This article appeared in a journal published by Elsevier. The attachedcopy is furnished to the author for internal non-commercial researchand education use, including for instruction at the authors institution

and sharing with colleagues.

Other uses, including reproduction and distribution, or selling orlicensing copies, or posting to personal, institutional or third party

websites are prohibited.

In most cases authors are permitted to post their version of thearticle (e.g. in Word or Tex form) to their personal website orinstitutional repository. Authors requiring further information

regarding Elsevier’s archiving and manuscript policies areencouraged to visit:

http://www.elsevier.com/authorsrights

Author's personal copy

The relaxation processes in the Al-(Nb, Mo, Ta, W) binaryamorphous thin films

T. Car a,*, J. Ivkov b, M. Jer�cinovi�c a, N. Radi�c a

aRudjer Bo�skovi�c Institute, Division of Materials Science, Bijeni�cka cesta 54, P.O.B. 1016, 10000 Zagreb, Croatiab Institute for Physics, Bijeni�cka cesta 46, 10000 Zagreb, Croatia

a r t i c l e i n f o

Article history:Received 4 July 2012Received in revised form3 September 2012Accepted 7 September 2012

Keywords:Thin filmsAmorphous alloysResistivityRelaxationCrystallization

a b s t r a c t

Structural relaxation and crystallization of Al-(Nb, Mo, Ta, W) amorphous thin films under isochronalcondition were examined by continuous in situ electrical resistance measurements in vacuum. Theamorphous Al-early transition metals (TE) thin films were prepared by simultaneous sputtering fromtwo independently controlled DC magnetron sources in the CMS 18 deposition device. The structure ofthe as-deposited, heat-treated, and crystallized films was investigated by the XRD method. Thedynamical crystallization temperature was estimated from the rapid change of the derivative of resis-tivity vs. temperature curve (dr/dT). For the isochronal heating, it was observed that the relaxationeffects decreased with an increase of the heating rate and decreased with the content of early transitionmetal in the film. Assuming the linear dependence of resistivity with temperature (Dr/rRT ¼ aDT) in theobserved temperature interval the linear r(T) dependence is extracted from the relaxation effects.Adopted experimental function of r(T) is fitted to a modified BlocheGrüneisen formula. Excellentagreement of experimental data and fitting function is obtained.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Recently, there hasbeen a significant increase in theexperimentalstudies and applications of amorphous solids [1]. Their possibleapplications are large, based on characteristic properties such aschemical reactivity or inertia, electronic-excitation phenomena, softmagnetic properties, superconductivity, etc. [2e4]. New nano-crystalline and quasicrystallinematerials can be obtained by thermaltreatment of amorphous alloys. Binary amorphous alloys of refrac-tory transitionmetals and highly electrically conductivemetals seemto be promisingmaterials according to the specific properties of theircomponents [5]. The aluminumeearly transition metal (AleTE)systems are particularly interesting due to their current andpossible applications in technology of integrated microelectronics[6e8]. For example, theAleWamorphousfilms also exhibit excellentcorrosion resistance [3,9]. However, for the application of thesealloys at elevated temperatures it is important to investigate theirthermal properties and stability.

The phase transformation kinetic during the isothermal andisochronal annealing has been widely investigated due to thedevelopment of the high-resolution measurement of phase trans-formation process and its analysis methods [10e12].

An amorphous phase is thermodynamically in a nonequilibriumstate and transforms into a crystalline phase on thermal treat-ments. Below the crystallization temperature, the structuralrelaxation is also known to occur. The nature of the physicalprocesses underlying this phenomenon is not well understood, andunraveling this behavior constitutes one of the main scientificchallenges in the solid state physics. The best method for theinvestigation of the changes of the structure in amorphous alloys, isa monitoring of the changes of the electrical resistivity r uponheating [13,14]. The resistivity measurement results, correlatedwith the measurements of the structural changes (XRD investiga-tion), allow a fairly comprehensive insight into the heat-inducedstructural transformations [15,16].

In this article, we present the structural relaxation and crystal-lization of Al-(Nb, Mo, Ta, W) amorphous thin films underisochronal condition, examined by continuous in situ electricalresistance measurements in vacuum. Assuming linear temperaturedependence of resistivity, relaxation effects were extracted fromthe experimental data and fitted to a modified BlocheGrüneisenformula.

2. Experimental

Amorphous thin films of binary alloys AlxW1�x (85 � x � 45),AlxNb1�x (95 � x � 20), AlxMo1�x (90 � x � 20), AlxTa1�x

(95 � x � 20) have been prepared by magnetron deposition in the* Corresponding author. Fax: þ385 1 4680 114.

E-mail addresses: car@rudjer.irb.hr, car@irb.hr (T. Car).

Contents lists available at SciVerse ScienceDirect

Vacuum

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

0042-207X/$ e see front matter � 2012 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.vacuum.2012.09.008

Vacuum 98 (2013) 75e80

Author's personal copy

CMS 18 sputtering system. The working gas was argon at a pressureofw0.67 Pa in a constant flowmode. Samples were deposited ontocircular (1 cm dia) substrates at room temperature. A typicaldeposition rate was about 0.17e0.35 nm/s, depending on the filmcomposition, while average film thickness was from 325 to 400 nm,depending on the film composition.

The structure of the as-deposited, heated, relaxed and crystal-lized films was investigated by the XRD method using a Philips PW1820 vertical goniometer with monochromatized CuKa radiation[17]. The range of amorphous, nanocrystalline and mixed phase ofthe as-deposited Al-(Nb, Mo, Ta, W) thin films are shown in Fig. 1.The amorphous range is wider for the Al-(Ta, Nb) combinations(Al with elements of 5a periodic group). For high concentrations ofaluminum or early transition metals all examined combinationshave nanocrystalline phase. For Al-(W, Ta) the mixed phase is alsoobserved. The heat-induced phase transformation of the amor-phous phase of Al80Nb20 thin film is shown in Fig. 2, as an example.For the as-deposited Al80Nb20 amorphous thin film there are notraces of crystalline phase. Extraction of intermetallic phase startsatw565 K. Phase transformation ends atw740 K. The end-productof the phase transformation was Al3Nb intermetallic compound.

For the isochronal heating, the films were produced by depo-sition onto the alumina ceramic substrate. In case of isochronalheating, the measurements were performed in a vacuum chamberat a pressure of about 10�3 Pa. The samples were radiatively heated.After either isochronal or isothermal heating of the samples, notraces of oxidation of the films were detected by the subsequent X-ray diffraction examination.

The isochronal resistivity measurements were performed byfour-probe method and by standard ac technique with computercontrolled data acquisition. For the high temperature measure-ments, the contacts were tungsten rods spring-loaded directly ontothe film. An intermittent noise, which was due to the mechanicaldisplacement of the spring-loaded contacts during heatingecooling cycle was the greatest source of measurement error.The maximum possible error from the contact displacementswas w5% [18].

3. The electrical resistivity model

The electrical resistivity of most materials changes withtemperature. Electrical resistivity of metals generally increases

with temperature. At high temperatures, resistivity of a metalincreases linearly with temperature as follows:

rðTÞ ¼ r0$½1þ aðT � T0Þ�; (1)

where a is the temperature coefficient of resistivity. As thetemperature of a metal is reduced, the temperature dependence ofresistivity follows a power law function of temperature. Resistivityof metals over the whole temperature range can be mathematicallyexpressed by the BlocheGrüneisen formula (BGF) [19,20]:

BGFnðxÞ ¼ xn$Z1=x

0

tn

ðet � 1Þ�1� e�t�dt (2)

where x¼ T/qD, qD is the Debye temperature, and n is an integer thatdepends upon the nature of interaction. For crystalline metals it isknown that resistivity behavior for n ¼ 2 is due to electroneelectron interaction, for n ¼ 3 is due to sed electron scatteringand for n ¼ 5 is due to scattering of electrons by phonons. Appli-cation of Eq. (2) to amorphous materials is based on the fact thattemperature variation of electrical resistivity of amorphous metals

Fig. 1. The structure of the Al-(Ta, Nb, Mo, W) as-deposited films. The estimateduncertainty of the film composition is about 5% relative to the minor component.

Fig. 2. Heat-induced phase transformation of the amorphous phase of Al80Nb20 thinfilm. End-product of the phase transformation was Al3Nb intermetallic compound.

T. Car et al. / Vacuum 98 (2013) 75e8076

Author's personal copy

is similar to the temperature variation of electrical resistivity ofcrystalline metals [13]. The amorphous phase has only smallerrelative difference in changes of resistivity. After extracting thelinear part of temperature variation of resistivity at high tempera-tures, only the contribution which should be responsible forrelaxation remains.

Analytical solution of the BlocheGrüneisen formula appropriatefor calculations and fitting is given as follows [21]:

BGFnðxÞ ¼ n!xn$

24zðnÞ �Xn

j¼0

x�j

j!Lin�j

�e�1=x

�35 (3)

where Lis(z) is the Polylogarithm function:

LisðzÞ ¼XNk¼1

zk

ks(4)

and z(n) is the Riemann zeta function:

zðnÞ ¼XNk¼1

1kn

Re n>1 (4a)

Assuming that the Al-(Nb, Mo, Ta, W) amorphous alloysat high temperatures have linear metallic behavior, the linearpart is extracted from the r(T) experimental curve:r(T) ¼ rlin(T) þ rnonlin(T), where:

f ðxÞ ¼ rnonlinðTÞr0

¼ rðTÞr0

� ½1þ aðT � T0Þ�: (5)

Experimental curve f(x) represents nonlinear part of relativeresistivity due to the relaxation effects. Adopted fitting functionbecomes as follows:

FðxÞ ¼ a$BGFnðxÞ þ b$xþ c; (6)

where fitting function F(x) is a linear combination of whole resis-tivity (a$BGFn(x)) minus linear part (b$x þ c) and

x ¼ T � TSqD

: (7)

Temperature Ts < Tc represents the temperature shift of the BGFfunction from 0 K to the temperature of relaxation. As the resistivityof amorphous alloys have its origin in the displacement of atomsand chemical disorder, transformed function F(x) can describerelaxation behavior of resistivity of amorphous alloys at shiftedtemperature Ts.

The Debye temperature is calculated according to the formulafor composite materials [22] as follows:

qDðAlXTE1�XÞ ¼ qAlqTE½rAlX þ rTEð1� XÞ�qAlrAlX þ qTErTEð1� XÞ ; (8)

where r is the density of the material.

Fig. 3. The electrical resistivity and the temperature coefficient of resistivity (TCR) ofthe Al-(Ta, Nb, Mo, W) as-deposited thin films at room temperature.

Fig. 4. The electrical resistivity and the temperature coefficient of resistivity (TCR) ofthe Al-(Ta, Nb, Mo, W) thin films after heating to the dynamical crystallizationtemperature.

T. Car et al. / Vacuum 98 (2013) 75e80 77

Author's personal copy

4. Results and discussion

The experimental results for the electrical resistivity r0 andtemperature coefficient of resistivity (TCR) a at the room temper-ature, and electrical resistivity rc and temperature coefficient ofresistivity ac after heating to the dynamical crystallizationtemperature are shown in Figs. 3 and 4, respectively. For the as-deposited films (Fig. 3) inside amorphous range (shown in Fig. 1)TCR has negative values. Values of r and a are in accordance withthe Mooij correlation [23], and reflect typical properties of theamorphous alloys containing early transition metals.

The dependence of the temperature variations of the resistivityon the maximum temperature in the heating cycle, for the Al78W22amorphous thin film, is shown in Fig. 5 as an example [24]. Thesample film was heated successively during the four heating cycles(r ¼ dT/dt ¼ 2 K/min) with the increasing maximum temperaturesof 300, 420, 520 and 730 �C, respectively. For initial three stepssample remain amorphous and only relaxation processes takeplace. At the fourth step, the sample was heated above Tc, andcorresponding XRD-pattern shown crystalline structure [24].

Structural relaxation after extraction of the (metallic) linearresistivity dependence for AleMo amorphous thin films of differentcomposition and for Al75TE25 amorphous thin films (TE ¼ W, Ta,Mo) are shown in Figs. 6 and 7, respectively. The changes of thestructure in amorphous alloys, due to monitoring of the changes ofthe electrical resistivity r upon heating were also investigated inRefs. [13,16,25,26]. The resistivity measurement results werecorrelated with the measurements of the structural changes(XRD investigation). The same type of behavior was also observedin the ternary amorphous alloys [27,28].

The dynamical crystallization temperature was estimated fromthe rapid change of the derivative of resistivity vs. temperature curve(dr/dT) [24] and is shown in Fig. 8. As we can see the most stablewere amorphous AlW combinations, but with the most narrowamorphous interval, and maximum in the resistivity and minimumin the a, which correspond to the strongest sped hybridization,coinciding with the shallow minimum of Tc around 75 at% Al.

Relaxation processes where fitted to Eq. (6) for various theo-retical (predefined) values of n, where unknown fitting parametersare Ts, a, b and c. Linear contribution of resistivity is calculated andextracted from r(T) experimental curve by inserting experimentallyestablished TCR (a) and rRT, shown in Fig. 3. Fitting of the f(x)

Fig. 5. The temperature dependence of the electrical resistivity of the Al78W22

amorphous thin film heated successively in four heating cycles (r ¼ 2 K/min) [24].

Fig. 6. The nonlinear temperature variation of the electrical resistivity duringisochronal heating of AleMo amorphous thin films of different composition. Heatingrate was r ¼ 2 K/min.

Fig. 7. The nonlinear temperature variation of the electrical resistivity duringisochronal heating of Al75TE25 amorphous thin films (TE ¼W, Ta, Mo). Heating rate wasr ¼ 2 K/min.

Fig. 8. The dynamical crystallization temperature (Tc) estimated from the isochronalheating of the Al-(Ta, Nb, Mo, W) amorphous alloys deposited onto alumina ceramicsubstrate.

T. Car et al. / Vacuum 98 (2013) 75e8078

Author's personal copy

experimental curves is performed with the assumptions thatinteger n only take known predefined values: n ¼ 2, n ¼ 3 or n ¼ 5.Excellent agreement of experimental data and fitting function isobtained for n ¼ 2 as shown in Figs. 9 and 10. Best fitting param-eters (Ts, a, b and c) according to Eq. (6) for n ¼ 2 and their relativecontributions are given in Table 1. For the crystalline metals, n ¼ 2means that resistivity behavior is due to electroneelectron inter-action. However, for the transition metals resistivity behavior dueto sed electron scattering is expected. It is well established that theelectronic properties in transition metal aluminides are stronglydetermined by the well defined valley in the electronic density ofstates at which the Fermi level EF, is placed [29,30]. Thisvalley, in amorphous AleTM alloys is due to the sped hybridization.Further increase of the resistivity upon the crystallization leadsto the combined effect of the diffraction by Bragg planes and thesped hybridization. Diffraction by Bragg planes further influencesthe transport properties through the increase of the electroneffective mass and through the decrease of Fermi velocityvF. Therefore, the increase in the structural order may result ina major increase of resistivity [31].

Comparison of the a and b coefficients shows that the smallestlinear contribution (relative contribution of the coefficient b) havethe most stable AleWamorphous alloy. For the AleMo amorphousalloys coefficient a increases with the increase of the Al content.This is in accordancewith the experimentally observed fact that therelaxation effects also increased with increasing Al content.

5. Summary and conclusions

Structural relaxation and crystallization of Al-(Nb, Mo, Ta, W)amorphous thin films under isochronal annealing condition wasexamined by continuous in situ electrical resistance measurementsin vacuum. The amorphous Al-(Nb, Mo, Ta, W) thin films wereprepared by co-sputtering from two independently controlled DCmagnetron sources. Assuming that the Al-(Nb, Mo, Ta, W) amor-phous films have the same linear dependence of resistivity r(T) asmetals, the linear part of resistivity is extracted from the experi-mental curves r(T). Analytical solution of the BlocheGrüneisenformula adopted for the relaxation processes at high tempera-tures is used to find best fit function and possible physical expla-nations for relaxation processes. Excellent agreement ofexperimental data and fitting function is obtained for n ¼ 2. For theAleMo amorphous alloys the BGF function contribution increaseswith the increase of the Al content, this is in accordance with theexperimentally observed fact that the relaxation effects alsoincreased with increasing Al content. The most stable AleWamorphous alloys have the smallest linear contribution. In theAleTE amorphous alloys, the structural relaxation enhancesshort range ordering. Therefore, small changes in interatomicdistances and the increase in both topological and chemical shortrange order during the process of the relaxation, may (through thesped interaction and the reduction of the density of states at EF)seriously affect the changes in the transport properties.

References

[1] Masumoto T, Hashimoto K, editors. Rapidly quenched and metastable mate-rials, part I. Tokyo: Elsevier Science; 1994.

[2] Hashimoto K, Kumagai N, Yoshioka H, Kawashima A, Asami K, Zhang BP.Mater Sci Eng 1991;A133:22.

[3] Wolowik A, Janik-Czachor M. Mater Sci Eng 1999;A267(2):301.[4] Lomakina SV, Kazanskii LP, Shatova TS, Tselykh OG. Prot Met 1997;

33(6):560.[5] Radi�c N, Car T, Tonejc A, Ivkov J, Stubi�car M, Metiko�s-Hukovi�c M. Physics and

technology of thin films IWTF 2003. In: Moshfegh AZ, Kanel HV, Kashyap SC,Wuttig M, editors. Proceedings of the international workshop. Teheran (Iran):World Scientific Publishing; Jun 2004.

[6] Bergstrom DB, Petrov I, Allen LH, Greene JF. J Appl Phys 1997;82:201.[7] Takeyama MB, Noya A. Jpn J Appl Phys Part 1 1999;38:2116.[8] Pantel R, Torres J, Paniez P, Auvert G. Microelectron Eng 2000;50:277.[9] Habazaki H, Tahakira K, Yamaguchi S, Hashimoto K, Dabek J, Mrowec S, et al.

Mater Sci Eng 1994;A181/182:1099.[10] Liu YC, Sommer F, Mittemeijer EJ. Acta Mater 2006;54:3383.[11] Venkataraman S, Hermann H, Sordelet DJ, Eckert J. J Appl Phys 2008;104:

066107.[12] Car T, Radi�c N, Ivkov J, Tonejc A. Appl Phys A 2005;80:1087.[13] Scott G. In: Luborsky FE, editor. Amorphous metallic alloys. London: Butter-

worths; 1983. p. 144.[14] Hofstetter W, Sassik H, Grossinger R, Trausmuth R, Vertesy G, Kiss LF. Mater

Sci Eng A 1997;226:213.[15] Car T, Radi�c N, Ivkov J, Babi�c E, Tonejc A. Appl Phys 1999;A 68:69.[16] Pratap A, Shanker Rao TL, Lad KN, Dhurandhar HD. J Non-Cryst Solids 2007;

353:2346.[17] Radi�c N, Gr�zeta B, Gracin D, Car T. Thin Solid Films 1993;228:225.[18] Ivkov J, Car T, Radi�c N, Babi�c E. Solid State Commun 1993;88:633.[19] Ziman JM. Electrons and phonons. Oxford: Clarendon; 2001.[20] Bass J, Pratt Jr WP, Scroeder PA. Rev Mod Phys 1990;62:645.[21] Cvijovi�c D. Theor Math Phys 2011;166(1):37.

Fig. 9. Fitting curves for the BGF exponent n ¼ 2 of the temperature variation of theelectrical resistivity of AleMo amorphous thin films of different composition. Errors ofthe fitting parameters are given in Table 1.

Fig. 10. Fitting curves for the BGF exponent n ¼ 2 of the temperature variation of theelectrical resistivity of Al75TE25 amorphous thin films (TE ¼ W, Ta, Mo). Heating ratewas r ¼ 2 K/min. Errors of the fitting parameters are given in Table 1.

Table 1Best fitting parameters a, b and Ts of adopted BGF function (Eq. (6)) for n ¼ 2, of AleTE compositions shown in Figs. 6 and 7.

Alloy a b Ts [K] jajjaj þ j:bj:

jbjjaj þ j:bj:

Al80Mo20 0.655 � 0.002 �0.456 � 0.002 400 0.590 0.410Al75Mo25 1.000 � 0.002 �0.781 � 0.002 384 0.561 0.439Al70Mo30 0.720 � 0.002 �0.655 � 0.002 396 0.523 0.477Al75W25 0.354 � 0.004 �0.088 � 0.003 340 0.800 0.200Al75Ta25 0.126 � 0.002 �0.034 � 0.002 340 0.779 0.221

T. Car et al. / Vacuum 98 (2013) 75e80 79

Author's personal copy

[22] Stoimenov S, Stojanov Z, Skeparovski A. JMater SciMater Electron 2003;14:777.[23] Mooij JH. Phys Status Solids 1973;A17:521.[24] Ivkov J, Radi�c N, Tonejc A, Car T. J Non-Cryst Solids 2003;319:232.[25] Hofstetter W, Sassik H, Grossinger R, Trausmuth R, Vertesy G, Kiss LF. Mater

Sci Eng A 1997;213:226.[26] Venkataraman S, Hermann H, Sordelet DJ, Eckert J. J Appl Phys 2008;104:

6107.[27] Haruyama O, Asahi N. J Material Sci 1992;27:5281.

[28] Morales-Sanchez E, Prokhorov EF, Gonzalez-Hernandez J, Mendoza-Galvan A.Thin Solid Films 2005;471:243.

[29] Mizutani U. Introduction to the electron theory of metals. CambridgeUniversity Press; 2001 [Chapter 15].

[30] Trambly de Laissardiere G, Nguyen-Manh D, Mayou D. Prog Mater Sci 2005;50:679.

[31] Rossiter PL. The electrical resistivity of metals and alloys. CambridgeUniversity Press; 2003. p. 164.

T. Car et al. / Vacuum 98 (2013) 75e8080