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IMPURITY-DEFECT INTERACTIONS
CHAPTER
9
IMPURITY-DEFECT INTERACTIONS
9.1
Introduction
Mechanical properties of metals are determined by the addition of elements and defects. The influence of elemental additions results from their microscopic state within the crystal matrix—such as substitutional, interstitial, precipitated, or defect trapped. The properties of metals depend on whether impurities are on substitutional or interstitial sites, whether they form precipitates or are trapped by defects. For example, interstitial atoms such as carbon in steel interact strongly with the stress field of a dislocation and tend to prevent its motion, thus strengthening the steel (solution strengthening). The precipitation of impurities, such as Cu in Al, can also impede the motion of dislocations (precipitation hardening). Segregation of impurities at grain boundaries, on the other hand, can lead to embrittlement, and such Sb segregation is one of the mechanisms that led to crack development in the Liberty ships. Commercial alloys usually contain a number of elemental additions, and such elements when incorporated into the host metal lattice are referred to as solutes. In addition, impurities are often unavoidably present and their influence must be controlled. For example, hydrogen is a species that leads to brittle fracture of high strength steels. Hydrogen can be readily introduced from external sources such as corrosion reactions, surface plating processes, or rapid diffusion from gas storage systems. Other undesirable impurities, such as the embrittling species P, A s , Sb, and Sn may be present in the original alloy fabrication. On the other hand, if defects trap embrittling species, their flow and accumulation at grain boundaries or other failure points may be impeded. 193
194
9.
IMPURITY-DEFECT INTERACTIONS
In most materials, vacancies, interstitials, and their clusters can inter act strongly with impurities. The influence of vacancies and interstitials can be distinguished by their temperature of migration. Their interactions with impurities can be monitored with channeling when the interaction results in a displacement of the impurity from normal lattice sites. In metals, interstitials generally have a lower activation energy of motion than do vacancies, so that appreciable migration of interstitials can occur at temperatures where vacancies are essentially immobile. For example, in Al, resistivity and positron annihilation measurements show free inter stitials migrate at = 4 5 Κ and vacancies at = 2 0 0 K. In this chapter w e discuss three different categories of defect interac tions in metal crystals: (1) irradiation of substitutional alloys to study metal-solute interactions with vacancies and interstitials, (2) interstitial gas atom interactions with point defects, and (3) defect accumulation during channeling analysis. Defect-impurity interactions can be studied since controlled numbers of interstitials and vacancies can be introduced by light ion irradiation, and solutes or impurities can be introduced into the sample by alloying, diffusion, or ion implantation.
9.2
Metal-Solute Interactions with Interstitials and Vacancies
Solute atoms in metal crystals can trap mobile defects. The size of the solute atom is one factor in determining the type of defect that is trapped. In general, small solute atoms trap interstitials of the host lattice, whereas large solute atoms trap host lattice vacancies, thereby minimizing the strain energy in the crystal. Swanson, H o w e , and their colleagues at Chalk River (Swanson et al., 1974, 1976, 1980a,b; Swanson and H o w e , 1979) carried out a series of investigations in which channeling effect measurements were used to monitor the lattice site of the solute atoms. By following the solute atom movement off and on lattice sites, the formation or annihilation of defect impurity centers can be observed. Measurements as a function of irradia tion and anneal temperatures allowed the relative role of vacancies and interstitials to be determined. The experimental procedure was simplified because the defects were created by radiation in situ using a beam of the same ions as were used for the channeling analysis. Studies of the irradiation of Al single crystals containing different sol ute atoms show that size is an important factor (Table 9.1). In fee metals such as Al, self-interstitial atoms have predominantly a split configuration in which two atoms symmetrically straddle one lattice site (Fig. 9.1). This dumbbell configuration has a (100) orientation in Al. Small solute atoms
9.2
METAL-SOLUTE INTERACTIONS WITH INTERSTITIALS AND VACANCIES TABLE Trapping
9.1 Configurations
Solute atom Cr Mn Fe Cu Zn Ag Ga Ge Sn Mg In
195
in Irradiated,
Dilute Aluminum
Trapping configuration -0.57 -0.47 —0.38 -0.38 -0.06 0.001 0.05 0.13 0.24 0.41 -0.21
0
(100) m.d. <100> m.d. m.d. (100) m.d. (100) m.d. (100) m.d. ~ ( 1 0 0 ) m.d. (100) m.d. v.t. v.t. v.t. e
e
Alloys
a
Defect to form center*
i i i i i i i V V V
° Adapted from Swanson et al. (1980a). A V / V is the expansion of the host lattice caused by alloying, expressed in atomic v o l u m e s per solute atom. m.d. is the mixed-interstitial dumbbell, and the crystallographic orientation of the dumbbell is given where k n o w n ; v.t. is vacancy trapping leading to a s o l u t e - v a c a n c y cluster. H o s t lattice defects: i, interstitial and v , v a c a n c y . Shallow trapping of Al interstitials also occurs for these solutes at l o w temperatures. 6
c
d
e
such as Mn can lower the energy of the system by trapping a selfinterstitial dumbbell to form mixed dumbbells. Large solute atoms such as Sn in Al can lower the strain energy by capturing vacancies to form a vacancy trap configuration.
FIG. 9.1 Schematic for the fee Al crystal lattice of (a) a s o l u t e - h o s t atom split interstitial (mixed-dumbbell) of (100) orientation, (b) a self-interstitial in a second (100) dumbbell configuration, and (c) a substitutional solute atom ( O , Al atoms; · , solute atoms).
196
9.
IMPURITY-DEFECT INTERACTIONS
Channeling measurements are sensitive to the presence of the mixed dumbbells and give the magnitude of the solute atom displacements in the trapping configuration (Matsunamief al., 1978). Figure 9.2 shows an angu lar scan for an Al crystal containing 0.09% Mn solute atoms that was irradiated at 70 Κ with H e ions. The presence of a peak in the Mn signal indicates that the Mn atoms have moved off substitutional sites into the central region of the channel. The origin of the peak in the Mn signal for the (110) scan is evident in Fig. 9.3, which illustrates the movement of the Mn atom toward the center of the (110) channel for a (100) split interstitial configuration. The shad ing in the figure indicates the boundaries of one channel. For channeling along the (100) axial direction, the dumbbell is displaced along the bound aries of the channel so that central flux peaks in the angular scans are not observed. For nonpreferential orientations of the (100) dumbbell, two1 . 1
I 0
0 9
0 8
ο
0
7
UJ
α
0.6
UJ
^
ζ
0. 5
a.
ο
0 4
0 3
0 2
0 1
0 0 -2
- I
0
ANGLE FROM < I I 0 >
DIRECTION
1 (deg)
FIG. 9.2 Angular scan for the normalized backscattering yield of 1-MeV H e incident near the < 110) axis of Al (O) containing 0.09 at. % of Mn ( · ) at 40 Κ after irradiation at 70 Κ by 7 χ 1 0 H e / c m at 0.5 MeV. [From Swanson and Maury (1975).] 15
2
9.2
METAL-SOLUTE INTERACTIONS WITH INTERSTITIALS AND VACANCIES
(a)
(b)
197
(c)
FIG. 9.3 Schematic of solute atom displacements upon (100) mixed-dumbbell forma tion in the fee Al lattice for various channeling directions: (a) < 110) axial channel for which all atoms are displaced into the channel; (b) (100) axial channel for which two-thirds of the atoms are displaced into the channel; (c) {100} planar channel for which one-third of the atoms are displaced into the channel. [Adapted from M. L. Swanson (unpublished).]
thirds of the Mn atoms will be displaced perpendicular to and one-third will be displaced along the (100) rows that steer the channeled particles. This latter one-third contribution will have an angular scan like that of host Al. For the {100} planar channel only one-third of the planar atoms are displaced into the channel with the other two-thirds remaining in the plane. The dynamics of mixed-dumbbell formation and annihilation depend on temperature. The self-interstitials are formed directly by irradiation with the analysis beam. At temperatures where the self-interstitial dumbbell migrates, motion to the solute atoms can occur and trapping of the interstitial results in the formation of a mixed dumbbell. At higher temperatures, where vacancies become mobile, the vacancies can migrate to the mixed dumbbell, annihilating these defects and leaving a substitu tional solute atom. This sequence of mixed-dumbbell formation and an nihilation with increasing annealing temperature is shown in Fig. 9.4 for four different solutes in Al. For these solutes, the relative fraction of displaced atoms rises at about 45 Κ where the self-interstitials become mobile in Al. The fraction of displaced atoms decreases toward zero around 200 K, correlating closely with the onset of vacancy migration in Al. The four solutes w h o s e behavior is illustrated in Fig. 9.4 are similar in that the atomic volume per solute atom is comparable to or less than that of Al (Table 9.1). In contrast, for Sn the atomic volume is substantially greater than that of the host Al crystal. The Sn atoms m o v e off substitutional sites, as shown in Fig. 9.5 after irradiation and annealing at temperatures ( > 2 0 0 K) where vacancies are mobile in Al. These channeling results indicate that vacancies cluster on Sn in Al, consistent with other irradiation studies of oversized solute atoms in Al crystals (Swanson et al., 1980a,b).
198
9.
IMPURITY-DEFECT INTERACTIONS
0
40
80
120 160 200 2 4 0 2 8 0
ANNEALING TEMPERATURE (K) FIG. 9.4 Relative fraction of displaced solute atoms (Ag, M n , Cu, and F e in Al) mea sured at 3 0 - 4 0 Κ after irradiation and 10-min isochronal annealing to the indicated tempera tures. Measurements were made along the Al (111) channel for Mn and the (100) channel for A g , Cu, and F e . The dashed line corresponds to the normalized irradiation-induced increase in dechanneling in the Al lattice for the Al-0.13 at. % Cu crystal. [From Swanson etal. (1978).]
The temperature dependence of defect trapping and annihilation for the undersized Ag and oversized Sn solute atoms is contrasted in Fig. 9.6. In the case of Sn, the increase in the number of displaced Sn atoms occurs in the temperature regime where the Ag atoms are moving back onto
1.2
He IRRADIATION Ί + 2 2 0 Κ ANNEAL
ANGLE FROM <100> DIRECTION (deg) FIG. 9.5 Angular scan for the normalized backscattering yield of 1-MeV H e incident near the <100) axis of Al containing 0.3 at. % Sn after 1.3 χ 1 0 H e / c m irradiated by 1-MeV H e at 35 Κ and subsequent annealing to 220 Κ ( Ο , Al; · , Sn). A l s o shown is the aligned Sn yield before the 220 Κ anneal and also before the H e irradiation. [From Swanson et al. (1980a).] 15
2
9.2
METAL-SOLUTE INTERACTIONS WITH INTERSTITIALS AND VACANCIES
(ο)'
1
'
I
'
199
τ
Αί - 0.1 at. % Ag Ο -I LU
0.4
\
>
a
0.2
g
0.0
Ζ Ο
0.8
UJ Ν
V I
<110>
ι
,
I
.
ι
(b) Ai - 0.04 at. % Sn
UJ
ζ ζ < ζ
ϋ
ο.4
μ <110>
0.0 1.0
l
lie)
Af
>
Ι Ο)
\ γ
^/STAGE I
(INTERSTITIAL MOTION)
^ /
Q 0.0
I
/STAGE III /(VACANCY MOTION)
I 100
200
300
ANNEAL TEMPERATURE (K) FIG. 9.6 Comparison of annealing data in ion-irradiated Al and dilute Al alloys for (a) mixed-dumbbell formation and annihilation for Ag in Al as measured b y the relative A g channeling yield; (b) S n - v a c a n c y cluster formation for Sn in Al also as measured by the relative Sn channeling yield; and (c) the defect annealing stages in Al as measured b y the residual resistivity. [Adapted from Swanson et al. 1980a).]
substitutional sites. This different temperature dependence indicates that the interstitials interact only weakly with the oversized Sn atoms, whereas vacancies have a strong interaction. Figure 9.6c shows the resistivity recovery stages for point defect motion in pure aluminum. This illustrates the close correlation between stage I interstitial motion at 45 Κ with mixed-dumbbell formation and stage III vacancy motion at 200 Κ with formation of S n - v a c a n c y clusters. The structures of the S n - v a c a n c y clus ters involve large Sn displacements as indicated by the flux peak in Fig. 9.5; however, the detailed nature of the structures is not well established.
200
9.
IMPURITY-DEFECT INTERACTIONS
These structures are believed to involve various aggregates of two to four vacancies with single Sn atoms. In analogy to the annihilation of mixed-dumbbell interstitials by the introduction of vacancies, the Sn-vacancy clusters can be annihilated by the introduction of interstitials (Swanson et al., 1980). Irradiation at 35 Κ followed by annealing at 220 Κ introduces mobile vacancies and results in the formation of the complex, while irradiation at 70 Κ results in the release of mobile interstitials and is observed to annihilate the complex. Thus w e see for Al that oversized solute atoms tend to trap vacancies, whereas similar or undersized solute atoms tend to trap host lattice inter stitials (Table 9.1). The demonstration that such c o m p l e x e s can be both formed and annihilated by the selective introduction of mobile vacancies or interstitials using ion beams provides a powerful additional tool for the understanding of solute-defect interactions in crystals. This is possible because ion channeling provides a way to determine the number of solute atoms that remain on their normal substitutional lattice sites and the num ber that have formed solute-defect complexes. The same techniques can be applied to impurities that normally occupy interstitial positions in metal host lattices, and these will be illustrated in the following section by channeling studies of the impurity hydrogen. In this case much less is known about the impurity-defect configurations, and so the channeling studies have given more emphasis to determining the lattice location of the hydrogen. 9.3
Hydrogen Trapping at Point Defects in Metals
Atoms of normally gaseous materials (gas atoms) interact strongly with vacancies in metals (Picraux, 1981). Hydrogen is probably the gas atom specie of greatest interest in metals; it is important to fisson and fusion reactions, as well as other energy-related technologies. Channeling is one of the few techniques that gives the lattice site of hydrogen and allows the study of the defect-hydrogen interactions. For heavier gas atoms (e.g., Xe) Mossbauer spectroscopy or other hyperfine techniques can often be utilized to probe the local environment around the atom; however, these techniques are not applicable for hydrogen. Ion implantation provides a convenient way to controllably introduce gas atoms and lattice defects in metals. After implantation, hydrogen usually occupies an interstitial site. An example of a channeling angular scan from implanted deuterium in Al is shown in Fig. 9.7. The strong flux peak for (100) axial and for the planar orientations is indicative of hydro gen location in the center of the channels. The sketches of angular scans for different channeling directions given in Fig. 9.8 show that the two
-1
Ο
+1
FIG. 9.7 Angular scans for the normalized backscattering and nuclear reaction yields from Al implanted with 1 0 / c m , 5-keV D at 33 Κ using a 730-keV H e beam. [From Bugeat et al. (1976).] 1 5
2
3
OCTAHEDRAL
FIG. 9.8 Schematic of projected positions in various channels for the tetrahedral and octahedral interstitial sites in the fee Al crystal lattice. The corresponding channeling angu lar scans e x p e c t e d are indicated by the dashed line for the interstitial site and the solid line for the host lattice signal. [From Bugeat et al. (1976).]
202
9.
IMPURITY-DEFECT INTERACTIONS
primary interstitial sites in the fee lattice give qualitatively different angu lar scans. Comparison of Figs. 9.7 and 9.8 show that the implanted deuterium is predominantly on tetrahedral interstitial sites. This site loca tion at 35 Κ in Al was found to be stable for anneal temperatures up to ~ 3 0 0 K, suggesting a defect-trapped configuration. Trapping is inferred since diffusion measurements indicate hydrogen would otherwise b e c o m e sufficiently mobile at lower temperatures for it to migrate to surface sites and to depths deeper than that probed by the channeling analysis. In this case implantation and anneals at various temperatures suggested that the implanted deuterium was trapped by vacancies introduced by the deuterium implantation (Bugeat et al., 1976). Other channeling studies have suggested that implanted hydrogen and deuterium may be trapped by vacancies in metals (Bugeat and Ligeon, 1979; Myers et al., 1979; Picraux, 1981a). For typical 10-30 keV Η and D implantations, there are about 10 vacancies and interstitials for every implanted atom. Because of its interstitial location, hydrogen is mobile at Pd(D) AXIS 1 1 1
1
1—ι
ANGLE
1
1
1
1
1—ι
OCTAHEDRAL SITE
(deg)
FIG. 9.9 Angular scans for the normalized H e channeling yields near the < 100) axis of Pd implanted with 5 χ 1 0 / c m , 10-keV D after implantation at 25 Κ and annealing to the various temperatures. The e x p e c t e d angular scans for the octahedral and tetrahedral intersti tial sites in fee Pd are sketched to the right. [Adapted from Bugeat and Ligeon (1979).] 3
1 5
2
9.3
HYDROGEN TRAPPING AT POINT DEFECTS IN METALS
203
lower temperatures than the vacancy. At some range of intermediate temperatures hydrogen may be trapped by the vacancy. The interstitial site of the mobile and trapped hydrogen may differ. An example believed to correspond to these different sites is shown in Fig. 9.9 for deuteriumimplanted Pd. For the as-implanted case and for anneals up to 80 Κ a significant fraction of the deuterium is near the octahedral site. These channeling measurements are consistent with site assignments by neutron scattering measurements made on high concentrations of hydrogen dif fused into Pd without the introduction of defects. After the samples are annealed at a slightly higher temperature between 80 and 90 K, the deuterium becomes sufficiently mobile to migrate to traps and a significant change in the lattice site is observed. From the flux peak it is apparent that the majority of the deuterium is trapped in the vicinity of the tetrahedral site (Bugeat and Ligeon, 1979). The hydrogen and deuterium need not be trapped exactly in one of the high symmetry interstitial cavities. For lower symmetry positions a num ber of angular scans along different orientations together with a detailed comparison with theoretical calculations (Chapter 3) are required. An example of this procedure is given in Fig. 9.10 and 9.11 for the case of deuterium-implanted Fe (Meyers et al. 1979), a bcc metal. In this case the deuterium was implanted at low temperature and annealed at sufficiently high temperatures so that all the deuterium was trapped. All the angular y
DISTORTED O-SITE I
Fe(D)
1
1
1
1
1
2
4
O-SITE
T-SITE
1.2 1.0
ΔΔΔ
Q uj >·
0.8
WW
UJ \~L 0.6 <
UJ *
0.4 0.2
<100> AXIS 1 -4
ι .2
0
TILT ANGLE (deg)
FIG. 9.10 Angular scans for the normalized H e channeling yields near the (100) axial direction of F e after implantation with 1 x 1 0 / c m , 15-keV D at 110 Κ and annealing to 200 K. The corresponding e x p e c t e d scans are s h o w n for various sites in the bcc F e crystal lattice. The distorted O-site is shown in Fig. 9.12 and the calculated angular scan for this site is shown by the dashed line on the left. [Adapted from Myers et al. (1979).] 3
1 6
2
204
9.
IMPURITY-DEFECT INTERACTIONS
DISTORTED O-SITE
OSITE
T-SITE
Fe(D)
1
1
6 = 0.3 _j
1
1
I
ι
r
A I
-1
L
0
1
(112) PLANE
UJ 0.2L1 -1
I
I
1
0 TILT ANGLE (deg)
1—l 1
FIG. 9.11 Angular scans near the {100} and {112} planar directions from D-implanted F e under the same conditions as Fig. 9.10. The dashed lines for the {100} angular scan are calculated for the distorted O-site shown in Fig. 9.12. [Adapted from Myers et al. (1979) and Picraux (1981a).]
scans could be explained assuming that the deuterium occupied a single unique site upon trapping that is displaced along the (100) direction to ward the nearest neighbor Fe lattice site, as shown in Fig. 9.12. The magnitude of the displacement w a s found to be 0.4 A, based primarily on the {100} planar scans (Fig. 9.11). The presence of the vacancy as the trap entity for this deuterium site in Fe can only be inferred, since the sur rounding lattice atom configuration cannot be determined by channeling. However, both experimental and theoretical results strongly point to the isolated vacancy as the trap entity (Myers et al., 1979; Picraux, 1981a). For detailed site determinations it is often difficult to assess the uniqueness of the interpretation based on angular scans along one to two directions. One reason is that the impurities may be distributed among different sites. For example, a combination of tetrahedral and substitu tional sites could produce angular scans qualitatively similar to those obtained along (100) axial and (100) planar directions. In these cases certain planar scans can be valuable in establishing symmetry require-
9.4
ANALYSIS BEAM-INDUCED DAMAGE
205
VACANCY D - SITE [001 010]
Fe
1100]
χ OCTAHEDRAL SITE + TETRAHEDRAL SITE
FIG. 9.12 Schematic of the D location in F e determined from the angular scans of Figs. 9.10 and 9.11 ( x , octahedral site; + , tetrahedral site). [From Myers et al. (1979).
ments for the site. For example, the {112} planar orientation would be expected to give a dip for combinations of tetrahedral and substitutional sites and a flux peak for the preceding distorted octahedral site (Picraux, 1981a). The observed peak in the scan (Fig. 9.11) is thus consistent with the site assignment shown in Fig. 9.12. 9.4
Analysis Beam-Induced Damage
From the solute trapping and hydrogen defect studies it is shown that the analysis beam creates vacancies and interstitials in the crystal. This beam-induced disorder can cause an increase in the aligned yield, an increase in the surface peak, an increase in the dechanneling rate, and, as shown in the previous sections, a movement of impurities off or onto lattice sites. In most cases of channeling analysis the beam-induced de fects do not play a role in determining disorder distributions or impurity site locations. Although one is bombarding a crystal with ions of MeV energies that are capable of producing a significant number of defects, such effects have not seriously hampered channeling analyses. There are several reasons for this insensitivity of channeling analysis to beaminduced defects. First, defects are created along the whole track of the beam with the maximum in nuclear stopping, and hence defect produc tion, at the end of the range some microns below the surface. The second reason is that the number of defects created in the near surface region during a single alignment measurement usually is relatively small com pared to the concentration of defects required in radiation damage studies analyzed by channeling. One can estimate the amount of beam-induced damage using the fun damental relations that govern ion-solid interactions. The large angle scat-
206
9.
IMPURITY-DEFECT INTERACTIONS
tering events that are the measured quantity in channeling experiments correspond to large energy transfers to the scattering atom, causing it to recoil energetically from its lattice site. For example, a 180° scattering of 1.0-MeV H e from Si transfers —440 keV to the Si atom, whereas the binding energy of the atom to its lattice site is —14 eV. Using the Ruther ford cross section w e can determine the total cross section for energy transfers greater than the lattice binding energy. The differential Rutherford cross section for transferring an energy Τ to a scattering atom is άσ* dT
4 π (ZAe*V 4M,M Ε \ 4 / (Mi + M )
1 T
2
2
f Q 2
2
Then the total Rutherford cross section σ (Ε > E ) for transferring an energy greater than the displacement energy £ is Η
D
D
σ (Ε >Ε )~ Η
Ό
[—^-j
Ύ
( M i
+
M i )
2 γ
υ
(9.2)
For 1.0-MeV He in Si ( £ = 14 eV) w e find σ (Ε > Ε ) = 3.9 χ 1 0 " c m . This is an overestimate of the actual displacement cross section since the Rutherford cross section is based on an unscreened potential. A more accurate screened Coulomb potential results in a smaller cross section; for example, for 1.0-MeV H e in Pt the cross section is reduced to one-half of the σ value. The average energy Τ transferred to a recoiling atom is 20
D
Η
2
Ό
κ
l =
L
Γ 'max
(9.3a)
d
or r - £
D
l n ( ^ ) *
(9.3b)
where 7 is the maximum energy transferred. For 1.0-MeV H e in Si Τ = 144 eV, which is = 1 0 £ . Such a low energy recoiling atom deposits nearly all of its energy into atomic displacements, thereby multiplying the num ber of displaced atoms due to this one hard collision. Thus for MeV H e the recoiling lattice atoms are the primary source of displacements. A method to estimate the total number of displaced atoms considers that portion of energy lost by the penetrating H e ion into nuclear pro cesses. This estimate then includes recoil contributions. A convenient way to apply this is given by the Kichin-Pease formulation of the dism a x
D
9.4
207
ANALYSIS BEAM-INDUCED DAMAGE
placement probability. The cross section is given by _
aS (E) n
where S (E) is the nuclear stopping power and α is a constant between 0.5 and 1. Using a value of S (E) of 0.088 x 1 0 ~ e V - c m (Johnson and Gibbons, 1970) for 1.0-Me V H e in Si, σ = 3 χ 1 0 ~ c m , t w o orders of magnitude greater than σ (Ε > Ε ) \ The Kichin-Pease formulation yields a reasonable estimate for atomic displacement due to nuclear collisions. It is these nuclear processes that are the primary mechanisms leading to atom displacements and the resulting defect production in metals and semiconductors. These defects can (1) interact with impurities in the host crystal, and (2) accumulate in the host crystal, eventually affecting the channeling process in the host crystal. We now consider what limits the preceding theoretical estimates place on channeling analysis and how these limits apply in given experimental situations. Since the channeling analysis is one in which only a few percent of the particles suffer close impact collisions in the near surface region of the solid, the effective number of radiation damage events is reduced by about a factor of 10 over that for a beam incident along a nonchanneling direc tion. For this reason aligned yields are measured before random yields when recording backscattering spectra and, in some cases, the analysis beam spot is moved to a n e w position on the sample after the initial alignment of tthe crystal with the beam. In some of the early channeling measurements of impurity lattice site location, the precaution of moving the analysis beam after alignment was not followed and incorrect site assignments were made. The analysis of A s implanted in Si is such an example (Mayer et al. 1970). In spite of the fact that A s has a high solubility in Si, routine channeling analyses indi cated that only 50-60% of the A s was on substitutional sites. Subse quently it was found that defects introduced by M e V H e ions caused A s ions to move off lattice sites [Haskell et al., 1972; Kool et al., 1976] and that high substitutional A s fractions were found if the analysis beam was shifted to a new position on the sample after the initial alignment. From the preceding K i c h i n - P e a s e displacement cross-section estimate and a typical He fluence for alignment of not more than 10 μ€ over 1 m m (6 χ 1 0 H e / c m ) w e obtain up to —0.02 atomic fraction of Si atoms that have undergone displacements. Channeling in the Si host lattice would not be significantly affected by this number of displacements, and, in addition, most of the Si lattice damage would be removed owing to the high mobil ity at room temperature of many of the defects created. At the same time the influence on the A s atom location can be readily accounted for if n
15
2
n
18
Κ
κ
2
Ρ
Ό
2
2
15
2
208
9.
IMPURITY-DEFECT INTERACTIONS
defects migrate to and are trapped by the A s atoms, since the typical A s concentrations were : S 1 0 " atom fraction, or more than a factor of 10 lower than the estimated number of Si displacements. There are two regimes in which the analyzing beam creates significant amounts of disorder in the host crystal itself during routine analysis: (1) double alignment in which factors of 10 to 10 higher analysis beam fluences are required because of the small solid angle of the detector; and (2) use of microbeams where the small size of the beam spot leads to two to four orders of magnitude increase in the number of i o n s / c m for an analysis. For normal area, single-alignment channeling analysis, a 1-mm beam spot is used and total beam fluences (doses) Φ = 0 . 1 - 1 0 0 Φ are required, where Φ = 1 / x C / m m or « 6 χ 1 0 i o n s / c m . Using σ the fractional number of defects created near the surface of Si by 1-MeV H e for Φ is 0.002, or about a tenth of the minimum yield for channeling. Indeed for very high fluences increases in the minimum yield are seen for He on Si (Fig. 9.13). The observed increase in the channeling minimum yield is very small and the first indication of beam-induced defect creation is in the dechanneling rate. The damage accumulation in the crystal is appreciably less than predicted by these estimates; this is attributed to room tempera ture annealing. Annealing of ion beam-induced defects in Si at room temperature has been well documented in studies of the ion implantation process. Similar measurements in Al of the increase in the (110) chan neling yield as a function of 2-MeV H e beam fluence along a random direction show similar increases in the rate of damage accumulation (Pic raux, 1981b). Appreciable annealing of defects in Al is also expected owing to the rapid point defect migration that occurs at room temperature. 3
2
2
2
0
2
14
2
0
Κ Ρ
0
The preceding considerations provide a guide in estimating the maxi mum beam-induced damage effects. These could apply, for example, in low temperature experiments where defect annealing is reduced. While these are finite limits, experimental analyses are almost always possible in semiconductors and metals. In insulators not only nuclear but also electronic excitations can result in atomic displacements. A s a "worst c a s e " estimate of the damage pro duction by an ion beam w e consider all the energy dissipated to result in atomic displacements. Then, since the electronic contribution to the stop ping power is a factor —600 greater than the nuclear contribution, the damage rate might be increased by as much as a factor of 600, i.e., from a defect concentration of 0.002 to =^ 1 for the standard fluence Φ in an alkali halide. While such large damage rates have not been observed, Hollis (1973) has shown a substantial increase in j c for 1-MeV H e bombard0
min
9.5
PERSPECTIVES
209
ENERGY (MeV) FIG. 9.13 Backscattering spectra for 2-MeV H e incident along the (110) aligned and random direction of Si. Inset s h o w s the increase in aligned yield with increasing d o s e s for 2-MeV H e bombardment along a random direction due to radiation damage by the beam. Normal fluence for a backscattering measurement is Φ to 10 Φ , where Φ = 1 /mC/mm ( ~ 6 χ 1 0 H e / c m ) . [From Picraux (1981b).] 4
2
0
14
0
0
2
ment of NaCl at the standard dose. Thus even in the difficult case of in sulators, channeling analyses are possible, but where ionization-induced defect production is prevalent the minimum possible fluence is required (Price and Kelly, 1975).
9.5
Perspectives
In this chapter w e have discussed the introduction of defects by energetic ion beams and shown how this can be used in combination with ion channeling to study impurity-defect interactions. The determination of the structure and stability of impurity-defect centers is difficult to obtain by any single technique. Ion channeling provides a method to look at the heart of such centers by determining the lattice location of the
210
9.
IMPURITY-DEFECT INTERACTIONS
impurity. The creation and annihilation of the impurity-defect center can usually be monitored as a function of defect introduction. This provides a means to identify the defect involved, as was illustrated for dumbbell interstitials in Al (Section 9.2). Diffuse x-ray scattering provides detailed structural information on impurity-defect centers and is applicable all the way down to single interstitials or vacancies. It has been used, for example, to show that the Al interstitial in Al is of (100) split (dumbbell) configuration. However, diffuse x-ray scattering has not been routinely applied to single impurity atom-defect centers, as it is not a widely used technique and interpretation requires detailed calculations. Hyperfine interaction methods, such as Mossbauer spectroscopy and perturbed angular correlation, probe the local environment surrounding an impurity. This directly complements the channeling technique, which can determine the impurity position but is insensitive to the local arrangement of the surrounding atoms. Hyperfine methods are even more sensitive for low concentrations of impurities than is ion channeling but, unlike channeling, are restricted to certain elements for which an appropriate isotope is available. Combined use of ion channeling and hyperfine interactions have provided a better understanding, for example, of impurity-vacancy interactions in a number of metals. Extended x-ray absorption fine structure ( E X A F S ) measurements also directly probe the atoms surrounding an impurity, allowing determination of bond distances. There has not been extensive use of E X A F S to study impurity-defect centers. For a variety of nonmetallic systems, most notably Si, electron spin resonance has been used to characterize impurity-defect centers of nonzero spin. Anelastic techniques such as internal friction can be sensitive to impurity-defect interactions and may allow the symmetry of the defect center to be inferred. Other techniques, including electrical resistivity and positron annihilation, have been used extensively to probe the interaction of impurities with defects, but in most cases detailed structural information cannot be obtained from these measurements. One of the difficulties in the study of defect-impurity structures is that the available techniques for a given problem are often few and limited in their scope. In this respect ion channeling is particularly versatile, since it is possible to probe essentially any impurity in any solid for which a single crystal can be obtained. The introduction of some defects by MeV beams during ion channeling analysis usually does not limit impurity-defect studies, but must be considered to ensure correct interpretation. Although further development of techniques is needed to extend our understanding of impurity-defect centers, this area remains an exciting one for contributions by the ion channeling technique.
REFERENCES
211
References Bugeat, J. P., and Ligeon, E . (1979). Phys. Lett. 71A, 93. Bugeat, J. P., Chami, A . C , and Ligeon, E . (1976). Phys. Lett. 58A, 127. Haskell, J., Rimini, E . , and Mayer, J. W. (1972). J. Appl. Phys. 4 3 , 3425. Hollis, M. J. (1973). Phys. Rev. B8, 9 3 1 . Johnson, W. S., and Gibbons, J. F. (1970). "Projected Range Statistics in S e m i c o n d u c t o r s . " Stanford U n i v . B o o k s t o r e , Stanford, California. K o o l , W. H . , Roosendaal, Η. E . , Wiggers, L . W., and Saris, F. W. (1976). Nucl. Instrum. Methods 132, 285. Matsunami, N . , S w a n s o n , M. L . , and H o w e , L . M. (1978). Can. J. Phys. 56, 1057. Mayer, J. W., Eriksson, L . , and D a v i e s , J. A . (1970). " I o n Implantation in Semiconduc t o r s . " A c a d e m i c Press, N e w York. Myers, S. M . , Picraux, S. T., and Stoltz, R. E . (1979). J. Appl. Phys. 5 0 , 5710. Picraux, S. T. (1981a). Nucl. Instrum. Methods 182/183, 413. Picraux, S. T. (1981b). Unpublished. Price, P. B . , and Kelly, J. C. (1975). In " A t o m i c Collisons in S o l i d s " ( S . Datz, B . R. Appleton, and C. D . Moak, e d s . ) , Vol. 2, p . 669. Plenum, N e w York. Swanson, M. L . , and H o w e , L . M. (1979). Radiat. Effects 4 1 , 129. Swanson, M. L . , and Maury, F. (1975). Can. J. Phys. 5 3 , 1117. Swanson, M. L . , H o w e , L . M., and Quenneville, A . F. (1976). J. Phys. F: Met. Phys. 6, 1629. S w a n s o n , M. L . , H o w e , L . M . , and Quenneville, A . F. (1978). J. Nucl. Mat. 69, 70, 372. S w a n s o n , M. L . , H o w e , L . M., and Quenneville, A . F. (1980a). Phys. Rev. Β 22, 2213. Swanson, M. L . , H o w e , L. M . , and Quenneville, A. F. (1980b). Nucl. Instrum. Methods 170, 427.
9
IMPURITY-DEFECT INTERACTIONS
9.1
Introduction
Mechanical properties of metals are determined by the addition of elements and defects. The influence of elemental additions results from their microscopic state within the crystal matrix—such as substitutional, interstitial, precipitated, or defect trapped. The properties of metals depend on whether impurities are on substitutional or interstitial sites, whether they form precipitates or are trapped by defects. For example, interstitial atoms such as carbon in steel interact strongly with the stress field of a dislocation and tend to prevent its motion, thus strengthening the steel (solution strengthening). The precipitation of impurities, such as Cu in Al, can also impede the motion of dislocations (precipitation hardening). Segregation of impurities at grain boundaries, on the other hand, can lead to embrittlement, and such Sb segregation is one of the mechanisms that led to crack development in the Liberty ships. Commercial alloys usually contain a number of elemental additions, and such elements when incorporated into the host metal lattice are referred to as solutes. In addition, impurities are often unavoidably present and their influence must be controlled. For example, hydrogen is a species that leads to brittle fracture of high strength steels. Hydrogen can be readily introduced from external sources such as corrosion reactions, surface plating processes, or rapid diffusion from gas storage systems. Other undesirable impurities, such as the embrittling species P, A s , Sb, and Sn may be present in the original alloy fabrication. On the other hand, if defects trap embrittling species, their flow and accumulation at grain boundaries or other failure points may be impeded. 193
194
9.
IMPURITY-DEFECT INTERACTIONS
In most materials, vacancies, interstitials, and their clusters can inter act strongly with impurities. The influence of vacancies and interstitials can be distinguished by their temperature of migration. Their interactions with impurities can be monitored with channeling when the interaction results in a displacement of the impurity from normal lattice sites. In metals, interstitials generally have a lower activation energy of motion than do vacancies, so that appreciable migration of interstitials can occur at temperatures where vacancies are essentially immobile. For example, in Al, resistivity and positron annihilation measurements show free inter stitials migrate at = 4 5 Κ and vacancies at = 2 0 0 K. In this chapter w e discuss three different categories of defect interac tions in metal crystals: (1) irradiation of substitutional alloys to study metal-solute interactions with vacancies and interstitials, (2) interstitial gas atom interactions with point defects, and (3) defect accumulation during channeling analysis. Defect-impurity interactions can be studied since controlled numbers of interstitials and vacancies can be introduced by light ion irradiation, and solutes or impurities can be introduced into the sample by alloying, diffusion, or ion implantation.
9.2
Metal-Solute Interactions with Interstitials and Vacancies
Solute atoms in metal crystals can trap mobile defects. The size of the solute atom is one factor in determining the type of defect that is trapped. In general, small solute atoms trap interstitials of the host lattice, whereas large solute atoms trap host lattice vacancies, thereby minimizing the strain energy in the crystal. Swanson, H o w e , and their colleagues at Chalk River (Swanson et al., 1974, 1976, 1980a,b; Swanson and H o w e , 1979) carried out a series of investigations in which channeling effect measurements were used to monitor the lattice site of the solute atoms. By following the solute atom movement off and on lattice sites, the formation or annihilation of defect impurity centers can be observed. Measurements as a function of irradia tion and anneal temperatures allowed the relative role of vacancies and interstitials to be determined. The experimental procedure was simplified because the defects were created by radiation in situ using a beam of the same ions as were used for the channeling analysis. Studies of the irradiation of Al single crystals containing different sol ute atoms show that size is an important factor (Table 9.1). In fee metals such as Al, self-interstitial atoms have predominantly a split configuration in which two atoms symmetrically straddle one lattice site (Fig. 9.1). This dumbbell configuration has a (100) orientation in Al. Small solute atoms
9.2
METAL-SOLUTE INTERACTIONS WITH INTERSTITIALS AND VACANCIES TABLE Trapping
9.1 Configurations
Solute atom Cr Mn Fe Cu Zn Ag Ga Ge Sn Mg In
195
in Irradiated,
Dilute Aluminum
Trapping configuration -0.57 -0.47 —0.38 -0.38 -0.06 0.001 0.05 0.13 0.24 0.41 -0.21
0
(100) m.d. <100> m.d. m.d. (100) m.d. (100) m.d. (100) m.d. ~ ( 1 0 0 ) m.d. (100) m.d. v.t. v.t. v.t. e
e
Alloys
a
Defect to form center*
i i i i i i i V V V
° Adapted from Swanson et al. (1980a). A V / V is the expansion of the host lattice caused by alloying, expressed in atomic v o l u m e s per solute atom. m.d. is the mixed-interstitial dumbbell, and the crystallographic orientation of the dumbbell is given where k n o w n ; v.t. is vacancy trapping leading to a s o l u t e - v a c a n c y cluster. H o s t lattice defects: i, interstitial and v , v a c a n c y . Shallow trapping of Al interstitials also occurs for these solutes at l o w temperatures. 6
c
d
e
such as Mn can lower the energy of the system by trapping a selfinterstitial dumbbell to form mixed dumbbells. Large solute atoms such as Sn in Al can lower the strain energy by capturing vacancies to form a vacancy trap configuration.
FIG. 9.1 Schematic for the fee Al crystal lattice of (a) a s o l u t e - h o s t atom split interstitial (mixed-dumbbell) of (100) orientation, (b) a self-interstitial in a second (100) dumbbell configuration, and (c) a substitutional solute atom ( O , Al atoms; · , solute atoms).
196
9.
IMPURITY-DEFECT INTERACTIONS
Channeling measurements are sensitive to the presence of the mixed dumbbells and give the magnitude of the solute atom displacements in the trapping configuration (Matsunamief al., 1978). Figure 9.2 shows an angu lar scan for an Al crystal containing 0.09% Mn solute atoms that was irradiated at 70 Κ with H e ions. The presence of a peak in the Mn signal indicates that the Mn atoms have moved off substitutional sites into the central region of the channel. The origin of the peak in the Mn signal for the (110) scan is evident in Fig. 9.3, which illustrates the movement of the Mn atom toward the center of the (110) channel for a (100) split interstitial configuration. The shad ing in the figure indicates the boundaries of one channel. For channeling along the (100) axial direction, the dumbbell is displaced along the bound aries of the channel so that central flux peaks in the angular scans are not observed. For nonpreferential orientations of the (100) dumbbell, two1 . 1
I 0
0 9
0 8
ο
0
7
UJ
α
0.6
UJ
^
ζ
0. 5
a.
ο
0 4
0 3
0 2
0 1
0 0 -2
- I
0
ANGLE FROM < I I 0 >
DIRECTION
1 (deg)
FIG. 9.2 Angular scan for the normalized backscattering yield of 1-MeV H e incident near the < 110) axis of Al (O) containing 0.09 at. % of Mn ( · ) at 40 Κ after irradiation at 70 Κ by 7 χ 1 0 H e / c m at 0.5 MeV. [From Swanson and Maury (1975).] 15
2
9.2
METAL-SOLUTE INTERACTIONS WITH INTERSTITIALS AND VACANCIES
(a)
(b)
197
(c)
FIG. 9.3 Schematic of solute atom displacements upon (100) mixed-dumbbell forma tion in the fee Al lattice for various channeling directions: (a) < 110) axial channel for which all atoms are displaced into the channel; (b) (100) axial channel for which two-thirds of the atoms are displaced into the channel; (c) {100} planar channel for which one-third of the atoms are displaced into the channel. [Adapted from M. L. Swanson (unpublished).]
thirds of the Mn atoms will be displaced perpendicular to and one-third will be displaced along the (100) rows that steer the channeled particles. This latter one-third contribution will have an angular scan like that of host Al. For the {100} planar channel only one-third of the planar atoms are displaced into the channel with the other two-thirds remaining in the plane. The dynamics of mixed-dumbbell formation and annihilation depend on temperature. The self-interstitials are formed directly by irradiation with the analysis beam. At temperatures where the self-interstitial dumbbell migrates, motion to the solute atoms can occur and trapping of the interstitial results in the formation of a mixed dumbbell. At higher temperatures, where vacancies become mobile, the vacancies can migrate to the mixed dumbbell, annihilating these defects and leaving a substitu tional solute atom. This sequence of mixed-dumbbell formation and an nihilation with increasing annealing temperature is shown in Fig. 9.4 for four different solutes in Al. For these solutes, the relative fraction of displaced atoms rises at about 45 Κ where the self-interstitials become mobile in Al. The fraction of displaced atoms decreases toward zero around 200 K, correlating closely with the onset of vacancy migration in Al. The four solutes w h o s e behavior is illustrated in Fig. 9.4 are similar in that the atomic volume per solute atom is comparable to or less than that of Al (Table 9.1). In contrast, for Sn the atomic volume is substantially greater than that of the host Al crystal. The Sn atoms m o v e off substitutional sites, as shown in Fig. 9.5 after irradiation and annealing at temperatures ( > 2 0 0 K) where vacancies are mobile in Al. These channeling results indicate that vacancies cluster on Sn in Al, consistent with other irradiation studies of oversized solute atoms in Al crystals (Swanson et al., 1980a,b).
198
9.
IMPURITY-DEFECT INTERACTIONS
0
40
80
120 160 200 2 4 0 2 8 0
ANNEALING TEMPERATURE (K) FIG. 9.4 Relative fraction of displaced solute atoms (Ag, M n , Cu, and F e in Al) mea sured at 3 0 - 4 0 Κ after irradiation and 10-min isochronal annealing to the indicated tempera tures. Measurements were made along the Al (111) channel for Mn and the (100) channel for A g , Cu, and F e . The dashed line corresponds to the normalized irradiation-induced increase in dechanneling in the Al lattice for the Al-0.13 at. % Cu crystal. [From Swanson etal. (1978).]
The temperature dependence of defect trapping and annihilation for the undersized Ag and oversized Sn solute atoms is contrasted in Fig. 9.6. In the case of Sn, the increase in the number of displaced Sn atoms occurs in the temperature regime where the Ag atoms are moving back onto
1.2
He IRRADIATION Ί + 2 2 0 Κ ANNEAL
ANGLE FROM <100> DIRECTION (deg) FIG. 9.5 Angular scan for the normalized backscattering yield of 1-MeV H e incident near the <100) axis of Al containing 0.3 at. % Sn after 1.3 χ 1 0 H e / c m irradiated by 1-MeV H e at 35 Κ and subsequent annealing to 220 Κ ( Ο , Al; · , Sn). A l s o shown is the aligned Sn yield before the 220 Κ anneal and also before the H e irradiation. [From Swanson et al. (1980a).] 15
2
9.2
METAL-SOLUTE INTERACTIONS WITH INTERSTITIALS AND VACANCIES
(ο)'
1
'
I
'
199
τ
Αί - 0.1 at. % Ag Ο -I LU
0.4
\
>
a
0.2
g
0.0
Ζ Ο
0.8
UJ Ν
V I
<110>
ι
,
I
.
ι
(b) Ai - 0.04 at. % Sn
UJ
ζ ζ < ζ
ϋ
ο.4
μ <110>
0.0 1.0
l
lie)
Af
>
Ι Ο)
\ γ
^/STAGE I
(INTERSTITIAL MOTION)
^ /
Q 0.0
I
/STAGE III /(VACANCY MOTION)
I 100
200
300
ANNEAL TEMPERATURE (K) FIG. 9.6 Comparison of annealing data in ion-irradiated Al and dilute Al alloys for (a) mixed-dumbbell formation and annihilation for Ag in Al as measured b y the relative A g channeling yield; (b) S n - v a c a n c y cluster formation for Sn in Al also as measured by the relative Sn channeling yield; and (c) the defect annealing stages in Al as measured b y the residual resistivity. [Adapted from Swanson et al. 1980a).]
substitutional sites. This different temperature dependence indicates that the interstitials interact only weakly with the oversized Sn atoms, whereas vacancies have a strong interaction. Figure 9.6c shows the resistivity recovery stages for point defect motion in pure aluminum. This illustrates the close correlation between stage I interstitial motion at 45 Κ with mixed-dumbbell formation and stage III vacancy motion at 200 Κ with formation of S n - v a c a n c y clusters. The structures of the S n - v a c a n c y clus ters involve large Sn displacements as indicated by the flux peak in Fig. 9.5; however, the detailed nature of the structures is not well established.
200
9.
IMPURITY-DEFECT INTERACTIONS
These structures are believed to involve various aggregates of two to four vacancies with single Sn atoms. In analogy to the annihilation of mixed-dumbbell interstitials by the introduction of vacancies, the Sn-vacancy clusters can be annihilated by the introduction of interstitials (Swanson et al., 1980). Irradiation at 35 Κ followed by annealing at 220 Κ introduces mobile vacancies and results in the formation of the complex, while irradiation at 70 Κ results in the release of mobile interstitials and is observed to annihilate the complex. Thus w e see for Al that oversized solute atoms tend to trap vacancies, whereas similar or undersized solute atoms tend to trap host lattice inter stitials (Table 9.1). The demonstration that such c o m p l e x e s can be both formed and annihilated by the selective introduction of mobile vacancies or interstitials using ion beams provides a powerful additional tool for the understanding of solute-defect interactions in crystals. This is possible because ion channeling provides a way to determine the number of solute atoms that remain on their normal substitutional lattice sites and the num ber that have formed solute-defect complexes. The same techniques can be applied to impurities that normally occupy interstitial positions in metal host lattices, and these will be illustrated in the following section by channeling studies of the impurity hydrogen. In this case much less is known about the impurity-defect configurations, and so the channeling studies have given more emphasis to determining the lattice location of the hydrogen. 9.3
Hydrogen Trapping at Point Defects in Metals
Atoms of normally gaseous materials (gas atoms) interact strongly with vacancies in metals (Picraux, 1981). Hydrogen is probably the gas atom specie of greatest interest in metals; it is important to fisson and fusion reactions, as well as other energy-related technologies. Channeling is one of the few techniques that gives the lattice site of hydrogen and allows the study of the defect-hydrogen interactions. For heavier gas atoms (e.g., Xe) Mossbauer spectroscopy or other hyperfine techniques can often be utilized to probe the local environment around the atom; however, these techniques are not applicable for hydrogen. Ion implantation provides a convenient way to controllably introduce gas atoms and lattice defects in metals. After implantation, hydrogen usually occupies an interstitial site. An example of a channeling angular scan from implanted deuterium in Al is shown in Fig. 9.7. The strong flux peak for (100) axial and for the planar orientations is indicative of hydro gen location in the center of the channels. The sketches of angular scans for different channeling directions given in Fig. 9.8 show that the two
-1
Ο
+1
FIG. 9.7 Angular scans for the normalized backscattering and nuclear reaction yields from Al implanted with 1 0 / c m , 5-keV D at 33 Κ using a 730-keV H e beam. [From Bugeat et al. (1976).] 1 5
2
3
OCTAHEDRAL
FIG. 9.8 Schematic of projected positions in various channels for the tetrahedral and octahedral interstitial sites in the fee Al crystal lattice. The corresponding channeling angu lar scans e x p e c t e d are indicated by the dashed line for the interstitial site and the solid line for the host lattice signal. [From Bugeat et al. (1976).]
202
9.
IMPURITY-DEFECT INTERACTIONS
primary interstitial sites in the fee lattice give qualitatively different angu lar scans. Comparison of Figs. 9.7 and 9.8 show that the implanted deuterium is predominantly on tetrahedral interstitial sites. This site loca tion at 35 Κ in Al was found to be stable for anneal temperatures up to ~ 3 0 0 K, suggesting a defect-trapped configuration. Trapping is inferred since diffusion measurements indicate hydrogen would otherwise b e c o m e sufficiently mobile at lower temperatures for it to migrate to surface sites and to depths deeper than that probed by the channeling analysis. In this case implantation and anneals at various temperatures suggested that the implanted deuterium was trapped by vacancies introduced by the deuterium implantation (Bugeat et al., 1976). Other channeling studies have suggested that implanted hydrogen and deuterium may be trapped by vacancies in metals (Bugeat and Ligeon, 1979; Myers et al., 1979; Picraux, 1981a). For typical 10-30 keV Η and D implantations, there are about 10 vacancies and interstitials for every implanted atom. Because of its interstitial location, hydrogen is mobile at Pd(D)
1
1—ι
ANGLE
1
1
1
1
1—ι
OCTAHEDRAL SITE
(deg)
FIG. 9.9 Angular scans for the normalized H e channeling yields near the < 100) axis of Pd implanted with 5 χ 1 0 / c m , 10-keV D after implantation at 25 Κ and annealing to the various temperatures. The e x p e c t e d angular scans for the octahedral and tetrahedral intersti tial sites in fee Pd are sketched to the right. [Adapted from Bugeat and Ligeon (1979).] 3
1 5
2
9.3
HYDROGEN TRAPPING AT POINT DEFECTS IN METALS
203
lower temperatures than the vacancy. At some range of intermediate temperatures hydrogen may be trapped by the vacancy. The interstitial site of the mobile and trapped hydrogen may differ. An example believed to correspond to these different sites is shown in Fig. 9.9 for deuteriumimplanted Pd. For the as-implanted case and for anneals up to 80 Κ a significant fraction of the deuterium is near the octahedral site. These channeling measurements are consistent with site assignments by neutron scattering measurements made on high concentrations of hydrogen dif fused into Pd without the introduction of defects. After the samples are annealed at a slightly higher temperature between 80 and 90 K, the deuterium becomes sufficiently mobile to migrate to traps and a significant change in the lattice site is observed. From the flux peak it is apparent that the majority of the deuterium is trapped in the vicinity of the tetrahedral site (Bugeat and Ligeon, 1979). The hydrogen and deuterium need not be trapped exactly in one of the high symmetry interstitial cavities. For lower symmetry positions a num ber of angular scans along different orientations together with a detailed comparison with theoretical calculations (Chapter 3) are required. An example of this procedure is given in Fig. 9.10 and 9.11 for the case of deuterium-implanted Fe (Meyers et al. 1979), a bcc metal. In this case the deuterium was implanted at low temperature and annealed at sufficiently high temperatures so that all the deuterium was trapped. All the angular y
DISTORTED O-SITE I
Fe(D)
1
1
1
1
1
2
4
O-SITE
T-SITE
1.2 1.0
ΔΔΔ
Q uj >·
0.8
WW
UJ \~L 0.6 <
UJ *
0.4 0.2
<100> AXIS 1 -4
ι .2
0
TILT ANGLE (deg)
FIG. 9.10 Angular scans for the normalized H e channeling yields near the (100) axial direction of F e after implantation with 1 x 1 0 / c m , 15-keV D at 110 Κ and annealing to 200 K. The corresponding e x p e c t e d scans are s h o w n for various sites in the bcc F e crystal lattice. The distorted O-site is shown in Fig. 9.12 and the calculated angular scan for this site is shown by the dashed line on the left. [Adapted from Myers et al. (1979).] 3
1 6
2
204
9.
IMPURITY-DEFECT INTERACTIONS
DISTORTED O-SITE
OSITE
T-SITE
Fe(D)
1
1
6 = 0.3 _j
1
1
I
ι
r
A I
-1
L
0
1
(112) PLANE
UJ 0.2L1 -1
I
I
1
0 TILT ANGLE (deg)
1—l 1
FIG. 9.11 Angular scans near the {100} and {112} planar directions from D-implanted F e under the same conditions as Fig. 9.10. The dashed lines for the {100} angular scan are calculated for the distorted O-site shown in Fig. 9.12. [Adapted from Myers et al. (1979) and Picraux (1981a).]
scans could be explained assuming that the deuterium occupied a single unique site upon trapping that is displaced along the (100) direction to ward the nearest neighbor Fe lattice site, as shown in Fig. 9.12. The magnitude of the displacement w a s found to be 0.4 A, based primarily on the {100} planar scans (Fig. 9.11). The presence of the vacancy as the trap entity for this deuterium site in Fe can only be inferred, since the sur rounding lattice atom configuration cannot be determined by channeling. However, both experimental and theoretical results strongly point to the isolated vacancy as the trap entity (Myers et al., 1979; Picraux, 1981a). For detailed site determinations it is often difficult to assess the uniqueness of the interpretation based on angular scans along one to two directions. One reason is that the impurities may be distributed among different sites. For example, a combination of tetrahedral and substitu tional sites could produce angular scans qualitatively similar to those obtained along (100) axial and (100) planar directions. In these cases certain planar scans can be valuable in establishing symmetry require-
9.4
ANALYSIS BEAM-INDUCED DAMAGE
205
VACANCY D - SITE [001 010]
Fe
1100]
χ OCTAHEDRAL SITE + TETRAHEDRAL SITE
FIG. 9.12 Schematic of the D location in F e determined from the angular scans of Figs. 9.10 and 9.11 ( x , octahedral site; + , tetrahedral site). [From Myers et al. (1979).
ments for the site. For example, the {112} planar orientation would be expected to give a dip for combinations of tetrahedral and substitutional sites and a flux peak for the preceding distorted octahedral site (Picraux, 1981a). The observed peak in the scan (Fig. 9.11) is thus consistent with the site assignment shown in Fig. 9.12. 9.4
Analysis Beam-Induced Damage
From the solute trapping and hydrogen defect studies it is shown that the analysis beam creates vacancies and interstitials in the crystal. This beam-induced disorder can cause an increase in the aligned yield, an increase in the surface peak, an increase in the dechanneling rate, and, as shown in the previous sections, a movement of impurities off or onto lattice sites. In most cases of channeling analysis the beam-induced de fects do not play a role in determining disorder distributions or impurity site locations. Although one is bombarding a crystal with ions of MeV energies that are capable of producing a significant number of defects, such effects have not seriously hampered channeling analyses. There are several reasons for this insensitivity of channeling analysis to beaminduced defects. First, defects are created along the whole track of the beam with the maximum in nuclear stopping, and hence defect produc tion, at the end of the range some microns below the surface. The second reason is that the number of defects created in the near surface region during a single alignment measurement usually is relatively small com pared to the concentration of defects required in radiation damage studies analyzed by channeling. One can estimate the amount of beam-induced damage using the fun damental relations that govern ion-solid interactions. The large angle scat-
206
9.
IMPURITY-DEFECT INTERACTIONS
tering events that are the measured quantity in channeling experiments correspond to large energy transfers to the scattering atom, causing it to recoil energetically from its lattice site. For example, a 180° scattering of 1.0-MeV H e from Si transfers —440 keV to the Si atom, whereas the binding energy of the atom to its lattice site is —14 eV. Using the Ruther ford cross section w e can determine the total cross section for energy transfers greater than the lattice binding energy. The differential Rutherford cross section for transferring an energy Τ to a scattering atom is άσ* dT
4 π (ZAe*V 4M,M Ε \ 4 / (Mi + M )
1 T
2
2
f Q 2
2
Then the total Rutherford cross section σ (Ε > E ) for transferring an energy greater than the displacement energy £ is Η
D
D
σ (Ε >Ε )~ Η
Ό
[—^-j
Ύ
( M i
+
M i )
2 γ
υ
(9.2)
For 1.0-MeV He in Si ( £ = 14 eV) w e find σ (Ε > Ε ) = 3.9 χ 1 0 " c m . This is an overestimate of the actual displacement cross section since the Rutherford cross section is based on an unscreened potential. A more accurate screened Coulomb potential results in a smaller cross section; for example, for 1.0-MeV H e in Pt the cross section is reduced to one-half of the σ value. The average energy Τ transferred to a recoiling atom is 20
D
Η
2
Ό
κ
l =
L
Γ 'max
(9.3a)
d
or r - £
D
l n ( ^ ) *
(9.3b)
where 7 is the maximum energy transferred. For 1.0-MeV H e in Si Τ = 144 eV, which is = 1 0 £ . Such a low energy recoiling atom deposits nearly all of its energy into atomic displacements, thereby multiplying the num ber of displaced atoms due to this one hard collision. Thus for MeV H e the recoiling lattice atoms are the primary source of displacements. A method to estimate the total number of displaced atoms considers that portion of energy lost by the penetrating H e ion into nuclear pro cesses. This estimate then includes recoil contributions. A convenient way to apply this is given by the Kichin-Pease formulation of the dism a x
D
9.4
207
ANALYSIS BEAM-INDUCED DAMAGE
placement probability. The cross section is given by _
aS (E) n
where S (E) is the nuclear stopping power and α is a constant between 0.5 and 1. Using a value of S (E) of 0.088 x 1 0 ~ e V - c m (Johnson and Gibbons, 1970) for 1.0-Me V H e in Si, σ = 3 χ 1 0 ~ c m , t w o orders of magnitude greater than σ (Ε > Ε ) \ The Kichin-Pease formulation yields a reasonable estimate for atomic displacement due to nuclear collisions. It is these nuclear processes that are the primary mechanisms leading to atom displacements and the resulting defect production in metals and semiconductors. These defects can (1) interact with impurities in the host crystal, and (2) accumulate in the host crystal, eventually affecting the channeling process in the host crystal. We now consider what limits the preceding theoretical estimates place on channeling analysis and how these limits apply in given experimental situations. Since the channeling analysis is one in which only a few percent of the particles suffer close impact collisions in the near surface region of the solid, the effective number of radiation damage events is reduced by about a factor of 10 over that for a beam incident along a nonchanneling direc tion. For this reason aligned yields are measured before random yields when recording backscattering spectra and, in some cases, the analysis beam spot is moved to a n e w position on the sample after the initial alignment of tthe crystal with the beam. In some of the early channeling measurements of impurity lattice site location, the precaution of moving the analysis beam after alignment was not followed and incorrect site assignments were made. The analysis of A s implanted in Si is such an example (Mayer et al. 1970). In spite of the fact that A s has a high solubility in Si, routine channeling analyses indi cated that only 50-60% of the A s was on substitutional sites. Subse quently it was found that defects introduced by M e V H e ions caused A s ions to move off lattice sites [Haskell et al., 1972; Kool et al., 1976] and that high substitutional A s fractions were found if the analysis beam was shifted to a new position on the sample after the initial alignment. From the preceding K i c h i n - P e a s e displacement cross-section estimate and a typical He fluence for alignment of not more than 10 μ€ over 1 m m (6 χ 1 0 H e / c m ) w e obtain up to —0.02 atomic fraction of Si atoms that have undergone displacements. Channeling in the Si host lattice would not be significantly affected by this number of displacements, and, in addition, most of the Si lattice damage would be removed owing to the high mobil ity at room temperature of many of the defects created. At the same time the influence on the A s atom location can be readily accounted for if n
15
2
n
18
Κ
κ
2
Ρ
Ό
2
2
15
2
208
9.
IMPURITY-DEFECT INTERACTIONS
defects migrate to and are trapped by the A s atoms, since the typical A s concentrations were : S 1 0 " atom fraction, or more than a factor of 10 lower than the estimated number of Si displacements. There are two regimes in which the analyzing beam creates significant amounts of disorder in the host crystal itself during routine analysis: (1) double alignment in which factors of 10 to 10 higher analysis beam fluences are required because of the small solid angle of the detector; and (2) use of microbeams where the small size of the beam spot leads to two to four orders of magnitude increase in the number of i o n s / c m for an analysis. For normal area, single-alignment channeling analysis, a 1-mm beam spot is used and total beam fluences (doses) Φ = 0 . 1 - 1 0 0 Φ are required, where Φ = 1 / x C / m m or « 6 χ 1 0 i o n s / c m . Using σ the fractional number of defects created near the surface of Si by 1-MeV H e for Φ is 0.002, or about a tenth of the minimum yield for channeling. Indeed for very high fluences increases in the minimum yield are seen for He on Si (Fig. 9.13). The observed increase in the channeling minimum yield is very small and the first indication of beam-induced defect creation is in the dechanneling rate. The damage accumulation in the crystal is appreciably less than predicted by these estimates; this is attributed to room tempera ture annealing. Annealing of ion beam-induced defects in Si at room temperature has been well documented in studies of the ion implantation process. Similar measurements in Al of the increase in the (110) chan neling yield as a function of 2-MeV H e beam fluence along a random direction show similar increases in the rate of damage accumulation (Pic raux, 1981b). Appreciable annealing of defects in Al is also expected owing to the rapid point defect migration that occurs at room temperature. 3
2
2
2
0
2
14
2
0
Κ Ρ
0
The preceding considerations provide a guide in estimating the maxi mum beam-induced damage effects. These could apply, for example, in low temperature experiments where defect annealing is reduced. While these are finite limits, experimental analyses are almost always possible in semiconductors and metals. In insulators not only nuclear but also electronic excitations can result in atomic displacements. A s a "worst c a s e " estimate of the damage pro duction by an ion beam w e consider all the energy dissipated to result in atomic displacements. Then, since the electronic contribution to the stop ping power is a factor —600 greater than the nuclear contribution, the damage rate might be increased by as much as a factor of 600, i.e., from a defect concentration of 0.002 to =^ 1 for the standard fluence Φ in an alkali halide. While such large damage rates have not been observed, Hollis (1973) has shown a substantial increase in j c for 1-MeV H e bombard0
min
9.5
PERSPECTIVES
209
ENERGY (MeV) FIG. 9.13 Backscattering spectra for 2-MeV H e incident along the (110) aligned and random direction of Si. Inset s h o w s the increase in aligned yield with increasing d o s e s for 2-MeV H e bombardment along a random direction due to radiation damage by the beam. Normal fluence for a backscattering measurement is Φ to 10 Φ , where Φ = 1 /mC/mm ( ~ 6 χ 1 0 H e / c m ) . [From Picraux (1981b).] 4
2
0
14
0
0
2
ment of NaCl at the standard dose. Thus even in the difficult case of in sulators, channeling analyses are possible, but where ionization-induced defect production is prevalent the minimum possible fluence is required (Price and Kelly, 1975).
9.5
Perspectives
In this chapter w e have discussed the introduction of defects by energetic ion beams and shown how this can be used in combination with ion channeling to study impurity-defect interactions. The determination of the structure and stability of impurity-defect centers is difficult to obtain by any single technique. Ion channeling provides a method to look at the heart of such centers by determining the lattice location of the
210
9.
IMPURITY-DEFECT INTERACTIONS
impurity. The creation and annihilation of the impurity-defect center can usually be monitored as a function of defect introduction. This provides a means to identify the defect involved, as was illustrated for dumbbell interstitials in Al (Section 9.2). Diffuse x-ray scattering provides detailed structural information on impurity-defect centers and is applicable all the way down to single interstitials or vacancies. It has been used, for example, to show that the Al interstitial in Al is of (100) split (dumbbell) configuration. However, diffuse x-ray scattering has not been routinely applied to single impurity atom-defect centers, as it is not a widely used technique and interpretation requires detailed calculations. Hyperfine interaction methods, such as Mossbauer spectroscopy and perturbed angular correlation, probe the local environment surrounding an impurity. This directly complements the channeling technique, which can determine the impurity position but is insensitive to the local arrangement of the surrounding atoms. Hyperfine methods are even more sensitive for low concentrations of impurities than is ion channeling but, unlike channeling, are restricted to certain elements for which an appropriate isotope is available. Combined use of ion channeling and hyperfine interactions have provided a better understanding, for example, of impurity-vacancy interactions in a number of metals. Extended x-ray absorption fine structure ( E X A F S ) measurements also directly probe the atoms surrounding an impurity, allowing determination of bond distances. There has not been extensive use of E X A F S to study impurity-defect centers. For a variety of nonmetallic systems, most notably Si, electron spin resonance has been used to characterize impurity-defect centers of nonzero spin. Anelastic techniques such as internal friction can be sensitive to impurity-defect interactions and may allow the symmetry of the defect center to be inferred. Other techniques, including electrical resistivity and positron annihilation, have been used extensively to probe the interaction of impurities with defects, but in most cases detailed structural information cannot be obtained from these measurements. One of the difficulties in the study of defect-impurity structures is that the available techniques for a given problem are often few and limited in their scope. In this respect ion channeling is particularly versatile, since it is possible to probe essentially any impurity in any solid for which a single crystal can be obtained. The introduction of some defects by MeV beams during ion channeling analysis usually does not limit impurity-defect studies, but must be considered to ensure correct interpretation. Although further development of techniques is needed to extend our understanding of impurity-defect centers, this area remains an exciting one for contributions by the ion channeling technique.
REFERENCES
211
References Bugeat, J. P., and Ligeon, E . (1979). Phys. Lett. 71A, 93. Bugeat, J. P., Chami, A . C , and Ligeon, E . (1976). Phys. Lett. 58A, 127. Haskell, J., Rimini, E . , and Mayer, J. W. (1972). J. Appl. Phys. 4 3 , 3425. Hollis, M. J. (1973). Phys. Rev. B8, 9 3 1 . Johnson, W. S., and Gibbons, J. F. (1970). "Projected Range Statistics in S e m i c o n d u c t o r s . " Stanford U n i v . B o o k s t o r e , Stanford, California. K o o l , W. H . , Roosendaal, Η. E . , Wiggers, L . W., and Saris, F. W. (1976). Nucl. Instrum. Methods 132, 285. Matsunami, N . , S w a n s o n , M. L . , and H o w e , L . M. (1978). Can. J. Phys. 56, 1057. Mayer, J. W., Eriksson, L . , and D a v i e s , J. A . (1970). " I o n Implantation in Semiconduc t o r s . " A c a d e m i c Press, N e w York. Myers, S. M . , Picraux, S. T., and Stoltz, R. E . (1979). J. Appl. Phys. 5 0 , 5710. Picraux, S. T. (1981a). Nucl. Instrum. Methods 182/183, 413. Picraux, S. T. (1981b). Unpublished. Price, P. B . , and Kelly, J. C. (1975). In " A t o m i c Collisons in S o l i d s " ( S . Datz, B . R. Appleton, and C. D . Moak, e d s . ) , Vol. 2, p . 669. Plenum, N e w York. Swanson, M. L . , and H o w e , L . M. (1979). Radiat. Effects 4 1 , 129. Swanson, M. L . , and Maury, F. (1975). Can. J. Phys. 5 3 , 1117. Swanson, M. L . , H o w e , L . M., and Quenneville, A . F. (1976). J. Phys. F: Met. Phys. 6, 1629. S w a n s o n , M. L . , H o w e , L . M . , and Quenneville, A . F. (1978). J. Nucl. Mat. 69, 70, 372. S w a n s o n , M. L . , H o w e , L . M., and Quenneville, A . F. (1980a). Phys. Rev. Β 22, 2213. Swanson, M. L . , H o w e , L. M . , and Quenneville, A. F. (1980b). Nucl. Instrum. Methods 170, 427.