Phase Stability and Anisotropic Sublimation of Cubic GeâSbâTe Alloy

Article The Journal of Physical Phase Stability Chemistry C is published by the American and Anisotropic Chemical Society. 1155 Sixteenth Street N.W., Sublimation of Cubic Washington, DC 20036 American Subscriber accessPublished providedbyby UNIV OF Chemical Society. NEW ENGLAND ARMIDALE Copyright © American Chemical Society.

Ge-Sb-Te Alloy Observed The by JournalInof Physical Chemistry C is published by the American Situ Transmission Chemical Society. 1155 Sixteenth Street N.W., Electron Microscopy Washington, DC 20036

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Katja Berlin, and Achim Trampert The Journal of Physical

J. Phys. Chem. C,Chemistry Just Accepted C is published by the 10.1021/ American Manuscript • DOI: Chemical Society. 1155 acs.jpcc.7b09855 • Publication Sixteenth Street N.W., Date (Web): 20 Dec 2017 Washington, DC 20036 American Subscriber accessPublished providedbyby UNIV OF Chemical Society. NEW ENGLAND ARMIDALE Copyright © American Chemical Society.

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and ethical guidelines that apply to the jo or consequences arising from the use of in The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 American Subscriber accessPublished providedbyby UNIV OF Chemical Society. NEW ENGLAND ARMIDALE Copyright © American Chemical Society.

Si

Page 1 of The 47 Journal of Physical Chemistry

640°C

[111]

1 2 3 4 5 26nm

GST

10 nm Te

[112]

Ge,Sb

ACS Paragon Plus Environment d111 t0

1.15 s

(111) 2.3 s

d111

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Phase Stability and Anisotropic Sublimation of Cubic Ge-Sb-Te Alloy Observed by In-Situ Transmission Electron Microscopy

Katja Berlin and Achim Trampert

∗

Paul-Drude-Institut für Festkörperelektronik, Hausvogteiplatz 5-7, 10117 Berlin, Germany

E-mail: [email protected]

Phone: +49 (0)30 20377280

1

ACS Paragon Plus Environment

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The Journal of Physical Chemistry

Abstract Phase stability and anisotropic sublimation dynamics of the cubic Ge-Sb-Te alloy have been investigated by in-situ transmission electron microscopy (TEM). Starting point of the phase transition study is an epitaxially aligned Ge1 Sb2 Te4 grain on a Si(111) substrate. Upon in-situ heating, the cubic phase remains stable up to the sublimation point without a transition to the thermodynamically stable trigonal crystal structure which is attributed to Si diusion into the GST grain. The sublimation process is made visible with atomic resolution. The anisotropic process leads to the formation of stable {111} facets via kink nucleation on stable steps and subsequent sublimation from those kink sites as predicated by the terrace-step-kink model. Kink nucleation sites are identied and are in accordance with the broken-bond model approach.

Introduction The ternary Ge-Sb-Te alloy has attracted great interest due to its broad application as phase change material in non-volatile storage devices utilizing the fast and reversible phase transformation between its amorphous and crystalline cubic phase. 13 Highly intensive local heating as well as extremely fast heating and cooling rates are required to switch with great speed between the phases whereby material degradation has to be avoided at the relevant operating temperatures. Generally, Ge-Sb-Te alloys crystallizes from the metastable amorphous into the cubic phase between 130 ◦ C and 150 ◦ C and undergoes a second phase transition into the trigonal phase at a temperature between 300 ◦ C and 350 ◦ C depending on the actual chemical composition. 46 While these solid-solid phase transitions as well as the transition into the molten state have been studied in detail, 610 only very few experiments address problems related to the phase stability. For example, volume shrinkage during re-crystallization can lead to void formation in encapsulated GST material after high temperature processes 6 and thus sublimation can occur at the crystal-void interface. Besides these technological aspects, thermally induced sublimation and its associated atomistic processes are of fundamental sig2



nicance. Since sublimation is a solid-vapor phase transition in which atoms dissolve away from the crystal lattice and move into the gas phase, the investigation of the underlying mechanisms on the atomic scale might shed additional light on the inverse process of crystal growth, which is not yet understood comprehensively. In-situ transmission electron microscopy (TEM) oers the possibility for direct observation of sublimation at the atomic scale and in real time. So far, almost all TEM investigations on sublimation were performed on nanostructures such as nanowires, nanorods, or nanoparticles consisting of relatively simple material systems in order to observe changes in shape, morphology or faceting. 1122 Atomic processes during sublimation were mostly observed on two-dimensional layered materials where projection problems are excluded naturally. In case of phase change materials, the in-situ TEM study of GeTe nanowires enclosed by a SiO 2 shell showed a size-dependent sublimation rate. The rate is used to evaluate the vaporization coefcient of the nanowire geometry. 13 On the other hand, Ge 2 Sb2 Te5 lms on SiO2 were studied by in-situ high-resolution TEM and electron energy-loss spectroscopy (EELS) with emphasis on the crystallization from the amorphous phase and the cubic-hexagonal phase transition. The sublimation process is mentioned briey in connection with electron irradiation eects but without submitting any further details. 23 In the present study, high temperature stability and sublimation of Ge 1 Sb2 Te4 thin lms deposited on Si(111) substrates are investigated with atomically resolved cross-sectional TEM in real time. At 600 ◦ C the cubic phase is still present and an anisotropic sublimation occurred via fast kink/step formation along h110i and h112i directions forming energetically favorable {111} facets. The results are discussed in the framework of a simple terrace-step-kink model.

Experimental Section An amorphous Ge1 Sb2 Te4 (GST124) lm was deposited at room temperature on a cleaned single crystalline silicon (111) wafer in an ultra-high vacuum chamber using eusion cells for

3


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the individual elements. Details about the deposition process can be found elsewhere. 24,25 The thickness of the as-grown lm as determined by cross-sectional transmission electron microscopy (TEM) amounts to 55 nm and furthermore, the chemical composition was examined by electron energy-loss spectroscopy in the TEM. 10 The TEM data were collected in a JEOL 2100F operating at 200 kV and equipped with an UltraScan 4000 (Model 895) CCD camera. The in-situ videos were recorded using the continuous mode for a (1k x 1k) image in Digital Micrograph TM software from Gatan giving us a temporal resolution of 1.15 sec. A micro-electro-mechanical system (MEMS)-based double-tilt sample holder from DENSsolutions (model D6+) is used to carry out the lowdrift in-situ heating measurements. The DENSsolutions system regulates the temperature by monitoring the resistance of a Pt wire using a 4-point measurement. 15 The cross-sectional TEM samples were prepared in a lamellae geometry and placed directly on the MEMS micro-hotplate. This preparation is done with a JEOL IB4501 system that combines a focused ion beam (FIB) and a scanning electron microscope (SEM). A thin lm of carbon is deposited onto the wafer with a carbon coater to protect the GST thin lm from direct Ga+ ion exposure. The lamella is cut out of the wafer and transferred to a half-moon copper grid by standard FIB lift-out procedure. 26 The transport inside the FIB vacuum chamber is done by a micro-manipulator from Kleindiek Nanotechnik GmbH. The lamella is glued onto the grid by ion beam assisted tungsten deposition. The intermediate step of transferring the lamella to a copper grid is necessary to rotate the lamella in a controlled way by 90◦ in order to place it at onto the MEMS micro-hotplate. The nal thinning to reach electron transparency was done on the chip and achieved by sputtering with the Ga+ ion beam using accelerating voltages down to 5 kV in order to minimize the thickness of the damage layer. During FIB preparation Ga + ions are unintentionally deposited on or incorporated into the sample mainly in the area of the carbon protective layer. During in-situ heating Ga atoms become mobile (TM,Ga = 29.8◦ C 27 ) and cluster into Ga droplets posing a risk of interfering

4



with the process under study. An eective way to suppress the interference by Ga droplets is the application of a sucient thickness of the protective carbon layer, in which case the Ga droplet will be formed away from the region of interest. (a) temperature (°C)

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(b)

epitaxial grains formed 600 observation of (c) sublimation

(d)

RT

carbon GST

GST

Si

400 200 0

RT

(c) (b)

625 °C Si

(d) time (min)

Figure 1: (a) Schematic experimental procedure for in-situ heating of GST thin lm rst from RT to 625 ◦ C to generate epitaxial aligned cubic grains and in second to 640 ◦ C for in-situ observation of sublimation of cubic grains, (b) BF-TEM image of a FIB-lamella on a DENSsolutions chip with GST thin lm in initial amorphous state featuring the Si substrate and carbon protective layer, scale bar = 1 µm. (c) Same lamella at 625 ◦ C showing the thinned areas and voids left by rst heat treatment, scale bar = 1 µm. (d) HRTEM image of cubic epitaxially aligned grain taken after cooling down to room temperature (image taken from similarly treated sample), scale bar = 2 nm. The temperature treatment of the GST thin lm inside the TEM is displayed in a schematic temperature-versus-time plot in Fig. 1a. A bright-eld (BF) scanning (S)TEM overview image of the as-deposited amorphous GST lm prepared in the lamella geometry is shown in Fig. 1b. In order to generate epitaxially aligned GST the amorphous lm was rst heated to 625 ◦ C followed by a quick cool down within 3 sec. At the high temperature, sublimation instead of melting has occurred because the lm was not encapsulated. 10 The BF-STEM image at 625 ◦ C in Fig. 1c shows that the GST thin lm decomposes leading to an overall thinning of the sample leaving faceted grains and holes behind. Simultaneously, reorientations of crystal grains with cubic structure proceeds resulting in an epitaxial 5


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alignment to the crystalline Si(111) substrate (cf. HRTEM image in Fig. 1d). Using Si as a reference, the lattice parameter of GST was determined to be 0.61 ±0.01 nm which is in good agreement with the reported lattice parameter of 0.60440 nm for GST124 with NaCl crystal structure. 28,29 The cubic grains produced in this way serve as the initial state for the sublimation study. During our in-situ TEM measurements, an impact of the high energy electron beam by local heating or knock-on processes can be neglected. On the one hand, Lotnyk

et al.

have shown that in GST the sputtering of Ge and Sb is much smaller than our observed sublimation rate. 30 And on the other hand, Kooi

et al.

demonstrated that the main eect of

the electron beam is displacement damage by knock-on collisions compared to local sample heating. 6

Results Thermal Evolution of GST Grain Structure The initial state of the GST grain before the sublimation process started is shown in Fig. 2a. The TEM micrograph is taken at room temperature along the [1 ¯ 10] zone axis of Si and displays an overview of the grain with projected size of about 130 nm × 50 nm. The highresolution image reveals a crystallographic alignment of the GST grain with the Si substrate as veried by the perfect matching of the {111} planes between cubic GST and Si across the interface (see magnied image of the edge of the grain in Fig. 2b). Based on this plane matching combined with the results of the Fourier analysis (inset in Fig. 2a), the following orientation relationship is deduced: (111)GST k (111)Si and [1¯ 10]GST k [1¯10]Si. Such a well-oriented grain is required for the in-situ heating study in order to be able to observe the time-dependent variations in shape and surface morphology with respect to crystallographic planes and directions with highest spatial resolution. Accordingly, the HRTEM image in Fig. 2c shows the very same GST grain after heating-up to 640 ◦ C. The micrograph is 6



(a)

23 °C

(220)

Page 8 of 47

(111)

(b)

GST (111) [111] [110]

[112]

Si 640 °C

(c)

(220)

(111)

(d)

(111)

GST Si

Figure 2: HRTEM image of cubic GST grain at (a) 23 ◦ C (initial state) and (c) 640 ◦ C (after start of sublimation) stitched together from several images. Black arrows in (c) mark some of the edges along [112] that formed during sublimation. Insets showing FFT of central region of the image containing Si and GST. Close-up views in (b) and (d) show the corresponding grain surface at Si-GST interface region. (a), (c) scale bar = 20 nm and (b), (c) scale bar = 2nm. recorded a few seconds after reaching the target temperature. Compared to the original status, which is described by a shapeless grain morphology, the short-time heated grain has already visibly modied its shape without changing the overall crystallographic orientation (cf. HRTEM in Fig. 2d). The initial surface roughness is remarkably attened, in particular in the thin areas of the grain on top and at the right side, accompanied with the formation of straight-lined {111} oriented steps as indicated by black arrows in Fig. 2c. The change in volume and shape is a result of surface and volume diusion and atom evaporation at this high temperature. Taking into account the melting point of the bulk 7


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GST124 of 616 ◦ C, and the partial pressures of Te ( ∼103 Pa) and Sb (∼101 Pa) 27 at the applied temperature, the in-situ TEM heating of GST is expected to lead to sublimation, even if the partial pressure for Ge is quite low ( ∼10−10 Pa 27 ) and in the range of the base pressure of the microscope. Moreover, the grain does not point to any Ge excess compared to the composition before annealing. In fact, our EELS analysis performed on similar treated samples has proven that there is no change in chemical composition of the GST after heating and partial sublimation.

Anisotropic Sublimation of Cubic GST The in-situ observation reported here demonstrates that sublimation of the cubic GST grain is distinctly anisotropic taken place via the predominant formation of kinks at {111} facets, which subsequently move along the h110i direction and thus leading to an observable step motion along the h112i direction. Figure 3a shows the tested grain after 17 min of overall sublimation time along the [1 ¯ 10] zone axis of Si. The grain is signicantly reduced in size compared to the situation displayed in Fig. 2c (onset of sublimation) leading to a thin crystal with a rhomboidal shape in projection and crystal edges whose projections are along

h112i directions. There are contrast modulations detectable along the cubic grain indicating a change in local thickness. The {111} facets are plausible low-index candidates to form stable surfaces featuring edges along h110i directions which lead to edges along h112i in [1¯ 10] projection. Figure 3b displays a 3D model of cubic GST where {111} facets form an octahedron. This {111} octahedron is the simplest shape to fulll the cubic symmetry and the projected rhomboidal shape with edges along h112i (cf. crystal structure projected along [1¯ 10] in Fig. 3b). Furthermore, the observed contrast modulations are consistent with thickness changes due to sloping {111} facets. On the other hand, abrupt transitions along crystallographic directions are visible in the HRTEM micrograph. Because of the slightly o-zone axis imaging condition, the surface structure contributes more strongly to the HRTEM contrast, and thus steps became clearly visible 31 indicating that the real shape 8



Page 10 of 47

of the crystal in Fig. 3a is more complex than a perfect equilateral {111} octahedron and might be composed of monolayer and multi-layer deep steps along h110i.

(c)

t0

GST

35.65 s

100.05 s

[112] [111]

[111]

Si

Figure 3:

Sample geometry and overview of sublimation process: (a) HRTEM image of

cubic GST grain at 640 ◦ C recorded 17 min after the start of sublimation and display close to the Si-[1¯ 10] zone axis. (b) Schematic 3D model of cubic GST with {111} facets forming an octahedron and a projection of the GST structure along [1 ¯ 10]. The Te atoms (green) make up the {111} surfaces and the Ge and Sb atoms as well as vacancies (light magenta) form the second layer. (c) HRTEM image series of the cubic GST grain on Si at 640 ◦ C featuring visible steps (red) moving along h112i. Scale bar = 10 nm. Figure 3c depicts a series of HRTEM images taken from a video sequence that shows subsequent stages of the sublimation process over a time period of 100 sec. (The video S1 in the supporting information shows the whole sequence). It is evident that the grain shrinks in a self-similar manner retaining the rhomboidal shape. Thereby, the sublimation occurs via kink-step-terrace formation mechanism. Several exemplary steps are marked with red and 9


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blue arrows in Fig. 3c. Note that "kinks" are not directly visible in the [1 ¯ 10] projection. It is assumed that after being nucleated, kinks propagate along the h110i direction creating a step on the {111} facet (cf. Fig. 3b) whose movement along h112i direction is then observed. The kink formation is initiated at edge corners of the grain (red arrows) and also at step-edges (blue arrows) because of the real shape being more complex than the perfect equilateral octahedron. The anisotropic and fast kink movement results in a reduction of the surface roughness and the development of straight-lined steps and nally terraces provided that the process is nucleation-limited. In the following, the sublimation process is discussed using the examples of the dynamics along [11¯ 1] (black arrow in Fig. 3c) and [¯1¯11] (blue arrow in Fig. 3c) direction. Figure 4 extensively illustrates the dynamics of step motion during sublimation at the atomic scale. The gure in (a) present three consecutive HRTEM snapshots of the border of the crystal. The images clearly resolve the {111} planes of cubic GST which terminate the edges of the grain forming an atomically sharp and straight facet. Figure 4b displays a model of the atomic arrangement of cubic GST in projection along our viewing direction. The measured lateral step height of 0.35 nm corresponds to the distance of the {111} lattice planes, d 111 =0.3489 nm. One set of {111} planes is composed of a pair of planes belonging to both sublattices, the Te atoms on the one hand and randomly distributed Ge and Sb atoms on the other hand. 29 For this reason, a step with a lateral expansion (step height) of one {111} plane ("single-step") involves the sublimation of all three atomic species within our spatial and temporal resolution. The kink nucleates at the edge corner where two facets build a "convex" crystal edge. From there, the kink propagates along the [1¯ 10] direction and is only visible as a step when the entire atomic row along the viewing direction ( [1¯ 10]) is removed. This kink movement is faster than our temporal resolution. The kink forms a single-step or occasionally a doublestep edge along the viewing direction and is easily recognizable in the HRTEM images (cf. red arrow in the central image of Fig. 4a). Most commonly, steps move across the entire

10



(b)

Si

(a)

GST

[112]

[111] d111

t0

1.15 s

d111

2.3 s

(111) Te Ge/Sb/ Vac

(c) Cum. length sublimed along [111] (nm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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12

Figure 4:

single-step-motion

8 4 0 0

30

60 time t-t0(s)

90

120

Sublimation at the [ ¯ 1¯11] facet via kink nucleation and single-step movements

along [¯ 1¯1¯2]: (a) Series of HRTEM images taken from a video of the cubic GST grain at 640 ◦ C showing the nucleation and movement along [ ¯ 1¯1¯2] (red arrow) of one step in three consecutive images, scale bar = 2 nm. (b) Atomic arrangement on a (110) plane where one set of atomic sites on (111) planes is occupied by Te, while the other is occupied by Ge/Sb/Vac. (c) The cumulative sublimed length is measured as a function of time along [11¯ 1] direction (black arrow in (a)) featuring mostly single-steps. length of the grain edge (about 13 nm) along the h112i directions within one consecutive frame, i.e. within 1.15 sec. The kink/step velocity can be therefore estimated to be equal or faster than 11 nm/s. To follow up the time dependent process more comprehensively, the cumulative sublimed length along [11¯ 1] direction is plotted as a function of time in Fig. 4c. The curve progression resembles an irregular step-function representing the linear shrinkage of the grain over a period of two minutes. Each step in the graph corresponds to the fast kink/step motion, whereas the step height corresponds to the lateral expansion of the crystal step and

11


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the plateau area measures the time between two nucleation events ranging mostly between 1.15 sec and 3.45 sec. Regardless of the low time resolution of our measurement, it must be concluded that the sublimation process is kink nucleation-limited as furthermore evidenced by the fact that straight facets develop and, accordingly, no step roughening is observed at this high temperature. This result is further supported by the observation of the sublimation along the [¯ 1¯11] direction, i.e. at the opposite site of the grain. Figure 5a presents the corresponding cumulative sublimed distance-versus-time plot. In spite of the large time frame of 7.5 min in total, only six nucleation events are observed (indicated by arrows). The time between two nucleation events ranges from 8 sec to 150 sec according to the plateau widths. The height of the jumps in the step-function reects the lateral step expansion, which is - in this case mostly larger than one {111}-layer indicating a multi-kink nucleation behavior. Indeed, the HRTEM image series in Fig. 5b reveals the presence and structure of a multi-step construction. The exemplary step ensemble covers four {111} planes with a staggered arrangement along the viewing direction and perpendicular to the {111} plane. The nucleation site is located at the GST/Si interface (see white short arrows) and the subsequent propagation of the step ensemble proceeds along the [112] direction until it crosses the transversely running {001} facet. The velocity of the multi-step ensemble depends on the number of step units involved, as shown in Fig. 5c, where the sublimed length is plotted over time. The estimated velocities in the linear sectors range from 0.5 to 1.8 nm/s where smaller velocities are observed for wider multi-step arrangements, i.e. v4-steps > v7-steps > v8-steps . This demonstrates the inuence of the number of kinks involved in the correlative ensemble motion. Compared to the velocity of the single-step conguration, these values are about one order of magnitude smaller.

12



(c) 12 8 4 0 40

multi-step motion single-step motion 80 120 160 200 240 280 320 360 400 440 time Δt=t-t0 (s)

Cum. length sublimed along [112] (nm)

(a) Cum. length sublimed along [111] (nm)

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12 8 1 layer 4 layer 7 layer 8 layer

4 0

0 5 10 15 20 25 30 time after nucleation (s)

(b) [111]

GST

Si [112]

t0

98.9 s

103.5 s

108.1 s

[001] 115.0 s

Figure 5: Sublimation at the [ 11¯ 1] facet via multi-kink nucleation and movement along [112] (exception: one single-step motion labeled with black arrow) (a) The cumulative sublimed length is measured as a function of time along [¯ 1¯11] direction (blue arrow in (b)) featuring ve multi-steps. (b) Series of HRTEM images taken from a video of the cubic GST grain at 640 ◦ C showing the nucleation of the rst kink after 98.9 sec (white arrow) followed by mass desorption from the kink site seen as step movement along [112] (red arrow), scale bar = 5 nm. (Video S2 in supporting information shows the whole sequence.) (c) Graph of step movement along [112] (red arrow in (c)) showing the cumulative sublimed length of each step starting after they nucleated at the Si-GST interface. The black line shows the faster movement of the sole single-step motion.

Discussion Stability of Cubic Phase at High Temperature As stated in previous reports, 9,32 annealing of cubic GST should rst lead to the formation of a vacancy layer ordering along the {111} planes, followed by the transition to the trigonal 13


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phase above 300 ◦ C. 4,5 Interestingly, the aligned GST grain retained the cubic NaCl-structure even up to the sublimation point in our study. A highly vacancy-ordered cubic structure could not be observed as no additional periodicity along the {111} planes were found as well as no indications of the trigonal phase. On the other hand, Fig. 2a,c reveal that the GST/Si interface becomes rough at higher temperatures as a result of Si diusion into the GST layer. In fact, EELS analysis (not shown here) demonstrates the emergence of a distinct Si signal besides Ge, Sb and Te after heating the sample to temperatures above the sublimation point and cooling it down again to room temperature. Qiao

et al.

33

have found that Si doping

(up to 10%) of GST is able to delay the transition from cubic to trigonal phase and thus stabilize the cubic structure at higher temperatures. They speculate that the formation of stronger covalent bonds with Si play a role. Consequently, one could conclude, that the Si atoms preferentially occupy the vacancy sites and there, avoid the ordering as the rst step towards phase transition. Although similar eects were measured for N doping of GST, 34 a comprehensive understanding of the stabilization mechanism is still far from being attained.

Kink Nucleation Site and Propagation According to the terrace-step-kink (TSK) model, 35 the sublimation of solid surfaces starts from sites with the lowest activation energy required to remove an atom from the surface. These preferential sites are discussed in terms of nearest neighbor bonds which must be broken. 35 Figure 6 shows a schematic drawing of the cubic grain to illustrate the four different possible kink nucleation start points, two for each opposing crystal edge. There are homogenous sites where only the GST crystal is involved in the sublimation process and heterogeneous sites where the GST and Si crystal form an interface. Additionally, the potential sites can be dierentiated in "convex" and "concave" depending on the crystal facets that meet at the specic site. Invoking the TSK model, the most preferable kink nucleation site is located at the homogenous, "convex" site of the grain (bonds to be broken: 1) compared to the other possible sites marked in Fig. 6. There is no "convex" site at the [11¯ 1] facet due 14



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Si 5 kink motion after nucleation [111]

[112]

heterogeneous, concave site GST

[112]

1 homogeneous, convex site 1

3 bonds to be broken

4 [112]

5 homogeneous, concave site

kink motion after nucleation [111] [001] [112]

octahedrally coordinated atom site with bonds viewed in 110 projection, number counts bonds to be broken Te - Ge/Sb/Vac bond bond to Si substrate broken bond


Figure 6: Schematic drawing to illustrate the dierent possible kink nucleation sites featuring two heterogeneous, concave sites at the GST-Si interface and two homogeneous sites where one is convex and the other one concave. The kink sites with the most broken bonds at each facet are marked in blue. Additionally, on the left and right hand site of the gure, the number of broken bonds after the kink nucleation and during the subsequent step motion along [112] and [¯ 1¯1¯2] direction, respectively, is illustrated. to a stable facet in [00¯ 1] direction crossing it. The second most favorable kink nucleation site considering the number of bonds is the heterogeneous, "concave" site on the [11¯ 1] facet (bonds to be broken: 4). The discussed preferred nucleation sites at each facet (marked in blue in Fig. 6) are those which are observed during sublimation. The rate with which the kinks are formed is 30 times faster for the [¯ 1¯11] facet compared to the opposing facet. As expected, the kink nucleation rate is much faster for the most preferable kink nucleation site. Besides the preferential starting points for kink formation, the subsequent kink propagation along [1¯ 10] direction should be identical on both crystal sites because of the same number of bonds which must be broken. Indeed, step velocities along [112] and [¯ 1¯1¯2] direction of about 11 nm/s and 5 nm/s, respectively, were estimated for the single step-motion. The apparent discrepancy is attributed to the fact that the step width along e-beam direction (local thickness) is dierent at both sides of the grain and therefore the kink propagation 15


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along [1¯ 10] takes longer as more material has to sublime for the same visible step motion along [¯ 1¯1¯2].

Surface Morphology and Crystal Shape During Sublimation Based on our observation of the grain morphology, shape and crystallographic orientation, we have concluded that {111} facets were predominately generated during the anisotropic sublimation process. Therefore, it is implied that these facets must be energetically favorable for cubic GST crystals at high temperature. From a general point of view, faceting of surfaces is driven by the anisotropy in surface energy γhkl as a function of the crystallographic orientation {hkl}. Due to the lack of data on specic surface energies for GST, a rst approximation can be made by applying the simplied broken-bond model on a rocksalt crystal structure and including the surface density of atoms. 36 This model yields that the {100} surface should have the lowest energy followed by the {110} and {111} surface, respectively. Consequently, a small particle in equilibrium shape consists primarily of those facet types. And indeed, we have observed cubic grains that have been formed after crystallization from melt droplet on a Si(111) substrate at 600 ◦ C exhibiting only {100}, {110} and {111} facets (shown in supplementary information S2). Furthermore, an estimation of the corresponding surface energies by applying the Wul-Kaishev construction demonstrate the following sequence γ111 < γ110 ≈ γ100 , which means that {111} surface has the lowest energy in accordance with the sublimation result. Nonetheless, during sublimation {111} facets are detected mainly pointing out that the shape might not be in equilibrium. The discrepancy can be ascribed on the inuence of the particular GST structure and the dierent partial pressure for the dierent atomic species: According to the crystal structure, the {111} surfaces consists of atoms from only one sublattice, either Te or Ge/Sb. 29 Due to the low vapor pressure of Ge, one can imagine that there is a preference for the Ge/Sb sublattice to form stable surfaces during sublimation. For the formation of {111} surfaces during the growth of trigonal GST grain, Kooi

et al.

6

also discussed the lowering of the surface energy by a 16



preference of Sb atoms to be at the surface. A dierent approach is to consider vacancies aiding the sublimation process by lowering the energies of bonds that need to be broken. Then, the plane where most vacancies are exposed to the surface is the stable facet. This would lead to the formation of {111} facets because vacancies are allocated on the Ge/Sb sublattice and are possibly already ordered to a certain degree which can not be observed yet in HRTEM phase contrast.

Conclusions The phase stability and sublimation behavior of cubic GST are investigated in this study. The cubic phase remains stable even up to the sublimation point and no ordering phenomena or transition to the trigonal phase is observed. This behavior could be related to Si diusion into GST at high temperatures. The sublimation of this ternary structure on a silicon substrate is observed with atomic resolution. The sublimation is anisotropic leading to the formation of {111} facets as plausible low-index candidates which is attributed to vacancies playing a role in the sublimation process. The observed dynamics are in accordance with the TSK-model for nucleation-limited dynamics: The sublimation happens via kink nucleation on stable steps and subsequent sublimation from those kink sites. Slow and fast kink nucleation in accordance with the broken-bond model and subsequent step movement with similar velocities is identied on opposing facets. Open questions include the formation process of the observed "multi"-steps. A possible approach is to study the inuence of interfacial defects which form due to a high lattice mismatch between Si substrate and GST thin lm on the sublimation mechanism.

Acknowledgement The authors would like to thank DENSsolutions for giving us the opportunity to perform the presented experiments by providing us with their heating sample holder (model D6+) and 17


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Dr. Michael Hanke for carefully reading the manuscript. Part of this work was nancially supported by the European Union and the state of Berlin via the EFRE project 2016011843.

Supporting Information Available The following les are available free of charge.

• Video1.avi: Video S1 shows the in-situ HRTEM overview sequence of the sublimation process of a cubic GST grain on a silicon substrate which is discussed in Fig. 3c.

• Video2.avi: Video S2 shows the in-situ HRTEM sequence of the multi-step sublimation process discussed in Fig. 5.

• SuppInfo.pdf: Supporting information about surface energies of GST.

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22



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Graphical TOC Entry Si

640°C

[111] GST

10 nm Te

[112]

Ge,Sb d111

2 nm

t0

(111)

1.15 s

2.3 s

23

d111


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Phase Stability and Anisotropic Sublimation of Cubic Ge-Sb-Te Alloy Observed by In-Situ Transmission Electron Microscopy

Katja Berlin and Achim Trampert

∗

Paul-Drude-Institut für Festkörperelektronik, Hausvogteiplatz 5-7, 10117 Berlin, Germany

E-mail: [email protected]

Phone: +49 (0)30 20377280

1



Abstract Phase stability and anisotropic sublimation dynamics of the cubic Ge-Sb-Te alloy have been investigated by in-situ transmission electron microscopy (TEM). Starting point of the phase transition study is an epitaxially aligned Ge1 Sb2 Te4 grain on a Si(111) substrate. Upon in-situ heating, the cubic phase remains stable up to the sublimation point without a transition to the thermodynamically stable trigonal crystal structure which is attributed to Si diusion into the GST grain. The sublimation process is made visible with atomic resolution. The anisotropic process leads to the formation of stable {111} facets via kink nucleation on stable steps and subsequent sublimation from those kink sites as predicated by the terrace-step-kink model. Kink nucleation sites are identied and are in accordance with the broken-bond model approach.

Introduction The ternary Ge-Sb-Te alloy has attracted great interest due to its broad application as phase change material in non-volatile storage devices utilizing the fast and reversible phase transformation between its amorphous and crystalline cubic phase. 13 Highly intensive local heating as well as extremely fast heating and cooling rates are required to switch with great speed between the phases whereby material degradation has to be avoided at the relevant operating temperatures. Generally, Ge-Sb-Te alloys crystallizes from the metastable amorphous into the cubic phase between 130 ◦ C and 150 ◦ C and undergoes a second phase transition into the trigonal phase at a temperature between 300 ◦ C and 350 ◦ C depending on the actual chemical composition. 46 While these solid-solid phase transitions as well as the transition into the molten state have been studied in detail, 610 only very few experiments address problems related to the phase stability. For example, volume shrinkage during re-crystallization can lead to void formation in encapsulated GST material after high temperature processes 6 and thus sublimation can occur at the crystal-void interface. Besides these technological aspects, thermally induced sublimation and its associated atomistic processes are of fundamental sig2


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nicance. Since sublimation is a solid-vapor phase transition in which atoms dissolve away from the crystal lattice and move into the gas phase, the investigation of the underlying mechanisms on the atomic scale might shed additional light on the inverse process of crystal growth, which is not yet understood comprehensively. In-situ transmission electron microscopy (TEM) oers the possibility for direct observation of sublimation at the atomic scale and in real time. So far, almost all TEM investigations on sublimation were performed on nanostructures such as nanowires, nanorods, or nanoparticles consisting of relatively simple material systems in order to observe changes in shape, morphology or faceting. 1122 Atomic processes during sublimation were mostly observed on two-dimensional layered materials where projection problems are excluded naturally. In case of phase change materials, the in-situ TEM study of GeTe nanowires enclosed by a SiO 2 shell showed a size-dependent sublimation rate. The rate is used to evaluate the vaporization coefcient of the nanowire geometry. 13 On the other hand, Ge 2 Sb2 Te5 lms on SiO2 were studied by in-situ high-resolution TEM and electron energy-loss spectroscopy (EELS) with emphasis on the crystallization from the amorphous phase and the cubic-hexagonal phase transition. The sublimation process is mentioned briey in connection with electron irradiation eects but without submitting any further details. 23 In the present study, high temperature stability and sublimation of Ge 1 Sb2 Te4 thin lms deposited on Si(111) substrates are investigated with atomically resolved cross-sectional TEM in real time. At 600 ◦ C the cubic phase is still present and an anisotropic sublimation occurred via fast kink/step formation along h110i and h112i directions forming energetically favorable {111} facets. The results are discussed in the framework of a simple terrace-step-kink model.

Experimental Section An amorphous Ge1 Sb2 Te4 (GST124) lm was deposited at room temperature on a cleaned single crystalline silicon (111) wafer in an ultra-high vacuum chamber using eusion cells for

3



the individual elements. Details about the deposition process can be found elsewhere. 24,25 The thickness of the as-grown lm as determined by cross-sectional transmission electron microscopy (TEM) amounts to 55 nm and furthermore, the chemical composition was examined by electron energy-loss spectroscopy in the TEM. 10 The TEM data were collected in a JEOL 2100F operating at 200 kV and equipped with an UltraScan 4000 (Model 895) CCD camera. The in-situ videos were recorded using the continuous mode for a (1k x 1k) image in Digital Micrograph TM software from Gatan giving us a temporal resolution of 1.15 sec. A micro-electro-mechanical system (MEMS)-based double-tilt sample holder from DENSsolutions (model D6+) is used to carry out the lowdrift in-situ heating measurements. The DENSsolutions system regulates the temperature by monitoring the resistance of a Pt wire using a 4-point measurement. 15 The cross-sectional TEM samples were prepared in a lamellae geometry and placed directly on the MEMS micro-hotplate. This preparation is done with a JEOL IB4501 system that combines a focused ion beam (FIB) and a scanning electron microscope (SEM). A thin lm of carbon is deposited onto the wafer with a carbon coater to protect the GST thin lm from direct Ga+ ion exposure. The lamella is cut out of the wafer and transferred to a half-moon copper grid by standard FIB lift-out procedure. 26 The transport inside the FIB vacuum chamber is done by a micro-manipulator from Kleindiek Nanotechnik GmbH. The lamella is glued onto the grid by ion beam assisted tungsten deposition. The intermediate step of transferring the lamella to a copper grid is necessary to rotate the lamella in a controlled way by 90◦ in order to place it at onto the MEMS micro-hotplate. The nal thinning to reach electron transparency was done on the chip and achieved by sputtering with the Ga+ ion beam using accelerating voltages down to 5 kV in order to minimize the thickness of the damage layer. During FIB preparation Ga + ions are unintentionally deposited on or incorporated into the sample mainly in the area of the carbon protective layer. During in-situ heating Ga atoms become mobile (TM,Ga = 29.8◦ C 27 ) and cluster into Ga droplets posing a risk of interfering

4


Page 28 of 47

Page 29 of 47

with the process under study. An eective way to suppress the interference by Ga droplets is the application of a sucient thickness of the protective carbon layer, in which case the Ga droplet will be formed away from the region of interest. (a) temperature (°C)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(b)

epitaxial grains formed 600 observation of (c) sublimation

(d)

RT

carbon GST

GST

Si

400 200 0

RT

(c) (b)

625 °C Si

(d) time (min)

Figure 1: (a) Schematic experimental procedure for in-situ heating of GST thin lm rst from RT to 625 ◦ C to generate epitaxial aligned cubic grains and in second to 640 ◦ C for in-situ observation of sublimation of cubic grains, (b) BF-TEM image of a FIB-lamella on a DENSsolutions chip with GST thin lm in initial amorphous state featuring the Si substrate and carbon protective layer, scale bar = 1 µm. (c) Same lamella at 625 ◦ C showing the thinned areas and voids left by rst heat treatment, scale bar = 1 µm. (d) HRTEM image of cubic epitaxially aligned grain taken after cooling down to room temperature (image taken from similarly treated sample), scale bar = 2 nm. The temperature treatment of the GST thin lm inside the TEM is displayed in a schematic temperature-versus-time plot in Fig. 1a. A bright-eld (BF) scanning (S)TEM overview image of the as-deposited amorphous GST lm prepared in the lamella geometry is shown in Fig. 1b. In order to generate epitaxially aligned GST the amorphous lm was rst heated to 625 ◦ C followed by a quick cool down within 3 sec. At the high temperature, sublimation instead of melting has occurred because the lm was not encapsulated. 10 The BF-STEM image at 625 ◦ C in Fig. 1c shows that the GST thin lm decomposes leading to an overall thinning of the sample leaving faceted grains and holes behind. Simultaneously, reorientations of crystal grains with cubic structure proceeds resulting in an epitaxial 5



Page 30 of 47

alignment to the crystalline Si(111) substrate (cf. HRTEM image in Fig. 1d). Using Si as a reference, the lattice parameter of GST was determined to be 0.61 ±0.01 nm which is in good agreement with the reported lattice parameter of 0.60440 nm for GST124 with NaCl crystal structure. 28,29 The cubic grains produced in this way serve as the initial state for the sublimation study. During our in-situ TEM measurements, an impact of the high energy electron beam by local heating or knock-on processes can be neglected. On the one hand, Lotnyk

et al.

have shown that in GST the sputtering of Ge and Sb is much smaller than our observed sublimation rate. 30 And on the other hand, Kooi

et al.

demonstrated that the main eect of

the electron beam is displacement damage by knock-on collisions compared to local sample heating. 6

Results Thermal Evolution of GST Grain Structure The initial state of the GST grain before the sublimation process started is shown in Fig. 2a. The TEM micrograph is taken at room temperature along the [1 ¯ 10] zone axis of Si and displays an overview of the grain with projected size of about 130 nm × 50 nm. The highresolution image reveals a crystallographic alignment of the GST grain with the Si substrate as veried by the perfect matching of the {111} planes between cubic GST and Si across the interface (see magnied image of the edge of the grain in Fig. 2b). Based on this plane matching combined with the results of the Fourier analysis (inset in Fig. 2a), the following orientation relationship is deduced: (111)GST k (111)Si and [1¯ 10]GST k [1¯10]Si. Such a well-oriented grain is required for the in-situ heating study in order to be able to observe the time-dependent variations in shape and surface morphology with respect to crystallographic planes and directions with highest spatial resolution. Accordingly, the HRTEM image in Fig. 2c shows the very same GST grain after heating-up to 640 ◦ C. The micrograph is 6


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(a)

23 °C

(220)

(111)

(b)

GST (111) [111] [110]

[112]

Si 640 °C

(c)

(220)

(111)

(d)

(111)

GST Si

Figure 2: HRTEM image of cubic GST grain at (a) 23 ◦ C (initial state) and (c) 640 ◦ C (after start of sublimation) stitched together from several images. Black arrows in (c) mark some of the edges along [112] that formed during sublimation. Insets showing FFT of central region of the image containing Si and GST. Close-up views in (b) and (d) show the corresponding grain surface at Si-GST interface region. (a), (c) scale bar = 20 nm and (b), (c) scale bar = 2nm. recorded a few seconds after reaching the target temperature. Compared to the original status, which is described by a shapeless grain morphology, the short-time heated grain has already visibly modied its shape without changing the overall crystallographic orientation (cf. HRTEM in Fig. 2d). The initial surface roughness is remarkably attened, in particular in the thin areas of the grain on top and at the right side, accompanied with the formation of straight-lined {111} oriented steps as indicated by black arrows in Fig. 2c. The change in volume and shape is a result of surface and volume diusion and atom evaporation at this high temperature. Taking into account the melting point of the bulk 7



GST124 of 616 ◦ C, and the partial pressures of Te ( ∼103 Pa) and Sb (∼101 Pa) 27 at the applied temperature, the in-situ TEM heating of GST is expected to lead to sublimation, even if the partial pressure for Ge is quite low ( ∼10−10 Pa 27 ) and in the range of the base pressure of the microscope. Moreover, the grain does not point to any Ge excess compared to the composition before annealing. In fact, our EELS analysis performed on similar treated samples has proven that there is no change in chemical composition of the GST after heating and partial sublimation.

Anisotropic Sublimation of Cubic GST The in-situ observation reported here demonstrates that sublimation of the cubic GST grain is distinctly anisotropic taken place via the predominant formation of kinks at {111} facets, which subsequently move along the h110i direction and thus leading to an observable step motion along the h112i direction. Figure 3a shows the tested grain after 17 min of overall sublimation time along the [1 ¯ 10] zone axis of Si. The grain is signicantly reduced in size compared to the situation displayed in Fig. 2c (onset of sublimation) leading to a thin crystal with a rhomboidal shape in projection and crystal edges whose projections are along

h112i directions. There are contrast modulations detectable along the cubic grain indicating a change in local thickness. The {111} facets are plausible low-index candidates to form stable surfaces featuring edges along h110i directions which lead to edges along h112i in [1¯ 10] projection. Figure 3b displays a 3D model of cubic GST where {111} facets form an octahedron. This {111} octahedron is the simplest shape to fulll the cubic symmetry and the projected rhomboidal shape with edges along h112i (cf. crystal structure projected along [1¯ 10] in Fig. 3b). Furthermore, the observed contrast modulations are consistent with thickness changes due to sloping {111} facets. On the other hand, abrupt transitions along crystallographic directions are visible in the HRTEM micrograph. Because of the slightly o-zone axis imaging condition, the surface structure contributes more strongly to the HRTEM contrast, and thus steps became clearly visible 31 indicating that the real shape 8


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of the crystal in Fig. 3a is more complex than a perfect equilateral {111} octahedron and might be composed of monolayer and multi-layer deep steps along h110i.

(c)

t0

GST

35.65 s

100.05 s

[112] [111]

[111]

Si

Figure 3:

Sample geometry and overview of sublimation process: (a) HRTEM image of

cubic GST grain at 640 ◦ C recorded 17 min after the start of sublimation and display close to the Si-[1¯ 10] zone axis. (b) Schematic 3D model of cubic GST with {111} facets forming an octahedron and a projection of the GST structure along [1 ¯ 10]. The Te atoms (green) make up the {111} surfaces and the Ge and Sb atoms as well as vacancies (light magenta) form the second layer. (c) HRTEM image series of the cubic GST grain on Si at 640 ◦ C featuring visible steps (red) moving along h112i. Scale bar = 10 nm. Figure 3c depicts a series of HRTEM images taken from a video sequence that shows subsequent stages of the sublimation process over a time period of 100 sec. (The video S1 in the supporting information shows the whole sequence). It is evident that the grain shrinks in a self-similar manner retaining the rhomboidal shape. Thereby, the sublimation occurs via kink-step-terrace formation mechanism. Several exemplary steps are marked with red and 9



blue arrows in Fig. 3c. Note that "kinks" are not directly visible in the [1 ¯ 10] projection. It is assumed that after being nucleated, kinks propagate along the h110i direction creating a step on the {111} facet (cf. Fig. 3b) whose movement along h112i direction is then observed. The kink formation is initiated at edge corners of the grain (red arrows) and also at step-edges (blue arrows) because of the real shape being more complex than the perfect equilateral octahedron. The anisotropic and fast kink movement results in a reduction of the surface roughness and the development of straight-lined steps and nally terraces provided that the process is nucleation-limited. In the following, the sublimation process is discussed using the examples of the dynamics along [11¯ 1] (black arrow in Fig. 3c) and [¯1¯11] (blue arrow in Fig. 3c) direction. Figure 4 extensively illustrates the dynamics of step motion during sublimation at the atomic scale. The gure in (a) present three consecutive HRTEM snapshots of the border of the crystal. The images clearly resolve the {111} planes of cubic GST which terminate the edges of the grain forming an atomically sharp and straight facet. Figure 4b displays a model of the atomic arrangement of cubic GST in projection along our viewing direction. The measured lateral step height of 0.35 nm corresponds to the distance of the {111} lattice planes, d 111 =0.3489 nm. One set of {111} planes is composed of a pair of planes belonging to both sublattices, the Te atoms on the one hand and randomly distributed Ge and Sb atoms on the other hand. 29 For this reason, a step with a lateral expansion (step height) of one {111} plane ("single-step") involves the sublimation of all three atomic species within our spatial and temporal resolution. The kink nucleates at the edge corner where two facets build a "convex" crystal edge. From there, the kink propagates along the [1¯ 10] direction and is only visible as a step when the entire atomic row along the viewing direction ( [1¯ 10]) is removed. This kink movement is faster than our temporal resolution. The kink forms a single-step or occasionally a doublestep edge along the viewing direction and is easily recognizable in the HRTEM images (cf. red arrow in the central image of Fig. 4a). Most commonly, steps move across the entire

10


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Page 35 of 47

(b)

Si

(a)

GST

[112]

[111] d111

t0

1.15 s

d111

2.3 s

(111) Te Ge/Sb/ Vac

(c) Cum. length sublimed along [111] (nm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


12

Figure 4:

single-step-motion

8 4 0 0

30

60 time t-t0(s)

90

120

Sublimation at the [ ¯ 1¯11] facet via kink nucleation and single-step movements

along [¯ 1¯1¯2]: (a) Series of HRTEM images taken from a video of the cubic GST grain at 640 ◦ C showing the nucleation and movement along [ ¯ 1¯1¯2] (red arrow) of one step in three consecutive images, scale bar = 2 nm. (b) Atomic arrangement on a (110) plane where one set of atomic sites on (111) planes is occupied by Te, while the other is occupied by Ge/Sb/Vac. (c) The cumulative sublimed length is measured as a function of time along [11¯ 1] direction (black arrow in (a)) featuring mostly single-steps. length of the grain edge (about 13 nm) along the h112i directions within one consecutive frame, i.e. within 1.15 sec. The kink/step velocity can be therefore estimated to be equal or faster than 11 nm/s. To follow up the time dependent process more comprehensively, the cumulative sublimed length along [11¯ 1] direction is plotted as a function of time in Fig. 4c. The curve progression resembles an irregular step-function representing the linear shrinkage of the grain over a period of two minutes. Each step in the graph corresponds to the fast kink/step motion, whereas the step height corresponds to the lateral expansion of the crystal step and

11



the plateau area measures the time between two nucleation events ranging mostly between 1.15 sec and 3.45 sec. Regardless of the low time resolution of our measurement, it must be concluded that the sublimation process is kink nucleation-limited as furthermore evidenced by the fact that straight facets develop and, accordingly, no step roughening is observed at this high temperature. This result is further supported by the observation of the sublimation along the [¯ 1¯11] direction, i.e. at the opposite site of the grain. Figure 5a presents the corresponding cumulative sublimed distance-versus-time plot. In spite of the large time frame of 7.5 min in total, only six nucleation events are observed (indicated by arrows). The time between two nucleation events ranges from 8 sec to 150 sec according to the plateau widths. The height of the jumps in the step-function reects the lateral step expansion, which is - in this case mostly larger than one {111}-layer indicating a multi-kink nucleation behavior. Indeed, the HRTEM image series in Fig. 5b reveals the presence and structure of a multi-step construction. The exemplary step ensemble covers four {111} planes with a staggered arrangement along the viewing direction and perpendicular to the {111} plane. The nucleation site is located at the GST/Si interface (see white short arrows) and the subsequent propagation of the step ensemble proceeds along the [112] direction until it crosses the transversely running {001} facet. The velocity of the multi-step ensemble depends on the number of step units involved, as shown in Fig. 5c, where the sublimed length is plotted over time. The estimated velocities in the linear sectors range from 0.5 to 1.8 nm/s where smaller velocities are observed for wider multi-step arrangements, i.e. v4-steps > v7-steps > v8-steps . This demonstrates the inuence of the number of kinks involved in the correlative ensemble motion. Compared to the velocity of the single-step conguration, these values are about one order of magnitude smaller.

12


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Page 37 of 47

(c) 12 8 4 0 40

multi-step motion single-step motion 80 120 160 200 240 280 320 360 400 440 time Δt=t-t0 (s)

Cum. length sublimed along [112] (nm)

(a) Cum. length sublimed along [111] (nm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


12 8 1 layer 4 layer 7 layer 8 layer

4 0

0 5 10 15 20 25 30 time after nucleation (s)

(b) [111]

GST

Si [112]

t0

98.9 s

103.5 s

108.1 s

[001] 115.0 s

Figure 5: Sublimation at the [ 11¯ 1] facet via multi-kink nucleation and movement along [112] (exception: one single-step motion labeled with black arrow) (a) The cumulative sublimed length is measured as a function of time along [¯ 1¯11] direction (blue arrow in (b)) featuring ve multi-steps. (b) Series of HRTEM images taken from a video of the cubic GST grain at 640 ◦ C showing the nucleation of the rst kink after 98.9 sec (white arrow) followed by mass desorption from the kink site seen as step movement along [112] (red arrow), scale bar = 5 nm. (Video S2 in supporting information shows the whole sequence.) (c) Graph of step movement along [112] (red arrow in (c)) showing the cumulative sublimed length of each step starting after they nucleated at the Si-GST interface. The black line shows the faster movement of the sole single-step motion.

Discussion Stability of Cubic Phase at High Temperature As stated in previous reports, 9,32 annealing of cubic GST should rst lead to the formation of a vacancy layer ordering along the {111} planes, followed by the transition to the trigonal 13



Page 38 of 47

phase above 300 ◦ C. 4,5 Interestingly, the aligned GST grain retained the cubic NaCl-structure even up to the sublimation point in our study. A highly vacancy-ordered cubic structure could not be observed as no additional periodicity along the {111} planes were found as well as no indications of the trigonal phase. On the other hand, Fig. 2a,c reveal that the GST/Si interface becomes rough at higher temperatures as a result of Si diusion into the GST layer. In fact, EELS analysis (not shown here) demonstrates the emergence of a distinct Si signal besides Ge, Sb and Te after heating the sample to temperatures above the sublimation point and cooling it down again to room temperature. Qiao

et al.

33

have found that Si doping

(up to 10%) of GST is able to delay the transition from cubic to trigonal phase and thus stabilize the cubic structure at higher temperatures. They speculate that the formation of stronger covalent bonds with Si play a role. Consequently, one could conclude, that the Si atoms preferentially occupy the vacancy sites and there, avoid the ordering as the rst step towards phase transition. Although similar eects were measured for N doping of GST, 34 a comprehensive understanding of the stabilization mechanism is still far from being attained.

Kink Nucleation Site and Propagation According to the terrace-step-kink (TSK) model, 35 the sublimation of solid surfaces starts from sites with the lowest activation energy required to remove an atom from the surface. These preferential sites are discussed in terms of nearest neighbor bonds which must be broken. 35 Figure 6 shows a schematic drawing of the cubic grain to illustrate the four different possible kink nucleation start points, two for each opposing crystal edge. There are homogenous sites where only the GST crystal is involved in the sublimation process and heterogeneous sites where the GST and Si crystal form an interface. Additionally, the potential sites can be dierentiated in "convex" and "concave" depending on the crystal facets that meet at the specic site. Invoking the TSK model, the most preferable kink nucleation site is located at the homogenous, "convex" site of the grain (bonds to be broken: 1) compared to the other possible sites marked in Fig. 6. There is no "convex" site at the [11¯ 1] facet due 14


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Si 5 kink motion after nucleation [111]

[112]

heterogeneous, concave site GST

[112]

1 homogeneous, convex site 1


4 [112]

5 homogeneous, concave site

kink motion after nucleation [111] [001] [112]

octahedrally coordinated atom site with bonds viewed in 110 projection, number counts bonds to be broken Te - Ge/Sb/Vac bond bond to Si substrate broken bond


Figure 6: Schematic drawing to illustrate the dierent possible kink nucleation sites featuring two heterogeneous, concave sites at the GST-Si interface and two homogeneous sites where one is convex and the other one concave. The kink sites with the most broken bonds at each facet are marked in blue. Additionally, on the left and right hand site of the gure, the number of broken bonds after the kink nucleation and during the subsequent step motion along [112] and [¯ 1¯1¯2] direction, respectively, is illustrated. to a stable facet in [00¯ 1] direction crossing it. The second most favorable kink nucleation site considering the number of bonds is the heterogeneous, "concave" site on the [11¯ 1] facet (bonds to be broken: 4). The discussed preferred nucleation sites at each facet (marked in blue in Fig. 6) are those which are observed during sublimation. The rate with which the kinks are formed is 30 times faster for the [¯ 1¯11] facet compared to the opposing facet. As expected, the kink nucleation rate is much faster for the most preferable kink nucleation site. Besides the preferential starting points for kink formation, the subsequent kink propagation along [1¯ 10] direction should be identical on both crystal sites because of the same number of bonds which must be broken. Indeed, step velocities along [112] and [¯ 1¯1¯2] direction of about 11 nm/s and 5 nm/s, respectively, were estimated for the single step-motion. The apparent discrepancy is attributed to the fact that the step width along e-beam direction (local thickness) is dierent at both sides of the grain and therefore the kink propagation 15



along [1¯ 10] takes longer as more material has to sublime for the same visible step motion along [¯ 1¯1¯2].

Surface Morphology and Crystal Shape During Sublimation Based on our observation of the grain morphology, shape and crystallographic orientation, we have concluded that {111} facets were predominately generated during the anisotropic sublimation process. Therefore, it is implied that these facets must be energetically favorable for cubic GST crystals at high temperature. From a general point of view, faceting of surfaces is driven by the anisotropy in surface energy γhkl as a function of the crystallographic orientation {hkl}. Due to the lack of data on specic surface energies for GST, a rst approximation can be made by applying the simplied broken-bond model on a rocksalt crystal structure and including the surface density of atoms. 36 This model yields that the {100} surface should have the lowest energy followed by the {110} and {111} surface, respectively. Consequently, a small particle in equilibrium shape consists primarily of those facet types. And indeed, we have observed cubic grains that have been formed after crystallization from melt droplet on a Si(111) substrate at 600 ◦ C exhibiting only {100}, {110} and {111} facets (shown in supplementary information S2). Furthermore, an estimation of the corresponding surface energies by applying the Wul-Kaishev construction demonstrate the following sequence γ111 < γ110 ≈ γ100 , which means that {111} surface has the lowest energy in accordance with the sublimation result. Nonetheless, during sublimation {111} facets are detected mainly pointing out that the shape might not be in equilibrium. The discrepancy can be ascribed on the inuence of the particular GST structure and the dierent partial pressure for the dierent atomic species: According to the crystal structure, the {111} surfaces consists of atoms from only one sublattice, either Te or Ge/Sb. 29 Due to the low vapor pressure of Ge, one can imagine that there is a preference for the Ge/Sb sublattice to form stable surfaces during sublimation. For the formation of {111} surfaces during the growth of trigonal GST grain, Kooi

et al.

6

also discussed the lowering of the surface energy by a 16


Page 40 of 47

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preference of Sb atoms to be at the surface. A dierent approach is to consider vacancies aiding the sublimation process by lowering the energies of bonds that need to be broken. Then, the plane where most vacancies are exposed to the surface is the stable facet. This would lead to the formation of {111} facets because vacancies are allocated on the Ge/Sb sublattice and are possibly already ordered to a certain degree which can not be observed yet in HRTEM phase contrast.

Conclusions The phase stability and sublimation behavior of cubic GST are investigated in this study. The cubic phase remains stable even up to the sublimation point and no ordering phenomena or transition to the trigonal phase is observed. This behavior could be related to Si diusion into GST at high temperatures. The sublimation of this ternary structure on a silicon substrate is observed with atomic resolution. The sublimation is anisotropic leading to the formation of {111} facets as plausible low-index candidates which is attributed to vacancies playing a role in the sublimation process. The observed dynamics are in accordance with the TSK-model for nucleation-limited dynamics: The sublimation happens via kink nucleation on stable steps and subsequent sublimation from those kink sites. Slow and fast kink nucleation in accordance with the broken-bond model and subsequent step movement with similar velocities is identied on opposing facets. Open questions include the formation process of the observed "multi"-steps. A possible approach is to study the inuence of interfacial defects which form due to a high lattice mismatch between Si substrate and GST thin lm on the sublimation mechanism.

Acknowledgement The authors would like to thank DENSsolutions for giving us the opportunity to perform the presented experiments by providing us with their heating sample holder (model D6+) and 17



Page 42 of 47

Dr. Michael Hanke for carefully reading the manuscript. Part of this work was nancially supported by the European Union and the state of Berlin via the EFRE project 2016011843.

Supporting Information Available The following les are available free of charge.

• Video1.avi: Video S1 shows the in-situ HRTEM overview sequence of the sublimation process of a cubic GST grain on a silicon substrate which is discussed in Fig. 3c.

• Video2.avi: Video S2 shows the in-situ HRTEM sequence of the multi-step sublimation process discussed in Fig. 5.

• SuppInfo.pdf: Supporting information about surface energies of GST.

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Graphical TOC Entry Si

640°C

[111] GST

10 nm Te

[112]

Ge,Sb d111

2 nm

t0

(111)

1.15 s

2.3 s

23

d111


Phase Stability and Anisotropic Sublimation of Cubic GeâSbâTe Alloy

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