Results of computer calculations using a one dimensional model of the silicon tandem junction solar cell with both front and back current collection are presented. Using realistically achievable geometrical and material parameters, the model predicts that with base widths of 50 micrometers and 100 micrometers and base resistivities between 1 ohm/cm and 20 ohm/cm, beginning of life efficiencies of 14% to 17% and end of life efficiencies of 12% to 14%, after about seven years in synchronous orbit, can be obtained

Baraona, C. R.

Goradia, C.

Vaughn, J.

English

NASA Technical Reports Server

THEORETICAL RESULTS ON THE DOUBLE-COLLECTING 
TANDAM JUNCTION SOLAR CELL 
Chandra Goradia and John Vaughn 
The Cleveland State University 
and 
Cosmo R. Baraona 
NASA Lewis Research Center 
Cleveland, Ohio 
SUMMARY 
Results of computer ca l cu la t ions  using a one-dimensional model of t he  
S i l i con  Tandem Junction Solar C e l l  (TJC) wi th  both f r o n t  and back cur ren t  col- 
l e c t i o n  are presented. Using r e a l i s t i c a l l y  achievable geometrical and material 
parameters, our model p r e d i c t s . t h a t  with base widths of 5Opm and 1OOpm and base 
r e s i s t i v i t i e s  between 1. ohm-cm and 20 ohm-cm, beginning-of-life (BOL) e f f i -  
c ienc ies  of 14% t o  17% and end-of-life (EOL) e f f i c i e n c i e s  of 12% t o  14%, a f t e r  
about seven years  i n  synchronous o r b i t ,  can be obtained. 
INTRODUCTION 
Both t h e o r e t i c a l  ( r e f .  1,2) and experimental ( r e f .  3) r e s u l t s  show t h a t  
t he  back-only co l l ec t ion  Tandem Junction s i l i c o n  s o l a r  ce l l  (TJC) s u f f e r s  a 
s i g n i f i c a n t  degradation i n  e f f i c i ency  a f t e r  exposure t o  1MeVelectron f luences  
g r e a t e r  than 1014 electrons/cm2. The reduction of the short-wavelength 
(<0.6vm) s p e c t r a l  response t o  neg l ig ib l e  values a t  high fluences of l M e V  
e l ec t rons  indicated t h a t  t he  one primary cause of t h e  radiation-induced 
degradation w a s  t h e  reduction of t he  base d i f fus ion  length and hence of t he  
minority carrier co l l ec t ion  e f f i c i ency  by t h e  back-only c o l l e c t o r  contacts.  
It w a s  reasoned then t h a t  with cur ren t  co l l ec t ion  from both the  f r o n t  and 
back n+ regions, as shown i n  f igu re  1, the  r ad ia t ion  degradation could be signi- 
f i c a n t l y  reduced while &ill re ta in ing  t h e  advantages offered by coplanar back 
contacts.  I n  t h e  double-collecting TJC s t r u c t u r e  of f i g u r e  1, t h e  f r o n t  m e t a l  
g r i d  f inge r s  may be wrapped around one edge of t h e  cell  and connected t o  the  
bus bar of t h e  m e t a l  f i n g e r s  contacting the  back n+ s t r i p e s .  
could then be regarded as e i t h e r  a TJC with add i t iona l  c o l l e c t i o n  from the  
f r o n t  o r  as a conventional wraparound contact s o l a r  ce l l  with add i t iona l  col- 
l e c t i o n  from t h e  i n t e r d i g i t a t e d  back n+ s t r i p e s .  
cur ren t  c o l l e c t i o n  would be expected t o  be from t h e  f r o n t ,  one would expect t he  
s t r u c t u r e  t o  behave more l i k e  a conventional f ront -co l lec t ing  s o l a r  c e l l  wi th  
respec t  t o  r ad ia t ion  degradation. It would c l e a r l y  be of i n t e r e s t  t o  see i f ,  
i n  theory, t h i s  double-collecting TJC s t r u c t u r e  o f f e r s  a higher BOL e f f i c i ency  
and higher r ad ia t ion  to le rance  than e i t h e r  t he  front-only co l l ec t ing  wraparound 
The s t r u c t u r e  
However, s ince  the  primary 
51 
https://ntrs.nasa.gov/search.jsp?R=19810009016 2020-03-21T08:58:22+00:00Z
con tac t  s o l a r  ce l l  o r  t h e  back-only c o l l e c t i n g  tandem j u n c t i o n  s o l a r  cell .  
t h i s  end, w e  der ived  a one-dimensional model of t h e  double-col lect ing TJC. 
To 
THEORETICAL MODEL 
The model of t h e  double-col lect ing TJC w a s  der ived  by cons ider ing  t h i s  
device  as a composite of e i g h t  s o l a r  cel ls  i n  p a r a l l e l ,  corresponding t o  t h e  
f r o n t  s u r f a c e  being i l lumina ted  o r  dark  (under m e t a l  g r i d  f i n g e r s ) ,  t h e  sur -  
face recombination v e l o c i t y  a t  t h e  f r o n t  s u r f a c e  being low o r  high (al lowing 
f o r  do t t ed  f r o n t  m e t a l  c o n t a c t s ) ,  and t h e  back s u r f a c e  being n+ c o l l e c t o r  o r  
no t .  The Ebers-Moll type  c u r r e n t s  w e r e  c a l c u l a t e d  f o r  each of t h e  e i g h t  cells  
under appropr i a t e  boundary cond i t ions  and added t o  g ive  t h e  o v e r a l l  i l lumina ted  
current-vol tage c h a r a c t e r i s t i c  of t h e  device.  The model a l s o  accounts  f o r  
s epa ra t e  series r e s i s t a n c e  components i n  t h e  emitter, base  and c o l l e c t o r  cur- 
r e n t  pa ths  as shownin figure 2,andallows t h e  c a l c u l a t i o n  of a l l  performance 
parameters as f u n c t i o n s  of  t h e  geometr ica l  and material parameters,  and 1 M e V  
e l e c t r o n  f luence .  
Computer c a l c u l a t i o n s  w e r e  made us ing  t h i s  model f o r  va r ious  base  resis- 
t i v i t i e s ,  base widths ,  base  d i f f u s i o n  l eng ths ,  s u r f a c e  recombination v e l o c i t i e s  
and 1MeVelectron f luences .  The r e s u l t s  of t h e s e  c a l c u l a t i o n s  are presented 
i n  t h i s  paper.  A l l  c a l c u l a t e d  r e s u l t s  are f o r  a 2 cmx2cm double-col lect ing 
T J C  wi th  18 g r i d  f i n g e r s  on t h e  f r o n t  f ace ,  36 n+ and p+ i n t e r d i g i t a t e d  s t r i p e s  
i n  t h e  back and t h e  t o t a l  back n+ and p+ areas of 3.4 cm2 and 0.4 cm2 
r e spec t ive ly .  
l a t i o n s  are g iven  i n  t a b l e  1. 
The nominal va lues  of a l l  o t h e r  parameters used i n  t h e  calcu- 
I n  t h e  r a d i a t i o n  damage c a l c u l a t i o n s ,  two sets of damage c o e f f i c i e n t s  
w e r e  used. These w e r e  t h e  l o w e s t  and the  h ighes t  ranges (curves) from t h e  
p l o t s  of 1MeVelectron damage c o e f f i c i e n t  ve r sus  p-type s i l i c o n  r e s i s t i v i t y  as 
given by Srour et .  a l .  ( r e f  4.)  and they f i t  t h e  fol lowing equat ions:  
Lowest Curve: 0.6254 K = 1.034 x (PB) 
Highest  Curve: K = 3.296 x 10-lo/(PB) 0.6164 
where K i s  t h e  1MeVelectron damage c o e f f i c i e n t  and p~ i s  t h e  r e s i s t i v i t y  i n  
ohm-ems of t h e  p-type s i l i c o n  base material. The above damage c o e f f i c i e n t  
dependences on base  r e s i s t i v i t y  are based on experimental ly  determined va lues  
and should be v a l i d  f o r  base  resistivities between lohm-cm and about 50 - 
100 ohm-cm. These allowed t h e  c a l c u l a t i o n  of t h e  minimum and t h e  maximum 
amounts of r a d i a t i o n  degrada t ion  t h a t  can be expected f o r  t h e  double-col lect ing 
TJC s o l a r  ce l l  f o r  v a r i o u s  combinations of geometr ical  and material parameters.  
The ca l cu la t ed  r e s u l t s  are given i n  t h e  fol lowing sec t ion .  
52 
CALCULATED RESULTS AND DISCUSSION 
-Figure 3 shows t h e  e f f e c t  of base width and base d i f fus ion  length  on t h e  
BOL AM0 e f f i c i ency  f o r  a 1 ohm-cm base r e s i s t i v i t y  s o l a r  cell .  
expected, f o r  a given base width, longer d i f fus ion  lengths  y i e ld  g rea t e r  AM0 
e f f i c i e n c i e s  and, f o r  a f ixed  d i f fus ion  length,  t he  smaller i ts  value, t he  
sho r t e r  t h e  base width a t  which t h e  peak e f f i c i ency  occurs. Note t h a t  s ince  
BOL d i f fus ion  lengths  g r e a t e r  than 300pm are now becoming poss ib le  f o r  f u l l y  
processed 1 ohm-cm base material s o l a r  cells, BOL AM0 e f f i c i ency  approaching 
17% and higher should be poss ib le  f o r  t h e  double-collecting TJC.  
A s  would be 
Figure 4 shows t h e  e f f e c t  of varying the  sur face  recombination ve loc i ty  
a t  the  uncontacted f r o n t  and back sur faces  on the  performance parameters, 
namely, t h e  sho r t - c i r cu i t  cur ren t  Isc, t h e  open-circuit vo l tage  Voc, t h e  f i l l  
f a c t o r  FF and the  conversion e f f i c i ency  q.  The r e s u l t s  are f o r  a 1 ohm-cm 
100p1 th ick  ce l l  with a BOL d i f fus ion  length  of 3 0 0 ~ .  It is seen t h a t  t he  
conversion e f f i c i ency  i s  e s s e n t i a l l y  constant f o r  sur face  recombination 
v e l o c i t i e s  less than about 103cm/s. 
surface recombination ve loc i ty  a t  less than 103cm/s. 
a physical explanation f o r  t h e  very s l i g h t  improvement i n  t h e  f i l l  f ac to r  f o r  
sur face  recombination v e l o c i t i e s  g rea t e r  than 106cm/s. 
Thus, i t  i s  e s s e n t i a l  t o  maintain t h e  
W e  do not present ly  have 
Figures 5 and 6 show the  conversion e f f i c i ency  r) versus  1MeVelectron 
fluence f o r  50pm and 1OOpm wide c e l l s  respec t ive ly ,  f o r  base r e s i s t i v i t i e s  of 
1 , 6  and 20 ohm-cm. The s o l i d  curves i n  each f igu re  correspond t o  the  lowest 
range of damage c o e f f i c i e n t s  while t h e  dashed curves correspond t o  the  h ighes t  
range of damage coe f f i c i en t s .  Note t h a t ,  as expected, t he  t h e o r e t i c a l  
r ad ia t ion  damage behavior of the  double-collecting TJC is  indeed s i m i l a r  t o  
that of t h e  conventional f ront -co l lec t ing  s o l a r  ce l l  and much b e t t e r  than t h a t  
of t h e  back-only co l l ec t ing  TJC (ref 1 2,3). I f  w e  def ine  end-of-life (EOL) 
as an exposure t o  a fluence of 3 x l O l i  1 MeV electrons/cm2 o r  t h e  equivalent 
of roughly seven years i n  geosynchronous o r b i t ,  then it is  seen from f igu res  5 
and 6 that while t h e  b e s t  EOL e f f i c i ency  i s  obtained f o r  a 50pm th i ck  1 ohm-cm 
c e l l ,  t he  least amount of percentage degradation i n  e f f i c i ency  occurs f o r  t he  
50pm th i ck  20 ohm-cm c e l l .  This f a c t  i s  shown even more c l e a r l y  i n  f i g u r e  7 
which p l o t s  t h e  percentage degradation i n  e f f i c i ency  versus  the  base resistivity 
f o r  50pm and 1001^ lm th i ck  s o l a r  cells. It is  then seen thae even wi th  t h e  
h ighes t  damage coe f f i c i en t ,  a percentage degradation i n  e f f i c i ency  of 15% can 
be achieved i n  a 50pm th ick ,  10 ohm-cm c e l l  whose BOL e f f i c i ency  would be 
about 14.5%. On t h e  o ther  hand, i f  t h e  processing-induced increase  of damage 
coe f f i c i en t  can be almost eliminated so t h a t  t h e  lowest damage c o e f f i c i e n t  
curves i n  f igu re  7 apply, then a percentage degradation of 15% can be achieved 
with a 50pm th ick ,  1 ohm-cm cel l  with a BOL e f f i c i ency  of about 16.5%. 
Figure 8 p l o t s  both t h e  BOL and t h e  EOL e f f i c i e n c i e s  versus base resis- 
t i v i t y  f o r  50pm, 1OOpm and 200pm t h i c k  cells. 
design guide i n  t h e  choice of base width and base r e s i s t i v i t y  t o  obta in  
spec i f ied  values of BOL o r  EOL e f f i c i e n c i e s .  
This f i g u r e  can serve  as a 
53 
CONCLUDING REMARKS 
The t h e o r e t i c a l  r a d i a t i o n  to le rance  of t h e  double-collecting TJC is 
s i g n i f i c a n t l y  superior t o  that of t h e  back-only co l l ec t ing  TJC. Since we have 
present ly  not made t h e o r e t i c a l  calcii lations on t h e  r ad ia t ion  damage i n  con- 
vent iona l  f ront -co l lec t ing  s o l a r  cells wi th  i d e n t i c a l  geometrical and material 
parameters, no quan t i t a t ive  comparison can as ye t  be made t o  the  r ad ia t ion  
to le rance  of these  cells. 
Using r e a l i s t i c a l l y  achievable values of geometrical and material para- 
meters, our model of t h e  double-collecting TJC p r e d i c t s  t h a t  i n  addi t ion  i f  
t he  1MeVelectron damage c o e f f i c i e n t  i n  a f in i shed  so la r  c e l l  can be kept as 
l o w  as i n  bulk material of t h e  s a m e  r e s i s t i v i t y ,  then a 1 ohm-cm, 50pm t h i c k  
double-collecting TJC w i l l  degrade by only 15% from a BOL rl of 16.5% t o  an  
EOL q of 14.1%. 
I n  theory, t he  double-collecting TJC o f f e r s  high BOL e f f ic iency ,  high 
r a d i a t i o n  tolerance,  and t h e  convenience of coplanar back contacts.  I n  
p rac t i ce ,  the  g rea t e r  complexity of f ab r i ca t ion  of the  double-collecting TJC 
compared t o  conventional 50pm t h i c k  c e l l s  with standard” o r  wraparound contac ts  
may be a n  important consideration i n  i t s  acceptance as a space s o l a r  c e l l .  
1. 
2. 
3. 
4. 
REFERENCES 
Goradia, C.; Vaughn, J.; and Baraona, C.: Theoretical  Resul t s  On The 
Tandem Junction Solar C e l l  Based On Its Ebers-Moll Trans is tor  Model. Conf. 
Rec .  Fourteenth IEEE Photovoltaic S p e c i a l i s t s  Conference, San Diego, CAY 
Jan. 1980, pp. 172-177. 
Goradia, C.: A One-Dimensioaal Theory of High Base R e s i s t i v i t y  Tandem 
Junction Solar C e l l s  I n  Low In jec t ion .  IEEE Trans. E l e c .  Dev. Vol. ED-27, 
No. 4, Apr. 1980, pp. 777-785. 
Anspaugh, B.E.; Miyahira, T.F.; and Scott-Monck, J.A.:  Electron 
I r r a d i a t i o n  of Tandem Junction Solar Cells. 
and Radiation Damage Solar  C e l l  Meeting, Cleveland, OH, June 1979, NASA 
Proc. of Third High Efficiency 
CR-2097, pp. 131-136. 
Srour, J .R . ;  Othmer, S . ;  Chiu, K.Y.; and Cur t i s ,  O.L. Jr.: Damage 
Coeff ic ien ts  i n  Low R e s i s t i v i t y  S i l icon .  NASA CR-134768, NRTC 75-23R, 
1975, p. 48. 
54 
TABLE I 
Parameter Values Used in Calculations 
Temperature 
Spectrum 
Front Refl. Coeff. %(A) 
Illuminated Area 
+ Number of n 
n+ Back Collector Area 
p+ Back Stripe Area 
p Gap Area in Back 
Front Grid Fioger Number & Area 
Surface Recombination Velocity at 
and p+ Back Stripes 
uncontacted front and back surfaces= 
Surface Recombination Velocity at 
Metal Contacts 
n+ Emitter and Collector Dopings 
n+ Emitter and Collector Depths 
BOL Diffusion Length in n' Emitter 
and Collector - 
Base Width - 
- 
= 
= 
BOL Base Diffusion Length = 
Base Resistivity - 
- Base Series Resistance 
Emitter and Collector Series 
Resistances - 
n+ Emitter and Collector Damage 
Coefficients - 
- Base Damage Coefficient 
300K 
AM0 
Measured values for AR-coated non- 
reflective surface 
4 cm 
36 each 
2 
3 . 4  cm 2 (85% coverage) 
0.2 cm 2 (5% coverage) 
0.4 cm2 (10% coverage) 
2 18, 0.2 cm (5% coverage) 
3 
9 
10 cm/s 
10 cm/s 
2.5 x 10 
0.3pm 
19 cm-3 
2vm 
100pm, variable 
300pm, variable 
1 ohm-cm, variable 
0.022 ohm 
Functions of Base Width and Base 
Res is t ivi t y 
2.0 x per electron 
Function of Base Resistivity 
55 
Figure 1. 
Collecting Tandem Junction Solar Cell. 
Schematic Diagram of a Double 
+ vo - 
Figure 2. 
Collecting TJC With Emitter, Base and Collector 
Components of Series Resistance. 
Schematic Representation of Double 
56 
Figure 3. Effect  of Base Width 
and Base Diffusion Length on BOL 
Efficiency. 
121 ' I t I L I 
0 50 100 150 200 
BASE WIDTH WB,)tm 
E 
m 
5 " I -  160 
SURFRCE RECOMBINATION V E L O C ~ T Y  
Figure 4 .  
on Performance Parameters. 
Effect  of Surface Recombination Velocity 
57 
I7 L 
I6 
I5 
I4 
13 
12 
I I  
b3 
3% IO rdb 3x10’4’ 
Figure 5. 
Fluence f o r  50pm Thick C e l l .  
Ef f ic iency  versus  1 M e V  Electron 
15 
10 
17 
16 
15 
14 
13 
I2 
11 
10 
CI 
8 
i 
M e V  ELECTRON FCUENCE K/cm.. 
Figure 6. 
Fluence f o r  100pm Thick C e l l .  
Ef f ic iency  versus  1 MeV Electron 
58 
Figure  7. 
versus  Base R e s i s t i v i t y .  
Percent  Degradation i n  Ef f i c i ency  
I I . I I l l . .  1 
6fir iE R E S I S T I V I T Y  e, ohm-cm 
Figure  8. 
ve r sus  Base R e s i s t i v i t y .  
BOL and EOL E f f i c i e n c i e s  
59 


Theoretical results on the double-collecting tandem junction solar cell

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