Local density change of a metal backing due to implanted ions: Effect on nuclear lifetimes obtained with the DSA method

Nuclear Instruments and Methods 216 (1983) 249-258 North-Holland Publishing Company

249

LOCAL DENSITY CHANGE OF A METAL BACKING DUE TO IMPLANTED EFFECT ON NUCLEAR LIFETIMES OBTAINED WITH THE DSA METHOD

IONS:

J. K E I N O N E N , A. L U U K K A I N E N , A. A N T T I L A a n d M. E R O L A Department of Physics, University of Helsinki, SF-O0170 Helsinki 17, Finland Received 31 January 1983

Density changes in the Ne and A1 implanted regions of the bcc metals Mo and Ta have been studied with the Doppler Shift Attenuation (DSA) method through the (p, "/) reaction. Evidence for the increase of the local density is observed. Using the new experimental method, the dependence of the local density change on the implanted dose was studied from concentrations of few at.% up to saturation values, 26 at.% for Ne in Mo and 100 at.% for AI in Mo and Ta. Effects of the local density changes on the nuclear lifetimes obtained with the DSA method are discussed.

1. Introduction

The only way to measure nuclear lifetimes in the region 1-1000 fs is often through the Doppler Shift Attenuation (DSA) method. The implantation of the target atoms into a heavy backing material is the only practical way to prepare targets from rare and gaseous isotopes and targets with the high effective stopping power necessary in the measurements of short lifetimes ~-< 100 fs (refs. 1-7). However, when high doses of implanted target atoms are used, about 10 21 a t o m s / m 2 or more, the DSA lifetimes are subject to uncertainties due to density changes in the implanted region of the target. The bombardment of metals by electrons, neutrons or energetic heavier ions has been known to cause swelling in the metal [8]. This swelling has been assumed to depend linearly on the implanted dose [9]. Very recently, Alexander et al. [10] showed that fluences from 2 to 7 × 10 21 3He/m2 cause swelling of Zr, Nb and Au foils, where the relative increase of the volume of the implanted region ( A V / V ) is 0.75 times the atomic concentration of 3He. They used, for the first time, the D S A method in deducing the proportionality coefficient. For heavier implants than 3He, which in most cases has been used as a target in the DSA measurements through inverse reactions, the location within a host crystal is a very important factor in deducing the atomic density of the target material. Different criteria for the final position of the implanted atom are given: (1) In the framework of the modified H u m e Rothery rules, the D a r k e n - G u r r y plots based on size and electronegativity of atoms in implanted alloys have been used to show whether or not a given implanted species 0167-5087/83/0000-0000/$03.00 © 1983 North-Holland

will be substitutional in a given host metal [11]. (2) In a more thermodynamic approach, two parameters related to the electronic work function of a binary alloy and to the electron density in the metal at the boundary of the Wigner-Seitz cell, have been developed to indicate substitutional or interstitial lattice sites for the implanted impurity [ 12,13]. (3) Instead of these two models, based on equilibrium alloys, the final positions of implants in non-equilibrium implanted systems have been shown to depend strongly on the dynamical processes occurring near the end of the range [14]; in this case, however, no predictions for the final sites can be given. The experimental information on the locations of implanted atoms is based on 4He+ channeling studies [15]. This method can, however, be used only for low doses of implants. At high doses transmission-electron diffraction patterns have been used to establish changes in the crystalline structure of the lattice and to study the locations of implanted impurities [15]. In the present work, our primary aim was to study, for the first time, the subsurface atomic density of a backipg material as a function of the implanted dose, ranging from the atomic concentration of a few percent up to a saturation value. Thus, it was possible to draw conclusions also from the lattice sites of the implants in this wide region of doses. Our second aim was to study, also for the first time in the case of heavy implants, the dependence of the DSA lifetimes on the implanted dose. The heavy bcc metals with high atomic densities Mo (6.40 × 1022 a t o m s / c m 3) and Ta (5.53 × 1022 a t o m s / c m 3 [16]) were selected for the backing materials, because they are normally used in DSA measurements. In order to study the size effects on the atomic density of the host, the inert gas Ne was used as an implant. For

250

J. Keinonen et al. / Local densi O, change of a metal backing

the inclusion of the effects arising from the electronegativity, AI was used as the second implant. As the ion channeling technique has been employed in the previous studies on the lattice sites of implants, the implants have been heavier atoms than the backing atoms. The present work illuminates for the first time what happens in the inverted case.

2. E x p e r i m e n t a l

o° ~

o

o

300O

o

--Mo

z z i

procedure

- MOo74Neo.26 2000

60 keY n N e ÷ ~ M o 9.4x 10~ i o n s / m 2

i 1

8 lOOO

2.1. General arrangement 0

The 2.5 MV Van de Graaff accelerator at the University of Helsinki supplied 4He+ ion beams of about 50 nA and proton beams of about 20 #A. The 22Ne and 27A1 targets were prepared by implanting 60 keV 22Ne+ ions into 0.4 mm thick Mo backings and 100 keV 27A1+ ions into 0.4 mm thick Mo and Ta backings in the isotope separator of the laboratory. The prepared targets are summarized in table 1. The targets were collected over an area of 100 m m 2 using a linear sweeping of the focused ion beam, with about 1 x 15 m m 2 cross section. At the collector end of the separator the vacuum was about 100/xPa.

. . LLO

.

.

.

.

480 CHANNEL NUMBER

5 0

Fig. 1. The Rutherford backscattering spectra from pure Mo target and from Mo,,Ne,, target prepared by implanting 22 Ne + ions into Mo backing.

E4,,~ = 2.0 MeV. The standard signal amplifying and analyzing equipment was used in conjunction with the detector. In order to determine the dead-time correction of the signal analyzing system, a pulser was connected to the preamplifier. To avoid uncertainties due to secondary electron emission in the comparison of different measurements, a beam chopper was placed in front of the target and the 4He+ particles scattered from the c h o p p e r vane were detected with another surface-barrier detector and used to normalize the number of 4He+ particles for each set of measurements. In the present case of a uniformly mixed layer of light 22Ne nuclei in a heavy substrate Mo, the 22Ne concentration can be determined from the difference of the backscattering spectra taken from pure Mo and from the c o m p o u n d Mo,,,Ne,,, as illustrated in fig. 1. The formalism given in our earlier paper [18] can be used in the analysis. ]-'he ratio n / m is in the present case

2.2. Collection curves o f 2-'Ne + ions implanted into Mo and -'TAl + ions implanted into M o and Ta The maximum concentrations of the implanted 22 Ne atoms in Mo were determined by backscattering of 2 MeV 4He+ ions. The 4He + particle spectra were recorded by means of a silicon surface-barrier detector with an active area of 50 m m 2. The counter was located at a distance of 8 cm from the target spot, the mean scattering angle being 167 ° relative to the beam direction. The resolution of the detector was 14 keV at

Table 1 Summary of the targets. 60 keV 22Ne+ -~ Mo a)

100 keV 2VAl+ --, Mo b)

100 keV 27A1+ ~ Ta bl

Implanted fluence (102o ions/m 2 )

Maximum concentration ~) (at.%)

Implanted fluence (1020 ions/m 2 )

Maximum concentration (at.%)

Implanted fluence (102° ions/m 2 )

Maximum concentration (at.%)

0.62 1.9 5.6 9.4 31 94

0.81 + 0.04 1.73 -+0.09 6.9 __+0.3 10.8 _+0.5 27.0 _+1.1 25.8 _+1.0

6.2 18.7 62 200

8.5 + 0.3 20.4 __+0.7 48.2+0.9 83.3+ 1.2

6.2 18.7 62 200

7.8 __+0.3 22.1 +__0.6 49.3_+0.8 81.5__+ 1.1

~) Experimental mean range /~= 60_+ 3 /~g/cm2 was obtained for the first three targets: the method of analysis is discussed in an earlier paper [17]. In the case of the other targets the uncertainty~ A R - 5 p~g/cm2, due to changes in the density is considerably higher than observed changes in the mean ranges. bl Ref. 17: AI ---,Mo; R-= 86_+3 ~g/cm 2. AI - , Ta: R = 118_+4/~g/cm 2. ~> The values given summarize the results from backscattering and y-ray yield measurements.

J. Keinonen et al. / Local density change of a metal backing

40

100(

80

i . . . .

~

120 i

160 -f

200 - -

0

251

DEPTH(nm) 200

,'.00

80

104F ~

60

~

40

~

60 keY 22Ne+6.2x10 m~ Mo

O ] OkeV t7At~Mo •O l OkeVZTAt÷~Ta

• 5.6x102° + 9.Z,xl02°

2o

oO~i03

z o

/

10

, ,

.~ ,,~

• 3.1Xl021 " o 9.L,x1021 "

-1 _~

60 keY 22Ne4"~Mo ,-

•

o

ions..../m2

•

20

~.JO

6'0

810

IMPLANTED FLUENCE(10z° IONS/mz)

~I01

Fig. 2. The collection curves obtained in the preparation of 27A1 targets in Mo and Ta backings and 22Ne targets in Mo backing.

"..

0.01 o

2,~~___~ooo2

io c

850

870

890

910

E o (keV)

given by the equation

-- = Ne m [¢]Mo

/4MomNen *'Mo

1 ,

(1)

where the stopping cross section factors [¢]Mo Mo a n d [ ¢]Mo Ne are analogous to what is given by eq. (14) in ref. 18. HMo a n d /•4"Mo M ° ' N e " are the plateau heights of the backscattering yield from M o nuclei in a pure M o target a n d from M o nuclei in the mixture MomNe,, respectively. The m a x i m u m atomic c o n c e n t r a t i o n s of 22 Ne in M o were calculated using the above equation; the results are given in table 1 a n d illustrated in fig. 2. Taking the backscattering spectra at different points, the targets were observed to be h o m o g e n e o u s over the area of implantation. The saturation value of the 22Ne conc e n t r a t i o n in M o was f o u n d to be (26.4 + 0.9) at.%. The relative m a x i m u m c o n c e n t r a t i o n s were det e r m i n e d also b y c o m p a r i n g the y-ray yields from the i m p l a n t e d targets. The y-rays were produced in the reaction 22Ne(p, y ) 2 3 N a at Ep = 856 keV. A n energy window of 2.6 < Ey < 10 M e V was used to count the y-rays, detected with a 12.7 × 10.2 cm NaI(TI) crystal. T h e yield curves are shown in fig. 3, and the results are given in table 1. In a c o m p a r i s o n of the y-ray yields from a nuclear reaction [19] in two targets, the ratio of atomic conc e n t r a t i o n is Cl

Y1 ¢1

e2

V2 ¢2'

(2)

where Yl a n d Y2 are the y-ray yields o b t a i n e d at the same b o m b a r d i n g energy, a n d q a n d ¢2 are the corres p o n d i n g s t o p p i n g cross sections. By assuming a virtual molecule M o . , N e . , the stopping cross section is given

Fig. 3. The y-ray yield curves from the 22Ne+ implantations into Mo backings: In converting the energy scale into the depth scale (nm), the proton stopping power has to be used and the correction due to the Ne concentration should be taken into account. The lower depth scale is for the target with 0.62 × 1020 22Ne/m2 and the upper one for 9.4X 10 21 22Ne/m2.

by ¢ = m¢(Mo) + n¢(Ne),

(3)

where m + n = 1 a n d ¢(Mo) and ¢(Ne) are the cross sections for pure M o a n d pure Ne [20], respectively, at the b o m b a r d i n g energy. The m a x i m u m concentrations of the i m p l a n t e d 27A1 a t o m s in M o and Ta were determined by c o m p a r i n g the y-ray yield from the i m p l a n t e d target with that from the p u r e A1 target. The yield was produced in the reaction 27Al(p, y)2Ssi at Ep = 992 keV. A n energy window was used to c o u n t the 10.76 MeV y-rays. The m a x i m u m atomic c o n c e n t r a t i o n s o b t a i n e d with the use of eqs. (2) a n d (3) are given in table 1 and illustrated in fig. 2. In the case of the solid i m p l a n t 27A1, the saturation value of the A1 c o n c e n t r a t i o n approaches 100 at.%. 2.3. DSA measurements and results 2.3.1. Measurements of the F(r) values In the D S A measurements, the velocity of recoiling nuclei at the m o m e n t of the y-ray emission depends on the stopping power of the slowing down material. The c h a n g e in the velocity due to changes of the stopping conditions can be o b t a i n e d from the F-factor, which is the ratio between the recoil atoms velocity c o m p o n e n t along the b e a m direction a n d the original velocity. H o w

252

J. Keinonen et al. / Local densiO' change of a metal backing

Table 2 Summary of the FO') measurements and mean lifetimes.

Ep

E×

F( ~") "1

(MeV)

Ev (keV)

Stopping medium

(keV)

Backing

(%)

(fs)

22 Ne(p, y)23Na

1005

2.64

2640

Mo

0.81 1.73 5.9 10.8 27.0 25.8

35.6 _+0.9(0.6) ~') 34.5 _+0.9(0.6) ~i 34.7_+0.5(0.3) 35.4_+0.5(0.3) 39.4+0.7(0.4) 38.9 4__0.7(0.4) adopted value

120+ 13(4) 120_+ ]3(4) 120_+ 13(4) 120 _+ 13(4) 117_+ 13(3) 117_+ 13(3) 119+ 5

2VAl(p, y)28Si

2490

4.62

2838

Mo

8.5 20.4 48.2 83.3

56.5_+ 1.7(1.1) d) 54.0_+ 1.7(1.1) 62.7 _+ 1.4(0.9) 69.0 + 1.3(0.9)

72_+ 73_+ 76+ 73+

9(5) 9(5) 9(5) 9(5)

Ta

7.8 22.1 49.3 8t.5 100

49.1 +2.0(1.3) 48.8_+ 1.7(1.1) 53.2+ 1.3(0.9) 70.2_+ 1.5(1.0) d) 73.6 + 0.7(0.5) d 1 adopted value

75+ 77_+ 75 + 63_+ 70 _+ 72+

9(5) 9(5) 9(3) 9(3) 9(3)

Reaction

~') b) I d)

The The The The

~o

2o

Na in Ne÷Mo

30

(a)j///

~

70f Si in A [ ÷ M o ~

&O

(b)

30~

70~ Si in AL.Ta 60

~0!

4

error limits shown are absolute errors. The relative accuracy between different measurements is given in parenthesis. error limits shown are absolute errors. The statistical error limits are given in parenthesis. value used in the deduction of the stopping parameters f~ and f j e t i m e value used in determining the experimental stopping parameters, see the text.

22NeCONCENTRATION(AT.%)

38

Maximum implant concentration (at.%)

,,r b )

(a) ~ ~ - ~

_ + ~%y..~--~

~fJ

"--'c~/---.

d i f f e r e n t a m o u n t s o f i m p l a n t e d target m a t e r i a l N e or Al effect t h e F ( ~ ) value, is g i v e n in table 2 a n d i l l u s t r a t e d in fig. 4. T y p i c a l D S A m e a s u r e m e n t s are s h o w n in fig. 5. T h e F(~') v a l u e s were m e a s u r e d for t h e 2.64 M e V s t a t e in 2 3 N a a n d for t h e 4.62 M e V s t a t e in 2~Si. T h e i r l i f e t i m e s [21] -r(2.64) = 100 _ 20 fs a n d -r(4.62) = 63 _+ 6 fs a r e in t h e region w h e r e the F(~') v a l u e s o b t a i n e d t h r o u g h t h e 22Ne(p, y ) 2 3 N a r e a c t i o n at Ep = 1005 k e V a n d t h r o u g h t h e 27Al(p, y)288i r e a c t i o n at Ep = 2490 k e V are m o s t s e n s i t i v e to c h a n g e s in t h e s l o w i n g d o w n c o n d i t i o n s . T h e y - r a y s p e c t r a were r e c o r d e d with a P G T 110 c m 3 G e ( L i ) d e t e c t o r at a n g l e s o f 0 ° a n d 90 ° to t h e b e a m a n d at a d i s t a n c e o f 7.5 c m f r o m t h e target. T h e e n e r g y r e s o l u t i o n o f t h e d e t e c t i o n s y s t e m w a s 2.0 k e V at E v = 1.3 M e V a n d 3.1 k e V at E v = 2.6 M e V . T h e y - r a y s p e c t r a were s t o r e d in a n 8 K m e m o r y . T h e stability o f t h e s p e c t r o m e t e r w a s c h e c k e d with a 2°8T1 y - r a y s o u r c e a n d t h e 4 ° K l a b o r a t o r y b a c k g r o u n d . T h e c o r r e c t i o n s for t h e solid a n g l e a t t e n u a t i o n were t a k e n into a c c o u n t u s i n g p r i m a r y y - r a y t r a n s i t i o n s . T h e d i s p e r s i o n w a s 0.79 keV/channel.

,'0o2 27AICONCENTRATION(AT.%) Fig. 4. The FO- ) values measured for different 22Ne targets in Mo and 27A1 targets in Mo and Ta: The dashed lines show the theoretical F(T) values in the case where the implants occupy

substitutional lattice sites in the host material [curve (a)] or interstitial lattice sites [curve (b)]. The solid lines show the theoretical FO- ) values of the present empirical model for the local subsurface density in the host.

J. Keinonen et aL / Local densi(y change of a metal backing i

E

i

i

i

taken into account by using the expression

22Ne(p,1)23Na 2000

Ep=1005keY /7 ~',, 26/+0 - - 0 keY //; ",~'~-~"~ /,'

./,,'

ooo

+

#

',

',

/,,

,,

2000I- o 0.81at.°/o / ° 25.8 at. %

+ I 1000

U = ( N - ' / 3 / f n )llog R I,

o O,=O \\

//

°\\ \t

~,/ ~ //' ',~

t

Oz:90*

/ II,

o J

3290

~,

t

3300 CHANNEL NUMBER

Fig. 5. The peaks of the 2640 keV "/-rays from 23Na recoiling in a Mo backing. The solid curves are the best fits for the 90 ° and 0 ° lineshapes with fn= 0.78+0.07 and fe = 1.00+0.17. The dashed curves correspond to "/-ray peaks of the primary transitions and illustrate the case where the emitting nuclei have the maximum velocity. At 90 °, where the lineshape is very sensitive to the solid angle, the solid angle subtended by the detector was limited to 4 ° in the horizontal plane with a lead collimator and by using the target-detector distance of 15 cm. At 0 ° the lead shielding was not necessary. The dispersion is 0.79 keV/ch. The intensity obtained with the 0.81 at.% 22Ne target at 90 ° is for the normalization multiplied by a factor of 1.9.

2.3.2. Stopping powers and D S A analysis The stopping power of the slowing down material is now given by the sum of the nuclear (n) and electronic (e) stopping power in the following way: (d~)

....

=fn(~)n'+'fe(dE]LSS dp ]e

'

253

(4)

where energy ~ and range P are given in the reduced units of the LSS theory [22]. Instead of using the analytical form given in the LSS theory for the uncorrected nuclear stopping cross section, the analysis was carried out by Monte Carlo calculations, where the scattering angles of the recoiling ions are directly derived from the classical scattering integral and the i n t e r - a t o m i c i n t e r a c t i o n is d e r i v e d f r o m the T h o m a s - F e r m i potential. Thus, the correction factor fn does not include the corrections which are needed when the analytical, approximative form of the nuclear stopping cross section is used. The stopping parameter f . is

(5)

for the distance between successive collisions. R is a random number (0 < R < 1) and N is the atomic density of the stopping material. In this method it is possible to correct N for the experimentally known concentration distribution of the implanted target nuclei. In the case of a composite stopping material, it is possible to take into account the correction parameters fo and fe for the nuclear and electronic stopping power, respectively, in each collision of the recoiling atoms with a host atom or with an implanted target atom. In this case, the random number R is generated before each collision and the collision is taken into account only if 0 < R ~
J. Keinonen et al. / Local density change of a metal backing

254

of Z~-atoms. Thus, it was assumed that the adoption of the values fn =f~ = 1.0 _+ 0.2 is an acceptable approximation in the present DSA analysis. It should be emphasized that, due to the low Ne concentrations (less than 27 at.%) the uncertainty in the description of the N a - N e scattering has a negligible effect in the F(~') values calculated; A F ( ~ ) is in all cases less than 0.2% for Afn = Afe = 0.20. The relevant data for description of the stopping of the recoiling 28Si in Ta were taken from an earlier study [24], where the experimental stopping parameters fn = 0.67 + 0.05 and f~ = 1.00 + 0.15 had been determined for 27A1 recoiling in Ta. On the basis of our systematic range studies [17] for AI in Mo and Ta, the stopping parameters f , = 0.61 + 0.12 and f~ = 1.0 + 0.2 with enlarged error limits were used in describing the slowing down of 28Si in Mo. These values were found to give the best fit for the F ( z ) and lineshape data of the 2838 keV y-ray in 28Si measured with the 8.5 at.% AI --* Mo target (table 2). By using the present F ( , ) value of 73.6 + 0.7% obtained for the 2838 keV y-ray in 28Si recoiling in pure AI (table 2) and the range values given in ref. 23 for 29Si slowing down in AI, the stopping parameters f~ = 1.00 + 0.18 and f¢ = 1.0 + 0.2 were determined. The F(~') values obtained for the Ne targets with atomic concentrations of 0.81 at.% and 1.73 at.%, and

22Ne CONCENTRATION(AT.%) 10 20 30

o "<--~'._ _l -20 _ _ . . . .

-

o@

+

-20 ~'-~,o 20

i

Ca~"---__ t (b)~-

01-"~ --. ~ ~ ! -ao[

in ,£.o q

-

Sl

in A[+ Ta

+

(a)'--, 20 40 60 80 100 27At CONCENTRATION (AT%)

Fig. 6. The dependence of the DSA lifetime on the implanted concentration: The dashed lines show the change of the lifetime value in the case where the implants would occupy substitutional lattice sites [curve (a)] or interstitial lattice sites [curve (b)]. For explanation of the solid line, see the text.

the experimental stopping parameters, yield the mean lifetime 120 _+ 9 fs for the 2.64 MeV state in 23Na. The F(~-) values (table 2) measured for the targets with the lowest A1 concentration in Mo (8.5 at.%) and Ta (7.8 at.%) and for the pure A1 target, yield a mean lifetime 72 _+ 5 fs in a DSA analysis where the above adopted stopping parameters are used. If the DSA analysis is now performed for the other F(~') values, assuming that the density of the slowing down material is not effected by the implants, the results deviate from the adopted values in the manner shown in fig. 6. It is clear that corrections for the local density changes must be included in the analysis.

2.3.3. Change in the local subsurface density If we assume that the implants Ne and A1 occupy substitutional lattice sites in the host materials Mo and Ta, as is expected on the basis of the Darken Gurry plot (subsect. 3.3), the F(~') value should increase as a function of the implanted concentration. For the dashed curve in fig. 4, which illustrates swelling of the Ne --* Mo target (a), the atomic density was assumed to be the atomic density of Mo (6.40 × l 0 22 a t o m s / c m 3 [16]) and Mo atoms were replaced by Ne atoms in accordance with the concentration. The experimentally known Ne distribution and the adopted stopping parameters were used in the F(~-) calculations. It can be seen in fig. 4 that, in order to reproduce the proposed lifetime ~- = 120 fs, the experimental F(~-) values should be much higher. For the A1 --* Mo and AI --~ Ta targets, the swelling was calculated assuming that the atomic density N ( z ) at depth z in the implanted material changes linearly as a function of the AI concentration c(z) from the atomic density of Mo (n2) or Ta [n 2 = 5.53 X 10 22 a t o m s / c m 3 (ref. 16)] to that of A1 In I = 6.02 x 10 22 a t o m s / c m 3 (ref. 16)] according to the following formula: N(z)=c(z)n

a+ [1 - c ( z ) ] n

2.

(6)

The experimentally known distributions of AI concentrations and the adopted stopping parameters were used in the calculations of the swelling limits (a) in fig. 4. It can be seen that the experimental F(-r) values should again be higher in order that the adopted lifetime could be reproduced. On the other hand, if we assume that the implants occupy only the interstitial lattice sites, the F 0 " ) value should decrease as a function of the implanted concentration. The atomic density as a function of the implanted concentration is then given by

U(z)=n2/[1 -c(z)].

(7)

In calculating the limits (b) in fig. 4 for the F(~') values the depth distributions of the implants and the adop/ed stopping parameters were used. It can be seen in fig. 4 that the experimental F(~-) values at low concentrations are much closer to the curve correspond-

J. Keinonen et al. / Local density change of a metal backing

ing to an increase in density than to the curve for swelling. Thus, swelling does not provide an acceptable explanation for the change of the local density in the target irradiated with heavy ions contrary to what is asumed to be the case for light ions (refs. 8-10). In order to have consistent lifetime values in the DSA analysis, the change of the F ( r ) value as a function of the atomic concentration was reproduced with a simple model where only one parameter was adjusted, namely the concentration corresponding to the maxim u m atomic density. It was assumed that the number of atoms per unit volume which occupy the interstitial lattice sites is U i ( z ) = max{0,

l-c(z)/2Co)C(2)Ut(z)

c ( z ) n , ( z ) + [l - c(z)ln2(z)

1-c(z)/2Co)C(Z )"

(9)

The atomic densities calculated with this expression are illustrated in fig. 7. The fit of the parameter c o indicated that the maximum density of ~he Ne--+ Mo target is reached at a concentration of about 13 at.%; for the AI ---, Mo target the maximum occurs at about 23 at.% and for the A1--+ Ta target, at about 35 at.%. By means of this parametrization of the atomic density, the D S A analysis yielded extremely consistent results for

22Ne CONCENTRATION(AT.%) 0 20 z.0 60 80 100 ----7 I q--~ ~ I 7 ~ Ne ~Mo (a) N= nMo nMo[ .

.

.

.

.

.

.

.

6 i, c

~

7L///

,_,

i

~

i

taJ D

*-"

~ /I"I \

7

aJ60keV Ne+~ Mo 4ZkeV Na+~'Ne÷M°

\

~2c82. ~ot I ~c)~~lr=llgf~ o_

/It

\

\

•) ~=°fS

(8)

where c o is a free parameter to be determined and Nt(z) is the total atomic density; Nt(z ) = N(z)+ Ni(z), where N(z) is the atomic density of the host material. The total atomic density can now be given by Nt(Z)-l-max{0,

255

100

20O DEPTH ( nm )

3O0

Fig. 8. The depth profile of the implanted 22Ne in Mo [line (a)]: The density, in units of g / c m 3, of the implanted area is shown in the upper part of the figure. The vertical line (b) indicates the depth at which the DSA measurements were performed. The depth profile of the recoiling nuclei at the emission of the y-rays, the dashed line (c), is the Monte Carlo simulation obtained with the present stopping data.

the F(~-) values obtained with different targets, table 2. The solid lines in fig. 4 illustrate the calculated F ( z ) values for different concentrations of the implants. The lineshape of the y-ray peak obtained in the DSA measurement describes the velocity distribution of the recoiling nuclei at the moment of the y-ray emission and thus includes detailed information on the slowing down conditions in the target. Fig. 8 illustrates the slowing down conditions during the flight of 23Na nuclei. When the variation of the density described by eq. (9) was taken into account in the DSA analysis, the Monte Carlo simulation shown in fig. 5 was obtained for the lineshape of the 2640 keV y-rays measured with the

i

(a, N=cnA[÷{1-C)riM° 9(Mo)= 10,2 g/cm 3

6'

nat

o3 z

b) ~

c~2CAI ~ Ta

'\

I[ 0

nA~

(a) fl 1

___

0

I

Co I

g ~1c

10p

a)100keV A[+~Mo 89keV Si+~Al+Mo

\

c)r=72fs

c)

~

20 /'0 6r0 80 100 27AI CONCENTRATION(AT.%)

Fig. 7. The atomic densities of the implanted targets. The curves shown are the predictions of the present simple model. They were used in the DSA analysis of different F(~') values.

J

i

100

\~.

I

200 DEPTH{ nm)

I

300

Fig. 9. The depth profile of the implanted 27Al in Mo [line (a)]: The density and the lines (b) and (c) are considered in the same way as in fig. 8.

J. Keinonen et al. / Local density change of a metal backing

256

y-E

23Na(2.641

17 g(fa)=16.6 g/cm3

~L z

2c-/

b) ~,

\

¢'0

~SENT

a)100keV A t * ~ Ta 89keY Si+~,-At+Ta

~ ~ ~l

>-

~c)

lo-2

b} "r: 0 fs

r=72fs

I

1o

~\c) ~\

L./I

~a)

ld 3 lOO

200 DEPTH ( n m )

300

Fig. 10. The depth profile of the implanted 27A1in Ta [line (a)]: The density and the lines (b) and (c) are considered in the same way as in fig. 8.

target where the m a x i m u m 22 Ne concentration was 25.8 at.%. The values of c o can be concluded to indicate those concentrations where implants produce such high strains in the lattice that its structure undergoes violent change towards disorder. Fig. 7 indicates alsQ that the inert gas Ne destroys the lattice structure more effectively than A1. It can also be seen that the lattice structure of Mo can be destroyed at lower doses than that of Ta. Due to the relatively low concentrations a n d small Z values of the implants, the local atomic densities at the saturation point c o have to be quite high in order to produce a significant effect in the F(~') value; the atomic density of the N e --, M o target increases by 7%, the AI ~ M o target by 13% a n d the A1 ~ Ta target by 23% (see fig. 7).

10-4

60

J

L r(fs) 100

,

1~0

180

1

Fig. 11. A plot of the weights of the 2.64 MeV level in 23Na vs. lifetime value. The weight of the measurement is taken to be (A'r) -2, where A~- is the quoted uncertainty. Two contours at %doptea +2(A~') are also shown.

density changes have to be k n o w n a n d taken into account in the D S A analysis. For the analysis of such measurements, the concentration limit c o should be studied experimentally. It can be concluded that the use of i m p l a n t e d targets in DSA m e a s u r e m e n t s d e m a n d s (1) experimental knowledge o n the correction for the cross section of the a t o m - a t o m scattering and (2) experimental knowledge on the slowing down conditions as modified during the p r e p a r a t i o n of the target.

2eSi(4.62)

3. Discussion 3.1. Dependence of the DSA lifetimes on the local density In figs. 4 and 6 it was shown how the F(I-) value a n d lifetime value change as a function of the implanted atomic concentration. The dashed lines in fig. 6 show how large an error is introduced into a lifetime, if the implants are assumed to produce swelling [curve (a)] or if they are assumed to increase the density of the host material (b). The solid lines indicate that, excluding any density changes, the correct lifetimes could be obtained for 23Na recoiling in M o up to a b o u t 14 at.%, for 28Si recoiling in M o up to a b o u t 25 at.% and for 28Si recoiling in T a up to a b o u t 35 at.%. According to the present model, the reason for these relatively high concentrations is that at low concentrations the effects due to the substitutional a n d interstitial implants cancel out. However, at higher doses, where measurements are easier to perform a n d the F(~-) values are more accurate, the

161 ENT

LU

10-~

10-

I 20

I

I t 60 ~(fs)

I 100

I

Fig. 12. A plot of the lifetime measurements of the 4.62 MeV level in 28Si. The weights are considered in the same way as in fig. 11.

257

J. Keinonen et al. / Local density change of a metal backing Table 3 A comparison of the lifetime values. Nucleus

State (MeV)

Mean lifetime (fs)

Ref.

Reaction

23Na

2.64

1194- 5 113_+ 6 94 _+ 1 4 146 _+12 a) 100 _+ 10 a) 363 _+60 80 1 0 0 _+40

present 2 26 27 28 29

22Ne(p, y)

200 _+90 95_+35 136_+20 b)

31 32 25

116_+ 4

adopted value

72_+ 4 57_+ 5 61 _+ 4 58_+ 10 42_+ 10 54_+ 10 39_+ 2 65_+12 c) 100_+ 12

present 1 33 34 35 36 37 38 39

25Mg(a, ny)

40

28Si(~, a'y)

2~Si

4.62

15 55 _+ 14 15 83+ -12 61 _+19 65_+ 5

23Na(p, P'7 )

30

12C(12C,p'f) 23Na(y~ 7)

27Al(p, y)

41 42

27A1(3He, d)

adopted value

al For the inclusion of the experimental stopping parameters in the reanalysis of the original F ( r ) value, see ref. 2. b) Resonance fluorescence method. c) Different methods of analysing the experimental F(~) values are given. The results vary from 45 to 75 fs. Since the new method presented in ref. 38 is erroneous, see ref. 43, the result of the X2 analysis is used here.

3.2. Comparison of the present and previous lifetime values

ever, the m e a s u r e m e n t s have been performed u n d e r widely varying conditions.

The lifetime of the 2.64 MeV state in 23Na a n d the 4.62 MeV state in 28Si have been measured several times. These earlier results, along with our measurements, are summarized in table 3 a n d displayed in figs. 11 a n d 12. In the figures the value of the weight of the m e a s u r e m e n t , on a logarithmic scale, is plotted as a function of the lifetime value. The weight is assumed to b e (zl~') -2 where A~- is the uncertainty quoted for the lifetime measurement. C o n t o u r s at + 2(A~-) are centered at the a d o p t e d lifetime value from table 3. The m e t h o d has been previously introduced by Alexander a n d Forster [4]. Except for the resonance fluorescence m e a s u r e m e n t [25] for the 2.64 M e V state in 23Na, all values given in the literature are o b t a i n e d with the D S A method. How-

3.3. Lattice sites of the implants W i t h the aid of the modified H u m e - R o t h e r y rules, the D a r k e n - G u r r y plots based on the size a n d electronegativity of atoms in i m p l a n t e d alloys have been used to predict the end position of an i m p l a n t e d atom. The empirical rule [11] based on experimental data states that: a metastable substitutional solution will be formed if the i m p l a n t e d species have (a) atomic radius within - 15% to 40% of the host radius a n d (b) electronegativity within + 0.7 of that of the host atoms. If we take the nearest n e i g h b o u r distance divided by two as the atomic radius, AI ( r = 1.43 ,~ [44]) comes well within the limits for the radius of M o ( r = 1.32 A [44]) a n d Ta ( r = 1.43 A [44]). The electronegativity of AI (1.5 [45]) is also

258

J. Keinonen et al. / Local densi O, change of a metal backing

within the limits relative to M o (1.8 [45]) a n d Ta (1.5 [45]). Thus, A1 should o c c u p y substitutional lattice sites in M o and Ta. This was, however, n o t the case in the p r e s e n t e x p e r i m e n t , fig. 4. A t high doses, the a p p r o a c h o f F ( r ) values to the s u b s t i t u t i o n a l i t y limit is obviously d u e to the a m o r p h i z a t i o n of the backing. In the case of inert gases the low electronegativity rules out substitutionality. Inert gases are also experim e n t a l l y k n o w n to o c c u p y only n o n - s u b s t i t u t i o n a l lattice sites [14]. This is seen at low doses also in the p r e s e n t work. A t the higher values o f the c o n c e n t r a t i o n , the F(~-) values a p p r o a c h the limit for substitutionality. This can also in this case be c o n c l u d e d to indicate the a m o r p h i z a t i o n of the backing. O n the o t h e r h a n d , the final p o s i t i o n s o f i m p l a n t s in n o n - e q u i l i b r i u m i m p l a n t e d systems have been s h o w n to d e p e n d strongly o n the d y n a m i c a l processes occurring near the e n d o f the range a n d n o p r e d i c t i o n s for the final sites can be given [14]. This implies, in a g r e e m e n t with the p r e s e n t results, that in each case a s e p a r a t e s t u d y is n e e d e d to d e s c r i b e the i m p l a n t e d i m p u r i t y - h o s t a t o m system. At high values of i m p l a n t e d doses, the o b v i o u s a m o r p h i z a t i o n of the host lattice m a k e s it also very difficult to p r e d i c t the local d e n s i t y of the system.

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