A measurement technique employing the scanning electron microscope is described in which values of the true bulk diffusion length are obtained. It is shown that surface recombination effects can be eliminated through the application of highly doped surface field layers. The influence of high injection level effects and low-high junction current generation on the resulting measurement was investigated. Close agreement is found between the diffusion lengths measured by this method and those obtained using a penetrating radiation technique

Weizer, V. G.

English

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DIFFUSION LENGTH MEASUREMENT USING
THE SCANNING ELECTRON MICROSCOPE
7 Gx 9 F Zby V. G. WeizerLewis Research Center
Cleveland, Ohio 44135
TECHNICAL PAPER to be presented at
Eleventh Photovoltaic Specialists Conference
spc a...j-ed by the Institute of Electrical and
Electronics Engineers
Phoenix, Arizona, May 6-8, 1975
MDIFFUSION LENGTH MEASUREMENT USING THE SCANNING ELECTRON MICROSCOPY.
V. G. Weller
Lewis Research Center
	
t'^. "l ; I N AL PAGE IS	 National Aeronautics and Space Administration
	
, i - 97, (IUALITY	 Cleveland, Ohio 44135
SUMMARY
A measurement technique employing the scarab 's eleo-
tren microscope Is dos, : ribed in which values of the true
bulk diffusion length am obtained. It is shown that surface
recombination effects ma be eliminated through the applies-
can of highly doped surface yield layers. The Influence of
high injection level affects and low-high junction current
generation on the resulting cressurement is investigated.
Close agreement is found between the diffusion lengths mea-
sured by this method and those obtained using a penetrating
radiation technique.
INTRODUCTION
for carrier srnorstion. The means for obtaining the news-
eary values of surface recombination velocity an described
a are the effects of factors such as Injection level and cur-
rant collection from a low-high Junetloh. It should ba brought
out that the technique described hom is limited to colls which
contain a back surface field layer. Also, the theoretical
treatment must be modified W Include tow-high )=oil= cur-
not contributions if calls with base resistivity higher than
10 ohm-cm an to be Investigated.
DEVELOPMENT OF TECHNIQUE
Theory
The determination of bulk diffusion lengths somi-
conductor devices is a diffieul, process. W:11 	 •ny tech-
nique. *,avo been employed to measure this parameter,
there is a serious lack of agreement between the values ob-
tained by the various methods.
One of these techniques, involving the use of the scan-
ning electron micreacope (SEM) electron beam to generate
carrion In a sample containing a collecting junction, has
been employed by several Investigators (1, 3). In this tech-
nique, the diffusion length is determined by measuring the
variation of the short circuit current as the location of the
Injecting beam in moved with respect to the collecting Juno-
it=. The main difficulty with this typo of measurement is
that carrier recombination at the beam entry surface must
be accounted for (3). This puts &ovum limitations on the use
of the method, especially for devices which have dimensions
comparable with a diffusion length. Furthermore surface
Inversion effects induced by the injecting electron boom on
P-type material make this technique extremely difficult to
apply to P-base devices of moderate to high resistivity, that
L, p z 10 ohm-cm. Elimination of the Influence of these
surface effects would greatly simplify these measurements.
A SEM technique has been developed here In which our-
face recombination is effectively controlled by the applica-
tion of highly doped at .race field layer to the samples being
Investigated. Furthermore, the application of the field layer
not only reduces surface recombination but also prevents the
occurrence of beam-induced Inversion layer effects, peranito
ting measurements to be made an
	
as well as N-base
devices. Because of the geometry involved and the large
magnitudes of diffusion length usually found therein, the
method is ideally suited for measurements In ellicon solar
cells.
It Is the purpose of this paper to describe this technique
and to compare the results to those obtained by an independ-
ent technique In which penetrating radiation (X-mys) is used
Let us consider injection of carrion by the BEM beam at
a point just inside the rear face of a silicon solar cell The
cell Is assumed to be a planar device with lateral dimensions
vory much larger than a diffusion length. Tho fmctlon of the
Injected carrion that is collected by the junction is directly
re!ated to 	 diffusion length. Tha collected fraction is,
however, sensitive to the recombination velocity at the boom
entry surface. Theme points am brought out by the following
analysis.
The continuity equation describing point injection of car,
rien In a planar solar cell of thickness d, at a distance xi
from the collecting junction is
V3nlx) .11V
 = 0	 (1)
L3
%.:ere L is the bulk diffusion length. The solution of Eq. (1)
under the boundary conditions:
(1) At the Junction, x = 0, n - 0
(3) At the nor face, x = d, D(dn/d)) = Sn
yields an expmssim for the short circuit current
1+•Ise =teas	
f/
	
IT
exp 
y3+^l+ 
\pxp
ss/
	
y8 aI
whom y  - (d- xI)/L, y2 = -xi/L, Imes is the carrier gen-
eration rate times the unit charge, and • = SL/D where S
is the rear surface recombination velocity and D is the
minority carrier diffusion coefficient.
Now consider generation of carrion just Inside the mar
surface of the cell. By setting xi = d in Eq. (1), the family
of curves shown in Fig. 1 can be obtained. Hem, Sec/imax'
the fraction of the injected carrier flux which is collected by
the junction, is plotted as a function of d/L. Once values
Of leas and s have been determinod, L can be obtained
from the measured value of Isc'
N
nm
A
A20 1 tag
A JEOL JSM-2 sovining electron microscope was used
In Nee 11170SUPtions. To permit SEM electron begin
Into the rear of Me cell, a small a men - 1 mm) window. • wus
chemically etchoi in the back contact metallization exposing
Me Pi
 layer Tao boars eurrant was measured by means
of a farnday cup mounted m the specimen holder.
Imas Denomination
Iran, can be determined theoretically from the known
pair productim energy (2. S ov for silicon (4)), the incident
begin
	 (40 kv used in this worn), the electron bmck-
n cattering coefficient (0. 16 for 40 kv elections normally m-
ordant on silicon (5), and the incident lumen current, IR.
Using these values the following ralatim is obtained:
Imm = 0.0.109 Ili
The calculated value was verified experimentally from
Ise measurements whon the carriers were injected in close
proximity to the junction where the collection efficiency is
expected to approach 100 percent. Agreement was found to
within 0.6 poment.
Surface Recombination Velocity
As can be seen from Fig. 1, Ise/Imas decreases mp-
idly as s Increases. In order to use Fig. I to determine
L. we meet know e. Furthermore, because of noise con-
sideratims, the lower the value of s, the greater the ease
and accuracy of the measurements.
A highly doped field layer applied to the rear surface of
a solar cell Is known to reduce s at the rear face of the cell
to low values (6). Hence it Is loglcel to make use of the field
layer in the present measurements to effect the desired m-
ductlon in s.
Although it is known that a is reduced by the addition of
a field layer, racertalnty,
 exists as to the quantitative nature
of the reduction. An experiment was devised, therefore, to
determine the degree of reduction in e effected by the addi-
tion of the field layer. Performed on P-base cells of special
geometry, the experiment Is essentially a measurement of
short circuit current as a function of cell thickness. The
cello studied were fabricated such that they contained
crescent-shaped slots, 1 met wide and about 1 cm in length,
cut in their rear faces (Fig. 2). Cell thickness at the bot-
tom of the slot was of the order of 26 pm. The geometry
selected permits the measurement of the variation of Ise
with cell thickness without the interferenco of edge effects
which could be present if an angle-lapped geometry were
used. After slotting, the P* layer was incorporated by
evaporating several micrometers of aluminum m the rear
surfaces and diffusing at 6760 C for 60 minutes. Subsequent
to the diffusion step, the remaining aluminum was removed
from the slot and a small adjacent area to permit entry of
the elenron beam.
Measurements of lac/Io ax were then made as a fumo-
tion of pmitim as the electron begin
	 the length of
the slot. The resulting •lata were than used with Eq. M to
determine the surface recombJnattm velocity on the rear
surface of the cell.
Hish Injection Level Effects
Measurements of the current gam. Nat is, the ratio of
the collected current to input berm current, wore made to
determine the possible innumce of high Injection level effects
m the measured short circuit current.
l.ow-lilgh Junction Effects
A low-high junctim Is formed near the rear taco of a
cell upon the application of a highly doped field layer (7).
Although this type of junction repels minority carriers It is
a collector of majority carriore. Thus it is expected that
such a junction would produce a photo current (and a photo-
voltage) through the collection of excess majority mr-
rlers. Contributions from this junction to the measured
short circuit current must be taken into account in the then-
retical model used. A pair of experiments wore performed,
therefore, In an attempt to detect possible low-high junction
current generation.
(1) Open circuit voltage measurements were made on
isolated PPS low-high junctions.
(2) The rear faces of a number of 10 ohm-em and
100 ohm-cm N"PP+
 BSF calls wore divided into two regions
by etching grooves across the rear faces of the calls (Fig. 0).
The lac was then measured (in the SE1f) from me of the
roar area* while carriers wore injected first into me of the
arms and than into the others. An increase in lac when
injection takes place on the motored side would be an indlca-
tlon of currant generation at the PP S junction.
Comparison to X-Ruy Measurements
Since agreement with the results of an independent
method would be verification of the present method, a com-
partaon was made between the results of the HEM measum-
ments on a number of 10 ohm-cm BSF solar cello with the
values of L determined by a ponetmtb.g radiation technique
employing X-my& as carrier generators. The details of the
X- my technique, which has been used at this laboratory for
several years, are presented elsewhere (8, 9).
RESULTS AND DISCUSSION
Surface Recombinatlm Velocity
Results of the measurement of Ite/IMgX as a funetim
of the location of carrier injection along the slot In me of
the specially fabricated cells is shown in Fig. 4. As can be
soon. Ia ,/Imas
 drops sharply as the injecting beam begins
to Impinge on the slotted arm, indicating a higher value of a
in the slot than on the net, unsloted region The increase
in a is probably due to res id, al lattice damage from the slot
grinding procedure,
The scatter in the data in Fig. 4 Is believed due to the
presence of tenacious aluminum-silicon alloy particles re-
maining on the surface which reduce the magnitude of the
t
bum current that enters the underlying silicon. Thus the
true respatse of the uncovered silicon Is best described by
the upper envelope of the data
The but fit of Eq. (21 to the data along the slotted region
Is indicated by the solid curve N Fig. 4. The theoretics) fit
requires a value of 0.316 for s and a value of 262µm for L.
This value of L can then be wed with Eq. (21 to detetmino s
on the flat, unaloted region. The results of such a calmda-
ton Indicate that on the Oat arm, e - 0.012. Upon trans-
lating these numbers to absolute values one finds r000nbina-
ton velocities of-400 cm/sec In the slot and x-16 cm/ace on
the Oat. The le tter value is several orders of magnitude
Isss tan the minority carrier diffusion velocity. This
mow that, for all practical purposes, the P` field layer
as described hero constitutes a perfectly reflecting barrier
to minority carrier ten+port, effectively preventing re-
combination at the roar surface of tine cell.
Hich Injection Level Effects
Measurements of the current gain as a function of bum
current were made for beam currents that ranged from a few
picoamporoe to over a n noampere for a wide range of de-
focusing conditions. No variation in the gain with beam cur-
rent was observed, indicating that the measurements ere
free of high Injection level effects.
Lev-High Junction Effects
The PN junctions were removed from a number of
10 ohm-cm N+pp+ IOF calls, isolating the Pp* junctions.
Von measurements on the isolated junctions under roughly
simulated AMO conditions show that no significant voltage is
produced when this material is wed, that Is, V 0 a 0.006
volt. Similarly treated 100 ohm-cm cells, however, yielded
open circuit voltages of 0.000 to 0. 100 volt.
In a second experiment, the backs of several cells were
divided into two regions, as previously described (Fig. 3).
For 10 ohm-cm calls, no increase in tar was found when
the Injecting beam was switched from the upon circuited side
to the metered side, whereas for 100 ohm-cm cells a sig if-
Icant (-S percon0 Increase wait observed. These results are
consistent with the voc measurements on Isolated PP+
junctions.
We can conclude, therefore, that for cells of 10 ohm-em
base resistivity, PP + current generation through the col-
lection of excess majority carriers Is not a concern.
Comparison to X-Ray Measurements
A comparison of the reaults o7 the :714 measurements
with the values of L determined zy The X-ray technique is
shown in Fig. S. As sew in . 1yurs
	
r a good cor-
relation between the results of L'•e ,	 .niques. The two
methods agree to within a multi-Hcative factor, the SEM
lengths being consistently about 1.0 times greater than those
determin: i by the X-ray method.
The fac': that there is a linear relationship between the
results of these two basically different techniqu._ indicates
the essential validity of both materials. A callbraumnal
error Is indiented, however, in one or both methods.
Beeswo the point Injection Method yields an absolute
value of L from a knowledge of a few easily determined pe-
mmetors, while the X- my technique depends upon rather
complex assumptions as to the carrier generation rate, It
appears more likely t,at the discrepancy can be attributed to
a miscallbration of ono X-ray method. This hypothesis to
supported by the results of short circuit measurements made
in the X-ray apparatus in 	 surface field cells before add
after removal of the field layer. In all cases the I 	 drops
so
observed upon the mwoval of the P+ layer exceeded Noss
expected under the original ci llbmtion conditions. For As-
ample, Table 1 gives the observed Ise drops, the expected
drops under the original calibration, and the expected drops
If the X-ray apparatus were mealibrated to agree with the
SEM results, for calls with :+oth aluminum and boron field
layers. The values of the expected drops were obtained from
the appropriate 1oc versus L -mrves (0), Assuming an
e - 0 back contact for the coil in the DSF condition and an
s - 108 cm/sec back contact for the P
+
-removed condition.
The fact that the measured drops are larger than those
predicted under the original calibration indicates that the
X-ray apparatus Is indeed mscallbroted and will yield erm-
enowly low values of L. The recalibration scheme, on the
other hand, predicts values that are consistent with the ex-
porimental data. It follows, then, that a recalibratim of the
X-ray method as dictated by the data in Table 1 will esson-
Wly eliminate the discrepancies between the two techniques.
CONCLUSIONS
The results of these investigations Into the we of the
scanning electron microscope to measure bulk diffusion
lengths can be summarized as follows:
(1) A technique for deforming bulk diffusion longthe in
silicon solar eels has been developed which yields an abso-
lute value of L from a knowledge of only the coil thickness
and the mllocted fraction of the injected carrier flux.
(l)
 This technique requires a means of reducing :.e mi-
nority carrier recorabination velocity at the coil rear face.
It has bean shown that the addition of a highly doped field
layer to the rear surface of a 10 ohm-cm call reduces the
minority carrier recombination velocity them to negligible
values.
(S) High injection level effects do not Influence the results
of this technique under normal operating conditions, that s,
40-kev electrons at beam ohrrenta less than L. 10-0
 ampere.
(4) For base maistvitles of 10 ohm-cm or less, contri-
butons to the me -oured short circuit current due to majority
carrier collection at (he low-high junction formed by the addl-
tlm of the field layer at the rear surface have boom shown to
be negligible. In order to use higher nose resistivity cells,
however, contributions from the low-high junetim must be
taken into account.
(6) Close agreement has hem shown between the results
of this technique and those obtained by a penetrating radiation
(X-ray) technique. The diffusion lengths determined by these
methods am found to be significantly larger (-I. S )) than
Table 1.
0beorvad GriglSal New
(ga) calibration calibration
Lip) lt0 1411) Ise
taa) (11a)
962-6 BSF 27 60 27 162 27
(Boron) nm BIF 21.6 80 26.6 162 20.7
HA	 23 B8F 66.7 216 66.7 410 66.7
fAlumt- ram BBF 29.9 216 22.6 410
nun)
28.1 1
F"
previous mpsuramonts "sate. The cause of this differ-
moo was shown to be an apparently erroneous calibration nt
She X-ray technique.
REFERENCES
1. Hackett, W. H.: JAP 49 1649 (1972).
2. Zimmerman, W.: PIWs. Stat. Sol. 12 671 (1972).
2. yon Roosebrosck, W.: JAP 26 280 (1065).
4. Guldbarg, J., Shrodsr, D. K.: IEEE Trans. ED-18
1029 (1971).
6. Bishop, H. E.: Ph.D. Dissertation, Cambridge (1868).
6. Godlawski, M. P., Banana, C. R., Bmadhomt, H. W.:
NASA TM X-71498 (1972).
7. Lade, R. W., Jordan, A. G.: J. Electronics Control 10
26 (1062).
S. I.araneek, ,. H.: NASA TM X-1894 (1969).
9. Boraces, C. R.: Private Communication.
i
ORIGINAL PAGE I$
POOR QUALITY
4
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-vl.€ 0
F,
0	 .2	 .4	 .6	 .!	 1.0	 1.2	 1.4
&L
Figure 1. -A plot of the collwW traction of In)KW car-
riers as a function of the ratio dIL
rn
Go
W
SIDE VIEW	 p
-----___-----—n'
MP VIEW	 MLAJ
T1-10 mm
Figure 2. - Schematic diagram of slowed all.
/	 --- —-	 -- ---^—p'
P
Figure 3. - Schematic diagram of relit-back configuration.
ORIGINAL PAGE LS
tlF ?MR QUALITY
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N
II
FUT L	 SLAT	 i
ISx0.
	
is -0.315)	 '1
0.
I	 I	 I
0.20 2 / 6 I 2 I
DISTANCE (mm)
Figure 4 - A Prot of the col ecbd fraction of InJecbd car-
riers as a function of distinct across beck of all.
%OF
'I.€
X-RAY DIFFUSION
LENGTH WI
Figure S. - A comparison of
diffusion lengths measured
In the SEM with those mas-
ured with penetrating radi-
ation.
ORIGINAL 
PAGEOF POOR QUALITY NASA-L.wi•
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Diffusion length measurements using the scanning electron microscope

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