- Email: [email protected]
Bound vacancy interstitial pairs in irradiated silicon
Nuclear Instruments
and Methods in Physics Research B 127/ 128 ( 1997) 27-3 1
8eemIntemotlons
with Yaterials 8 Atoms
ELSEVIER
Bound vacancy interstitial pairs in irradiated silicon H. Zillgen, P. Ehrhart
*
IFF, Forschungszenrrum Jiilich GmbH. D-52425 Jiilich, Germany
Abstract Frenkel defects are produced by MeV electron irradiation of Si with an introduction rate of = 1 cm-’ and we show that defect concentrations as high as lOi cm-j can be frozen in at 4 K. From X-ray diffraction we deduce that a large fraction of the defects is stabilized in the form of close Frenkel pairs and that the long range displacement fields of interstitial atoms and vacancies cancel nearly exactly. Additional larger defect agglomerates are observed at higher irradiation doses. The defect patterns observed after 4 K irradiations are compared to those of room temperature irradiations and the relative importance of ionization induced and thermally activated migration is discussed. Results for Cz-Si are compared to those obtained for FZ-Si and the thermal annealing is discussed with special emphasis to the reduction of the effective defect mobility by trapping reactions.
1. Introduction Point defects determine the electrical properties of semiconductors and have therefore been investigated in great detail for Si. The thermal equilibrium concentrations of the intrinsic point defects, vacancies and interstitial atoms, are very low and most information has therefore been obtained from low temperature electron irradiation experiments. Electron irradiations produce Frenkel pairs (FPs) in a reproducible manner, however, due to the possibility of an ionization induced mobility of interstitial atoms [l], many defect complexes may be formed by trapping of interstitial atoms at dopants even at an irradiation temperature of 4 K. Such complexes as well as vacancy type defects could be investigated in detail by spectroscopic methods [l], but no clear evidence for the presence of undisturbed interstitial atoms or FPs has been found so far. As most of these spectroscopic studies are limited to low defect concentrations or irradiation doses (@r< 10” e-/cm*), there is little known about the fate of FPs at higher doses, which is most relevant to the understanding of defect reactions after ion irradiations. Starting from the established knowledge about interstitial mobility there are two possibilities, i.e. the defect concentration saturates as there are no traps left (saturated traps), or larger clusters are formed around the impurities as nucleation centers (unsaturable traps). There is evidence for the formation of small defect agglomerates after very
high dose irradiations in the high voltage electron microscope (@t 2 lo** e-/cm2> [2], however, the nucleation (intrinsic or extrinsic) and growth is not quantitatively understood. The present investigation is based on X-ray diffraction techniques, as these methods yield information on defect concentrations and defect structures and are applicable just within this gap of irradiation doses.
2. Experimental
methods
The investigations of the diffuse scattering intensity and of the change of the lattice parameter were performed with CuK,, radiation at a measuring temperature of 6 K (for details see e.g. Ref. [3]). The theory necessary to exploit the information contained in the measured diffuse scattering cross section S is well documented [4], and for small deviations q of the scattering vector k from a reciprocal lattice vector G the scattering cross section of the Huang Diffuse Scattering (HDS) is given by: S,(k) = cf*IGs(q>]1*; s(q) is the Fourier transform of the displacement field of an isolated defect, c is the defect concentration, and f is the atomic scattering factor. Due to the l/r* decrease of the long range displacement field around a point defect we obtain the characteristic l/q2 decrease of S,. Expressing the strength of the displacement field s(r) by the relaxation volume V”’ of the defect we obtain: s, - C(V”r’)*G*/q2.
* Corresponding author. Tel.: +49 2461 61 6074, fax: + 49 2461 61 2550, e-mail: [email protected]. 0168-583X/97/$17.00 0 1997 Elsevier Science B.V. All rights reserved PI/ SOl68-583X(96)00851-8
(1)
S, yields the product c(Vre’)*, and by combination with the change of the lattice parameter, A a/a - cV “r’/3, the two unknown numbers c and V re’ can be determined both.
1. FUNDAMENTALS/BASICS
H. Z&en,
28
P. Ehrhart/Nucl.
Instr. and Meth. in Phys. Res. B 127/ 128 (1997) 27-31
As we consider FPs, the experiment yields average values from contributions of interstitials and vacancies: S, - c( ( vim’)’ + (VT)*) and
A a/a N c( Vire’ + V:'
).
(2)
These equations show that defects with opposite sign of V re’ can cancel in A a/a, however, the diffuse scattering S, adds up. Therefore S, is a measure of the changes of the defect concentration even where As/a vanishes. This approach will be modified if the basic assumption of a random distribution of defects is no longer valid. Generally, c must be replaced in Eq. (1) by the Fourier transform of the concentration fluctuations which yield deviations from the characteristic l/q2 behavior of S,. We have to consider here two special situations: (i) For the case of a clustering of defects we observe a stronger increase of S, at small values of q and a final enhancement: S, (cluster)
= nS, (single defect) .
(3)
n is the number of defects in the cluster, and the total defect concentration is kept constant. Due to this enhancement HDS can very sensitively indicate the onset of cluster formation. (ii) A close FP presents a special defect correlation as it combines defects with opposite signs of s, which are separated by a certain minimum distance. Such a pair is characterized by large additive displacements between
I
L
I
I
,
1.5x 10'9 A
.
1
.
001
4 dose (10” e-/cm”)
Fig. 2. Dose dependence of the average value of the HDS intensity obtained at (5 1 l)- and (4CK%reflections after electron irradiation at 4 K. Cz-Si and FZ-Si are distinguished by different symbols.
the vacancy and the interstitial atom and compensation of the displacements at larger distances. These displacements yield a decrease of the intensity at small q values as discussed in detail for InP [3] and GaAs [5]. The samples were slightly p-doped(3 X 10” Bcmm3), and Cz-Si as well as FZ-Si wafers were used in order to check for a possible influence of oxygen on the defect reactions. With this low doping level carriers are removed after very low doses and we have highly ohmic Si over the range of doses investigated here. The irradiations were performed with 2.5 MeV electrons at the Jiilich irradiation facility [6] with current densities between 5 and 10 pA/cm2.
3. Defects after 4 K irradiation kAA
*
0.02
0.03
.
0.04
‘1
0.05
q/G
Fig. 1. Scattering function of the HDS close to the (5 1 1).reflection of irradiated Si. The scattering function has been normalized in order to consider the elastic anisotropy of the crystal and is multiplied by 4’; for such a plot of S,q’ a constant value is expected for isolated point defects. Results are shown for irradiation doses of 0.75, 1.7, and 3.5X 10” e-/cm’; open symbols characterize Cz-Si and full symbols Fz-Si. The lines are a guide to the eye for the data points referring to different irradiation doses.
Fig. 1 shows the defect induced HDS after different irradiation doses. For the lower irradiation doses we observe the characteristic decrease of S,q2 at small values of q instead of the constant value, expected in such a plot for a random distribution of defects. Combined with additional features of the distribution of the scattering intensity we can conclude, that there is a dominant contribution of close ITS with a typical distance of 1-2 lattice constants present after irradiation. The average values of S, taken over the region of q 4 0.03 A-’ are shown in Fig. 2 and show no significant difference between Cz and FZ wafers. There is a nearly linear increase of S, with irradiation dose up to @t = 2 X lOi e-/cm’, i.e. a continuous production of additional FPs. For higher doses we observe a change of the intensity distribution (Fig. 1) and a faster increase (Fig. 2). These observations can be consistently explained by the formation of interstitial clusters, which grow slowly out of a high concentration of ITS and get an average size of n = 3 at the highest dose (Eq. (3)). In contrast to the increase of S, we observe no systematic change of the lattice parameter (ha/a 5 (0.5 f 0.5)
29
H. Zillgen, P. Ehrhart /Nucl. Instr. and Meth. in Phys. Res. B 127 / 128 11997) 27-31
I 0.04
0.02 Fig. 3. Schematic view of the interaction potential between vacancy and interstitial atom: full line for thermal equilibrium and dotted line for the electronically excited state.
x 10M5). From Eq. (2) we conclude therefore, that the displacement fields of interstitials and vacancies must nearly compensate, i.e. Vi”’ = -V,“‘. For this condition Eq. (2) allows no separation of c and (V re’)2 and we have to make assumptions on one of these quantities. If we (f2 is the atomic volume) we assume Vvx’ = -0SR obtain an introduction rate 2 = c/@f = 1 cm-’ which corresponds to an average displacement threshold of 40 eV for Si. The given values should be considered as a maximum for IVrr’l and a minimum for 2, as discussed in detail for InP [3]. In contrast to the expectation we therefore observe neither a saturation of the defect concentration at the concentration of the doping atoms (= lOI cm - 3>, nor the beginning of cluster growth at the corresponding dose. The observation of more than 10” FPs/cm3 and the similarity of the results for the Cz and FZ wafers clearly show, that these defects are intrinsic and not stabilized by impurities. Finally, we have to ask: why have these defects not been observed by other methods and how are they compatible with a fast athermal mobility? (i) From the observed compensation of the displacements of interstitials and vacancies it is obvious that very precise early lattice parameter measurements [7] observed only small effects and/or saturation at defect concentrations similar to the doping level. Similar to the HDS the attenuation of the anomalous X-ray transmission should change independent of the sign of the displacements and, although no quantitative interpretation was possible, there are observations in agreement with our results [8]. (ii) As electrical and spectroscopic methods rely on charged defects and/or energy levels within the bandgap, we might speculate about the FP as an acceptor-donor pair which appears nearly neutral from the outside. (iii) At the first moment the observed defects might best be explained by the continuous production of immobile IT’s which would, however, be at variance to the high athermal defect mobility deduced from reactions of dopants [l]. Although there are different ways to resolve this discrepancy [9], we presently prefer a model which is consistent with the earlier conclusions: the interstitials can
0.06
q/G Fig. 4. Scattering function of the HDS (similar to Fig. 1) as observed close to the (@O&reflection of RT irradiated Si. Data points measured after 4 K irradiation and after subsequent annealing at RT arc shown for comparison.
escape from their vacancy and can form other complexes, however, as soon as all extrinsic traps are saturated the vacancies necessarily become the dominant traps and retrap mobile interstitials [3,5]. This means that there is a binding energy as well as a recombination barrier for the FP as shown schematically in Fig. 3. Such a recombination barrier is not an ad hoc assumption as similar potentials have been proposed earlier in order to explain the temperature dependence of the displacement cross section [lo] or details of the kinetics of oxidation enhanced diffusion [ 1 I]. It seems remarkable, that the dissociation barrier of the pair can be rather easily overcome by ionization induced jumps and that the recombination barrier is much more difficult to overcome. Such a behavior can be explained by a Coulomb repulsion in the “excited” charge state.
-I
0.0
0.5
1.0
1.5
dose (10”
2.0
2.5
3.0
e-/cm*)
Fig. 5. Dose dependence of the average value of the HDS for RT irradiated Si (similar to Fig. 2). The dotted lines show the increase of S, after 4 K irradiation, i.e. the initial slope of Fig. 2, and an average slope for the remaining intensity after subsequent annealing at 300 K which is a good approximation for the medium doses (Fig. 4).
1. FUNDAMENTALS/BASICS
30
H. Zillgen, P. Ehrhart/Nucl.
4. Defects after room temperature
Instr. und Meth. in Phys. Res. B 127/ 128 (1997) 27-31
irradiation
During room temperature (RT) irradiation we expect a thermally activated defect mobility in addition to the atherma1 mobility. Figs. 4 and 5 show the changes of the distribution of the scattered intensity and of the dose dependence of S, as compared to the 4 K irradiations and the subsequent annealing at RT. Fig. 4 shows for the example of medium dose irradiated Cz-Si that during annealing to RT about 50% of the intensity is lost and that the scattering distribution does no longer indicate close pairs. After RT irradiations we observe a very similar intensity distribution as after annealing to RT; hence the close PPs recombine by thermally activated jumps. For RT irradiations there are, however, important differences between Cz-Si and FZ-Si (Fig. 5): for the Cz-Si the damage rate is higher by more than a factor of 3. In contrast to the low temperature irradiation where the nucleation of stable intrinsic defect complexes seems possible starting from the high initial defect concentrations, impurities seem necessary to stabilize - at least temporarily - the defects at RT. In order to explain the buildup of the observed high densities of small defects we might speculate about a kind of catalytic reaction of the oxygen: e.g. the formation of di-interstitials close to oxygen sites and later on the, possibly ionization assisted, detrapping of interstitial oxygen. Combining these observations we conclude that, similar to MgO [12], there are quite different defect interactions for the different jump modes (Fig. 3): during athermal migration the interstitials seem not to surpass the recombination threshold, but with additional thermal activation the probabilities for recombination and escape become comparable. However, for a final survival the trapping at oxygen or other traps is necessary, and there is indication that the binding state with oxygen is also much easier reached by thermally activated jumps. As a common feature it remains very difficult to nucleate larger defects like dislocation loops.
5. Defect annealing Finally, we summarize the annealing of S,, as shown 6, without discussing any details. After low dose irradiation we observe between 40 and 200 K primarily the recombination of the FPs. If more stable small complexes are formed at high doses the annealing below RT is much suppressed, and the rather continuous decrease of S, up to the final annealing at 900 K indicates a steady loss of defects by recombination without remarkable growth of the clusters. From the observed temperature locations of the reactions we may deduce some estimates for the characteristic energies: the recombination barrier of the PPs varies bein Fig.
look,
4b t\
I
.
,
,
,
.
,
4
\
-I-WI Fig. 6. Isochronal annealing (At = 15 min) of the HDS cross section of Si after irradiation at 4 K. The electron irradiation doses are given in the figure in units of e-/cm*; open symbols refer to FZ-Si and full symbols to Cz-Si.
tween 0.2 and 0.6 eV. The dissociation energy of the FP may be estimated from the beginning of the annealing of the optical absorption line of the divacancies at around 200 K [ 131 which yields a value of 2 0.6 eV. As soon as small complexes have formed, the dissociation energy for defects is fast increasing and can reach values of 2-3 eV. These values are still below the value of 3.6 eV, which characterizes the escape from interstitial dislocation loops [ 141.
6. Conclusions We have shown that in Si a high concentration of intrinsic bound FPs can be frozen in which had not been observed earlier. In spite of their ‘electrical invisibility’ these FPs may have important consequences for the modeling of defect reactions during implantation and annealing: (8 Although the individual FPs anneal below RT, the defects can form much more stable complexes, which become dominant if the local density reaches values of the order of 2 x 10” cme3. (ii) The reaction rates differ for ionization induced and thermally activated migration jumps. (iii) The observation of strongly bound FPs shows, that intrinsic trapping reactions must be considered as a possible mechanism for the reduction of the effective mobility of interstitials and vacancies in addition to the trapping by impurities. This trapping might even contribute to the differences in the defect mobility deduced from irradiation experiments [ 11 and diffusion data [ 151.
Acknowledgements We thank Prof. W. Schilling for many helpful discussions and we gratefully acknowledge the technical assistance by W. Bergs and U. Dedek and the support by Dr. F. Dworschak and B. Schmitz during the irradiations.
H, Zillgen, P. Ehrhart/Nucl.
Instr. and Meth. in Phys. Res. B 127/128
References [I] G.D. Watkins, in: Electronic Structure and Properties of Semiconductors, Materials Science and Technology, Vol. 4, ed. W. Schroeter (VCH, Weinheim, 1992) p. 105. [2] H. Fall, Inst. Phys. Conf. Ser. 23 (1975) 233. [3] K. Karsten and P. Ehrhart, Phys. Rev. B 51 (1995) 10508. [4] P.H. Dederichs, J. Phys. F 3 (1973) 471. [5] A. Pilhkat, K. Karsten and P. Ehrhart, Phys. Rev. B 53 (1996) 7823. [6] J. Hemmerich, W. Sassin and W. Schilhng, Z. Angew. Phys. 29 (1970) 20. [7] N.E. Moyer and R.C. Buschert, in: Radiation Effects in Semiconductors, ed. F.L. Vook (Plenum, New York, 1968) [8j g. E&h
(1997) 27-31
31
[9] S. Bausch, H. Zillgen and P. Ehrhart, Mater. Sci. Forum I%/201 (1995) 1141. f IO] J. W. Corbett and J.C. Bourgoin, in: Point Defects in Solids, Vol. 2, eds. J.H. Crawford and L.M. Slifiin (Plenum, New York, 1975) p. 1. [ 1l] P.M. Fahey, P.B. Griffm and J.D. Plummer, Rev. Mod. Phys. 61 (1989) 289. 1121 C. Scholz and P. Ehrhart, MRS Symp. Proc. 279 (1993) 427. [ 131 Unpublished results. [14] P.A. Stalk, H.J. Gossmann, D.J. Eaglesham, DC. Jacobson, H.S. Luftman and J.M. Poate, MRS Symp. Proc. 354 (1995) 307. [I51 H. Bracht, N. A. Stolwijk and H. Mehrer, in: Semiconductor Silicon 1994, eds. H.R. Huff, W. Bergholz, K. Sumino (The Electrochemical Society, 1994) p. 593.
and J.S. Koehler, Phys. Rev. B 23 (1981) 1859.
1. FUNDAMENTALS/BASICS
and Methods in Physics Research B 127/ 128 ( 1997) 27-3 1
8eemIntemotlons
with Yaterials 8 Atoms
ELSEVIER
Bound vacancy interstitial pairs in irradiated silicon H. Zillgen, P. Ehrhart
*
IFF, Forschungszenrrum Jiilich GmbH. D-52425 Jiilich, Germany
Abstract Frenkel defects are produced by MeV electron irradiation of Si with an introduction rate of = 1 cm-’ and we show that defect concentrations as high as lOi cm-j can be frozen in at 4 K. From X-ray diffraction we deduce that a large fraction of the defects is stabilized in the form of close Frenkel pairs and that the long range displacement fields of interstitial atoms and vacancies cancel nearly exactly. Additional larger defect agglomerates are observed at higher irradiation doses. The defect patterns observed after 4 K irradiations are compared to those of room temperature irradiations and the relative importance of ionization induced and thermally activated migration is discussed. Results for Cz-Si are compared to those obtained for FZ-Si and the thermal annealing is discussed with special emphasis to the reduction of the effective defect mobility by trapping reactions.
1. Introduction Point defects determine the electrical properties of semiconductors and have therefore been investigated in great detail for Si. The thermal equilibrium concentrations of the intrinsic point defects, vacancies and interstitial atoms, are very low and most information has therefore been obtained from low temperature electron irradiation experiments. Electron irradiations produce Frenkel pairs (FPs) in a reproducible manner, however, due to the possibility of an ionization induced mobility of interstitial atoms [l], many defect complexes may be formed by trapping of interstitial atoms at dopants even at an irradiation temperature of 4 K. Such complexes as well as vacancy type defects could be investigated in detail by spectroscopic methods [l], but no clear evidence for the presence of undisturbed interstitial atoms or FPs has been found so far. As most of these spectroscopic studies are limited to low defect concentrations or irradiation doses (@r< 10” e-/cm*), there is little known about the fate of FPs at higher doses, which is most relevant to the understanding of defect reactions after ion irradiations. Starting from the established knowledge about interstitial mobility there are two possibilities, i.e. the defect concentration saturates as there are no traps left (saturated traps), or larger clusters are formed around the impurities as nucleation centers (unsaturable traps). There is evidence for the formation of small defect agglomerates after very
high dose irradiations in the high voltage electron microscope (@t 2 lo** e-/cm2> [2], however, the nucleation (intrinsic or extrinsic) and growth is not quantitatively understood. The present investigation is based on X-ray diffraction techniques, as these methods yield information on defect concentrations and defect structures and are applicable just within this gap of irradiation doses.
2. Experimental
methods
The investigations of the diffuse scattering intensity and of the change of the lattice parameter were performed with CuK,, radiation at a measuring temperature of 6 K (for details see e.g. Ref. [3]). The theory necessary to exploit the information contained in the measured diffuse scattering cross section S is well documented [4], and for small deviations q of the scattering vector k from a reciprocal lattice vector G the scattering cross section of the Huang Diffuse Scattering (HDS) is given by: S,(k) = cf*IGs(q>]1*; s(q) is the Fourier transform of the displacement field of an isolated defect, c is the defect concentration, and f is the atomic scattering factor. Due to the l/r* decrease of the long range displacement field around a point defect we obtain the characteristic l/q2 decrease of S,. Expressing the strength of the displacement field s(r) by the relaxation volume V”’ of the defect we obtain: s, - C(V”r’)*G*/q2.
* Corresponding author. Tel.: +49 2461 61 6074, fax: + 49 2461 61 2550, e-mail: [email protected]. 0168-583X/97/$17.00 0 1997 Elsevier Science B.V. All rights reserved PI/ SOl68-583X(96)00851-8
(1)
S, yields the product c(Vre’)*, and by combination with the change of the lattice parameter, A a/a - cV “r’/3, the two unknown numbers c and V re’ can be determined both.
1. FUNDAMENTALS/BASICS
H. Z&en,
28
P. Ehrhart/Nucl.
Instr. and Meth. in Phys. Res. B 127/ 128 (1997) 27-31
As we consider FPs, the experiment yields average values from contributions of interstitials and vacancies: S, - c( ( vim’)’ + (VT)*) and
A a/a N c( Vire’ + V:'
).
(2)
These equations show that defects with opposite sign of V re’ can cancel in A a/a, however, the diffuse scattering S, adds up. Therefore S, is a measure of the changes of the defect concentration even where As/a vanishes. This approach will be modified if the basic assumption of a random distribution of defects is no longer valid. Generally, c must be replaced in Eq. (1) by the Fourier transform of the concentration fluctuations which yield deviations from the characteristic l/q2 behavior of S,. We have to consider here two special situations: (i) For the case of a clustering of defects we observe a stronger increase of S, at small values of q and a final enhancement: S, (cluster)
= nS, (single defect) .
(3)
n is the number of defects in the cluster, and the total defect concentration is kept constant. Due to this enhancement HDS can very sensitively indicate the onset of cluster formation. (ii) A close FP presents a special defect correlation as it combines defects with opposite signs of s, which are separated by a certain minimum distance. Such a pair is characterized by large additive displacements between
I
L
I
I
,
1.5x 10'9 A
.
1
.
001
4 dose (10” e-/cm”)
Fig. 2. Dose dependence of the average value of the HDS intensity obtained at (5 1 l)- and (4CK%reflections after electron irradiation at 4 K. Cz-Si and FZ-Si are distinguished by different symbols.
the vacancy and the interstitial atom and compensation of the displacements at larger distances. These displacements yield a decrease of the intensity at small q values as discussed in detail for InP [3] and GaAs [5]. The samples were slightly p-doped(3 X 10” Bcmm3), and Cz-Si as well as FZ-Si wafers were used in order to check for a possible influence of oxygen on the defect reactions. With this low doping level carriers are removed after very low doses and we have highly ohmic Si over the range of doses investigated here. The irradiations were performed with 2.5 MeV electrons at the Jiilich irradiation facility [6] with current densities between 5 and 10 pA/cm2.
3. Defects after 4 K irradiation kAA
*
0.02
0.03
.
0.04
‘1
0.05
q/G
Fig. 1. Scattering function of the HDS close to the (5 1 1).reflection of irradiated Si. The scattering function has been normalized in order to consider the elastic anisotropy of the crystal and is multiplied by 4’; for such a plot of S,q’ a constant value is expected for isolated point defects. Results are shown for irradiation doses of 0.75, 1.7, and 3.5X 10” e-/cm’; open symbols characterize Cz-Si and full symbols Fz-Si. The lines are a guide to the eye for the data points referring to different irradiation doses.
Fig. 1 shows the defect induced HDS after different irradiation doses. For the lower irradiation doses we observe the characteristic decrease of S,q2 at small values of q instead of the constant value, expected in such a plot for a random distribution of defects. Combined with additional features of the distribution of the scattering intensity we can conclude, that there is a dominant contribution of close ITS with a typical distance of 1-2 lattice constants present after irradiation. The average values of S, taken over the region of q 4 0.03 A-’ are shown in Fig. 2 and show no significant difference between Cz and FZ wafers. There is a nearly linear increase of S, with irradiation dose up to @t = 2 X lOi e-/cm’, i.e. a continuous production of additional FPs. For higher doses we observe a change of the intensity distribution (Fig. 1) and a faster increase (Fig. 2). These observations can be consistently explained by the formation of interstitial clusters, which grow slowly out of a high concentration of ITS and get an average size of n = 3 at the highest dose (Eq. (3)). In contrast to the increase of S, we observe no systematic change of the lattice parameter (ha/a 5 (0.5 f 0.5)
29
H. Zillgen, P. Ehrhart /Nucl. Instr. and Meth. in Phys. Res. B 127 / 128 11997) 27-31
I 0.04
0.02 Fig. 3. Schematic view of the interaction potential between vacancy and interstitial atom: full line for thermal equilibrium and dotted line for the electronically excited state.
x 10M5). From Eq. (2) we conclude therefore, that the displacement fields of interstitials and vacancies must nearly compensate, i.e. Vi”’ = -V,“‘. For this condition Eq. (2) allows no separation of c and (V re’)2 and we have to make assumptions on one of these quantities. If we (f2 is the atomic volume) we assume Vvx’ = -0SR obtain an introduction rate 2 = c/@f = 1 cm-’ which corresponds to an average displacement threshold of 40 eV for Si. The given values should be considered as a maximum for IVrr’l and a minimum for 2, as discussed in detail for InP [3]. In contrast to the expectation we therefore observe neither a saturation of the defect concentration at the concentration of the doping atoms (= lOI cm - 3>, nor the beginning of cluster growth at the corresponding dose. The observation of more than 10” FPs/cm3 and the similarity of the results for the Cz and FZ wafers clearly show, that these defects are intrinsic and not stabilized by impurities. Finally, we have to ask: why have these defects not been observed by other methods and how are they compatible with a fast athermal mobility? (i) From the observed compensation of the displacements of interstitials and vacancies it is obvious that very precise early lattice parameter measurements [7] observed only small effects and/or saturation at defect concentrations similar to the doping level. Similar to the HDS the attenuation of the anomalous X-ray transmission should change independent of the sign of the displacements and, although no quantitative interpretation was possible, there are observations in agreement with our results [8]. (ii) As electrical and spectroscopic methods rely on charged defects and/or energy levels within the bandgap, we might speculate about the FP as an acceptor-donor pair which appears nearly neutral from the outside. (iii) At the first moment the observed defects might best be explained by the continuous production of immobile IT’s which would, however, be at variance to the high athermal defect mobility deduced from reactions of dopants [l]. Although there are different ways to resolve this discrepancy [9], we presently prefer a model which is consistent with the earlier conclusions: the interstitials can
0.06
q/G Fig. 4. Scattering function of the HDS (similar to Fig. 1) as observed close to the (@O&reflection of RT irradiated Si. Data points measured after 4 K irradiation and after subsequent annealing at RT arc shown for comparison.
escape from their vacancy and can form other complexes, however, as soon as all extrinsic traps are saturated the vacancies necessarily become the dominant traps and retrap mobile interstitials [3,5]. This means that there is a binding energy as well as a recombination barrier for the FP as shown schematically in Fig. 3. Such a recombination barrier is not an ad hoc assumption as similar potentials have been proposed earlier in order to explain the temperature dependence of the displacement cross section [lo] or details of the kinetics of oxidation enhanced diffusion [ 1 I]. It seems remarkable, that the dissociation barrier of the pair can be rather easily overcome by ionization induced jumps and that the recombination barrier is much more difficult to overcome. Such a behavior can be explained by a Coulomb repulsion in the “excited” charge state.
-I
0.0
0.5
1.0
1.5
dose (10”
2.0
2.5
3.0
e-/cm*)
Fig. 5. Dose dependence of the average value of the HDS for RT irradiated Si (similar to Fig. 2). The dotted lines show the increase of S, after 4 K irradiation, i.e. the initial slope of Fig. 2, and an average slope for the remaining intensity after subsequent annealing at 300 K which is a good approximation for the medium doses (Fig. 4).
1. FUNDAMENTALS/BASICS
30
H. Zillgen, P. Ehrhart/Nucl.
4. Defects after room temperature
Instr. und Meth. in Phys. Res. B 127/ 128 (1997) 27-31
irradiation
During room temperature (RT) irradiation we expect a thermally activated defect mobility in addition to the atherma1 mobility. Figs. 4 and 5 show the changes of the distribution of the scattered intensity and of the dose dependence of S, as compared to the 4 K irradiations and the subsequent annealing at RT. Fig. 4 shows for the example of medium dose irradiated Cz-Si that during annealing to RT about 50% of the intensity is lost and that the scattering distribution does no longer indicate close pairs. After RT irradiations we observe a very similar intensity distribution as after annealing to RT; hence the close PPs recombine by thermally activated jumps. For RT irradiations there are, however, important differences between Cz-Si and FZ-Si (Fig. 5): for the Cz-Si the damage rate is higher by more than a factor of 3. In contrast to the low temperature irradiation where the nucleation of stable intrinsic defect complexes seems possible starting from the high initial defect concentrations, impurities seem necessary to stabilize - at least temporarily - the defects at RT. In order to explain the buildup of the observed high densities of small defects we might speculate about a kind of catalytic reaction of the oxygen: e.g. the formation of di-interstitials close to oxygen sites and later on the, possibly ionization assisted, detrapping of interstitial oxygen. Combining these observations we conclude that, similar to MgO [12], there are quite different defect interactions for the different jump modes (Fig. 3): during athermal migration the interstitials seem not to surpass the recombination threshold, but with additional thermal activation the probabilities for recombination and escape become comparable. However, for a final survival the trapping at oxygen or other traps is necessary, and there is indication that the binding state with oxygen is also much easier reached by thermally activated jumps. As a common feature it remains very difficult to nucleate larger defects like dislocation loops.
5. Defect annealing Finally, we summarize the annealing of S,, as shown 6, without discussing any details. After low dose irradiation we observe between 40 and 200 K primarily the recombination of the FPs. If more stable small complexes are formed at high doses the annealing below RT is much suppressed, and the rather continuous decrease of S, up to the final annealing at 900 K indicates a steady loss of defects by recombination without remarkable growth of the clusters. From the observed temperature locations of the reactions we may deduce some estimates for the characteristic energies: the recombination barrier of the PPs varies bein Fig.
look,
4b t\
I
.
,
,
,
.
,
4
\
-I-WI Fig. 6. Isochronal annealing (At = 15 min) of the HDS cross section of Si after irradiation at 4 K. The electron irradiation doses are given in the figure in units of e-/cm*; open symbols refer to FZ-Si and full symbols to Cz-Si.
tween 0.2 and 0.6 eV. The dissociation energy of the FP may be estimated from the beginning of the annealing of the optical absorption line of the divacancies at around 200 K [ 131 which yields a value of 2 0.6 eV. As soon as small complexes have formed, the dissociation energy for defects is fast increasing and can reach values of 2-3 eV. These values are still below the value of 3.6 eV, which characterizes the escape from interstitial dislocation loops [ 141.
6. Conclusions We have shown that in Si a high concentration of intrinsic bound FPs can be frozen in which had not been observed earlier. In spite of their ‘electrical invisibility’ these FPs may have important consequences for the modeling of defect reactions during implantation and annealing: (8 Although the individual FPs anneal below RT, the defects can form much more stable complexes, which become dominant if the local density reaches values of the order of 2 x 10” cme3. (ii) The reaction rates differ for ionization induced and thermally activated migration jumps. (iii) The observation of strongly bound FPs shows, that intrinsic trapping reactions must be considered as a possible mechanism for the reduction of the effective mobility of interstitials and vacancies in addition to the trapping by impurities. This trapping might even contribute to the differences in the defect mobility deduced from irradiation experiments [ 11 and diffusion data [ 151.
Acknowledgements We thank Prof. W. Schilling for many helpful discussions and we gratefully acknowledge the technical assistance by W. Bergs and U. Dedek and the support by Dr. F. Dworschak and B. Schmitz during the irradiations.
H, Zillgen, P. Ehrhart/Nucl.
Instr. and Meth. in Phys. Res. B 127/128
References [I] G.D. Watkins, in: Electronic Structure and Properties of Semiconductors, Materials Science and Technology, Vol. 4, ed. W. Schroeter (VCH, Weinheim, 1992) p. 105. [2] H. Fall, Inst. Phys. Conf. Ser. 23 (1975) 233. [3] K. Karsten and P. Ehrhart, Phys. Rev. B 51 (1995) 10508. [4] P.H. Dederichs, J. Phys. F 3 (1973) 471. [5] A. Pilhkat, K. Karsten and P. Ehrhart, Phys. Rev. B 53 (1996) 7823. [6] J. Hemmerich, W. Sassin and W. Schilhng, Z. Angew. Phys. 29 (1970) 20. [7] N.E. Moyer and R.C. Buschert, in: Radiation Effects in Semiconductors, ed. F.L. Vook (Plenum, New York, 1968) [8j g. E&h
(1997) 27-31
31
[9] S. Bausch, H. Zillgen and P. Ehrhart, Mater. Sci. Forum I%/201 (1995) 1141. f IO] J. W. Corbett and J.C. Bourgoin, in: Point Defects in Solids, Vol. 2, eds. J.H. Crawford and L.M. Slifiin (Plenum, New York, 1975) p. 1. [ 1l] P.M. Fahey, P.B. Griffm and J.D. Plummer, Rev. Mod. Phys. 61 (1989) 289. 1121 C. Scholz and P. Ehrhart, MRS Symp. Proc. 279 (1993) 427. [ 131 Unpublished results. [14] P.A. Stalk, H.J. Gossmann, D.J. Eaglesham, DC. Jacobson, H.S. Luftman and J.M. Poate, MRS Symp. Proc. 354 (1995) 307. [I51 H. Bracht, N. A. Stolwijk and H. Mehrer, in: Semiconductor Silicon 1994, eds. H.R. Huff, W. Bergholz, K. Sumino (The Electrochemical Society, 1994) p. 593.
and J.S. Koehler, Phys. Rev. B 23 (1981) 1859.
1. FUNDAMENTALS/BASICS