# Phase Transitions in Germanium Telluride Nanoparticle Phase-Change Materials
Studied by Time-Resolved X-Ray Diffraction

Ann-Katrin U. Michel  Optical Materials Engineering Laboratory, Department of
Mechanical and Process Engineering, ETH Zurich, 8092 Zurich, Switzerland
Felix Donat  Laboratory of Energy Science and Engineering, Department of
Mechanical and Process Engineering, ETH Zurich, 8092 Zurich, Switzerland
Aurelia Siegfried  Optical Materials Engineering Laboratory, Department of
Mechanical and Process Engineering, ETH Zurich, 8092 Zurich, Switzerland
Olesya Yarema  Institute for Electronics, Department of Information Technology
and Electrical Engineering, ETH Zurich, 8092 Zurich, Switzerland  Hanbing Fang
Optical Materials Engineering Laboratory, Department of Mechanical and Process
Engineering, ETH Zurich, 8092 Zurich, Switzerland  Maksym Yarema  Institute
for Electronics, Department of Information Technology and Electrical
Engineering, ETH Zurich, 8092 Zurich, Switzerland  Vanessa Wood  Institute for
Electronics, Department of Information Technology and Electrical Engineering,
ETH Zurich, 8092 Zurich, Switzerland  Christoph R. Müller  Laboratory of
Energy Science and Engineering, Department of Mechanical and Process
Engineering, ETH Zurich, 8092 Zurich, Switzerland  David J. Norris
<EMAIL_ADDRESS>Optical Materials Engineering Laboratory, Department of
Mechanical and Process Engineering, ETH Zurich, 8092 Zurich, Switzerland

###### Abstract

Germanium telluride (GeTe), a phase-change material, is known to exhibit four
different structural phases: three at room temperature (one amorphous and two
crystalline, $\alpha$ and $\gamma$) and one at high temperature (crystalline
$\beta$). Because transitions between the amorphous and crystalline phases
lead to significant changes in material properties (e.g., refractive index and
resistivity), GeTe has been investigated as a phase-change material for
photonics, thermoelectrics, ferroelectrics, and spintronics. Consequently, the
temperature-dependent phase transitions in GeTe have been studied for bulk and
thin-film GeTe, both fabricated by sputtering. Colloidal synthesis of
nanoparticles offers a more flexible fabrication approach for amorphous and
crystalline GeTe. These nanoparticles are known to exhibit size-dependent
properties, such as an increased crystallization temperature for the
amorphous-to-$\alpha$ transition in sub-10 nm GeTe particles. The
$\alpha$-to-$\beta$ phase transition is also expected to vary with size, but
this effect has not yet been investigated for GeTe. Here, we report time-
resolved X-ray diffraction of GeTe nanoparticles with different diameters and
from different synthetic protocols. We observe a non-volatile amorphous-
to-$\alpha$ transition between 210∘C and 240∘C and a volatile
$\alpha$-to-$\beta$ transition between 370∘C and 420∘C. The latter transition
was reversible and repeatable. While the transition temperatures are shifted
relative to the values known for bulk GeTe, the nanoparticle-based samples
still exhibit the same structural phases reported for sputtered GeTe. Thus,
colloidal GeTe maintains the same general phase behavior as bulk GeTe while
allowing for more flexible and accessible fabrication. Therefore,
nanoparticle-based GeTe films show great potential for applications, such as
in active photonics.

##  I Introduction

Germanium telluride (GeTe) is a metal chalcogenide that exhibits three
structural phases at room temperature and one phase at high
temperature.Schlieper  _et al._ (1999); Bletskan (2005) The room-temperature
phases are amorphous GeTe and crystalline rhombohedrally distorted $\alpha$\-
as well as orthorhombic $\gamma$-GeTe. The high-temperature crystalline cubic
phase is known as $\beta$-GeTe. While the atoms of such a phase-change
material are covalently bonded in its amorphous (A) state, metavalent bonding
can be found in the crystalline (C) states.Raty  _et al._ (2019) These two
types of bonds lead to very different properties. The amorphous phase has a
relatively low optical reflectivity $R_{A}$ and high electrical resistivity
$\rho_{A}$. Upon crystallization, the resistivity decreases by five orders of
magnitude with $\rho_{A}$ $\approx$ 102 $\Omega$cm and $\rho_{C}$ $\approx$
10-3 $\Omega$cm.Jost  _et al._ (2015) Simultaneously, the reflectance contrast
$\Delta R$ defined by $[(R_{C}$ \- $R_{A})$ / $R_{C}]$ $\times$ 100 is about
43% in the near-infrared spectral range (wavelengths near 1 µm).111The
reflectances $R_{A}$ and $R_{C}$ were calculated via Fresnel coefficients for
a 100 nm GeTe film between a silicon and an air half-space, under normal
incidence, and with the dielectric function of GeTe according to Ref. Shportko
_et al._ , 2008. The definition of the reflectance contrast $\Delta R$ was
taken from Ref. Schlich  _et al._ , 2015.

The room-temperature amorphous phase of GeTe crystallizes at $T_{C,1}$ =
185∘C.Jost  _et al._ (2015) Thermal annealing, optical pulses, or electrical
pulses can be used to induce this structural relaxation. However, only laser
or electrical pulses allow for quenching of the GeTe melt and thus, re-
amorphization. The melting temperature of GeTe is $T_{M}$ = 723 ∘C.Schlieper
and Blacknik (1996)

The strong property contrast between the non-volatile phases can be exploited
for optical data storage and memristive memories.Raoux, Wełnic, and Ielmini
(2010); Wright  _et al._ (2012) The latter are one of the most promising
candidates for neuromorphic computing.Boybat  _et al._ (2018) While ternary
and quaternary phase-change materials, such as germanium antimony telluride or
silver indium antimony telluride, have been applied in phase-change memories,
germanium telluride has gained interest for active photonics.Wuttig,
Bhaskaran, and Taubner (2017); Carrillo  _et al._ (2019); Hail  _et al._
(2019); Michel  _et al._ Furthermore, GeTe exhibits ferromagnetism with a
Curie temperature of about 920∘C, while doping GeTe with Mn, Fe, or Cr leads
to a Curie temperature $\leq$ 420∘C.Kriener  _et al._ (2016) Moreover, GeTe
has recently been identified as a Rashba ferroelectric.Wang  _et al._ (2020)

All of the aforementioned applications and effects have been investigated
either for epitaxially grown or sputtered GeTe films ranging from several tens
of nanometers to several micrometers in thickness. Recently, spatially
confined phase-change materials have been studied, mainly due to two
opportunities. First, nanowires and nanoparticles offer an alternative
approach to fabricate films of phase-change material or patterned
arrays.Milliron  _et al._ (2007); Chung  _et al._ (2009); Caldwell  _et al._
(2010); Yarema  _et al._ (2018) Thereby, the purchase of dedicated expensive
equipment (e.g. magnetron sputtering tool) can be avoided. In addition,
preformed, high-aspect-ratio voids or patterns can be filled. Second,
nanoscale phase-change materials allow for studying size-dependent properties
of these compounds. For example, localized surface plasmon resonances have
been reported for crystalline GeTe nanoparticles,Polking  _et al._ (2013) and
a bandgap increase has been observed.Michel  _et al._ (2020); Yarema  _et al._
(2020) Furthermore, several studies on the size-dependent shift of the
crystallization temperature $T_{C,1}$ have been published, as shown for GeTe
in Tab. 1. The listed values for $T_{C,1}$ refer to the transition from the
amorphous phase to the rhombohedrally distorted $\alpha$-GeTe and reveal that
$T_{C,1}$ increases with decreasing particle diameter $d$. We also note that
the observed crystallization temperature depends not only on the material
dimensions but also on the characterization technique. For example, the drop
in resistivity associated with crystallization does not require a phase change
of the entire GeTe volume; a conductive crystalline channel in the film is
sufficient. Another important factor is the applied heating rate $\vartheta$
throughout the measurement. A well-known example is the shifted peak
temperature to higher $T$ upon increase of $\vartheta$ in differential
scanning calorimetry (DSC). All of the aforementioned effects have to be taken
into account when comparing the values for $T_{C,1}$ and making conclusions
about size-dependent effects.

While $T_{C,1}$ has been reported for spatially confined GeTe, the high-
temperature crystalline $\beta$ phase has neither been observed for ultra-
small, nor initially amorphous nanoparticles so far (cf. Tab. 1). Here we
study the reversible crystalline-to-crystalline phase transition from
$\alpha$\- to $\beta$-GeTe at $T_{C,2}$ and back to the $\alpha$-phase for
sub-10 nm GeTe nanoparticles, which were initially amorphous after synthesis.
This is realized by collecting X-ray diffraction (XRD) patterns for repeated
heating and cooling cycles of drop-casted particles, which are synthesized in
their amorphous phase.

Table 1: Comparison of crystallization temperatures $T_{C,1}$ and $T_{C,2}$ for different GeTe samples, determined by different characterization methods (XRD - X-ray diffraction, at a synchrotron (${}_{\textnormal{s}}$) if applicable, $\rho(T)$ \- resistivity measurement during heating and cooling, and DSC - differential scanning calorimetry) with varied heating rates given in ∘C/min. The samples have either been synthesized (approx. spherical particle diameter $d$) or sputtered (approx. film thickness $t$). Initially, the GeTe has either been in its amorphous (A) or crystalline (C) state. The sputtered thin films are given for reference and separated by a horizontal line. † and ‡ mark a surface-oxidized and TaN-capped GeTe film, respectively. Size [nm] | TC,1 [∘C] | TC,2 [∘C] | Method |  $\vartheta$ [∘C/min] | Ref.
---|---|---|---|---|---
$d_{A}$ = 1.8 | 400 | - |  in-situ XRD${}_{\textnormal{s}}$ | 60 | Caldwell  _et al._ ,2010
$d_{A}$ = 2.6 | 350 | - |  in-situ XRD${}_{\textnormal{s}}$ | 60 | Caldwell  _et al._ ,2010
$d_{A}$ = 3.4 | 320 | - |  in-situ XRD${}_{\textnormal{s}}$ | 60 | Caldwell  _et al._ ,2010
$d_{A}$ = 3.5 | 340 | - | $\rho(T)$ | 300 - 1.800 | Caldwell  _et al._ ,2010
$d_{A}$ = 6.0 | 227 | - |  in-situ XRD | 7 | Yarema  _et al._ ,2018
| 170 | - | $\rho(T)$ | - | Yarema  _et al._ ,2018
| 223 - 240 | - | DSC | 2.5 - 30 | Yarema  _et al._ ,2018
$d_{A}$ = 8.7 | 237 | - | DSC | 5 | Arachchige  _et al._ ,2011
$d_{A}$ = 10.6 | 224 | - | DSC | 5 | Arachchige  _et al._ ,2011
$d_{A}$ = 18.5 | 209 | - | DSC | 5 | Arachchige  _et al._ ,2011
$d_{C}$ = 17.0 | - | 355 |  in-situ XRD${}_{\textnormal{s}}$ | 60 | Polking  _et al._ ,2011
$d_{C}$ = 100 | - | 360 |  in-situ XRD${}_{\textnormal{s}}$ | 60 | Polking  _et al._ ,2011
$d_{C}$ = 500 | - | 370 |  in-situ XRD${}_{\textnormal{s}}$ | 60 | Polking  _et al._ ,2011
$t_{A}$ = 50 | 170 | 350 |  in-situ XRD${}_{\textnormal{s}}$ | 180 | Raoux  _et al._ ,2009
| 175 | - | $\rho(T)$ | 60 | Raoux  _et al._ ,2009
$t_{A}$ = 80 | 185 | - | $\rho(T)$ | 5 | Jost  _et al._ ,2015
$t_{A}$ = 100† | 180 | - | $\rho(T)$ | 10 | Kolb  _et al._ ,2019
$t_{A}$ = 100‡ | 230 | - | $\rho(T)$ | 10 | Kolb  _et al._ ,2019
$t_{A}$ = 150 | 180 | - | $\rho(T)$ | 10 | Mantovan  _et al._ ,2017

##  II Experimental methods

We prepared colloidal dispersions of amorphous monodisperse GeTe nanoparticles
following two different protocols. All studied spherical nanoparticles had a
diameter $d$ < 10 nm since size-dependent crystallization had previously been
identified for this size regime (Tab. 1).

###  II.1 Nanoparticle synthesis

The syntheses of the amorphous (A-)GeTe nanoparticles followed protocols
adapted from Caldwell et al.Caldwell  _et al._ (2010) and reported by Yarema
et al.Yarema  _et al._ (2018)

The first batch was synthesized through a hot-injection route as schematically
shown in Fig. 1(a). Anhydrous germanium(II) iodide (GeI2, 163 mg) was
dissolved in 2 ml trioctylphosphine (TOP) in a glove box and stirred
overnight. The following day, 2 g of trioctylphosphine oxide (TOPO) were added
and the yellow solution was transferred to a reaction flask which was purged
with nitrogen beforehand. After heating the solution to 235∘C, 240 µl
dodecanethiol and 30 s later 667 µl 0.75 M Te-TOP solution (previously
prepared) were injected. About 40 s later, the color of the solution in the
flask changed from yellow to dark brown, indicating nucleation of
nanoparticles. After 4 min, the reaction was terminated and the flask was
cooled rapidly by acetone mist and, later, with pressurized air. The crude
solution of GeTe nanoparticles was transferred air-free to the glove box where
anhydrous ethanol was added (3:1). The black precipitate was separated by
centrifugation (4000 rpm, 10 min) and dispersed in 1 ml anhydrous chloroform.
After centrifuging (4000 rpm, 10 min), ethanol was added to the dark brown
solution (2:1). Another centrifugation step resulted in a clear liquid and a
black precipitate. The latter was dispersed in 1 ml toluene, forming a colloid
that remained stable for multiple weeks. We refer to this synthetic protocol
below as synthesis 1.

The alternative synthetic approach, synthesis 2, led to several batches with
different GeTe particle sizes. This amide-promoted synthesis is schematically
shown in Fig. 1(b) and described in detail in Ref. Yarema  _et al._ , 2018.
While the A-GeTe nanoparticles obtained from synthesis 1 were covered by TOP
ligands [cf. Fig. 1(c)], the particles from synthesis 2 were covered with an
oleate shell.

From transmission electron microscopy (TEM) observations, the average size of
each particle synthesis was estimated. The A-GeTe particle size available from
synthesis 1 was 5.5 $\pm$ 1.6 nm; synthesis 2 provided A-GeTe particles with
diameters 4.8 $\pm$ 0.6 nm, Fig. 1(d), and 6.9 $\pm$ 0.9 nm, Fig. 1(e). It has
to be noted that synthesis 2 led to particles with a much narrower size
distribution, as visible in Fig. 1(f): the green size distribution refers to
the particles from synthesis 1 and the blue and red size distributions refer
to the particles from synthesis 2.

Upon annealing, the A-GeTe particles will relax into the crystalline phase if
$\Delta T\,>\,T_{C,1}$. However, due to the large surface-to-volume ratio of
small nanoparticles, coalescence is energetically favorable. Thus, coalescence
of sub-10 nm particles has been reported either at temperatures above
$T_{C,1}$,Yarema  _et al._ (2018) or at lower temperatures. Thus, it occurs
prior or throughout crystallization [cf. Fig. 1(g)].Keitel, Weidman, and
Tisdale (2016)

Figure 1:  Sketch of the hot-injection methods 1, (a), and 2, (b), used for
the synthesis of amorphous (A) sub-10 nm GeTe nanoparticles, covered by
organic ligands, such as trioctylphosphine (TOP), shown in (c). TEM images of
the particles with an average diameter of 4.8 nm, (d), and 6.9 nm, (e), allow
for the determination of the particle size distributions shown in (f). The top
(blue) and bottom (red) distribution relate to particles from synthesis 2,
(b); the middle (green) distribution is for synthesis 1, (a). (g) Heating of
the A-GeTe particles with $\Delta T$ $\geq$ $T_{C,1}$ results in crystalline
(C) GeTe particles which are likely to coalesce prior or throughout the
crystallization process (dashed and solid arrow, respectively).

###  II.2 Time-dependent X-ray diffraction

Samples were prepared for each particle size by repeated drop casting onto a
circular quartz substrate (diameter 1.3 cm). The sample thickness and weight,
including the nanoparticles, ligands, and residual solvent, were not
determined. However, the sample deposition was conducted with a particle
concentration of about 5 mg/ml and an estimated deposited amount of 5 mg. To
avoid oxidation, the colloid was deposited air-free in a nitrogen glove box.
The samples were mounted in an Anton Paar XRK 900 reactor chamber that was
purged with nitrogen (flow rate: 200 ml/min, measured at ambient temperature
and pressure) throughout the entire measurement. The samples were
characterized with a PANalytical Empyrean diffractometer equipped with a
X’Celerator Scientific ultrafast line detector and Bragg-Brentano HD incident
beam optics. The instrument was operated at 45 kV and 40 mA using Cu K$\alpha$
radiation (1.54060 Å). The temperature was measured and controlled in the
vicinity of the sample using a type K thermocouple; separate control
measurements with a second thermocouple placed at the exact position of the
sample indicated that the temperature difference between the two thermocouples
was < 5∘C for temperatures $T$ < 800∘C.

Fig. 2(a) shows the applied temperature curve. The XRD chamber temperature $T$
is plotted as a function of the time $t$ during two heating and cooling
cycles. The samples were heated and cooled at a rate of $\vartheta$ =
10∘C/min. At each $T$, the chamber was held for 6 min total, which includes 1
min for equilibration and 5 min for the actual XRD scan.

In the case of bulk stoichiometric compounds, we expect the crystallization of
the initially A-GeTe to the $\alpha$ phase. $\alpha$-GeTe will then remain
stable to $T_{C,2}$ = 357∘C.Bletskan (2005) Above this temperature, the
$\beta$ phase becomes stable. If GeTe is rich in tellurium (> 50.9%), A-GeTe
crystallizes to the $\gamma$ phase. At elevated temperatures, a
$\gamma$-to-$\beta$ transition can be observed.Bletskan (2005) An overview of
the crystalline structures and the corresponding reference patterns of GeTe
are given in Tab. 2 and Fig. 2(b), respectively. Additionally, the reference
patterns of crystalline Te and Ge, which are known impurities observed in
GeTe,Caldwell  _et al._ (2010); Yarema  _et al._ (2018); Jost  _et al._ (2015)
are shown.

Table 2: Overview of the crystalline phases observed for bulk GeTe. As mentioned in Sec. I, $\alpha$\- and $\gamma$-GeTe are stable at room temperature, while $\beta$-GeTe is the high-temperature phase. Phase | Crystal system | Space group no. | Space group | Ref.
---|---|---|---|---
$\alpha$ | trigonal | 160 | R3m | Goldak  _et al._ ,1966
$\beta$ | cubic | 225 | Fm$\bar{3}$m | Shelimova, Abrikosov, and Zhdanova,1965
$\gamma$ | orthorhombic | 62 | Pnma | Karbanov, Zlomanov, and Novoselova,1968

During the first heating, we collected an XRD pattern every 25∘C for $T$
$\leq$ 200∘C and every 10∘C for 200∘C < $T$ $\leq$ 450∘C. This was based on
prior knowledge of the crystallization with $T_{C,1}$ > 200∘C observed for
small nanoparticles (cf. Tab. 1) and the $\alpha$-to-$\beta$ transition
$T_{C,2}$ < 400∘C as reported for bulk GeTe.Bletskan (2005) Since we focused
on monitoring the reversible crystalline-to-crystalline transition and no
further events were expected for GeTe at lower temperatures during repeated
cooling and heating, we adapted our temperature intervals accordingly. Thus,
we chose $\Delta T$ = 10∘C for 450∘C $\geq$ $T$ $\geq$ 350∘C and $\Delta T$ =
25∘C for $T$ < 350∘C.

For a reference value regarding the $\alpha$-to-$\beta$ transition temperature
of bulk GeTe, we characterized flakes of a crystalline GeTe sputter target
with in-situ XRD as described above. The temperature-dependent diffractograms
are shown in Fig. 2(c). The transitions from a peak doublet to a single peak
for both 2$\theta$ = 24 - 27∘ and 2$\theta$ = 41 - 44∘ allow for the
confirmation of the $\beta$ phase of GeTe. Based on the XRD scans taken every
10∘C, $T_{C,2}$ is extracted as 380∘C [Fig. 2(d)]. This matches the transition
temperature of GeTe with a Te content between 50.2 and 50.5% given by the
phase diagram in Ref. Bletskan, 2005. Hence, we can conclude that the
reference sample is stoichiometric.

Figure 2:  (a) XRD chamber temperature $T$ as a function of the time $t$
during two heating and cooling cycles with $\vartheta$ = 10∘C/min for heating
and cooling. (b) Reference XRD patterns for all crystalline GeTe phases,
tellurium, and germanium.Shelimova, Abrikosov, and Zhdanova (1965); Karbanov,
Zlomanov, and Novoselova (1968); Goldak  _et al._ (1966); Bradley (1924);
Cooper (1962) The insets show the angular ranges and Miller indices which
allow for a distinction between $\alpha$\- and $\beta$-GeTe. (c) The in-situ
XRD pattern of flakes from a crystalline GeTe sputter target shows the
transition from $\alpha$\- to $\beta$-GeTe during the first heating cycle and
back to $\alpha$-GeTe during the following cooling (the relevant temperature
ranges are marked by white dashed rectangles). (d) The individual XRD patterns
corresponding to the 2$\theta$\- and $T$-range of the $\alpha$-to-$\beta$
transition show the peak doublets and singlets with the reflexes marked in
green and red, respectively.

##  III Results and discussion

In the following, we will discuss the temperature-dependent XRD patterns for
three nanoparticle-based samples. First, we will focus on the structural
evolution of the GeTe particles from synthesis 1, which showed a broad size
distribution. Second, we will analyze the diffractograms obtained for the
particles from synthesis 2, which had a narrower size distribution. Also, it
provided two samples with sizes smaller and larger than the average size of
the particles from synthesis 1.

All diffractograms were normalized by dividing the intensity values by the
maximum intensity for each particular diffractogram, meaning
$I$/$I_{\textnormal{max}}$, which allows for a better graphical
representation. Additionally, the patterns are displayed with a constant
offset [($I$/$I_{\textnormal{max}}$)+ 0.25 between each diffractogram] to show
the structural evolution of the sample over time. Such waterfall plots
facilitate the interpretation of time-dependent XRD data since interpolation
as used in 2D contour plots [cf. Fig. 2(c)] is avoided. Nevertheless, it has
to be noted that the time axis has been adapted to follow the XRD patterns.
Thus, the spacing is not necessarily equal. This is due to the fact that we
chose $\Delta T$ = 25∘C for $T$ $\leq$ 200∘C between each measurement in
heating 1 as well as for $T$ $\leq$ 350∘C in cooling 1, heating 2, and cooling
2. For higher temperatures in each cycle, we chose $\Delta T$ = 10∘C for a
better resolution. These temperature choices were defined by the expected
structural transitions (cf. Tab. 1).

In the discussion of all time-dependent XRD diffractograms, we focus on three
angular ranges of 2$\theta$ to investigate $T_{C,1}$ and $T_{C,2}$:

  * •

24-27∘: transition from (003)/(021)-doublet to (111)-singlet marks
$\alpha$-to-$\beta$ transition (and vice versa),

  * •

29-30∘: appearance of (202)-peak marks crystallization, and

  * •

41-44∘: transition from (024)/(220)-doublet to (220)-singlet marks
$\alpha$-to-$\beta$ transition (and vice versa).

Since the doublet-to-singlet transition is more pronounced between 41 and 44∘
[cf. reference in Fig. 2(b)], we use this angular range to identify $T_{C,2}$.
The transition temperatures are marked by dashed rectangles in Figs. 3-5 and
the values for $T_{C,1}$, $T_{C,2}$, and $T_{C,2^{\prime}}$ are noted next to
the pattern. $T_{C,2}$ refers to the $\alpha$-to-$\beta$ transition during
heating and $T_{C,2^{\prime}}$ refers to the reverse transition, $\beta$ to
$\alpha$, during cooling.

For orientation, all diffractograms we will discuss below are color-coded with
respect to the heating curve and the temperature scaling. In addition to the
transition temperatures $T_{C,1}$, $T_{C,2}$, and $T_{C,2^{\prime}}$, we mark
the transition points between each cycle, i.e. $T_{\textnormal{min}}$ = 75∘C
and $T_{\textnormal{max}}$ = 450∘C on the right of the XRD patterns.

###  III.1 In-situ XRD on polydisperse GeTe nanoparticles

The diffractograms of the GeTe nanoparticles from synthesis 1, which led to a
broad size distribution [cf. Fig. 1(f)], are shown in Fig. 3. The XRD patterns
start at $T$ = 100∘C in the first heating cycle. During heating 1, a narrowing
of the intensity peak close to 2$\theta$ = 30∘ as well as a convergence of the
(024)/(220)-doublet can be seen. First, we focus on the interpretation of the
width of the (202) and (200)-peak of the $\alpha$ and $\beta$ phase,
respectively. In a general and simplified consideration, the full width at
half maximum (FWHM or $w$) of an XRD peak can be related to the lattice strain
and the crystallite size $D$. It has to be noted, that $D$ is not necessarily
identical with the particle size $d$. In case of coalescence for example, $D$
can be larger than the initial $d$. Hence, without a high-resolution TEM
investigation it is difficult to judge whether the particle or domain sizes
are determined via XRD. This ambiguity has to be kept in mind when the term
crystallite is used for $D$.Girgsdies (2015) Nevertheless, its size can
theoretically be estimated from the well-known Scherrer equation:

$D=[K\cdot\lambda]/[w\cdot cos(\theta)]$

with $K$ being the shape factor or Scherrer constant (often approximated by
0.9), $\lambda$ being the X-ray wavelength in nm, and $\theta$ being the angle
of diffraction in rad.Girgsdies (2015) The observed peak width
$w_{\textnormal{obs}}$ in rad has to be corrected by subtracting the
instrumental broadening $w_{\textnormal{instr}}$ in rad:

$w=w_{\textnormal{obs}}-w_{\textnormal{instr}}.$

In our case, $w_{\textnormal{instr}}$ $\approx$ 0.1∘ and thus, up to 72% of
$w_{\textnormal{obs}}$. Therefore, it would be necessary to collect the
diffractograms with a much higher resolution (e.g. at a synchrotron) to obtain
a better estimate of $D$. Nevertheless, a qualitative approximation of $D$
based on the XRD patterns is possible. In a simplified picture, the initial
particle diameter $d$ $\approx$ 5.5 nm determined by TEM would imply
$w_{\textnormal{obs}}$ $\approx$ 1.6∘ (assuming $D$ = $d$, $K$ = 0.9,
$w_{\textnormal{instr}}$ = 0.1∘, and $\lambda$ = 0.15406 nm). In contrast,
Fig. 3 shows 0.14∘ $\leq$ $w_{\textnormal{obs}}$ $\leq$ 0.2∘. Thus, it seems
very likely that the GeTe nanoparticles coalesced during the initial
crystallization. Thereby, it has to be emphasized that XRD patterns represent
only an averaged signal, and no conclusion on the individual particles can be
drawn.

Between $T$ = 240 and 300∘C the peak width decreases further, indicating
continued growth of $D$. This could relate to further coalescence or growth of
larger grains at the expense of smaller ones.Polking  _et al._ (2011); Yarema
_et al._ (2018) Further thermal treatment showed no influence on the width of
the (202)- or (200)-peak of $\alpha$\- or $\beta$-GeTe, respectively. Thus, it
can be assumed that grain growth stopped. Apart from the narrowing of the
(202)-peaks, a slight shift to smaller angles upon heating can be seen. During
cooling, the peak position shifts back to its initial value. A similar
behavior can be seen for the second heating and cooling. This can be
rationalized by the relaxation of the distorted $\alpha$-phase to the cubic
$\beta$ phase.Polking  _et al._ (2011); Boschker, Wang, and Calarco (2017)

For $T$ = 260∘C, the (024)/(220)-doublet becomes clearly visible and converges
smoothly towards the (220)-singlet for increasing $T$ $\geq$ 360∘C. This
indicates a slow transition from the rhombohedrally distorted $\alpha$-phase
to the relaxed cubic $\beta$-phase. Something similar has been observed for
larger GeTe nanoparticles, which were crystalline after synthesis.Polking  _et
al._ (2011) During the first cooling cycle, the gradual splitting of the
(220)-peak towards the (024)/(220)-doublet can be seen. The related
$\beta$-to-$\alpha$-transition temperature was $T_{C,2^{\prime}}$ = 400∘C
according to the diffractogram. A similar behavior can be found for heating
and cooling 2, where the (024)/(220)-doublet transitions into the
(220)-singlet at $T_{C,1}$ = 420∘C and the high-temperature phase transitions
back into the room-temperature phase at $T_{C,2^{\prime}}$ = 400∘C. Thus, the
transition between the two C-GeTe phases is reversible for the sample based on
nanoparticles from synthesis 1.

Figure 3:  Structural evolution of GeTe nanoparticles from synthesis 1 with a
diameter of 5.5 $\pm$ 1.6 nm [green histogram in Fig. 1(f)]. Each XRD pattern
is normalized to the maximum peak intensity ($I$/$I_{\textnormal{max}}$). The
colors represent the scan temperature $T$, as shown on the left side. Upon
heating, amorphous GeTe (A-GeTe) crystallizes into $\alpha$-GeTe, $T_{C,1}$ =
240∘C, and relaxes into the $\beta$-phase. The transition between $\alpha$\-
and $\beta$-GeTe continues during further heating and cooling with $T_{C,2}$ =
420∘C and $T_{C,2^{\prime}}$ = 400∘C. The small peak at 2$\theta$ $\approx$
27∘ (black asterisk) could indicate a small amount of crystalline Te or Ge
impurity, cf. Fig. 2(b). Figure 4:  Structural evolution of A-GeTe
nanoparticles prepared by synthesis 2 and with a diameter of 4.8 $\pm$ 0.6 nm
[blue histogram in Fig. 1(f)]. Normalization, temperature profile, and color
code are similar to Fig. 3. Upon heating the A-GeTe nanoparticles, they
crystallize into $\alpha$-GeTe at $T_{C,1}$ = 240∘C and relax into the
$\beta$-phase at $T_{C,2}$ = 400∘C. The transition between $\alpha$\- and
$\beta$-GeTe continues during further heating and cooling with $T_{C,2}$ =
$T_{C,2^{\prime}}$ = 390∘C. We ascribe the small peak at 2$\theta$ $\approx$
27.2∘ (black asterisk) to a small amount of crystalline Te or Ge impurity, cf.
Fig. 2(b). The small peak at 2$\theta$ $\approx$ 25.7∘ (black rhombus) could
not be matched with any reference diffractograms given (cf. Appendix B).
However, carbon shows a strong peak at this angle and could have contaminated
the sample.

The aforementioned reversible change is less evident for the
(003)/(021)-doublet to (111)-singlet transition at 2$\theta$ = 24$\ldots$27∘.
This was expected due to the low intensity of these peaks in the reference
[cf. Fig. 2(b)]. Nevertheless, the transition is visible, but does not allow
for a determination of the transition temperatures $T_{C,2}$ and
$T_{C,2^{\prime}}$.

###  III.2 In-situ XRD on nanoparticles with narrower size distribution

In Figs. 4 and 5 the diffractograms of the nanoparticles from synthesis 2 are
shown. These two samples had a smaller and larger average size and a narrower
size distribution than the GeTe nanoparticles discussed in the previous
section.

While the XRD patterns were collected, normalized, and plotted similarly to
Fig. 3, it is obvious that the diffractograms in Figs. 4 and 5 for the
amorphous samples with 100∘C $\leq$ $T$ $\leq$ 250∘C are noisier. One possible
reason could be that the total amount of sample from synthesis 2 was lower
compared to samples from synthesis 1 due to different sample contributions
from the TOP and oleic acid ligands (cf. Section II.1). Another reason could
be the normalization $I$/$I_{\textnormal{max}}$. This leads to a pronounced
increase of the signal-to-noise ratio (SNR) for XRD patterns above $T_{C,1}$,
where $I_{\textnormal{max}}$ $\gg$ $I$, but does not affect the SNR of
amorphous diffractograms (cf. Appendix A).

In Fig. 4, the first sign of crystallization into $\alpha$-GeTe can be
observed for $T$ = 240∘C which matches what we already observed in Fig. 3.
Again, the peak width indicates a coalescence of particles prior to or during
crystallization. Already the XRD pattern for the next temperature step shows a
clear (024)/(220)-doublet. Further heating leads to a quick divergence of the
two peaks, while the high-angle peak seems to overlap with another small peak.
At the same time, the (202) peak shifts quite strongly to lower angles and a
weak (003)/(021)-doublet becomes visible. The latter shows a prompt divergence
and an overlapping additional peak (for $T$ = 370 - 390∘C) as well. The
described trends remain for all three diffractive signatures of the
$\alpha$-phase until $T$ = 400∘C. For this temperature, a prompt shift of the
central peak occurs and both doublet-to-singlet transitions are observed.
Thus, we define the onset of the $\alpha$-to-$\beta$-transition at $T_{C,2}$ =
400∘C. Further heating leads to a relaxation of the peaks and the subsequent
cooling shows the smooth and reversible transition between $\beta$\- and
$\alpha$-GeTe. This behavior is similar to what was seen in Fig. 3. Only the
transition temperatures are slightly lower with $T_{C,2^{\prime}}$ = 390∘C and
$T_{C,2}$ = $T_{C,2^{\prime}}$ from there on.

It has to be noted, that the (024)/(220)-doublet shows very small split peaks.
This could be related to the fact that we used CuKα,1 and CuKα,2. Since the
peaks are sharper compared to what we found for the diffractograms in Fig. 3,
this effect might appear more strongly for the sample investigated here.
Furthermore, the narrower peaks shown in Fig. 4 indicate a larger crystallite
size $D$ and thus, more pronounced coalescence than observed for the GeTe
particles from synthesis 1 can be assumed. This is surprising since oleic acid
ligands are used for the particles from synthesis 2. These molecules are much
longer than the TOP ligands, which are shown in Fig. 1(c), and thus, a more
pronounced nanoparticle separation and potentially less coalescence could be
expected.Yarema  _et al._ (2018)

Similar to the diffractograms in Fig. 3, a small additional peak not matching
the $\alpha$\- or $\beta$-lattice was found. It appears at 2$\theta$ $\approx$
27.2∘ for $T$ $\geq$ 310∘C, but it disappears for $T$ $\geq$ 380∘C and does
not reoccur throughout the following temperature treatment. Due to the angular
position of this peak, it could indicate traces of crystalline Te or Ge in the
sample. Since the most pronounced peaks for both crystalline patterns are
almost overlapping [cf. Fig. 2(b)], an unambiguous identification is not
possible. Nevertheless, Te impurities have been reported for annealed
initially amorphous GeTe nanoparticles.Caldwell  _et al._ (2010) Additionally,
segregated Te has been observed as a result of surface oxidation of GeTe (cf.
Appendix B).Kolb  _et al._ (2019)

In Fig. 5, a very weak crystalline signal can already be identified for $T$ =
100∘C. The (202)-peak is very broad and flat, thus indicating a much smaller
$D$ than what we found for the smaller GeTe nanoparticles (cf. Figs. 3 and 4).
Due to this initial (partial) crystallization of the particles, the
determination of $T_{C,1}$ is difficult. Therefore, we use the enhancement of
this hump at 2$\theta$ $\approx$ 29.6∘ and the simultaneous onset of a
crystalline signal in the high-angle range, which we define for $T_{C,1}$ =
210∘C. However, this is less reliable than $T_{C,1}$ defined for the samples
based on the smaller GeTe nanoparticles discussed above.

Further heating leads to more pronounced peaks for the three considered
angular ranges. Thereby, the (202)-peaks narrow, while the peak width
$w_{\textnormal{obs}}$ remains relatively broad compared to what is shown in
Figs. 3 and 4. This would imply that coalescence did not progress as far as
for these samples. If we could apply the simplified logic of longer ligands
resulting in a lower degree of particle sintering, we would expect
$D_{\textnormal{5.5}}$ > $D_{\textnormal{6.9}}$ (particles with an average
diameter $d$ $\approx$ 5.5 nm and TOP ligands versus particles with $d$
$\approx$ 6.9 nm and oleate ligands).

Similar to what we observed before, the (202)- and (200)-peak, respectively,
shift smoothly. However, during the first heating, we cannot determine
$T_{C,2}$. Instead, during cooling a broadening and subsequent peak splitting
from the (220)-singlet to the (024)/(220)-doublet can be observed, starting at
$T_{C,2^{\prime}}$ = 350∘C. The following $\alpha$-to-$\beta$-transition sets
in at $T_{C,2^{\prime}}$ = 370∘C with the transition back to $\alpha$ at the
same temperature during the second heating cycle. The (003)/(021)-doublet
cannot be observed before the end of the last cooling, i.e. $T$ = 75∘C.

Figure 5:  Structural evolution of A-GeTe nanoparticles from synthesis 2 with
a diameter of 6.9 $\pm$ 0.9 nm [red histogram in Fig. 1(f)]. Normalization,
temperature profile, and color code are similar to Figs. 3 and 4. Upon
heating, A-GeTe crystallizes at $T_{C}$ = 210∘C. Presumably, $\alpha$-GeTe
relaxes into $\beta$-GeTe since the transition back to the $\alpha$ phase can
be found at $T_{C,2^{\prime}}$ = 350∘C. During further heating and cooling the
crystalline-to-crystalline transitions can be found at $T_{C,2}$ =
$T_{C,2^{\prime}}$ = 370∘C.

##  IV Conclusion

We synthesized ultrasmall nanoparticles of the phase-change material GeTe with
diameters below 10 nm. In the literature, these sizes have been identified to
show size-dependent material properties. We studied the crystallization
behavior of drop-casted nanoparticle films using in-situ XRD while heating the
films under a nitrogen atmosphere. All nanoparticle-based samples showed
crystallization to $\alpha$-GeTe followed by a crystalline-to-crystalline
transition to the high-temperature $\beta$-phase of GeTe. During cooling, this
transition was reversible and could be repeated for a second heating and
cooling cycle. All samples showed increased crystallization temperatures
$T_{C,1}$ and $T_{C,2}$ compared to bulk GeTe.

Figure 6:  (a) Comparison of the GeTe transition temperatures $T_{C,1}$ (disk)
and $T_{C,2}$ (diamonds) determined for different particle sizes $d$ and film
thicknesses $t$. The colors represent the different characterization
techniques and samples. The larger the symbol area, the higher was the applied
heating rate $\vartheta$. Exemplary values of $\vartheta$ are noted in the
plot. (b) A magnified plot for the section in (a) where most $T_{C,1}$ were
determined for small $d$.

Fig. 6 compares our results to the values obtained by previous studies (cf.
Tab. 1). While we observed coalescence, similar to the literature, we list the
transition temperatures as a function of the initial particle size $d$. Fig. 6
reveals that the literature values follow a general trend of an increasing
$T_{C,1}$ and $T_{C,2}$ for decreasing $d$ below 10 nm. However,
quantification of the size-dependent $T_{C,1}$ and $T_{C,2}$ is complicated by
coalescence. We propose to perform a similar study with separated
nanoparticles, e.g. by using atomic layer deposition. Furthermore, in-situ
TEM, in-situ Raman spectroscopy, and ultrafast DSC could give further insights
into the crystallization of individual nanoparticles.Chen  _et al._ (2016);
Polking  _et al._ (2011); Pries  _et al._ (2019) This would be especially
interesting for GeTe, since a decrease of $T_{C,1}$ has been found for
decreasing particle size $d$ for Ge2Sb2Te5, which is one of the most prominent
phase-change materials.Shportko  _et al._ (2008); Wuttig, Bhaskaran, and
Taubner (2017) In contrast, Ref. Raoux, Jordan-Sweet, and Kellock, 2008
reported an increased $T_{C,1}$ for sputter-deposited doped GeSb, Sb2Te, and
Ge2Sb2Te5 films with thicknesses $t$ < 10 nm. Nevertheless, Ref. Simpson  _et
al._ , 2010 showed for Ge2Sb2Te5 that this behavior can be ascribed to
(capping-dependent) strain in the thin films. The crystallization of
nanoparticles will likely be influenced by the large surface-to-volume ratio
and presumably, significant strain. Moreover, Kolb et al. reported on the
nucleation of non-oxidized bulk GeTe at 230∘C. In this context, the
crystallization at 180∘C was found to be induced by surface oxidation and
related elemental segregation, which led to Te serving as nucleation
sites.Kolb  _et al._ (2019)

Apart from the initial crystallization, our study focused on the reversible
$\alpha$-to-$\beta$-transition which we observed for the three nanoparticle
samples. These particles were initially amorphous, synthesized following two
different protocols, and had different diameters. The transition temperatures
were higher compared to the thin films and crystalline nanoparticles discussed
in the literature (cf. Tab. 1), even if particle coalescence is assumed. It is
promising that samples based on very small solution-deposited amorphous
nanoparticles still show reversible phase change behavior along with an
increased bandgap and tunable refractive index.Michel  _et al._ (2020) This is
potentially useful for the scalability of active photonic, phase-change random
access memory, and optical data storage.

###### Acknowledgements.

This project was funded by the European Research Council under the European
Union’s Seventh Framework Program (FP/2007-2013)/ERC Grant Agreement Number
339905 (QuaDoPS Advanced Grant). A.-K.U.M. acknowledges funding from the ETH
Zurich Postdoctoral Fellowship Program and the Marie Curie Actions for People
COFUND Program (Grant 17-1 FEL-51). M.Y. acknowledges funding from the SNF
Ambizione Fellowship (No. 161249). The authors thank H. Rojo Sanz, S. Meyer,
and I. Giannopoulos for technical assistance and P. Knüsel, M.D. Wörle, and J.
Schawe for fruitful discussions. TEM measurements were performed at the
Scientific Center for Optical and Electron Microscopy (ScopeM) at ETH Zurich.

## Data Availability

The data that support the findings of this study are available from the
corresponding author upon reasonable request.

##  Appendix A Full-range XRD diffractograms

For comparison, the full XRD patterns are shown for examplary temperatures in
Fig. 7 with Fig. 7(a) related to Fig. 3, Fig. 7(b) related to Fig. 4, and Fig.
7(c) related to Fig. 5. The XRD diffractograms are shown for:

  * •

50∘C, which is the lowest $T$ for which XRD was conducted,

  * •

the respective $T_{C,1}$,

  * •

320∘C for $\alpha$-GeTe related to heating 1,

  * •

the respective $T_{C,2}$, if applicable,

  * •

450∘C, which is the highest $T$ for which XRD was conducted, and

  * •

75∘C for $\alpha$-GeTe after cooling 1.

Figure 7:  Diffractograms of A-GeTe nanoparticles shown in (a), Fig. 3, (b),
Fig. 4, and (c), Fig. 5, for the full angular range of detection. The
normalization and color code are similar to Figs. 3 \- 5. The Miller indices
are noted next to the peaks. The reference patterns for $\alpha$\- and
$\beta$-GeTe are marked in black and gray, respectively, at the bottom of each
subfigure. Additional features are marked similarly to Figs. 3 and 4: (a), (b)
black asterisk for Te or Ge impurities, and (b) black rhombus for an
unidentified small peak, potentially associated with carbon.

##  Appendix B Identification of XRD peak at 2$\theta$ $\approx$ 25.7∘

Considering the particles right after synthesis, the XRD patterns in Fig. 4
show a small peak at 2$\theta$ $\approx$ 25.7∘. According to the potential
reference patterns, this would only match $\beta$-GeTe which can be excluded
as this phase is expected only at higher temperatures. Furthermore, it has
been reported that oxidation and segregation can be expected for annealed
GeTe.Kolb  _et al._ (2019) To prevent this, synthesis and XRD measurements
were performed oxygen-free. Nevertheless, if oxygen had been present (at
elevated temperatures) only amorphous GeOx and crystalline Te would be
expected.Kolb  _et al._ (2019) The small initial XRD peak at about 25.7∘
cannot be explained by this. Another possibility could be residual germanium
diiodide which is used as precursor in the synthesis. However, the strongest
XRD peaks would be expected at 2$\theta$ $\approx$ 30.4 and 26.2∘ according to
Ref. Avilov and Imamov, 1968.

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