Investigation of mass transfer surface self-di?usion
on palladium
I.Beszeda
a,*
,E.G.Gontier-Moya b ,D.L.Beke
a
a
Department of Solid State Physics,University of Debrecen,Egyetem ter 1,H4032Debrecen,Hungary
b
L2MP,UMR 6137,Marseille,France
Received 2July 2003;accepted for publication 16October 2003
Abstract
Growth of voids in thin palladium layers (8–20nm)on alumina and silica substrates has been investigated by Auger electron spectroscopy and atomic force https://www.doczj.com/doc/1b9385230.html,ing the Brandon–Bradshaw ?s model,based on capillarity forces,the surface self-di?usion coe?cients of palladium have been evaluated in the temperature range of 583–823K.We have found that the results are independent of the substrate,in agreement with the assumption that the growth of voids is controlled by surface self-di?usion on the metal.The mass transfer surface self-di?usion coe?cients are expressed by D s em 2=s T?1:1?10à7exp ?à97?13ekJ =mol T=RT .These new results are compared with literature data.The experi-mental and theoretical values for intrinsic di?usion coe?cients on oriented surfaces disclose much lower activation energies than that found in the present work,and the di?erences are related to the formation energy of the defects responsible for surface di?usion.
ó2003Elsevier B.V.All rights reserved.
Keywords:Auger electron spectroscopy;Atomic force microscopy;Surface di?usion;Surface energy;Palladium;Aluminum oxide;Metallic ?lms
1.Introduction
The long term stability of thin ?lms is hampered by the formation of hillocks and holes,induced by interface capillarity and stress driving forces [1].In some cases,which are for example noble metals deposited on oxide sensors to improve their se-lectivity and their sensitivity,the dewetting phe-nomena is used to agglomerate the ?lm into particles [2,3].The morphological evolution of such ?lms is governed mainly by surface di?usion.
In a previous work [4],using Auger electron spectroscopy (AES)and atomic force microscopy (AFM),we investigated the evolution of gold ?lms,of about 10–20nm thickness,deposited on sapphire surfaces.At temperatures above 573K the ?lm was unstable:voids appeared after a very short time (almost immediately),and the fraction of uncovered sapphire area increased as a function of time.Finally,the metal agglomerated into particles or ?beads ?.The conditions required for the observation of this process have been discussed in [5].Di?erent kinetics models of void growth have been examined in [6].We found that the Brandon–Bradshaw model [7]can be used to relate the growth of a void to the surface self-di?usion
*
Corresponding author.Tel./fax:+36-52-316-073.
E-mail address:beszedai@dragon.klte.hu (I.Beszeda).
0039-6028/$-see front matter ó2003Elsevier B.V.All rights reserved.
doi:10.1016/j.susc.2003.10.019
Surface Science 547(2003)
229–238
https://www.doczj.com/doc/1b9385230.html,/locate/susc
coe?cient of the https://www.doczj.com/doc/1b9385230.html,ing this procedure,gold surface self-di?usion coe?cients have been evalu-ated at several temperatures,and the results pre-sented in[4]were found in quite reasonable agreement with other published data.
In the present paper,we report similar mea-surements carried out on palladium?lms depos-ited on sapphire and amorphous silica.Palladium is often used on oxide substrates as an activator or a catalyst.However,we do not?nd,in the litera-ture,any data about mass transfer surface di?usion on this metal.Mass transfer,which takes into ac-count the number of mobile defects,di?ers from intrinsic surface di?usion[8–10].In the latter case, the literature provides experimental and theoreti-cal data for di?usion of single adatoms on oriented palladium surfaces(for example in[11]and refer-ences therein).In addition to the determination of mass transfer surface di?usion parameters,we study the evolution of thin palladium?lms,taking advantage of the high Auger peak of this metal to check two fundamental points of the Brandon–Bradshaw model[7]:(i)the radius of a hole de-pends on the?lm thickness at the power)3/5and (ii)the substrate does not in?uence the growth kinetics of the voids.For this purpose,di?erent ?lm thicknesses and two kinds of substrates,sap-phire and amorphous silica,have been used.
2.Theoretical background
In the Brandon–Bradshaw model[7],it is as-sumed that the kinetics of a hole growth is con-trolled by surface self-di?usion on the metal,as illustrated in Fig.1.The hole area,A?p r2,varies with time as[12]:
A5=4?5p7=4mx2c D s
3=2
t;e1T
where h is the thickness of the?lm,D s is the sur-face mass transfer self-di?usion coe?cient of the metal,m and x are the surface density and atomic volume of metal atoms,respectively,c is the sur-face energy of the metal,k the Boltzman constant and T the temperature.
Using AES technique,we can follow the in-tensity changes of Auger electron emission from both the substrate(here Al2O3or SiO2)and the deposited metal.Assuming that the oxygen inten-sity coming from the substrate,I OxetT,is propor-tional to the uncovered surface(i.e.the area of the holes),one can write:
I OxetT?cn p r2;
where n is the number of holes under the electron beam,and c is a proportionality constant.
After heating the sample in conditions where a complete evaporation of the deposit is achieved, the?nal oxygen intensity is:
I OxefT?cS;
where S is the area of the exposed surface under the electron beam.The proportionality constant c holds if the conditions of analysis are unchanged. Hence,the ratio of I OxetTover I OxefTgives:
I OxetT
I OxefT
?
n
S
p r2?N s p r2?N s A;e2T
where N s is the surface density of holes(i.e.num-ber of holes per unit area).This value can be evaluated using a microscopic technique,such as AFM.
Upon inserting A,derived from(2),into(1),the time dependence of the oxygen Auger-intensity takes the form
I OxetT
I OxefT
5=4
?
5
2
p7=4
mx2c
kT
N5=4
s
h3=2
D s t?mt;e3T
where m denotes the slope of the normalized in-tensity at the power5/4vs.time.From this slope, D s can be expressed as:
D s?
2mh3=2kT
5N5=4
s
p7=4mx2c
:e4T
At the very beginning of the process,I Oxe0Tshould be equal to zero for su?ciently thick?lms.
At Fig.1.Model of a growing void in a metallic?lm.h is the?lm thickness,r is the radius of the void.The atoms move on the surface in the direction indicated by the arrow.
230I.Beszeda et al./Surface Science547(2003)229–238
t >0the oxygen signal is low,because of the small fraction of uncovered substrate.Hence,the elec-tronic noise induces large ?uctuations of this sig-nal.
A better accuracy is obtained when the deposit signal (here of Pd),which is higher than the oxygen one,can be counted.In this case,we have to in-troduce I Pd in the left hand side of Eq.(3).At t ?0,the surface is completely covered by the metal,and the initial palladium intensity is pro-portional to the area under the electron beam:I Pd e0T?c 0S ;
where c 0is the new proportionality constant.
Later,at t >0the palladium signal is propor-tional to the surface covered by the metal:I Pd et T?c 0eS àn p r 2T:Similarly to Eq.(2),we get:I Pd et TPd ?1àn p r 2?1àI Ox et T
Ox ;e5T
and (3)can be rewritten in the form:1 àI Pd et TI Pd e0T 5=4?
I Ox et TI Ox ef T
5=4
?52p 7=4mx 2c kT N 5=4
s h 3=2
D s t ?mt :e6T3.Experimental
Two di?erent oxide substrates were used,
namely sapphire and silica.The sapphire plates,provided by the Kyocera company,were cleaned successively with detergent and pure water and ?nally ultrasonically rinced in alcohol.The sam-ples of amporphous silica,of about 300l m thickness,grown on silicon,were cleaned in hot tetrachlorine–ethylene,then rinced in alcohol and in pure water.
The Auger spectroscope was equipped to carry out in-situ deposition of metal ?lms and sub-sequent annealings of the samples.A small plate of oxide sample was ?xed on a Ta-wire heating ele-ment,which was mounted on the manipulator in the UHV chamber.A thin Pd layer was deposited at room temperature by evaporation from a
Knudsen cell.The thickness of the deposit,in the range of 8–20nm,was evaluated by calibration of the evaporation rate with a quartz balance.The sample was then rotated in front of the electron gun.We were sure that the deposit was continuous when the oxygen peak,characteristic of uncovered oxide substrate,had completely disappeared (see Fig.2).
The Auger peak heights (in derivate mode)of palladium and oxygen were monitored and stored by a computerized Auger system at ?xed time in-tervals.The duration of a cycle was constant and its value was determined carefully.In this way,the record of the intensities I Pd et Tand I Ox et Tas a function of the number of cycles could easily be transformed into a kinetics curve.After some cy-cles,used to obtain stable signals,the current of the heating element was switched on.The tem-perature of the sample was measured by a ther-mocouple pressed on the surface.After an initial period,the Pd signal begun to decrease and the oxygen signal to increase.When they reached a plateau,we assumed that the dewetting process was achieved.The deposit was then completely evaporated (see Fig.3)at a higher temperature (about 1113–1153K),and the ?nal oxygen signal intensity,I Ox ef T,of the clean substrate surface was measured.
During these experiments,the residual pressure in the chamber was about 3–6·10à9mbar.
A slight electric charging of the samples,that caused a few eV shift of the Auger peaks to
lower
Fig.2.Auger spectrum of a surface completely covered by Pd (the oxygen signal has completely disappeared).
I.Beszeda et al./Surface Science 547(2003)229–238231
energies,was observed,but there was no change in the Auger intensities.
4.Results and discussion 4.1.Density of holes
According to Eq.(4),it is necessary to know the surface density of holes at the beginning of the dewetting of the metal ?lm.This determination was made by AFM.For this purpose,some sam-ples were taken out of the apparatus after short annealings.The images obtained on di?erent parts
of the surface proved that the density of holes is practically constant.For example,Fig.4shows the aspect of an 8nm thick Pd ?lm on sapphire after an annealing of 10min at 773K.We count 270holes on an area of 15·15l m 2,which yields N s ?1:2?1012holes/m 2.On silica,we count 80holes on an area of 4·4l m 2,which gives N s ?5?1012holes/m 2.When using Eq.(4),we assume that N s is constant for the di?erent samples prepared with the same substrate and the same deposit thickness and that this value is practically independent of time.This assumption is based on the observation that the induction time is negli-gible in the conditions of our experiments.Al-though,the holes in Fig.4have irregular shapes,we use the circular-hole approximation which should be valid during the initial dewetting stage.Circular shaped holes can form at longer times during the measurements.A continuous observa-tion of the ?lm morphology during the dewetting process would yield more accurate results,but this could not be achieved with the present equipment.4.2.Analysis of substrate and deposit signals
Typical curves of palladium and oxygen inten-sities as a function of time are plotted in Fig.5(on sapphire substrate at 723K).
The useful part of these curves corresponds to the increasing oxygen signal and to the
simulta-
Fig.3.Auger spectrum after removal of the deposit above 1113
K.
Fig.4.AFM image of a 8nm thick Pd layer on sapphire after a short annealing at 773K for 10min.Dark areas correspond to the holes.
232I.Beszeda et al./Surface Science 547(2003)229–238
neously decreasing palladium one.According to Eq.(6),the normalized Auger intensities at the power 5/4are plotted as a function of time.Ex-amples for Pd on alumina at 773K can be seen in Fig.6a,where the two curves,derived from I Ox et Tand I Pd et T,are plotted.The slopes of these curves are slightly di?erent.As mentioned in Section 2,the higher peaks of palladium,compared to that of oxygen,make the accuracy of the palladium curve better than that of oxygen.Therefore,in the fol-lowing,the Pd signal is used in the calculations.In the same way,Fig.6b illustrates a curve
?I Ox et T=I Ox ef T 5=4
vs.time derived from the Pd sig-nal on amorphous silica at 583K.
The data points in Fig.6a and b can be ?tted by a linear curve,which con?rms both the validity of the model and the previous assumption that N s is independent of time.
By using the values m ?1:66?1019m à2,x ?1:47?10à29m 3,c ?2J/m 2[13],and the ex-perimental values of h ,N s and m ,one can calculate the D s coe?cients from Eq.(6).The results,ob-tained with di?erent conditions analysed below,are reported in Table 1and Fig.7.4.3.In?uence of the deposit thickness
In the Brandon–Bradshaw model [7],the radius of a hole depends on 1=h 3=5,where h is the initial ?lm thickness.Consequently,the hole area varies with 1=h 6=5?1=h 1:2.Roughly,at a given time,the
Auger signal of the substrate should be inversely proportional to the initial thickness.
We have prepared four sapphire samples coated with palladium ?lms of di?erent thicknesses:10;13.7;16.8and 20nm.These samples were annealed at the same temperature (773K).Fig.8presents the time dependence of Pd-intensities measured on the above samples.Clearly,the slope of the curve obtained with a ?lm of 20nm is lower than those corresponding to thinner ?lms,in accordance with the expected trend.However,with the 10;13.7;16.8nm thick ?lms,there is no systematic order of the lines in relation with the thickness.We suppose that this discrepancy arises from two parameters which could be insu?ciently controlled:(i)the evaporation rate from the Knudsen cell and (ii)the structure of the ?lms,i.e.the initial densities of holes (or triple junctions of grain
boundaries),
Fig.5.Oxygen and palladium Auger intensities vs.time at 773K on sapphire.n and r are Pd and oxygen signals at room temperature,m and }are Pd and oxygen signals at 773
K.
Fig.6.Normalized Auger intensities ?I Ox et T=I Ox ef T 5=4vs.time curves.(a)Calculated from I Ox (}symbols)and I Pd (with Eq.(6))(m symbols)on sapphire at 773K and (b)calculated from I Pd on silica at 583K.
I.Beszeda et al./Surface Science 547(2003)229–238233
which was assumed to be identical for the di?erent samples.In spite of these uncertainties,the four D s values (collected also in Table 2)lie within the same order of magnitude,which can be considered as the error limit of the method.This allows us to conclude that the Brandon–Bradshaw model [7],extended to an ensemble of holes,is suitable to describe our experiments.4.4.In?uence of the substrate
Fig.7shows that palladium surface di?usion coe?cients calculated from experiments on alu-mina and silica substrates ?t the same Arrhenius straight line.So,provided that the initial void density,N s (Eq.(6)),is measured on each sub-strate,the results are independent of the nature of the substrate.This is in agreement with the con-dition,implied in the Brandon–Bradshaw model,that the growth of an isolated void is controlled by surface self-di?usion on the metal surface.4.5.In?uence of the temperature
The dewetting experiments were carried out in the range 673–823K for sapphire substrate and 583–743K for silica substrate.Previous experi-ments on sapphire have shown that the evapora-tion rate of the metal is quite negligible at these temperatures.
Taking into account all the experimental points plotted in Fig.7,the Pd surface self-di?usion co-e?cient are expressed by:
D s e583–823K T?1:1?10à7
?exp
àe97?13TkJ =mol RT m 2
s
:e7T
Table 1
Pd surface self-di?usion coe?cients on sapphire and silica
On sapphire On silica T (K)D s (m 2/s)T (K)D s (m 2/s)6738.27·10à16583 2.69·10à16673 1.27·10à15623 3.19·10à16693 1.23·10à14643 5.29·10à15723 1.29·10à14743 1.33·10à14723 1.87·10à14743
1.29·10à14
773 1.50·10à14773 4.08·10à14773 1.19·10à147739.38·10à14798 4.73·10à14823
7.05·10à14
Fig.7.Arrhenius plot of Pd surface self-di?usion coe?cients
measured on alumina (r )and on silica (}).
Fig.8.Dependence of Pd Auger intensities on the initial layer thickness:10nm (}),13.7nm (j ),16.8nm (N )and 20nm (
).
Table 2
Pd surface self-di?usion coe?cients at 773K,on alumina,for di?erent ?lm thicknesses h (nm)D s (m 2/s)10 1.50·10à1413.7 4.08·10à1416.8 1.19·10à1420
9.38·10à14
234I.Beszeda et al./Surface Science 547(2003)229–238
4.6.Uncertainties in the determinations
Fig.7shows the error bars on D s determina-tions,estimated from the errors on the density of holes(±25–33%),the temperature measurements (±10K),the initial thicknesses(±1.5–3nm)and the slopes of the straight lines?1àI PdetT=I Pde0T 5=4 vs.time.The uncertainty on Q s,±13kJ/mol,is calculated by applying the least squares line?tting method to the ensemble of experimental data.It should be noticed that the Arrhenius line?ts well the experimental points within the error limits. https://www.doczj.com/doc/1b9385230.html,parison with other data
The above results?ll the lack of experimental surface di?usion data of palladium.In Table3,we report literature data about volume di?usion of palladium,and surface and volume di?usion of platinum,metal which belongs to the same chem-ical group as palladium.These data are taken from Ref.[14].In addition,we indicate the mass transfer surface self-di?usion coe?cients estimated from Gjostein?s correlation,quoted in Ref.[15]:
T>0:75T m;
D sem2sà1T?7:4?10à2expeà15T m=TT;while
T<0:75T m;
D sem2sà1T?1:4?10à5expeà7T m=TT;
where T m is the melting temperature.Since our experiments have been carried out in the low temperature range,we use only the relation for T<0:75T m.The corresponding Arrhenius curves are plotted in Fig.9.
Table3and Fig.9show that the published volume di?usion coe?cients of palladium and platinum are very close.Consequently,it is not surprising to measure surface di?usion data of
Table3
Comparison of literature data
Palladium(T m?1827K)Platinum(T m?2043K)
D°(m2sà1)Q v,Q s(kJ/mol)Reference D°(m2sà1)Q(kJ/mol)Reference Volume di?usion 2.05·10à5266[14]5·10à6258[14] Surface di?usion 1.1·10à797This work4·10à7108[14] Surface di?usion on(110)surface
[001]direction 4.0309[21]
[1 10] 2.9·10à4164
Surface di?usion,Gjostein correlation,
low temperature regime
1.4·10à5106[15] 1.4·10à5119[15]
Intrinsic surface di?usion on oriented
palladium surfaces
D°(m2sà1)Q m(kJ/mol)Reference
Pd(111) 1.6·10à814Simulation[11]
9.1·10à812Simulation[16]
9·10à434Experiment[18]
Pd(100) 1.1·10à758Simulation[11]
68Simulation[19]
%58Experiment[20]
Theoretical evaluation of formation and
migration energies of surface defects[17]
Q f(kJ/mol)Q m(kJ/mol)Q s(kJ/mol)
Adatoms,Pd(111)792.499.4
Adatoms,Pd(100)5461115
Vacancies,Pd(111)7568143
I.Beszeda et al./Surface Science547(2003)229–238235
palladium close to those found in the literature for platinum.
The surface di?usion coe?cients of platinum and palladium are one to two orders of magnitude lower than those given by the corresponding Gjostein ?s correlation.However,it should be no-ticed that the experimental activation energies di?er only of about 10kJ/mol from those indicated by this correlation.
4.8.Relation with intrinsic surface di?usion The intrinsic surface self-di?usion coe?cient,D si ,characterises the jump of one atom between two neighboring equilibrium sites,whereas the mass transfer surface self-di?usion coe?cient,D s ,takes into account the number of di?using species.For example,assuming that surface di?usion takes place by an adatom mechanism,one can write:D s ?D si ?n ad =N o ;where n ad =N o is the relative adatom concentration (the number of adatoms over that of adsorption sites).This ratio being much lower than 1,D s should be lower than D si .The temperature de-pendence of n ad =N o is related to the formation energy of the defect Q f .Consequently,for mass transfer di?usion,Q s includes Q f as well as the adatom migration energy Q m ,i.e.Q s ?Q f tQ m .Several theoretical and experimental determi-nations [11,14–19]describe the intrinsic surface di?usion of Pd adatoms on oriented surfaces (Table 3).We can assume that the (111)surface,which presents the lowest energy,is mostly in-volved in the morphological evolution of thin ?lms.On this surface Q m is very low (Q m ?7,12or 14kJ/mol from theoretical calculations in [11,16,17],re-spectively,and 34kJ/mol from experiment [18])and consequently the intrinsic di?usion coe?cient on this face is several orders of magnitude higher than the mass transfer di?usion coe?cient.The adatom formation energy,given by Q f ?Q s àQ
m
Fig.9.Arrhenius lines for palladium and platinum bulk and surface di?usion,and Gjostein ?s correlation applied to surface di?usion on these metals in the low temperature regime.
236I.Beszeda et al./Surface Science 547(2003)229–238
would be equal to90,85,83or63kJ/mol de-pending on the value attributed to Q m.The expo-nential term deduced from these values is around 10à6–10à4at773K.This implies that the surface concentration of adatoms is low,in agreement with what is generally expected for high density surfaces.
We consider also the results of theoretical cal-culations of activation energies for surface di?u-sion by an adatom or a vacancy[17].According to these values,reported in Table3for the(111) surface,the adatom mechanism is the most fa-vorable.We note that the theoretical activation energy(Q s?Q ftQ m?99:4kJ/mol)is in good agreement with our experimental value(Q s?97 kJ/mol),whereas the vacancy mechanism would lead to a higher activation energy(143kJ/mol).In the temperature range where our experiments have been carried out,the adatom mechanism appears as the most likely.
Experiments based on the evolution of surface morphologies can be considered as averaging several orientations.After(111)surfaces,we should consider(100)facets,which are charac-terised by higher values of Q m,(Q m?58,61,68or 58kJ/mol,as reported in Table3from[11,17,19] and[20])but lower values of Q f.According to[17], adatom di?usion mechanism on palladium(100) surface is described by the activation energy Q s?Q ftQ m?54t61?115kJ/mol.This value is also relatively close to our result Q s?97kJ/mol.
In the case of(110)surfaces,an additional complication arises from the atomic structure which results in a directional anisotropy.Experi-ments relating mass transfer surface di?usion on platinum(110)[21]show that the activation en-ergy is higher along[001]direction than along [1 10]direction(see Table3).However,given that the surface free energy of(110)orientation is higher than that of(111)and(100),we assume that the spontaneous evolution of thin?lms in-volves mainly the two surfaces of lowest energies.
5.Conclusions
AES and AFM techniques have been used to follow the growth of voids in thin palladium?lms (8–20nm)deposited by evaporation on sapphire and amorphous silica substrates.In the tempera-ture range583–823K,the kinetics of growth of voids in metallic?lms,interpreted by the Brandon–Bradshaw model,allows to evaluate the surface self-di?usion of Pd.Investigations of the e?ects of the thickness of the deposit(in the range10–20 nm),and of the nature of the substrate,con?rm the validity of the model.The Pd surface self-di?usion coe?cients,expressed by D se583–823KT?1:1?10à7expeà97?13ekJ=molT=RTTm2/s,are very close to those of platinum.The experimental and theoretical values for intrinsic di?usion coe?cients on oriented surfaces disclose much lower activation energies than that found in the present work,and the di?erences are related to the formation energy of the defects responsible for surface di?usion. Acknowledgements
This work has been supported by the Hunga-rian Grant FKFP0188/2001and by a post doc-toral grant of the French Ministery of Research. References
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