2359-9
Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
Ettore Vittone
13 - 24 August 2012
University of Turin Italy
Theory of the Ion Beam Induced Charge Technique (IBIC)
Trieste 14.08.2012
Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
1
ETTORE VITTONE
Dipartimento di Fisica, Università di Torino
www.dfs.unito.it/solid
Theory of the Ion Beam Induced Charge Technique (IBIC).
Trieste 14.08.2012
Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
2
Bibliography
Books:M.B.H. Breese, D.N. Jamieson, P.J.C. King, “Materials Analysis Using a Nuclear Microprobe”, John Wiley and Sons, 1996
Articles:M. B. H. Breese, E. Vittone, G. Vizkelethy, P.J. Sellin, “A review of ion beam induced charge microscopy”, Nuclear Instruments and Methods in Physics Research B 264 (2007) 345–360.See slides
Links:http://www.dfs.unito.it/solid/RICERCA/IBA/IBA_index.html
Trieste 14.08.2012
Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
3
Theory of the Ion Beam Induced Charge Technique (IBIC).
From nuclear spectroscopy to material analysis Principles of IBIC From spectroscopy to microspectroscopy Basic equations Validation of the theory Charge sharing
Trieste 14.08.2012
Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
4
IBIC for thefunctional characterization of
semiconductor materials and devices
Measurement of the their electronic properties and performances
Main physical observable: currentCurrent = F(carrier density; carrier transport)
Free carriers (electron/hole) transportTwo mechanisms: Drift electric field v=μ·EDiffusion concentration gradient
Carrier generation by MeV ionsGeneration profileRecombination/trappingCarrier lifetime
Trieste 14.08.2012
Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
5
PrinciplesPrinciples ofof radiationradiation detection detection techniquestechniquesDeposited Energy
Free charge generation and transport
Output Electrical Signal Vout
Transport)Carrier Free Energy, Deposited(FVout
Nuclear spectroscopy
Incoming radiation
V
Q
Incoming radiation
V
Vout
Well known
Measured
Trieste 14.08.2012
Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
6
IBIC principlesIBIC principles
Transport)Carrier Free Energy, Deposited(FVout
Incoming radiation
V
Q
Incoming radiation
V
Vout
MeasuredWell known Material Characterization
Deposited Energy
Free charge generation and transport
Output Electrical Signal Vout
Trieste 14.08.2012
Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
7
IBIC principlesIBIC principles
Transport)Carrier Free Energy, Deposited(FVout
Incoming radiation
V
Q
Incoming radiation
V
Vout
MeasuredWell known
MeV ion energy deposition
Electron/hole pair generation
Charge carrier transport
Induced Charge at the sensing electrode
Output Signal Vout
Trieste 14.08.2012
Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
8
Electrode energy loss very small ( 1%)SRIM (Stopping and Range of Ion in Matter)
Using MeV ions to probe
the electronic features of semiconductors
analysis through thick surface layerscharge pulses height spectra almost independent on topography .profiling
long range
low lateral scattering
a wide choice of ion ranges and electronic energy losses
0 5 10 15 20 25 300
1x107
2x107
3x1070
50
100
150
200
3 keV Photon current: 5*107 photons/sXBIC
X-ra
y en
ergy
loss
rate
(keV
\(m
s-1)
Depth (m)
IBICH+ ion energy (MeV)
1.71.51.31.10.90.7
Stop
ping
pow
er
(keV
m-1)
Trieste 14.08.2012
Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
9
IBIC principlesIBIC principles
Transport)Carrier Free Energy, Deposited(FVout
Incoming radiation
V
Q
Incoming radiation
V
Vout
MeasuredWell known Material Characterization
MeV ion energy deposition
Electron/hole pair generation
Charge carrier transport
Induced Charge at the sensing electrode
Output Signal Vout
Trieste 14.08.2012
Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
10
Electron/Hole pair generation eh
ioneh
EN
A. Lo Giudice et al. Applied Physics Letters 87, 22210 (2005)
1 MeV ion in diamond generates about 77000 e/h pairsEach high energy ion creates large numbers of charge carriers to be measured above the noise level.
εeh=average energy expended by the primary ion to produce one electron/hole pair
Trieste 14.08.2012
Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
11
IBIC principlesIBIC principles
Transport)Carrier Free Energy, Deposited(FVout
Incoming radiation
V
Q
Incoming radiation
V
Vout
MeasuredWell known Material Characterization
MeV ion energy deposition
Electron/hole pair generation
Charge carrier transport
Induced Charge at the sensing electrode
Output Signal Vout
Trieste 14.08.2012
Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
12
J.R. Haynes, W. Shockley,
“The mobility and life of injecting holes and electrons in germanium,
Phys. Rev. 81, (1951), 835-843.
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Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
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C. Canali et al., Nucl. Instr. Meth. 160 (1979) 73-77
400 m thick natural diamond, biased at 40 V @ RT
P-doped Ge;resistivity about 15 Ω·cm; dielectric constant =1.4pF/cm; Dielectric relaxation time = 21 ps.Charge neutrality maintained
IIa diamond; resistivity about 1015 Ω·cm; dielectric constant =0.5 pF/cm; Dielectric relaxation time = 500 s.Charge neutrality not maintained
J.R. Haynes, W. Shockley, Phys. Rev. 81, (1951), 835-843.
Trieste 14.08.2012
Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
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IBIC principlesIBIC principles
Transport)Carrier Free Energy, Deposited(FVout
Incoming radiation
V
Q
Incoming radiation
V
Vout
MeasuredWell known
MeV ion energy deposition
Electron/hole pair generation
Charge carrier transport
Induced Charge at the sensing electrode
Output Signal Vout
Trieste 14.08.2012
Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
15
Physical Observable:Induced current/charge
Vbias
Vout
q
dxqQ
Q0+Q
d
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Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
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Vbias
Vout
Physical Observable:Induced current/charge
W. Shockley, J. Appl. Phys. 9 (1938) 635.
S. Ramo, Proc. I.R.E. 27 (1939) 584.
dvq)t(I
T
0
dt)t(I)t(Q
q
d)t(xq)t(Q
Q0+Q(t)
d
v
Trieste 14.08.2012
Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
17
dvq)t(I
T
0
dt)t(I)t(Q
Constant velocity v
Trieste 14.08.2012
Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
18
-2 0 2 4 6 8 10 12 14
0.000
0.025
0.050
0.075
0.0
0.2
0.4
0.6
0.8
1.0
I
Time
Q
dvq)t(I
-2 0 2 4 6 8 10 12 14 16
0.000
0.025
0.050
0.075
0.0
0.2
0.4
0.6
0.8
1.0
I
Time
Q
texpdvq)t(I
drift time
Trieste 14.08.2012
Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
19
C. Canali et al., Nucl. Instr. Meth. 160 (1979) 73-77
400 m thick natural diamond,
biased at 40 V @ RT
IIa diamond; resistivity about 1015 Ω·cm; dielectric constant =0.5 pF/cm; Dielectric relaxation time = 500 s.
Charge neutrality not maintained
Trieste 14.08.2012
Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
20
V
Vout
d
v
Ed
dECCE
e
e
exp1 K. Hecht, Z. Physik 77, (1932) 23
Generation at the anode Induced signal from the
Hole motion
Generation at the cathode Induced signal from the
electron motion
Trieste 14.08.2012
Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
21
C. Canali, E. Gatti, S.F. Koslov, P.F. Manfredi, C. Manfredotti, F. Nava, A.
QuiriniNucl. Instr. Meth. 160 (1979) 73-77
400 m thick natural diamond,
biased at 40 V @ RT
Electrons:
Drift velocity; v dTR
Mobility; d2/(TR *VBias)
Characterization of the transport properties in diamond
Trieste 14.08.2012
Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
22
dvq)t(I
Shockley-Ramo Theorem
Induced current
Ev The current is induced by the motion of charges in
presence of an electric field
Trieste 14.08.2012
Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
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Si-face
Starting Material: 360 m n-type 4H-SiC by CREE (USA)Epitaxial layer from Institute of Crystal Growth (IKZ), Berlin, GermanyDevices from Alenia Marconi System
4H-SiC Schottky diode
1.5 MeV H+
CC
E
2 MeV H+
0 20 40 60 80 1001201400,00,20,40,60,81,0
Applied Bias Voltage (V)
1.5 or 2.0
MeV H+
CCE=Charge Collection Efficiency=
(Charge collected)/(Charge generated)
Trieste 14.08.2012
Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
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50 m thick N-type epitaxial 4H-SiC layerSchottky electrode
Frontal ion Irradiation
Dep
letio
n R
egio
n
FAST DRIFT
COMPLETE COLLECTION DIFFUSION
0 5 10 15 20 25 30 350
20
40
60
80
100
120
140
160
180
0
20
40
60
80
100
120
140En
ergy
Los
s (k
eV/
m-1)
Depth (m)
2 MeV1.5 MeV
Bragg.opj
Applied B
ias Voltage (V)
Trieste 14.08.2012
Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
25
Generation of electrons and holes in the
Depletion Region Neutral RegionD
eple
tion
regi
on
Electric Field
Neu
tral
re
gion
Electrons
Holes
Dep
letio
n re
gion
Neu
tral
re
gion
Electrons
Holes
Complete charge collection Only holes injected in the depletion region by diffusion induce a charge
Electric Field
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Frontal ion Irradiation
0 5 10 15 20 25 30 350
20
40
60
80
100
120
140
160
180
0
20
40
60
80
100
120
140
Ener
gy L
oss
(keV
/m
-1)
Depth (m)
2 MeV1.5 MeV
Bragg.opj
Applied B
ias Voltage (V)
4H-SiC Schottky diode
Trieste 14.08.2012
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Frontal ion Irradiation
0 5 10 15 20 25 30 350
20
40
60
80
100
120
140
160
180
0
20
40
60
80
100
120
140
Ener
gy L
oss
(keV
/m
-1)
Depth (m)
2 MeV1.5 MeV
Bragg.opj
Applied B
ias Voltage (V)
4H-SiC Schottky diode
Trieste 14.08.2012
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Frontal ion Irradiation
0 5 10 15 20 25 30 350
20
40
60
80
100
120
140
160
180
0
20
40
60
80
100
120
140
Ener
gy L
oss
(keV
/m
-1)
Depth (m)
2 MeV1.5 MeV
Bragg.opj
Applied B
ias Voltage (V)
4H-SiC Schottky diode
Trieste 14.08.2012
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Frontal ion Irradiation
0 5 10 15 20 25 30 350
20
40
60
80
100
120
140
160
180
0
20
40
60
80
100
120
140
Ener
gy L
oss
(keV
/m
-1)
Depth (m)
2 MeV1.5 MeV
Bragg.opj
Applied B
ias Voltage (V)
4H-SiC Schottky diode
Trieste 14.08.2012
Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
30
Lp=(9.0±0.3) m
Dp = 3 cm2/s
p = 270 ns
minority carrier
diffusion length
1.5 MeV
CC
E
2 MeV
0 20 40 60 80 1001201400,00,20,40,60,81,0
Applied Bias Voltage (V)
4H-SiC Schottky diode
Active region width
4
5
6
7
8
9
10
100 150 200 250 300 350 4000,0100,0150,0200,0250,0300,0350,0400,0450,050 (b)
(a)
L p (
m )
L-2 p(
m-2 )
T (K)
Temperature dependent IBIC (TIBIC)
TTDTL ppp
Trieste 14.08.2012
Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
32
4
5
6
7
8
9
10
100 150 200 250 300 350 4000,0100,0150,0200,0250,0300,0350,0400,0450,050 (b)
(a)
L p (
m )
L-2 p(
m-2 )
T (K)
Two trapping levels
SRH recombination model
2 0.50.5p p p B Bt
D B
1 1 1 1 1 1 1 1AL D D (T) T EBT T exp
N k T
The fitting procedure provides a trapping level of about
0.163 eV which is close to the value found in similar
4H SiC Schottky diodes by DLTS technique (S1 level).
E. Vittone et al., NIM-B 231 (2005) 491.
Temperature dependent IBIC (TIBIC)
Trieste 14.08.2012
Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
33
Time resolved IBIC (TRIBIC)Silicon Power diode Mesa Rectifier
V
Charge sensitive preamplifier
ADC
Proton beam (2-3-4 MeV)
n p+ W
C
n+
IBIC
Digital oscilloscope TRIBIC
Shaping amplifier
Mesa Rectifier 168
Ballistic deficit
p+
n
n+
Electrodes (Ag-Ni-Cr)
30 m 160 m 110 m
Passivation “Mesa Glass”
Trieste 14.08.2012
Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
34
Time resolved IBIC (TRIBIC)Silicon Power diode Mesa Rectifier
lifetime
0 = (5 1) s
Trieste 14.08.2012
Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
35
From Spectroscopy to micro-spectroscopy
Use of focused ion beams
Trieste 14.08.2012
Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
36
20 m
20 m
Electrons10 keV
Electrons40 keV
2 MeV H+ in Si 3 MeV H+ in Si
4 MeV H+ in Si
2 m
4 m
6 m
47 m 90 m 147 mTrajectories
One advantage of IBIC over other forms of charge collection microscopy is that it provides high spatial resolution analysis in thick layers since the focused MeV ion beam tends to stay ‘focused’ through many micrometers of material.
Trieste 14.08.2012
Trieste 14.08.2012
Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
38
M.B.H.Breese et al. NIM-B 181 (2001), 219-224; P.Sellin et al. NIM-B 260 (2007), 293-294Intra-crystallite charge transport
Single grain IBIC line scan
Position (nm)0 50 100 150 200 250
Cou
nts
0
1000
2000
3000
4000
5000 200 V370 V
IBIC imaging with 2 MeV H+
Under
illumination
Dark
conditions
Polycrystalline
CVD diamond
Frontal IBIC
Trieste 14.08.2012
Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
39
GaAs Schottky diodeFrontal IBIC
0 5 10 15 20 25 300
500
1000
1500
2000 FRB L12, frontale30 V
Pixe
l
Efficiency (%)
0 20 40 60 80 100 1200
20
40
60
80
100
120
X Axis
Y A
xis
19.34 -- 20.84 17.84 -- 19.34 16.34 -- 17.84 14.84 -- 16.34 13.34 -- 14.84 11.84 -- 13.34 10.34 -- 11.84 8.840 -- 10.34 7.340 -- 8.840 5.840 -- 7.340
2 mm
1 cm
2 mm
1 cm
pre-amplifierSchottky contact
ohmic contact
(frontal irradiation)2 MeV protonmicrobeam
0.1
mm GaAs
sample holder
active region
Effects of inhomogeneous cabon dopingPoor spectral
resolution
E. Vittone et al., Nuclear instruments and Methods in Physics Research B 158 (1999) 470-47
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Frontal ion Irradiation
Schottky electrode 50 m thick N-type epitaxial 4H-SiC layer
0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5 5 00
2 0
4 0
6 0
8 0
1 0 0
1 2 0
1 4 0
1 6 0
1 8 0
1 .71 .51 .31 .10 .9
Ene
rgy
Loss
(keV
/m
-1)
D e p t h ( m )
0 .7 Neutral region
Diffusion transport
Incomplete collection
Depletion region
Fast drift transport
Complete collection
0 , 2 0 0 00 , 2 5 0 00 , 3 0 0 00 , 3 5 0 00 , 4 0 0 00 , 4 5 0 00 , 5 0 0 00 , 5 5 0 00 , 6 0 0 00 , 6 5 0 00 , 7 0 0 00 , 7 5 0 00 , 8 0 0 00 , 8 5 0 00 , 9 0 0 00 , 9 5 0 01 , 0 0 0
0 1CCE
1 mm
M. Jaksic et al.Nuclear Instruments and Methods in PhysicsResearch B 188(1-4) (2002) 130-134
Surface defects
Bulkdefects
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ANGLE RESOLVED IBIC (ARIBIC)2 MeV proton beam
L=(9.9±0.8) m
Dead layer energy loss of 235 keV at =0°.
A. Lo Giudice et al. Nuclear Instruments and Methods in PhysicsResearch B 249 (2006) 213–216
Trieste 14.08.2012
Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
42
ElectrodeElectrode
Microbeam Microbeam raster area raster area for lateral for lateral IBICIBIC
5 MeV proton
Anode
Cathode
xy
z
xy
z
y
z
p+
n+Polished and passivated lateral
surface
Leakage current below 100 nA @ 100 V
Lateral IBIC
Si p-n diodeIon Microbeam Facility of Ruder Boskovich Institute, Zagreb (HR)
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p+ n
pLxexpxη
DepletionRegion
3 MeV proton
xy
z
xy
z
y
zLateral IBIC
Si p-n diode
minority carrier diffusion length
ppp DL
C. Manfredotti et al., Nuclear instruments and Methods in PhysicsResearch B 158 (1999) 476-480
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Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
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50 100 150 200 250
0,2
0,4
0,6
0,8
11
Lp = ( 61.4 ± 0.8 ) m = (2.90 ± 0.08)s
71.3 V
58.7 V
41.7 V
20.3 V
icnmta98.si_DIODE.articolsidiode.fig4
Col
lect
ion
effic
ienc
y
Depth (m)50 100 150 200 250
0,080,10,1
0,2
0,4
0,6
0,811
Lp = ( 27.3 ± 0.8 ) m = (0.57 ± 0.03)s 117.5 V
90.6 V
60.4 V28 V
icnmta98.si_DIODE.articolsidiode.fig5
Col
lect
ion
effic
ienc
yDepth (m)
Pristine diode Au doped diode
Trieste 14.08.2012
Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
45
Gunn’s theorem
Pulse shapes calculation
V-qI
Ev
Shockley-Ramo theorem
d1-qI v
Weighting field
Gunn theorem
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Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
46
dtdrv Equation of motion:
Weighting potential:
VV www
E
AB
B
A
B
A
B
A
VVq)()(q
dEqdtEqIdtQ
AwBw
w
t
tw
t
t
rr
r
r
rr
rv
The induced charge Q into the sensing electrode
w-qV
-qI EvEv
is given by the difference in the weighting potentials between any two positions (rA and rB) of the moving charge
Weighting field
Induced current into the sensing electrode
Trieste 14.08.2012
Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
47Depth Depth W
eigh
ting
Wei
ghtin
gpo
tent
ial
pote
ntia
l 11
00
Wei
ghtin
gW
eigh
ting
field
field
Ele
ctric
E
lect
ric
Fiel
dFi
eld
Vw
EE
Vw
Depth Depth
Depth Depth
NeutralNeutralnn--typetype
Schottky Schottky barrierbarrier
DepletionDepletionRegionRegion
VVbiasbias
Trieste 14.08.2012
Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
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Wei
ghtin
gW
eigh
ting
pote
ntia
lpo
tent
ial
11
00
Vw
Electric fieldElectric field
h+
e-
positioninitial
positionfinal VV
Electrons/holes
Electrostatics
Transport properties
Induced charge
Depth Depth
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Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
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Wei
ghtin
gW
eigh
ting
pote
ntia
lpo
tent
ial
Vw
11
00
h+
Depth Depth xx00
e-
Electric fieldElectric field
Trieste 14.08.2012
Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
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Wei
ghtin
gW
eigh
ting
pote
ntia
lpo
tent
ial
Vw
11
00
h+ e-
Electric fieldElectric field
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Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
51
Wei
ghtin
gW
eigh
ting
pote
ntia
lpo
tent
ial
Vw
11
00 Depth Depth xx00
e-
wx
electrons ofNumber Totalq
VVq
QQCCE
electronspositioninitial
positionfinal
Generated
collected 01
Electric fieldElectric field
h+
Trieste 14.08.2012
Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
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Wei
ghtin
gW
eigh
ting
pote
ntia
lpo
tent
ial
Vw
11
00 Depth Depth xx00
Electric fieldElectric field
h+
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Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
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Wei
ghtin
gW
eigh
ting
pote
ntia
lpo
tent
ial
Vw
11
00
h+
Electric fieldElectric field
wx
holes ofNumber Totalq
VVq
QQCCE
holespositioninitial
positionfinal
Generated
collected 0
11 00
wx
wx
holesholes
electronselectronsCCE
Generated
collected
Generated
collectedToT
Trieste 14.08.2012
Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
54
To evaluate the total induced charge
Magnetic effects are negligible;
Electric field propagates instantaneously
Free carrier velocities much smaller than the light speed
Excess charge does not significantly perturb the electric field
equation sPoisson’ thesolvingby potential actual theEvaluate
equations y)(continuitrt transpo theSolve
electrode sensitive at the potential bias theis VV
potentialweightingsGunn' theEvaluate
AB rr VV
qQThe induced charge Q into the sensing electrode is given by the difference in the weighting potentials between any two positions (rA and rB) of the moving charge
Trieste 14.08.2012
Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
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Basic assumptionsMagnetic effects are negligible;
Electric field propagates instantaneously
n,p
UGJtp
UGJtn
ppp
nnn
Free carrier velocitiesmuch smaller than the lightspeed
Excess charge does notsignificantly perturb thefield within the detector
)n,p(
UGJtp
UGJtn
ppp
nnn
)n,p(
pGJtp
nGJtn
ppp
nnn
Linearization of ULinearization of U
QuasiQuasi--steadysteady--state modestate mode
ELECTROSTATICSELECTROSTATICS
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Basic formalism
p
pp0p
nnn0n
0
pGpDptp
nGnDntn
charge space ,conditions boundary by defined potential the
using equations continuity the Solve
dt)t,dQ(r)t,I(r
current induced the Evaluate
Sd)t,(r)t,Q(rcharge induced the Evaluate
00
00
)n,p( equation sPoisson’ the solving by
potential actual the Evaluate
0tat point Generation r)t()rr(G
0
0pn,
Rectifying contact
Ohmic contact
Semiconductor bulk
Insulator-Semiconductorinterface
Boundary conditionsBoundary conditions
Initial conditionsInitial conditions
For mapping charge pulsesFor mapping charge pulses
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Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
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Vip0n0
t
0i V
)r(E)r(v)r;'t,r(p)r(v)r;'t,r(nrd'dtq)t(Q
charge induced the Evaluate
constant held are conductors other the all of potentials The
E equation sPoisson’ the solving by
VE
potential weightedsGunn' the Evaluate
i
p
pp0p
nnn0n
0
pGpDptp
nGnDntn
charge space ,conditions boundary by defined potential
the using equations continuity the Solve
Rectifying contact
Ohmic contact
Semiconductor bulk
Insulator-Semiconductorinterface
Bou
ndar
y B
ound
ary
cond
ition
sco
nditi
ons
Initial conditionsInitial conditions
For mapping charge pulsesFor mapping charge pulses
0tat point Generation r)t()rr(G
0
0pn,
Formalism based on the Gunn’s theorem
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Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
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equation continuity electron the for function sGreen' the isV
)r(E)r(v)r;'t,r(nrd'dtq)t(Q
electrons from Induced Charge
Vin0
t
0in
The continuity equation involves linear operators
The charge induced from electrons can be evaluated by solving a single, time dependent adjoint equation.
n
n*
n0nnGnDn
tn
inn
in
VEG
Qn
T.H.Prettyman, Nucl. Instr. and Meth. in Phys. Res. A 422 (1999) 232-237.
Short-cutAdjoint equation Method
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Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
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Monte Carlo MethodShockley-Ramo-Gunn TheoryA charge moving in a non-zero electric field induces a current to the sensitive electrode.∂ψ/∂V is the Gunn’s weighting potential, where ψ is the electric potential and V the bias voltage
Short-cut
Follow the carrier trajectories by a Monte Carlo approachTaking into accountphysical parameters (geometry, electric field, transport properties)experimental set-up (noise, threshold, beam spot size)
P. Olivero et al., Nucl. Instr. Meth. B 269 (2011) 2350
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Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
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Diamond Schottky diode structure: homoepitaxial growth on HPHT
substrates (type Ib, 440.4 mm3) slightly B
doped (Acceptor concentration 1013-1014 cm-3)
heavily B-doped buffer layer asback contact (Acceptorconcentration 1018-1019 cm-3)
25 μm thick intrinsic layer asactive volume
Schottky contact: frontal Al circularcontact ( = 2 mm, 200 nm thick) onintrinsic layer
back contact on B-doped layer ohmiccontact
sample cleaved in order to expose itscross section for IBIC characterization
S. Almaviva et al. “Synthetic single crystal diamond dosimeters for conformal radiation therapyapplication”, Diamond & Related Materials 19 (2010) 217–220
ideality factor: n = (1.51 0.04)series resistance: Rs = (5.1 1.6) kΩ
back B-doped contactshunt resistance: Rsh = (900 6) GΩ@ 50 V -> I<50 pA
Lateral IBIC of a diamond Schottky diode
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Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
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ion species and energy: H+ @ 2 MeV ion current: 103 ions s-1 no pile up
or charging effects ion beam spot on the sample:
FWHM = 3 μm raster-scanned area: S = 6262 μm2
charge sensitive electronic chain and synchronous signal
acquistition with microbeam scanning
Lateral IBIC measurements performed at the ion microbeam line of the AN2000 accelerator of the
National Laboratories of Legnaro (LNL-INFN)
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Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
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Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
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Plateaux:Depletion region(active region)
Vs.Bias voltage
30 35 40 45 50
5
10
15
202530
30 35 40 45 50
5
10
15
202530
30 35 40 45 50
5
10
15
202530
30 35 40 45 50
5
10
15
202530
30 35 40 45 50
5
10
15
202530
30 35 40 45 50
5
10
15
202530
30 35 40 45 50
5
10
15
202530
60
50
4025
15
5Vbias=0
Exponential-like decay outside the highly efficient depletion
region
2ee
eee
cm/V)3.057.2( : lifetimeMobility
m)17.057.2(DL :lengthdiffusion Electron
A. Lo Giudice et al, Physica Status Solidi Rapid Research Letters 5 (2011) 80-82
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CHARGE SHARING IN MULTIELECTRODE DEVICES
positioninitial
positionfinal VV
The induced charge Q at the sensing electrode is given by the difference in the weighting potentials between any two positions (rA and rB) of the moving charge
Actual potential Weighting potential
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Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
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Actual potential Weighting potential
Sensitive electrode
66
Actual potential
Sensitive electrode
02468
10121416
0,0
0,5
1,0
1,5
2,0
2,5
CH
AR
GE
time
CU
RR
ENT
time
positioninitial
positionfinal VV
Actual potential Weighting potential
67
positioninitial
positionfinal VV
Sensitive electrode
Actual potential Weighting potential
0
2
4
6
8
10
12
0.00
0.05
0.10
0.15
0.20
0.25
CH
AR
GE
time
CU
RR
ENT
time
68
Sensitive electrode
Actual potential Weighting potential
-4
-3
-2
-1
0
1-0,5
-0,4
-0,3
-0,2
-0,1
0,0
0,1
CH
AR
GE time
CU
RR
ENT
time
positioninitial
positionfinal VV
69
Sensitive electrode
Actual potential Weighting potential
-1,0-0,8-0,6-0,4-0,20,00,20,40,60,81,0
-0,04
-0,02
0,00
0,02
0,04
CH
AR
GE
time
CU
RR
ENT
time
positioninitial
positionfinal VV
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IBIC map1.5 MeV H+
ElectrostaticPotential map
Vbias=100V
E.Vittone et al. Nuclear Instruments and Methods in PhysicsResearch B 266 (2008) 1312–1318.
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Weighting potential maps
S SG
S SG
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Calculated CCE maps10 V
70 V
130 V
0 , 2 0 0 00 , 2 5 0 00 , 3 0 0 00 , 3 5 0 00 , 4 0 0 00 , 4 5 0 00 , 5 0 0 00 , 5 5 0 00 , 6 0 0 00 , 6 5 0 00 , 7 0 0 00 , 7 5 0 00 , 8 0 0 00 , 8 5 0 00 , 9 0 0 00 , 9 5 0 01 , 0 0 0
0 1CCE
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Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
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-60 -40 -20 0 20 40 600.20.30.40.50.60.70.80.91.0
CC
E
10 V
20 V30 V40 V50 V70 V
Position (m)
0.9 MeV protons
-60 -40 -20 0 20 40 600.20.30.40.50.60.70.80.91.070 V
50 V
30 V20 V
10 V
Position (m)
40 V
-60 -40 -20 0 20 40 600.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Position (m)
10 V
20 V30 V40 V50 V70 V
-60 -40 -20 0 20 40 600.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
CC
E
Position (m)
A
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Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
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0,2
0,3
0,4
0,5
0,6
0,7
-60 -40 -20 0 20 40 60
CC
E
Position (m)
50 V60 V
30 V20 V
CC
E
10 V
-60 -40 -20 0 20 40 600,2
0,3
0,4
0,5
0,6
0,7
110 V120 V130 V
90 V80 V70 V
-60 -40 -20 0 20 40 600.20.30.40.50.60.70.80.91.0
CC
E
10 V
20 V30 V40 V50 V70 V
Position (m)
-60 -40 -20 0 20 40 600.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
CC
E
Position (m)
A
0.9 MeV protons 1.5 MeV protons
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-70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
130 V
1500 keVCC
E
Position (m)
900 keV
S SG
10 20 30 40 50 60
0,2
0,3
0,4
0,5
0,6
0,7 900 keVConfiguration A
1500 keVConfiguration A
10 20 30 40 50 60
0,2
0,3
0,4
0,5
0,6
0,7
900 keVConfiguration B
CC
E
Position (m)
The electrode edges are highlighted by the vertical black line.
CCE profile detailshole diffusion length = 8.7 m. hole lifetime = p = 250 ns
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Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
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Horizontal electric field
positioninitial
positionfinal VV
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2 MeV He+
CCE AS FUNCTION OF ION STRIKE POSITION
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Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
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2 MeV He+
ION STRIKE POSITIONAS FUNCTION OF CCE
POSITION SENSITIVE DETECTOR
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A SUB-MICROMETER POSITION SENSITIVE DETECTOR
J. Forneris et al. Modeling of ion beam induced charge sharing experiments for the design of high resolution position sensitive detectors, Submitted to NIMB
2 MeV He beam @ NEC 5U Pelletron, Melbourne1 m spot size
400 nm resolution
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Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
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IBIC(Ion Beam Induced Charge Collection)
Control of in-depth generation profile
Suitable for finished devices (bulk analysis).
Micrometer resolution
CCE profiles: Active layer extension; Diffusion length
Robust theory; FEM and MC approaches
Analysis of multi-electrode devices
In-situ analysis of radiation damage
Analytical technique suitable for the measurement of transport properties in semiconductor materials and devices
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Joint ICTP-IAEA Workshop on Physics of Radiation Effect and its Simulation for Non-Metallic Condensed Matter
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