Size-independent stresses in Al thin ?lms thermally
strained down to à100°C
E.Eiper a ,J.Keckes
a,b
,K.J.Martinschitz a ,I.Zizak c ,M.Cabie
′a,d
,G.Dehm
a,b,*
a
Erich Schmid Institut fu ¨r Materialwissenschaft,O
¨sterreichische Akademie der Wissenschaften,Leoben,Austria b
Department fu ¨r Materialphysik,Montanuniversita ¨t Leoben,Austria
c
Hahn-Meitner-Institut fu ¨r Struktur-und Festko ¨rperforschung,Berlin,Germany
d
CEMES-CNRS,Toulouse,France
Received 7September 2006;received in revised form 25October 2006;accepted 26October 2006
Available online 16January 2007
Abstract
Size and temperature dependencies of thermal strains of {111}textured Al thin ?lms were determined by in situ X-ray di?raction (XRD)in the temperature range of à100to 350°C.The experiments were performed on 50–2000nm thick Al ?lms sputter-deposited on oxidized silicon (100)substrates.The in-plane stresses were assessed by measuring the {331}lattice plane spacing at each temperature in steps of 25°C during thermal cycling.At high temperatures,the ?lms could only sustain small compressive stresses.The obtained stress–temperature evolutions show the well-known increase of ?ow stresses with decreasing ?lm thickness for ?lms thicker than 400nm.However,for thinner ?lms,the measured stress on cooling is independent of the ?lm thickness.This lack of size e?ect is caused by the ?ow stresses in the thinnest ?lms exceeding the maximum stress that can be applied to these samples using thermomechanical loading down to à100°C.Thus,the measured stresses of $770MPa in the thinnest ?lm represent a lower limit for the actual ?ow stres-ses.The observed stresses are also discussed taking microstructural information and possible constraints on dislocation processes into account.
ó2006Acta Materialia Inc.Published by Elsevier Ltd.All rights reserved.
Keywords:X-ray di?raction;Thin ?lm;Flow stress;Low temperature;Stress plateau
1.Introduction
Thermally induced mechanical stresses in small-scale structures,such as thin ?lms on sti?substrates,quite often exhibit values of several hundred MPa after processing or during service [1].Such high stresses can induce defects in the thin ?lm structures that may ?nally cause failure of the metal ?lms or components in microelectronic devices.Therefore,a detailed understanding of thin ?lm stress evo-lution is necessary,including the e?ects of dimensional con-straints and microstructural information,in addition to the
non-elastic behavior and mechanical size e?ects of poly-crystalline thin ?lms which are not yet fully understood.Recent studies on stress evolutions of thin metal ?lms reveal a strong dependency of the ?ow stresses on the ?lm thickness and/or grain size [2].In general,the ?ow stress increases with decreasing ?lm thickness and/or grain size.This phenomenon was explained by Nix and Freund [3–5]as a con-sequence of geometrical constraints on dislocations in thin ?lms.Dislocations channeling through the ?lm are forced to deposit interfacial dislocation segments at the ?lm/substrate interface.Recently,studies on Al and Cu ?lms have experi-mentally veri?ed aspects of the Nix–Freund model [6].
However,for polycrystalline ?lms the observed stresses signi?cantly exceed the predictions of the Nix–Freund model.Alternative models assume that dislocation nucle-ation is causing the observed size e?ect [7].The sizes of
1359-6454/$30.00ó2006Acta Materialia Inc.Published by Elsevier Ltd.All rights reserved.doi:10.1016/j.actamat.2006.10.052
*
Corresponding author.Tel.:+433842804112.
E-mail address:gerhard.dehm@notes.unileoben.ac.at (G.Dehm).
https://www.doczj.com/doc/6d11384342.html,
Acta Materialia 55(2007)
1941–1946
dislocation sources are believed to shrink with a reduction in grain size and?lm thickness.Furthermore,back-stresses arising from previously emitted dislocations piling-up at interfaces may hinder dislocation sources from emitting additional dislocations.Dislocation plasticity and di?u-sional processes are superimposed during thermal straining of thin metal?lms.In Ag and Cu?lms a di?usive exchange of matter between the grain boundaries and the free surface was predicted by Gao et al.[8]and experimentally observed by Kobrinsky and Thompson[9]and Weiss et al.[10].In contrast to free standing?lms,the di?usional stress relaxa-tion can be constrained by a substrate interface and will only partly relax the stresses in thin?lms,as demonstrated by simulating stress temperature curves using Gibbs’model [10,11]in comparison to the prediction of Gao et al.[8,10].
For thermally loaded Ag,a decrease in?ow stress was observed for?lm thicknesses below400nm[9,12]and for Cu a stress plateau at?lm thicknesses below400nm [13,14].This,at?rst glance surprising observation was assigned to constrained di?usional creep as the prevalent stress relaxation mechanism for ultra-thin?lms[14].
However,stress plateaus were recently also observed for passivated thermally loaded Cu[15]and Al?lms[16].Nev-ertheless,it is still unclear which mechanism is responsible for a stress plateau at room temperature in passivated poly-crystalline layers after thermal cycling.Such stress plateaux are not reported in the literature for tensile-tested metallic ?lms,indicating that it may arise in thermally strained?lms due to the limitation in applied strain.In that respect it is necessary to verify the experimental data and extend them to higher strains by applying lower temperatures.In this work,the temperature dependency of the stress plateau e?ect is studied for polycrystalline Al?lms on Si substrates, which were partly investigated earlier by substrate curva-ture measurements[16].In the present approach the stress measurements were also performed down toà100°C using in situ X-ray di?raction(XRD).In addition,the experi-ments were extended to?lm thicknesses down to50nm. The in?uence of?lm microstructure on experimentally obtained?ow stress is discussed.
2.Experimental
Thin Al?lms with{111}?bre texture and thickness ranging from50to2000nm(see Table1)were deposited on oxidized Si substrates by magnetron sputtering and characterized using in situ XRD techniques.The growth procedure is reported in[6]and brie?y summarized in this section.The Si wafers were(100)oriented,300l m thick, 50mm in diameter and possessed a50nm thick amorphous SiO x(a-SiO x)layer.Prior to the deposition,the substrates were cleaned by200eV Ar-ion etching for$3min.The deposition was performed at room temperature using a 99.9%pure Al target.The sputter deposition chamber pos-sessed a base pressure of$2·10à7Pa.The deposition was performed at a power of200W,which corresponds to a growth rate of30nm minà1.Directly after deposition, the specimens were annealed at450°C for15min without breaking the vacuum.Most of the?lms were thermally cycled in a substrate curvature system as described in Ref.[6].
For the current XRD measurements,the specimens were cut into pieces of$10·5mm2.XRD texture measure-ments were performed prior to the in situ XRD thermal cycling experiments.The Al?lms reveal a$15°broad?bre texture with the?111?Al direction perpendicular to the sample surface.Structural properties of the samples such as grain size and?lm thicknesses(Table1)were character-ized using scanning electron microscopy(SEM;Zeiss Ste-reoscan440),electron backscatter di?raction(EBSD), focused ion beam(FIB;Leo1540XB)microscopy and transmission electron microscopy(TEM;Philips CM-12). Most grains were columnar even though the median grain size measured from plan-view images was in several cases smaller than the?lm thickness(Table1).Stress relaxations due to hillock formation were identi?ed and studied by ex situ optical microscopy and SEM observations of the sam-ple surfaces.The thermal strains(stresses)were measured during cyclic thermal loading betweenà100and350°C in25°C intervals at the KMC-2beamline of the synchro-tron facility BESSY(Berlin,Germany).KMC-2is equipped with a double crystal silicon monochromator and a focusing mirror which provides106photons sà1 and the beam-wavelength was set to copper K a.The mea-surement setup featured a Huber6-circle goniometer,an area-sensitive multiwire proportional detector(Bruker AXS)and a combined cooling-heating stage(DCS350, Anton Paar Inc.[17]).During thermal cycling,the sample chamber was purged with N2to prevent oxidation of the Al?lms at elevated temperatures.
Table1
Stresses r11,T(MPa)of the textured Al?lms with thickness h(nm),measured during cooling from350°C down toà100°C at speci?c temperatures T(°C)
h r11,à100°C[MPa]r11,à75°C[MPa]r11,à50°C[MPa]r11,à25°C[MPa]r11,0°C[MPa]d[l m]r11,350°C[MPa]
2000166142155187192 1.00±0.2à43 10003253443232992730.56±0.07à62 6005044684704374160.54±0.07à67 4006986646195755170.43±0.08à91 2007507106465815260.32±0.09à125 1007707326796005500.14±0.1à50 507867436816395600.2±0.1à20
The error of the stress values is$10%d represents the grain size for each?lm thickness obtained from FIB images using the line intercept method(2000–400nm)and TEM-images using an area?tting method(200–50nm).For comparison,the stress values at350°C are also shown.
1942 E.Eiper et al./Acta Materialia55(2007)1941–1946
Films were subjected to heating and cooling at12.5°C minà1,with a dwell time of2min at the set-point temper-ature to allow a homogeneous temperature distribution prior to recording the sin2w data.Each sin2w measurement took$6min,thus enabling samples to be heated or cooled by25°C every10min.
The strains of the Al?lms were determined using the sin2w method[18,19].The lattice spacing d hkl;T of the {331}Al re?ections was measured at di?erent sample tilt angles w.Since the?lms had a broad{111}?ber texture, several azimuthal positions of the{331}crystallographic planes could be used.For?lms exceeding200nm thick-ness,four di?erent tilting angles were used to measure the strain and three tilting angles could be used for thinner ?lms.The measurements were performed starting at room temperature,heating up to350°C,cooling down to à100°C and heating back to room temperature in steps of25°C.From the temperature-dependent lattice spacing d hkl;T,the isotropic in-plane stress r11;T was calculated as described in Refs.[20–24].Referring to the sin2w method, the peak positions of the di?racting pro?les were plotted as a function of the tilting angle w and from linear regres-sions of the?t the stresses were calculated using tempera-ture-and texture-dependent elastic constants of Al.The
stress free lattice spacing d0
hkl;T was determined from inter-
sections of the linear regressions in the sin2w dependencies obtained from the heating and cooling cycles for every spe-ci?c temperature T according to the procedure described by Kraft et al.[25].Furthermore,the temperature-depen-dent biaxial modulus of Al,M111;T,was used to relate the stresses to measured strains according to[26]:
M111;T?6áec11;Tt2c12;TTác44;T
c11;Tt2c12;Tt4c44;T
;e1T
where c ij;T are the temperature-dependent single crystalline elastic constants of Al taken from Ref.[27].An error of up to10%may be expected in results due to instrument mis-alignment,thermal shift,di?raction pro?le?tting and regression techniques for the calculation of stresses.How-ever,this10%represents an upper limit.
Prior to the XRD measurements all samples were annealed at400°C for15min to compensate stress relax-ations during the long sample storage time.To verify if reasonable values were observed,the sin2w-deduced stress–temperature curves were compared with substrate curvature measurements performed several years earlier on the same sample[6].The stresses obtained from a laser-assisted substrate curvature method applied in[6] were determined from the radius of curvature for the ?lm/substrate system measured in10°C intervals between 40and400°C using Stoney’s equation[28]and a biaxial modulus M100?180:5GPa for the Si(100)substrate.
3.Results
Fig.1shows a typical stress–temperature dependence curve for a600nm thick Al?lm.It compares the stress–temperature data obtained with the sin2w method and an earlier measurement of the same sample performed with
a substrate-curvature system as reported by Dehm et al.
[16].The comparison shows good agreement between the stress–temperature curves,with a maximum deviation of 40MPa.The stress values measured at room temperature at the end of the cycles are equal within the accuracies of both techniques,with values of340?34MPa for the XRD and360±36MPa for the substrate–curvature mea-surements.The nearly coinciding stress–temperature hys-teresis indicates that no degradation of the samples occurred during sample storage.
Subsequently,all Al?lms were thermally strained in the temperature rangeà100to350°C and the stress values determined from the sin2w data.Fig.2shows the stress–temperature curves for three di?erent?lm thicknesses. Additionally,calculated stress values assuming fully elastic behaviorer11;T?D a TáD TáM111;TTare indicated in Fig.2. For the calculation,the temperature-dependent linear expansion coe?cients a film;T and a sub;T[26,27]were used. Comparing the stress–temperature curve of the50nm thick ?lm with the calculated curve assuming fully elastic behav-ior shows that the slopes agree at temperatures below 150°C.At temperatures above150°C,the slope of the experimental curve decreases,indicating inelastic deforma-tion by di?usion and/or dislocation plasticity.However, the hysteresis between the heating and cooling cycle is small.
Upon heating from room temperature,most?lm thick-nesses deformed elastically up to175°Ce$0:5áT melt?K T.
E.Eiper et al./Acta Materialia55(2007)1941–19461943
The1000and2000nm thick?lms exhibited plastic deformation at temperatures of100°Ce$0:4áT melt?K T. Thicker?lms(exceeding600nm)deformed under compres-sion at typicallyà50MPa,while thinner?lms commenced yielding under tension at$200MPa.While Bauschinger e?ects or kinematical work hardening are frequently reported for thin?lms in the literature[29,30],a clear inter-pretation is prevented due to the coupling of strain and temperature change.Instead,isothermal stress–strain mea-surements as proposed by Xiang and Vlassak would be required to study?lm thickness in?uences on the Bauschin-ger e?ect[31,32].
Furthermore,the area of the stress temperature hystere-sis increased with increasing?lm thickness,while the stress values at the end of the cycle decreased(6200nm,Table1). This behavior is related to an increasing amount of plastic-ity for thicker?lms,while plasticity becomes increasingly suppressed with decreasing?lm thickness.A calculation of the experimentally observed elastic strain e el in the?lms
byerà100 Càr350 CTáMà1
111indicates an increase from
$0.2%for the2000nm specimen to$0.8%for the 200nm and$0.7%for the50nm.
In agreement,the experimentally obtained plastic strains e pl in the?lms,calculated from the width of the hysteresis D T with e pl?D Táa film,decreased from$0.5%for the 2000nm thick?lm to$0.2%for the50nm?lm at an applied thermal strain of1%.The widths D T were deter-mined by the distance between the elastic slopes upon heat-ing and cooling at the temperature whereupon heating plasticity starts.The predominant elastic response of the ?lms with thicknesses less than400nm can be seen in Fig.2for the50nm thick?lm,especially upon cooling below$175°C.Due to the lower stress values for thicker ?lms,the accuracy in determining the width of the hyster-esis decreases,leading to an underestimation of the plastic strain values.The stresses measured on cooling below 25°C are summarized in Fig.3as a function of?lm thick-ness.For?lms thicker than400nm it should be noted that with decreasing?lm thickness the thermal stresses increased signi?cantly(Figs.2and3;Table1),as found in several earlier studies,such as Ref.[5].This size e?ect can be observed down to a critical?lm thickness of about h c=400nm.When the?lm thickness decreases to values less than400nm,the stresses became independent of the ?lm thickness.However,the stress values increased with decreasing temperature.The?ow stresses of the individual Al?lms are summarized for temperatures below25°C in Fig.3.The grey dashed line at1019MPa represents the cal-culated thermo-elastic limit atà100°C.The comparison is given for the maximum experimentally determined stress values that occur atà100°C for?lm thickness smaller than 400nm with values between698and786MPa.
In contrast to the stress plateau upon cooling,a di?erent behavior is observed at elevated temperatures.With respect to the?lm thickness,the observed stress values at350°C show lower compressive stresses,and no clear size e?ect can be attributed due to the accuracy of the experimental data points,which would suggest for?lms thicker than 200nm a compressive stresses increase proportional to hàx(x P1)and for?lms thinner than200nm a decrease proportional to h+x(x P1)(see Table1).
It is also noteworthy that optical microscopy and SEM studies of the?lm surface revealed a fully dense metal layer only for?lm thicknesses over200nm.Thinner?lms are also continuous,but reveal,for example in the case of
1944 E.Eiper et al./Acta Materialia55(2007)1941–1946
the 50nm thick ?lm,several areas of $20l m in diameter which consist of Al islands (Fig.4(a)).The Al surface cov-erage amounts to 73%for the nominally 50nm thick ?lm and 97%for the 100nm thick ?lm.
Hillock formation was observed for ?lm thicknesses exceeding 200nm,with an increase in hillock density with increasing ?lm thickness.4.Discussion
The in situ XRD experiments con?rmed the strong depen-dency of plastic ?ow stresses on ?lm thickness (Fig.3)above a critical thickness,h c =400nm even for temperatures down to à100°C.In agreement with other studies [5,16,33],the ?ow stress increase follows a h x relationship,as suggested by Nix [1],with values of x between à0.6and à0.9.These values change only slightly with the minimum temperature of the cycle and thus it is believed the slopes indicate disloca-tion plasticity as the main reason for the observed size e?ect,in accordance with earlier studies [5,16,33].
For ?lms with thicknesses of less than $400nm,the increase of thermal stress with decreasing ?lm thickness disappears,leading to a stress plateau (Table 1,Fig.3).This stress plateau is believed to be a result of the limited applied strain which is not su?cient to induce plastic defor-mation in the thinnest ?lms and thus provides a lower limit for the ?ow stress.This interpretation is supported by the increase of stress upon cooling from 0to à100°C (Table 1).The observed stress increase of D r =64MPa for a D T of 25°C for the 50nm thick ?lm ?ts the calculated thermo-elastic stress increase of D r (D T =25°C)=66MPa.A stress plateau occurs since,below 150°C e$0:45áT melt ;Al ?K T,the stress–temperature evolution for Al ?lms thinner than 400nm is purely elastic.Although the thinnest ?lms (50nm,100nm)do not fully cover the substrate,it is not believed that this caused the stress plateau or in?u-enced the stresses (strains)deduced from the sin 2w mea-surements.In contrast to wafer-curvature measurements,XRD directly measures the lattice strains in the ?lms.The large coverage of 73%for the 50nm thick ?lm still results in a continuously connected ?lm which is thermally strained.This is veri?ed by the agreement between the
thermo-elastic slope of the 50nm thick ?lm upon cooling down to à100°C with that predicted theoretically (see Fig.2).
The shear stresses s 111on the slip planes,calculated via Schmid’s law with s 111?r flow ácos u ácos k ,exceed 200MPa without inducing noticeable dislocation plastic-ity.Here,u and k are the angles between the {111}Al ?lm normal and the {111}glide plane normal and the Burgers vector,respectively.
The predominant elastic response of ?lms thinner than 400nm is con?rmed by post-mortem TEM studies.While 600nm thick ?lms reveal dislocations [16],very few dislo-cations are observed in ?lms thinner than 400nm.One of the few exceptions is shown in Fig.5for a 50nm thick Al ?lm.In a grain 1200·500nm 2and a grain 350·250nm 2,periodic arrays of dislocations on inclined {111}planes are visible (Fig.5).This is one of the rare occasions where dislocations were detected.This suggests that the usual dislocation multiplication is prevented by the small dimensions.No other defects such as stacking faults or twins were
observed.
Fig.4.SEM images of (a)50nm and (b)200nm thick Al ?lms.(c)Optical micrograph of a 2000nm thick Al ?lm.Hillocks can be observed in (b)and (c),while the 50nm thick ?lm appears to be devoid of hillocks.Some areas of the 50nm thick ?lm are not fully Al coated (see black regions in
(a)).
Fig.5.Dislocation contrast in a 50nm thick Al ?lm was only observed very rarely.Some regular dislocation patterns are indicated in the plan view TEM image by arrows.
E.Eiper et al./Acta Materialia 55(2007)1941–19461945
In contrast to low temperatures,plastic deformation occurs at temperatures over150°Ce$0:45áT melt;Al?K Tfor all?lm thicknesses(Fig.2).Di?usional processes and/ or dislocation glide partly relax the stresses between150 and350°Ce0:45–0:6áT melt;Al?K T(see stress hysteresis in Fig.2).Normally,for thinner?lms di?usional distances become shorter and due to smaller grain sizes(Table1)the distances between grain boundaries are also reduced,making grain boundary di?usional creep processes more likely.
However,the surface oxide prevents mechanisms such as constrained di?usional creep[8,10,14,34].It is well known that hillocks form in Al thin?lms to relax compres-sive stresses[5,33].This was observed in our studies down to?lm thicknesses of200nm(Fig.4).For thinner?lms (50nm,100nm),the SEM images provide no indication of hillocks.This may be caused by a transition in deforma-tion mechanism,e.g.,from hillock formation to surface roughening or some limited thermally activated dislocation processes.Also,short-range di?usional processes as reported by Chaudhari[35]may act as a stress relaxation mechanism and cause the0.2%plasticity in the50nm thick Al by interface and lattice di?usion at high temperatures. The exact mechanisms that act at elevated temperatures are not clear and further investigations are needed on Al ?lms which are only tens of nanometers thick.
5.Summary and conclusion
The novel approach of this work can be summarized as follows.
1.A stress plateau was observed for?lms thinner than
400nm upon cooling to room temperature and below.
The stress-plateau is a consequence of the limited ther-mal strain which can be applied to thin?lms by thermal straining.
2.With decreasing?lm thickness,the stress–temperature
dependencies of Al?lms tended to a linear elastic behav-ior.Up to0.8%elastic strain was induced in the?lms by thermal straining.This resulted in thermal stresses of 786MPa for a50nm thick Al?lm atà100°C.
3.The compressive stresses at350°C remained similar for
all?lm thicknesses.Hillocks relaxed compressive stres-ses for?lms that are200nm and thicker.For thinner ?lms,surface roughening may have occurred in prefer-ence to hillocking.
4.All?lms were continuous;however,the50and100nm
thick?lms only covered the substrate by73%and 97%,respectively.Nevertheless,this should not have in?uenced the present XRD measurements(as outlined in the Discussion).
Acknowledgements
This work was partly supported by the Country of Styria within the project‘‘Multimethodenanalytik Nanoteilchen und Nanoteilchenverbunden’’and by the Austrian NANO Initiative via a grant from the Austrian Science Fund FWF within the project‘‘Stress Design–Development of Funda-mentals for Residual Stress Design in Coated Surfaces’’.
The synchrotron experiments at BESSY were supported by the European Community–Research Infrastructure Action under the6th Framework Program‘‘Structuring the European Research Area’’(through the Integrated Infrastructure Initiative‘‘Integrating Activity on Synchro-tron and Free Electron Laser Science’’–Contract R II3-CT-2004-506008).Growth of the Al?lms at the Max-Plank-Institute for Metals Research(Stuttgart)is gratefully acknowledged.
JK is grateful to Anton Paar GmbH for providing the heating–cooling stage DCS350.
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