IEEE
T ansac ions
on
Nuclea Science,
Vol.
35,
No.
4,
Augus
1988 1067
RADIATION DAMAGE EVALUATION ON ALGAAS/GAAS SOLAR CELLS
E. G. Mo eno, R. Alcubilla, L. P a and
L.
Cas a ie
Depa amen o de Elec dnica. U.P.C.
Jo ge Gi ona Salgado s/n
-
Ba celona
08034
-
SPAIN
Abs ac
A piecewise model o e alua e adea ion
damage on AlGaAs based sola cells has been
de eloped, which gi es comple e elcc Lca1
pa ame e s o he cells in he ope a ing
empe a u e ange. Di e en s uc u es,
including g aded band gap and double
he e o ace can be analyzed. The cell
s uc u e is sliced in o laye s o cons an
pa ame e s, allowing he model o ake in o
accoun nonuni o m damage p oduced by low
ene gy p o ons wi hou excess compu e ime.
P o on damage coe icien s as well as p o on
damage a ios can be calcula ed o ene gies
be ween
30
and
lo4
keV wi h only wo
adjus able pa ame e s. In addi ion,
coi adia ion expe imen s wi h di e en
ene gy p o ons can be simula ed, by imp o ing
he con en ional me hod o deg ada ion
compu e ing.
In oduc ion
Gallium A senide sola cells a e
conside ed as especially sui able o space
pu poses because o hei high e iciency and
adia ion esis ance. The use o GaAs sola
cells in space powe sys ems scheduled o
7
yea s o ope a ing li e ime
111
equi es
p edic ion capabili ies o he expec ed sola
cell deg ada ion. This wo k mus include bo h
labo a o y es measu emen s and simula ion
wo k o be e unde s anding o he
unde lying phenomena as well as o de elop
ools o acili a e cell design.
The common me hod o p edic sola cell
deg ada ion in space is o ela e he damage
p oduced by any kind o pa icles, o damage
p oduced by pa icles o e e ence, usually
1
MeV elec ons o
10
MeV p o ons, and o
calcula e he o al equi alen luence
121.
Al hough he equi alence damage me hod has
been ex ensi ely used, cases o ailu e when
GaAs sola cells a e conce ned ha e been
de ec ed, mainly due o he di e en
deg ada ion beha iou o hese cells in
compa ison wi h Silicon cells, in pa icula
i coi adia ion wi h low and high ene gy
p o ons is conside ed
111.
In he wo k epo ed he e he ocus is
placed on he elec ical beha iou o he
sola cell in he p esence o ha m ul
adia ion en i onmen assumed o concen a e
i s e ec s in he mino i y ca ie li e ime
deg ada ion. I has been ound ha many
o
he expe imen al da a o deg ada ion o
elec ical cha ac e is ics may be explained
by assuming a mino i y ca ie li e ime
deepness- dependen om he su ace on which
pa icles a e impinging. The shape
o
he
li e ime inside he sample, will be ob iously
dependen on he ype and ene gy o he
pa icles, as well as on he kind o
i adia ion, i.e. i he pa icles ha e
no mal o iso opic incidence.
Manusc ip ecei ed on Feb ua y
5,
1988
A e y i s in e es o he wo k is o
p o ide a ool o calcula e he expec ed
deg ada ion o sola cells in any kind o
i adia ion en i onmen , by simply knowing
he expe imen al esul s a e no mal
i adia ion wi h a monoene ge ic pa icle
luence a
1
MeV elec ons and
10
MeV
p o ons. Damage p oduced by hese pa icles
is easily measu ed in ea h labo a o ies. The
model should be capable o explain he
ailu e o con en ional p edic ion models
when co-i adia ion wi h di e en ene gy
p o ons is conce ned.
Sola cell model
Comple e simula ion o sola cells
equi es sol ing a se o non linea
di e en ial equa ions including Poisson,
anspo and con inui y equa ions o bo h
ca ie ypes. The solu ion needs complica ed
and ime consuming nume ical me hods. Simple
models assume cons an alue pa ame e in
each egion o he cell hen inding
analy ical solu ions. Howe e hey a e no
able o explain adequa ely he cell
deg ada ion by low ene gy p o ons, because
he non uni o mi y o he damage.
These p e ious analy ical models o GaAs
cell deg ada ion, ei he calcula e he mean
alue o ca ie li e ime in each egion cell
as a unc ion o pa icle luence and
ene gy, o i hey akes in o accoun he non
uni o mi y o he damage, hey a e only able
o calcula e he sho ci cui cu en
educ ion
131.
Al e na i ely, cell deg ada ion a e
ominidi ec ional adia ion can be compu ed
om he expe imen al deg ada ion cu e a e
no mal adia ion, by calcula ing he o al
damage in he cell
141.
Again, he non
uni o mi y o he damage is neglec ed.
The model he e p esen ed is basPO on a
piecewise qpp oach ah di ides he cell
s uc u e in an adap a i e numbe o slices,
Inside a pa icula slice he semiconduc o
pa ame e s a e cons an , consequen ly, i is
easy o ind an analy ical solu ion o he
semiconduc o anspo equa ions wi h
sui able bounda y condi ions o he
in e aces wi h he adjacen slices.
Mo e speci ically, he bounda y
condi ions applied o cu en con inui y a e
ela ed o in e ace ecombina ion
eloci ies,
S,
and he bounda y condi ions
applied o mino i y ca ie concen a ion a e
€o
a
P
ype egion gi en by
whe e
n
is
he
eLec on
concen a ion in
p- ype slice and E, is he conduc ion band
ene gy le el, Nimp he dopan concen a ion
and m* he elec on e ec i e mass.
The selec ed p ocedu e o pe o m he
0018-9499/88/08~107$01.00
0
1988
IEEE
1068
cell s uc u e di ision is shown in Figu e
1.
The emi e , base and deple ion egions a e
sliced in o laye s when he dopan
Aluminium concen a ion a e cons an . This
me hod is able o accomoda e s uc u es wi h
AlGaAs laye s a he op o he bo on o he
cell as well as o conside a iable gap
s uc u es.
DEPLETION
EMITTER REGION BASE
II
Fig.
1
Di ision o sola cell s uc u e in o
slices.
As i will be shown la e , he adia ion
is expec ed o c ea e e y sha p li e ime
a ia ions in he semiconduc o bulk. Fo
his eason, a selec ion o he slices and
spacial dis ibu ion mus be pe o med in
o de o place a g ea e numbe o slices in
he semiconduc o egion whe e sha pe
a ia ions in he li e ime a e p esen .
Finally, he compu e p og am ha has
been de elopped calcula es he o al I(V)
cha ac e is ics by adding he con ibu ions
o he emi e , base and space cha ge egions
unde AM0 illumina ion condi ions. Spec al
esponse is, o cou se, an ou pu o he
p og am. All he pa ame e s o he model a e
analy ically ela ed o he empe a u e,
composi ion o he semiconduc o (Aluminium
concen a ion) and dopan concen a ion
(Nimp). Table I shows he de ini ion o
pa ame e s and he dependeces conside ed in
he model. Analy ical exp essions ha e been
gi en elsewhe e
15
I.
Table
I.
Elec ical Pa ame e
Band ene gy
E ec i e mass ml*,, mi (XAL)
In insic conc. ni (Band ene gy, m* ,Temp)
Ca ie mobili y
l+
(Nimp m*
I
Temp)
Ca ie li e ime Tn Tp (Nimp, m*
,
Temp)
Dielec ic cons an
E
(XAL, Temp)
Abso ion coe icien
a
(h.
Band ene qy)
EG, EL, Ex (XAL, Temp)
__
Re lec i i y R
(
h,
ARC)
Radia ion e ec s
I is well known ha he elec on and
p o on adia ion c ea es de ec s in he
semiconduc o bulk ha ac s as ecombina ion
cen e s o ca ie s. The e a e se e al ypes
o ecombina ion cen e s, each one
cha ac e ized by he cap u e c oss sec ion
and he si ua ion in he gap. These
ecombina ion cen e s modi y he ca ie
li e ime
whe e
TO
Qi
as ollows
11
-
=
7
+
Nl
i
h
01
is he mino i y ca ie li e ime
be o e i adia ion (BOL)
is he cap u e c oss sec ion o he
i ype cen e
Ni is he desi y o he i ype cen e
V h is he he mal eloci y
Fo sake o simplici y we will ake only
one ype o cen e , placed a he cen e o
he gap, wi h he same cap u e c oss sec ion
o bo h ypes o ca ie s.
Because he ange o he
1
MeV elec ons
is much g ea e han he hickness o he
GaAs cell, i is commonly assumed ha he
ecombina ion cen e densi y is uni o m
h ough he cell s uc u e. In ha case he
mino i y ca ie li e ime
!
a e an elec on
luence o
@e
1
MeV e-/cm can be ela ed o
he Begining O Li e li e ime as ollows
(3)
-=
i+KO~ h
ee
whe e Ke is he li e ime deg ada ion cons an ,
aking in o accoun he cap u e c oss
sec ion o he cen e and he p opo ionali y
be ween he de ec s and he densi y o
ecombina ion cen e s.
The i adia ion wi h p o ons leads o a
mo e complex si ua ion, on he one hand
because he ange alue is compa able o he
cell dep h and, on he o he hand because o
he nonuni o m dis ibu ion o he de ec s
along he ange. Mo e p ecisely, he numbe
o p ima y collisions o a p o on, wi h
ins an aneous ene gy E, is he ecip ocal o
he mean ee pa h, 1(E),
161
(4)
whe e O(E) is he nuclea s opping c oss
sec ion, and N is he a omic densi y. Each
p ima y collision p oduces a ce ain numbe
o a omic displacemen s, (E), ela ed o he
ins an aneous ene gy h ough he Kinchin and
Pease heo y. The o al numbe o a omic
displacemen s p oduced by he p o on pe
uni y pa h leg h is
(5)
To ela e he ins an aneous ene gy, E, o
a p o on wi h inciden ene gy
Eo
o he
pene a ion, x, we ha e i ed he ange
da a, R(Eo), o Ande sen and Ziegle
171
ob aining
175'
(R-x)
E=
(7)
1
+
.67*(R-~)'.~'
Fo
iso opic i adia ion he unc ion
~(R-X)
has
Po
be 'a e ac ed
€o
all he
inciden angles as ollows
1
Hence he li e ime alue a e a p o on
luence o
oP
p'/cm2 is
,
whe e KP ac s o he p o ons as Ke o he
elec ons. Bo h cons an s, K and
IC.?,
a e
used o adjus he model o ge expe imen al
esul s.
To ake in o accoun he co e glass
e ec s on he dis ibu ion unc ion C(Eo,x)
he coo dina e o igin is displaced o a
deepness o xo om he su ace.
xo
is
calcula ed as he GaAs hickness needed in
o de o ha e he same s opping powe as he
co e glass.
Once he unc ion T(To,x) has been
calcula ed, a disc e iza ion p ocedu e
ollows, conce ning he whole cell s uc u e.
The disc e iza ion is au oma ically pe o med
acco ding o he alue o he inciden ene gy
and he i adia ion ype.
Figu e
2
shows he esul s o such a
disc e isa ion o i adia ions wi h a
luence o
10l1
cm-2 di ec ional and
iso opic, a wo di e en ene gies. As
expec ed, he shape o he disc e iza ion is
,in)
hg in he iso opic case.
U
~51
0
6.5 1.0 1.5
2.0
Dep h
(l~
m)
Fig.
2
Hole li e ime educ ion a e
lo1'
10
MeV p o on/cm2 i adia ion.
-
ii~l mdi
-_
iso opic.
Resul s
The model has been used o simula e he
elec ical beha iou o an he e o ace AlGaAs
sola cell epo ed in he li e a u e
111,181,
in o de o check i s capabili ies.
These cells ha e been quali ied by he NASDA
o space use,
so
i s beha iou unde
i adia ion a e well known.
The main physical pa ame e s and he
elec ical pe o mance
BOL
a
28OC
a e lis ed
in Table
11.
Se ies and shun esis ences,
and in insic ca ie li e ime a e chosen o
ma ch expe imen al esul s
181
a his
empe a u e. Figu e
3
shows he sho ci cui
cu en , open ci cui ol age, and maximum
powe plo ed as a unc ion o he
empe a u e. Expe imen al poin s epo ed in
e e ence
8
a e also supe posed.
To calcula e he beha iou unde
i adia ion we s a se ing he alues o Ke
and
KP.
This is done in o de o i he
expe imen al esul s a e no mal i adia ion
by
1
MeV elec ons and
10
MeV p o ons
espec i ely. The o me is shown in Figu e 4
wi h expe imen al poin s aken om (8).
Figu e
5
shows he spec al esponse
BOL,
a e
1
MeV elec on no mal i adia ion
a a luence o
5 1015
cm-2, and a e
combina ed no mal i adia ion wi h
1
MeV
elec on and
10
MeV p o on a luences
o
1069
,
1Ol5
cm-2 and
5 10l2
cm-2, espec i ely
,"I
60
60
iM
LM
Tempe a u e
(OC)
FI,~
{ Tempe a u e cha ac e is ics
o
P,,
Iy
l,,,
b'OL.
!oo
-
-
&i
0
"Eo
U
Id
W
n
.:
60
c
?I
c
E
W
g40
I
I
10
l4
10
l5
10
Ib
1
MeV elec on luence (cm-')
n
m3i
":
i- -.
-<
'1
F,
~
I MeV e ec on ELuence.
1
'I
111
/
1
0.3
0.4
0.5
0.6
0.7
0.8 0.9
Wa eleng h
(
.I
m)
.
q
Spec al esponse o
sola
cell (a)
be o e i adia ion (b) a e 5-1015
cm-2 1MeV elec on i adia ion (c) a e
5-1015
cm-2 1MeV elec on and
5-1012
cm-2 loMeV p o on i adia ion.
These p e ious adjus emen s allow us o
calcula e he deg ada ion o he sola cell
1070
GaAs laye
pe o mances a e p o on i adia ion o
a bi a y ene gy and luence, iso opic o
di ec ional. Figu e
6
shows he e iciency
deg ada ion as a unc ion o p o on ene gy
o se e al luences. Two ea ly conclusions
can be gi en, i s he e is an ene gy ha
p oduces maximum deg ada ion, a ound
200
keV,
and second, o high ene gy p o ons iso opic
i adia ion p oduces wo se damage.
Thickness
(!.nu)
0.5
Impu i y concen a ion (cm-3)
1018
In e ace ec eloci y (cm/s)
104
Emi e
p- ype
Base
n- ype
Gene al
Elec ical
cha ac
supe posi ion o he damage p oduced by he
di e en pa icle ypes o calcula e he
o al equi alen luence. E o s p oduced by
his assump ion can be impo an , mainly when
low ene gy p o ons is conce ned.
Co-i adia ion expe imen s wi h se e al
ene gy p o ons ha e been pe o med showing
his misma ch
111.
Table
11.
Cell pa ame e s
Impu i y concen a ion (cm-3)
1018
Su ace ec eloci y (cm/s)
106
Thickness
(p)
6.0
I
Impu i y concen a ion (~m-~)
4.1016
Ac i e laye
______~.__
Thickness
(pn)
200
Subs a e Impu i y concen a ion (cm-3)
1018
-1
Back su ace ec eloci y (cm/s)
1010
Size (cmL) 2x2
Con ac su ace co e ed
(%)
3
ARC Si3Nq
Se ies esis ence
(
52
)
0.4
Shun esis ence
(
52
)
250
__
-~
__
.
__
___
Isc (mA) 125.
oc (V) 0.97
Fill Fac o 0.77
Pmax (mw)
94.8
____._____I
-
-
-
..
.
-
I
Mo eo e , we can calcula e he
deg ada ion o he cell in any kind o
adia ion en i onmen by calcula ing he
de ec s accumula ed a each dep . This
allows
us
o p edic he cell li e ime in a
gi en o bi .
Damage coe icien s
Damage coe icien s a e de ined as he
luence o
10
MeV p o ons equi ed o educe
one elec ical cell pa ame e (usually Isc,
Voc! o Pma,) a empe a u e
T
by pe cen ,
di ided by he luence o p o ons o ene gy E
equi ed o ha e he same educ ion in he
chosen pa ame e , a he same empe a u e.
P o on damage a ios a e de ined in
a
simila way o he damage coe icien s, bu
aking
1
MeV elec ons
as
e e ence
pa icles. Bo h pa ame e s a e ex ensi ely
used o p edic he use ul li e o
pho o ol aic a ays in space o a gi en
o bi , con e ing he o al i adia ion in an
equi alen luence o e e ence pa icles.
Howe e , his me hod has some d awbacks.
Fi s , he damage coe icien s a e no
uniquely de ined o a gi en ene gy. They
depend on he i adia ion kind (no mal o
iso opic) and on pe cen deg ada ion
conside ed.
So
he e a e se e al alue ables
and hei handling is di icul .
Second, damage coe icien s depend
s ongly on he physical s uc u e o he
cell conside ed. Ex apola ion o ano he
cell ype, e en simila , is no possible. Fo
his eason hey a e no sui able o
pu poses o op imiza ion s uc u es.
Mo eo e he me hod applies
The me hod p oposed in his wo k, based
on he use o a powe ul simula ion model
i ed bo h expe imen al esul s BOL, and
a e
1
MeV elec on and
10
MeV p o on
i adia ion, can o e come he abo e men ioned
d awbacks.
As an example, deg ada ion p oduced by
combina ed i adia ion wi h se e al ene gy
p o ons has been calcula ed. Fi s ly he
p o on damage coe icien s ha e been ob ained
om he cu es o Figu e
6,
o
=
20
%
o
Pmax, and hey a e shown in Figu e
7.
These
esul s closely ag ee wi h hose epo ed in
0-
0.1
1
10
P o on ene gy (MeV)
Fig.
b
Pmax deg ada ion e sus o on ene gy
o
(a)
1O1O cm-2
(b)
lop1
cm-2
and
(c) 1012 cm-2 luences.
-
-
no mal
-
iso opic.
100
ul
+J
c
.-I
U
.-I
u
w
m
0
U
10
01
0
m
E
m
n
0.1
F
I
<3
.
7
0
-10
0
-10
0
-10
Fig.
8
/'
i
Iso opic
0.1
1
10
P o on ene gy (MeV)
20% Pmax damage coe icien s.
<
100
keV
I
0.1
1
.o
10
Ene gy (MeV)
Di e ences be ween emaining Pmax
calcula ed h ough he PDM me hod and
by he model. Coi adia ion o se e al
ene gy p o ons and (a)
100
KeV, (b)
500
KeV and (c)
10
MeV p o ons. All he
luences causes 20%
Pmax
deg ada ion.
e e ence
4.
A e ha , deg ada ion p oduced
by co-i adia ion wi h 0.1,
0.5
and
10
MeV
p o ons and p o ons o di e en ene gies a
luences which causes 20
%
Pmax deg ada ion
has been calcula ed (a) by he con en ional
equi alen damage me hod, and (b) by di ec
calcula ion o ca ie li e ime deg ada ion.
The di e ence be ween bo h me hods is shown
in Figu e
8.
As we can see, hese di e ences
a e mo e impo an o co-i adia ion wi h
low ene gy and high ene gy p o ons.
Conclusion
We ha e de eloped a ma hema ical model
o GaAs sola cells. This model is able o
p edic elec ical pe o mance deg ada ion
a e p o on o elec on i adia ion o low
and medium ene gies.
This in o ma ic ool allows us o
o e come he main disad an ages o he
con en ional me hod
o
p edic ion, i.e. he
damage coe ien me hod. Mo eo e , only wo
pa ame e s a e necesa y o adjus he model
o expe imen al alues, Ke and K
,
bo h
easily measu eable in ea h lago a o ies,
1071
wi h
1
MeV elec on and
10
MeV p o ons
i adia ion, o ins ance.
The qbili y o he model o i
expe imen al esul s o monoene ge ic
pa icle luence on he e o ace AlGaAs sola
cells has been p o ed. Resul s o
co-i adia ion expe iences wi h se e al
ene gy pa icles has been also p esen ed. The
p og am can be now used o pe o m s udies o
i adia ion ha dness wi h ano he AlGaAs cell
ypes like g aded band gap o double
he e o ace cells.
Re e ences
N.
Taka a, K. To iyama e al., "Ene gy
dependence o p o on i adia ion damage
in GaAs sola cells and e ec s O
combina ed
adia ion
on hem". 5 h Eu op.
Symp. Pho Gen. in Space.
1986.
pp.
H.Y.
Tada, J.R. Ca e J ., B.E. Anspaugh
and R.G. Downing, "Sola Cell Radia ion
Handbook" 3 d Edi ion,
JPL
Publica ion
82-69, No embe 1982.
425-433.
131
J.Y.
Young, "A model o p o on damage in
Silicon and GaAs sola cells". 17 h IEEE
Pho . Spec. Con .
1984.
pp. 1084-1087.
141
B.E. Anspaugh and R.G. Downnig
,
"Radia ion e ec s in Gallium A senide
sola Cells using iso opic and no mally
inciden adia ion".
17 h
IEEE Pho .
Spec. Con .
1984.
pp. 23-30.
151
L.
P a ,
E.G.
o e no
and
L.
Cas a ie ,
"He e o ace Gallium A senide sola cells
induced deg ada ion. Analy ical model".
IEEE T ans. on NUC. Sci., Vol. NS-33.
161
Yu. V. Bulgako and M.A. Kumako ,"Spa ial
dis ibu ion o adia ion de ec s in
ma e ials wi h beams o monoene ge ic
pa icles". So ie Physics Semicond.
Vol. 2 No
11.
1969.
pp. 1334-137.
171 H.H. Ande sen and
J.F.
Ziegle , "zid ogen
__-
elemen s". Vol. 3. pe gamon P ess Inc.
1977.
181
S.
Ma suda,
M.
O oda e al.,
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