A determination of diffusivity on solar cells is here reported which utilizes a one dimensional treatment of diffusion under sinusoidal excitation. An intensity-modulated beam of a scanning electron microscope was used as a source of excitation. The beam was injected into the rear of the cell, and the modulated component of the induced terminal current was recovered phase sensitively. A Faraday cup to measure the modulated component of beam current was mounted next to the sample, and connected to the same electronics. A step up transformer and preamplifier were mounted on the sample holder. Beam currents on the order of 400-pA were used in order to minimize effects of high injection. The beam voltage was 34-kV, and the cell bias was kept at 0-V

Hopkins, M. A.

Othmer, S.

English

NASA Technical Reports Server

MEASUREMENT OF MINORITY-CARRIER DRIFT MOBILITY I N  SOLAR CELLS 
USING A MODULATED ELECTRON BEAM* 
Siegfried Othmer and M. A. Hopkins 
Northrop Research and Technology Center  
Palos Verdes Peninsula, California 
The hypothesis has been advanced that  processing effects  on minority- 
car r ie r  d r i f t  mobility may explain variations i n  open-circuit voltage among 
space-quality s i l icon solar  ce l l s  subjected to  different  processing protoco1s.l 
Also, some evidence exis ts  t ha t  integrated c i r cu i t  process flows may resu l t  i n  
degradation of d r i f t  mobility.2 I t  is therefore of in te res t  to  determine the 
mobility or, equivalently, the diffusivi ty  i n  solar  c e l l s ,  w i t h o u t  subjecting 
them t o  additional processing steps. 
A determination of diffusivi ty  on solar  ce l l s  i s  here reported which 
u t i l i zes  a one-dimensional treatment of diffusion under sinusoidal excitation. 
Cells used were the same as those employed in Ref. 1. 
beam of a scanning electron microscope (SEM) was used as a source of excita- 
t ion.  The beam was injected into the rear of the c e l l ,  and the modulated com- 
ponent of the induced terminal current was recovered phase-sensi t ively.  A 
Faraday cup t o  measure the modulated component of beam current was mounted 
next  t o  the sample, and connected to  the same electronics,  as shown i n  Fig- 
ure 1. 
holder. 
effects  of h i g h  injection. 
kept a t  O V .  
An intensity-modulated 
A step-up transformer and preamplifier were mounted on the sample 
Beam currents on the order of 400 pA were used i n  order to  minimize 
The beam voltage was 34 kV, and the cel l  bias was 
The amplitude of the junction terminal current as a function of modula- 
tion frequency is  presented i n  Figure 2 for  two types of specimens. The ra t io  
of the sample current t o  measured beam current is shown. 
response was detected as the beam was injected into the back surface. 
resul ts  were obtained a f t e r  a groove was cut into the back surface u s i n g  a 
diamond saw. 
by h i g h  recombination velocity. 
be discussed below. 
spect to  Faraday cup current are  given i n  Figure 3 for  the same two ce l l s .  
In i t i a l ly ,  l i t t l e  
Good 
T h i s  served to  cut through a back surface layer characterized 
Curves shown are  for  model calculations to  
Measurements of phase delay of sample current with re- 
Results were analyzed u s i n g  a one-dimensional treatment of diffusion 
under sinusoidal excitation, following McKelvey.3 Low injection conditions 
were assumed. The continuity equati'on to  be sa t i s f ied  for  excess density 
A n ( x , t )  is 
a XL I 
* Work supported by the Solar Energy 
to  the Department of Energy, under 
Contract No. EG-77-C-01-4042. 
Research Ins t i tu te ,  a prime contractor 
Subcontract No. XS-9-8313-1, Prime 
61 
https://ntrs.nasa.gov/search.jsp?R=19810009017 2020-03-21T08:58:15+00:00Z
where D i s  the d i f fus iv i ty  and T the minority-carrier l ifetime. 
The solution for  sinusoidal excitation is 
A n ( x , t )  = A n ( x )  cos(wt) = A n @ )  e cos(wt - yx/L)  
for  diffusion i n  the positive x-direction and excitation source a t  the 
origin.  L is the diffusion length. Here $ and y are  given by 
and 
In  the present case, the solar cel l  junction samples the excess density 
a t  some distance x = R from the point of injection. 
served amplitude dependence is  obtained by varying the diffusion length and 
the l ifetime. 
obtained by use of the equation Lz = D T . )  
ure 2 ,  along w i t h  f i t s  for  other values of L to  indicate the sens i t iv i ty  of 
the f i t  to  choice of L.  Us ing  the best value fo r  L ,  a f i t  of the phase de- 
pendence ( F i g .  3) is  obtained by choice of l ifetime o r ,  equivalently, diffu- 
s iv i ty .  An additional f i t  t o  the data, obtained u s i n g  a different  value of 
diffusion length (discussed below), i s  also shown. 
A best f i t  to  the ob- 
(In t h i s  manner, an approximate value of diffusivi ty  can be 
The  best f i t s  are shown in Fig- 
2 The best value f diffusivi ty  for  specimen 672-5 appears t o  be 17 cm /sec, 
Einstein relationship, eD= pkT.  The  calculated mobilities a re  660 and 540 cm2/ 
V-sec, respectively. The base r e s i s t i v i ty  i n  these ce l l s  i s  0.1 ohm-cm,l and 
published values of d r i f t  mobility for  this r e s i s t i v i ty  are i n  the range of 
400-440 cm2/V-sec.4¶5 The present experimental values exceed the reported 
ones, contrary t o  expectations on the basis of processing e f fec ts .  The qual- 
i t y  of the theoretical f i t s  suggest tha t  application of a one-dimensional 
model is legitimate. The magnitude of sca t te r  i n  the data indicates that  
d i f fus iv i t ies  are obtained to  within about 15% precision. Possible sources 
of systematic error  include effects  of h i g h  injection, and our assumption 
t h a t  excitation occurs a t  the surface, rather than a t  f i n i t e  depth. Effec- 
t ive  d e p t h  of excitation could be as . la rge  as 3 pm for  the 25 keV beam used, 
amounting to  ~ 6 %  of the effective cel l  thickness (measured from the bottom 
of the cu t ) .  
phase delay for  different  degrees of beam defocus. No observable e f fec t  on 
the phase was noted. (By contrast ,  the amplitude showed a s l i gh t  ( ~ 1 0 % )  
decrease upon defocussing.) 
s i n g  sequence.1 A long emitter diffusion was followed by etch-back and a 
and for 664-1, 14 cm 8 /sec. Equivalent mobilities may be determined using the 
Effects of h i g h  injection were tested for  by measurement of 
The ce l l s  measured here had been subjected t o  an unconventional proces- 
62 
secondary emit ter  diffusion. 
ination conditions yielding identical  shor t -c i rcu i t  currents (25 mA/cm2) was 
observed fo r  long primary diffusion times. A decrease i n  d i f fus iv i ty  was 
postulated t o  explain this r e su l t .  T h i s  supposition was supported by ce l l  
measurements which showed t h a t  the diffusion lengths i n  the samples were 
nearly ident ica l ,  b u t  t ha t  l i fe t imes differed.  Judging from the amplitude 
dependence shown i n  Figure 2 ,  i t  appears t h a t  nei ther  the diffusion lengths 
nor the l i fe t imes i n  the two samples a re  ident ical .  We a re  re luctant  t o  
draw quant i ta t ive conclusions from the amp1 i tude  data,  since the assumption 
of one-dimensional transport  i s  much more questionable i n  t ha t  case than i n  
the case of  the phase measurements. Moreover, e f f ec t s  of rear  surface re- 
combination have not been taken in to  account. Finally,  the diffusion lengths 
measured under ac  conditions may be governed by trapping ra ther  than recombi- 
nation, and would be smaller than those determined under dc conditions. Fortu- 
nately,  assumptions of diffusion l e n g t h  have only minor influence on the de- 
termination of d r i f t  mobility on the basis of the phase data.  I f  we assume, 
fo r  example, t h a t  the diffusion lengths are  -250 pm, as determined’ from ce l l  
measurements,l the d i f f u s i v i t i e s  calculated a re  found to  be 18 and 15 cm2/sec 
f o r  the samples 672-5 and 664-1, respectively,  vs. 17 and 14 determined above. 
I t  should be noted tha t  the diffusion l e n g t h  which yielded the best f i t  t o  the 
amplitude data of sample 664-1, about 35 pm, a l so  yielded the best f i t  t o  the 
phase data. 
4-hour primary diffusion,  should exhibi t  a higher d i f fus iv i ty  than the speci- 
men 672-5, which was subjected t o  a 41-hour primary diffusion. 
been confirmed i n  the present measurements. 
An increase i n  open-circuit voltage under i l l u m -  
I t  was anticipated tha t  sample 664-1, which was subjected t o  a 
T h i s  has n o t  
I 
REFERENCES 
1. M.P. Godlewski, T.M. Klucher, G . A .  Mazaris, and V . G .  Weizer, Conference 
Record, 14th IEEE Photovoltaic Spec ia l i s t s  Conference, 1980, p ,  166. 
2. S. Othmer, Scanning Electron Microscopy, 1978, Vol. I ,  SEM, Inc., p . 7 2 7 .  
3. John P. McKelvey, Solid S ta te  and Semiconductor Physics, Harper & Row, 
New York, 1966, p.  439. 
4. 
5. 
S.M. Sze and J.C. I rvin,  Solid S ta te  Electronics 11, 599 (1968). 
K.B. Wolfstirn, J .  Phys. Chem. Solids 16, 279 (1960). 
801 18 
Figure 1. Experimental ar-  
rangement f o r  the measure- 
ment of ce l l  response i n  
amplitude and phase under 
conditions of rear-surface 
inject ion u s i n g  a modulated 
beam. 
6 3  
, 
'!, , 
CELL 672-5, R = 105 pm 
ACELL 664-1, R=52pm 
41 -hr PRIMARY DIFFUSION 
4-hr PRIMARY DIFFUSION 
5 -  
- 
, 
I I i I \  I I 
10 2 5 2 5 1 
FREQUENCY (MHz) 
0.1 
80143 
Figure 2.  Amplitude ra t io  of solar  cell  current t o  beam current 
as a function o f  frequency for  two solar  ce l l s .  Theoretical 
f i ts  are shown for  different assumptions of b u l k  d i f f u s i o n  
length. 
junction. 
R is the distance of the p o i n t  of injection from the 
64 
60( 
50 ( 
- 40( 
L 
v) 
Q) 
0, 
Q) n 
Y 
30( - 
I 
v) 
w 
v) 
I 
a 
p 20( 
10( 
( 
80144 
I I I I 1 
1 2 3 4 5 
FREQUENCY (MHz) 
Figure 3. Phase s h i f t  o f  s o l a r  c e l l  cur ren t  w i t h  respect t o  beam 
cur ren t  f o r  the  two c e l l s  t rea ted  i n  Figure 2. 
t heo re t i ca l  f i t  f o r  the  bes t  choice o f  d i f f u s i v i t y  under assump- 
t i o n  o f  d i f f u s i o n  lengths determined from Figure 2, as we l l  as 
the f i t under assumption o f  250 pm d i f f u s i o n  length. 
Shown i s  the 
65 


Measurement of minority-carrier drift mobility in solar cells using a modulated electron beam

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