Physica B 406 (2011) 4436–4439

Contents lists available at SciVerse ScienceDirect

Physica B

0921-45

doi:10.1

n Corr

E-m

journal homepage: www.elsevier.com/locate/physb

The thickness dependence of the crystallization behavior in sandwichedamorphous Ge2Sb2Te5 thin films

G. Bai a, R. Li b, H.N. Xu a, Y.D. Xia a, Z.G. Liu a,n, H.M. Lu a, J. Yin a

a Department of Materials Science and Engineering and National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, PR Chinab Department of Physics and National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, PR China

a r t i c l e i n f o

Article history:

Received 19 May 2011

Received in revised form

8 August 2011

Accepted 1 September 2011Available online 7 September 2011

Keywords:

Phase change

Thin films

Crystallization

Thickness dependence

Thermodynamic

26/$ - see front matter & 2011 Elsevier B.V. A

016/j.physb.2011.09.003

esponding author.

ail address: liuzg@nju.edu.cn (Z.G. Liu).

a b s t r a c t

The thickness dependent crystallization behavior of thin amorphous Ge2Sb2Te5(GST) films sandwiched

between different cladding materials has been investigated based on a thermodynamic model. It is

revealed that there is a critical thickness below which the crystallization cannot occur. The critical

thickness is determined by the energy difference Dg between the crystalline GST/substrate interface

energy and the amorphous GST/substrate interface energy, the melting enthalpy, and the mole volume.

The calculated result is in good agreement with the experiments. Furthermore, the crystallization

temperature is also affected by interface energy difference Dg. Larger Dg gives rise to a higher

crystallization temperature, and vice versa. This impact becomes stronger as the film thickness is

decreased.

& 2011 Elsevier B.V. All rights reserved.

1. Introduction

Investigation of phase transition between amorphous andcrystalline states in sandwiched thin films of phase changematerials is of great importance for both basic research andtechnological applications such as phase-change random accessmemory (PCRAM) [1–3]. The phase change memory is based on thereversible switching between amorphous and crystalline states inphase change materials. For the transformation from the stablecrystalline phase to the metastable amorphous phase, the amor-phous state can be obtained by melting the crystalline phase andthen quenched rapidly by using a high and narrow voltage pulse.For the reverse transition, a longer and lower voltage pulse is usedto heat the amorphous region over its crystallization temperatureTx for a sufficient time, with which the amorphous state cancrystallize. In recent years, the thickness effect on amorphous–crystalline phase transition has been extensively explored in phasechange materials. Together with the scaling of the PCRAM devices,an understanding of the thickness dependence of the crystalliza-tion behavior become crucial. It has been reported that for thinfilms of phase change materials, such as Ge2Sb2Te5, nitrogen dopedGe2Sb2Te5, Ge–Sb with 15 at% Ge, Sb2Te, and Ag- or In-dopedSb2Te, crystallization temperatures increase with the reduction offilm thickness for films thinner than 10–15 nm [4]. The increasedcrystallization temperatures Tx has been fitted successfully to a

ll rights reserved.

exponential function [4,5]. However, it is noted that the crystal-lization temperature can decrease with reducing film thicknessdepending on the cladding materials, such as metals [6] and ZnS–SiO2 [7]. Simpson et al. [7] proposed that the increase or decreaseof crystallization temperature results from the interface stress(increase for higher stress and decrease for lower stress). So moreresearch is needed to clarify the thickness effect on the crystal-lization temperature for phase change materials. The critical scaleof a phase change material where phase transition does not occuranymore is one of its most important parameters. It determines itsultimate scaling limit of technological applications such as rewri-table optical storage media and phase-change random accessmemory (PCRAM). The thinnest films that can still be crystallizedas detected by XRD are found to be 1.3–2 nm [4].

Although the interface energy played a key role in the phasetransformation of the thin films sandwiched between two claddingmaterials, especially in the case of ultrathin films, so far an accuratecalculation of the thickness dependence of the crystallization beha-vior of phase change thin films still lacks. The present study focuseson quantitative determination of critical thickness, under which thecrystallization cannot occur, and explanation of the thickness-depen-dent crystallization temperature for Ge2Sb2Te5(GST) thin films sand-wiched different materials based on a thermodynamic theory.

2. Model and theory

To understand the thickness effects in phase change thin film,a thermodynamic model is established by considering the

G. Bai et al. / Physica B 406 (2011) 4436–4439 4437

interface energy. We assume here that the crystallization nucleusis cylinder shaped in the amorphous thin film sandwichedbetween top and bottom cladding materials, as schematicallyindicated in Fig. 1. The Gibbs free energy change DG for thecylindrical nucleus during crystallization is given by

DG¼�DGacpr2dþgac2prdþDg2pr2 ð1Þ

where DGac is the Gibbs free energy difference per mol volumebetween crystalline and amorphous phases. For semiconductor,DGac has been estimated by [8]

DGacHmTðTm�TÞ

T2mVm

ð2Þ

where Tm, Hm and Vm are the melting temperature, meltingenthalpy, and the mol volume, respectively. gac, Dg (Dg¼gcs�gas)are defined as the interface energy between the amorphous andcrystalline phases of phase change material and the differencebetween the crystalline thin film/substrate interface energy gcs

and the amorphous thin film/substrate interface energy gas. Dgmust be positive according to Eq. (19) in Ref. [5] based on a factthat the melting point must be higher than the crystallizationtemperature. Because the amorphous phase is considered as asupercooled liquid, according to the Gibbs–Thomson equation, gac

is assumed to be the solid–liquid interface energy [9],

gac ¼ 2hSvibHm=3VmR ð3Þ

where h is atom diameter, R is the ideal-gas constant, Svib is thevibrational part of melting entropy Sm¼Hm/Tm.

A similar treatment can be considered for the film/substrateinterface. However, because the film and the substrate aredifferent materials, as a first-order approximation, the amorphousthin film/substrate interface energy gas is given as

gas ¼ 2hSvibHm=3VmR ð4Þ

where h,Hm,Svib, and Vm are the mean values of correspondingparameters of substrate and thin film.

substrate

GST r

substrate

d

Fig. 1. Schematic diagram for nucleation process of a nucleus with radius r formed

in an amorphous GST film with thickness d sandwiched in two substrate materials.

Table 1Parameters used in the thermodynamic calculation.

h (nm) Vm (cm3/g-atom) H

Ge2Sb2Te5 0.3 [12] 18.6b 1

ZnS [14] 0.234 11.9 2

W [15] 0.271 9.53 3

Al2O3 [10] 0.324 5.11 2

Cu [10] 0.2806 7.1 1

Pt [16] 0.2775 9.1 1

Al [16] 0.2863 10 1

a For metal, Svib¼Sm [16]; and for semiconductor, Svib¼Sm�R [b Vm¼M/r with M and r being g-atom weight and the densi

r¼18.6 cm3/g-atom.

Because the solid–solid interface energy is about twice of thesolid–liquid interface energy of the corresponding materials [11],as a first-order approximation, the crystalline thin film/substrateinterface energy gcs is given as

gcs ¼ 4hSvibHm=3VmR ð5Þ

The nucleation critical radius and the nucleation work aregiven by qDG/qr¼0,

rk ¼gac

DGac�2Dg=dð6Þ

DGk ¼�pDGacg2

acdþ2pg2acdðDGac�2Dg=dÞþ2pg2

acDgðDGac�2Dg=dÞ2

ð7Þ

In Eq. (6), the denominator must be no less than zero,otherwise, the critical nucleation radius has not the physicalmeaning.

DGac�2Dg

dZ0 ð8Þ

Substituting Eq. (2) into Eq. (8), this expression becomes

HmTðTm�TÞ

T2mVm

�2Dg

dZ0 ð9Þ

The expression above is satisfied only when (Hm/TmVm)2�

4(�Hm/Tm2 Vm)(�2Dg/d)Z0,

so we can deduce the thin film critical thickness

dmin ¼8DgVm

Hmð10Þ

Under the case of dodmin, the amorphous thin film cannotcrystallize.

3. Results and discussion

Firstly, we consider the film was sandwiched between thesame material. Table 2 shows the critical thickness of GST thinfilms sandwiched by oxide, metal, and sulfide. The thermody-namic parameters used in calculations are shown in Table 1. ForGST thin film sandwiched by Al2O3, our calculation result is ingood agreement with the experiment results [4] Table 2.

According to Eq. (10), the critical thickness dmin is directlyproportional to the interface energy difference Dg, mol volume Vm

of thin films and inverse proportional to melting enthalpy Hm ofthin films. Melting enthalpy and mol volume are intrinsic para-meter of thin film material. The extrinsic parameter interfaceenergy difference Dg plays an important role in critical thickness,which implies the interplay strength of atoms between thin filmand substrate materials. So the critical thickness depends on theinterface energy difference Dg. When the thickness of thin film isreduced, the crystallization temperature and melting temperature

m (KJ/g-atom) Svib (J/g-atom-K)a Tm (K)

1.3 [13] 4.39 900 [13]

1.5 1.89 2100

2.64 8.87 3680

2.28 3.832 2326

3.05 9.613 1358

9.6 9.58 2045

0.8 11.56 933

17].

ty. For GST, M¼114.07 g/g-atom, r¼6.13 g/cm3 [12], Vm¼M/

Table 2Critical thickness of GST thin films sandwiched by

oxide, metals, and sulfide.

dmin (nm)

ZnS/GST/ZnS 0.95

W/GST/W 3.11

Al2O3/GST/Al2O3 1.91 (2a)

Cu/GST/Cu 2.02

Pt/GST/Pt 2.36

Al/GST/Al 1.9

a Ref. [4].

T

Tm

Tx

dmin d

Amorphous phase

Crystalline phase

Liquid phase

T

Tm

Tx

dmin d

Amorphous phase

Crystalline phase

Liquid phase

Fig. 2. Schematic phase diagram of crystallization and melting temperature as a

function of film thickness: (a) large Dg; (b) small Dg.

Fig. 3. The work of crystalline formation of GST thin film sandwiched by Pt, ZnS,

and Al2O3 at T¼450 K, respectively, as a function of thickness.

Table 3Amorphous/crystalline interface energy of GST

thin film and the interface energy difference of

substrate and crystalline or amorphous thin film.

Dg (J/m2)

ZnS/GST/ZnS 0.0726

Pt/GST/Pt 0.181

Al2O3/GST/Al2O3 0.146

gac (J/m2)

GST 0.0646

G. Bai et al. / Physica B 406 (2011) 4436–44394438

depending on the interface energy of thin film and substrateconformably increase or decrease, see Fig. 2. The cross point ofcrystallization temperature and melting temperature as a func-tion of film thickness corresponds to the critical thickness, bellowwhich the amorphous film will not crystallize, but melt directlywith increasing temperature. So crystallization cannot occur.

Fig. 3 shows the calculated nucleation work of GST thin filmsandwiched by Pt, ZnS, and Al2O3 at T¼450 K, respectively, as afunction of thickness. As shown in Table 3, for Pt and Al2O3

substrates, the interface energy difference Dg is much larger thanthe interface energy gac of GST thin film between the amorphousand crystalline states, so the nucleation work increases as thethickness of thin film decreases due to the strong interface effectand crystallization temperature increases in the film. For ZnSsubstrate, the interface energy difference Dg equals approximatelythe interface energy gac of GST thin film between the amorphousand crystalline states, so the work of crystalline formation

decreases as the thin film thickness is reduced until 2 nm due tothe weak interface effect. Correspondingly, crystallization tem-perature decreases.

4. Conclusion

In summary, a thermodynamic model is used to investigatethe thickness dependent crystallization behavior of the sand-wiched phase change thin films. A theoretical expression of thecritical thickness is deduced, under which the crystallizationcannot occur. The critical thickness depends on the interfaceenergy difference Dg, the melting enthalpy, and the mole volume.Furthermore, the crystallization temperature shows a dependenceon the interface energy difference Dg. Larger Dg gives rise to theincrease of crystallization temperature, and smaller Dg decreasesthe crystallization temperature. This effect becomes stronger withdecreasing the film thickness.

Acknowledgments

This work was financially supported by the State Key Programfor Basic Research of China (Grant no. 2007CB935401), the StateKey Program for Science and Technology of China (Grantno.2009ZX02039-004) and National Natural Science Foundationof China (61076008).

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