Transcript Vaitkus-mobility-RD50 - Indico

Analysis of electron mobility
dependence on electron and neutron
irradiation in silicon
J.V.VAITKUS, A.MEKYS, V.RUMBAUSKAS, J.STORASTA,
Institute of Applied Research,
Vilnius University, Vilnius, Lithuania
Classical effects, that works well in the classical situations,
can be used for analyze conditions in the samples that are
not traditional: irradiated-Si
The free carrier mobility is on of most important parameters in radiation
detector analyze because as usually it goes together with the electric field:
vdrift=E.
Therefore the knowledge of mobility predicts a correct
values of electric field in the devices.
Our attempts: an investigation of low field
electron mobility in the irradiated by neutrons
Si, taking in account that at high fluence
sample may became inhomogeneous due to
overlap of the clusters space charge regions,
therefore we measured the Hall and
magnetoresistance mobilities.
μH = rH μ, μM = rH ζ μ = rM μ.
It was found the ratio of magnetoresistance and Hall mobilities
μM/μH = 1.15.
[A. Mekys, V. Rumbauskas, J. Storasta, L. Makarenko, N. Kazuchits, J.V. Vaitkus. Hall
effect and magnetoresistance investigation of fast electron irradiated silicon. Lithuanian
(And presented earlier RD50
Workshop.)
Journal of Physics, 54, 94–98 (2014)].
Hall effect measurement scheme. 1Sample; 2- electrometer (KEITHLEY 6514);
3- source meter (KEITHLEY 6430); 4magnet source; 5- thermo resistance meter
(Agilent 34401A); 6- heater source (TTi
QL564P); 7- computer; 8- magnet; 9cryostat.
Electron mobility dependence on the fluence in the irradiated and
annealed Si samples.
1400
T (K) MR
260
280
1200
O
After annealing 24h @ 80 C
T (K)
260
280
1200
 , cm /Vs
1000
2
2
 , cm /Vs
1000
800
600
800
600
12
10
13
10
14
15
10
cm
10
16
10
12
10
-2
13
10
1 /   1 /  phon(i.e.,independent on fluence)  S
phon = 1260 cm2/sV & S=1.5·10-17 sV
14
15
10
10
-2
 , cm
16
10
Probably the crystal
became similar to the
disordered media.
in the just-irradiated Si
phon
= 1300 cm2/sV & S=0.2·10-17 sV in the annealed for 24 h@800.
Hall and magnetoresistance dependence on T
(the Fig. was presented in the previous workshops)
Fluence
2
(n/cm )
M
1000
12
2
H, m (cm /Vs)
10
13
10
14
3*10
15
10
16
10
H
12
100
180
•
•
•
•
•
200
220
240
260
T (K)
280
300
10
13
10
14
3*10
15
10
16
10
The magnetoresistance mobility dependence on
temperature was similar to predicted for scattering on the
clusters, however the mobility value at room temperature
was not far away from limited by scattering by phonons.
Therefore it was necessary to analyse contributions of
all possible scattering processes using the Matthiesen rule
and to use the approximation of mobility dependence on
temperature as =aT, where  index depends on the
scattering mechanism, and analyse performed in a narrow
range of temperature.
As the simulation [Huhtinen] showed the neutron irradiation creates rather compact generation
of defects, and a remaining material volume is free from the defects.
Therefore the simulation of mobility dependence on temperature has to take into account the
scattering of carriers as in a high quality silicon crystal that could be approximated by a power
law =aT with =(-2.4), but in the compensated samples =(-1.4) was observed, that could be
a result of additional scattering on the ionized impurities.
For the scattering on the point defects that can be charged =1.5.
If the defects are neutral, their contribution can be independent on temperature with =0.
The scattering of clusters is most indefinite:
–
–
it could follow the same dependences with = (-1.0) or (-5/6)
the contribution of dipole scattering that could appear due to difference of vacancies and interstitials
location inside the cluster. The dipole scattering can be approximated by  ~ T0.5.
Fitting of mobility dependence on T
2500
1800
1400
1600
1400
2
Mcm /sV
2
H, m (cm /Vs)
1600
1200
2
Fluence, n/cm Experiment Approximation
1e12
1e13
3e14
1e15
1e16
3e16
2000
2
Fluence n/cm Experiment Approximation
12
10
13
10
14
3*10
15
10
16
10
, cm /Vs
1800
2
1200
1000
Si-KEF2 nonirradiated
a fit (Table 1, line to 10)
-2
Si-KEF2 irradiated F=1e14 cm
a fit (Table 1, line to 11)
-2
Si-KEF2 irradiated F=1e15 cm
a fit (Table 1, line to 12)
1500
1000
800
800
600
180 200 220 240 260 280 300
600
220
240
260
T (K)
280
300
T, K
1000
200
225
250
275
T, K
Hall mobility and magnetoresistive mobility dependence on temperature in the neutron
irradiated samples. The fluence and the mobility type are shown in the inset. a. – the
high resistivity Si samples, b. annealed samples, c – the low resistivity Si samples.
300
Table 1. The parameters used for a fit of experimental data to the relation:
= 1/(1/phon+1/ionized+1/clusters+1/dipoles)=
=1/(1/aT + 1/bT1.5 + 1/cT-1+ 1/dT0.5)
Fluence
cm-2
Sample
Phonons
( value before
irradiation)
a

Ionized
point
defects
Clusters
Dipoles
c
D
b
12
1·10
1·1012
1·1013
3·1014
3·1014
1·1015
1·1015
1·1016
3·1016
nonirradiated
1·1014
1·1015
J-I HR
Annealed HR
J-I HR
J-I HR
Annealed HR
J-I HR
Annealed HR
J-I HR
Annealed HR
KEF2
KEF2
KEF2
-1.4
-1.4
-1.4
-1.4
-1.4
-1.4
-1.4
-1.4
-1.4
-2
-2
-2
6
4.2·10
4.6·106
4.2·106
4.2·106
4.2·106
4.2·106
4.2·106
4.2·106
4.2·106
1.1·108
1.1·108
1.15·108
1.5
1
1.8
3
1.1
2
1
3
0.8
4
3.3
8
0.8·107
1·107
2·106
6.5·105
6.5·105
5·105
6.5·105
5·105
5·105
0
1.2·108
4·107
1.6·103
4·103
1·103
1·103
4·103
1·103
4·103
1·103
2·104
0
3.4·103
5·103
The cluster model
12
10
15
10
13
10
12
10
13
10
15
3 10
14
10
16
10
11
Ec-EM, meV
134,
- deepest,
220,
260,
10
-3
10
9
10
8
10
7
10
shallow,
270,
70 ,
280
13
NM-NK or NM , cm
10
-3
10
360
E
400
12
10
n, cm
14
14
3 10
16
3 10
ni
E
410 410 410 430 430 440
10
11
10
C
F
10
10
9
10
8
6
10
5
10
10
7
10
0.004
0.006
0.008
1/T, 1/K
0.010
12
10
13
10
14
15
10
10
-3
Fluence, cm
E
16
10
V
The temperature dependence of the
electron concentration in the
irradiated samples. The fluence value in
neutrons/cm2 is given in the insets. The lines
correspond to the result of fitting to the experimental
data.
The cluster model that
allows an existence of
the dipole
x
Electron irradiation (6,6 MeV, “low resistivity” Si)
KDBMH300
KDBMH250
KEFMH300
KEFMH250
A Linear fit
2400
2200
2000
1800
1400
2
H (cm /Vs)
1600
600
550
500
450
400
350
0
1
2
3
16
4
5
2
Fluence x 10 e/cm
A.Mekys, V.Rumbauskas, J.Storasta, L.Makarenko, J.V.Vaitkus. Defect analysis in
fast electron irradiated silicon by Hall and magnetoresistivity means. NIMB 338, 95100 (2014)
This work is performed in frame of CERN RD50 collaboration.
Thanks to Lithuanian Science Council for the grant TAK-10001
and Lithuanian Academy of Sciences for continuing support of
this research and grants CERN-VU-2013-2015
.
Thank you
for your attention!
CERN
Mobilities:
• Magnetoresistant mobility in this work was calculated using the
following relation:
(1)
• Here B is the magnetic field induction, I0 is the electric current in the
sample when magnetic field is not present and IB is the same
current with the presence of the magnetic field.
• The Hall mobility was calculated using:
(2)
• Here l is the distance between the electric current contacts (1,2) and
UX is the voltage applied, w is the distance between the Hall
contacts (3,4).