Ti multilayers studied by electrical conductance measurements

Ti multilayers studied by electrical conductance measurements

~) Splid State Communications, Vol. 80, No. 9, pp. 663-667, 1991. Printed in Great Britain. 0038-1098/9153.00+.00 Pergamon Press plc AMORPHIZATION ...

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Splid State Communications, Vol. 80, No. 9, pp. 663-667, 1991. Printed in Great Britain.

0038-1098/9153.00+.00 Pergamon Press plc

AMORPHIZATION OF Ni/Ti MULTILAYERS STUDIED BY ELECTRICAL CONDUCTANCE MEASUREMENTS M.BOUHKI, A.BRUSON, P.GUILMIN Laboratoire de physique du solide. ( U.A. au CNRS 155 ) Universit~ de Nancy1 BP 239 54506 Vandoeuvre les Nancy Cedex Received 15july 1991 by P. Burlet ABSTRACT: Ni/Ti multilayers with composition-modulation wavelengths ranging from 35 to 103 A were annealed at 458 K during approximately 30 h and studied by electrical resistivity measurements and transmission electron microscopy (TEM). The diminution of the electrical conductance during the solid state reaction can be explained by the formation of an amorphous phase at every Ni/Ti interface. The variation of the conductance follows a shifted t 1/2 law for long times. We deduced values of interdiffusion coefficients which are in good agreement with those measured by other methods. A linear time law for short times is expected for an interface limited reaction.

INTRODUCTION: During the last years it was shown [1,2] that amorphization occurs when certain combinations of multilayers are annealed at moderate temperatures. The formation of such metastable amorphous phases is preferred over the stable crystalline state if the combination of the multilayers has a large negative heat of mixing which acts as a driving force for the reaction and if one of the elements of the multilayer shows an anomalously fast mobility. Generally the amorphous phase forms as a planar interlayer between the elemental layers [3] showing a diffusion controlled growth for longer reaction times [4,5]. For short reaction times, deviations from a t 1/2 law is already noticed [6]. Ni/Ti multilayers system shows a large negative enthalpy of mixing [7] and an anomalously fast mobility of Ni in a-Ti has been reported [8]. The occurrence of amorphization in Ni/Ti has been observed earlier [1]. In this paper we study the early stages of the solid state reaction in Ni/Ti modulated samples by electrical conductance measurements, using the four points probe method which is a sensitive indication for the kinetics of the reaction.

Amorphization is followed by T.E.M observations, and interdiffusion constants are provided. EXPERIMENTS: Multilayers of polycrystalline Ni and Ti with composition modulation wavelengths A equal to 35.5, 70 and 103 A were evaporated in an ultra-high vacuum system and condensed onto substrates kept at liquid nitrogen temperature. The evaporation rate of each element being held constant was controlled by two independent quartz monitoring systems. An alternating shutter pneumatically operated was driven by a computer in order to obtain the desired wavelengths. For each composition modulation wavelength two kinds of samples were prepared: (i) Electron microscopy samples were deposited onto copper grids previously coated with amorphous carbon. (ii) Resistance samples were deposited onto thin glass slides with terminal preevaporated gold electrodes. Typical parameters of the Ni/Ti samples studied are reported in table 1. The number of bilayers was choosen in order to have approximately the same total thickness for




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Table1 : Typical parameters of Ni/Ti multilayered samples. Column (A): Number of bilayers for electrical conductance measurements. Column (B): Number of bilayers for T . E M experiments. A=dNi+dTi (~) dNi(~)























all the multilayers and the relative thicknesses of each component were taken in order to have a composition close to

Ni5oTi5o. The samples were annealed at 458 + 5 K during 27h in a vacuum furnace under a pressure less than 10 -6 Torr. During the heating up and cooling down phases the values of the resistivity were collected in order to determine the temperature coefficient of resistance (T.C.R) before and after amorphization.

RESULTS AND DISCUSSION: Typical diffraction patterns are shown in Fig 1. Respectively F i g l a is obtained for the unreacted Ni/Ti multilayer ( A = 7 0 ] k ) (a) ~


I . ~ 11!

ll\OO T,

amo pha~


Fig1: Typical electron diffraction patterns of a multilayered Ni/Ti sample with a modulation composition wavelength A = 7 0 ~ a) structural observation of the as prepared sample. Both Ni and Ti are crystalline . b) After an isothermal annealing at T=458K during 27 hours the amorphous phase has been formed.

where sharp rings denote the crystallinity of the components Ni and Ti; figlb is for the same sample after one isothermal run. It is an evidence that an amorphous phase has appeared but some sharp rings from unreacted metals are still present indicating an incomplete reaction. For the three multilayers studied by T . E . M in no case was complete amorphization observed; in all the specimens some amorphous phase formed and then the reaction apparently stopped. The values of the T.C.R (o~=I/R AR/z~T) obtained before and after the isothermal annealing are collected in table 2 for the different samples. The negative values of the T.C.R measured after isothermal annealing and the increasing of the resistivity [9] are also an evidence of the formation of an amorphous phase. To monitor the thickness of the growing amorphous phase we measured the electrical conductance of the multilayers during the isothermal treatment. The layer growth model [10] predicts that for diffusion limited growth, the t h i c k n e s s of the growing layers will evolve as the square root of time. In fig 2 we have plotted (versus t 1/2) the electrical conductance G(t) of the multilayer divided by G(0) its electrical conductance measured at the beginning t=0 of the isothermal run. G(t)/G(0) decreases strongly during the isothermal annealing. That is a consequence of a structural modification. For all the samples the curves present three stages (arrow on the curves). The part number two indicates agreement with the expected time

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1,d2 o~, 0,98


0,94 QQ









de(o ,



~ riB(t) .'Z////.//////./.. ~".~(')"




t l / 2 ( S 1/2 )

Fig 2: Normalized electrical conductance of Ni/Ti multilayers versus square root of time for three different modulation composition wavelengths ( + A=35.5, • 70, [] 103 .~,) at 458K. growth process. Deviation of the kinetics from the parabolic time law can be noted at short times (part 1) and larger times (part 3). For short reaction times the plot of G(t)/G(0) versus t (fig 3) shows that kinetics follows a linear time law, due to an interface limited growth. The deviation at longer times might be caused [5,11] by a release of mechanical stresses, that affects the average concentration. To explain the time dependence of the electrical conductance we can use the simple model which was applied by Schr6der and S a m w e r [12] for a Zr/Co bilayer. For the case of a stack of N bilayers (fig 4) we explain here the basic ideas. Due to the planar geometry the conductance G(t) of the multilayer is given by the sum of the conductances of the simple layers. G(t) = N[ GTi(t ) +GNi(t) ] +(2N -1) Gam(t )

tFina I ---) dam(tFinal) = A/2

where Garn(t) is the conductance of the amorphous phase growing at the interface Ni/Ti, with the initial condition Gain(t--0)=0. We can write: G(t) = N[oTidTi(t) +ONidNi(t)] +(2N-1)Gam(t) G(t=0) N[oTidTi(0 ) +ONidNi(0)] where c i is the conductivity of the specie i and di(0 ) its initial thickness at time t=o (i=Ti, Ni) If x is the average volume fraction of Ti in the growing amorphous phase according to dTi(t)= dTi(0) - 2Xdam(t ) dNi(t)= dNi(0) - 2(1-X)dam(t ) we get: G(t) =1 - 2dam(t)[x°Ti+(l"X)°Ni] + 2N-1 Garn(t) G(0) oTidTi(0)+ONidNi(0) N G(0) If we assume that the average concentration of a bilayer is equal to the mean concentration of the growing amorphous phase

1,002 vO

Fig 4: Shematic diagram showing p a r t of multilayers. Hatched zones are for amorphous phase at time t. Boundaries conditions: t=0 -~ dam(0 ) = 0,

0,999 0,996

X=dTi(0)/A , we can write

O 0,993 0,990 - 1000 t(s)


Fig 3: Normalized electrical conductance of Ni/Ti multilayets versus t at the beginning of the reaction (same symbols as fig2).


G(t) = 1-2dam(t) + 2 N - 1 Gain(t) G(0) 4. N G(0) with the approximation G(0)= A where < C o > is the mean conductivity of the multilayer having a composition modulation



wavelength A, and with N large we obtain

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1 0 .23


i +A

G(t) = 1 -2dam(t) (1 - ~am(t)) G(0) A (00) '~ E

When the thicknesses of the cristalline layers are larger than the thickness of the growing amorphous phase Gam(t)/<~0 > can be neglected due to the low conductivity ~am(t) of the amorphous phase compared to the conductivities of the crystalline layers. It follows G (t)/G (0)= 1 - 2d a rn(t)/A which is similar to that derived by Schr6der. In order to understand the deviation at short times from a parabolic time law, Deal and Grove [13] have proposed a model which was achieved by the introduction of reaction barriers at the interfaces. According to this model SchrSder and Samwer have shown that the thickness of the growing phase dam(t ) is related to the reaction time by d2am(t) + Adam(t ) - Bt = 0 With A=2D (1/c~ +1/~) and B = 2D where o: and [3 are interface parameters and D the diffusion constant. Solving this equation we obtain :


1 02 4

/ 1 0 "2~








Fig 5: Values of the diffusion coefficient D versus modulation wavelength: A. this work, ~1, Ref [14], • Ref [15], + Ref [16]. Table 2: Electrical resistivities and T.C.R of multilayered Ni/Ti samples. Po : Resistivity at room temperature before annealing. p* : Resistivity at room temperature after 27 h isothermal annealing at T=458 K. T.C.R 1" Deduced from the heating up to 458 K. T.C.R $ Deduced from cooling down to room temperature. ** Only after 75 h annealing was observed T.C.R negative.

dam(t) = ~[-1 + (1 A+~2 )1/21 wich gives the amorphous thickness as a function of time. Two limiting forms of this equation can be examined: i) At short times 4Bt/A 2 << 1 leads to dam(t ) = (B/A)t + ... ii)For larger times 4Bt/A 2 >> 1 gives dam(t ) - (Bt) 1/2 - A/2 This means than one expects a linear time law for the growth of the amorphous layer at short times and a shifted parabolic time law for long reaction time. In the case of a parabolic time law for the growth of the amorphous phase (dam(t)= (2Dt) 1/2) a plot of G(t)/G(0) versus t 1/2 should give straight lines. Fig 2 shows that this behaviour is followed (stage 2 of the curves) for t>0.4 h. From the slope one can deduce the coefficient D for the interdiffusion at T = 458 K. These values are reported in fig 5 for each sample studied together with the values determined by glancing angles X Ray diffraction [14,15],

Sample wavelength





Po (p.~cm)




p* (pO.c m)




T.C.R $(10-4 K)




T.C.R $(104K)




and small angles neutron diffraction [16]. Deviation that occurs in stage 3 of the curves are explained by different authors [5,17] by the release of mechanichal stresses which are important to change the reaction rate. This change of the diffusion constant was also seen in the X Ray analysis of Unruh [18]. In summary measurements of the electrical conductance can be used to follow the kinetics of solid state reactions. We have seen that for long times the amorphous

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phase grows according to a shifted t 1/2 law and that for short times the thickness of the growing phase evolves nearly linear with time. This indicate that the beginning of the reaction is controlled by an interfacial process as already shown by Deal and Grove[13]. The values of the diffusion constant measured are in good agreement with those measured by other techniques. Acknowledgements: The authors would like to thank G. Marchal for the samples preparation and M.Gerl for suggestions and discussions. REFERENCES:

[1] B.M.Clemens, Phys.Rev.B. 33, 7615 (1986) [2] R.B.Schwarz and W.L.Johnson, Phys.Rev.Lett. 51, 415 (1983) [3] H.SchrSder, K.Samwer, U.K0ster. Phys. Rev. Lett 54, 197, (1985) [4] M.van Rossum, M.A.Nicolet, and W.L.Johnson, Phys.Rev.B 29 5498 (1984). [5] K.Samwer, H.SchrOder, and M.Moske, Mater.Res.Soc.Proc. 57 405 (1987)


[6] H.SchrSder and K.Samwer, Z.Phys.Chem, 157, 265 (1988) [7] A.R.Miedema, Philips Tech.Rev.36, 217 (1979) [8] G.MHood and R.J.Schulz, Philos.Mag. 26, 329 (1972) [9] K.H.J.Buschow,J.Phys.F 13, 583 (1983) [10] B.M.Clemens, W.L.Jonhson, R.B.Schwarz, J. Non. Cryst. solids. 61 and 62, 817, (1984) [11] H.U.Krebs, K. Samwer. Europhys. Lett. 2, 141 (1986) [12] H.SchrSder and K.Samwer, JMater.Res.3, 461 (1988) [13] B.E. Deal, A.S.Grove J. Appl. Phys. 36, 12, 3770 (1963) [14] M.Bouhki, A.Bruson, P.Guilmin accepted for publication in Solid. State Com. (1991) [15] Hitoshi Kondo, Tadashi Mizoguchi, MRS Int'l. Mtg. on Adv. Mats. Mater. Res. Soc. 10, 445, (1989) [16] C. Janet, B. George. A. Bruson, Europhys. Lett, 12, 143 (1990) [17] H. Schr0der. K. Samwer Zei. phys. Chem. 157, 265 (1988) [18] K.M.Unruh, W.J.Meng, W.L.Johnson, A.P.Thakoor, S.K.Khanna .Mater. Res. Soc. Symp. Prec. 37, 551 (1985)