Transcript Vaitkus-Barcelona-Cluster_model_in_Si

Cluster model in Si
VAITKUS, Juozas
GAUBAS, Eugenijus, STORASTA, Jurgis
ŽąSINAS, Ernestas; MEKYS, Algirdas
(Vilnius University)
J.Vaitkus. 16th RD50 Workshop, 31 May – 02 June 2010, Barcelona
The starting point:
This dependence show the recombination is controlled by a
single factor with a small influence of other semiconductor
properties:
It is most easy to propose that this factor is the clusters if the
stopping range of the neutrons is bigger the sample
thickness.
What was changed in semiconductor during irradiation?
J.Vaitkus. 16th RD50 Workshop, 31 May – 02 June 2010, Barcelona
1

 PR  aF
The detectors structure is following:
p* – n – n*
I
EF
But material properties more
easy to investigate using the
more simple sample.
The wafer piece (initial high
resistivity Si) was used for the
Hall sample fabrication.
The Hall mobility and free
carrier concentration was
measured.
B
Magnetic field up to 2 T
UH
E
Digital processing: High input impedance, small capacitance
J.Vaitkus. 16th RD50 Workshop, 31 May – 02 June 2010, Barcelona
Measurement principles:
Hall mobility can be measured using two ways:
by measurement of Hall effect
VH
H 
BV X
M 
and
by measurement of magnetoresistance effect
 B  0
0
1
B
The mobility depends on the phonons and ionized, also the neutral, defects:
1
 H t 

1
0
   vSi t N i t 
i
,
Therefore if the sample is excited by light, all ionized defects can be recharged,
and
1  1
1 
1
 
 ( SN )   (S0 N0  SN ) 


Y t 
v  H 0 H t   vH 0
i
i
J.Vaitkus. 16th RD50 Workshop, 31 May – 02 June 2010, Barcelona
Then the time dependence of free carrier concentration and mobility
can be used to understand what is going in the sample after the
excitation was switched off.
I
t
Intense
pulse
laser
B
The WODEAN series of samples
were investigated:
Silicon wafer n-MCz <100>
1 kcm
The samples were irradiated with
reactor neutrons at the
research reactor of the Jozef
Stefan Institute in Ljubljana.
Magnetic field up to 2
T
Digital processing:
High input impedance, small capacitance
!
The samples irradiation fluence
was
1012 cm-2, 1013 cm-2,
1014 cm-2, 3 1014 cm-2,
1015 cm-2, 3 1015 cm-2,
1016 cm-2, 3 1016 cm-2.
J.Vaitkus. 16th RD50 Workshop, 31 May – 02 June 2010, Barcelona
What was observed in the sample 1012 cm-2?
 H ,  m (cm /Vs)
1000
At room temperature both
mobilities coincide;
•
At lower T the Hall mobility
obtained by the Hall effect
decreases in comparison
with the Hall mobility
measured by the
magnetoresistence effect.
•
The M dependence on
temperature follows the 1/T
law (the cluster scattering).
Fluence
2
100
180
•
10
12
n/cm
2
H
M
200
220
240
260
T (K)
280
300
The conclusions:
The mobility is defined by the scattering of extended defects - clusters (1/T
dependence);
The sample is homogeneous at room temperature, but it becomes inhomogeneous
at lower temperatures.
J.Vaitkus. 16th RD50 Workshop, 31 May – 02 June 2010, Barcelona
Hall effect in the homogeneous and
Inhomogeneous samples
–
-+
Due to EH
-+
+
+
+
The Hall field compensate the
Lorentz force effect.
The Hall field redistributes between
the inhomogeneities and gives the
false value.
J.Vaitkus. 16th RD50 Workshop, 31 May – 02 June 2010, Barcelona
If the sample is non-uniform:
MG1 - the case of percolating cell walls and nonpercolating cell interior inclusions
MG2 - the case of a high-resistivity percolating phase (‘‘cell interiors’’) and interrupted (nonpercolating) cell walls.
J. Appl. Phys. 81 (7), 1 April 1997
Hall mobility lowering in undoped n-type bulk GaAs due to cellular-structure related nonuniformities
W. Siegel, S. Schulte, and G. Kuhnel
Institute fu¨r Experimentelle Physik, TU Bergakademie Freiberg Silbermannstr. 1, Freiberg, Germany
J. Monecke Instit fu¨r Theoretische Physik, TU Bergakademie Freiberg Cottastrasse 4, Freiberg, Germany
J.Vaitkus. 16th RD50 Workshop, 31 May – 02 June 2010, Barcelona
In the samples irradiated to the higher fluences the
inhomogeneity effect was clearly seen at room
temperature, too.
O
Mobility before 80 C 24 hrs treatment
o
Mobility after 24 hrs 80 C treatment
Fluence
2
(n/cm )
1/T
M
3
13
3*10
10
10
10
2
10
2
 H ,  m (cm /Vs)
10
12
 m,H (cm /Vs)
1000
15
16
14
H
100
10
10
220
240
260
280
T (K)
10
10
10
13
3*10
200
2
12
14
15
200
16
250
300
350
T (K)
M - weak dependence on fluence in
comparison of H dependence on fluence
“initial” sample annealed @ 80 C 24 h
J.Vaitkus. 16th RD50 Workshop, 31 May – 02 June 2010, Barcelona
What will happen if the sample was excitated by the light
pulse?
The homogeneous intrinsic excitation by light pulse
generate the e-h pairs and recharge the ionized defects.
J.Vaitkus. 16th RD50 Workshop, 31 May – 02 June 2010, Barcelona
In the sample irradiated to the fluence 1012 cm-2:
•
2400
sample 10
1600
cm
-2
I=2,83 10
23
cm /s
I=7,38 10
20
cm /s
sample 10
2
, cm /sV
2000
12
13
cm
-2
-2
-2
I=2,83 10
23
cm /s
I=7,38 10
20
cm /s
-2
-2
1200
800
0
5
10
15
20
25
30
At high excitation the Hall
mobility reach the value more
than 2200 cm2/sV that
corresponds to the drift
mobility equal to 1160 cm2/sV
if the Hall factor rH=1.93 was
used.
35
t, s
• This drift mobility value is a
bit less to the mobility limited
by scattering of the electrons
by lattice vibrations (1400
cm2/sV ).
• The difference is probably
related to the scattering on
40 the neutral impurities which
concentration is
approximately 4 1016 cm-3.
Sample ie13 cm-2
J.Vaitkus. 16th RD50 Workshop, 31 May – 02 June 2010, Barcelona
The values of concentration and mobility in the dark allow
to propose the model of the sample with the
inhomogeneities.
As the defects are charged, therefore the electric fielld
around them is defined by the Debye length:
(n’ is a sum of free carrier and ionized centers concentration).
0 kT
rDebye 
2
4e n'
100
1200

1E13
0
 24h @ 80 C
H
600
M
-3
n, cm
10
 (k  cm)
1E12
800
2
 * (cm /Vs)
1000
1E11
400
1
200
1E12
12
10
13
10
14
10
2
 (n/cm )
15
10
16
1E13
1E14
1E15
1E16
-2
F, cm
10
This value measured in the diode structure
J.Vaitkus. 16th RD50 Workshop, 31 May – 02 June 2010, Barcelona
The neutron interaction with Si is weak therefore the distance
between the neutron induced defects (clusters) is proportional to the
Fluence. The average distance between the clusters and the Debye
length (only the free carrier concentration was used, i.e, in the real
case, this distance is shorter) in the dark and in the excited sample
are shown:
1000
Lav
rD
rD exc max
rD exc min
rD , L av , m
100
10
1
12
10
13
10
14
15
10
10
-2
F, cm
16
10
The results show:
• the electric field between the clusters
overlaps;
• the clusters compensate the bulk of
the samples if F> 1012 cm-2.
The question: how big is the field
between the clusters?
•
If to propose that the barrier
height is a few kT, then the electric
field across the free carrier drift
direction should be
(0.026 eV x 34 / 0.0050.00005 =
20 – 2000 V/cm.,
i.e., it cannot be neglected in the samples
irradiated to the high fluence.
Also, the space charge of the clusters
fills all bulk of the sample.
J.Vaitkus. 16th RD50 Workshop, 31 May – 02 June 2010, Barcelona
The real sample: the question – what is a
sign of the barrier?
E+
X
A dotted red curve – the percolation path.
The answer can be found by measurement of free carrier
capture cross section.
J.Vaitkus. 16th RD50 Workshop, 31 May – 02 June 2010, Barcelona
Photoconductivity decay
• If the intensity of excitation was increased the
nonlinear filling of recombination centers can occur.
• In this case the instantaneous decay constant
becomes dependent on the nonequilibrium free
carrier concentration:
1

  ( PR 0  n)
This dependence allows to determine recombination coefficient
and calculate the capture cross section:
nM =  / vnT ,
cm2,
where vnT = 2.3·107 cm/s is the electron thermal velocity (T=300 K).
J.Vaitkus. 16th RD50 Workshop, 31 May – 02 June 2010, Barcelona
From photoconductivity and magnetoresistance mobility the free carrier
concentration kinetics is found:
15
10
23
1.22*10
22
3.03*10
22
6.02*10
21
1.71*10
-2
cm /s
-9
3
R =4±1 10 cm /s
I = 7,38 10
23
2.83*10 ;
22
7.04*10 ;
21
1.40*10 ;
20
1/ , s
-3
n (cm )
7.38*10
14
21
-2
cm /s
-9
3
R = 2,4±0,1 10 cm /s
I = 6 10
X
10
20
-2
cm /s
-9
3
R = 2,7±0,2 10 cm /s
I = 1,7 10
1.6
21
3.72*10 ;
-1
JV61AK
0.8
21
13
10
0
5
10
15
20
0.0
5.0x10
t (s)
13
1.0x10
14
1.5x10
14
-3
n, cm
5x10
7
4x10
7
3x10
7
2x10
7
14
13
-1
10
14
0,1
1/ , s
 , rel.u.
1
-2
Sample irradiated to the fluence 10 cm
experimetal
Linear fit
Upper 95% Confidence Limit
Lower 95% Confidence Limit
10
14
10 (noise removed)
6
1/ = 4,1 ±1,5 10 s
-1
-5
3
 =1,2 ±0,1 10 cm /s
0,01
1x10
0,1
0,2
0,3
0,4
0,5
t, s
7
1x10
12
2x10
12
n, cm
3x10
12
-3
• As the recombination is non-linear, the recombination coefficient can be determined.
The capture cross section (in the non-annealed samples)
• in the sample irradiated to the fluence 1012 cm-2 – 3 10-16 cm2 ;
• in the sample irradiated to the fluence 1013 cm-2 – 8.3 10-16 cm2;
• in the sample irradiated to the fluence 1014 cm-2 – 5.2 10-13 cm2.
J.Vaitkus. 16th RD50 Workshop, 31 May – 02 June 2010, Barcelona
The recombination becomes faster in the higher fluence samples
and the
Photoresponse amplitude, rel. u.
decrease is linear to the fluence
0
10
-1
10
-2
10
-3
10
12
10
13
10
14
10
15
10
16
10
-2
Fluence, cm
i.e., the lifetime decreases with the fluence, as it
was demonstrated by transient microwave PC
decay measurement.
J.Vaitkus. 16th RD50 Workshop, 31 May – 02 June 2010, Barcelona
The electronic scheme of the cluster: the Fermi level
is pinned by the deep centers inside the cluster
E
EC
EF
EV
a.
b.
c.
The main compensation centers are clusters and the space
charge regions in the high resistivity Si overlaps, other centers
modulate the main process.
Due to the reduction of the effective bandgap around the cluster the attractive electric
field for both signs of free carriers can appear in the compensated semiconductor.
J.Vaitkus. 16th RD50 Workshop, 31 May – 02 June 2010, Barcelona
Conclusions:
• The clusters create the non-uniformity of the electric field in
the sample.
• The low T annealing changed of the electric field between the clusters.
• The fast capture of non-equilibrium carriers in the highly
irradiated Si can be caused by the bandgap reconstruction
induced attraction of both signs of carriers.
• Both above presented effects have to cause the increase of free
carrier capture by clusters (“trapping”) in highly irradiated samples.
• The “carrier multiplication” can be caused by the impact
processes in the cluster environment or can be as a result of the
“secondary photocurrent – photoelectrical gain” if the bias is high enough
(details in the E.Gaubas talk).
J.Vaitkus. 16th RD50 Workshop, 31 May – 02 June 2010, Barcelona
Thank You for the attention!
J.Vaitkus. 16th RD50 Workshop, 31 May – 02 June 2010, Barcelona
All results can be understood by the cluster transform model:
1) the kick off by neutron Si atom creates the vacancy-interstitials cluster (Huhtinen –
track consisting vacancies and Si disorder.
2) the generation-recombination induced phonons and low temperature annealing
leads to the cluster reconstruction to the different vacancy clusters and the gettering of
other defects.
3) the reconstruction of the conductivity and valence bands leads to the Fermi level
pinned to the cluster defects.
number of vacancies
E, eV
0
2
4
6
8
10
-1,0
-0,9
-0,8
-0,7
-0,6
-0,5
-0,4
-0,3
-0,2
-0,1
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
J.L. Hastings, S.K. Estreicher, P.A. Fedders.
Vacancy aggregates in silicon. Phys. Rev. B, Vol.
56 (16), p. 10215-10220 (1997).
J. Dong, D. A. Drabold. Atomistic Structure of Band-Tail
States in a-Si. Phys. Rev. Lett. Vol. 80 (9) p. 1928-1931
(1998). The valence tail is primarily due to structural disorder,
while the conduction tail is much more sensitive to temperature and
originates in thermal disorder.
J.Vaitkus. 16th RD50 Workshop, 31 May – 02 June 2010, Barcelona
Effective carrier density versus reciprocal temperature
Effective carrier density vs reciprocal temperature
o
O
after 24 hrs 80 C treatment
before 80 C 24 hrs treatment
14
13
13
3*10
10
10
15
10
12
10
15
3*10
11
10
9
X
10
n
8
10
12
10
13
9
10
8
10
16
6
10
10
16
3*10
5
10
3
4
15
10
10
14
10
3*10
10
10
10
6
14
11
15
7
10
7
10
10
-3
3*10
10
10
n (cm )
16
X
M
-3
(cm )
10
13
10
10
16
3*10
12
10
14
12
10
5
6
7
8
9
10
1000/T(K)
J.Vaitkus. 16th RD50 Workshop, 31 May – 02 June 2010, Barcelona
4
5
6
7
1000/T(K)
8
9
10