Carrier recombination and emission lifetimes in heavily irradiated
pad–detectors and their impact on operational characteristics of pin
diodes
E.Gaubas1, T.Čeponis1, R.Grigonis2, A.Uleckas1, and J.Vaitkus1
1Vilnius
University, Institute of Applied Research, Vilnius, Lithuania (VU)
University, Laser Research Center, Vilnius, Lithuania (VU)
2Vilnius
Outline
 Carrier capture (MW-PCD/E) and emission (I-V) lifetime variations
 Barrier capacitance variations with fluence (BELIV)
 Time and spectral resolved priming of BELIV transients
 Summary
Recombination lifetime during and after irradiation
During protons irradiation/ protons pre-irradiated (MW-PCD)
- wafer samples
10
-1
12
pre-irradiated >10 cm
6 MeV protons
fixed 1.5 nA
simulated
12
Ncl,0=10 cm
10
10
10
2
10
1
10
0
10
-1
10
-2
0
10
1
10
10
1
10
0
=1
10
2
n<n0
=1/3
MCZ Si wafer
8 MeV protons at 285K :
fixed 4nA
varying current by steps
-2
-2
10
3
-2
2
-1
R (ns)
experiment
10
=2
Exposure time (s)
10
10
-1
10
0
4
10
3
10
2
10
1
-2
-1
0
1
10
0
Okmetic MCZ<100> 1kOhm·cm 300 m
MWR, CIS 8556- 14 wafers 1 - 63 passivated
CIS 8556- 14 wafers measured by DG technique
CIS 8556-01 diodes neutron irradiated
2
10
experiment
varying current
0.2 -4 by steps
fixed 4 nA
simulated
R,cluster,
c=0.33, n-fixed, 0=10
10
-2
10
10
10
10
10
Exposure time under irradiation by protons (s)
M=0/en0
-1
10
12
10
recombination prevails
-18
cm
13
10
14
10
15
10
16
2
Fluence (n/cm )
2
10
1
10
2
non-irradiated
3
10
Exposure time (eqv. 4 nA) (s)
Neutron irradiated
FZ diodes
n-epi diodes
p-epi diodes
2
6
10
 (ns)
- diode samples with applied field
ICDC, MW-PCT-E (s)
R (s)
R (s)
0
R (s)
10
After irradiation - wafer and diode samples
irradiated by neutrons and protons
1
10
ICDC
MW-PCT-E
4
R
0
10
13
n<ni<<n0
2
0
10
100
texposure (s)
recombination competes with
multi-trapping effect
10
14
10
15
10
Fluence (cm-2)
16
10
Impact of recombination within ENR
with R M might be crucial (if n0~1/)
on functionality of junction
rec, gen
Carrier capture-recombination-generation lifetimes (simple S-R-H approach)
Without applied E field
T
Photo-injection
n-Si
UR
With applied dc E field
15
100
taug( x)
taur( x  0.01)
10
taur( x  0.001)
taur( x  0.0001)
ni/ND
ne · pe - ni2 =0 R>0
ne · pe < ni2
e e
2
Eqv. n p > ni G<0
 rec
2n
E E i
n
1


[1  ei cosh( DL
]
R vN DL
n
kT
 gen
E  Ei
2 cosh( DL
)
kT
 ni / G 
vN DL
1
n0
10
0
10
x
(EDL-Ei)/kT
20
20
EC
Single-type
prevailing traps
of M=NDL<<n0
M
x
Traps with barriers, multitrapping
multi-charge/multi-valency defects
Traps with exp distributed levels
Redistribution of carriers via interaction of traps
Photo-, thermo- quenching effects
20
 20
at nvn pvp
J.S. Blakemore, in: Semiconductor Statistics, Ch. 8,
Pergamon Press, (1962)
1
EV
S-R-H is limited by conditions:
i)
M<<n0. then traps are filled by n0 without change in n0;
ii) single type centers dominate
iii) traps do not interact
iv) charge on traps can be ignored relatively to dopants one
Thus, validity of S-R-H conditions should be estimated in applications
A.Rose. Concepts in photoconductivity and allied problems.
Interscience Publishers, John Wiley & Sons, New York-London, 1963.
Carrier recombination lifetimes (for M>>n0)


n
 n 0 ( P0  PvM )   p 0 n0  N cM  M 1  0
N cM


p 
1
1

n0  
N cM 
 1 

p 0  n0  M 1 
n0 
  N cM  
 p 0 (n0  N cM )   n 0  p0  PvM

n 



1



e
1

p0  
 
 M 1 
P
vM  


1

p   P
p 0  n0  M 1  0  1  vM
p0
 PvM  



M
m0 
  M  F
kT

1
M
N cM
1
n0
M
PvM
1
p0
Although relaxation to
equilibrium/steady-state
is kept by M=pM+nM
1
M0, n 0, S-R-H
M 
Single-species (type) traps
M, M>>n0, S-R-H invalid
n  N cM
p  PvM
   p   n   p0 0
  n0 0
n0  p0
n0  p0

 p   p 0 1 

Capture coefficient <n> should be used
instead of v within rigorous analysis
 P
 n   n0 1  vM
p0

r  n  n N f Ph E f 
EC
N cM
n0

1
1




n
0
  (M  m )
 nM
n
0


n p
r  N f Ph E f   E Pe E g c E dE
Ec

  E P E g E dE
e
n 
c

1

  m   p0
p 0

x
EV
Ec

 P E g E dE
e
c
Ec
J.S. Blakemore, in: Semiconductor Statistics, Ch. 8,
Pergamon Press, (1962)
 rec
1
1


vM   n  M
 gen 
exp(
EC  EM
E  EM
) exp( C
)
kT
kT

vN C
   NC
Carrier recombination=capture lifetimes (for M>>n0)
Only deep slow levels
can be filled
and observed as carrier emitters
Single-species (type) traps
X
X
invalid
-3
10
11
-5
10
-7
10
-9
10
-3
NT=8x10 cm
cp
14
R
SC
d
12
em
11
cp, NT=8x10 cm
14
cp, NT=10 cm
-13
10
0.0
-3
-3
Space charge
generation current
SC
-3
11
NT=10 cm
R, NT=8x10 cm
-3
M
M
-11
10
-3
ND=10 (cm )
em
0.1
400
Electron irradiation
300
Cz Si (doped 10 cm )
15 2
10 e /cm
16 2
10 e /cm
14
0.2
0.3
0.4
0.5
E (eV)
Only shallow dopants of proper density
are able to support fast
operation (w(U)) of a diode ~1/M <1/em
to ensure maj. carriers on level are in equilibrium with band
0.6
DLS (mV)
em, cp, SC, R, M (s)
-1
10
-3
200
100
0
100
150
200
T (K)
250
300
Interaction of several type centers appears
due to carrier redistribution through bands
Carrier recombination lifetimes for Mi,s>n0
multi-valency(i)/multi-species(s) centers
Interaction of the whole system of centers appears due to carrier redistribution through bands, by
inter-center recombination (capture-emission) and via charging /configurational transforms of defects
System neutrality is supported by free and localized charges/fields.
Relaxation is long and complicated.
It is similar to the random-walk processes in disordered materials.
S.Havlin and D.Ben-Avraham, Advances in physics 51, 187 (2002).
L.Pavesi, J. Appl. Phys. 80, 216 (1996).
The stretched-exponent model is widely used UCPC =U0exp[–(t/se)]
10
1
2
0
experimental decay
in stretched-exponent time scale
CPC excited with 355 nm light pulse of 30 ps
MWA excited with 355 nm light pulse of 30 ps
UCPC (arb.units)
Normalized photoresponse
UCPC, MWA/Umax
E. Gaubas, S. Juršenas, S. Miasojedovas, J. Vaitkus, and A. Žukauskas
JOURNAL OF APPLIED PHYSICS VOLUME 96, NUMBER 8 15 OCTOBER 2004
1
10
10
1
10
0
-1
2
0
2000
4000
t ( s)
6000
8000
Relaxation is similar to multi-exponential in any
narrow display segment
Different techniques may give different lifetime values
0
2
4
t
=0.7
6

(ms )
A single lifetime parameter se can be extracted only when
stretched-exponent time scale is employed
Carrier generation/emission lifetime (for M>>n0)
b
-3
10
-5
I (A)
10
-7
10
13
-9
-2
=10
cm
-2
=10 cm
16
-2
=10 cm
10
14
-11
10
-13
10
-200
-150
-100
-50
0
50
U (V)
-3
6
10
-1
5
IL (A)
10
IL|UR=100V
IL|UR=200V
1/IL|UR=100V
-5
10
10
4
10
R (ns)
-4
g~1/IL (A )
10
10
4
10
3
10
2
10
1
10
0
10
Okmetic MCZ<100> 1kOhm·cm 300 m
MWR, CIS 8556- 14 wafers 1 - 63 passivated
CIS 8556- 14 wafers measured by DG technique
CIS 8556-01 diodes neutron irradiated
-1
10
-6
10
3
10
13
10
14
15
10
2
 (n/cm )
10
16
10
Qualitative emission lifetime dependence on fluence
can be estimated from I-V
12
10
13
10
14
10
15
10
16
2
Fluence (n/cm )
Nearly linear reduction of generation lifetime
with enhancement of fluence is similar to that of
of recombination lifetime characteristic
 Examined MW-PCT characteristics imply prevailing of intricate system of
defects and reduction of majority carriers. The recombination capture lifetimes
become shorter than dielectric relaxation time.
 Carrier emission lifetime decrease (increase of leakage current – at UR in I-V),
follows capture lifetime reduction (increase of serial resistance R~1/n0 - at UF
in I-V), and both manifest a close to a linear decrease with enhancement of
fluence
Items to clarify:
 Whether diode/detector is functional under heavy irradiations?
 What is a system of defects and levels, which governs extraction of carriers
(UR) and state of material?
 Which models are acceptable for prediction of charactreristics?
The Barrier Evaluation by Linearly Increasing Voltage (BELIV) transient technique
has been employed to clarify, how a reduction of carrier capture lifetime
and emission affects junction and material
Reverse bias
BELIV technique
At
C b
2U bi
dq U
Abrupt junction
iC (t ) 

(C b  U
)  AC b0
At 3 / 2
dt
t
U
(1 
)
U bi
2 At
[1 
]
3 Ubi , Lg
iC , Lg  AC b0, Lg
Linearly grade junction
At
[1 
]4 / 3
Ubi , Lg
1
pin
diode
GLIV
RL=50 
oscilloscope
At
eAt

2U bi
en Sw
At 1 / 2
k BT
i R (t )  iC (t )  i diff (t )  i g (t )  AC b0
 i diff (1  e
)  i 0 (1 
)
At 3 / 2
g
U bi
(1 
)
U bi
1
te 
U bi iC (0)
i (0)
3
[
 i g (0)  ( c ) 2  ic (0)i g (0) ]
Ai g (0) 4
4
2
iCM (t ) 
| i(t ) | FD  eS
te
1
t
(t  x)
 RC
0
 RC
 iC ( x) exp[ 
]dx
dU C
dU C (t )
d dn dp  0 S dU C
d n0
S
(  )
 eS
 C geom
e
n0  nU C (t )  C geom
2 dt dt
d
dt
2  tr
dt
2d
dt
Variations of BELIV transients with
temperature and priming by steady-state IRBI
as well as dc UF
Priming by IR illumination increases n0 and
barrier capacitance observed in BELIV transients
restores a junction but enhances leakage current
when fast carrier capture/emission is present
Reduction of temperature increases (e) and
decreases space charge generation current,
however, Cb0Cg at UC<0.3 V
Short carrier capture lifetime reduces n0ND and increases
a serial resistance of ENR. Supply of majority carriers from
rear electrode by dc UF priming (due to shrinkage of depletion
w width, forward current) restores a junction.
Combined priming of BELIV transients
by temperature reducing (increased e) and by IR illumination
(n0) leads to restore of a junction
Barrier capacitance as a function of fluence extracted at 300 K
3
10
Cb0 (pF)
Cb0: BELIV, PL=1.4 s
Neutron irradiated diodes
reverse bias
forward bias
2
10
Cgeom
1
10
12
10
13
10
14
10
15
10
2
Fluence (n/cm )
16
10
C-V’s as a function of fluence at 100 kHz and 300 K
displacement in barrier capacitance is controlled by (LRC) measurements of
phase shift for the ac test signal at fixed frequency in routine C-V
C (pF)
MCz Si diodai, T=300K
Neutron irradiated diodes
f=100 kHz, Uac=1V
U ac =20 mV, f=100 kHz
12
-2
 =10 cm :
Cs
100
Cp
14
-2
Cp
-2
 =10 cm :
Cp
10
0
50
100
150
16
-2
16
-2
Cs, 10 cm
Cs
Cs
-2
Cp, 10 cm
 =10 cm :
16
-2
14
Cs, 10 cm
C (pF)
Cs
-2
14
Cp, 10 cm
-2
 =10 cm :
-2
12
Cs, 10 cm
Cp
13
12
Cp, =10 cm
2
10
1
10
50
100
150
UR (V)
U (V)
Applicability of LRC measured C-V is doubtful
for diodes irradiated with > 1E13 n/cm2
200
250
 Barrier partially recovers by n0 priming with IR, dc UF and combined priming with
temperature (emission lifetime) decreasing only in diodes irradiated with fluence of <1014
n/cm2.
 Short carrier capture and emission times determine low barrier capacitance (capability to
to collect charge (transient) at fixed voltage) and large space charge generation (leakage)
current in heavily irradiated diodes.
 The space charge generation current prevails in heavily irradiated diodes over barrier
charging (displacement, which is controlled by measurements of phase shift for the ac test
signal in routine C-V), therefore applicability of C-V technique is doubtful for control of
heavily irradiated detectors.
 Carrier capture and emission lifetimes are short, and barrier capacitance decreases to
geometrical its value at low (U< Ubi) applied voltage of the diodes with enhancement of
fluence. Operation of a diode is similar to that of capacitor.
Items to clarify:
Whether diode/detector of the present design is functional after heavy irradiations?- doubtful
What is the system of defects and levels, which governs extraction of carriers (UR) and state of
material?- material becomes similar to insulator.
Additonal issues: - if there are filled levels those compensate material;
- how rapidly these levels are able to response to external voltage changes
Which models are acceptable for prediction of characteristics?
EC
EC
EV
EV
The BELIV technique with spectrally resolved fs pulsed IR (1.1 – 10 µm) biasing
has been employed to clarify what is a system of levels and if these levels are filled
Variations of BELIV transients by pulsed IR of varied spectrum
OPO DFG
fs pulse
OPO DFG wavelength/quantum for which
appears suppression of traps,
i.e. recover of BELIV transient of Cb,
indicates a system of filled single type deep levels
mono-polar photoconductivity

change of charge state- capacitance
To approve principles
structure with known technological defects
For qualitative understanding
(within depletion approximation):
Cb~(ND=n0)1/2~1/w(n0)
Cb(t) ~1/M=(en0|tr)/0
UBELIV (a.u.)
0.2
Si junction
pulsed bias illumination OPO-DFG
pulse= 100 fs, rep rate 1kHz
ex= 4 m, Epulse = 30 J
0.1
IR limit h= 0.31eV
Carrier capture rate
0.0
using extended depletion
approximation)
(
for transient processes
0  dr ,
2
e2
M 



en0
2
2U  e[ EC ( )  EC ( ENR)]
0
20
t (s)
40
60
Variations of BELIV transients by pulsed IR of varied spectrum
in neutron irradiated detectors
E4 h 0.51eV
E3 h 0.41eV
E2 h 0.36 eV
The shallowest
E1 h 0.3 eV
Variations of BELIV transients by pulsed IR of varied spectrum
in neutron irradiated detectors
The most shallow filled
Ered threshold =h 0.5 eV
Edeepest -h 1.08eV
The most shallow filled,
or a half of two step generation
14
ex= 1.15m
0.12
1.3
1.5
2.4
2.5
2.6
0.09
0.06
0.03
0.00
0
5
10
t (s)
15
For 1E14 n/cm2 and h> 0.83 eV possible
partial recovering of a barrier, while for
h≤ 0.5 eV space charge
generation current prevails (rapid
capture/emission processes
Ered threhold =h 0.52 eV
2
16
BELIV signal (a.u.)
BELIV signal (a.u.)
MCz Si diode irradiated 10 n/cm
ULIV= 12V
20
Edeepest -h 1.08eV
MCz Si diode irradiated 10 n/cm
ULIV= 12V
0.12
2
ex= 1.2m
1.5
2.4
2.6
3.0
0.09
0.06
0.03
0.00
0
3
t (s)
6
9
For 1E16 n/cm2 only space charge
generation current increases (extremely rapid
capture/emission processes) while barrier capacitance
is close to Cgeom
 A clear structure of deep levels is absent in heavily irradiated diodes >1014
n/cm2 while carriers are generated by inter-band excitation.
Items to clarify:
Whether diode/detector of the present design is functional after heavy irradiations?- doubtful
What is the system of defects and levels, which governs extraction of carriers (UR) and state of
material?- material becomes similar to insulator
Additonal issues: - if there are filled levels those compensate material;
- no, high density of various species levels is more probable those are only weakly filled by small n0
- how rapidly these levels are able to response to external voltage changes
- fast capture of excess carrier and fast space charge generation current response
But system relaxes to equilibrium state very slowly – as estimated from I-V point-by-point
measurements at T<150 K
Which models are acceptable for prediction of characteristics?
The disordered material models-?
Summary
 Examined MW-PCT characteristics imply prevailing of intricate system of
defects and reduction of majority carriers. The recombination capture lifetimes
become shorter than dielectric relaxation time.
 Carrier emission lifetime (increase of leakage current – at UR in I-V), follows
capture lifetime (increase of serial resistance R~n0 - at UF in I-V)
Barrier capacitance decreases to geometrical value of the diodes with
enhancement of fluence. Carrier capture and emission lifetimes are short. The
pointed system of deep levels can be revealed only in diodes irradiated with
fluence of <1014 n/cm2.
 A clear structure of deep levels is absent in heavily irradiated diodes >1014
n/cm2 while carriers can be generated by inter-band excitation.
Thanks to G.Kramberger for neutron irradiations.
E.Tuominen, J.Harkonen and J.Raisanen are appreciated
for samples (substrates and pin diodes) as well as for proton irradiations.
Thank You for attention!
P.Blood and J.W.Orton. The electrical
characterization of semiconductors: majority
carriers and electron states, (Academic Press,
London –San Diego-New York, 1992).
Depletion aproximation for material
d 2
1

 ( x)
2
dx
0
containing only dopants:
y
y

1 
 ( x)  ()  
 y   ( z )dz   z ( z )dz 
0  

 y  x
xn

xd
 ( z )dz 
xp
  ( z)dz  0
 xm
 ()  V 
1
xn
0 x
x ( x)dx
p
 ( x)  eN d  n( x)
d 2 ( x)
e 
 e ( x) 


 N d  n0 exp 
2
dx
0 
 kT 
E 2 ( x) 
2e  
kT  kT
 e ( x) 
N d exp 

 N d   ( x)   
0  
e  e
 kT 
x
 ( x)
xd
0
 dx    E
E ( x) 
1
2eN d
  ( x) 
0
( )d
only numerical integration
 ( x)  kT / e
  ( x)
gives depletion
approximation
eN d
( xd  x) 2
20
eN d 2
V
xd
20
Limitations:
for steady-state
assumption
2
tr
 e2 Nd

n( x)  N d exp 
( x d  x) 2  
 2 0 kT

2

 1  xd  x  

 
 N d exp  
2 L

  D  

M 

 1  x  x  2 


  
 ( x)  eN d 1  exp   d
 2  LD   



1
d
eN
E ( x)  
  d ( xd  x)
dx
0
for transients
  kT  2
LD   20 
 e Nd 
1 x
V   d
2  LD
2
 kT
 
 e
 tr
2

2
tr
2 U 
Transient currents in depletion region
in deep traps containing material
tr
x
J c ( x)   (e)
x2
Test harmonic signal
Uac<kT/e, to evaluate Cb,,
by control of phase shift
avoiding xd>tr , i.e.
desirable regime EC(x)-EC(xd)<kT.
dn
dn
dx  (e)( x  x2 )
dt
dt
J c ( x )  (  e) x
 E ( x, t ) 
D
t
e
 0
dn
 dp 
 e(W  x)  
dt
 dt 


(W  x) N   N t  nt (t ) 
e
 0
N c (t )

x
V
dN
 dn 
 e(W  x)  t   e c
dt
 dt 

e  
W2
 N c (t )W 
( N  N t  nt (t ))
 0 
2

dN c W dnt

dt
2 dt
D
W  dn

 e x   t
t
2  dt

P.Blood and J.W.Orton. The electrical
characterization of semiconductors:
majority carriers and electron states,
(Academic Press, London –San DiegoNew York, 1992).
 dn
dp 
W  dp dn 
eW  dn dp 
J (t )  e x
 (W  x)
  x      
  
dt 
2  dt dt 
2  dt dt 
 dt