon is one of the fingerprints of resonance bonding. The true crystal structure of Sb is not a simple cubic structure, but the A7 structure, which can be described as a distorted simple nature materials VOL 7 AUGUST 2008 www.nature.com/naturematerials


ARTICLES cubic structure. This distortion increases electron localization because the two limiting electron configurations shown in Fig. 5 are no longer energetically equivalent. Thus, resonance bonding is weakened by the distortion, which is frequently denoted as a Peierls-like distortion. Hence, it is important to note that the distortion does not give rise to the large electronic polarizability and phase-change behaviour, but rather endangers it. The size of the contribution of resonance bonding can best be estimated from amorph − 1. the relative increase of the electronic polarizability, εcryst ∞ /ε ∞ This number is listed in the third column of Table 1. Resonance bonding is the cause of the large optical dielectric constant observed in many crystalline IV–VI compounds24,25 . It results in larger optical dielectric constants than in pair-bonded materials because it gives smaller average bandgaps (bonding– antibonding splitting) and larger optical matrix elements than electron pair bonding, as shown by Littlewood25 . The crystal structures of phase-change materials are all based on distorted cubic structures and all possess resonant bonding. It is therefore the cause of their higher optical dielectric constants. The existence of resonant bonding requires a longer-range order than the conventional electron pair bond of the 8-N rule. An electron pair only requires the ordering of the nearest neighbours forming the pair bond. Resonant bonding, on the contrary, requires the second and higher neighbours to be aligned. In the amorphous state, this higher level of ordering is not possible, and so the structure reverts to a simple 8-N rule structure, which requires a lower level of ordering, as noted by Lucovsky and White26 . This emphasizes that the bonding between the phases differs not only in coordination numbers as seen by EXAFS spectroscopy but also in their mediumrange order. The simplest example of resonant bonding is the trigonal structure of crystalline Se and Te. In these elements, the spiral chains of Se and Te are also distortions of simple cubic structures, in which there is a strong ordering between bonds on adjacent chains so that the p-orbitals again form into linear chains as in the A7 structure27,28 . However, on amorphizing the trigonal structure, this order is lost; their structure becomes more molecular with shorter interchain distances and longer interchain distances, and no obvious correlations between chains29 . The dielectric constant shows a strong fall from trigonal Te to amorphous Te and trigonal Se to amorphous Se (Table 1)29–32 . Thus, the decrease in ε∞ values between the amorphous and crystal phases of phase-change materials can be taken as clear evidence that the medium-range order needed for resonant bonding is absent in their amorphous phases. This change in bonding between the amorphous and crystalline phases, with a strong rearrangement of the next-nearest neighbours, is at least as significant as the lowering of the Ge coordination to four, or the formation of Ge–Ge bonds. This difference is more difficult to see in EXAFS. The row-five elements Te and Sb have the strongest difference in bonding between the amorphous and crystalline phases, while still having a bandgap. Their crystalline phases have more resonant bonding, in that their short-bond and long-bond distances are closer than in the equivalent row-four elements Se and As. Thus, bonds in Se even in the crystalline phase are close to electron pair bonds (see data in Table 1). In this way, Se and selenides are good glass formers, whereas Te and tellurides are poor glass formers, and have the rapid crystallization rates needed for phasechange materials. For all amorphous phases, we observe a very similar behaviour for both phase-change materials as well as sp3 bonded, tetrahedrally coordinated covalent semiconductors. On the contrary, only phase-change materials exhibit a significant increase in polarizability on crystallization. This finding is

attributed to a unique change of both structure and chemical bonding, giving rise to resonance bonding effects. Hence, from the viewpoint of property contrast, it is not the amorphous phase but the crystalline phase that is unique. The search for materials exhibiting the necessary optical contrast required for phase-change memory applications can hence be redirected. Those compounds need to be identified that are prone to the occurrence of this particular type of covalent bonding. As resonance bonding can only occur for semiconductors that possess unsaturated covalent bonds, all sp3 -bonded materials can immediately be excluded. In addition, materials that rearrange to form saturated covalent bonds by pronounced local distortions also will not possess resonance bonding. Therefore, it becomes possible to derive structure–property maps based on an understanding for which compositions resonance bonding can be expected in the crystalline state. Such maps are not only useful because they identify candidates for storage applications. More importantly, the understanding of the bonding characteristics contained in such data will provide insight into systematic property changes, which can help to tailor materials for specific storage applications. The measurement scheme presented provides both a recipe for the identification of candidates that show resonant bonding and quantifies the strength of this bonding mechanism. This information provides a basis for the discussion of differences in bonding as a function of stoichiometry.

METHODS SAMPLE PREPARATION To prepare the samples, a 150 nm Au layer is deposited using a homebuilt thermal evaporator (background pressure 2 × 10−5 mbar, 0.4 nm s−1 deposition rate, Au of 99.99% purity) onto a glass substrate. Subsequently, the phasechange films (500 or 1,000 nm) are d.c. sputter-deposited with an LS 320 von Ardenne system (background pressure 4 × 10−7 mbar, 20 s.c.c.m. Ar flow, deposition rates 0.1–0.2 nm s−1 , operating in constant power mode using 20–25 W) using stoichiometric targets of 99.99% purity. The as-deposited amorphous films were annealed in Ar atmosphere for 30 min at temperatures about 20 ◦ C above the corresponding crystallization temperature to obtain polycrystalline samples. The structure of the phase-change samples was checked by X-ray diffraction. The film densities were determined by accompanying measurements on 80 nm thin films with X-ray reflectometry. The phase-change layer thickness was determined on reference samples prepared in the same sputter session using an Alpha-Step 200 profilometer (Tencor Instruments). Nine thickness values were taken at different positions and their average value was used as a reference for the optical simulations. OPTICAL MEASUREMENTS Reflectance spectra have been measured in the range from 0.025 to 1 eV, using a Bruker IFS 66v/s spectrometer with a resolution of 0.12 meV using a globar. The reflectance spectra of the reference and the sample were measured subsequently to exclude drift effects. For normalization, the final spectrum was obtained by dividing the measured spectrum by the reference spectrum. The angle of incidence of the incoming beam was kept constant at 10◦ with respect to the surface normal. The relative measurement error for the reflectance is 0.2% in the measured wavelength range. Ellipsometry spectra have been measured in the range from 0.7 to 5.2 eV using a Woolam M-2000UI using angles of incidence of 60◦ , 69◦ and 78◦ . Deuterium and halogen lamps served as light sources. As detectors, a silicon charge-coupled device camera was used for the visible and ultraviolet range, whereas the lower energy range was covered by an InGaAs diode array. This detector uses 584 channels with an average resolution of about 7 meV. Both ellipsometry and FTIR spectra have been recorded at room temperature. MODELLING OF THE SPECTRA Both experimental ellipsometry and FTIR spectra were analysed simultaneously in the range from 0.05 to 3 eV using the SCOUT software. The model dielectric function ε(ω) used is composed of the following summands: (1) a constant,



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ARTICLES which accounts for the polarizability in the higher energy range (for example, contribution of core electrons), (2) a Drude-type contribution for free carriers in the case of the crystalline samples, and finally, (3) a Tauc–Lorentz oscillator33,34 to describe the onset of optical transitions:

ε (ω) = εconst + εDrude (ω) + εTauc–Lorentz (ω) εDrude (ω) =

Im (εTauc–Lorentz (ω)) =

ω2p ω (ω + iγ )

1 S2 ω0 γ ω − ωgap Θ ω − ωgap . ω ω2 − ω20 2 + ω2 γ 2

A layer stack as presented in Fig. 1b was simulated, with the dielectric function of gold taken from a database. The latter was checked to be in excellent agreement with the optical properties of the reference specimen, the gold coating. The film thickness of the semiconductor layer was fitted within the confidence interval of the Alpha-Step measurement. The error of ε∞ was estimated by quantifying its variation with respect to the film thickness. The optical gap Eg was identified as the energy where the absorption α exceeds 10.000 cm−1 . The optical dielectric constant ε∞ was determined from the dielectric function as ε1 (0.05 eV) = ε∞ , in the crystalline case after subtracting the Drude contribution.

Received 6 March 2008; accepted 16 June 2008; published 11 July 2008. References 1. Wuttig, M. & Yamada, N. Phase-change materials for rewriteable data storage. Nature Mater. 6, 824–832 (2007). 2. Welnic, W., Botti, S., Reining, L. & Wuttig, M. Origin of the optical contrast in phase-change materials. Phys. Rev. Lett. 98, 236403 (2007). 3. Ovshinsky, S. R. Reversible electrical switching phenomena in disordered structures. Phys. Rev. Lett. 21, 1450–1453 (1968). 4. Lankhorst, M. H. R., Ketelaars, B. W. S. M. M. & Wolters, R. A. M. Low-cost and nanoscale non-volatile memory concept for future silicon chips. Nature Mater. 4, 347–352 (2005). 5. Lacaita, A. L. & Wouters, D. in Nanotechnology Vol. 3 (ed. Waser, R.) (Wiley–VCH, Weinheim, 2008). 6. Ielmini, D. & Zhang, Y. G. Analytical model for subthreshold conduction and threshold switching in chalcogenide-based memory devices. J. Appl. Phys. 102, 054517 (2007). 7. Lee, B. S. et al. Investigation of the optical and electronic properties of Ge2 Sb2 Te5 phase change material in its amorphous, cubic, and hexagonal phases. J. Appl. Phys. 97, 093509 (2005). 8. Mendoza-Galvan, A. & Gonzalez-Hernandez, J. Drude-like behavior of Ge:Sb:Te alloys in the infrared. J. Appl. Phys. 87, 760–765 (2000). 9. Luo, M. B. & Wuttig, M. The dependence of crystal structure of Te-based phase-change materials on the number of valence electrons. Adv. Mater. 16, 439–443 (2004). 10. Yamada, N. & Matsunaga, T. Structure of laser-crystallized Ge2 Sb2+x Te5 sputtered thin films for use in optical memory. J. Appl. Phys. 88, 7020–7028 (2000).

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11. Jellison, G. E. Spectroscopic ellipsometry data analysis: Measured versus calculated quantities. Thin Solid Films 313, 33–39 (1998). 12. Ashcroft, N. & Mermin, D. Solid State Physics 542 (Holt-Saunders, Philadelphia, 1976). 13. Levine, B. F. Bond susceptibilities and ionicities in complex crystal-structures. J. Chem. Phys. 59, 1463–1486 (1973). 14. Olsen, J. K., Li, H. & Taylor, P. C. On the structure of Gex Sby Te1−x−y glasses. J. Ovonics Res. 1, 1–6 (2005). 15. Kolobov, A. V. et al. Understanding the phase-change mechanism of rewritable optical media. Nature Mater. 3, 703–708 (2004). 16. Baker, D. A., Paesler, M. A., Lucovsky, G., Agarwal, S. C. & Taylor, P. C. Application of bond constraint theory to the switchable optical memory material Ge2 Sb2 Te5 . Phys. Rev. Lett. 96, 255501 (2006). 17. Jovari, P. et al. Local order in amorphous Ge2 Sb2 Te5 and Ge1 Sb2 Te4 . Phys. Rev. B 77, 035202 (2008). 18. Rabe, K. M. & Joannopoulos, J. D. Structural properties of GeTe at T = 0. Phys. Rev. B 36, 3319–3324 (1987). 19. Robertson, J., Xiong, K. & Peacock, P. W. Electronic and atomic structure of Ge2 Sb2 Te5 phase change memory material. Thin Solid Films 515, 7538–7541 (2007). 20. Peierls, R. E. Quantum Theory of Solids (Oxford Univ. Press, Oxford, 1956). 21. Gaspard, J. P. & Ceolin, R. Hume-Rothery rule in V–VI compounds. Solid State Commun. 84, 839–842 (1992). 22. Wuttig, M. et al. The role of vacancies and local distortions in the design of new phase-change materials. Nature Mater. 6, 122–127 (2007). 23. Pauling, L. Nature of Chemical Bond (Cornell Univ. Press, New York, 1939). 24. Littlewood, P. B. The crystal structure of IV–VI compounds: I. Classification and description. J. Phys. C 13, 4855–4873 (1980). 25. Littlewood, P. B. Dielectric-constant of cubic IV–VI compounds. J. Phys. C 12, 4459–4468 (1979). 26. Lucovsky, G. & White, R. M. Effects of resonance bonding on properties of crystalline and amorphous semiconductors. Phys. Rev. B 8, 660–667 (1973). 27. Robertson, J. New model for structure of amorphous selenium. Phil. Mag. 34, 13–31 (1976). 28. Joannopoulos, J. D., Schluter, M. & Cohen, M. L. Electronic-structure of trigonal and amorphous Se and Te. Phys. Rev. B 11, 2186–2199 (1975). 29. Leiga, A. G. Optical properties of trigonal selenium in vacuum ultraviolet. J. Opt. Soc. Am. 58, 880–884 (1968). 30. Leiga, A. G. Optical properties of amorphous selenium in vacuum ultraviolet. J. Opt. Soc. Am. 58, 1441–1445 (1968). 31. Tutihasi, S., Roberts, G. G., Keezer, R. C. & Drews, R. E. Optical properties of tellurium in fundamental absorption region. Phys. Rev. 177, 1143–1150 (1969). 32. Bammes, P., Tuomi, T., Klucker, R. & Koch, E. E. Anisotropy of dielectric-constants of trigonal selenium and tellurium between 3 and 30 eV. Phys. Status Solidi B 49, 561–570 (1972). 33. Potts, W. J. Chemical Infrared Spectroscopy (Wiley, New York, 1963). 34. Schubert, M. Infrared Ellipsometry on Semiconductor Layer Structures (Springer Tracts in Modern Physics, Vol. 209, Springer, Berlin, 2004). Supplementary Information accompanies this paper on www.nature.com/naturematerials.

Acknowledgements We gratefully acknowledge the design of Fig. 5 by P. Merkelbach, the careful preparation of phase-change targets by Umicore (Liechtenstein) within the EU project CAMELS and financial support by the Deutsche Forschungsgemeinschaft.

Author information Reprints and permission information is available online at http://npg.nature.com/reprintsandpermissions. Correspondence and requests for materials should be addressed to M.W.

