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A model for hillock growth in Al thin films controlled by plastic deformation

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A model for hillock growth in Al thin films controlled by plastic deformation
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  A model for hillock growth in Al thin films controlledby plastic deformation Soo-Jung Hwang  a , William D. Nix  b , Young-Chang Joo  a,b,* a Department of Materials Science and Engineering, Seoul National University, Seoul 151-744, Republic of Korea b Department of Materials Science and Engineering, Stanford University, Stanford, CA, USA Received 17 April 2007; received in revised form 30 May 2007; accepted 31 May 2007Available online 20 July 2007 Abstract The dependence of total hillock volume (per unit area) on film thickness and annealing temperature has been studied in pure alumi-num films. The total hillock volume (per unit area) increases linearly with both the film thickness and annealing temperature. Other char-acteristics involve a critical temperature and a critical thickness for hillock formation. It is shown that these phenomena can be explainedby assuming that hillock growth is controlled by plastic deformation in the surrounding film. A simple analytical model is developed toaccount for these observations.   2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords:  Aluminum; Plastic deformation; Creep; Hillock; Thin films 1. Introduction During integrated circuit fabrication processing, inter-connect metals are subjected to a number of thermal cycles.The differences in the thermal expansion coefficientsbetween the various materials in these devices give rise tolarge thermal stresses, which may result in hillock or whis-ker formation when the stresses are compressive. Hillockscan cause reliability problems, such as dielectric cracksand interconnection shorts. To obtain highly reliabledevices, it is important to understand the mechanisms of hillock formation.In metal films, various mechanisms, including interfacialdiffusion [1], surface diffusion [2] and grain-boundary diffu- sion [3,4], have been proposed as the controlling processfor hillock growth. Chaudhari proposed that hillockgrowth is a form of stress relaxation in which atomic spe-cies diffuse along the film–substrate interface to the baseof the hillock and that the hillock, in turn, extrudes outof the plane of the film [1]. A different view was given byChang et al. [2], who suggested that hillock growth is a sur-face diffusion controlled process, based on the observationthat during annealing large hillocks became larger whilesmaller hillocks decreased in size and eventually disap-peared, thereby increasing the hillock size and decreasingthe hillock density. Iwamura et al. [3] suggested that theatoms diffuse from the film into the hillock, which gives riseto lateral diffusion along the grain boundaries that lie in theplane of the film and around the hillock. They consideredthat the driving force for lateral diffusion is a gradient of stress, which is established by stress relaxation near the hill-ock. Ericson et al. [4] observed that hillocks are formed attriple junctions using cross-sectional transmission electronmicroscopy (TEM) and also suggested that grain-boundarydiffusion is the controlling mechanism of hillock growth.Until now, most studies of the controlling mechanism of hillock growth have focused on diffusion. However, evenif the hillock grows locally by diffusive processes, the in-plane displacements that drive the hillock growth can stillbe controlled by plastic deformation in the surroundingfilm. 1359-6454/$30.00    2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.doi:10.1016/j.actamat.2007.05.046 * Corresponding author. Address: Department of Materials Science andEngineering, Seoul National University, Seoul 151-744, Republic of Korea. Tel.: +82 2 880 8986; fax: +82 2 883 8197. E-mail address:  ycjoo@snu.ac.kr (Y.-C. Joo). www.elsevier.com/locate/actamat Acta Materialia 55 (2007) 5297–5301  In an effort to identify the dominant mechanism of hill-ock growth, Al films of various thicknesses have been pre-pared and studied. The hillock volume (per unit area) wasmeasured quantitatively for different film thicknesses andannealing temperatures. From these results, a model forhillock formation controlled by plastic deformation wasdeveloped. 2. Experiments Pure Al films of different thickness (250, 400 and600 nm) were deposited by sputtering onto a Mo barrier(50 nm)/glass substrate (700  l m). The Al sputtering pro-cess was performed at a sputter power of 16 kW and anAr pressure of 0.42 Pa without breaking the vacuum. Thebase pressure prior to deposition was lower than 10  6 Torr.All of the Al films were annealed in an annealing chamber(<10  3 Torr) for 400 min at 180, 200, 220, 250 and 280   Cwith a heating rate of 5   C min  1 (five different samples foreach of three thicknesses).The samples were observed using a field emission scan-ning electron microscope (FE-SEM; JEOL JSM 6330F)before and after annealing. The hillocks in the SEM imageswere marked on transparency papers that were scanned todigitize and transform them to a binary form. Then theindividual hillock areas were analyzed by means of animage analysis program (Scion Corp.). In each of the sam-ples, four different locations, with dimensions 30  ·  40  l m,were examined. The diameters of the hillocks ( D i ) were cal-culated from the measured individual hillock areas ( A i ),assuming that the hillocks are circular in shape  D i  ¼ 4  A i p   1 = 2   . The total hillock volume in a unit area of the film ( V  hillock ) was calculated by adding the individualhillock volume in a measured film area ( A film ) assumingthat the hillocks are hemispherical in shape.The stress change in the 600 nm thick Al film was mea-sured by means of a wafer curvature system using a two-dimensional laser array deflected from the sample (k-SpaceAssociates, Multi-beam Optical System) during heatingfrom room temperature to 200   C and during isothermalannealing for 400 min at 200   C. The biaxial stresses inthe films were derived from the measured curvature usingStoney’s formula. 3. Results The total hillock volume in a unit area of film,  V  hillock ,was calculated for all Al samples annealed at various tem-peratures and plotted against annealing temperature(Fig. 1a) and film thickness (Fig. 1b). Fig. 1a shows that the  V  hillock  increases linearly with annealing temperaturefor all film thicknesses. The slope of   V  hillock  vs.  T   increaseswith increasing film thickness. To further investigate thesedependencies, we made use of a linear fit. The fittingparameters, such as the slopes and  x -axis intercepts, aresummarized in Table 1a. The  x -axis intercept indicates thatthere is a critical temperature,  T  cr , needed for hillockgrowth [4,5]. Another characteristic of  Fig. 1a is that the critical temperature increases as the film thicknessdecreases.Fig. 1b shows that  V  hillock  increases linearly with the filmthickness at temperatures between 180 and 280   C. Fromthe linear fit, the slopes and  x -axis intercepts were obtainedand are summarized in Table 1b. The  x -axis intercepts of Fig. 1b indicate that there is a critical thickness,  h cr , neededfor hillock growth. The critical thicknesses increase withdecreasing annealing temperature. A similar relationship 50100150200250300012345678  600 nm 400 nm 250 nm    H   i   l   l  o  c   k  v  o   l  u  m  e   /  a  r  e  a ,      V      h     i     l     l    o    c     k    [  n  m   ]  Annealing temperature, T   [ o C] 0100200300400500600012345678 Film thickness, h [nm]    H   i   l   l  o  c   k  v  o   l  u  m  e   /  a  r  e  a ,      V      h     i     l     l    o    c     k    [  n  m   ]  280 o C 250 o C 220 o C 200 o C 180 o C Fig. 1. The total hillock volume in a unit area of film assuming the hillockis a hemisphere (scatter) distributed as a function of (a) the annealingtemperature and (b) the film thickness. Their linear fit is plotted with asolid line.Table 1Summary of (a) slopes of   V  hillock  vs.  T   and critical temperatures,  T  cr  and(b) slopes of   V  hillock  vs.  h  and critical thicknesses,  h cr (a)Film thickness (nm) 250 400 600Slope (nm   C  1 ) 0.016 0.024 0.036 T  cr  (  C) 158 90 82(b)Annealing temperature (  C) 180 200 220 250 280Slope 0.008 0.012 0.010 0.014 0.013 h cr  (nm) 155 189 135 128 895298  S.-J. Hwang et al. / Acta Materialia 55 (2007) 5297–5301  between the film thickness and critical temperature wasreported by Ericson et al. [4]. They found that, as the filmthickness increases from 0.25 to 2.2  l m, the critical temper-ature decreases from 150 to 90   C.Fig. 2 shows the variation of biaxial stress in the 600 nmAl film as a function of temperature between 20 and200   C. Note that the  y -axis is the change in stress, notthe absolute stress. With increasing temperature to120   C, the biaxial stress decreases and becomes more com-pressive because of a thermal expansion mismatch and thenremains nearly constant with further increasing tempera-ture. During isothermal annealing at 200   C, the stressdecreases by relaxing the compressive stress by approxi-mately 75 MPa. 4. Discussion and model development The total hillock volume increases linearly as the filmthickness increases from 250 to 600 nm and as the anneal-ing temperature increases from 180 to 280   C. Further-more, there is a critical temperature and critical filmthickness for hillock growth. These results can be under-stood using a model based on stress relaxation, assumingthat hillock formation is the only plastic deformationmechanism to play a role in the relaxation of the compres-sive stresses and also that the hillocks are fully grown dur-ing the lengthy annealing time at the highest temperature[5]. We describe a model for the dependence of hillock vol-ume (per unit area) on film thickness and annealing tem-perature, which also accounts for the film thicknessdependence of the critical temperature and the temperaturedependence of the critical thickness. Hillocking is taken tobe the relaxation mechanism for the compressive stresses inthe metal film. Thus, if the small change in films thicknessdue to the stress is neglected, the amount of stress relaxeddue to the hillock formation ( D r relax ) can be expressed asfollows: D r relax  ¼  M  V     hillock 2 hA film ;  ð 1 Þ where  h  is the film thickness,  M   is the biaxial elastic mod-ulus, and  V     hillock  is the hillock volume on a surface area of  A film  [6,7]. This result is valid for both diffusive and plastichillock growth.We can rewrite this equation as a hillock volume (perunit area),  V  hillock , as follows: V    hillock  ¼  2 h M   D r relax :  ð 2 Þ We note that  D r relax  is positive for positive hillock growth;that is, compressive stresses in the film are relieved by hill-ock growth and become more tensile.We consider now complete relaxation of the stress in thefilm by hillock growth. Chaudhari [1] suggested that if hill-ock growth is the only mechanism for relaxing the compres-sive stresss then  D r relax  for complete relaxation would be: D r relax  ¼  M  D a ð T     T  0 Þ ;  ð 3 Þ where  T   is the annealing temperature,  T  0  is the temperatureat which the stress changes from tension to compression. If we put Eq. (3) into (2),  V  hillock  can be expressed as: V    hillock  ¼  2 h D a ð T     T  0 Þ :  ð 4 Þ From Eq. (4), we can explain the linear dependence of  V  hillock  on the film thickness and annealing temperature.However, this cannot explain the existence of critical thick-ness,  h cr , for hillock formation or the dependence of thecritical thickness on the annealing temperature. Further-more, the critical temperature  T  cr  should be the same as T  0 , the temperature at which the stress changes from ten-sion to compression.In order to explain the dependence of the critical thick-ness on the annealing temperature and critical temperatureon the film thickness, we assume that hillock growth is con-trolled by plastic deformation of the surrounding film.According to this picture hillock growth occurs only if plastic flow occurs in the surrounding film; having a netcompressive stress in the film is an insufficient conditionfor plastic flow and hillock growth. In this case,  D r relax would be expressed as follows: D r relax  ¼  M  D a ð T     T  yield Þ þ D r iso ;  ð 5 Þ where  T  yield  is the temperature at which the compressiveyielding is initiated and  D r iso  is the additional stress relax-ation during the isothermal annealing at high temperature(Fig. 2).Because the compressive yield stress can be expressed asthe thermal stress that develops from  T  0  to  T  yield  and theyield stress is thickness dependent [8,9], we may assumethat the  T  yield  of the Al film is thickness dependent, asfollows: T  yield    T  0  ¼  Ah  ;  ð 6 Þ where  A  is a proportionality constant. 020406080100120140160180200220-350-300-250-200-150-100-50050100  600 nm Al films    C   h  a  n  g  e   i  n  s   t  r  e  s  s   [   M   P  a   ] Temperature [ o C] T  yield  T  o Fig. 2. Change in stress during thermal cycling and isothermal annealingwas measured by the wafer curvature method in 600 nm Al films. Thecalculated  T  0  is shown by the dotted line. The solid line shows thethermoelastic phase, during which thermal strain is accommodatedpredominantly by elastic strain. S.-J. Hwang et al. / Acta Materialia 55 (2007) 5297–5301  5299  If we put Eqs. (5) and (6) into (2) and define  B   as  B ¼ T  0   r iso  M  D a , then  V  hillock  can be expressed as follows: V    hillock  ¼ 2 D a hT    2 D a  A  2 D a hB :  ð 7 Þ Now we may obtain the slopes and  x -axis intercepts of  V  hillock  vs.  T   and  V  hillock  vs.  h , respectively, by arrangingEq. (7) to reveal the temperature ( T  ) dependence and filmthickness ( h ) dependence. Those parameters are summa-rized in Table 2. From Table 2, we can expect the slopes of   V  hillock  vs.  T   and  V  hillock  vs.  h  to increase linearly withthe film thickness and the annealing temperature, respec-tively, and  T  cr  and  h cr  to be inversely proportional to thethickness and the annealing temperature, respectively.In order to determine if this model for hillock growthmatches the experimental results, the slopes and  x -axisintercepts obtained experimentally can be compared withthe model predictions. First, the slopes of   V  hillock  vs.  T  and  V  hillock  vs.  h  were plotted against film thickness(Fig. 3a) and annealing temperature (Fig. 3b), respectively. The slopes of the lines in Fig. 3a and b should be 2 D a according to the model. The expected difference of thermalexpansion coefficient, D a , can then be calculated from thesehillocking data; we find 29 and 24 ppm   C  1 , respectively.These values of   D a  are somewhat larger than the knownvalue of   D a , 20 ppm   C  1 ( a Al  = 23.8 ppm   C  1 ,  a glass  =3.8 ppm   C  1 ). One possible explanation for this differenceis that there is a discrepancy between the calculated and theactual hillock volumes, because of the assumption that thehillocks have a hemispherical shape [5,10]. If the hillockshape is not hemispherical, but has a spherical cap with acontact angle between the film and the hillock under 90  ,the value of total hillock volume will decrease. Then the D a  values measured from slopes of   V  hillock  vs.  T   and  V  hillock vs.  h  will also decrease. In this case, if the hillocks have acontact angle of 78  , the measured value  D a  from the slopeof   V  hillock  vs.  T   will fit well with the known difference inthermal expansion coefficients.From Table 2, the  x -axis intercept  T  cr  of   V  hillock  vs.  T  should be inversely proportional to the film thickness.From a plot of ln  T  cr  vs. ln  h , we obtained  A  =34,000 nm   C  1 and  B   = 17   C. Using these values of   A and  B  , the critical temperature can be predicted as a func-tion of film thickness. Fig. 4a shows the measured values of critical temperature (square) along with the expected valuesbased on the present analysis (line). Likewise,  h cr  should beinversely proportional to the temperature. From reciprocalfitting, we obtained  A  = 25,000 nm   C  1 and  B   = 25   C.Fig. 4b shows the measured values of   h cr  (square) alongwith the expected values (line). Fig. 4a and b may havesome practical importance because we can describe thedependence of critical thickness on annealing temperatureand the dependence of critical temperature on film thick-ness, respectively. When the film is thin, a high critical tem-perature,  T  cr , is needed for hillock growth, but when thefilm is thick,  T  cr  decreases. Likewise, when the annealingtemperature is high, even thin flms can exhibit hillocking,but when the annealing temperature is low, only thick filmscan be expected to hillock.Using the values of   A  and  B   obtained from the hillock-ing experiments, we can calculate  T  0  and  T  yield . From  B ¼  T  0   r iso  M  D a   ,  T  0  can be determined using the expectedvalue of   r iso / M  D a  = 38   C; this is found by taking  r iso  tobe 75 MPa (measured from Fig. 2),  M   to be 100 GPa,and  D a  to be 20 ppm   C  1 . Then  T  0  is about 55 and63   C when  B   is 17 and 25   C, respectively. The calculatedvalue of   T  0  is shown to be around 60   C in Fig 2. From thecalculated value of   T  0 ,  T  yield  can be calculated using Eq.(6). When  T  0  is 55 or 63   C,  T  yield  is calculated as 112 or107   C, respectively. Fig. 2 also shows that a yield temper-ature, in this case about 120   C, is needed to initiate plasticflow in the film. Therefore, the calculated value of   T  yield matches with experimental result well.It should be noted that, while the present model assumesthat hillock growth is controlled by compressive plastic orcreep flow in the surrounding film, local diffusive processes Table 2Summary of slopes and  x -axis intercepts of   V  hillock  vs.  T   and  V  hillock  vs.  h from Eq. (7)Slope  x -axis interceptTemperature dependence ( V  hillock  vs.  T  ) 2 D a h  Ah þ  B Thickness dependence ( V  hillock  vs.  h ) 2 D a ( T   B  )  AT    B Here,  B ¼ T  o   r iso  M  D a . 200 400 6000.010.020.030.04    S   l  o  p  e  o   f    V    h   i   l   l  o  c   k   v  s   T    [  n  m   /   o    C   ] Film thickness [nm] 2 ∆α 160 180 200 220 240 260 280 3000.0060.0080.0100.0120.0140.016    S   l  o  p  e  o   f    V    h   i   l   l  o  c   k   v  s   h  Annealing temperature [ o C] 2 ∆α Fig. 3. (a) Slope of   V  hillock  vs.  T   distributed as a function of film thickness(scatter) and its linear fit (line). (b) Slope of   V  hillock  vs.  h  distributed as afunction of annealing temperature (scatter) and its linear fit (line).5300  S.-J. Hwang et al. / Acta Materialia 55 (2007) 5297–5301  are still needed at the hillock to accommodate those plasticor creep displacements. We consider the rate-limiting pro-cess to involve plastic or creep displacements in the sur-rounding film, even if diffusion occurs locally. Acomparison of purely diffusion-controlled hillock growthwith hillock growth controlled by power-law creep in thesurrounding film is currently being made [11]. 5. Summary Aluminum films of thickness 250–600 nm were annealedin the temperature range 180–280   C. After annealing, thetotal hillock volume was measured quantitatively usingan image analysis program. The total hillock volume in aunit area of film was found to be linearly proportional bothto the film thickness and the annealing temperature. A crit-ical thickness and critical temperature were observed belowwhich no hillocks were formed; the critical thickness andcritical temperature decrease with annealing temperatureand film thickness, respectively. A simple analytical modelfor hillocking was proposed based on plastic deformationof the surrounding film. The model can explain theobserved linear dependences of hillock volume (per unitarea) on annealing temperature and film thickness as wellas the existence of a critical temperature and critical thick-ness for hillock formation. Acknowledgements This work was supported by the Ministry of Educationand Human Resources Development (MOE), the Ministryof Commerce, Industry and Energy (MOCIE) and theMinistry of Labor (MOLAB) through the fostering pro- ject of the Lab of Excellency. Y.-C. Joo acknowledges a2005 LG Yonam Foundation Fellowship for the partialsupport of his stay at Stanford University. The supportof one of the authors (WDN) by a Grant from the USDepartment of Energy (DE-FG02-04-ER46163) is grate-fully acknowledged. References [1] Chaudhari P. J Appl Phys 1974;45:4339.[2] Chang CY, Vook RW. J Mater Res 1989;4:1172.[3] Iwamura E, Ohnishi T, Yoshikawa K. Thin Solid Films 1995;270:450.[4] Ericson F, Kristensen N, Schweitz J-A˚. J Vac Sci Technol B1991;9:58.[5] Hwang S-J, Lee J-H, Jeong C-O, Joo Y-C. Scripta Mater 2007;56:17.[6] Kim D-K, Heiland B, Nix WD, Arzt E, Deal MD, Plummer JD. ThinSolid Films 2000;371:278.[7] Kim D-K, Ph.D. Dissertation, Stanford University, CA, USA; 2001.[8] Nix WD. Met Trans A 1989;20 A:2217.[9] Thompson CV. J Mater Res 1993;8:237.[10] Hwang S-J, Lee Y-D, Park Y-B, Lee J-H, Jeong C-O, Joo Y-C.Scripta Mater 2006;54:1841.[11] Berla L, Joo Y-C, Nix WD, Unpublished research, StanfordUniversity. 200 400 600 800 1000 1200 1400050100150200250300350400      C    r     i     t     i    c    a     l     t    e    m    p    e    r    a     t    u    r    e ,       T     c    r      [     o  C     ] Film thickness[nm]measured valueour modelNo hillockHillock 100 200 300 400 050100150200250300350  measured valueour model      C    r     i     t     i    c    a     l     t     h     i    c     k    n    e    s    s ,       h     c    r      [    n    m     ]  Annealing temperature[ o C]No hillockhillock Fig. 4. (a) The measured value of critical temperature (square) due to filmthickness and its expected value (line). (b) The measured value of criticalthickness (square) due to annealing temperature and its expected value(line). S.-J. Hwang et al. / Acta Materialia 55 (2007) 5297–5301  5301
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