An experimental method is presented that can be used to interpret the relative roles of bandgap narrowing and recombination processes in the diffused layer. This method involves measuring the device time constant by open-circuit voltage decay and the base region diffusion length by X-ray excitation. A unique illuminated diode method is used to obtain the diode saturation current. These data are interpreted using a simple model to determine individually the minority carrier lifetime and the excess charge. These parameters are then used to infer the relative importance of bandgap narrowing and recombination processes in the diffused layer

Brandhorst, H. W., Jr.

Godlewski, M. P.

Lindholm, F. A.

Sah, C. T.

English

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N A S A  T E C H N I C A L  
M E M O R A N D U M  
NASA TM X- 73455 
In 
1176-26694 (I h S A- T E- X - 7 3 4 5 5 )  
IIJVESTIGBTICU CF THE IXCESS C H A R G E  A X f  TIHE 
C 3 L S I A A T  CF R I R C Z I T P  C898IERS IN TBE THIS 
E X E E R I E E bi 1 A L 2 
cc 
k DfFFCJSEC LAYER CP 0.1 ohm-cs S I L I C C C  SCLAF Ucclas s CELLS (EASI) 7 p HC 13.50 CSCL 10A G3/44 44461 c 
EXPERIMENTAL INVESTiGAnON OF THE EXCESS CHARGE AND 
TIME CONSTANT OF MINORITY CARRIERS IN THE THIN DIFFUSED 
LAYER GF 0.1 OHM-CM SILICON SOLAR CELLS 
by M. P. Godlewski and Henry W. Brandhorst, Jr. 
Lewis Research Center 
Cleveland, Ohio 44135 
F. A. Lindholm 
University of Florida 
Gainesville, Florida 
andC. T. Sah 
University of Illinois 
Urbana, Illinois 
TECHNICAL PAPER to be presented at 
Materials Research Conference sponsored by 
the American Institute of Mining, Metallurgical, and Petroleum Engineers 
Salt Lake City, Utah, June 23-25, 1976 
https://ntrs.nasa.gov/search.jsp?R=19760019606 2020-03-22T14:02:03+00:00Z
Gx33-1, INVESTIGATION OF TIE EXmS CHARCZE AND 
TIM3 COLJSW OF MINORITY CARRIEFE IN "€E THIN DIFFUSEI! 
MYEB OF 0.1 OHSCM SILICON SOLAR CELLS 
by M. P. Godlewski and Henry W. Brandhorst , Jr. 
XASA-Lewis Research Center 
Cleveland, Ohio 
and F. A. Lindholm 
University of Florida 
Gainesville, Florida 
and C. T. Sah 
University of I l l i no i s  
U r b a n a ,  I l l i no i s  
INTRODUCTION 
The measured open-circuit voltage of 0.1 :-an n on p s i l i con  so la r  
ce l l s  is about 100 mv lower tban predicted by simple diffusion theory 
(1). It has beer, shown (2)  t'mt the A i r  Miss Zero (AMI) conversion effi- 
ciency of s i l i con  solar ce l l s  can be increased t o  about 18% prwiding the  
processes limiting open-circuit voltage are overcome. 
Dark and illuminated e l ec t r i ca l  measurements strongly suggest tha t  
the  low open-c i rx i t  voltage in  0.1 fi-cm solar ce l l s  is related t o  an 
excessively high diode saturation current resulting from processes 
occuring i n  the diffused layer. Theoretical analyses have shown that 
e i ther  high recombination ra tes  ( 3 )  or bandgap narrowing effects (1) 
can explain tk high sat.uration current. There is ,  however, inscffi- 
cient experimental information about the  diffused layer properties t o  
assess t h e  re la t ive  jmportance of these physical processes. 
The purpose of t h i s  paper i s  t o  present an experimental method that 
can be used t o  interpret  the r e l i t i v e  roles  of bandgap narrowing and 
recombination processes i n  the  diffused layer. This method involves 
measuring t h e  device time constant by open-circuit voltage decay an& 
the  base region diffusion length by X-ray excitation. A unique i l l u m i -  
nated diode method is used t o  obtain the diode saturation current. These 
data a re  interpreted using a simple model t o  determine individually the 
minority carr ier  l ifetime and the excess charge. These parameters are then 
used t o  infer the relat ive importance of bandgap narrowing and recaubina- 
t i on  processes i n  the diffused layer. 
THEORY 
The theoret ical  work of Lindholm and Sah (3 4) describes a straight- 
forward charge-control treatment t o  identSy  the physical mecknisms can- 
t r o l l i n g  carrier transport -h the diffbsed layer (emitter). 
c e l l  current ( I )  can le expressed as 
The solar 
1 = 1  + I L  D 
vhere ID and IL are t h e  dark diode and l igh t  generated current 
ly. 
charge (I 
respective- 
The diode current can be written as the sum of emitter (%) space 
), and base currents (IB): s c  
I n  the range of voltages for which the space charge region current is neg- 
l igible,  the diode current (5) is the sum of the  emitter and base region 
cmponents : 
ID = 5 + IB (3)  
Warn Shockley's diode theory ( 5 ) ,  the diode current can also be expressed: 
where the diode saturation current (Io) is the sup of the emitter and base 
regior? components ( %o, I ~ ) .  
By charge-control theory (3, G), 5 can be writ ten i n  tenus of the  
stored charge (Q) and time constant 1: 
Q E 9 3  I = -  + -  
B D 1 
( 5 )  
Since for t h e  voltage range under considerat ion , Q = 
where % is a reference charge, equation 3 can be writ ten as (exp kT *- l), 
In  t h i s  model the diode saturation current is expressed as: 
1 = - + -  $0 % 
B T E 0 . T  
2 
qn;% 
NB 
where  &80 = - for  a base of constant doping. 
minority carr ier  diffusion length and the  impurity concentration in t he  
base region. 
Here 5 and NB are the 
F'rom (4)  Io can be written as: 
- & E o + %  
T 
0 
Io - 
w h e r e  T~ is the dominant normal mode or t he  reciprocal of the dominant nat- 
ural frequency of the device as determined by measuring the open-circuit 
voltage decay. 
Equations 7 ana 8 involve s i x  parameters sa, T , %, TB, Io and To. 
They form a basis for  the separate detennination ofEQEo, TE, whereas pre- 
viously only the C+dTE r a t io  has been evaluated. The reference charge 
(%) can be associated w:th bandgap narrowing, while the  recombination 
time ( T ~ )  re f lec ts  recombht ion  erffects in  the  diffused layer. 
perimental methods employed t o  obtain these parameters are described in 
the  next section. 
The ex- 
EXPERIMENTAL METHODS 
A. Device Fabrication 
S i x  n on p s i l i con  so lar  ce l l s  s n m  i n  figure 1 were constrvcted using 
vacuum f loa t  zone, < I l l  > a standard processing technique. 
orientation, 0.1 ohm-cm, p-type s i l icon  wafers were f i rs t  chemically polished 
i n  an HF -HNO - g lac i a l  acet ic  acid solution. 
phorus diffusJd in  a €021 
880" C t o  form t h e  p-n j d c t i o n .  
0.2 pm. 
aluminum contacts were thermally evaporated t o  form the large are& p-side 
contact and t h e  gridded contact t o  the th in  diffused lay-er. Contact adher- 
ence was insured by s inter ing the  ce l l s  i n  argon at 550" C for several  m i n -  
utes. 
The 1 x 2 an, 
The wafers were then phos- 
atmosphere for  45 minutes a t  a temperature of 
"he calculated junction depth is about 
Arter removal of the phospnorus oxide glass with HF, silver- 
B. E l e c t r i c a l  AMeasurements 
Current -Voltage 
Dark forward and illuminated current-voltage character is t ics  were meas- 
ured for  each c e l l  using a calculator controlled data acquisit ion system. 
A xenoc-light solar simulator was used for  the AM3 (outer space condition) 
illuminated measurements. The open-circuit voltages (Voc) and short-cir- 
cuit  currents (Isc), of these 0.1 R - a n  s i l icon ce l l s  are s h m  i n  Table I. 
Open Circuit Voltaae Decay 
The time constants character is t ic  of small area sections of the  t e s t  
ce l l s  were measured using the open-circuit voltage decay method (6, 7) 
and the  measurement c i rcu i t ry  shown in  Figure 2. 
3 
The devices were forward 
biased w i t h  a one millisecond duration square wave voltage pulse. The 
voltage decay, shown in figure 3, was displayed on a Tektronix 555 
oscilloscope with a Type L plug-in unit and photographed. 
t i m e  constants ( T ~ )  sham in Table I were measured i n  the 0.55 to 0.63 
voltage decay range. The slope factor (A)  determined fram the illumi- 
nated I-V characterist ics is found t o  be nearly unity in t h i s  range. 
The decay 
Diode Saturation Current 
The illuminated method used t o  obtain the current-voltage charac- 
teristics involves measurement of t h e  Voc and I developed by the  c e l l  
under various levels of l igh t  intensity. 
pared t o  tha t  u t i l i z ing  t h e  1-1' character is t ic  of a dark diode, include 
minimization of ser ies  resistance effects  and duplication of effects of 
illumination on recombhation center s ta tes .  
identification of the  diffusion dominated (A X 1 )  portion of the  forward 
I -V  character is t ic ,  and hence an accurate extrapolation of t h i s  cume t o  
determine the d i f f u s  ion-controlled diode saturation current. The satura- 
t i on  currents (Io) for  each c e l l  are sham in  Table I. Typical dark for- 
ward and illuminated current-voltage characterist ics are shown i n  figure 4. 
Advanfgges of this method, CQP- 
The method permits the 
P-Base Diffusion Length and Recombination Time 
The minority car r ie r  base region diffusion lengths ( ) (and TB) 
determined by the X-ray method (8) are shown i n  Table I. 9 n t h i s  technique 
the  current generated byauniformly absorbed beam of X-rays and collected 
across the junction is proportima1 t o  the base region minority car r ie r  
diffusion length. The base recombination time and t h e  diffusion length 
are  related by the expression, GB = DBTB. 
DISCUSS ION 
The emitter charge (&Eo) and recombination time (Te) calculated using 
the  experimental data of Table I and equations 7 and 8 from the  charge- 
control model are given i n  Table 11. Conventional diode theory (3) un- 
modified by band p narrowing effects  predicts an emitter charge ( 
The charge deduced by the experimental methods shown here is about 5 orders 
of magnitude greater than t h i s  predicted value. As discussed i n  (3, 4 )  the  
presence of a large stored emitter charge indicates a first order influence 
of bandgap narrowing. 
of about 1 x 10-g coulombs/cm2 for  the  c e l l  structures considered 
Theanitter recombinaticn times sham i n  Table I1 are about 0.2 x 
see. Using equation 7 and the emitter charge from conventional theory 
yields a value of the  emitter contribution t o  Io tha t  is small compared t o  
that from the base region. This suggests tha t  T~ is suff ic ient ly  long such 
t h a t  major improvements i n  the open-circuit voltage of the ce l l s  considered 
here w i l l  be achieved by reductions in  the emitter charge rather thsn h- 
prwements in  the recombination t h e .  
4 
CONCUSION 
This paper has presented an experimentalnrethod for  individually 
determining the emitter stored charge and recombination time. Previous 
work has only been able t o  assess the r a t i o  of these device parameters. 
As a result of the findings presented here, it is concluded that band- 
gap narrowing effects  have a f i rs t  order significance in  determining 
the  charge car r ie r  transport controlling t h e  open-circuit voltage of 
0.1 0-cm s i l icon  solar cel ls .  
REFERENCES 
1. Godlewski, M. P. ; Brandhorst , H. W., Jr.; and Baraona, C. R. : Effects 
of High Doping Ievels on Sil icon Solar Cell Performance, Eleventh 
IEEE Photovoltaic Specialists Conference Proceedings , 1975, pg. 32. 
2. Brandhorst , Henry W. , Jr. : Solar C e l l  Efficiency - Practice and 
Promise , Ninth Photovoltaic Specialists Conference Proceedings , 
&Y 2-5, 1976. 
3. Lindholm, F. A.; L i ,  S . ;  Sah, C. T.:  Eleventh Photovoltaic Specialists 
Conference Proceedings, 1975, Pg. 3. 
4. Lindholm, Fredrik A.;  Sah,  C. Tang: Normal Modes of pn Junction Devices 
for  k t e r i a l  Parameter Determination, Z Applied Physics, September 1976, 
in press. 
5. Shockley, W. : B e l l  System Technical J., vol. 28, PP 435-469, J d Y  1949. 
6. Lederhandler, S. R.;  an6 Giacoletto, L. J. : Proc. Inst .  Radio Engrs. 
U Y  477 (19551. 
7. Bassett, R. J. ; Filop, W. : and Hogarth, C. A. : Bt. J.  Electronics, 
V O ~ .  35, NO. 2, 177-192 (1973). 
8. Lsmneck, J. H . ,  Jr.: Diffusion Lengths i n  Silicon Obtained by an X-ray 
Method, NASA TM X-1894, Oct. 1969. 
5 
TABU I 
P- 1 
Q-2 
Q- 3 
K- 1 
K- 2 
K- 3 
CdARACIZRISTI'JS OF 0.1 A L C M  
SILICON SOLAR CELLS, RUN 526 
.16 
-24 
.l8 
.18 
17 
.I5 
oc 
v 
( VOLTS ) 
1 
I d 
W U R E D  IN THE 0.55 TO 0.63 VOLTAGE DEWY RANGE 
* 595 
. G I 2  
,604 
.605 
.600 
.607 
39 
41.2 
41.2 
b1 
40 
42 
- 
T 
0 
(AMP x lo-") 
TAB= I1 
3.9 
2.2 
2.9 
2.8 
3.4 
2.5 
DlFFLTSED LAYE9 RECOMBINATIaN TIME 
AND C H A E E  USING TABU I DATA AND 
EQUATIONS 7 AND 8 
6 

CIAIm TJnrmixSH 
Type 1 Plug-In 
Fi 2 - Optn-Circuit Voitqp Decay Awardus 
, , I 
V 
IV0lw 
0 
0 2 4 6 8 D 1214 U 
Rrovcy lima 
IN krorccmds) 
Fig. 3 - Open-Circull Voltage Decay of 0.1 Q-cm Cell 52643 
m1 m43 
- dm 
- 4  
o lllutn!nrtcd 
- 2  i 
,'> 
- 1  . 2  . 3  .4  . 5  .6 . 7  
vm ( V o m  
Fig. 4 - Forward Current-Vollag8 Characteristics of 0.1 k m  
Sillcon Cell Measured by Dark and llluminld Bias 
Methods 
I 


Experimental investigation of the excess charge and time constant of minority carriers in the thin diffused layer of 0.1 ohm-cm silicon solar cells

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