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Low energy ion induced damage in silicon at 50 K
N U C L E A R I N S T R U M E N T S AND METHODS
I32 (i97.6) 2 8 1 - 2 8 4 ;
©
NORTH-HOLLAND
PUBLISHING
CO.
L O W E N E R G Y I O N I N D U C E D D A M A G E IN S I L I C O N AT 50 K* D . A . THOMPSON and R.S. WALKER
Department of Engineering Physics and Institute for Materials Research, McMaster University, Hamilton, Ontario, Canada, L8S 4M1 A systematic investigation has been undertaken to study the damage created in silicon due to bombardments by light and medium mass ions at 50 K. The results are interpreted in terms of the average cascade damage density. For cascade damage densities ~< l0 -a, the results are consistent with linear cascade theory. For higher cascade damage densities, non-linear effects suggest the existence of spike phenomena.
1. Introduction It has been suggested 1) that implantation disorder can be correlated by a single parameter, namely the amount of ion energy deposited/s into atomic collisions (atomic energy rate). Investigations 1) indeed showed that the damage created in Si at 87 K by light ions ( 1 0 0 k e V O ÷) and heavy ions ( 2 0 0 k e V S b ÷) is the same for equal atomic energy rate per unit implant volume. However, at room temperature, where significant annealing can occur, the light ion-induced damage was less than that for the heavy ion, apparently due to an enhanced recovery for the more dilute cascade energy density. A simple means of confirming this is to use molecular versus atomic ion bombardments. A diatomic ion with the same energy/atom as the corresponding monatomic ion deposits double the energy into about the same cascade volume. If annealing can occur, this increased cascade energy density may inhibit the process, so that the number of displaced atoms per diatomic ion would be greater than twice the number for the monatomic ion. Such a "molecular effect" (,~50%) was first measured 2) in GaAs bombarded at 300 K with 40 keV As + and 20 keV As +. The above implies that a more relevant characterization of implantation disorder is in terms of the individual cascade energy density into atomic processes. This has recently been borne out by studies 3) of Si and Ge bombarded at r o o m temperature with a variety of monatomic and diatomic ions. "Molecular effects" of 40-70% were again observed. Also, a positive correlation existed between the cascade damage density (FD) and the deposited energy density (E) of the form FDOCL"/'6. This paper reports upon a systematic study of the damage created in silicon bombarded with light through medium mass ions at 50 K. No defect an* Research supported by the National Research Council of Canada and the Defence Research Board.
nealing has been observed in this temperature region except for the inferred exchange, during electron irradiation at 4.2 K, between silicon interstitials and group III substitutional impurities4). Again, the data are interpreted in terms of cascade disorder and energy density to examine the nature of the correlation. The "molecular effect" is also investigated at these low temperatures.
2. Experimental and analysis Etch-polished (111) oriented silicon samples were bombarded at 50 K using the McMaster 150 keV accelerator fitted with a Danfysik 911A ion source. Targets were mounted on the x - y goniometer surrounded by an electrically connected cold shield (also at 50 K) both to reduce surface contamination and provide accurate dosimetry ( ~ 5 % ) . An x - y beam sweep system ensured a uniform ( < 5 %) implant. The use of an off-axis aperture system prevented any neutral ion component created before the sweep system from reaching the target. Sufficiently low irradiation doses were used such that no damage saturation effects existed. All implants were performed ~ 8 ° from normal incidence and 10 ° from a [110] channel. Average swept beam currents were 10-30 nA/cm 2. The damage levels were measured in-situ at 50 K by Rutherford backscattering of 1 MeV He + ions, from a Van der Graaffaccelerator, channeled along the ( 111 ) axis. In the case of the heavier, low energy ion bombardments a linear dechanneling correction was used to subtract off the random component of the beam. However, when the damage distribution extended well beyond the detector resolution limit (,~ 300 A) a single scattering dechanneling approximation was used5).
3. Results and discussion In a recent publication6), inexplicable discrepancies were found to exist in the measured damage, resulting V. DAMAGE
282
D. A. T H O M P S O N A N D R. S. W A L K E R
from 300 keV Kr + bombardment of GaAs and GaP at 25 K, as determined by channeling along the < 111 ) and directions. Since a reliable value for the concentration of displaced atoms (No) is required for this study, it was considered necessary to investigate whether any possible anisotropic damage effects existed in silicon. Implants of 20 keV N +, 40 keV N + and 8 0 k e V Z n + were carried out at 50 K and the damage analysed in-situ along both the <111) and < 110) axes of the same target. In each case the damage levels for the different directions agreed within < 10 %. Moreover, the damage depth profiles obtained along both directions showed good agreement. This can be seen from fig. 1, which shows <111) and <110) analysed damage profiles for 40 keV N + bombardment at 50 K. These profiles were generated using an iterative procedure s) based on a single scattering dechanneling model. The profiles are weakly dependent on the value chosen for the aligned stopping power. The values chosen for this analysis were 0.8S R and 0.65SR for and (110), respectively7), where SR is the nonaligned stopping power for 1 MeV He + in silicona). The damage data has been interpreted in terms of the cascade damage density (FD), which is defined as FD = 0.35 N*/Nv, where N~ is the number of displaced atoms/incident ion, and Nv/0.35 is the number of atoms in the cascade volume. N v is calculated assuming that the cascade can be approximated as an ellipsoid of revolution having transverse and longitudinal straggling [as interpreted from Winterbon9)] as the minor and major axes, respectively. The factor, 0.35, is obtained since if a Gaussian distribution is assumed,
then about 35% of the damage will be contained within this ellipsoid. To obtain a value for N~ it is necessary, in some cases, to consider the way in which the damage, No, increases with ion dose, qS. Some results are shown in fig. 2. In fig. 2a it can be seen that for low doses of nitrogen the increase in damage is non-linear with dose. However, at higher doses it becomes linear. In these cases N* is taken as dND/dC~ in the linear region. For the heavier ion bombardments, e.g. Zn (see fig. 2b), it is found that ND is linear with ~b, hence N* = ND/q5is used. It is difficult to say at present whether the non-linearity for low dose, light ion bombardments is related to the dechanneling correction or the channeling technique. The non-linear effect was even more dramatic for He + and higher energy oxygen bombardments. Table 1 lists the experimental data obtained at 50 K and the corresponding values for the cascade damage density, F D. The calculated values for the energy deposited in the cascade (E = 0.35 Eo/Nv, where E o is the incident ion energy) and the energy deposited into atomic processes in the cascade [E'~ = 0.35 v(Eo)/N v, where v(Eo)/E o is the calculated fraction 9) of the incident ion energy that goes to atomic collision processes] are also listed in the table. It should be
+0+ENS50°K/ :
300
,, 4 0 KeV 8 0 KeV
N+ + N2
o 2 0 KeV
N+
•
~ 20C
P C3 txl
/
~ ioc ~
co
50 1
40
50
• o
oO
I
o
o
o
(o) o_ 6c
• o
o"
~
~ 8c m 40 °e °o o oo •
-
I
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20
y
ION
D O S E ( c r n ~ ) x 10-13
12(2
o o
I
I 16
8 oe
500
ATOMtC
I 12
o
o"
o• o
I 8
4
0
oe
oo
•
o o ~ • • o o~
20 z uJ
/8 j
4Dose 0 KeVI 5x], N~~!4$1N+ / cr'm r' : z° K • <111> Arsch/ss o Anolism
• LU
./2 _ ""
--
/
/e/
/ / / / / j //j/.-
~///w"
TARGET
/J
Si
oSOKeV • .,oK0v o 2oKe. • +OKeV
z
50°K
Z~ z." zo+ A'
I I I I
L
1500
DETW'~ I A N G S T R O M S ]
Fig. 1. D a m a g e distributions in silicon bombarded at 50 K with 40 keV N + as measured using <111 > and < 110> channeling o f ! MeV He +.
I
(b)
2 ATOMIC
3 ION
4 DOSE
5
6
( c m - Z ) x tO -+3
Fig. 2. Displaced atom concentration at 50 K for various doses of: (a) 80 keV and 40 keV N ~ , and 40 keV and 20 keV N+; (b) 30 keV Ar + and 80,40 and 20 keV Z n +.
LOW
ENERGY
ION
INDUCED
283
DAMAGE
TABLE 1 E x p e r i m e n t a l d a t a i n t e r p r e t e d in t e r m s o f t h e c a s c a d e d a m a g e d e n s i t y (FD) a n d t h e c a l c u l a t e d e n e r g y d e n s i t i e s ( E a n d / 2 ~ ) . Ion
Energy, E0
N~
species
(keV)
(disp./ion)
Cd + Cd~ Zn + Zn + Zn + Ar + N+ N+ N+ N+ O+ He +
15 30 20 40 80 30 20 40 40 80 300 a 30
Nv
3659 11732 3014 4833 9162 2967 1408 2816 2214 4428 4650 b 313 b
8.35 8.35 3.28 1.54 8.0 5.41 1.34 1.34 8.3 8.3 8.45 1.66
x x x x x x x x x x x x
103 103 104 105 10 a 105 106 10 o 10 a 106 10 s l0 s
1.53 x 4.92 x 3.22x 1.10 x 4.0 x 1.92 x 3.68 x 7.35 x 9.3 x 1.86 x 1.92 x 8.24 x
v (E0)
gv
(eV/atom)
E0
(eV/atom)
6.28 x 10-1 1.26 2.13 x 10 -1 9.12 x 10 2 3.5 x 10 . 2 2 . 2 6 x 10 2 5.22 x 1 0 - 3 1.04 x 1 0 - 2 1.69 x 10 3 3.38 x 1 0 - 3 1.24 x 10-4 6.33 x 10 5
0.7354 0.7354 0.6988 0.6614 0.6149 0.6213 0.5424 0.5424 0.4503 0.4503 0.1839 0.1679
4 . 6 2 x 10 -1 9.24 xlO 1 1.49 x 10 -1 6.03 x 10 - 2 2.15 x 10 -2 1.41 × 1 0 2 2.83 x 10 -3 5.66 x 10 - 3 7.6 x l O 4 1.52 × 1 0 3 2.29 x 10-3 1.06 x 10 - 5
E"
FD
10-1 10-1 10 - 2 10 2 10-3 10-a 10-4 10 - 4 10-5 10 - 4 10-6 10-7
a Experiment carried out at Chalk River Nuclear Laboratories. b N ~ a p p r o x i m a t e s i n c e ND n o t l i n e a r in q~ o v e r r e g i o n i n v e s t i g a t e d .
noted that for the cases of monatomic and diatomic nitrogen bombardments, no "molecular effect" was observed. This is also clearly evident in fig. 2a, where it can be seen that molecular nitrogen creates the same amount of damage as the equivalent atomic energy and atomic dose of monatomic nitrogen. However, for the high density cascades resulting from Cd + and Cd~- implants, a significant "molecular effect" (~1.6) is observed, consistent with the previous 300 K data3). The data for F D vs E~. and E" obtained at 50 K are IO
50 ° K 50 o K
I o > IOv
500*K o
/ °/~ f J
500" K .tier J.B MITCHELL/
Eu
z / l0~
"z /
oo~ o /I
~"
, /2
I-
o
l 0~
,,/ ~ e// / p," /
TARGE T
SILICON
_/ ~
1(5~ iO7
i ~/ 10`6
I lO 5 CASCADE
Fig. the and 300
I 10-4
I iO*S
DAMAGE
I IO a
DENSITY
I iO I FO
3. M e a s u r e d c a s c a d e d a m a g e d e n s i t y (FD) a s a f u n c t i o n o f e n e r g y d e p o s i t e d i n t o a t o m i c p r o c e s s e s (/20 a t b o t h 50 K 3 0 0 K a n d as a f u n c t i o n o f t h e t o t a l e n e r g y d e p o s i t e d ( E ) a t K.
shown plotted in fig. 3. Also shown is the 300 K data previously obtained by Mitchell et al. 3). There exists an obvious correlation, particularly for FD VS E~ (50 K) over several orders of magnitude. For values of F o up to ~ 1 0 -3 a linear relationship exists such that FDOCE'v. in the case of FD vs E (50 K), lines have been drawn through the atomic and equivalent molecular N data. The relationship is linear, since no "molecular effect" exists. However, these lines do not intersect, nor is the gradient consistent with that necessary to connect the entire data. Thus it is meaningless to attempt to correlate the data in terms of E in this damage density region. In contrast, for Fo vs Ev (50 K), a gradient of unity connects all points below F o ~ 10-3 resonably well. However, the lowest damage density data has strong non-linear dose effects which results in N* being significantly underestimated. The linearity of damage with atomic energy density is a reasonable expectation from linear cascade theory. For the higher density cascades (FD>10-3), it can be seen that Fo increases faster than linearly with E,. and tends towards the gradient observed in the 300 K data (F o ocE 1"6) 3). In this region, the weak variation of v(E) makes little difference in whether E or E~ is taken as the relevant parameter. It can be observed that the 50 K data show an offset ( ~ 2 × ) over the previous 3 0 0 K data, indicating that some annealing may have occurred at room temperature even for these dense cascades. In some instances, room temperature bombardments were undertaken. For the light ions, a dramatic reduction in N~ occurs due to annealing, e.g. N*(5OK)~-3ON* (300 K) for a 20 keV N + bombardment. These results V. D A M A G E
284
D. A. THOMPSON AND R. S. W A L K E R
are also shown in fig. 3. For 50 K implants and F D> 10 -3, the non-linearity cannot be accounted for by annealing effects. This, and the observation of a molecular effect, would appear to be evidence that nonlinear "spike effects" are occurring as previously suggested4). The observed onset of these effects even at such low cascade damage densities (>~ 10-3) is not improbable since the realistic cascade structure is one of many denser subcascades enclosed within the calculated cascade envelope. Further evidence of the "spike effect" is demonstrated in fig. 4 where the "effective" displacement energy (E~fr) is shown as a function of FD. E~ff is calculated from the modified Kinchin and Pease formula' '), E~fr = 0.42 v(Eo)/N ~. For nitrogen data (FD< 10-3), the value for E~fr is relatively constant (i.e. in region where F D is linear with E',.), and is considerably lower than the accepted value of Fo = 14 e V 12) as determined from electron irradiation studies. Departures are noted for the very dilute cascades resulting from 30 KeV He + and 300 keV O + bombardment; however, as previously stated, N* is underestimated for these points resulting in an overestimation of E~ft. For F D > 1 0 - 3 , E~ff is seen to decrease, extrapolating to a value of ~ 0 . 4 e V , at Fo = 1, which is comparable to the average energy per atom of silicon at the melting temperature, T m (average energy/atom at the melting point is 3kTm = 0.44 eV for Si). The tendency of the effective displacement
energy to approach the heat of melting is consistent with a spike model. Clearly, the observation that F D ~ I and shows no saturation, indicates that the cascade volume is no longer an adequate description of the damage volume. This is also borne out by the fact that as FD~>40%, E v > E ~ ft. 4. Conclusions
l) For light ion bombardments at 50 K, where annealing is not present, no "molecular effect" is observed. It appears that the energy density into atomic processes, E,, is the single parameter determining the observed cascade damage for cascade damage densities < 10-3 (i.e. F D ~ E , . ) . 2) For damage densities > 10-3, non-linear effects are observed at 50 K which cannot be related to annealing. It is suggested that the non-linearity at both 50 K and 300 K is related to the presence of spike phenomena from the observations that: (a) FD~I and shows no tendency to saturate; (b) "molecular effects" occur; (c) as FD--,I, E~fr tends to the average energy/atom at the melting temperature; (d) Ev becomes > E~ft. The authors wish to thank Dr J. A. Davies for many useful discussions and K. B. Winterbon for supplying a preprint of his book. References
> >-
o l0
•
THIS WCRK
o
JBMITCHELL
et
81TM
Ld
~-
8
~6 £ w 4 _>
.....
~
~
X~o
B2
~"~
0
I id *
i0 -~
P I0 5
I
I
IC ~
CASCADE
13 ~
DAMAGE
1 bJ a
DENSITY
~.. E Iq 4
I I
IO
Fo
Fig. 4 "Effective" displacement energy as a function of the cascade damage density.
a) S.T. Picraux and F. L. Vook, Rad. Effects 11 (1971) 179. 2) j . A . Moore, G. Carter and A. W. Tinsley, Rad. Effects 25 (1975) 49. s) j . B . Mitchell, J . A . Davies, L . M . Howe, R.S. Walker, K. B. Winterbon, G. Foti and J . A . Moore, Proc. 4th Int. Conf. on Ion implantation into semiconductors and other materials, Osaka, Japan (1974). 4) G. D. Watkins, Radiation damage in semiconductors, (Dunod, Paris, 1964) p. 97. 5) K. Schmid, Rad. Effects 17 (1973) 201. 6) j. Bottiger and J. L. Whitton, Rad. Effects 19 (1973) 201. 7) F. H. Eisen, GI J. Clark, J. Bottiger and J. M. Poate, Rad. Effects 13 (1972) 93. 8) j. F. Ziegler and W . K . Chu, At. Nucl. Data Tables 13 (1974) 463. 9) K. B. Winterbon, Ion implantation range and energy distributions (Plenum Press, New York, in press) vol. 2. 10) p. Sigmund, Appl. Phys. Lett. 25 (1974) 169. 11) p. Sigmund, Appl. Phys. Lett. 14 (1969) 114. 12) j . j . Loferski and P. Rappaport, J. Appl. Phys. 30 (1959) 1296.
I32 (i97.6) 2 8 1 - 2 8 4 ;
©
NORTH-HOLLAND
PUBLISHING
CO.
L O W E N E R G Y I O N I N D U C E D D A M A G E IN S I L I C O N AT 50 K* D . A . THOMPSON and R.S. WALKER
Department of Engineering Physics and Institute for Materials Research, McMaster University, Hamilton, Ontario, Canada, L8S 4M1 A systematic investigation has been undertaken to study the damage created in silicon due to bombardments by light and medium mass ions at 50 K. The results are interpreted in terms of the average cascade damage density. For cascade damage densities ~< l0 -a, the results are consistent with linear cascade theory. For higher cascade damage densities, non-linear effects suggest the existence of spike phenomena.
1. Introduction It has been suggested 1) that implantation disorder can be correlated by a single parameter, namely the amount of ion energy deposited/s into atomic collisions (atomic energy rate). Investigations 1) indeed showed that the damage created in Si at 87 K by light ions ( 1 0 0 k e V O ÷) and heavy ions ( 2 0 0 k e V S b ÷) is the same for equal atomic energy rate per unit implant volume. However, at room temperature, where significant annealing can occur, the light ion-induced damage was less than that for the heavy ion, apparently due to an enhanced recovery for the more dilute cascade energy density. A simple means of confirming this is to use molecular versus atomic ion bombardments. A diatomic ion with the same energy/atom as the corresponding monatomic ion deposits double the energy into about the same cascade volume. If annealing can occur, this increased cascade energy density may inhibit the process, so that the number of displaced atoms per diatomic ion would be greater than twice the number for the monatomic ion. Such a "molecular effect" (,~50%) was first measured 2) in GaAs bombarded at 300 K with 40 keV As + and 20 keV As +. The above implies that a more relevant characterization of implantation disorder is in terms of the individual cascade energy density into atomic processes. This has recently been borne out by studies 3) of Si and Ge bombarded at r o o m temperature with a variety of monatomic and diatomic ions. "Molecular effects" of 40-70% were again observed. Also, a positive correlation existed between the cascade damage density (FD) and the deposited energy density (E) of the form FDOCL"/'6. This paper reports upon a systematic study of the damage created in silicon bombarded with light through medium mass ions at 50 K. No defect an* Research supported by the National Research Council of Canada and the Defence Research Board.
nealing has been observed in this temperature region except for the inferred exchange, during electron irradiation at 4.2 K, between silicon interstitials and group III substitutional impurities4). Again, the data are interpreted in terms of cascade disorder and energy density to examine the nature of the correlation. The "molecular effect" is also investigated at these low temperatures.
2. Experimental and analysis Etch-polished (111) oriented silicon samples were bombarded at 50 K using the McMaster 150 keV accelerator fitted with a Danfysik 911A ion source. Targets were mounted on the x - y goniometer surrounded by an electrically connected cold shield (also at 50 K) both to reduce surface contamination and provide accurate dosimetry ( ~ 5 % ) . An x - y beam sweep system ensured a uniform ( < 5 %) implant. The use of an off-axis aperture system prevented any neutral ion component created before the sweep system from reaching the target. Sufficiently low irradiation doses were used such that no damage saturation effects existed. All implants were performed ~ 8 ° from normal incidence and 10 ° from a [110] channel. Average swept beam currents were 10-30 nA/cm 2. The damage levels were measured in-situ at 50 K by Rutherford backscattering of 1 MeV He + ions, from a Van der Graaffaccelerator, channeled along the ( 111 ) axis. In the case of the heavier, low energy ion bombardments a linear dechanneling correction was used to subtract off the random component of the beam. However, when the damage distribution extended well beyond the detector resolution limit (,~ 300 A) a single scattering dechanneling approximation was used5).
3. Results and discussion In a recent publication6), inexplicable discrepancies were found to exist in the measured damage, resulting V. DAMAGE
282
D. A. T H O M P S O N A N D R. S. W A L K E R
from 300 keV Kr + bombardment of GaAs and GaP at 25 K, as determined by channeling along the < 111 ) and
then about 35% of the damage will be contained within this ellipsoid. To obtain a value for N~ it is necessary, in some cases, to consider the way in which the damage, No, increases with ion dose, qS. Some results are shown in fig. 2. In fig. 2a it can be seen that for low doses of nitrogen the increase in damage is non-linear with dose. However, at higher doses it becomes linear. In these cases N* is taken as dND/dC~ in the linear region. For the heavier ion bombardments, e.g. Zn (see fig. 2b), it is found that ND is linear with ~b, hence N* = ND/q5is used. It is difficult to say at present whether the non-linearity for low dose, light ion bombardments is related to the dechanneling correction or the channeling technique. The non-linear effect was even more dramatic for He + and higher energy oxygen bombardments. Table 1 lists the experimental data obtained at 50 K and the corresponding values for the cascade damage density, F D. The calculated values for the energy deposited in the cascade (E = 0.35 Eo/Nv, where E o is the incident ion energy) and the energy deposited into atomic processes in the cascade [E'~ = 0.35 v(Eo)/N v, where v(Eo)/E o is the calculated fraction 9) of the incident ion energy that goes to atomic collision processes] are also listed in the table. It should be
+0+ENS50°K/ :
300
,, 4 0 KeV 8 0 KeV
N+ + N2
o 2 0 KeV
N+
•
~ 20C
P C3 txl
/
~ ioc ~
co
50 1
40
50
• o
oO
I
o
o
o
(o) o_ 6c
• o
o"
~
~ 8c m 40 °e °o o oo •
-
I
tOOO
20
y
ION
D O S E ( c r n ~ ) x 10-13
12(2
o o
I
I 16
8 oe
500
ATOMtC
I 12
o
o"
o• o
I 8
4
0
oe
oo
•
o o ~ • • o o~
20 z uJ
/8 j
4Dose 0 KeVI 5x], N~~!4$1N+ / cr'm r' : z° K • <111> Arsch/ss o
• LU
./2 _ ""
--
/
/e/
/ / / / / j //j/.-
~///w"
TARGET
/J
Si
oSOKeV • .,oK0v o 2oKe. • +OKeV
z
50°K
Z~ z." zo+ A'
I I I I
L
1500
DETW'~ I A N G S T R O M S ]
Fig. 1. D a m a g e distributions in silicon bombarded at 50 K with 40 keV N + as measured using <111 > and < 110> channeling o f ! MeV He +.
I
(b)
2 ATOMIC
3 ION
4 DOSE
5
6
( c m - Z ) x tO -+3
Fig. 2. Displaced atom concentration at 50 K for various doses of: (a) 80 keV and 40 keV N ~ , and 40 keV and 20 keV N+; (b) 30 keV Ar + and 80,40 and 20 keV Z n +.
LOW
ENERGY
ION
INDUCED
283
DAMAGE
TABLE 1 E x p e r i m e n t a l d a t a i n t e r p r e t e d in t e r m s o f t h e c a s c a d e d a m a g e d e n s i t y (FD) a n d t h e c a l c u l a t e d e n e r g y d e n s i t i e s ( E a n d / 2 ~ ) . Ion
Energy, E0
N~
species
(keV)
(disp./ion)
Cd + Cd~ Zn + Zn + Zn + Ar + N+ N+ N+ N+ O+ He +
15 30 20 40 80 30 20 40 40 80 300 a 30
Nv
3659 11732 3014 4833 9162 2967 1408 2816 2214 4428 4650 b 313 b
8.35 8.35 3.28 1.54 8.0 5.41 1.34 1.34 8.3 8.3 8.45 1.66
x x x x x x x x x x x x
103 103 104 105 10 a 105 106 10 o 10 a 106 10 s l0 s
1.53 x 4.92 x 3.22x 1.10 x 4.0 x 1.92 x 3.68 x 7.35 x 9.3 x 1.86 x 1.92 x 8.24 x
v (E0)
gv
(eV/atom)
E0
(eV/atom)
6.28 x 10-1 1.26 2.13 x 10 -1 9.12 x 10 2 3.5 x 10 . 2 2 . 2 6 x 10 2 5.22 x 1 0 - 3 1.04 x 1 0 - 2 1.69 x 10 3 3.38 x 1 0 - 3 1.24 x 10-4 6.33 x 10 5
0.7354 0.7354 0.6988 0.6614 0.6149 0.6213 0.5424 0.5424 0.4503 0.4503 0.1839 0.1679
4 . 6 2 x 10 -1 9.24 xlO 1 1.49 x 10 -1 6.03 x 10 - 2 2.15 x 10 -2 1.41 × 1 0 2 2.83 x 10 -3 5.66 x 10 - 3 7.6 x l O 4 1.52 × 1 0 3 2.29 x 10-3 1.06 x 10 - 5
E"
FD
10-1 10-1 10 - 2 10 2 10-3 10-a 10-4 10 - 4 10-5 10 - 4 10-6 10-7
a Experiment carried out at Chalk River Nuclear Laboratories. b N ~ a p p r o x i m a t e s i n c e ND n o t l i n e a r in q~ o v e r r e g i o n i n v e s t i g a t e d .
noted that for the cases of monatomic and diatomic nitrogen bombardments, no "molecular effect" was observed. This is also clearly evident in fig. 2a, where it can be seen that molecular nitrogen creates the same amount of damage as the equivalent atomic energy and atomic dose of monatomic nitrogen. However, for the high density cascades resulting from Cd + and Cd~- implants, a significant "molecular effect" (~1.6) is observed, consistent with the previous 300 K data3). The data for F D vs E~. and E" obtained at 50 K are IO
50 ° K 50 o K
I o > IOv
500*K o
/ °/~ f J
500" K .tier J.B MITCHELL/
Eu
z / l0~
"z /
oo~ o /I
~"
, /2
I-
o
l 0~
,,/ ~ e// / p," /
TARGE T
SILICON
_/ ~
1(5~ iO7
i ~/ 10`6
I lO 5 CASCADE
Fig. the and 300
I 10-4
I iO*S
DAMAGE
I IO a
DENSITY
I iO I FO
3. M e a s u r e d c a s c a d e d a m a g e d e n s i t y (FD) a s a f u n c t i o n o f e n e r g y d e p o s i t e d i n t o a t o m i c p r o c e s s e s (/20 a t b o t h 50 K 3 0 0 K a n d as a f u n c t i o n o f t h e t o t a l e n e r g y d e p o s i t e d ( E ) a t K.
shown plotted in fig. 3. Also shown is the 300 K data previously obtained by Mitchell et al. 3). There exists an obvious correlation, particularly for FD VS E~ (50 K) over several orders of magnitude. For values of F o up to ~ 1 0 -3 a linear relationship exists such that FDOCE'v. in the case of FD vs E (50 K), lines have been drawn through the atomic and equivalent molecular N data. The relationship is linear, since no "molecular effect" exists. However, these lines do not intersect, nor is the gradient consistent with that necessary to connect the entire data. Thus it is meaningless to attempt to correlate the data in terms of E in this damage density region. In contrast, for Fo vs Ev (50 K), a gradient of unity connects all points below F o ~ 10-3 resonably well. However, the lowest damage density data has strong non-linear dose effects which results in N* being significantly underestimated. The linearity of damage with atomic energy density is a reasonable expectation from linear cascade theory. For the higher density cascades (FD>10-3), it can be seen that Fo increases faster than linearly with E,. and tends towards the gradient observed in the 300 K data (F o ocE 1"6) 3). In this region, the weak variation of v(E) makes little difference in whether E or E~ is taken as the relevant parameter. It can be observed that the 50 K data show an offset ( ~ 2 × ) over the previous 3 0 0 K data, indicating that some annealing may have occurred at room temperature even for these dense cascades. In some instances, room temperature bombardments were undertaken. For the light ions, a dramatic reduction in N~ occurs due to annealing, e.g. N*(5OK)~-3ON* (300 K) for a 20 keV N + bombardment. These results V. D A M A G E
284
D. A. THOMPSON AND R. S. W A L K E R
are also shown in fig. 3. For 50 K implants and F D> 10 -3, the non-linearity cannot be accounted for by annealing effects. This, and the observation of a molecular effect, would appear to be evidence that nonlinear "spike effects" are occurring as previously suggested4). The observed onset of these effects even at such low cascade damage densities (>~ 10-3) is not improbable since the realistic cascade structure is one of many denser subcascades enclosed within the calculated cascade envelope. Further evidence of the "spike effect" is demonstrated in fig. 4 where the "effective" displacement energy (E~fr) is shown as a function of FD. E~ff is calculated from the modified Kinchin and Pease formula' '), E~fr = 0.42 v(Eo)/N ~. For nitrogen data (FD< 10-3), the value for E~fr is relatively constant (i.e. in region where F D is linear with E',.), and is considerably lower than the accepted value of Fo = 14 e V 12) as determined from electron irradiation studies. Departures are noted for the very dilute cascades resulting from 30 KeV He + and 300 keV O + bombardment; however, as previously stated, N* is underestimated for these points resulting in an overestimation of E~ft. For F D > 1 0 - 3 , E~ff is seen to decrease, extrapolating to a value of ~ 0 . 4 e V , at Fo = 1, which is comparable to the average energy per atom of silicon at the melting temperature, T m (average energy/atom at the melting point is 3kTm = 0.44 eV for Si). The tendency of the effective displacement
energy to approach the heat of melting is consistent with a spike model. Clearly, the observation that F D ~ I and shows no saturation, indicates that the cascade volume is no longer an adequate description of the damage volume. This is also borne out by the fact that as FD~>40%, E v > E ~ ft. 4. Conclusions
l) For light ion bombardments at 50 K, where annealing is not present, no "molecular effect" is observed. It appears that the energy density into atomic processes, E,, is the single parameter determining the observed cascade damage for cascade damage densities < 10-3 (i.e. F D ~ E , . ) . 2) For damage densities > 10-3, non-linear effects are observed at 50 K which cannot be related to annealing. It is suggested that the non-linearity at both 50 K and 300 K is related to the presence of spike phenomena from the observations that: (a) FD~I and shows no tendency to saturate; (b) "molecular effects" occur; (c) as FD--,I, E~fr tends to the average energy/atom at the melting temperature; (d) Ev becomes > E~ft. The authors wish to thank Dr J. A. Davies for many useful discussions and K. B. Winterbon for supplying a preprint of his book. References
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a) S.T. Picraux and F. L. Vook, Rad. Effects 11 (1971) 179. 2) j . A . Moore, G. Carter and A. W. Tinsley, Rad. Effects 25 (1975) 49. s) j . B . Mitchell, J . A . Davies, L . M . Howe, R.S. Walker, K. B. Winterbon, G. Foti and J . A . Moore, Proc. 4th Int. Conf. on Ion implantation into semiconductors and other materials, Osaka, Japan (1974). 4) G. D. Watkins, Radiation damage in semiconductors, (Dunod, Paris, 1964) p. 97. 5) K. Schmid, Rad. Effects 17 (1973) 201. 6) j. Bottiger and J. L. Whitton, Rad. Effects 19 (1973) 201. 7) F. H. Eisen, GI J. Clark, J. Bottiger and J. M. Poate, Rad. Effects 13 (1972) 93. 8) j. F. Ziegler and W . K . Chu, At. Nucl. Data Tables 13 (1974) 463. 9) K. B. Winterbon, Ion implantation range and energy distributions (Plenum Press, New York, in press) vol. 2. 10) p. Sigmund, Appl. Phys. Lett. 25 (1974) 169. 11) p. Sigmund, Appl. Phys. Lett. 14 (1969) 114. 12) j . j . Loferski and P. Rappaport, J. Appl. Phys. 30 (1959) 1296.