Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
Vol
.
6
,
No
. 2,
J
une
2
0
1
5
,
pp
. 21
6~
22
4
I
S
SN
: 208
8-8
6
9
4
2
16
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJPEDS
Modeling the Dependence of Powe
r Diode on Temperature and
Radiation
S.M. El-G
han
a
m
*
, A.
M.
A
b
d El-M
ak
so
od
**
, F.
A.S.
S
o
liman
**
*Res
. L
a
b.
, P
h
ys
ics
D
e
pt
.,
F
acu
lt
y
of W
o
m
e
n for
A
r
ts
,
Science, and Education
,
Ai
n-Sham
s Univ.,
Cairo,
Eg
ypt
**Nuclear
Mater
i
als Author
ity
,
P
.
O. Box 530
, M
aadi-11728
, C
a
ir
o, Eg
y
p
t
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Feb 3, 2015
Rev
i
sed
Ap
r
11
, 20
15
Accepte
d
May 1, 2015
A theoretical st
udy
had been carried out on th
e effect of radiation on th
e
electrical properties of
silic
on po
wer diodes. Co
mp
ut
e
r
progra
m
"PDRAD2015
"
was developed to solve the diode equatio
ns and to
i
n
t
r
o
d
u
c
e
t
h
e
o
p
e
r
a
t
i
n
g
c
o
n
d
i
t
i
o
n
s
a
n
d
rad
i
ation
eff
e
cts
upon
its
pa
ra
m
e
te
rs. Tempe
r
at
ure
i
n
c
r
ea
se interrupt
s the
el
ect
ri
cal
prope
rt
ie
s of the
d
i
o
d
e
i
n
t
h
e
d
i
r
e
c
t
i
o
n
of drop voltag
e
decrease
across the p-n junction
.
The
model was analyzed und
er th
e
in
fluence of
differ
e
nt r
a
diation
ty
p
e
(
g
a
m
m
a
-
ray
s
, neutrons, protons and
electr
ons) with various dose
levels and
energies
. The carrier’s
diffus
i
on lengths were
s
e
r
i
ou
s
l
y a
f
f
e
c
t
e
d
l
e
a
d
i
n
g
to a large i
n
cre
a
s
e
in t
h
e forwa
r
d volta
ge. The
s
e effect
s
were
found to
be
functio
n of radi
ation t
y
p
e
,
f
l
u
e
n
c
e
a
n
d
e
n
e
r
g
y
.
Keyword:
D
i
ffusi
on
l
e
ng
t
h
El
ect
ri
cal
propert
i
e
s
Physical radia
tion effects
P-n ju
nct
i
ons
R
a
di
ati
on effe
ct
s
Sem
i
conduct
o
r d
i
o
d
e
s
Silico
n
d
i
od
es
Copyright ©
201
5 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
S.M
.
El
-G
ha
na
m
,
Res. La
b., P
h
ysics
Dep
t
., Facu
lty o
f
Wo
m
e
n
fo
r Arts, Scien
ce,
an
d Ed
u
cation
,
Ain-Sh
am
s Un
iv
., Cairo
,
Egyp
t
1.
INTRODUCTION
Sem
i
cond
uct
o
r
devi
ce m
odel
i
ng creat
es m
odel
s
f
o
r
beha
vi
o
r
of t
h
e di
s
c
ret
e
, el
em
ent
a
ry
devi
ces
(t
ran
s
i
s
t
o
rs
, i
n
duct
o
rs
, di
o
d
es
, et
c.) base
d o
n
fu
ndam
e
nt
al
phy
si
cs, ge
om
etry
, desi
g
n
a
nd
ope
rat
i
o
n co
nd
i
t
i
ons
[1
, 2]
. Al
so
, r
a
di
at
i
on ef
fect
st
udi
es are o
f
great
i
n
t
e
rest
,
whe
r
e el
ect
ro
ni
c com
pone
nt
s and sy
st
em
s
whe
n
expose
d to the
hars
h ra
diation envi
ronm
ents of s
p
ace, or nuclea
r
powe
r plants and mines m
a
y degra
d
e
or
ev
en
fail d
u
e
t
o
th
e effects of io
n
i
zing
rad
i
atio
n
.
Th
is
is p
a
rticu
l
arly i
m
p
o
r
tan
t
in
reliab
ility stu
d
i
es and
when
trying to
predi
c
t the survi
v
al of t
h
es
e syste
m
s
in space.
Finally, m
u
ch work
had bee
n
done by
the
a
u
t
h
ors
a
n
d
ot
he
rs w
h
i
c
h
i
n
cl
ude ex
p
e
ri
m
e
nt
al and
/
or t
h
e
o
ret
i
cal
dat
a
on t
e
m
p
erat
ure an
d ra
di
at
i
on e
ffect
s i
n
sem
i
cond
uct
o
r
s
[3-
8
]
.
S
o
, t
h
e
prese
n
t
pape
r
i
s
a t
r
i
a
l t
o
shed fu
rt
he
r l
i
ght
on s
u
ch
very
i
n
t
e
rest
an
d im
po
rt
ant
field
.
In th
is
co
n
c
ern
,
a com
p
u
t
er p
r
og
ram
is u
tilized
in
o
r
d
e
r to characterize, and stud
y th
e effects
of
t
e
m
p
erat
ure
an
d
radi
at
i
o
n
(w
i
t
h
di
f
f
ere
n
t
t
y
pes,
fl
ue
nc
ies and
ene
r
gies) on
the electrical
properties of
t
h
e
p
o
wer silico
n
d
i
od
es.
2.
THEORY OF OPERATION
The m
o
st
im
port
a
nt
t
y
pi
cal
re
qui
rem
e
nt
s for
a po
we
r di
ode
s a
r
e
:
1
)
h
i
g
h
c
u
r
r
e
n
t
c
a
p
a
b
i
l
i
t
y
,
2
)
l
o
w
leakage
curre
nt,
and
3
)
l
o
w
f
o
r
w
a
r
d
v
o
l
t
a
g
e
d
r
o
p
a
t
h
i
g
h
c
u
r
r
e
n
t
s
.
N
o
w
,
t
o
a
n
a
l
y
z
e
t
h
e
f
o
r
w
a
r
d
(
I
-
V
)
r
e
l
a
t
i
o
n
s
h
i
p
f
o
r
p
o
w
e
r
di
ode l
e
t
us exam
i
n
e a typi
cal
power
di
ode m
o
del
,
where i
t
s
p
h
y
s
i
c
a
l
co
nstr
u
c
tion are show
n in
Figu
r
e
1.
F
i
n
a
l
l
y
,
c
h
e
c
k
i
n
g
t
h
e
d
i
f
f
u
s
i
o
n
l
e
n
g
t
h
(L)
at
h
i
gh
inj
ecti
o
n, on
e g
e
t
s
[9]
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 6,
No
.
2,
Ju
ne 20
15
:
216
–
2
24
2
17
L = (D
τ
)
1
/
2
=
(
μ
)
1/
2
(
1
)
whe
r
e :
D :
di
ff
usi
o
n
c
onst
a
nt
,
τ
: ave
r
age
life
t
im
e of free ele
c
trons,
μ
: m
o
b
ility,
K :
B
o
l
t
z
m
a
nn'
s const
a
nt
,
T : ab
so
lu
t
e
te
mp
era
t
u
r
e
,
an
d
q : electron cha
r
ge
.
Figure
1. Physical characte
r
is
tics fo
r a
ty
pical po
we
r
dio
d
e
So
lv
in
g
for the to
tal v
o
ltag
e
d
r
o
p
acro
ss th
e ju
n
c
tio
n
,
fo
r a
c
e
r
t
a
i
n
c
u
r
r
e
n
t
v
a
l
u
e
(
I
)
,
g
i
v
e
s
[
1
0
]
:
V =
ln
(
2
)
where:
W
:
base wi
dt
h
,
A : a
r
ea, and
n
i
: i
n
trinsic ca
rrier conce
n
trat
ion.
Had t
h
e di
ff
us
i
on l
e
n
g
t
h
bee
n
sh
o
r
t
com
p
ared t
o
t
h
e
base
wi
dt
h
,
o
n
l
y
a po
rt
i
o
n o
f
t
h
e
base re
gi
o
n
wo
ul
d
be i
n
hi
gh i
n
ject
i
o
n. T
h
e el
ect
ro
ns i
n
ject
ed i
n
t
o
the
base re
gion woul
d rec
o
m
b
ine at a
m
ean distanc
e
(L
)
from
t
h
e junct
i
o
n an
d a
m
a
jori
t
y
curr
ent
wo
ul
d
fl
o
w
t
h
r
o
ug
h t
h
e
very
hi
g
h
res
i
st
ance base r
e
gi
o
n
.
Ho
we
ver
,
t
h
e
m
i
nori
t
y
cur
r
e
n
t
fl
ow t
h
r
o
ug
h t
h
e
o
h
m
i
c resi
st
ance can
be
ve
ry
hi
gh i
n
t
h
e
regi
ons
w
h
ere
n >
N
A
sin
ce th
e resistiv
ity o
f
sili
co
n
for
N
A
=1
.4
0x1
0
14
/cm
3
is
ab
ou
t 1
3
0
Ω
/
c
m
.
A hi
gh cu
rr
ent
t
h
ro
u
gh t
h
i
s
hi
gh
resi
st
i
v
i
t
y
regi
on
ad
d si
gni
fi
cant
l
y
dr
o
p
t
o
t
h
e f
o
rwa
r
d
v
o
l
t
age. S
o
,
t
h
e
f
o
r
w
ar
d
v
o
l
t
a
ge
fo
r a
p
o
w
er
di
ode
i
s
kept
sm
all
by
a l
o
n
g
di
f
f
u
s
i
o
n
l
e
ngt
h
o
r
a
l
o
n
g
m
i
nori
t
y
carr
i
er l
i
f
et
im
e.
3.
RA
DI
ATIO
N PHY
S
IC
S
Whe
n
hi
g
h
e
n
ergy
radi
at
i
o
n
i
s
i
n
ci
de
nt
o
n
a sem
i
con
duct
o
r
de
vi
ce, t
h
e
ener
gy
i
s
dep
o
s
i
t
e
d i
n
t
h
e
sem
i
cond
uct
o
r
vi
a t
w
o m
a
in m
echani
s
m
s
, at
om
i
c
collisions a
n
d electronic
io
n
i
zat
io
n
s
. Th
e
relativ
e
im
port
a
nce
o
f
t
h
ese t
w
o m
e
cha
n
i
s
m
s
i
n
a sem
i
-con
d
u
ct
or
de
pen
d
s
o
n
bot
h t
h
e t
y
pe
of
ra
di
at
i
on a
nd t
h
e
nat
u
re
of t
h
e
d
e
vi
ce. F
o
r el
ec
t
r
o
n
s,
pr
o
t
ons
and
gam
m
a-ray
s
envi
ro
nm
ent
,
m
o
st
of t
h
e
dep
o
si
t
e
d
ene
r
gy
g
o
es
i
n
t
o
i
o
ni
zat
i
o
n
pr
ocess
e
s, i
.
e
.
, exci
t
a
t
i
o
n a
n
d
pai
r
pr
o
duct
i
on
. F
o
r
fast
ne
ut
r
ons
en
vi
r
o
n
m
ent
,
a l
a
r
g
e f
r
act
i
on
of the
de
posite
d e
n
ergy re
sult
s directly in atom
ic displ
acement dam
a
ge from
collisions.
Th
e in
itially
p
r
od
u
c
ed
d
e
fect fro
m
g
a
mma o
r
elect
ron
-
irrad
i
atio
n
is q
u
ite sim
p
le
an
d
can
b
e
expresse
d a
s
a
single dis
p
lac
e
d latti
ce atom and its as
soci
ated
vacancy
(
F
rankel
Defec
t
[1
1]
).
O
n
the
oth
e
r
hand, irra
diation with fast
neutrons
produce re
gion
s of dam
a
ge,
each contains
se
veral hundre
d
dis
p
laced
at
om
s.
Hence,
t
h
e
i
n
t
e
ract
i
o
n of ra
di
at
i
on wi
t
h
sem
i
cond
uct
o
r cry
s
t
a
l
s
i
s
si
m
p
ly
descri
be
d by
t
h
e n
u
m
b
er of
defects/cm
3
created [12].
It
can be s
h
o
w
n t
h
at
poi
nt
defect
s
(Fran
k
el
Defects) resu
lt in
th
e in
trod
u
c
tion
o
f
allowed
en
erg
y
states with
in
th
e fo
rb
idd
e
n
g
a
p
o
f
th
e sem
i
c
o
ndu
ctor [1
3
]
wh
ich
affects
main
ly
th
e
m
i
n
o
rity carriers lifeti
m
e.
The
de
gra
d
a
t
i
on i
n
m
i
nori
t
y
carri
er
l
i
f
et
im
e is us
ual
l
y
ex
pre
ssed as:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Mo
del
i
n
g
t
h
e
Depe
n
d
ence
of
Pow
e
r
Di
ode
on
Te
mper
at
ur
e a
n
d
R
adi
at
i
o
n (
S
.M.
El
-G
h
a
n
a
m
)
21
8
d(1/
τ
) / d
Φ
=
K
τ
,
(
3
)
whe
r
e,
K
τ
is t
h
e lifetim
e d
a
mag
e
con
s
tan
t
, and
Φ
i
s
t
h
e
ra
di
at
i
on
fl
ue
nce
.
So
m
e
literatu
res d
i
scu
ss a d
i
ffu
s
ion
len
g
t
h
d
a
mag
e
as:
1L
⁄
1/L
K
∅
(
4
)
Whe
r
e,
L
f
, a
n
d
L
0
are t
h
e
di
ff
usi
o
n l
e
ngt
h a
f
t
e
r an
d
bef
o
re
i
rradi
at
i
o
n,
an
d
K
L
is th
e
di
ff
usi
o
n l
e
ngt
h
d
a
m
a
ge
constant.
The effects of
radiation on the po
wer
d
i
od
e
p
e
rform
a
n
ces is
m
a
in
ly d
u
e
to
th
e chang
e
in
lifeti
m
e o
f
m
i
nori
t
y
carri
e
r
s co
nt
ai
ne
d i
n
t
h
e base
re
gi
o
n
,
whi
c
h o
b
ey
s t
h
e rel
a
t
i
o
ns
m
e
nt
i
oned
ab
o
v
e.
In t
h
i
s
co
n
cern
,
t
y
pi
cal
pu
bl
i
s
hed
val
u
es
f
o
r t
h
e
di
ff
usi
o
n l
e
n
g
t
h
dam
a
ge c
o
n
s
t
a
nt
(
K
L
), for protons a
n
d electrons a
r
e
illu
strated
in
T
a
bl
e 1 [1
4,
15]
. On t
h
e ot
her
han
d
, f
o
r ne
ut
r
ons
, i
t
i
s
obser
ved t
h
at
t
h
e da
m
a
ge const
a
nt
i
s
a
fun
c
tion
o
f
t
h
e in
j
ection
ratio
(n
/
p
)
and
h
a
s
t
h
e v
a
lu
es
lis
t
e
d i
n
Tabl
e
2
[
1
6,
1
7
]
.
Fi
nal
l
y
,
fo
r
gam
m
a-radi
at
i
on,
i
t
i
s
fou
nd t
h
at
fo
r co
bal
t
-
6
0
,
t
h
e di
f
f
usi
on l
e
ngt
h dam
a
ge con
s
t
a
nt
has a
val
u
e
of
1.
27
x
1
0
-11
p
a
rticles
-1
[
18,
19]
.
Tabl
e 1. Di
f
f
us
i
on
l
e
ngt
h dam
a
ge
c
o
n
s
t
a
nt
d
u
e
t
o
el
ect
ro
ns
and
p
r
ot
o
n
s
Tabl
e
2.
Di
f
f
us
i
on l
e
ngt
h
dam
a
ge c
o
n
s
t
a
nt
d
u
e t
o
ne
ut
r
o
n i
r
radi
at
i
o
n
Da
m
a
g
e
co
nsta
nt
[Pa
r
ticl
es
-1
]
Injection ratio
7.
80 x 10
-9
10
0
7.
40 x 10
-8
10
-4
1.
47 x 10
-7
10
-6
4.
RESULTS
A
N
D
DI
SC
US
S
I
ONS
R
e
sul
t
s
obt
ai
n
e
d by
R
a
ge
h, et
al
. [20]
hav
e
been anal
y
z
e
d
usi
n
g t
h
e p
r
op
ose
d
com
p
u
t
er pr
og
ram
(A
pp
en
di
x A
)
for cal
cul
a
t
i
n
g t
h
e di
f
f
usi
o
n l
e
ngt
h at
hi
gh i
n
ject
i
o
n l
e
vel
and
pl
ot
t
i
ng t
h
e f
o
rwa
r
d (I
-V
)
rel
a
t
i
ons
hi
p
.
The e
ffect
o
f
d
i
ffere
nt
radi
at
i
o
n
t
y
pes
(
g
am
m
a
-ray
s
, el
ect
r
ons
,
ne
ut
r
ons
a
n
d
p
r
ot
o
n
s)
,
fl
uence
(
f
r
o
m
1
.
0
x10
8
/
cm
2
u
p
to
1
.
0
x10
20
/
c
m
2
)
an
d
en
erg
y
(
f
r
o
m
1
.
0
MeV
u
p
to
100 MeV
)
ar
e stu
d
ied
.
A
l
so, th
e ef
f
ect of
t
e
m
p
erat
ure
va
ri
at
i
on
(i
n t
h
e
r
a
nge
f
r
om
30
0
K
up
t
o
8
0
0
K
)
i
s
co
nsi
d
e
r
ed.
4.1. Tem
p
erature Effects
Th
e
forward
(I–
V
) ch
aracteristics o
f
th
e
silico
n
p
o
wer d
i
od
e is calcu
lated
u
s
ing
t
h
e relation
men
tio
n
e
d in Eq
.
2
,
wh
ere it is well
k
nown th
at
bo
th
;
vo
ltag
e
tem
p
eratu
r
e co
efficien
t
(KT/q
)
and
the intrin
si
c
conce
n
t
r
at
i
o
n of
el
ect
ro
ns
(n
i
)
are te
m
p
erature
depe
ndent
[21]. In t
h
is
concern, Figure
2 s
h
ows
the
effects of
te
m
p
eratu
r
e on th
e electri
cal p
r
op
erties
o
f
silico
n
power
dio
d
e
calcu
lated u
s
ing
t
h
e
p
r
op
o
s
ed program. Th
e
(I
–V
) c
u
r
v
es s
h
i
f
t
p
r
of
ou
n
d
l
y
t
o
wa
rd
s t
h
e l
o
w val
u
es
of
d
r
op
v
o
l
t
a
ge
fo
r
t
h
e sam
e
for
w
a
r
d c
u
rre
nt
val
u
es, t
h
e
m
a
t
t
e
r whi
c
h
was s
h
o
w
n t
o
be i
n
cl
ose ag
r
e
em
ent
wi
t
h
w
o
r
k
do
ne
by
X.
Kan
g
, et
al
.
,
a
nd
p
ubl
i
s
hed a
t
onl
i
n
e
El
ect
roni
cs
Gu
i
d
e [2
2, 2
3
]
.
T
h
i
s
effect
, of c
o
urse
, i
s
due
to
th
e in
crease in
th
e v
o
lta
ge te
m
p
erature coefficient
and t
h
e i
n
t
r
i
n
s
i
c carri
er'
s
den
s
i
t
y
of t
h
e m
i
no
ri
t
y
el
ect
ron
s
cont
ai
n
e
d i
n
t
h
e base re
gi
on
of t
h
e
di
o
d
e
wi
t
h
increasing t
h
e
te
m
p
erature
[21]. From
whic
h, a
linear
de
p
e
nde
nce o
f
fo
r
w
ar
d v
o
l
t
a
ge on
t
e
m
p
erat
ur
e
was
obt
ai
ne
d,
as
w
e
l
l
,
as em
pi
ri
cal
equat
i
o
n
co
ul
d
be
ded
u
ce
d a
s
:
V
=
1
.
37
554
–
0
.
0
015
T
(
5
)
wh
ere, V is th
e fo
rward
vo
ltag
e
, an
d
T is th
e te
m
p
erature in Kelv
i
n
.
4.
2. R
a
di
a
t
i
o
n
E
ffec
t
s
Perm
anent
rad
i
at
i
on dam
a
ge i
n
silico
n
power
d
i
od
es is
m
a
in
ly a
ttrib
u
t
ed
to
th
e chan
g
e
in
t
h
e
min
o
r
ity carriers lifetim
e. Co
n
s
eq
u
e
n
tly, the m
ean
d
i
ffu
s
i
o
n length of t
h
e ca
rriers als
o
c
h
anges
.
So, duri
ng
th
e p
r
esen
t stud
y, d
i
ff
er
en
t r
a
d
i
atio
n
typ
e
s
w
e
r
e
used
an
d
th
e co
rr
esp
ondin
g
d
a
m
a
g
e
ef
fects o
n
th
e d
i
ffu
sion
P
r
ot
ons [P
art
i
cles
-1
]
Electrons [
P
articl
es
-1
]
Energy [MeV]
3.
8 x 10
-5
1.
0 x 10
-1
0
1
3.
8 x 10
-6
2.
7 x 10
-1
0
10
8.
5 x 10
-7
4.
0 x 10
-1
0
50
4.
7 x 10
-7
5.
0 x 10
-1
0
100
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 6,
No
.
2,
Ju
ne 20
15
:
216
–
2
24
2
19
len
g
t
h are
rep
r
esen
ted in
Fi
gu
re
3
.
A prono
un
ced
redu
ctio
n in
t
h
e
d
i
ffusio
n
len
g
t
h
o
c
cu
rs fro
m
its i
n
itial
val
u
e
(
1
3
7
µm
)
do
wn
t
o
a cer
t
a
i
n
val
u
e w
h
i
c
h
depe
n
d
s
o
n
r
a
di
at
i
on t
y
pe,
f
l
uence a
n
d e
n
e
r
gy
.
The re
sul
t
s
are
pl
ot
t
e
d
fo
r t
h
e
di
ffe
re
nt
t
y
pes
of
radi
at
i
o
n,
whe
r
e i
t
i
s
n
o
t
i
ced t
h
at
ra
di
at
i
on
fl
ue
nce
s
mo
r
e
t
h
a
n
1
0
9
/c
m
2
are shown to be effective,
where it wa
s found t
h
at a close
agreem
e
n
t with
tho
s
e
resu
lts
pu
bl
i
s
he
d
by
C
a
rl
so
n, et
.al
[
24]
was
o
b
t
a
i
n
ed.
Dam
a
ge d
u
e t
o
p
r
ot
o
n
i
r
radi
at
i
o
n i
s
s
h
ow
n t
o
be
very
st
ro
n
g
especi
al
l
y
i
n
t
h
e l
o
w ene
r
gy
b
a
nd
. F
o
r c
o
m
p
ari
s
o
n
,
usi
n
g a con
s
t
a
nt
p
r
ot
o
n
fl
ue
nce
of
10
13
/c
m
2
, t
h
e
di
ff
usi
o
n
l
e
ngt
h
was re
d
u
ced t
o
4
8
µm
and
13
0 µm
f
o
r
pr
ot
o
n
ene
r
gi
es of
1.
0 M
e
V an
d 1
00 M
e
V res
p
ect
i
v
el
y
.
Thi
s
phe
n
o
m
e
non,
of c
o
u
r
se,
d
o
es
not
h
o
l
d
fo
r t
h
e case of el
ect
r
on i
r
ra
di
at
i
on,
whe
r
e t
h
e
dam
a
ge i
s
sh
ow
n t
o
be a
di
rect
f
u
nct
i
o
n
of
b
o
t
h
ra
di
at
i
o
n
fl
uence
an
d
ener
gy
.
I
n
case of
n
e
utr
o
n
ir
r
a
d
i
ation
,
the d
a
m
a
g
e
o
c
cu
r
s
st
r
ongl
y f
o
r f
l
u
e
n
ces
ab
ov
e
10
13
/c
m
2
depe
nd
i
n
g
up
o
n
t
h
e i
n
jec
t
i
on rat
i
o
(
n
/
p
). Fi
nal
l
y
, ga
m
m
a
-ray
s
pro
duce t
h
e sam
e
dam
a
ge on t
h
e di
f
f
u
s
i
o
n l
e
ngt
h at
flue
nces
higher than 10
17
/cm
2
.
The ab
o
v
e m
e
nt
i
one
d
dam
a
ges are at
t
r
i
but
e
d
t
o
w
h
at
i
s
cal
l
e
d "di
s
pl
ace
m
e
nt
cross
-
sec
t
i
on" f
o
r t
h
e
radiation type
and e
n
ergy.
Figure (4) i
n
dicates that the displacem
ent cross
-
section
for both
gamma-and-
el
ect
ron
-ra
di
at
i
o
n
i
s
a
di
rect
f
unct
i
o
n
o
f
t
h
e
ener
gy
[
1
1,
1
2
]
. On
t
h
e
ot
her
han
d
,
p
r
ot
o
n
s
are c
h
ar
ged
pa
rt
i
c
l
e
s,
sim
i
l
a
r t
o
el
ect
ro
ns,
an
d i
t
m
i
ght
be e
x
pect
e
d
t
h
at
b
o
t
h
p
r
o
duce
t
h
e
sam
e
deg
r
ee
of
dam
a
ge.
Thi
s
i
s
n
o
t
t
h
e
case, beca
use
proton has larger m
a
ss and i
t
can im
part
m
u
ch
m
o
re energy to th
e nucleus tha
n
an
electron
wh
en
co
llisio
ns with lattice o
ccu
r.
0.
0
0
.
1
0.
2
0
.
3
0.
4
0
.
5
0.
6
0
.
7
0.
8
0
.
9
1.
0
0.
0
0.
5
1.
0
1.
5
2.
0
F
o
rw
a
r
d
C
u
rr
e
n
t,
A
F
o
r
w
ar
d
V
o
l
t
ag
e,
V
T
e
m
p
.,K
80
0
60
0
50
0
40
0
30
0
(a)
2
0
0
300
40
0
5
0
0
60
0
7
00
8
0
0
9
00
0.
0
0.
2
0.
4
0.
6
0.
8
1.
0
For
w
a
r
d
Vol
t
age,
v
Tem
p
er
a
t
ur
e
,
K
V (
V
ol
t
)
=
1.
3
7
5
5
4
-
0.
00
15
*
T 9
K
)
Co
r
.
=
-
0
.
9
9
4
(b
)
Fi
gu
re
2.
Ef
fec
t
s of
t
e
m
p
erat
ure
on
t
h
e
fo
r
w
a
r
d
(
I
-
V
)
cha
r
ac
t
e
ri
st
i
c
cur
v
es
of
Si
-
p
o
w
e
r
di
ode
(a
)
and the linear
depe
ndence
of
th
e fo
rw
ar
d voltag
e
on
tem
p
er
atu
r
e,
cal
cul
a
t
e
d a
ppl
y
i
ng t
h
e
de
vel
ope
d c
o
m
put
er
p
r
o
g
ram
m
i
ng (b
)
1E
8
1
E14
1
E
2
0
0
20
40
60
80
100
120
140
160
Di
f
f
u
si
on Lengt
h,
um
F
l
uence,
cm
2
N
e
ut
r
ons
,
I
n
j
e
ct
i
on Le
vel
:
10
E
-
6
10
E
-
4
1.
0
Ga
mm
a
-
R
a
y
s
(a)
(b
)
Fi
gu
re
3.
E
ffe
ct
s of
ra
di
at
i
o
n
wi
t
h
di
f
f
ere
n
t
t
y
pes, fl
uenci
e
s an
d e
n
er
gi
es
on
t
h
e
di
f
f
u
s
i
o
n l
e
n
g
t
h
o
f
t
h
e
silico
n
p
o
wer d
i
od
e
{(a)- Neu
t
ro
n
s
and
g
a
mma
-rays, and (b
)-electron
s
an
d pro
t
on
s)}.
1
E
8
1
E1
2
1
E1
6
1
E2
0
0
20
40
60
80
100
120
140
160
Di
f
f
u
s
i
on
Le
n
g
t
h
,
um
Fl
uene,
cm
2
E
l
e
c
t
r
ons
E
n
er
gy
,
M
e
V
1.
0
10
10
0
Pr
o
t
o
n
s
En
e
r
g
y
,
M
e
V
10
0
10
1.
0
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Mo
del
i
n
g
t
h
e
Depe
n
d
ence
of
Pow
e
r
Di
ode
on
Te
mper
at
ur
e a
n
d
R
adi
at
i
o
n (
S
.M.
El
-G
h
a
n
a
m
)
22
0
Fig
u
re 4
.
Disp
lace
m
e
n
t
cross sectio
n
v
e
rsu
s
en
erg
y
for
silico
n
,
di
ffe
re
nt
ra
di
at
i
on t
y
pe
s are
s
h
o
w
n (
c
om
pi
l
e
d
by
t
h
e a
u
t
h
o
r
).
F
o
r
p
r
ot
ons
wi
t
h
hi
ghe
r
e
n
er
gi
es,
m
o
st
of
t
h
e
en
ergy
m
a
y
be
t
r
ansfe
rre
d
i
n
t
o
ki
net
i
c
ene
r
gy
and
a
decrease
in t
h
e
displacem
ent
cross-section
occurs due t
o
the dec
r
ease
i
n
t
h
e
possibility of
proton ca
pturing.
She
n
g, S
.
L.
[25]
ha
s
per
f
o
r
m
e
d
n
u
m
e
ri
cal
cal
c
ul
at
i
ons
o
f
t
h
e t
o
t
a
l
di
ode
vol
t
a
ge
dr
op
a
s
a
fu
nct
i
o
n
o
f
th
e
ratio
W/L
for bo
th
o
h
m
ic an
d
m
a
j
o
rity carrier co
n
t
acts.
Th
eir
resu
lts fo
r t
h
e inv
e
stig
ated
silico
n
po
wer
diode a
r
e c
onsi
d
ere
d
.
The di
ff
usi
o
n l
e
ngt
h, aft
e
r ex
pos
u
r
e t
o
ra
di
a
t
i
on, ca
n be
ob
t
a
i
n
ed f
r
om
t
h
e
m
i
nori
t
y
carr
i
er l
i
f
et
im
e
as:
/
/
∅
/
(
6
)
whe
r
e, R and R
0
are the recom
b
ination rat
e
s afte
r and
b
e
fo
re irra
diation
,
an
d K
τ
is th
e
m
i
n
o
r
ity
carrier
l
i
f
et
im
e dam
a
ge co
nst
a
nt
.
O
n
th
e
o
t
h
e
r
han
d
, th
e d
i
o
d
e
v
o
ltag
e
is
g
i
v
e
n
in Figu
r
e
5 in
ter
m
s o
f
t
h
e
v
o
ltag
e
w
ithout in
j
ection
o
r
I(e
W
/
A
)
[
2
0]
,
whe
r
e:
Ir =
I
(
e
W
/
A
)
=
I
W/q
μ
AN
A
(
7
)
Hence
,
f
r
om
Fi
gu
re 5,
fo
r t
h
e val
u
e o
f
I
r
a
nd
W/
L
,
a
ppl
i
e
d v
o
l
t
a
ge can
be o
b
t
a
i
n
ed a
t
vari
o
u
s o
p
e
r
at
i
ng
co
nd
itio
ns.
0.
5
1
.
0
1
.
5
2
.
0
2.
5
3
.
0
3.
5
1
10
100
1
000
I(
W
P
/A
)
,
V
A
p
p
l
ie
d
V
o
lt
a
g
e
,
V
W/
L
=
5
.
0
W/
L
<
1
.
0
W/
L
=
7
.
0
Fi
gu
re
5.
V
o
l
t
a
ge-c
ur
re
nt
rel
a
t
i
ons
f
o
r
N
+
PP
+
po
we
r di
o
d
e.
1
1
0
100
1E-
2
1
1E-
2
0
1E-
1
9
D
i
s
p
lace
m
e
nt cro
ss-se
ction
En
e
r
g
y
,
M
e
V
G
a
mma ra
y
s
:
r
ang
e f
r
om 2.
0E
-24
u
p
t
o
13
.0
E-
24 c
m
2
E
l
ec
t
r
o
n
s
:
r
ang
e f
r
om 2.
0E
-21
u
p
t
o
28
.0
E-
21 c
m
2
P
r
ot
o
n
s
:
ra
nge
from 1.
0
E
-2
1 up
t
o
3.
0
E
-1
9 c
m
2
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 6,
No
.
2,
Ju
ne 20
15
:
216
–
2
24
2
21
The
obt
ai
ne
d
r
e
sul
t
s
, aft
e
r i
n
t
r
o
d
u
ci
n
g
t
h
e e
ffect
s
of
radi
at
i
on,
o
n
t
h
e e
q
uat
i
o
n
s
m
e
nt
i
oned a
b
ove
,
are sh
o
w
n i
n
Fi
gu
res
6 t
h
ro
ug
h
8.
A l
a
r
g
e i
n
crease i
n
t
h
e f
o
r
w
a
r
d
v
o
l
t
a
ge val
u
e i
s
sho
w
n f
o
r t
h
e
sam
e
forwa
r
d curre
nt, closely ident
i
cal with
th
e resu
lts pu
b
lish
e
d b
y
J.R.Srou
r
[
2
6
]
. Th
is in
crease is a fun
c
tion
of;
radi
at
i
o
n t
y
pe,
ener
gy
a
n
d
fl
u
e
nce.
It
i
s
so
e
a
sy
t
o
no
tice t
h
at fo
r all th
e rad
i
atio
n pro
c
esses, th
e
d
e
v
i
ce lo
ses
its
m
a
in features as a
rectifying de
vice a
n
d
beha
ves
as a
li
near resistance
at a certain
ra
di
at
i
on
fl
ue
nce
.
As
a
n
exam
pl
e, for e
l
ect
ron
(wi
t
h
e
n
er
gy
o
f
1.
0
M
e
V) wi
t
h
fl
u
e
nce val
u
e o
f
5.
4x
1
0
19
/c
m
2
resu
lts in
th
e dev
i
ce
com
p
lete dam
a
ge.
Increasi
n
g
the ene
r
gy of t
h
e inci
de
nt
el
ect
ro
ns
up
t
o
1
0
0
M
e
V ca
uses
t
h
e di
ode
brea
kd
o
w
n
at less flu
e
n
ce
lev
e
ls
(9x
1
0
18
/c
m
2
). M
o
re
ove
r, di
ode
fai
l
u
re
due t
o
pr
ot
on
i
rradi
at
i
o
n occ
u
rs at
1
.
5
4
x1
0
14
/c
m
2
an
d 1.1x1
0
17
/cm
2
f
o
r pr
o
t
o
n
en
erg
i
es
o
f
1.0
MeV
an
d 100
MeV
r
e
sp
ectively.
High
er g
a
mm
a
-flu
e
n
ces are sh
own
n
ecessary to
af
fect t
h
e po
wer
silico
n
d
i
od
e p
e
rforman
ces (Fig
.
8)
. A t
h
res
h
ol
d
fl
ue
nce val
u
e
of
5.
0
x
1
0
18
/cm
2
is j
u
st requ
ired
to
increase
th
e fo
rward
v
o
ltag
e
fro
m
its
i
n
itial
val
u
e
of
0.
8
V
(at
0.
3
A o
f
f
o
rwa
r
d c
u
rre
nt
)
up t
o
1
.
0
5
V a
nd a
fl
ue
nce
v
a
l
u
e o
f
4
.
2
5
x
1
0
20
/c
m
2
is en
ou
gh
f
o
r
dio
d
e fo
rwa
r
d failure.
1E
14
1E
15
1E
16
1E
17
1E
18
1E
19
1E
20
0.
5
1.
0
1.
5
2.
0
2.
5
3.
0
3.
5
4.
0
1.
0
10
50
100
E
l
ect
r
o
n
E
n
er
g
y
,
MeV
:
F
o
r
w
ar
d
V
o
l
t
ag
e,
v
E
l
ect
r
o
n F
u
e
nce,
cm
2
(a)
1E
11
1E
12
1E
13
1E
14
1E
15
1E
16
1E
17
1E
18
0.
5
1.
0
1.
5
2.
0
2.
5
3.
0
3.
5
4.
0
P
r
ot
on E
n
er
gy
;
M
e
V
:
1.
0
10
50
10
0
Fo
r
w
ar
d Vo
l
t
ag
e,
V
P
r
o
t
on
Fl
u
e
nce,
cm
2
(b
)
Fi
gu
re
6.
Ef
fec
t
s of
el
ect
ro
n
(
a
)- a
n
d
pr
ot
o
n
(b
)
-i
rra
di
at
i
o
n
s
wi
t
h
di
f
f
ere
n
t
fl
ue
nces a
n
d e
n
er
gi
es
on
th
e fo
rward vo
ltag
e
o
f
th
e
silico
n
p
o
wer
d
i
od
e
(I
F
= 0.3
A
)
.
0.
0
0
.
5
1
.
0
1
.
5
2.
0
2
.
5
3.
0
3
.
5
4.
0
0.
0
0.
2
0.
4
0.
6
0.
8
1.
0
1.
2
1.
4
1.
6
1.
8
4.
25E
20
3.
1E
20
1.
3
6
E
20
5E
1
8
0
N
e
u
t
r
o
n
F
l
u
e
n
ce,
cm
2:
Fo
r
w
a
r
d Cu
r
r
e
nt
,
A
F
o
r
w
ar
d
V
o
l
t
ag
e,
V
0
.
00
E
+
0
0
0
2
.
00E
+0
20
4.
00E
+02
0
6.
0
0
E
+
020
0.
0
0.
5
1.
0
1.
5
2.
0
2.
5
3.
0
3.
5
Fo
r
w
a
r
d V
o
l
t
age,
V
N
e
u
t
r
ons
I
r
r
a
d
i
a
t
i
o
n Fl
u
e
nc
e
,
c
m
2
V
= 0.
838 + 4.
96E
-
2
1
*
F
l
u
e
n
c
e
C
r
.=
0
.
9
9
1
Fig
u
re
7
.
Effects o
f
n
e
u
t
ron
irrad
i
ation
o
n
the fo
rward
vo
ltag
e
d
r
op
o
f
silico
n
power d
i
o
d
e (I
F
= 0.
3 A).
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Mo
del
i
n
g
t
h
e
Depe
n
d
ence
of
Pow
e
r
Di
ode
on
Te
mper
at
ur
e a
n
d
R
adi
at
i
o
n (
S
.M.
El
-G
h
a
n
a
m
)
22
2
1
E
1
4
1E
15
1E
16
1E
17
1
E
1
8
0.
5
1.
0
1.
5
2.
0
2.
5
3.
0
3.
5
4.
0
n/
p
=1
E
-
6
n/
p
= 1
E
-
4
n/
p
=1
Fo
r
w
ar
d Vol
t
ag
e,
V
G
a
m
m
a-
I
r
rad
i
at
i
o
n
F
l
u
e
n
c
e,
c
m
2
Fi
gu
re
8.
Ef
fec
t
s of
gam
m
a i
rradi
at
i
on
wi
t
h
d
i
ffere
nt
fl
ue
nce
s
o
n
t
h
e f
o
rwa
r
d
v
o
ltag
e
dro
p
of th
e silicon
p
o
wer d
i
o
d
e
(I
F
=0
.3
A
)
.
Fi
nal
l
y
, Fi
g
u
re
9 s
h
o
w
s a c
o
m
p
ari
s
on f
o
r t
h
e cal
cul
a
t
e
d c
h
an
ges i
n
f
o
r
w
ard
v
o
l
t
a
ge
val
u
es
due
t
o
radi
at
i
o
n e
x
p
o
s
u
re
wi
t
h
di
f
f
er
ent
t
y
pe, e
n
e
r
g
y
and
fl
uence
.
1E
8
1
E1
4
1
E2
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
Fo
r
ward V
o
l
t
a
g
e,
V
F
l
ue
nce, cm
2
Pr
otons
,
1
0
M
e
V
N
e
utr
ons
, n/
p=1
0
E
-6
E
l
ect
r
o
n
s
, 10
0 M
e
V
E
l
ect
r
o
n
s
, 1.
0 M
e
V
Gam
m
a
-R
ay
s
,
C0
-6
0
Fi
gu
re 9.
C
a
l
c
ul
at
ed
c
h
a
nge
i
n
fo
rwa
r
d vol
t
a
ge val
u
es
d
u
e t
o
ra
di
at
i
o
n
ex
po
su
re
wi
t
h
di
ffe
re
nt
t
y
pe,
ener
gy
a
n
d
fl
u
e
nce.
5.
CO
NCL
USI
O
N
A co
m
p
u
t
er
pro
g
ram
h
a
s b
e
en
d
e
v
e
l
o
p
e
d
to an
alyze th
e characteristics o
f
p
o
wer silico
n
d
i
od
e
u
n
d
e
r
th
e inf
l
u
e
n
ce
of
var
i
ou
s
r
a
d
i
atio
n
typ
e
s and
te
m
p
er
atu
r
e v
a
r
i
atio
n
con
d
itio
n
s
. Fro
m
w
h
ich
,
it
w
a
s
f
ound
th
at
increasing the
device tem
p
erature interr
u
p
t
s
its (I-V) cu
rv
es in
th
e d
i
rectio
n
of
d
e
cr
easing th
e f
o
r
w
ard
vo
ltage
for th
e sam
e
fo
rward
curren
t v
a
l
u
es. As well, an
i
n
crease i
n
the
integrated
ra
diation
flu
x
c
a
uses
a
m
onotonous increase in the
forward
vo
ltage
and
differe
n
tial resistance a
nd
t
h
e silicon
diode tends to
becom
e
a
linear high ohm
i
c
resistor.
Ir
radi
at
i
o
n wi
t
h
l
o
w ene
r
gy
pr
ot
o
n
s
has st
r
o
n
g
ef
fect
w
h
ere t
h
e d
e
vi
ce
i
s
com
p
l
e
t
e
ly dam
a
ged at
1.
45
x
1
0
14
/cm
2
. O
n
t
h
e
ot
he
r
han
d
,
gam
m
a
-ray
s
em
i
t
t
e
d f
r
om
cobal
t
-
6
0
so
urc
e
ca
uses
t
h
e s
a
m
e
def
ect
o
n
devi
ces at
4.
25
x1
0
20
/cm
2
.
On the other
hand the da
m
a
ge effect cause
d
by
el
ect
rons an
d neut
ro
ns i
r
radi
at
i
o
n
l
i
e
s bet
w
ee
n t
h
at
o
b
t
a
i
n
e
d
b
y
pr
ot
o
n
s a
n
d
gam
m
a
. Al
l
d
e
fect
s are
s
h
o
w
n
t
o
be
f
unct
i
on
o
f
r
a
di
at
i
o
n t
y
pe
,
flue
nce a
n
d energy.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 6,
No
.
2,
Ju
ne 20
15
:
216
–
2
24
2
23
Appe
ndix A
Th
e f
o
llo
w
i
ng
p
r
og
r
a
m
h
a
s b
een
d
e
v
e
lop
e
d
by th
e au
th
o
r
s to car
r
y
o
u
t
t
h
e
cal
cu
l
a
ti
ons
of
power
di
ode
c
h
a
r
a
c
t
e
r
i
s
ti
c
s
unde
r di
ffe
re
nt
ope
ra
t
i
ng co
nditio
n
s
o
f
tem
p
er
atu
r
e and
r
a
d
i
atio
n
ex
po
su
r
e
. A
s
w
e
ll,
h
e
r
e
fol
l
o
ws t
h
e
def
i
ni
t
i
ons
of
t
h
e
sym
bol
s u
s
ed
i
n
t
h
e
m
e
nt
i
one
d
pr
o
g
ram
:
WO
L
:
W
/
L
NA
: N
A
U
N
:
m
o
b
ili
ty
KTOQ
: K
T
/
q
A
K
L:
di
ff
usi
o
n
l
e
n
g
t
h
dam
a
ge con
s
t
a
nt
R
A
D
:
radi
at
i
o
n
fl
ue
n
ce
L
F
:
d
i
ffu
s
i
o
n leng
th
after irrad
i
ati
o
n
D
N
: di
ff
usi
o
n
co
nst
a
nt
10
REM
PROG
"P
DRA
D
2013
"
20
OPT
I
O
N
BASE
1
30
DIM
I
(
30)
,
IR
(30), R
A
D(
3O
),
Z1(
3
O
)
,
Z
2
(
3
O)
,
Z3(
3
0)
, Z
4
(
3
0)
4
0
D
I
M
Z5(3
0)
, Z6(3
0)
,
Z7
(30
)
, LF(
30)
,
WO
L(
30),
V(
30).
50
Q =
1.
6
E -
1
9
6
0
U
P
= 500
70
A =
0.
0
1
80
N
A
= 1.
2 E 1
4
9
0
L
=
0
.
000
13
7
100
W
=
0.000
095
11
0
TI
NF
=
0.
00
0
0
0
5
12
0
N
D
=
1.
0 E
9
1
3
0
UN
=
144
0
1
4
0
K
= 1.38 E -23
15
0
D
N
=
3
7
16
0
FOR
J =
1
TO
2
1
17
0
R
E
A
D
I(
J)
18
0
NE
XT J
190 D
A
TA. 0
5
, .1, .2, .3, .
4
, .
5
, .6, .7, .
8
,
.
9
,
1
,
1
.
1
,
1
.
2,
1.
3, 1
.
4,
1.5,
1.
6,
1.7,
1.8,
1.
9,
2.0
20
0
F
O
R
J
=
1 T
O
1
3
21
0
R
E
AD
R
A
D
(
J)
22
0
NEX
T
J
2
3
0
DATA
1
E
8
,
lE9
,
1
E
l
0
, l
E
ll, lEl2
, lEl3,
l
E
l
4
,
1E15,
l
E
16,
l
E
17,1E18,
l
E
19,
l
E
20
24
0
I
N
P
U
T T
25
0
I
N
P
U
T A
K
L
26
0
IF
T =
2
5
0
T
H
E
N
27
0
E
L
SE
29
0
2
7
0
NI
= 1.7
E 8
280 G
O
TO 4
6
0
29
0
IF
T =
3
0
0
T
H
E
N
30
0
E
L
SE
32
0
30
0
N
I
=
1
.
5
E
1
0
310 G
O
TO 4
6
0
32
0
IF
T =
4
0
0
T
H
E
N
33
0
E
L
SE
35
0
33
0
N
I
=
8
E
12
340 G
O
TO 4
6
0
35
0
IF
T =
5
0
0
T
H
E
N
36
0
E
L
SE
38
0
36
0
N
I
=
4E
1
4
370 G
O
TO 4
6
0
38
0
IF
T =
6
0
0
T
H
E
N
39
0
E
L
SE
41
0
39
0
N
I
=
5
E
1
6
400 G
O
TO 4
6
0
41
0
IF
T =
7
0
0
T
H
E
N
42
0
E
L
SE
44
0
42
0
N
I
=
2
.
5
E
1
6
430 G
O
TO 4
6
0
44
0
IF
T =
8
0
0
T
H
E
N
45
0
E
L
SE
47
0
4
5
0
NI
= 2.0
E 17
46
0 LPRINT
"T =";T;"NI=";NI
47
0
K
T
O
Q
=
KT/
Q
480
Z4
= 2 Q
*
A *
D
* N
I
49
0
F
O
R
J 1 TO 2
1
50
0
Z
5
(J
) =
I(
J)/
W
51
0
Z
6
(J
) =
Z
5
(J
)/Z4
52
0
Z
7
(J
) =
L
O
G
(
Z
6
(J
))
5
3
0
V(
J)
= 2*
K
T
G(O
Q
* Z7
(J)
54
0
N
E
XT
J
550
LPR
I
NT "******************
"
56
0
F
O
R
J =
1 T
O
2
1
570
LPR
I
NT
J
,
I
(
J)
,
V(J
)
58
0
N
E
XT
J
59
0 LPRINT
"AKL = ";A
K
L
60
0
F
O
R
J =
1 T
O
1
3
61
0 Z(J)
= (
AKL
* R
A
D
(
J))*(
L
*
*2)
620
Zl
(J)
= 1 + Z(J)
630
Z2
(J) = (L**2)
/Zl(J)
64
0
Z
3
(J
)
= S
Q
R(Z
2
(J
))
65
0
LF
(J)
= Z
3
(J
)
6
6
0
WO
L
(
J
)
= W
/
(L
F
(
J
)
)
67
0
N
E
XT
J
680
LPR
I
NT"*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
"
6
9
0
FO
R J
= 1
TO
25
700 LPR
I
NT
J, R
AD(J), LF(J), WOL(J)
71
0
N
E
XT
J
720
LPR
I
NT"*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
"
73
0
F
O
R
J =
1 T
O
2
1
74
0 IR(J) =
(
I(J)*
W)/(
Q
*
U
P*
A*
NA)
75
0
N
E
XT
J
76
0
F
O
R
J =
1 T
O
2
1
770
LPR
I
NT
J
,
I
(
J)
, IR
(J)
78
0 N
E
X
T
J
7
9
0
L
P
R
I
N
T
"
*
***
***
***
***
***
***
"
80
0
E
N
D
REFERE
NC
ES
[1]
T.
M.
Na
sse
r,
et al.
, “Characterization and modeling of
power electronics device”, Int.
J
.
of power elec
troni
cs
an
d
derive s
y
stem, V
o
l. 5
,
No
. 2
,
pp
.
135-141, 2014
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Mo
del
i
n
g
t
h
e
Depe
n
d
ence
of
Pow
e
r
Di
ode
on
Te
mper
at
ur
e a
n
d
R
adi
at
i
o
n (
S
.M.
El
-G
h
a
n
a
m
)
22
4
[2]
M. Louzazni,
et al.
, “Modeling and simulation of a solar power source
for a clean
energ
y
without
pollution
”
, Int. J.
of electrical and
computer eng
i
neeri
ng, Vol. 3, No
. 4
,
pp
. 568-576
, 2013.
[3]
H.
Asai,
et al.
,
“Terrestrial n
e
utron-induced
sin
g
le-ev
e
nt burno
ut in SiC
power
diodes”,
Nuc
l
ea
r Sc
ie
nc
e,
IE
EE
Trans. on
Nu
c.
Sci., Vol. 59, No
. 4
,
pp
. 880-885
, Aug. 2012
.
[4]
Cla
y
M
a
yb
err
y
,
“
R
adiation eff
e
c
t
s
res
earch and
devic
e
evalu
a
tio
n”, Air F
o
rce Res
earch L
a
b. Ki
rtland AF
B NM
Space Veh
i
cles,
ADA559901: Apr. 2012
.
[5]
Liu Chaoming,
et al.
,
“
T
he equi
valen
ce of displac
e
m
e
nt dam
a
ge
in silicon bipo
lar junct
i
on tran
sistors”, Nuclea
r
Instruments and
Methods in Ph
y
s
ic
s Research
Section A, Vol. 677,
No.11, pp. 61-6
6
, June 2012.
[6]
Liu S
h
iYao
,
et al
.,
“
T
ot
al ion
i
zing dos
e
eff
e
cts
on tr
iple
-gat
e F
ETs
”
,
S
o
lid
- S
t
at
e and
I
n
tegra
t
ed C
i
rcui
t
Techno
log
y
(IC
SICT), IEEE 11
th
Intr. Conf., pp
.
1-5, Oct. 29
–
Nov. 1
,
2012
.
[7]
C.R. Drag,
et al.,
" Semicond
uctor device op
timization in th
e pres
ence of thermal effects
"
, J. of Applied
Mathematics an
d Mechan
ics, V
o
l.
93
, No
. 9
,
pp
. 700-705, Sep. 2
013.
[8]
M.
Ama
i
ri,
et al
.
,
“
T
em
perat
u
re depend
enc
e
of silicon
and
silic
on c
a
rbid
e
power devic
e
s:
An experim
e
nt
al
anal
ys
is
”
,
Ele
c
tr
otechn
i
ca
l Conf
e
r
ence
(M
EL
EC
ON), 16
th
IEEE
Mediterr
anean,
pp. 97-101
, 25-2
8
March
2012.
[9]
Nassir H. Sabah
,
“
E
le
ctroni
cs:
Basic,
Analog, a
nd Digita
l with
PSpice”, Te
chno
log
y
&
Engine
e
r
ing, CRC Press
,
USA, Dec 21, 2
009.
[10]
A.P. Godse, and
U.A. Baksh, “El
ectron
i
c D
e
vic
e
s
and C
i
rcu
its
”,
T
ec
hnical Publications
, Jan
1, 200
9.
[11]
I.
Pa
shay
e
v
,
“St
u
dy
of
e
l
ec
t
r
ic
al
prope
rties of Schottk
y
diodes in
differen
t
trea
tments”, Int. J. on Tech.
and Ph
y
s
ical
Problems of Eng
.
(IJTPE)
, Vol.
1
3
, No. 4, pp. 1-4, 2012.
[12]
G. Vizekeleth
y
,
“Investigation
of
ion b
eam indu
ced rad
i
ation d
a
mage
in Si PN
dio
d
es”,
Nuclear
In
str. and
Methods
in
Ph
y
s
ics Research, Sec. B,
Vol. 306, pp. 176-18
0, 2013
.
[13]
D. Makowski, “The impact of radiati
on on el
ectr
onic devic
e
s
with the s
p
ecial
con
s
ideration of neutron and gamma
radiation monito
ring”, A th
esis o
f
Ph.D., Dep
t
. o
f
Mi
croelectronics and
computer
, Tech
. Un
iv
. of
Lodz, 2006.
[14]
J.R. Cart
er and
R.G. Downing,
“
E
ff
ects of low energ
y
protons
and high energ
y
elec
trons on silicon”
, Nation
a
l
Aeronauti
c
s and
Space Adm
i
nistr
a
tion
,
Vol
.
404
,
1966.
[15]
S. Väy
r
y
n
en, “Ir
r
adiation of silicon
particle d
e
tectors with MeV-protons”,
Tech
. Report: HU-P-D173, Division of
Materials Ph
y
s
.,
Dept. of
Ph
y
s
., Fac. of
Sci., Univ
. of Helsink
i
, Fin
l
and, 2010.
[16]
M.S.I. R
a
geh,
et al.
, “Neutron
ir
radiation
effects
on th
e perfo
rmance
of some semiconductor d
e
vices”, Isotop
en-
praxis, Ak
ademie Verlag, Ber
lin, German
y
,
Vol.
27, No. 9, pp. 34
9-352, 1988
.
[17]
F. Mota,
and R.
Vila, “
P
rim
a
r
y
displa
cement damage calculatio
n induced b
y
n
e
utron and ion us
ing binar
y
colli-
sion approximation techniques
”
,
1
st
Te
ch.
M
eet
in
g on P
r
im
ar
y R
a
d. Da
mage, IAEA, Vienn
a
, Octo
ber 1
‐
4
,
2012
.
[18]
J.R. Srour,
et al
.
,
“
R
eview of d
i
splac
e
m
e
nt dam
a
ge eff
ects in
sili
con devices”, IEEE Tr
ans.
Nucl.
Sci.
, Vol.
50,
No.
3, pp
. 653-670
, J
une 2003.
[19]
F
.
A.S
.
S
o
lim
an,
“
S
om
e anal
y
s
i
s
of radiation e
ffects
on
PNP devices”,
Isotop
epraxis,
Ac
ade
m
e-Verlag, Ber
l
in,
German
y
,
Vol. 2
6
, No. 15, pp. 22
5-229, 1990
.
[20]
M.
S.
I.
Ra
ge
h,
A
.
Z
.
E
l
-Be
h
ay
, F.A.
S.
Solima
n
,
“Applic
a
tion of commercial silico
n diodes for dose rate measure-
ments”, In
ter
n
ational S
y
mp
. on
High Dose
Dosimetr
y
,
IAEA, Vienna, O
c
t. 8-12,1
984.
[21]
Dong
Jiang, et al.,
“Temper
a
tur
e
-Dep
enden
t
Ch
aracteristics of
SiC Devi
ces: Performance Evaluation
and
Loss
Calculation”,
IEEE Transactions
on Pow
e
r Electronics
, Vol.27, N
o
. 2
,
pp
. 1013-1
024, 2012
.
[22]
X. Kang, et al
.
,
“
P
aram
eter E
x
trac
tion for a
P
o
wer Diode Circuit S
i
m
u
la
tor
M
odel Includi
ng Tem
p
erature
Dependent Eff
e
cts”, 7
th
Annual I
EEE Appli
e
d Power Elec
troni
cs Conf
erenc
e
and
Exposition
,
2002. APEC 20, Vo
l.
1, pp
. 452
– 458
, 10-14 Mar
2002
.
[23]
Concepts
E
l
e
c
t
r
onics
: Onlin
e
Ele
c
troni
cs
Guide, “
E
ffe
ct
of tem
p
era
t
u
r
e on diod
e
char
act
eris
ti
cs
”,
concep
ts
ele
c
tr
on
ics
.
com/d
i
odes
/
e
ffe
ct
-temperature-diode-
c
haracteristics
. Feb. 28, 2015.
[24]
R.O. Ca
rlson, Y
.
S. Sun,
and H
.
B. Assalit
, “
L
if
e
tim
e con
t
rol
in s
ilicon
power
de
vices b
y
e
l
ec
tro
n
or gam
m
a
irr
a
d-
iation
”
, IEEE Tr
ans. on
Electr
on
Devi
ces, Vol. 24
, No. 8, pp. 1103
-1108, 2005
.
[25]
S.L. Sheng
,
“P-
N
junction diod
es”,
P1: O
TE/SPH P2: OTE, Chap. 11
, 2005
.
[26]
J.R. Srour, “
R
eview of displace
m
e
nt dam
a
ge effects in s
ilicon de
vices”
,
IEE
E
Tr
ans. on Nuclear
Scienc
es, Vol. 59,
No. 3, pp. 653-6
70, 2003
.
Evaluation Warning : The document was created with Spire.PDF for Python.