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Ion beam mixing: Basic experiments
Nuclear instruments and Methods in Physics Research B7/8 (1985) 666-675 North-Hohand, Amsterdam
666
ION BEAM MIXING: BASIC EXPERIMENTS 3.M. PAINE
R.S. AVERBACK Materials
Science and Technology DIUISIO~, Argonne Nattonal
Laboratory,
Argonne, Illinots 6W9,
USA
We review basic quantitative experiments in ion heam mixing of simple layered sohd systems. Most have etnpmyed ions with mass from 20 to 136 amu and enerf$es between 50 and 600 keV, while sample configurations fail into two categories: - 10 A “marker” layers of impurity atoms buried in otherwise homogeneous media, and “bilayers” of two materials of several hundred A each. We tabulate the quantitative results of all such measurements reported to date for marker systems, and the low temperature (in the temperature-independent regime, or < 300 K) results far hilayers. We also compare the collected results with quantitative calculations of collisional mixing and qualitative pictures of relaxation and thermal diffusion mixing from moIecular dynamics simulations and chemical rate theory.
1.
Introd~on Ion beam mixing of layered solid systems has been
the subject of increasing
interest for the past five years. In &if timq it has been recognized that there are several basic mechanisms which may contribute to the phenom-
enon. The details of these mechanisms, their magnitudes, and their dependence on the system and conditions of the irradiation are still not well understood, However- there are now sufficiently many experiments reported in the literature that it is reasonable to begin trying to answer these questions. For this purpose, we present a summary of the main quantitative results of these studies and list the trends that are observed. We then discuss the interpretation of these results in terms of basic models. To facilitate our discussion, we first outline the basic mechanisms that are thought to be important. The best picture of the atomic motions following the entry of an energetic ion into a crystalline solid is currently obtained from molecular dynamics calculations (see ref. [l], and more recently ref. [Z]). ln this approach, individual cascades are simulated by solving the equations of motion for the primary recoil atom, together with other lattice atoms it encounters plus atoms in up to three coordination shells, with a realistic interatomic potential [3]. This is done successively at small time intervals (less than 1 x lo-l4 s) until all displacement motion is quenched, and repeated many times for random initiaf recoil directions so that reasonable averaging is obtained. In calculations reported so far, the atoms of the solid have been assumed to be initially at rest at their lattice sites. 016%583X/SS/gO3.U 0 EIsevier Science Publishers B.V. (Noah-Holland Physics Pubhshing Division)
These calculations indicate that different atomic transport mechanisms operate during different time intervals following the initial impact. Within the first - 2 X lo-t3 s, the transport is predominantly co% sionah atomic displacements are caused by screened Coulomb collisions with the primary atom or other recoiling atoms. Displacements are terminated when the recoils do not receive sufficient energy to leave their lattice sites. Since the energies involved in such displacements are high (2 5 eV), the mixing can be described just as well by 2-body collisions fl]. One would therefore expect the mixing during this stage of the cascade to be insensitive to the temperature of the bulk materi& and aside from kinematic factors, to the atomic numbers of the constituents. Whilst there will be a small number of displacements in the keV range leading to relatively long seeoils in the direction of the incident ions, (“recoil mixing” [4]) most of the events wiI1 be lower energy higher order displacements in random directions [5,6]. Thus the relocations will essentially follow a random walk pattern. As long as the cascade is not so dense that the energy required to displace atoms is reduced (an “energy spike” f7])_the amonnt of mixing should scale with F,, the energy per ion deposited in the lattice per unit depth [S]. Immediately following the displacement phase, and lasting up to a few times IO-” s, there is a “relaxation” phase, during which the kinetic energy of the recoiled particles is thermaliid. Atomic motion will be rapid and short-range, remaining essentially witbin the vicinity of the original coliision cascade. The molecular dynamics calculations [1,2] show that these will include athermal relaxation of unstable configurations such as
B.M. Pame, R.S. Averback / Ion beam mixmg: basw experiments close Frenkel pairs, and motion of radiation-induced defects, stimulated by the residual agitation of the lattice by the ion [9]. For a dense cascade triggered by a relatively heavy ion incident on a relatively heavy substrate, the kinetic energies in some regions after the collisional phase may be high enough such that there will be bulk diffusional motion as in a liquid. For example, Johnson et al. [lo] have shown that for 600 keV Xe ions incident on Pt and Au, the bulk of the mixing occurs when kinetic energies are of the order of 1 eV. The major evidence for such phenomena would be a super-linear dependence of the mixing on FD. The transport in this time frame will be mostly insensitive to sample temperature around 300 K or below. It may still have the character of a random walk, but since it is now strongly subject to the interatomic potentials and hence to chemical driving forces, the random walk may be substantially biased. At about IO-” s, the atoms in the vicinity of the initial cascade will have reached thermal equilibrium. Then atomic motion occurs by thermal diffusion of irradiation-induced defects, known as radiation-enhanced diffusion [12] (RED). Depending on the irradiation conditions (sample temperature and defect and sink densities), the RED mixing may vary with temperature and irradiating ion flux [12]. This type of transport occurs over time intervals of 10-i’ s up to 1 s or more, and can be described by chemical rate theory (121.
2. Experiments and analysis 2. I. Marker systems The simplest system for studying the diffusion mechanisms during ion beam mixing consists of a layer of about 10 A of an impurity (a “marker”) buried in an otherwise homogeneous medium. Analysis of this configuration is simple, and since the ion beam will usually disperse the layer widely in a very short time, the role of chemical driving forces is expected to be minimized. The mixing is usually quantified by u2, the irradiationinduced increase in the standard deviation of the marker distribution. This can be converted to the square of the effective diffusion length Dt = a2/2. In table 1, we summarize the major results from the marker experiments that have been reported to date. Marker M in host H is denoted H(M). Unless noted otherwise, each marker thickness was approximately 10 A, analysis was by backscattering spectrometry (BSS) with the sample at room temperature, and the marker profiles after irradiation were approximately Gaussian. Irradiation fluences were mostly between 1 x 1015 and 3 X lOI ions/cm2. We list the range of sample temperatures during the irradiations, T,, and the observed dependence of Dt on T,, and irradiation fluence +.
667
It is not obvious how best to normalize Dt for tabulation so it is most easily compared from system to system on some physical basis. As we see from the table, Dt almost always depends linearly on $J and F,, the energy per unit depth deposited in nuclear collisions by an ion, so it should clearly by normalized for these quantities. Some authors have chosen to multiply this by N, the atomic density of the medium, which converts it to a quantity proportional to (r2)/E,,, the ratio of the mean squared displacement distance and the effective minimum displacement energy in collisional cascade mixing theory [6,8]. It could be argued that one should further multiply by a factor of N2 to obtain (r2) in units of atoms per unit area, or by N213 for units of lattice spacings. However, to avoid such unnecessary complications, we have chosen to denote the efficiency of mixing simply as Dt/+F,, with units of As/eV. We have deduced this whenever practical, finding FD for each system by interpolation of the tables published by Winterbon [13]. When Dt had been measured over a range of temperatures, and appeared to be varying with temperature, only the value measured at the lowest temperature was used. When a range of temperatures had been spanned, and Dt did not vary beyond experimental uncertainties, the average of all measurements was taken. We have not attempted to quantify the mixing efficiency in the strongly temperature-dependent regimes. When Dt was found to vary from sample to sample [14,15] (assumed by those authors to be an impurity effect, and noted “impurities” in the table), the average of the reported values has been adopted. Realistic absolute uncertainties in Dt/+F, are probably of the order of +50%, while the relative uncertainties within a series of measurements are expected to be about 20%. 2.2. Biiayer systems Bilayer systems (two discrete layers of several hundred A or more) are the most commonly employed systems for studies of ion beam mixing, and are of the most interest for potential applications. In this configuration, supplies of both components are unlimited for the doses that are typically used, so the system is free to form binary phases of any composition, and chemical energies may therefore be relevant. Again, sample analysis is usually by BSS. Several authors [16-181 have identified a small long range component of mixing (2 500 A), quantified by measuring the area1 density of atoms relocated from the upper layer past a fixed plane in the lower layer. This component is found to scale linearly with irradiation dose and be independent of temperature, leading those authors to identify it with energetic collisional events (“recoil mixing”). Also the magnitude is found to be in good agreement with collisional calculations of such events [6,19]. This compoVIII. ION BEAM MIXING
668
B. M. Paine, R.S. Averback / ion beam mixmg: basic expertments
Table 1 Summary of measurements of ion beam mixing of marker samples ‘) Medium (marker)
Marker depth (A)
Ion
Al(Ti) Al( Fe) Al{Ni)
650 650 500
Al(Sb)
600 600 400 400 200 400 650 650
AI Al(In) Ai Al(W) At@)
Al(Au)
AI 20s(Ti) Al,Os(Fe) AlsO, AlaO, Al,O,(Au) Si(Ni)
2)
Xe Xe Ar
300 300 300
500
Ar Ar Ar Ar Ar Ar Xe Xe Ar
110 110 70 70 70 70 300 300 300
650 500
Xe Ar
300 300
550 550 550 550 550
Xe Xe Xe Xe Xe
var.
Var.
var.
var. Ar
300 300 300 300 300 var. var. 300
80 80 18,80, 300 90-300 370 295 295 295 295 80-500 80 18,80, 300 80-400 18,809 300 80 80 80-500 80 80-500 96-300 523 18,80, 300 96-523 40,300 34,77 96-523
500
Var.
var. 110 200 var.
var. Ar
var. 110
500 390 200 650 650 500
var. Xe Xe var. var. Xc Ar Xe Xe Xe Ar
var. 300 300 var. var. 300 110 200 300 300 300
var. 650 650 500
var. Xe Xe Ar
var. 300 300 300
600 600 600 600
Xe Xe Xe Xe
300 300 300 300
Si(Ge)
Var.
Si(Pd)
170 200 var.
Si(Sn)
VU.
360 Si(Sb) Si(W) Si(Pt)
var. 650 400 VW. Var.
Si(Au)
SiOs (Ti) SQ(cOI SiO,(Ni) SiO,(Hfj
Dependence of Dt on
E
(keV)
var. Ar Xe
96-523 40.59, 300 77-523 80-500 300 77,300 523 90 90 34,77 80-400 500 18, 80, 300 77,300 80-400 500 18. 80, 300 300 300 300 300
Ti,
Dt
cp
x (A’/ev)
linear linear
16 20 40
independent ind.
Other results
Notes
c.ht
linaar
43
- linear - linear - linear
64 56
-
36 21 24 60
TEM Dt(80) - F,,
25 60
Dt(80) - FD
Dt(370) :, Dt(300)
ind.
linear
tin. (80 K) linear
ind. ind. ind.
ind. ind. - ind. Di(523) c etch) ind.
lin. (80 K)
linear linear tin. (80 K) linear lin. (80 K)
TEM TEM
90
13 15 18 14 17 31
0 0 0 0 W zh)
h) b.h)
Dt(80) - FD
W
Dt(80)
W dt
- FD
45
ch)
d)
VtieS
79 80 0 -
ind. ind.
57 53
- ind. Dt(300) -9;Dt(40) Dt(34,77) = 0
hn. (80 K) ind.
ind. ind.
lin. (77 K) lin. (300 K)
Dt(300) = Dt(77f
lin(77 K)
Dt(77) = Dt(34)
ind.
0) C)
non&( > 173 K)
d) d) e>
d)
72 24 143 59
Dt(80) - FD DC-F,
linear
75
non-Gaussian shift in shift in
linear lin. (300 K)
74 74
b, n d)
8)
8) C)
Dt(500) < Dr(400)
ind. Dt(300) = Dt(77)
md. Dr(500) z.=Dt(400) ind.
e,h)
75 117 lin. (300 K) 114 130 14 18 21 34
Ref.
d)
Dt(80) + F.
b, b) e.h)
I481 1481 I491 I491 [491 1491 V61 1461 I471 w1 [471 1461 V61 V61 WI WI [22.231 1231 [471 122,231 v91 WI [2X23] 122331 (291 [22,23] w,501 1511 1231 v31 [421 1521 WI I46.501 [5Ol t471 1231 [46,501 WI I471 [SO] 1501 [5OI [501
B.M. Paine, R.S. Averback
/ Jon beam mixing: b&c
669
experimenrs
Table 1 (continued) Medium (marker)
Marker depth (A)
Ion
E (keV)
Dependence
% (K)
-‘Dt
of Dr on
T ITT
+
WD
Other results
Notes
Ref.
(A’/ev) SiO, ( W) SiO,(Pt) SiO,(Au)
600 600 600 600 400 400 430 360 375
Xe Xe Xe Xe Ar Ar Xe Ar Kr
400 400 400 400 400 400 400 400 400 400 440 350
N Ne Ar Ar Ar Sb,Sb, Xe Xe Xe Kr Xe Kr
200 420 200 200 380
Xe Xe Xe Xe Xe
150 150 150 150 150 250 500 500 500 500 300 500 1800 295 300 295 295 750
Ge(Pt)
330
Xe
150
Pd(Si) Hf(Ti)
180 375
Xe Kr
300 750
Hf(Ni)
375 375
Kr Kr
750 750
Fe( Pt) Ni(Si) Ni(Hf) Ni(Au)
Cu(Cu) Cu(W) Cu(Au) Ge(AI) Ge(Si)
a) b, ‘) d, ‘) o *) h, ‘) ‘)
300 300 300 300 150 150 300 110 750
300 300 300 SO-500 20 29-345 96,300 40,300 10, 80, 295 - 20,295 20,295 20,295 300-480 480-600 - 20 20-370 370-480 480-700 10,295 300 10, 80, 295 34 96,300 34 77 6, 77, 300 6,300, 493 96,300 10, 80, 295 lo,80 295
linear linear linear ind. Dr(20) < Dr(29) ind. Dr(300) = Dr(96) Dr(300) = Dr(40) ind.
Dr(295) = Dr(295) = incr. with incr. with
Dr(20) Dr(20) T,, T,,
ind. incr. with T,, incr. with T,, Dr(295) = Dr(10)
42 14 11 - linear lin. (20 K) lin. (20 K)
lin. (20 K) lin. (20 K)
8.0 7.5 9.2
-9.2 14
Dr(80) - F,, impurities no &dep. shift (300 K)
23 24
b) e) C) 0 4
c.h.0 c.h) e.h) c.e.h)
impurities impurities no &dep.
e)
&dep. no &dep. Sb, higher no &dep.
-9 c.e.h) c.e.h)
C)
+-dep. no dep.
5) i.h.fl
shift in Dr(80, 295) -
c.h)
1501 I501 ]501 ]461 1141 1141 1221 1291 [451 u51 I151 132.151 [321 ~321 I151 132,151 1321 1321 [361 I541 [451
FD
- linear - linear - linear
90 110 90 9 88
WI WI WI WI (301
- linear
145
1301
- linear
Dr(300) = Dr(96) Dr(77) 4: Dr(34) incr. slowly incr. slowly varies ind.
7.2 8.1
linear - linear
linear
-
40 42 37 29
nonG(300 13
Dr(80) = Df(10) Dr(295) < Dr(80)
17 6
K)
o e.h.0
c.h.0 e.0
[231 [451 I451 [451
See text for full explanation. Measurements were also conducted with Ne, Ar and Kr ions. Similar results were found for Ni(Pt). Average of Xe results with those for 50 keV Ne, 110 keV Ar and 220 keV Kr. Backsctteting analysis conducted in situ at the temperature of the ion irradiation. Marker thickness - 25-30 A. Pt marker layer was - 5 A on average. FD calculated with TRIM (see ref. [21]). Analysis by SIMS. See ref. [37] for analysis of F,-dependence.
nent of the mixing will not be considered further here. The shorter range mixing (displacements 2 500 A) typically involve - lo3 more atoms. However, analysis of the diffusion in this sample geometry presents several problems. The first problem is that the effective diffusion coefficient in the mixed region may depend on
composition because either the transport processes or the energy deposition are inhomogeneous in the mixed region. The other problem is that the atomic densities and electronic stopping powers in this region will not be known well, adding additional uncertainties to analysis by BSS. Nevertheless, it is of interest to do simple VIII. ION BEAM MIXING
under layer
500 350 750 700 300 530 1160 550 550 640 200 250 1440 450 450 450 450 450 450 400 500 500 500 500 500 500 500 500 -500 -500 -500 -500 -500 1200
(A)
Xe Kr Kr Kr Xe Xe Xe Ar Kr Xe Kr Xe Si He Ne Ar Kr Xe Xe Xe Xe Xe Xe Xe Xe Xe Xe Xe Xe Xe Xe Xe Xe Kr
Ion
low temperature
Interface depth
of quantitative
500 500 140 200 300 300 300 250 280 300 220 300 275 300 225 250 275 300 160 300 600 600 600 600 600 600 600 600 600 600 600 600 600 1000
(kev)
E
measurements
samples.
6,295
loo-550 77-518 77-518 10-443 10-400 90-430 96,295 96,295 298-636 10,293,393 10,293,393 10.293.393 10,293,393 10.293.393 10.293.393 90-430 90 90 90 90 90 90 90 90 90 90 90 90 90
40-500 10,295 -100 -100
Tirr (K)
of bilayer of e or X on
o(10) ~(10) ~(293) - ~(10) ~(293) - ~(10)
a(77) a(77) K a(293) - ~(10)
(r drops at 295 K
_ _ _ _ _ _
T,-300K T,-300K r,-300K T,-200K T,-200K T,-160K a(300) a(300) T, - 470 a(393) ~(293) ~(293) ~(393) ~(393) - ind.
_
T,-300K ~(295) - ~(10)
T ,lT
Dependence
‘)
See text for full explanation. Sample analysis conducted in situ at the temperature of the ion irradiation. Checked for dependence of Df/+ on 4 in this system at T both above and below T,. None was found. Chemical formula gives only the stoichiometry deduced by backscattering spectrometry. Oxygen impurities reduced u by 30%.
Au/AS Pt/Pd Hf/Zr Ta/Nb W/MO Cu/Bi
Pt/(Si) Pt/Ti pt/v Pt/Cr Pt/Mn Pt/Ni Au/Ti Au/Cr Au/Co
Nb/(Si) Si/Pt
Ge/(Si)
Cr/( Si) Co/Si Si/Co Ni/(Si)
AI/Au
CUjC”
Cu/AI
top layer /
System
Table 2 Summary
9
85 25 74 71 324 100 171 544 45 79 105 173 171 188 616 427 227 133 214 132 543 229 132 265 40 22 13 13 95
20 144 153
Dl/$J=, #j/eij
Pt,Si
NbSi,,
NbsSi,
Au 2 Al, AuAl 2 Au,Al, AuAI, CrSi 2 Co,Si Co,Si Ni,Si Ni,Si Ni,Si _ _
Phases identified
b)
_
d)
b)
b)
b)
b)
b)
b)
d)
b.d)
b.c.d,
_
W
b.c,
Notes
[361 [261 (261 1341 1561 [561 1241 (241 [311 [551 I551 1251 (381 13'31 I381 I381 1381 I381 I311 WI WI WI WI WI WI WI WI [411 I411 (411 (411 (411 (531
I161
Ref.
B.M. Parne. R.S. Averback / Ion beam mixing: basic expertments
quantitative BSS analyses of the mixing of bilayer systems, assuming the Bragg Ruie [20] for stopping powers, and taking the atomic densities to vary linearly with concentration. In some systems such analysis reveals that the concentrations of the two components vary monotonically across the region of the initial interface. In this case, the mixing is best quantified by fitting error functions with a~uments (x - a),/$%%, where x is depth and a is a fitting parameter, to plots of concentration versus depth for one of the components before and after irradiation, or conducting a Boltzmann-Matano analysis. In other situations, the short-range mixing gives rise to a well-defined layer of fixed stoichiometry lying between the two original layers. Since u is half the distance between the locations of 16% and 84% of full height in the case of an error function profile [20] we take DI equal to X2/8 where X is the thickness of the grown layer. Table 2 summarizes the results of quantitative measurements of low temperature mixing of bilayer samples reported to date. Layer L on substrate S is denoted L/S. Unless noted otherwise, analysis was by BSS, and the concentration profiles across the layer interface took the approximate shape of an error function. When a value of T, is given in column 6, this indicates that Dr is approximately independent of temperature from the lowest limit of T,,, up to T,, and above T, it increases or decreases with temperature. Our criteria for including results in the table were that CTor X could be extracted, and that the range of T,, that was covered extended below either T, or 295 K, if T, is not known. We have again listed the quantity Dt/q+F,,, calculated from the value of (I or X reported for the lowest limit in the range of irradiation temperatures that was covered. For this purpose Fo was taken to be the average of the values calculated on either side of the interface, by means of the TRIM code [21]. When a layer of constant composition develops, this is identified by an entry under the heading “Phases identified”, and unless indicated to the contrary, each phase was a crystalline compound identified by X-ray diffraction. 2.3. Results The general characteristics of ion beam mixing of marker and bilayer systems that have emerged from the work listed in tables 1 and 2 are as follows: 2.3. I. Profiles The profiles of marker systems after mixing are almost always Gaussian. The exceptions are the Si(Pd) and Pd(Si) systems 122,231and Si(Pt) at 500 K (231. The profiles of the components of the bilayer systems essentially have the form of error functions after irradiation at low temperatures. In addition, the Ni/Si [24] and Nb/Si [25] systems after low temperature mixing ap
671
pear to have small steps superimposed on them, wrrespending to narrow layers of fixed stoichiometry, possibly corresponding to a single phase. Compound formation below T, has so far been reported for only one metal-metal system (Al/Au) [26], but this system was analyzed at room temperature, i.e. at or above the temperature for the onset of migration of vacancies in these metals [27]. At T, and above, many bilayer systems develop well-defined layers of fixed stoichiometry which have been identified by X-ray diffraction to contain a single crystalline phase. 2.3.2. Temperature For both markers and bilayers, mixing appears to be independent of temperature at low temperatures (below - 80 K). The results of Clark et al. 1281for Si(Ge) and Ge(Si) are exceptions to this. However, other in situ measurements on these systems [29,30] showed little or no temperature dependence from 7 K to 295 K. The only other exception to this is the observation by Rottiger et al. [14] of a step in the tern~ratur~~d~~ curve for Fe(Pt) at about 25 K. This was a smaI1 effect, and appeared to be connected with the presence of oxygen impurities. For most systems, the mixing begins to increase or decrease with temperature at higher temperatures. The temperatures T, at which this has been found to occur range from about 160 K (3If to about 470 K 1251. In some systems, no change with temperature has been observed up to 500 K. 2.3.3. Flux Dt does not vary with the irradiation flux (b below T, in the cases that have been checked. Averback et al. checked for &dependence in the Ni/Si system 1241, as did Bettiger et a1. for Fe(Pt) [14] and Ni(Au) [32]. Above T,, no &dependence was observed for Ni/Si [24] while a small (- 20%) reduction of Dt with increase in (b was reported for Ni(Au) [32]. The latter effect disappeared above T, + 100 K. 2.3.4. Fltcence Below T, (or below 300 K when T, is not known), Dr is found to vary linearly with 9. The only exception to this rule is the result of Clark et al. for Si(Ge) [28]. There is some evidence that the relation may drop in some systems to less than linear dependence on dose at high fluences 1151, but the effect is smdf. Above c, or 300 K, Dt is mostly proportional to +, although it has been found to be proportional to d for two metal/Si systems: Au/Si [33] and Cr/Si [34]. (We note, however, that in an earlier investigation of Au/f%, Tsaur and Mayer (351 reported a linear dependence on + at 300 K.) 2.3. S. Energy density Below T,, Dr varies linearly with FD for markers in Al, Al,O,, Si, SiO,, irradiated with Ne, Ar, Kr, and Xc VIII. ION BEAM MIXING
B.M. Phine, RS.. Averback / Ion beam mixing: basic experiments
672
ions (371 and Cu irradiated with 0.5 and 1.8 MeV Kr ions [45]. For the 9 marker species tested, only Si(Au) [37] is a possible exception to this. However, about a factor of 2 more mixing has been reported for Xe ions than for N, Ne, Ar, and Sb ions on Ni(Au) [15]. The only low temperature &,-dependence reported for mixing of bilayers was for Si layers on Pt and revealed substantially higher mixing efficiencies by about a factor of 4 for heavy ions (Kr and Xe) than for light ions (He, Ne) [38]. The results of the latter two experiments are summarized in fig. 1. 2.3.6. Heats of mixing When bilayer pairs with similar atomic masses and thicknesses are irradiated with Xe ions at 90 K, Dt/+F, is found [40] to vary roughly linearly with the heat of mixing (-AH,,,) calculated by Miedema [39]. 2.3.7. Binding energies When bilayer systems with similar atomic masses, the same configurations, and small heats of mixing are irradiated with Xe ions at 90 K, the mixing is found to vary approximately inversely with sublimation energies of the components (411.
3. Discussion To evaluate the results of table 1 further, we have plotted Dt/+F, for all of the systems so far investi-
I I
I
(b) SI loymron
I
I
Pt.
'T_
-1 ll-r=lOK Avrbock .t al..1984 I -$, Ha,
0. 1
gated at irradiation temperature below IO0 K as a function of the atomic number Z of the marker. Fig. 2 shows the results for media of Si and Ge, while fig. 3 shows them for Al,O,, SiO, and the metals. Where more than one measurement had been reported, we have taken the average value of Dt/#F,, except on two occasions when a measurement conflicted with at least two other results, which were in excellent agreement, in which case it was omitted from the average. In fig. 2, 6 of the points have been measured at least twice and Si(Pt) and Ge(Si) have been measured 5 and 4 times, respectively. Figs. 2 and 3 also show the results of theoretical calculations of low energy collisional mixing in these systems by Sigmund and Gras-Marti [5,6]. This model requires an estimate of E,,, the effective threshold energy for collisional displacement of an atom, and ( r2), the mean squared displacement distance for collisional events. Ed is not known for impurity atoms in specific media. Therefore a representative constant value of 25 eV was adopted. For (r2), the reasonable figure of 10 A was chosen. Molecular dynamics simulations [1,2] show that short replacement sequences can result in displacement distances that are considerably smaller (- 3 A). But the numbers of atoms that are involved are higher by about a factor of 3, and the energies are reduced ( - 5 eV). The net result is roughly the same as would be calculated from the original numbers. An attempt was made by Sigmund and Gras-Marti [6] to explain the larger mixing in such systems in terms of high energy recoils of host atoms past the marker (“matrix relocation”). But this mechanism should lead to a net shift of a heavy marker in a relatively light
Ar i
KrX* -
Iar*'b I
1
10 Fg W/II)
I
100
1000
Fig. 1. Plots of measured mixing efficiencies, Dr/+Fn, as a funtion of Fn. the energy deposited by an ion in nuclear collisions per unit depth. Different values of FD were achieved by irradiation with different ions. Part (a) shows the results of Bottiger et al. [IS] for a Au marker buried 400 A deep in Ni (see table 1). Different symbols correspond to separately-prs pared samples. Part (b) shows the data for a 450 A Si layer on Pt. by Averback et al. [38] (see table 2). Uncertainties in Fr, in both parts of the figure may be as much as a factor of 2.
0
10
20
30
40
SO 60 2 (&n-bar)
70
60
90
100
Fig. 2. The efficiency of marker mixing, Dt/+F,, plotted as a function of the atomic number of the markers in Si and Ge media. The plotted points are the averages of all reported data for irradiations below 100 K (see table 1). ‘Ihe dashed line is calculated from the low energy collision cascade model of Sigmund and Gras-Marti [5,6].
B. M. Poine,
R.S.Averback / Ion beom mixing: basic experiments
A
- AI203
v
- SIO2
0 0
10
20
30
40
50 60 2 (Markad
70
80
90
100
Fig. 3. The efficiency of marker mixing, W/+FD, plotted against the atomic number of the marker, for metal and oxide media. Again, the plotted points are the average of all reported data for irradiations below 100 K (see table 1). The dashed line is calculated from the low energy collision cascade model of Sigmund and Gras-Marti [SW.
matrix in the direction toward the surface. In a measurement of the movement of a Pt marker in Si relative to another Pt marker lying beyond the range of the ions, a slight shift was actually found in the other direction
1421. Matteson et al. 1431 incorporated both high and low energy recoils in a model of isotropic cascade mixing, to find a standard deviation of mixing comparable to those that are observed for Si(M). But according to Signnund and Gras-Marti [6] the relocation profile of high energy isotropic mixing is Lorentzian, segmentally, one always measures the convolution of the mixed profile and an instrumental broadening, which is usually close to Gaussian. Since the full widths at half maximum (fwhm) of these functions are comparable and they are always observed on top of a background with relatively large statistical fluctuations, it is impossible to determine the precise shape of the relocation function. If it is Lorentzian, then the fwhm predicted by Matteson et al. becomes much less than what is observed. Clearly neither collisional model can explain the large variations of the results for Si and Ge with marker species. Collisional mixing might vary abruptly between marker species by virtue of differences in Ed [8], but it is unlikely to vary by more than factor of 2, and certainly not by the factors of 3 and 4 that are evident in fig. 2. Indeed the large differences in the mixing efficiencies between different markers suggest that the chemical nature of the marker must play an important roie. Also, the average mixing efficiencies are larger than predicted by Sigmund and Gras-Mar& low energy collisional model by factors of 13 and 110 for Si and Ge, respectively. Thus we conclude that relaxation or RED mecha-
673
nisms must be contributing substantially to the ion beam mixing in these semiconductor systems. The hope that chemical driving forces would be small in the marker configuration is not realized, at least for these media. For markers in the metals and oxides the magnitudes of the mixing are mostly a lot less than those for Si and Ge media. However, their average value is still about a factor of 4 higher than the collisional calculation so it is most likely that relaxation and RED mechanisms are contributing in these systems also. We can dismiss spike events as possibly contributing to most of the marker results because of the observed linear dependences on FD_ Presumably this is because FD is small in most of them. However, the increased mixing at very large FD in Ni(Au) [see fig. l(a)] f38] is evidence for this mechanism. Indeed, spike phenomena may be partly responsible for the strong mixing observed in the Ge(M) systems, also. For irradiations with light ions, the big variations in Dt/cpF, observed by Bottiger et al. [15] between samples prepared at different times suggest that impurities may be affecting the mixing, i.e. that point defects are involved. One can speculate that the effect disappears for heavier ions because with denser cascades the impurities are quickly dispersed widely by collisional events, whereas for light ions they are only displaced a short distance and therefore promptly back-diffuse. It is not possible at this stage to estimate the relative contributions of relaxation and RED events. Certainly fast diffusion of irradiation-induced interstitial atoms will occur in most media, whether amorphous or crystalline. A simple theoretical model has been proposed for such events 1441,but it conflicts with recent results 1451. Also by standard chemical rate theory applied to RED [12], when the temperature is raised above T,, and the mixing becomes dependent on temperature, D/g, should be proportional to 4-i”. But the effect observed by Bottiger et al. [32] for Ni(Au) was smaller than this, and disappeared at T, + 100 K, while the temperaturedependence remained. Therefore the diffusional mixing that occurs probably does not conform to the current conventional models for RED [12]. These models treat only point defect diffusion, whereas complex defect states are also likely to be produced after a typical collision cascade. Looking now at the bilayer results below T, or beIow 300 K, we first observe that unlike for the marker conf$uration, many systems with large I;;, (2 300 eV/A) have been investigated. Since significant non-linear dependence on FD has been observed in this regime [see fig. l(b)], it is not very useful to compare Df/+F,, for different systems with different FD. Nevertheless, it is clear from the table that the magnitude of the mixing efficiency for bilayers is much greater than for markers for more than half of the VIII. ION BEAM MIXING
674
B.M.
Paine, R.S. Averbock
/ Ion beam mixtng: bahic experiments
reported measurements.
One probable reason for this is the fact that chemical forces (e.g. heats of formation and heats of mixing) can influence the mixing more strongly in the bilayer configuration than for markers. The full range of concentrations, and hence of accessible binary phases, is present for bilayers while for marker systems, collisional events tend to rapidly reduce the concentrations of markers atoms, thus reducing the range of possible phases. The correlation with heats of mixing observed by Cheng et al. [40] when other parameters were held constant supports this. Also, from these arguments, one would expect that in the mixing of an element with itself, the same mixing should
occur for markers and bilayers. This was indeed found to be true for mixing of different Cu isotopes, profiled by SIMS (361.The results were Dr/+F, = (23 f S)A’/eV for Cu(Cu) and (20 f S)K/eV for Cu/Cu. Another reason for the generally larger mixing in the
bilayer configurations is that many of them include at least one heavy component, making spikes more probable, whereas most of the marker systems have so far incorporated light host media. A spike model, with explicit dependence on thermodynamic parameters (heats of mixing and sublimation energies), was proposed at this conference by Johnson et al. [lo]. Above 300 K the strong variations of mixing with temperature observed in many systems suggest that radiation-enhanced diffusion (RED) may contribute. However, again the lack of flux dependence conflicts with existing conventional models for RED. We acknowledge helpful discussions with Drs W.L. Johnson and M. Van Rossum, and are grateful to Dr J. Bettiger and Mr Y.-T. Cheng for permission to quote their results before publication. We also acknowledge Mrs M. Parks for her skilled handling of secretarial and administrative matters. This work was supported by the National Aeronautics and Space Administration, monitored by the Jet Propulsion Laboratory, California Institute of Technology (D.B. Bickler), and the Office of Naval Research under Contract No. NOOO14-84-K-0275 (D. Polk) at the California Institute of Technology, and by the Department of Energy at Argonne National Laboratory.
References
[II M.W. Guinan
and J.H. Kinney, J. Nucl. Mater. 103/104 (1981) 1319. 121W.E. King and R. Benedek, J. Nucl. Mater. 117 (1983) 26. [31 R.A. Johnson and W.D. Wilson, in: Proc. Intern. Conf. on Interatomic Potential and Simulations of Lattice Defects, eds., P.C. GehIen, J.R. Beeler Jr and RI. Jaffee (Plenum, New York, 1971) p. 301. 141U. Littmark and W.O. Hofer, Nucl. Instr. and Meth. 168 (1980) 329.
[S] A. Gras-Marti and P. Sigmund, Nucl. Instr. and Meth. 180 (1981) 211. (61 P. Sigmund and A. Gras-Marti, Nucl. Instr. and Mel. 182/183 (1981) 25. [7] D.A. Thompson, Radiat. Effects 56 (1981) 105. [8] H.H. Andersen, Appl. Phys. 18 (1979) 131. 191 R.S. Averback, J. Nucl. Mater. 108/109 (1982) 33. 1101 W.L. Johnson, Y.-T. Cheng, M. Van Rossum and. M-A. Nicolet, these Proceedings (IBMM ‘84) Nucl. Instr. and Meth. B7/8 (1985) 657. IllI P. Sigmund, Appl. Phys. Lett. 25 (1974) 169; Appl. Phys. Lett. 27 (1975) 52. .I121 R. Sixmann, J. Nucl. Mater. 69/70 (1968) 386; G.J. Dienes and A.C. Damask, J. Appl. Phys. 29 (1958) 1713. Ion Implantation Range and Energy I131 K.B. Winterbon, Deposition Distributions, Vol. 2 (Plenum, New York, 1975). 1141J. Bettiger, S.K. Nielsen, H.J. Whitlow and P. Wriedt, Nucl. Instr. and Meth. 218 (1983) 684. WI J. Bottiger, S.K. Nielsen and P.T. Thorsen, these Proceedings (IBMM ‘84) Nucl. Instr. and Meth. B7/8 (1985) 707. WI F. Besenbacher, J. Bottiger, S.K. Nielsen and H.J. Whitlow, Appl. Phys. A29 (1982) 141. 1171 S.T. Picraux, D.M. Follstaedt and J. Delafond, in: Metastable Materials Formation by Ion Implantation, eds., S.T. Picraux and W.J. Choyke (Ehevier-North-Holland. New York, 1982) p. 71. WI T.C. Banwell, B.X. Liu, I. Golecki and, M-A. Nicolet, Nucl. Instr. and Meth. 209/210 (1983) 125. 1191 L.A. Christel, J.F. Gibbons and S. Mylroie, Nucl. Instr. and Meth. 182/183 (1981) 187. 1201 W.K. Chu, J.W. Mayer and M-A. Nicolet, Backscattering Spectrometry (Academic Press, New York, 1978). 1211 J.P. Biersack and L.G. Haggmark, Nucl. Instr. and Meth. 174 (1980) 257. PI S. Matteson, G. Mexey and M-A. Nicolet, in: Proc. Symp. on Thin Film Interfaces and Interactions, Los Angeles, 1979, eds., J.E.E. Baghn and J.M. Poate (Electrochemical Society, New Jersey, 1980) p. 242. v31 S. Matteson, B.M. Paine, M.G. GrimaIdi, G. Mexey and M-A. Nicolet, Nucl. Instr. and Meth. 182/183 (1981) 43. 1241 R.S. Averback, L.J. Thompson Jr, J. Moyle and M. Schalit, J. Appl. Phys. 53 (1982) 1342. WI S. Matteson, J. Roth and M-A. Nicolet, Radiat. Effects 42 (1979) 217. WI C.T. Chart8 S.U. Campisano, S. Cannavo and E. Rimini. J. Appl. Phys. 55 (1984) 3322. 1271 W. Schilling, G. Burger, K. Isbcck and H. WenxI, in: Vacancies and Interstitials in Metals, eds., A. Seeger, D. Schumacher, W. Schilling and J. Diehl (North-Holland, Amsterdam, 1970) p. 255. WI G.J. Clark, A.D. Marwick and D.B. Poker, Nucl. Instr. and Meth. 209/210 (1983) 107. 1291 B.M. Paine, M-A. Nicolet. R.G. Newcombe and D.A. Thompson, Nucl. Instr. and Meth. 182/183 (1981) 115. R.S. Averback and P. Baldo, 1301 S.J. Kim, M-A. N&let, Appl. Phys. Lett., to be published (1985). [311 L.S. Wieluhski, B.M. Paine, B.X. Liu, C.-D. Lien and M-A. N&let. phys. stat. sol. (a)72 (1982) 399. 1321 J. Bottiger, S.K. Nielsen and P.T. Thorsen, Materials Research Society European Meeting, Strasbourg, France (1984); to be published in J. de Phys. (1984).
B. M. Paine, R.S. Averback
[33) D.B.
[34] 1351 (361 [37]
(381
[39]
[40] [41] [42] [43]
/ Ion beam mixing: basic experiments
Poker, O.W. Holland and B.R. Appleton, in: Ion Implantation and Ion Beam Processing of Materials, eds., G.K. Hubler, O.W. Holland, C.R. Ch+yion and C.W. White (Elsevier Science Publishing, New York, 1984) Mat. Res. Sot. Symp. Proc. Vol. 27, p. 73. J.W. Mayer, B.Y. Tsaur, S.S. Lau and L.S. Hung, Nucl. Instr. and Meth. 182/183 (1981) 1. B.Y. Tsaur and J.W. Mayer, Philos. Mag. A43 (1981) 345. R.S. Averback and D. Peak, unpublished (1984). M-A. Nicolet, T.C. Banwell and B.M. Paine, in: Ion Implantation and Ion Beam Processing of Materials, eds., G.K. Hubler, O.W. Holland, C.R. Clayton and C.W. White (Elsevier Science Publishing, New York, 1984) Mat. Res. Sot. Symp. Proc. VoI 27, p. 3. R.S. Averback, L.J. Thompson and L.E. Rehn, in: Ion Implantation and Ion Beam Processing of Materials, eds.. G.K. Hubler, O.W. Holland, CR. Clayton and C.W. White (EIsevier Science Publishing, New York, 1984) Mat. Res. See. Symp. Proc. Vol. 27, p. 25. A.R. Miedema, Philips Technical Review 36 (1976) 217; A.R. Miedema, F.R. de Boer and R. Boom, Calphad 1 (1977) 341. Y.-T. Cheng, M. Van Rossum, M-A. Nicolet and W.L. Johnson, Appl. Phys. Lett. 45 (1984) 185. M. Van Rossum, Y.-T. Cheng, W.L. Johnson and M-A. Nicolet, Appl. Phys. Lett., to be published (1985). B.M. Paine, J. Appl. Phys. 53 (1982) 6828. S. Matteson, B.M. Paine and M-A. N&let, Nucl. Instr. and Meth. 182/183 (1981) 53.
[44] [45] [46] (471
[48]
[49] [SO] [51] 1521 [53]
1541 [55]
1561
675
P. Sigmund, Appl. Phys. A30 (1983) 43. R.S. Averback and D. Peak, unpublished (1984). A. Barcz and M-A. Nicolet, Appl. Phys. A33 (1984) 167. S. Mantl, L.E. Rehn, R.S. Averback and L.J. Thompson, these Proceedings (IBMM ‘84) Nucl. Instr and Meth. B7/8 (1985) 622. B.M. Paine, M-A. Nicolet and T.C. BanweII, in: Metastable Materials Formation by Ion Implantation, eds., S.T. Picraux and W.J. Choyke (Elsevier-North-Holland, New York, 1982) p. 79. Y. Fujino, S. Yamaguchi, H. Naramoto and K. Gaawa, Nucl. Instr. and Meth. 218 (1983) 691. A. Barcx, B.M. Paine and M-A. Nicolet, Appl. Phys. Lett. 44 (1984) 45. B.Y. Tsaur, S. Matteson. G. Chapman, Z.L. Liau and M-A. Nicolet, Appl. Phys. Lett. 35 (1979) 825. B.M. Paine and M-A. Nicolet, Nucl. Instr. and Meth. 209/210 (1983) 173. R.S. Averback, P.B. Okamoto, A.C. Baily and B. Stritzker, these Proceedings (IBMM ‘84) Nucl. Instr. and Meth. B7/8 (1985) 556. Z.L. Wang, J.F.M. Westendorp and F.W. Saris, Nucl. Instr. and Meth. 209/210 (1983) 115. G. Mexey, S. Matteson and M-A. Nicolet, in: Thin Film Interfaces and Interactions, Vol. 80-2, eds., JEE. Baglin and J.M. Poate (EIectrochem. Sot., New Jersey, 1980) p. 256. A. Hamdi and M-A. Nicolet, Thin Solid Films, in press (1984).
VIII. ION BEAM MIXING
666
ION BEAM MIXING: BASIC EXPERIMENTS 3.M. PAINE
R.S. AVERBACK Materials
Science and Technology DIUISIO~, Argonne Nattonal
Laboratory,
Argonne, Illinots 6W9,
USA
We review basic quantitative experiments in ion heam mixing of simple layered sohd systems. Most have etnpmyed ions with mass from 20 to 136 amu and enerf$es between 50 and 600 keV, while sample configurations fail into two categories: - 10 A “marker” layers of impurity atoms buried in otherwise homogeneous media, and “bilayers” of two materials of several hundred A each. We tabulate the quantitative results of all such measurements reported to date for marker systems, and the low temperature (in the temperature-independent regime, or < 300 K) results far hilayers. We also compare the collected results with quantitative calculations of collisional mixing and qualitative pictures of relaxation and thermal diffusion mixing from moIecular dynamics simulations and chemical rate theory.
1.
Introd~on Ion beam mixing of layered solid systems has been
the subject of increasing
interest for the past five years. In &if timq it has been recognized that there are several basic mechanisms which may contribute to the phenom-
enon. The details of these mechanisms, their magnitudes, and their dependence on the system and conditions of the irradiation are still not well understood, However- there are now sufficiently many experiments reported in the literature that it is reasonable to begin trying to answer these questions. For this purpose, we present a summary of the main quantitative results of these studies and list the trends that are observed. We then discuss the interpretation of these results in terms of basic models. To facilitate our discussion, we first outline the basic mechanisms that are thought to be important. The best picture of the atomic motions following the entry of an energetic ion into a crystalline solid is currently obtained from molecular dynamics calculations (see ref. [l], and more recently ref. [Z]). ln this approach, individual cascades are simulated by solving the equations of motion for the primary recoil atom, together with other lattice atoms it encounters plus atoms in up to three coordination shells, with a realistic interatomic potential [3]. This is done successively at small time intervals (less than 1 x lo-l4 s) until all displacement motion is quenched, and repeated many times for random initiaf recoil directions so that reasonable averaging is obtained. In calculations reported so far, the atoms of the solid have been assumed to be initially at rest at their lattice sites. 016%583X/SS/gO3.U 0 EIsevier Science Publishers B.V. (Noah-Holland Physics Pubhshing Division)
These calculations indicate that different atomic transport mechanisms operate during different time intervals following the initial impact. Within the first - 2 X lo-t3 s, the transport is predominantly co% sionah atomic displacements are caused by screened Coulomb collisions with the primary atom or other recoiling atoms. Displacements are terminated when the recoils do not receive sufficient energy to leave their lattice sites. Since the energies involved in such displacements are high (2 5 eV), the mixing can be described just as well by 2-body collisions fl]. One would therefore expect the mixing during this stage of the cascade to be insensitive to the temperature of the bulk materi& and aside from kinematic factors, to the atomic numbers of the constituents. Whilst there will be a small number of displacements in the keV range leading to relatively long seeoils in the direction of the incident ions, (“recoil mixing” [4]) most of the events wiI1 be lower energy higher order displacements in random directions [5,6]. Thus the relocations will essentially follow a random walk pattern. As long as the cascade is not so dense that the energy required to displace atoms is reduced (an “energy spike” f7])_the amonnt of mixing should scale with F,, the energy per ion deposited in the lattice per unit depth [S]. Immediately following the displacement phase, and lasting up to a few times IO-” s, there is a “relaxation” phase, during which the kinetic energy of the recoiled particles is thermaliid. Atomic motion will be rapid and short-range, remaining essentially witbin the vicinity of the original coliision cascade. The molecular dynamics calculations [1,2] show that these will include athermal relaxation of unstable configurations such as
B.M. Pame, R.S. Averback / Ion beam mixmg: basw experiments close Frenkel pairs, and motion of radiation-induced defects, stimulated by the residual agitation of the lattice by the ion [9]. For a dense cascade triggered by a relatively heavy ion incident on a relatively heavy substrate, the kinetic energies in some regions after the collisional phase may be high enough such that there will be bulk diffusional motion as in a liquid. For example, Johnson et al. [lo] have shown that for 600 keV Xe ions incident on Pt and Au, the bulk of the mixing occurs when kinetic energies are of the order of 1 eV. The major evidence for such phenomena would be a super-linear dependence of the mixing on FD. The transport in this time frame will be mostly insensitive to sample temperature around 300 K or below. It may still have the character of a random walk, but since it is now strongly subject to the interatomic potentials and hence to chemical driving forces, the random walk may be substantially biased. At about IO-” s, the atoms in the vicinity of the initial cascade will have reached thermal equilibrium. Then atomic motion occurs by thermal diffusion of irradiation-induced defects, known as radiation-enhanced diffusion [12] (RED). Depending on the irradiation conditions (sample temperature and defect and sink densities), the RED mixing may vary with temperature and irradiating ion flux [12]. This type of transport occurs over time intervals of 10-i’ s up to 1 s or more, and can be described by chemical rate theory (121.
2. Experiments and analysis 2. I. Marker systems The simplest system for studying the diffusion mechanisms during ion beam mixing consists of a layer of about 10 A of an impurity (a “marker”) buried in an otherwise homogeneous medium. Analysis of this configuration is simple, and since the ion beam will usually disperse the layer widely in a very short time, the role of chemical driving forces is expected to be minimized. The mixing is usually quantified by u2, the irradiationinduced increase in the standard deviation of the marker distribution. This can be converted to the square of the effective diffusion length Dt = a2/2. In table 1, we summarize the major results from the marker experiments that have been reported to date. Marker M in host H is denoted H(M). Unless noted otherwise, each marker thickness was approximately 10 A, analysis was by backscattering spectrometry (BSS) with the sample at room temperature, and the marker profiles after irradiation were approximately Gaussian. Irradiation fluences were mostly between 1 x 1015 and 3 X lOI ions/cm2. We list the range of sample temperatures during the irradiations, T,, and the observed dependence of Dt on T,, and irradiation fluence +.
667
It is not obvious how best to normalize Dt for tabulation so it is most easily compared from system to system on some physical basis. As we see from the table, Dt almost always depends linearly on $J and F,, the energy per unit depth deposited in nuclear collisions by an ion, so it should clearly by normalized for these quantities. Some authors have chosen to multiply this by N, the atomic density of the medium, which converts it to a quantity proportional to (r2)/E,,, the ratio of the mean squared displacement distance and the effective minimum displacement energy in collisional cascade mixing theory [6,8]. It could be argued that one should further multiply by a factor of N2 to obtain (r2) in units of atoms per unit area, or by N213 for units of lattice spacings. However, to avoid such unnecessary complications, we have chosen to denote the efficiency of mixing simply as Dt/+F,, with units of As/eV. We have deduced this whenever practical, finding FD for each system by interpolation of the tables published by Winterbon [13]. When Dt had been measured over a range of temperatures, and appeared to be varying with temperature, only the value measured at the lowest temperature was used. When a range of temperatures had been spanned, and Dt did not vary beyond experimental uncertainties, the average of all measurements was taken. We have not attempted to quantify the mixing efficiency in the strongly temperature-dependent regimes. When Dt was found to vary from sample to sample [14,15] (assumed by those authors to be an impurity effect, and noted “impurities” in the table), the average of the reported values has been adopted. Realistic absolute uncertainties in Dt/+F, are probably of the order of +50%, while the relative uncertainties within a series of measurements are expected to be about 20%. 2.2. Biiayer systems Bilayer systems (two discrete layers of several hundred A or more) are the most commonly employed systems for studies of ion beam mixing, and are of the most interest for potential applications. In this configuration, supplies of both components are unlimited for the doses that are typically used, so the system is free to form binary phases of any composition, and chemical energies may therefore be relevant. Again, sample analysis is usually by BSS. Several authors [16-181 have identified a small long range component of mixing (2 500 A), quantified by measuring the area1 density of atoms relocated from the upper layer past a fixed plane in the lower layer. This component is found to scale linearly with irradiation dose and be independent of temperature, leading those authors to identify it with energetic collisional events (“recoil mixing”). Also the magnitude is found to be in good agreement with collisional calculations of such events [6,19]. This compoVIII. ION BEAM MIXING
668
B. M. Paine, R.S. Averback / ion beam mixmg: basic expertments
Table 1 Summary of measurements of ion beam mixing of marker samples ‘) Medium (marker)
Marker depth (A)
Ion
Al(Ti) Al( Fe) Al{Ni)
650 650 500
Al(Sb)
600 600 400 400 200 400 650 650
AI Al(In) Ai Al(W) At@)
Al(Au)
AI 20s(Ti) Al,Os(Fe) AlsO, AlaO, Al,O,(Au) Si(Ni)
2)
Xe Xe Ar
300 300 300
500
Ar Ar Ar Ar Ar Ar Xe Xe Ar
110 110 70 70 70 70 300 300 300
650 500
Xe Ar
300 300
550 550 550 550 550
Xe Xe Xe Xe Xe
var.
Var.
var.
var. Ar
300 300 300 300 300 var. var. 300
80 80 18,80, 300 90-300 370 295 295 295 295 80-500 80 18,80, 300 80-400 18,809 300 80 80 80-500 80 80-500 96-300 523 18,80, 300 96-523 40,300 34,77 96-523
500
Var.
var. 110 200 var.
var. Ar
var. 110
500 390 200 650 650 500
var. Xe Xe var. var. Xc Ar Xe Xe Xe Ar
var. 300 300 var. var. 300 110 200 300 300 300
var. 650 650 500
var. Xe Xe Ar
var. 300 300 300
600 600 600 600
Xe Xe Xe Xe
300 300 300 300
Si(Ge)
Var.
Si(Pd)
170 200 var.
Si(Sn)
VU.
360 Si(Sb) Si(W) Si(Pt)
var. 650 400 VW. Var.
Si(Au)
SiOs (Ti) SQ(cOI SiO,(Ni) SiO,(Hfj
Dependence of Dt on
E
(keV)
var. Ar Xe
96-523 40.59, 300 77-523 80-500 300 77,300 523 90 90 34,77 80-400 500 18, 80, 300 77,300 80-400 500 18. 80, 300 300 300 300 300
Ti,
Dt
cp
x (A’/ev)
linear linear
16 20 40
independent ind.
Other results
Notes
c.ht
linaar
43
- linear - linear - linear
64 56
-
36 21 24 60
TEM Dt(80) - F,,
25 60
Dt(80) - FD
Dt(370) :, Dt(300)
ind.
linear
tin. (80 K) linear
ind. ind. ind.
ind. ind. - ind. Di(523) c etch) ind.
lin. (80 K)
linear linear tin. (80 K) linear lin. (80 K)
TEM TEM
90
13 15 18 14 17 31
0 0 0 0 W zh)
h) b.h)
Dt(80) - FD
W
Dt(80)
W dt
- FD
45
ch)
d)
VtieS
79 80 0 -
ind. ind.
57 53
- ind. Dt(300) -9;Dt(40) Dt(34,77) = 0
hn. (80 K) ind.
ind. ind.
lin. (77 K) lin. (300 K)
Dt(300) = Dt(77f
lin(77 K)
Dt(77) = Dt(34)
ind.
0) C)
non&( > 173 K)
d) d) e>
d)
72 24 143 59
Dt(80) - FD DC-F,
linear
75
non-Gaussian shift in shift in
linear lin. (300 K)
74 74
b, n d)
8)
8) C)
Dt(500) < Dr(400)
ind. Dt(300) = Dt(77)
md. Dr(500) z.=Dt(400) ind.
e,h)
75 117 lin. (300 K) 114 130 14 18 21 34
Ref.
d)
Dt(80) + F.
b, b) e.h)
I481 1481 I491 I491 [491 1491 V61 1461 I471 w1 [471 1461 V61 V61 WI WI [22.231 1231 [471 122,231 v91 WI [2X23] 122331 (291 [22,23] w,501 1511 1231 v31 [421 1521 WI I46.501 [5Ol t471 1231 [46,501 WI I471 [SO] 1501 [5OI [501
B.M. Paine, R.S. Averback
/ Jon beam mixing: b&c
669
experimenrs
Table 1 (continued) Medium (marker)
Marker depth (A)
Ion
E (keV)
Dependence
% (K)
-‘Dt
of Dr on
T ITT
+
WD
Other results
Notes
Ref.
(A’/ev) SiO, ( W) SiO,(Pt) SiO,(Au)
600 600 600 600 400 400 430 360 375
Xe Xe Xe Xe Ar Ar Xe Ar Kr
400 400 400 400 400 400 400 400 400 400 440 350
N Ne Ar Ar Ar Sb,Sb, Xe Xe Xe Kr Xe Kr
200 420 200 200 380
Xe Xe Xe Xe Xe
150 150 150 150 150 250 500 500 500 500 300 500 1800 295 300 295 295 750
Ge(Pt)
330
Xe
150
Pd(Si) Hf(Ti)
180 375
Xe Kr
300 750
Hf(Ni)
375 375
Kr Kr
750 750
Fe( Pt) Ni(Si) Ni(Hf) Ni(Au)
Cu(Cu) Cu(W) Cu(Au) Ge(AI) Ge(Si)
a) b, ‘) d, ‘) o *) h, ‘) ‘)
300 300 300 300 150 150 300 110 750
300 300 300 SO-500 20 29-345 96,300 40,300 10, 80, 295 - 20,295 20,295 20,295 300-480 480-600 - 20 20-370 370-480 480-700 10,295 300 10, 80, 295 34 96,300 34 77 6, 77, 300 6,300, 493 96,300 10, 80, 295 lo,80 295
linear linear linear ind. Dr(20) < Dr(29) ind. Dr(300) = Dr(96) Dr(300) = Dr(40) ind.
Dr(295) = Dr(295) = incr. with incr. with
Dr(20) Dr(20) T,, T,,
ind. incr. with T,, incr. with T,, Dr(295) = Dr(10)
42 14 11 - linear lin. (20 K) lin. (20 K)
lin. (20 K) lin. (20 K)
8.0 7.5 9.2
-9.2 14
Dr(80) - F,, impurities no &dep. shift (300 K)
23 24
b) e) C) 0 4
c.h.0 c.h) e.h) c.e.h)
impurities impurities no &dep.
e)
&dep. no &dep. Sb, higher no &dep.
-9 c.e.h) c.e.h)
C)
+-dep. no dep.
5) i.h.fl
shift in Dr(80, 295) -
c.h)
1501 I501 ]501 ]461 1141 1141 1221 1291 [451 u51 I151 132.151 [321 ~321 I151 132,151 1321 1321 [361 I541 [451
FD
- linear - linear - linear
90 110 90 9 88
WI WI WI WI (301
- linear
145
1301
- linear
Dr(300) = Dr(96) Dr(77) 4: Dr(34) incr. slowly incr. slowly varies ind.
7.2 8.1
linear - linear
linear
-
40 42 37 29
nonG(300 13
Dr(80) = Df(10) Dr(295) < Dr(80)
17 6
K)
o e.h.0
c.h.0 e.0
[231 [451 I451 [451
See text for full explanation. Measurements were also conducted with Ne, Ar and Kr ions. Similar results were found for Ni(Pt). Average of Xe results with those for 50 keV Ne, 110 keV Ar and 220 keV Kr. Backsctteting analysis conducted in situ at the temperature of the ion irradiation. Marker thickness - 25-30 A. Pt marker layer was - 5 A on average. FD calculated with TRIM (see ref. [21]). Analysis by SIMS. See ref. [37] for analysis of F,-dependence.
nent of the mixing will not be considered further here. The shorter range mixing (displacements 2 500 A) typically involve - lo3 more atoms. However, analysis of the diffusion in this sample geometry presents several problems. The first problem is that the effective diffusion coefficient in the mixed region may depend on
composition because either the transport processes or the energy deposition are inhomogeneous in the mixed region. The other problem is that the atomic densities and electronic stopping powers in this region will not be known well, adding additional uncertainties to analysis by BSS. Nevertheless, it is of interest to do simple VIII. ION BEAM MIXING
under layer
500 350 750 700 300 530 1160 550 550 640 200 250 1440 450 450 450 450 450 450 400 500 500 500 500 500 500 500 500 -500 -500 -500 -500 -500 1200
(A)
Xe Kr Kr Kr Xe Xe Xe Ar Kr Xe Kr Xe Si He Ne Ar Kr Xe Xe Xe Xe Xe Xe Xe Xe Xe Xe Xe Xe Xe Xe Xe Xe Kr
Ion
low temperature
Interface depth
of quantitative
500 500 140 200 300 300 300 250 280 300 220 300 275 300 225 250 275 300 160 300 600 600 600 600 600 600 600 600 600 600 600 600 600 1000
(kev)
E
measurements
samples.
6,295
loo-550 77-518 77-518 10-443 10-400 90-430 96,295 96,295 298-636 10,293,393 10,293,393 10.293.393 10,293,393 10.293.393 10.293.393 90-430 90 90 90 90 90 90 90 90 90 90 90 90 90
40-500 10,295 -100 -100
Tirr (K)
of bilayer of e or X on
o(10) ~(10) ~(293) - ~(10) ~(293) - ~(10)
a(77) a(77) K a(293) - ~(10)
(r drops at 295 K
_ _ _ _ _ _
T,-300K T,-300K r,-300K T,-200K T,-200K T,-160K a(300) a(300) T, - 470 a(393) ~(293) ~(293) ~(393) ~(393) - ind.
_
T,-300K ~(295) - ~(10)
T ,lT
Dependence
‘)
See text for full explanation. Sample analysis conducted in situ at the temperature of the ion irradiation. Checked for dependence of Df/+ on 4 in this system at T both above and below T,. None was found. Chemical formula gives only the stoichiometry deduced by backscattering spectrometry. Oxygen impurities reduced u by 30%.
Au/AS Pt/Pd Hf/Zr Ta/Nb W/MO Cu/Bi
Pt/(Si) Pt/Ti pt/v Pt/Cr Pt/Mn Pt/Ni Au/Ti Au/Cr Au/Co
Nb/(Si) Si/Pt
Ge/(Si)
Cr/( Si) Co/Si Si/Co Ni/(Si)
AI/Au
CUjC”
Cu/AI
top layer /
System
Table 2 Summary
9
85 25 74 71 324 100 171 544 45 79 105 173 171 188 616 427 227 133 214 132 543 229 132 265 40 22 13 13 95
20 144 153
Dl/$J=, #j/eij
Pt,Si
NbSi,,
NbsSi,
Au 2 Al, AuAl 2 Au,Al, AuAI, CrSi 2 Co,Si Co,Si Ni,Si Ni,Si Ni,Si _ _
Phases identified
b)
_
d)
b)
b)
b)
b)
b)
b)
d)
b.d)
b.c.d,
_
W
b.c,
Notes
[361 [261 (261 1341 1561 [561 1241 (241 [311 [551 I551 1251 (381 13'31 I381 I381 1381 I381 I311 WI WI WI WI WI WI WI WI [411 I411 (411 (411 (411 (531
I161
Ref.
B.M. Parne. R.S. Averback / Ion beam mixing: basic expertments
quantitative BSS analyses of the mixing of bilayer systems, assuming the Bragg Ruie [20] for stopping powers, and taking the atomic densities to vary linearly with concentration. In some systems such analysis reveals that the concentrations of the two components vary monotonically across the region of the initial interface. In this case, the mixing is best quantified by fitting error functions with a~uments (x - a),/$%%, where x is depth and a is a fitting parameter, to plots of concentration versus depth for one of the components before and after irradiation, or conducting a Boltzmann-Matano analysis. In other situations, the short-range mixing gives rise to a well-defined layer of fixed stoichiometry lying between the two original layers. Since u is half the distance between the locations of 16% and 84% of full height in the case of an error function profile [20] we take DI equal to X2/8 where X is the thickness of the grown layer. Table 2 summarizes the results of quantitative measurements of low temperature mixing of bilayer samples reported to date. Layer L on substrate S is denoted L/S. Unless noted otherwise, analysis was by BSS, and the concentration profiles across the layer interface took the approximate shape of an error function. When a value of T, is given in column 6, this indicates that Dr is approximately independent of temperature from the lowest limit of T,,, up to T,, and above T, it increases or decreases with temperature. Our criteria for including results in the table were that CTor X could be extracted, and that the range of T,, that was covered extended below either T, or 295 K, if T, is not known. We have again listed the quantity Dt/q+F,,, calculated from the value of (I or X reported for the lowest limit in the range of irradiation temperatures that was covered. For this purpose Fo was taken to be the average of the values calculated on either side of the interface, by means of the TRIM code [21]. When a layer of constant composition develops, this is identified by an entry under the heading “Phases identified”, and unless indicated to the contrary, each phase was a crystalline compound identified by X-ray diffraction. 2.3. Results The general characteristics of ion beam mixing of marker and bilayer systems that have emerged from the work listed in tables 1 and 2 are as follows: 2.3. I. Profiles The profiles of marker systems after mixing are almost always Gaussian. The exceptions are the Si(Pd) and Pd(Si) systems 122,231and Si(Pt) at 500 K (231. The profiles of the components of the bilayer systems essentially have the form of error functions after irradiation at low temperatures. In addition, the Ni/Si [24] and Nb/Si [25] systems after low temperature mixing ap
671
pear to have small steps superimposed on them, wrrespending to narrow layers of fixed stoichiometry, possibly corresponding to a single phase. Compound formation below T, has so far been reported for only one metal-metal system (Al/Au) [26], but this system was analyzed at room temperature, i.e. at or above the temperature for the onset of migration of vacancies in these metals [27]. At T, and above, many bilayer systems develop well-defined layers of fixed stoichiometry which have been identified by X-ray diffraction to contain a single crystalline phase. 2.3.2. Temperature For both markers and bilayers, mixing appears to be independent of temperature at low temperatures (below - 80 K). The results of Clark et al. 1281for Si(Ge) and Ge(Si) are exceptions to this. However, other in situ measurements on these systems [29,30] showed little or no temperature dependence from 7 K to 295 K. The only other exception to this is the observation by Rottiger et al. [14] of a step in the tern~ratur~~d~~ curve for Fe(Pt) at about 25 K. This was a smaI1 effect, and appeared to be connected with the presence of oxygen impurities. For most systems, the mixing begins to increase or decrease with temperature at higher temperatures. The temperatures T, at which this has been found to occur range from about 160 K (3If to about 470 K 1251. In some systems, no change with temperature has been observed up to 500 K. 2.3.3. Flux Dt does not vary with the irradiation flux (b below T, in the cases that have been checked. Averback et al. checked for &dependence in the Ni/Si system 1241, as did Bettiger et a1. for Fe(Pt) [14] and Ni(Au) [32]. Above T,, no &dependence was observed for Ni/Si [24] while a small (- 20%) reduction of Dt with increase in (b was reported for Ni(Au) [32]. The latter effect disappeared above T, + 100 K. 2.3.4. Fltcence Below T, (or below 300 K when T, is not known), Dr is found to vary linearly with 9. The only exception to this rule is the result of Clark et al. for Si(Ge) [28]. There is some evidence that the relation may drop in some systems to less than linear dependence on dose at high fluences 1151, but the effect is smdf. Above c, or 300 K, Dt is mostly proportional to +, although it has been found to be proportional to d for two metal/Si systems: Au/Si [33] and Cr/Si [34]. (We note, however, that in an earlier investigation of Au/f%, Tsaur and Mayer (351 reported a linear dependence on + at 300 K.) 2.3. S. Energy density Below T,, Dr varies linearly with FD for markers in Al, Al,O,, Si, SiO,, irradiated with Ne, Ar, Kr, and Xc VIII. ION BEAM MIXING
B.M. Phine, RS.. Averback / Ion beam mixing: basic experiments
672
ions (371 and Cu irradiated with 0.5 and 1.8 MeV Kr ions [45]. For the 9 marker species tested, only Si(Au) [37] is a possible exception to this. However, about a factor of 2 more mixing has been reported for Xe ions than for N, Ne, Ar, and Sb ions on Ni(Au) [15]. The only low temperature &,-dependence reported for mixing of bilayers was for Si layers on Pt and revealed substantially higher mixing efficiencies by about a factor of 4 for heavy ions (Kr and Xe) than for light ions (He, Ne) [38]. The results of the latter two experiments are summarized in fig. 1. 2.3.6. Heats of mixing When bilayer pairs with similar atomic masses and thicknesses are irradiated with Xe ions at 90 K, Dt/+F, is found [40] to vary roughly linearly with the heat of mixing (-AH,,,) calculated by Miedema [39]. 2.3.7. Binding energies When bilayer systems with similar atomic masses, the same configurations, and small heats of mixing are irradiated with Xe ions at 90 K, the mixing is found to vary approximately inversely with sublimation energies of the components (411.
3. Discussion To evaluate the results of table 1 further, we have plotted Dt/+F, for all of the systems so far investi-
I I
I
(b) SI loymron
I
I
Pt.
'T_
-1 ll-r=lOK Avrbock .t al..1984 I -$, Ha,
0. 1
gated at irradiation temperature below IO0 K as a function of the atomic number Z of the marker. Fig. 2 shows the results for media of Si and Ge, while fig. 3 shows them for Al,O,, SiO, and the metals. Where more than one measurement had been reported, we have taken the average value of Dt/#F,, except on two occasions when a measurement conflicted with at least two other results, which were in excellent agreement, in which case it was omitted from the average. In fig. 2, 6 of the points have been measured at least twice and Si(Pt) and Ge(Si) have been measured 5 and 4 times, respectively. Figs. 2 and 3 also show the results of theoretical calculations of low energy collisional mixing in these systems by Sigmund and Gras-Marti [5,6]. This model requires an estimate of E,,, the effective threshold energy for collisional displacement of an atom, and ( r2), the mean squared displacement distance for collisional events. Ed is not known for impurity atoms in specific media. Therefore a representative constant value of 25 eV was adopted. For (r2), the reasonable figure of 10 A was chosen. Molecular dynamics simulations [1,2] show that short replacement sequences can result in displacement distances that are considerably smaller (- 3 A). But the numbers of atoms that are involved are higher by about a factor of 3, and the energies are reduced ( - 5 eV). The net result is roughly the same as would be calculated from the original numbers. An attempt was made by Sigmund and Gras-Marti [6] to explain the larger mixing in such systems in terms of high energy recoils of host atoms past the marker (“matrix relocation”). But this mechanism should lead to a net shift of a heavy marker in a relatively light
Ar i
KrX* -
Iar*'b I
1
10 Fg W/II)
I
100
1000
Fig. 1. Plots of measured mixing efficiencies, Dr/+Fn, as a funtion of Fn. the energy deposited by an ion in nuclear collisions per unit depth. Different values of FD were achieved by irradiation with different ions. Part (a) shows the results of Bottiger et al. [IS] for a Au marker buried 400 A deep in Ni (see table 1). Different symbols correspond to separately-prs pared samples. Part (b) shows the data for a 450 A Si layer on Pt. by Averback et al. [38] (see table 2). Uncertainties in Fr, in both parts of the figure may be as much as a factor of 2.
0
10
20
30
40
SO 60 2 (&n-bar)
70
60
90
100
Fig. 2. The efficiency of marker mixing, Dt/+F,, plotted as a function of the atomic number of the markers in Si and Ge media. The plotted points are the averages of all reported data for irradiations below 100 K (see table 1). ‘Ihe dashed line is calculated from the low energy collision cascade model of Sigmund and Gras-Marti [5,6].
B. M. Poine,
R.S.Averback / Ion beom mixing: basic experiments
A
- AI203
v
- SIO2
0 0
10
20
30
40
50 60 2 (Markad
70
80
90
100
Fig. 3. The efficiency of marker mixing, W/+FD, plotted against the atomic number of the marker, for metal and oxide media. Again, the plotted points are the average of all reported data for irradiations below 100 K (see table 1). The dashed line is calculated from the low energy collision cascade model of Sigmund and Gras-Marti [SW.
matrix in the direction toward the surface. In a measurement of the movement of a Pt marker in Si relative to another Pt marker lying beyond the range of the ions, a slight shift was actually found in the other direction
1421. Matteson et al. 1431 incorporated both high and low energy recoils in a model of isotropic cascade mixing, to find a standard deviation of mixing comparable to those that are observed for Si(M). But according to Signnund and Gras-Marti [6] the relocation profile of high energy isotropic mixing is Lorentzian, segmentally, one always measures the convolution of the mixed profile and an instrumental broadening, which is usually close to Gaussian. Since the full widths at half maximum (fwhm) of these functions are comparable and they are always observed on top of a background with relatively large statistical fluctuations, it is impossible to determine the precise shape of the relocation function. If it is Lorentzian, then the fwhm predicted by Matteson et al. becomes much less than what is observed. Clearly neither collisional model can explain the large variations of the results for Si and Ge with marker species. Collisional mixing might vary abruptly between marker species by virtue of differences in Ed [8], but it is unlikely to vary by more than factor of 2, and certainly not by the factors of 3 and 4 that are evident in fig. 2. Indeed the large differences in the mixing efficiencies between different markers suggest that the chemical nature of the marker must play an important roie. Also, the average mixing efficiencies are larger than predicted by Sigmund and Gras-Mar& low energy collisional model by factors of 13 and 110 for Si and Ge, respectively. Thus we conclude that relaxation or RED mecha-
673
nisms must be contributing substantially to the ion beam mixing in these semiconductor systems. The hope that chemical driving forces would be small in the marker configuration is not realized, at least for these media. For markers in the metals and oxides the magnitudes of the mixing are mostly a lot less than those for Si and Ge media. However, their average value is still about a factor of 4 higher than the collisional calculation so it is most likely that relaxation and RED mechanisms are contributing in these systems also. We can dismiss spike events as possibly contributing to most of the marker results because of the observed linear dependences on FD_ Presumably this is because FD is small in most of them. However, the increased mixing at very large FD in Ni(Au) [see fig. l(a)] f38] is evidence for this mechanism. Indeed, spike phenomena may be partly responsible for the strong mixing observed in the Ge(M) systems, also. For irradiations with light ions, the big variations in Dt/cpF, observed by Bottiger et al. [15] between samples prepared at different times suggest that impurities may be affecting the mixing, i.e. that point defects are involved. One can speculate that the effect disappears for heavier ions because with denser cascades the impurities are quickly dispersed widely by collisional events, whereas for light ions they are only displaced a short distance and therefore promptly back-diffuse. It is not possible at this stage to estimate the relative contributions of relaxation and RED events. Certainly fast diffusion of irradiation-induced interstitial atoms will occur in most media, whether amorphous or crystalline. A simple theoretical model has been proposed for such events 1441,but it conflicts with recent results 1451. Also by standard chemical rate theory applied to RED [12], when the temperature is raised above T,, and the mixing becomes dependent on temperature, D/g, should be proportional to 4-i”. But the effect observed by Bottiger et al. [32] for Ni(Au) was smaller than this, and disappeared at T, + 100 K, while the temperaturedependence remained. Therefore the diffusional mixing that occurs probably does not conform to the current conventional models for RED [12]. These models treat only point defect diffusion, whereas complex defect states are also likely to be produced after a typical collision cascade. Looking now at the bilayer results below T, or beIow 300 K, we first observe that unlike for the marker conf$uration, many systems with large I;;, (2 300 eV/A) have been investigated. Since significant non-linear dependence on FD has been observed in this regime [see fig. l(b)], it is not very useful to compare Df/+F,, for different systems with different FD. Nevertheless, it is clear from the table that the magnitude of the mixing efficiency for bilayers is much greater than for markers for more than half of the VIII. ION BEAM MIXING
674
B.M.
Paine, R.S. Averbock
/ Ion beam mixtng: bahic experiments
reported measurements.
One probable reason for this is the fact that chemical forces (e.g. heats of formation and heats of mixing) can influence the mixing more strongly in the bilayer configuration than for markers. The full range of concentrations, and hence of accessible binary phases, is present for bilayers while for marker systems, collisional events tend to rapidly reduce the concentrations of markers atoms, thus reducing the range of possible phases. The correlation with heats of mixing observed by Cheng et al. [40] when other parameters were held constant supports this. Also, from these arguments, one would expect that in the mixing of an element with itself, the same mixing should
occur for markers and bilayers. This was indeed found to be true for mixing of different Cu isotopes, profiled by SIMS (361.The results were Dr/+F, = (23 f S)A’/eV for Cu(Cu) and (20 f S)K/eV for Cu/Cu. Another reason for the generally larger mixing in the
bilayer configurations is that many of them include at least one heavy component, making spikes more probable, whereas most of the marker systems have so far incorporated light host media. A spike model, with explicit dependence on thermodynamic parameters (heats of mixing and sublimation energies), was proposed at this conference by Johnson et al. [lo]. Above 300 K the strong variations of mixing with temperature observed in many systems suggest that radiation-enhanced diffusion (RED) may contribute. However, again the lack of flux dependence conflicts with existing conventional models for RED. We acknowledge helpful discussions with Drs W.L. Johnson and M. Van Rossum, and are grateful to Dr J. Bettiger and Mr Y.-T. Cheng for permission to quote their results before publication. We also acknowledge Mrs M. Parks for her skilled handling of secretarial and administrative matters. This work was supported by the National Aeronautics and Space Administration, monitored by the Jet Propulsion Laboratory, California Institute of Technology (D.B. Bickler), and the Office of Naval Research under Contract No. NOOO14-84-K-0275 (D. Polk) at the California Institute of Technology, and by the Department of Energy at Argonne National Laboratory.
References
[II M.W. Guinan
and J.H. Kinney, J. Nucl. Mater. 103/104 (1981) 1319. 121W.E. King and R. Benedek, J. Nucl. Mater. 117 (1983) 26. [31 R.A. Johnson and W.D. Wilson, in: Proc. Intern. Conf. on Interatomic Potential and Simulations of Lattice Defects, eds., P.C. GehIen, J.R. Beeler Jr and RI. Jaffee (Plenum, New York, 1971) p. 301. 141U. Littmark and W.O. Hofer, Nucl. Instr. and Meth. 168 (1980) 329.
[S] A. Gras-Marti and P. Sigmund, Nucl. Instr. and Meth. 180 (1981) 211. (61 P. Sigmund and A. Gras-Marti, Nucl. Instr. and Mel. 182/183 (1981) 25. [7] D.A. Thompson, Radiat. Effects 56 (1981) 105. [8] H.H. Andersen, Appl. Phys. 18 (1979) 131. 191 R.S. Averback, J. Nucl. Mater. 108/109 (1982) 33. 1101 W.L. Johnson, Y.-T. Cheng, M. Van Rossum and. M-A. Nicolet, these Proceedings (IBMM ‘84) Nucl. Instr. and Meth. B7/8 (1985) 657. IllI P. Sigmund, Appl. Phys. Lett. 25 (1974) 169; Appl. Phys. Lett. 27 (1975) 52. .I121 R. Sixmann, J. Nucl. Mater. 69/70 (1968) 386; G.J. Dienes and A.C. Damask, J. Appl. Phys. 29 (1958) 1713. Ion Implantation Range and Energy I131 K.B. Winterbon, Deposition Distributions, Vol. 2 (Plenum, New York, 1975). 1141J. Bettiger, S.K. Nielsen, H.J. Whitlow and P. Wriedt, Nucl. Instr. and Meth. 218 (1983) 684. WI J. Bottiger, S.K. Nielsen and P.T. Thorsen, these Proceedings (IBMM ‘84) Nucl. Instr. and Meth. B7/8 (1985) 707. WI F. Besenbacher, J. Bottiger, S.K. Nielsen and H.J. Whitlow, Appl. Phys. A29 (1982) 141. 1171 S.T. Picraux, D.M. Follstaedt and J. Delafond, in: Metastable Materials Formation by Ion Implantation, eds., S.T. Picraux and W.J. Choyke (Ehevier-North-Holland. New York, 1982) p. 71. WI T.C. Banwell, B.X. Liu, I. Golecki and, M-A. Nicolet, Nucl. Instr. and Meth. 209/210 (1983) 125. 1191 L.A. Christel, J.F. Gibbons and S. Mylroie, Nucl. Instr. and Meth. 182/183 (1981) 187. 1201 W.K. Chu, J.W. Mayer and M-A. Nicolet, Backscattering Spectrometry (Academic Press, New York, 1978). 1211 J.P. Biersack and L.G. Haggmark, Nucl. Instr. and Meth. 174 (1980) 257. PI S. Matteson, G. Mexey and M-A. Nicolet, in: Proc. Symp. on Thin Film Interfaces and Interactions, Los Angeles, 1979, eds., J.E.E. Baghn and J.M. Poate (Electrochemical Society, New Jersey, 1980) p. 242. v31 S. Matteson, B.M. Paine, M.G. GrimaIdi, G. Mexey and M-A. Nicolet, Nucl. Instr. and Meth. 182/183 (1981) 43. 1241 R.S. Averback, L.J. Thompson Jr, J. Moyle and M. Schalit, J. Appl. Phys. 53 (1982) 1342. WI S. Matteson, J. Roth and M-A. Nicolet, Radiat. Effects 42 (1979) 217. WI C.T. Chart8 S.U. Campisano, S. Cannavo and E. Rimini. J. Appl. Phys. 55 (1984) 3322. 1271 W. Schilling, G. Burger, K. Isbcck and H. WenxI, in: Vacancies and Interstitials in Metals, eds., A. Seeger, D. Schumacher, W. Schilling and J. Diehl (North-Holland, Amsterdam, 1970) p. 255. WI G.J. Clark, A.D. Marwick and D.B. Poker, Nucl. Instr. and Meth. 209/210 (1983) 107. 1291 B.M. Paine, M-A. Nicolet. R.G. Newcombe and D.A. Thompson, Nucl. Instr. and Meth. 182/183 (1981) 115. R.S. Averback and P. Baldo, 1301 S.J. Kim, M-A. N&let, Appl. Phys. Lett., to be published (1985). [311 L.S. Wieluhski, B.M. Paine, B.X. Liu, C.-D. Lien and M-A. N&let. phys. stat. sol. (a)72 (1982) 399. 1321 J. Bottiger, S.K. Nielsen and P.T. Thorsen, Materials Research Society European Meeting, Strasbourg, France (1984); to be published in J. de Phys. (1984).
B. M. Paine, R.S. Averback
[33) D.B.
[34] 1351 (361 [37]
(381
[39]
[40] [41] [42] [43]
/ Ion beam mixing: basic experiments
Poker, O.W. Holland and B.R. Appleton, in: Ion Implantation and Ion Beam Processing of Materials, eds., G.K. Hubler, O.W. Holland, C.R. Ch+yion and C.W. White (Elsevier Science Publishing, New York, 1984) Mat. Res. Sot. Symp. Proc. Vol. 27, p. 73. J.W. Mayer, B.Y. Tsaur, S.S. Lau and L.S. Hung, Nucl. Instr. and Meth. 182/183 (1981) 1. B.Y. Tsaur and J.W. Mayer, Philos. Mag. A43 (1981) 345. R.S. Averback and D. Peak, unpublished (1984). M-A. Nicolet, T.C. Banwell and B.M. Paine, in: Ion Implantation and Ion Beam Processing of Materials, eds., G.K. Hubler, O.W. Holland, C.R. Clayton and C.W. White (Elsevier Science Publishing, New York, 1984) Mat. Res. Sot. Symp. Proc. VoI 27, p. 3. R.S. Averback, L.J. Thompson and L.E. Rehn, in: Ion Implantation and Ion Beam Processing of Materials, eds.. G.K. Hubler, O.W. Holland, CR. Clayton and C.W. White (EIsevier Science Publishing, New York, 1984) Mat. Res. See. Symp. Proc. Vol. 27, p. 25. A.R. Miedema, Philips Technical Review 36 (1976) 217; A.R. Miedema, F.R. de Boer and R. Boom, Calphad 1 (1977) 341. Y.-T. Cheng, M. Van Rossum, M-A. Nicolet and W.L. Johnson, Appl. Phys. Lett. 45 (1984) 185. M. Van Rossum, Y.-T. Cheng, W.L. Johnson and M-A. Nicolet, Appl. Phys. Lett., to be published (1985). B.M. Paine, J. Appl. Phys. 53 (1982) 6828. S. Matteson, B.M. Paine and M-A. N&let, Nucl. Instr. and Meth. 182/183 (1981) 53.
[44] [45] [46] (471
[48]
[49] [SO] [51] 1521 [53]
1541 [55]
1561
675
P. Sigmund, Appl. Phys. A30 (1983) 43. R.S. Averback and D. Peak, unpublished (1984). A. Barcz and M-A. Nicolet, Appl. Phys. A33 (1984) 167. S. Mantl, L.E. Rehn, R.S. Averback and L.J. Thompson, these Proceedings (IBMM ‘84) Nucl. Instr and Meth. B7/8 (1985) 622. B.M. Paine, M-A. Nicolet and T.C. BanweII, in: Metastable Materials Formation by Ion Implantation, eds., S.T. Picraux and W.J. Choyke (Elsevier-North-Holland, New York, 1982) p. 79. Y. Fujino, S. Yamaguchi, H. Naramoto and K. Gaawa, Nucl. Instr. and Meth. 218 (1983) 691. A. Barcx, B.M. Paine and M-A. Nicolet, Appl. Phys. Lett. 44 (1984) 45. B.Y. Tsaur, S. Matteson. G. Chapman, Z.L. Liau and M-A. Nicolet, Appl. Phys. Lett. 35 (1979) 825. B.M. Paine and M-A. Nicolet, Nucl. Instr. and Meth. 209/210 (1983) 173. R.S. Averback, P.B. Okamoto, A.C. Baily and B. Stritzker, these Proceedings (IBMM ‘84) Nucl. Instr. and Meth. B7/8 (1985) 556. Z.L. Wang, J.F.M. Westendorp and F.W. Saris, Nucl. Instr. and Meth. 209/210 (1983) 115. G. Mexey, S. Matteson and M-A. Nicolet, in: Thin Film Interfaces and Interactions, Vol. 80-2, eds., JEE. Baglin and J.M. Poate (EIectrochem. Sot., New Jersey, 1980) p. 256. A. Hamdi and M-A. Nicolet, Thin Solid Films, in press (1984).
VIII. ION BEAM MIXING