Figure 7.1 is a typical sequence showing the annihilation of cascade damages during irradiation with a 750keV electron dose rate of 6.7x1Q22 e/m2s. Some o f cascade damages disappear during continuous electron irradiation through the shrinkage of their contrasts without any structural change such as loop formation. The number of cascade contrasts decreases with increasing electron irradiation time. The area density of cascade contrasts is adopted here as the density of cascade damages, because the range of 30ke V Xe+ ions in Ge is 12.9nm which is much smaller than the specimen thickness (about 100nm). Figure 7.2 shows the annihilation of cascade contrasts under irradiation with 1MeV electron dose rates of 0.7, 2, 5 and 7 x 1o23 e/m2s. The density decreases exponentially with increasing irradiation time. From this result, a hypothesis may be drawn that each cascade damage annihilates by absorbing definite number of interstitial atoms. In the case of specimens whose surfaces act as dominant sinks for interstitial atoms and vacancies, interstitial atoms keep their concentration to be the constant value
qo
which is written as(7.1)
where, od is the displacement cross section of Ge,
<t>
the electron dose rate, Mi the mobility of interstitial atoms andCs
the sink concentration of surface. The annihilation of cascade damages is based on the absorption of interstitial atoms, and its behavior is described by using eq.(5.10.a) without considering the ion irradiation term(Pi=O).
New variables N and 'A instead of CA andPe
in eq.(5.10a) follow the equation125
j.-4
N 0\
18Lsec 354sec 85s,ec 1350s Os
oo· 'Tj
� '"1 ('01
:--1
...
Figure 7.1 A sequence of weak-beam dark-field images showing annihilation of cascade contrasts under irradiation with a 750keV electron dose rate of 6.7x1Q22 e/m2s. Cascade contrasts are previously induced by irradiation with a
1.2 '7.FluxDep(N&t)fitG'
Electron Dose Rate
tl.l 1.0
[
e/m2 s]
"'0 Q)
� �
6.7xl022
tl.l 0
� 0.8
u 1.9xl023
c... •
0 4.6xl023
� D
...
0.6
·-6.7x10 23
riJ
= •
Q Q)
"'0 Q) 0.4
·-N
-
� 0s 0.2
s.... 0
0 0
z
0.0
0 400 800 1200 1600
Irradiation Time
[s]
Figure 7.2 The annihilation process of cascade con trasts for various electron dose rates. The density of cascade contrasts is n ormalized by the density at the initial value. The solid curves are based on eq.
(
7.2) so as to fit to the experimental data.127
dN = -AN
dt (7.2)
where N, t and A represent, respectively, the area density of cascade contrasts, electron irradiation time and the annihilation constant independent of t and proportional to
qo.
Fitting curves derived from eq.(7.2) are also shown in figure 7 .2. Figure 7.3 shows electron dose rate dependence of 'A, and indicates A to be almost lin early proportional to the electron dose rate, confirming the prediction by eqs. (7.1) and (7.2). In case of specimens irradiated with 30ke V Xe+ ions, cascade damages are formed near the incident specimen and controlled also by the constant concentration of interstitial atoms described by eq.(7.1).The cross section for displacements depends on electron energy as review ed in chapter 2. The annihilation process of cascade damages, therefore, is expected to depend on electron energy. Figure 7.4 shows the annihilation process of cascade contrasts under irradiation with a 100, 160, 200, 500, 750, 1000 or 1250keV electron dose rate of 6.7x 1022 e/m2s. The density decreases with increasing irradiation time and with increasing electron
energy. The solid curves are theoretically calculated from eq.(7.2) with the value of A so as to provide the best fit to the experimental results. The values of A thus obtained are plotted in figure 7. 5 as a function of electron energy.
The cross section for the atomic displacement in Si can be derived from the integration of eq.(2.15) with 16eV for the displacement threshold energy of Ge, showing the critical electron energy to produce displacements to be about 450keV. Non-trivial values below 450keV are not due to the atomic displacements but due to a thermal migration of point defects. It is, therefore, hypothesized that the annihilation process of cascade contrasts is controlled by
,..., ....__ t:n 1...1 �
c-<!
'lamda&fai.MD'
10 -� ������--�����--����
10 -2
10 -3
Electron Dose Rate [e/m2 s]
10 25
Figure 7.3 The annihilation constant of cascade contrasts, A, as a function of electron dose rate.
129
'7. Acc.Dep(N&t).fitMD' 1.2
o lOOkeV
en • 160keV
� 1.0
o 200keV
"'0 � c.; 0 • SOOkeV
en 0
A 750keV
� 0.8 u
• lOOOkeV
�
0 + 1250keV
� �
·-en 0.6
= �
Q
"'0 � 0.4 .�
-�
s � 0.2 z 0
0.0
0 1000 2000 3000
Irradiation Time [s]
Figure 7.4 The annihilation process of cascade contrasts for variou s energies of electrons. The density of cascade contrasts is normalized by the density at the initial value. The solid curves are based on to eq. (7 .2). Note that irradiation with 100, 160 and 200ke V electrons induce no displacements of atoms, but annihilate cascade contrasts.
'7 .lamda&ener .MD'
0.010 .---�--r-r---r---r--.---�--r--r-...,....---r---.-...,....---.
0.008
0.006
0.004
0.002
0 200 400 600
•
800 1000 1200 1400
Electron Energy [ke V]
Figure 7.5 Annihilation constant of cascade contrasts, 'A, as a function of energy of electrons. Solid curves are derived from eq. 7.3 based on the annihilation process controlled by the atomic displacement
('Ad)
and the a thermal migration of point defects(Am).
131
two kinds of irradiation processes; those are the displacement of atoms and the irradiation-induced migration of point defects. The reason the electronic excitation is not taken into account the annihilation process is that the value of
"A is of trivia in contrast to the larger cross section below lOOkeV. Both of the
cross sections for the irradiation processes were derived from the integration of eq.(2.15) with the domain from the migration energy of interstitial atoms (0.2e V) to the displacement threshold energy
Ed
for the irradiation-induced migration and with one fromEd
t o Tm
ax for the displacement of atoms, respectively. The annihilation constant A is then written as(7.3)
where y and
<P
are, respectively, a dimensionless constant and electron dose rate. The subscripts d and m are for the displacement and the migration. The values of J;j, yd
andYm
were calculated so as to fit the theoretical values based on eqs.(2.18) and (7.3) to the experimental values of'A(E).
The cross sections for the displacement('Act)
and that for the a thermal migration of point defects('Am)
thus obtained, are shown in figure 7 .5. It should be noted that the value ofEd
is determined to be 33e V which is about twice of the literature value [141]. The values for Yct andYm
are estimated as 8.2xlo-3 and 1.2xlo-7,respectively. The physical meaning ofy is the efficiency of the contribution of each process to the annihilation of cascade damages.
As revealed in chapter 6, electrons with the lower energy are the more effective for preventing the ion-induced amorphization in contrast to the result in figure 7 .5. The difference of these phenomena is caused based on the
and electrons and the other is post-irradiation with electrons after ion irradiation. During concurrent irradiation with electrons and ions, cascade damages, isolated point defects and irradiation-induced migration of point defects are introduced. The concurrent effects could be introduced under this condition. One possible concurrent effect is that isolated point defects are introduced by ions, and athermal migration and electronic excitation induce
the diffusion of them.
The value of A depends also on observation conditions which are described as g vector and deviation parameters. The g and s dependences of A are shown in figure 7. 6. It can be seen in the figure that the lower index of g vector ascribes to the higher value of A and that the value of A depends on the values except for g=111. In case of g=111, the value of A at s=O is quite larger than the others at different values of s. The reason is thought to be due to the electron diffraction channeling [150]. The electron diffraction channeling is described as the excitation of the coherent Bloch wave whose probability at the atom positions depends on the direction of the incident electrons, the diffraction condition and penetration depth of the specimen. The channeling effect appears notably high at the exact Bragg condition (s=O) and decreases as increasing the value of s. The channeling effect induces relatively high concentration of point defect to provide high value of A.
The next experiment consists of in-situ observation of cascade damages in Ge produced by 20 and 30ke V Xe+ ions under the isochronal annealing from 300 to 670K in the HVEM. Figure 7. 7 shows the area density of cascade contrasts induced by irradiation with 30keV Xe+ ions as a function of annealing temperature. The density of cascade contrasts decreases with
133
�
w ..J::..
�
r-1
I
0
Q)
N rn
I
0
�
"--"'