70
IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. ED-35, NO. I , JANUARY 1988
The Effect of Doping Density and Injection Level on
Minority-Carrier Lifetime as Applied to Bifacial
Dendritic Web Silicon Solar Cells
DANIEL L. MEIER, MEMBER, IEEE, JEONG-MO HWANG, MEMBER, IEEE,
Abstract-The decrease of minority-carrier lifetime with resistivity
and with illumination level in bifacial dendritic web silicon solar cells
is addressed. This variation of lifetime is shown to be consistent with
the presence of a distribution of defect levels in the bandgap that arise
from extended defects in the web material. The extended defects are
precipitates, recently shown to be oxide precipitates, that decorate dislocation cores. It follows that the sensitivity to this background distribution of defect levels increases with doping because the Fermi level
moves closer to the majority-carrier band edge. It is not necessary that
the dopant atom itself, or a complex including the dopant atom, acts
as a recombination center in order to explain the observed decrease in
lifetime with doping density. Good agreement is obtained between calculated and measured values of short-circuit current and quantum efficiency for bifacial cells covering a range of doping density ( 6 x lOI4
to 3 x 10l6 ~ m - and
~ ) illumination level (0.001 to 1 sun), with illumination from either back or front of the cell. The implications of this
approach extend to concentrator cells and to other devices in which
minority-carrier lifetime is an important parameter. This includes devices made using Czochralski-grown silicon, where oxygen and oxide
precipitates likewise play an important role in determining lifetime.
I. INTRODUCTION
HE SHORT-CIRCUIT current density ( J S c )in a conventional silicon p-n junction solar cell is strongly dependent on the lifetime of the minority carriers in the base
of the cell [ l ] . This simply follows from the fact that the
longer a photogenerated carrier exists, the greater are its
chances of being collected by the electric field at the junction and of contributing to the photocurrent. For dendritic
web silicon solar cells, J,, has been found to decrease as
resistivity decreases. This is particularly important for bifacial cells, which are designed to respond to light incident on either the front or the back surface.
Bifacial cells fabricated from dendritic web silicon substrates have an n+-p-p+ structure. J,, values for light incident upon the front (n'-p) surface of the cell ranged
from 32 to 27 mA/cm2 for the resistivity of the borondoped base ranging from 90 to 0.5 fl * cm [2]. The corresponding values for light incident on the back (p'-p)
surface ranged from 3 1-to only 5 mA/cm2. These cells
had a nominal thickness of 150 pm, and the light intensity
T
Manuscript received February 2, 1987; revised July 27, 1987.
D. L. Meier and J.-M. Hwang are with the Westinghouse Research and
Development Center, Pittsburgh, PA 15235.
R. B. Campbell is with the Westinghouse Advanced Energy Systems
Division, Pittsburgh, PA 15236.
IEEE Log Number 8717335.
AND
ROBERT B. CAMPBELL
was 100 mW/cm2 with an air mass 1 (AM1) spectrum.
This variation of J,,, particularly for back illumination, is
a result of the decrease of minority-carrier (electron) lifetime with resistivity.
Furthermore, it was found that the ratio of short-circuit
current under back illumination to short-circuit current
under front illumination ( J , , ( back) / J,, ( front ) ) is not
constant, but rather decreases, as the light intensity is decreased from l to 0.0016 sun. This variation of the shortcircuit current ratio with light intensity became more pronounced as the base resistivity of the cells was increased.
At the lowest resistivity (0.5 fl * cm) the ratio was nearly
constant. The observed variation of the short-circuit current ratio with light intensity indicates that the minoritycarrier lifetime depends on the concentration of excess
carriers in the base of the cell as well as on the substrate
doping.
The decrease of lifetime with resistivity has also been
observed for Czochralski (CZ) silicon [3]. However, the
best float zone (FZ) silicon has been reported to have a
minority-carrier lifetime that is high ( - 1000 p s ) and
nearly constant in both n-type and p-type substrates for
doping ranging from 1014 to 10I6 cmP3 [4]. Above 10l6
cmP3 doping, the lifetime in the FZ substrates decreases
with doping density because of Auger recombination.
The reason for this decrease of lifetime with resistivity
in dendritic web silicon and in CZ silicon is not well
understood. However, several facts are known. The dopant impurities (e.g., boron) themselves are not likely to
be responsible for this trend because these impurities introduce only shallow levels into the bandgap. In addition,
heavily doped FZ silicon (0.2 fl cm, boron doped) with
high lifetime is commercially available, for example, from
Wacker Siltronic. This material has been used by several
groups to produce solar cells with efficiencies ranging
from 18 to 21 percent [5]-[7].
It might be speculated that the dopant atoms enter into
a complex with other impurity atoms (e.g., boron-oxygen
complex) or with point defects (e.g., boron-vacancy complex). Such a complex may act as a recombination center.
The lifetime would then be degraded as the silicon is
doped more heavily, since more complexes would be
formed in the process. Complexes of this type are small,
regarded as point defects, and therefore would be ex-
0018-9383/88/0100-0070$01.OO @ 1988 IEEE
1
1 -
MEIER et al. : EFFECT OF DOPING DENSITY AND INJECTION LEVEL
71
pected to give rise to well-defined energy levels in the
The purpose of this paper is to show that the observed
bandgap. Such levels have been sought in dendritic web variation of short-circuit current with resistivity and illucells by deep-level transient spectroscopy (DLTS) mea- mination level in bifacial dendritic web silicon solar cells
surements from 77 to 300 K, but none have been system- is consistent with a continuous distribution of defect levatically observed [8]. The DLTS measurements were car- els in the bandgap. Possible sources of such defect levels
ried out with beveled samples, so that the material could are cited, the physical reasons for low-resistivity material
be probed to a depth of 60 pm.
being more sensitive than high-resistivity material to these
A second point that argues against the dopant impurity defect levels are developed, and the calculated values of
forming an electrically active complex with another im- lifetime as a function of doping density and illumination
purity or defect that is in abundance in the silicon web level are presented. In addition, calculations of short-cir(e.g., oxygen) can be stated. Low-resistivity web silicon cuit current under front or back illumination of bifacial
(0.37 fl cm, boron doped) has been produced that cells as a function of light intensity and base resistivity
yielded cells having a high lifetime (13 p s by the open- are presented and compared with measured values. The
circuit voltage decay technique) and a high efficiency results obtained have implications for concentrator solar
(16.9 percent) [SI. These relatively high values of life- cells or any silicon device in which minority-carrier lifetime and efficiency were obtained even though the web time is important and oxide precipitates, dislocations, or
had a high concentration of boron ( 7 X 10l6 cmP3) and other extended defects are present. This includes
oxygen (typically lo1*cmP3). The fact that boron and Czochralski-grown silicon, in which microscopic oxide
oxygen did not limit the lifetime in this particular web cell precipitates may be present.
suggests that the boron-oxygen complex is not the major
factor in limiting the lifetime for web cells in general. The
11. RECOMBINATION
MODELING
same argument could be made for other possible com- A . Mechanism for Recombination via Defect Levels
plexes in which the boron combines with some point deFig. l shows the sequence that is required to complete
fect that is present in all web cells.
As another counterexample, solar cells were fabricated a recombination event at a defect level ( E t ) . The recornfrom web that was doped with both boron and phospho- bination event requires:
rus, each to a concen&ation of - 3 X 10l6 crnz3, as de1) initial occupation of the level by a majority carrier;
termined by SIMS measurements. The net doping of this
2) capture and retention of a minority carrier;
compensated material was 7 . 2 X lOI5 cmP3, n-type, from
3) capture of a majority carrier to restore the initial state
Hall measurements. In spite of the relatively large conof the defect level.
centration of both boron and phosphorus, the hole diffusion length in the base of cells fabricated from this ma- Note that the occupation of a defect level by a majority
terial was 124 pm, as measured using the surface carrier depends on the position of the Fermi level ( E F ) .
photovoltage technique. Cells fabricated from this com- If the defect level is located in the bandgap at a position
pensated material had an efficiency of 10.3 percent with- where it is not normally occupied by a majority carrier
out an antireflective coating. The expected efficiency with (e.g., close to the conduction band edge in n-type matean antireflective coating is 15.5 percent, which is reason- rial), then the above sequence cannot occur and that deably high for web cells. This result also supports the con- fect level does not participate in recombination activity.
tention that in dendritic web silicon, the dominant recom- This picture is valid in equilibrium (where the Fermi level
bination centers are not associated with the dopant atoms is meaningful) or under very low-level injection condithemselves or with complexes involving the dopant at- tions.
oms.
For lightly doped n-type silicon, where the Fermi level
An alternate explanation for the decrease of lifetime lies close to the center of the bandgap, most defect levels
with resistivity is that the dopant is playing an indirect in the upper half of the bandgap lie above the Fermi level.
role in the recombination activity within an operating cell. Such levels are not occupied by electrons and conseThe primary role is played by the defects that exist in the quently cannot mediate recombination events. As the reweb material, wholly independently of the dopant itself. sistivity is decreased, however, the Fermi level moves
Such defects could be extended (not point) defects such away from the center of the bandgap and toward the conas dislocations or precipitates that are introduced during duction band edge. In doing so, it uncovers defect levels
crystal growth or device processing. Defects of this type and makes them available as recombination centers (step
are expected to give rise to a distribution of energy levels 1). If the silicon bandgap is “cluttered” in this way with
within the bandgap. Each such level can mediate a recom- energy levels associated with defects, then the minoritybination event via the Shockley-Read-Hall mechanism. carrier lifetime will decrease as the resistivity is deBecause the Fermi level is set by the concentration of the creased. However, if the bandgap is free from these dedopant impurity, low-resistivity material is sensitive to a fect levels, then the lifetime will remain at a high value
larger fraction of these defect levels than is high-resistiv- as the resistivity is decreased. This is the case for FZ sility material. Consequently, low-resistivity material is ex- icon.
pected to have a smaller lifetime than high-resistivity maThus far, only those defect levels lying between midgap
terial.
and the majority-carrier band edge (e.g., the conduction
-
_-
I
1
-
I
12
IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. ED-35, NO. I , JANUARY 1988
E L
6 ----4 -.*.-E!
-
A
-----
--*
----_
--*
-
-.*.-
-
(a)
(b)
(C)
Fig. 1. Sequence of events in the recombination of a free electron and a
free hole at a defect level ( E , ) for an n-type semiconductor. Shown are
the initial condition (a) in which the defect level is occupied by a majority carrier (electron), and an electron is present in a state near the
conduction band edge ( E c ) , and a hole is present in a state near the
valence band edge (Ec,); the intermediate condition (b) after the minority
carrier (hole) has been captured by the defect level; and the final condition (c) after the majority c a m e r (electron) has been captured by the
defect level. In condition (c), the trap associated with the defect level
has been “reset” to mediate another recombination sequence.
band edge in n-type silicon) have been considered. Defect
levels lying in the other half of the bandgap can also mediate recombination events, and these too are affected by
the position of the Fermi level. For simplicity, assume
that the capture cross section for holes ( u p )is equal to the
capture cross section for electrons (a,) for a given defect
level. Then, those defect levels lying between the minority-carrier band edge and a certain critical energy play a
different role in recombination than other levels. This critical energy level, measured relative to the minority-carrier band edge, is equal to the energy difference between
the Fermi level and the majority-carrier band edge. Defect levels with energies less than this critical value have
a greater probability for emitting a trapped minority-carrier back to the minority-carrier band than for capturing a
majority carrier to complete a recombination sequence
(step 3). This means that defect levels in this part of the
bandgap are not effective recombination centers.
If the capture cross sections are not equal for electrons
and holes, then the energy at which the probability for
emission of a trapped minority carrier is equal to the probability for capture of a majority carrier is modified somewhat. For n-type material, this critical energy ( E t c ) is
given relative to the intrinsic energy ( E , ) in terms of the
electron concentration ( n) and intrinsic carrier concentration ( n ,) as
to 400 K [lo]. This is entirely consistent with the picture
presented above, since an increase in temperature moves
the Fermi level closer to midgap. For example, the “window of sensitivity” ( 2 I EF - E, I ) is 1.1 eV at 77 K and
0.4 eV at 400 K for 1 X lOI5 cm-3 doping. This “window” is thereby reduced as the temperature is increased,
and the lifetime increases, as expected. Since the lifetime
was measured for a particular sample, the distribution of
defect levels in the bandgap is fixed. It is only the movement of the Fermi level that is responsible for the variation in lifetime. Similar comments apply to the enhancement in EBIC images that have been reported when a
sample is cooled from room temperature to 77 K [ l l ] .
The increased recombination activity that is observed at
77 K may well be associated with the movement of the
Fermi level away from midgap as the EBIC sample is
cooled.
B. Possible Source and Distribution of Defect Levels
While point defects (e.g., heavy metal impurities) or
complexes consisting of only a few point defects (e.g.,
divacancy) give rise to well-defined energy levels in the
bandgap, extended defects (e.g., dislocations or oxide
precipitates) create a distribution of energy levels. Such a
distribution of defect levels has been shown to exist for
oxide precipitates in Czochralski silicon [ 121, [ 131. These
precipitates can exist in several forms, depending on prior
thermal history [ 141. Dislocations and precipitates that
have nucleated on the dislocation cores have been observed by cross-sectional TEM in dendritic web silicon
[8]. Recent experimental results, obtained using time-offlight mass spectrometry in conjunction with a field ion
microscope, indicate that the composition of these precipitates is SiO, [ 151. Infrared spectroscopy measurements
(ASTM F121-80) have shown that dendritic web silicon
contains interstitial oxygen atoms, which are introduced
from the quartz crucible during crystal growth, at a concentration of approximately 1 X lo’* cmP3. Thus, there
is a plentiful supply of oxygen from which oxide precipitates ( SiO,) can be formed.
Further indication that these precipitates in dendritic
E,, - E, = -kTln [ ( u n / u p )* ( n / n , ) ] .
( 1 ) web silicon may be oxide precipitates follows from the
If E, lies below this critical energy level, then it will not response of solar cells fabricated from web material to
hydrogen ion implantation. Atomic hydrogen is expected
act as an efficient recombination center.
Thus, the position of the Fermi level defines a “win- to passivate defect states associated with the interface bedow” in the bandgap. Defect states lying within this win- tween the silicon matrix and the SiO, precipitate. It was
dow are effective recombination centers; those lying out- shown that this is the case for Czochralski silicon in which
side are not. As the resistivity is lowered, the window is SiO, precipitates were intentionally created [ 161. Similar
widened and the lifetime decreases. No new defect levels results have been obtained for dendritic web silicon, in
are associated with the additional dopant atoms as such, that the minority-carrier diffusion length in the base of
but pre-existing defect levels are simply exposed when solar cells was found to increase as a result of hydrogen
the doping concentration is increased.
ion implantation [ 171. This increase may be attributed to
In the situation described above, the position of the a passivation of the defect states associated with the siliFermi level is changed by changing the dopant concentra- con-precipitate interface, along with a passivation of postion. The position of the Fermi level in the bandgap can sible defect states associated with the dislocation core italso be changed by temperature. It has been reported that self.
In order to simulate a continuous distribution of defect
the lifetime of minority carriers in the base of p-n junction
solar cells increases as the temperature is raised from 77 levels in the bandgap, a set of 10 discrete levels was as-
-.
1 -
MEIER
et a/. :
EFFECT OF DOPING DENSITY AND INJECTION LEVEL
r
Fig. 2. Set of 10 discrete defect levels in the bandgap used to simulate a
continuous distribution of such states for calculation of minority-carrier
lifetime using Shockley-Read-Hall theory.
sumed, as shown in Fig. 2. The levels were spaced 0.1
eV apart. Since the interface states associated with the
up po
"=
+ A p + ni exp
10"](cm)
-3
defect level relative to the Fermi level, is valid under
equilibrium or very low-level injection conditions. However, a solar cell operates under steady state conditions
which may differ significantly from those at equilibrium.
The nonequilibrium Shockley-Read-Hall theory [2 11,
[22] must then be used to determine lifetime as a function
of doping density and the density of carriers in excess of
the equilibrium density. The lifetime here is the lifetime
of the excess carriers (both electrons and holes), and is the
same as the minority-carrier lifetime.
The rate ( U ) at which volume electron-hole recombination occurs for a single defect level is given by the
Shockley-Read-Hall expression
(EikE')]
- +
a,[no
planar Si0,-Si interface have a "U-shaped" distribution,
a parabolic distribution was assumed for these defect levels in web cells. An expression describing the concentration of each of the assumed defect levels is
+ [1 x
73
(2)
where Et - E, is the energy (in electronvolts) of a particular defect level relative to the intrinsic energy level, and
Nt is the concentration of that defect level (in reciprocal
cubic centimeters). From (2) and Fig. 2 , the concentration of an individual defect level ranges from 1.25 x 10"
cm-3 near midgap to 2.12 x 10" near the band edges.
The states in the upper half of the bandgap were taken
to be acceptor-like, with capture cross sections of 5 X
cm2 for holes. For
cm2 for electrons and 5 X
acceptor-like states, ap is much greater than a, because
such a state is assumed to carry a negative charge when
occupied by an electron and to be neutral when not occupied by an electron. Similarly, the states in the lower
half of the bandgap were taken to be donor-like, with capture cross sections of 5 X
cm2 for electrons and 5
x
cm2 for holes. Donor-like states are taken to be
neutral when occupied by an electron and positively
charged when not occupied by an electron. Thus, up is
assumed to be much less than u, for these states.
The values for capture cross sections and for defect level
density were chosen to be consistent with literature values
[18]-[20] and also to permit a reasonably good match between measured and calculated values of spectral quantum efficiency for bifacial cells under low-level illumination. Three different base resistivities were considered
for the bifacial cells in arriving at the choice of parameters.
C. Effect of Injection Level on Lifetime
The qualitative description of lifetime as a function of
doping density given earlier, based on the location of the
+ An + niexp
(3)
where the symbols have the following meaning:
are the capture cross sections for electrons,
holes (in square centimeters);
is the thermal velocity of carriers (in centimeters per second);
is the concentration of traps (in reciprocal cubic centimeters );
are the equilibrium concentrations of electrons, holes (in reciprocal cubic centimeters );
are the excess concentrations of electrons,
holes (in reciprocal cubic centimeters);
is the intrinsic carrier concentration (in reciprocal cubic centimeters);
is the intrinsic energy level (in electronvolts);
is the trap energy level (in electronvolts);
is Boltzmann's constant ( in electronvolts per
degree Kelvin); and
is the absolute temperature (in degrees Kelvin).
For light-generated excess carriers, An = A p .
To maintain a steady-state recombination rate ( U ) ,
during a certain period of time ( r )the excess carriers ( A n )
must be replaced. Here, r is the lifetime of the excess
carriers. The local lifetime of excess electrons ( r , ( x ) ) is
given by
In (4),the recombination rate ( U ( x ) )is determined from
(3) over a volume sufficiently small that the excess carrier
density ( A n ( x ) ) can be considered constant. Over this
small volume the local lifetime ( r , ( x ) ) is constant.
For multiple defect levels, the total recombination rate
is assumed to be the sum of the recombination rates from
the individual levels. Hence, the lifetime for excess carriers is the ratio of the excess carrier density to the total
recombination rate. For the specific case of electrons, this
14
lifetime is expressed as
7JX)
=
An(.)
~
c Ui(X)'
(5)
A multistep recombination process, in which a carrier
transits from one defect level to another before recombining, is neglected in this analysis. This approach is valid
provided the average spatial distance assoSiated with two
defect levels is sufficiently large ( >50 A ) that the two
corresponding wavefunctions do not overlap. Assuming
an interface state density of 10I2 cmP2 at an Si-Si02 interface, which is the worst case for thermally grown oxides, the average distance ass9ciated with the two states
is estimated as more than 100 A. This distance is too great
for multistep recombination to occur.
lor
$
-
:. :
;
i
kcerr Carrier concentration cm-?
D. Calculations of Lifetime
The excess carrier lifetime for the parabolic distribution
of levels given in Fig. 2 and in (2) was calculated from
(3) to ( 5 ) . This lifetime is plotted as a function of excess
carrier concentration in Fig. 3 , with substrate doping density as a parameter. An estimate of the excess carrier concentration at some insolation level can be made. For example, at 1 sun the flux of photons with wavelengths
between 0.4 and 1.1 pm ( 4 ) is 1017 cmP2 s-' [23].
For a cell 100 pm in thickness ( t ) , a volume generation
rate (g,) of l O I 9 e-h pairs/(cm3 s ) is obtained. The
excess carrier concentration is then expressed as
-
-
An
gop7
(+/t)r.
(6)
A lifetime of 1 ps thus corresponds to an excess carrier
concentration of
1013 cm-3 at 1-sun illumination, according to (6).
Note from Fig. 3 that the calculated values of minoritycarrier lifetime range from 0.7 to 60 ps. The low-level
injection lifetime (excess carrier concentration < IO"
~ m - increases
~ )
as the doping density decreases, as expected. This lifetime varied from 0.7 ps at a doping density of lOI7 cm-3 to 6 ps at a doping density of lOI3
~ m - ~ .
The calculated lifetime also increases significantly with
excess carrier concentration, and approaches an asymptotic value at high concentration levels. This is consistent
with reports of an increase in lifetime with light intensity
in silicon material [24] and in solar cells [25], [26]. Such
an increase results from "trap saturation." While one minority carrier is trapped by a defect level, other minority
carriers can stream by without danger of being captured.
At an injection level associated with 1-sun illumination
(excess carrier concentration
lOI3 to lOI4 crnp3), the
calculated lifetime varied considerably from 0.7 ps at l O I 7
cm-3 doping to 52 ps at 1013cmP3doping. These lifetime
values agree with typical values measured by the opencircuit voltage decay method for dendritic web solar cells
over the corresponding range of resistivities. This variation in lifetime is due solely to the dependence of the electron occupancy of the defect levels on doping concentration.
=
=
-
-
Fig. 3. Calculated lifetimes for silicon with a parabolic distribution of defect levels, as given in Fig. 2 and in (2).
The largest value of lifetime is reached when the excess
carrier concentration is approximately equal to the doping
density. The curve for l O I 3 cmP3doping first peaks at an
excess carrier concentration of lOI3 cm-3 and then decreases gradually toward the asymptotic value. This decrease is associated with defect states near the band edges
entering into the recombination activity as more and more
excess carriers are present in the material.
-
111.
BIFACIAL SOLAR CELL
MODELING
The contribution to the total short-circuit current density associated with light that is absorbed in the base of
the bifacial cell has been calculated for several different
illumination levels and for several different base resistivities. The cell was assumed to have an n+-p-p+ structure,
a junction depth ( n+-p or p'-p) of 0.2 pm, and an effective back-surface recombination velocity of 100 cm/s.
Calculations were made for back surface (p'-p) illumination as well as for front surface ( n + - p ) illumination.
The calculation was carried out by solving the steadystate continuity equation for the spatially dependent excess carrier concentration [ A n ( A, x ) ], assuming singlewavelength ( A ) illumination and carrier movement by diffusion only. For front illumination this equation is given
by
exp [ - c Y ( x ) x ] - A n ( A, x ) = 0
(7)
7,
where D, is the diffusion constant for electrons, x is the
distance into the base of the cell measured relative to the
edge of the depletion region in the base, CY(A ) is the absorption coefficient for light of wavelength X,F ( A ) is the
flux of photons at wavelength X incident upon the base
layer, and r n ( x ) is the lifetime of minority-carrier elec-
1
1
1 -
MEIER et ul. : EFFECT OF DOPING DENSITY AND INJECTION LEVEL
trons. For back illumination, a similar equation applies:
75
TABLE I
CALCULATED
VALUES
OF SHORT-CIRCUIT
CURRENT
DENSITY
UNDERFRONT
A N D BACK
ILLUMINATION
AS A FUNCTION
OF LIGHT
INTENSITYFOR THREE
BASEDOPING
CELLS WITH DIFFERENT
a)
where H is the thickness of the base of the cell.
Equation (7) or (8) cannot be solved analytically for
A n ( X, x ) because the lifetime depends on A n ( x ) , as
shown in Fig. 3 . Here, A n ( x ) is the total excess carrier
concentration at position x , and is obtained by summing
the contributions [ A n ( A, x ) 3 from all wavelengths in the
spectrum. In order to solve (7) or (8), an effective lifetime
(which is constant) was obtained. The appropriate equation (7) or (8) was then solved iteratively, with the value
of the lifetime adjusted after each iteration. The continuity equation was solved over the base region with the usual
short-circuit current boundary conditions applied at the
edge of the depletion region ( A n = 0 ) and at the p-pf
back junction ( D , ( d A n / d u ) = - s , A n ) . Here, s, is the
effective surface recombination velocity (100 cm/s) at
the p-side of the p-p+ junction.
The iterative sequence then proceeds as follows. First,
A n ( x ) is calculated using the constant low-level injection
lifetime that is appropriate for the particular doping density. Using the values obtained for A n (x), a new lifetime
is calculated at each point in the base using (3) to (5). An
average, or effective, lifetime is then determined with the
optical generation rate G ( x ) as a weighting function.
Here, G ( x ) is the total generation rate at position x for
all wavelengths. The effective lifetime is then given by
S
(7,)
=
~ ( x 7 )n ( x )
s
(9)
G(xW
.
Using this effective lifetime, which is constant, (7) or (8)
is resolved for A n ( X, x ) . By summing over all wavelengths, a new expression for A n ( x ) is obtained, and this
leads to a new expression for r , ( x ) . An effective (constant) lifetime is then determined from (9), as before.
The short-circuit current density for a given wavelength
is determined by evaluating
at the edge of the depletion region. The total value of J,,
is obtained by summing the contributions from all wavelengths in the spectrum. This sequence of recalculating
An ( x ) , ( r, ), and .I,
is,repeated until J,, converges.
IV. RESULTS
A . Short-circuit Current Calculations and
Measurements
The results of the calculations are given in Table I at
five different intensity levels for each of the three bifacial
-.
Base Doping:
6.0 X 1014
Thickness:
130 p
Light Intensity
(mw/cm2)
100.
34.2
10.9
0.813
0.159
b)
Base Doping:
Thickness:
100.
34.2
10.8
0.913
0.158
c)
Base Doping:
Thickness:
100.
34.2
10.9
0.913
0.159
(22 n-cm, p-type)
Jsc (front)
(d/cm2)
30.0
10.2
3.24
0.271
0.0471
2.0 x
150 p
28.2
9.85
3.17
0.265
0.0462
Jsc (back)
(d/cm2)
25.7
7.33
1.82
0.121
0.0206
cm-3 ( 6 . 7
n-a,
Jsc (back)/Jsc (front)
0.856
0.720
0.564
0.447
0.437
p-type)
16.3
3.85
1.02
0.0764
0.0132
0.557
0.397
0.322
0.288
0.286
3 . 0 x lo1’ cm-3 (0.50 0-cm, p-type)
160 p
27.4
9.36
2.98
0.250
0.0435
2.86
0.857
0.298
0.0248
0.00432
0.108
0.102
0.100
0.0992
0.0991
Notes:
1.
2.
3.
4.
Back surface recombination velocity is 100 cm/sec
AM1.5 spectrum assumed
Contribution o Jsc fro%emitter is ‘gnored
Nt = (1 x l0”)(Et - Ei) + (1 X lo1*) for 10 evenly-spaced levels
cells. The calculations were carried out assuming an
AM1.5 spectrum, and a parabolic distribution of defect
levels as described in Fig. 2 and in (2). The doping density in the base of the bifacial cells ranged from 6.0 X
1014 to 3.0 X 10l6 cm-3 in the calculations. These calculated values are to be compared with the measured
short-circuit current densities for the p-base cells that are
given in Table 11. These were made with the aid of neutral
density filters from Melles-Griot with measured transmissivities of 34.2, 10.9, 0.913, and 0.159 percent.
Note that the calculated and measured ratios
J,, (back) / J s c(front) decrease as the illumination level
decreases. This is because the lifetime is enhanced near
the back of the cell under back illumination when the excess carrier concentration is comparable to or greater than
the doping density, as indicated in Fig. 3. This enhancement occurs primarily near the back surface because the
light intensity decreases exponentially with depth into the
silicon. The enhanced lifetime aids in the transport of a
significant fraction of the carriers away from the back surface and toward the front p-n junction. When the front is
illuminated at the same intensity, a similar lifetime enhancement occurs near the front surface. This enhancement is of lesser consequence, however, because the carriers are already close to the junction and do not need an
enhancement in lifetime to be collected.
The measured data of Table I1 agree qualitatively with
the calculated values of Table I. This indicates that the
assumptions on which the calculations are based are con-
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76
IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. ED-35, NO. I , JANUARY 1988
TABLE I1
MEASURED
VALUES OF SHORT-CIRCUIT
CURRENT
DENSITY
UNDERFRONT
AND BACK
ILLUMINATION AS A FUNCTION
OF LIGHT
INTENSITY FOR THREE
WEBSILICON
BIFACIAL
CELLS
DENDRITIC
Cell 7C (22 n-cm, 130 p thick)
a)
Light Intensity
(mw/cm21
Jsc (front)
(d/cm21
Jsc (back)
(d/cm21
100.
34.2
10.9
0.913
0.159
33.3
11.3
3.82
0.340
0.0595
30.8
10.2
3.40
0.280
0.0439
0.926
0.901
0.888
0.825
0.738
t
Cell 68C ( 6 . 4 0-cm, 150 pm thick)
b)
100.
34.2
10.9
0.913
0.159
31.2
10.2
3.44
0.290
0.0434
0.856
0.818
0.767
0.592
0.485
26.7
8.40
2.64
0.172
0.0210
rm
m
rn
7m
Wawlenglh I nnome(trs)
wo
im,
111
Fig. 4. Measured internal quantum efficiency for a bifacial cell fabricated
from a dendritic web silicon substrate with 22-fl . cm resistivity (Cell
7C).
Cell 37C (0.47 n-cm, 160 pm thick)
c)
100.
34.2
10.9
0.913
0.159
27.2
9.01
3.05
0.266
0.0390
0.154
0.131
0.119
0.122
0.112
4.19
1.18
0.363
0.0324
0.0044
Front Illumination
~
Notes:
1.
2.
3.
.,
Exposed cell area during measurement was
7 cut2.
Ay1.5 spectrum.
Light Intensity attenuated by neutral density filters.
a
cell 68 c
E
5
sistent with the observed trend. Note in particular that the
ratio J,, (back) /Is,( front) is low and relatively constant
with light intensity for the cell with the most heavily doped
base, and that the ratio becomes larger and more sensitive
to intensity as the base doping is decreased. From the lifetime curves of Fig. 3, this is the expected behavior. Because the density and distribution of extended defects
(primarily oxide precipitates decorating dislocation cores)
varies from crystal to crystal in web silicon, quantitative
agreement between measured values and values calculated from a fixed distribution of defect levels cannot be
expected.
B. Internal Quantum Eflciency Calculations and
Measurements
The internal quantum efficiency has also been measured
as a function of wavelength under either front or back illumination for dendritic web cells 7C (22 il * cm), 68C
(6.4 Q * cm), and 37C (0.47 il cm). The results are
given in Figs. 4, 5, and 6, respectively. These measurements were made using a monochromator and a light
source of modest intensity, so very low-level injection
conditions ( 0.001 sun) prevailed.
Calculations of the internal quantum efficiency were
made for the doping levels of interest. The variation of
lifetime with doping density and excess carrier concentration, as illustrated in Fig. 3, was incorporated as described previously. The illumination level was taken to be
0.1 mW/cm2 (0.001 sun) to match the level used in the
measurements. Shown in Fig. 7 are the results of the calculation for a doping density of 2.0 x lOI5 cm-3 (corresponding to web cell 68C) for both front and back illu-
-
-
Base Resistivity: 64 R-crn ( Baron)
Thickness: l M p m
Electron Diffusion Length: 89 pm
40
t
Wavelength I n a n m e t e r s l
Fig. 5. Measured internal quantum efficiency for a bifacial cell fabricated
from a dendritic web silicon substrate with 6.4-fl . cm resistivity (Cell
68C).
I00 ,
L
I
,
I
,
I
,
i
,
Bp"a
front Illumination
j-/
E
60-
cell 31c
Base Resistivity: 0.47 R-cm IBaron1
Thickness: l W p m
Electron Dlffusion Length: 36 prn
E
-E,
40-
a -
a
M-
0
41
m
m
11
BM
Wavelength ( nanometers)
wa
Im,
1100
Fig. 6. Measured internal quantum efficiency for a bifacial cell fabricated
from a dendritic web silicon substrate with 0.47-R . cm resistivity (Cell
37C).
mination with 0.001-sun intensity. These are in qualitative
agreement with measured results given in Fig. 5 . The effect of increasing the light intensity from 0.001 to 1 sun
on the calculated back-illuminated quantum efficiency is
given in Fig. 8 for the three doping levels of interest. Note
the significant increase in quantum efficiency with light
T
- -
1
1'
71
MEIER et a / .: EFFECT OF DOPING DENSITY A N D INJECTION LEVEL
5100
G
-s
n
I
-
I
I
I
I
I
I
I
I
I
I
I
I
I
-
/
-
80
I
Front Illumination
a
l
E 60-
6
2
-
-
-
40Back Illumination
m
a 123-
-
\
L
c
5 0
1
400
l
500
1
1
1
1
1
1
1
1
1
600 700 800 900
Wavelength I Nanometers)
1
1
1
loo0 1100
Base Doping : 2 o x
cm-3 ( p-type)
Thickness: 150 p m
Back SRV: 100 cmlsec
Intensity: 0.001 sun
y ( E , )= [ 1x
( E , )2 + 1 x
I cm-3
Fig. 7. Calculated internal quantum efficiency under front and back ilIlumination for 0.001-sun intensity with material parameters as shown.
"t
40
I
400
I
Ism7
500
7m
m 9 ~ ) lax,
Wavelength f Nanometers)
600
nm
Fig. 8. Calculated internal quantum efficiency under back illumination
(0.001 sun and 1 sun) for three different base resistivities, all having the
same quadratic distribution of defect levels.
intensity for the more lightly doped base, and the relative
insensitivity to light intensity for the more heavily doped
base.
V . CONCLUSION
The measured short-circuit current density in bifacial
dendritic web silicon solar cells has been found to de-
crease with decreasing base resistivity, particularly under
back illumination. In addition, the ratio of short-circuit
current under back illumination to short-circuit current
under front illumination was observed to vary with light
intensity. These observations reflect the fact that the minority-carrier lifetime in the base of these cells is a function of the base resistivity and the illumination level. The
dopant was assumed to play only an indirect role in determining lifetime. The formation of electrically active
complexes involving the dopant atom are not thought to
be a significant factor in explaining the observed decrease
in lifetime as the doping density increases because DLTS
measurements on web cells have failed to indicate any
systematic discrete deep levels even for depths up to 60
pm. Instead, this decrease in lifetime is shown to follow
from a distribution of defect levels in the bandgap. These
levels are a consequence of extended defects that have
been observed in the web material. The extended defects
are oxide precipitates and the dislocation cores that they
decorate. The dopant, then, acts only in the indirect role
of moving the Fermi level over an existing background
distribution of defect levels that arise from the extended
defects.
A parabolic distribution of defect levels in the bandgap
was assumed, and minority-carrier lifetime was calculated as a function of doping density and excess carrier
concentration (illumination level) using the ShockleyRead-Hall theory. The short-circuit current densities that
were calculated using these lifetimes agreed reasonably
well with measured values for bifacial dendritic web silicon solar cells. The measurements were made over a
range of doping densities ( 6 x 1014 to 3 x 10l6(31-r~~
)
and illumination levels (0.001 to 1 sun) for both front and
back illumination of the bifacial cells. The qualitative
agreement over a variety of conditions that results from a
single choice of defect level distribution lends credibility
to this approach.
The implication of these calculations is that if a distribution of defect levels within the bandgap exists, then the
higher resistivity material will be less affected by their
presence than will the low-resistivity material. In order to
obtain low-resistivity material ( -0.2 Q * cm) with adequate lifetime to produce high-efficiency cells, the density
of such defects in the bandgap must be kept to a low value.
Apparently, this is the case in high-quality FZ silicon.
Solar cells fabricated using high-resistivity substrates, on
the other hand. are more tolerant of such defect levels.
The interplay of extended defects, doping density, and
injection level is also important in any device in which
minority-carrier lifetime is an important parameter. Examples include heavily doped emitters in bipolar devices
and solar cells, substrates for high-voltage power devices,
and oxygen-precipitated silicon substrates to inhibit
latchup in CMOS devices. In addition, the tendency of
lifetime to increase with injection level for a distribution
of defect levels in the bandgap is expected to be of interest
to those working in the field of concentrator solar cells.
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78
IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. ED-35, NO. I, JANUARY 1988
ACKNOWLEDGEMENT
The authors gratefully acknowledge J. B. McNally for
sample preparation, F. S . Youngk and L. E. Hohn for
measurements, P. A. Palaschak for assistance in the computer calculations, and G . S. Law for document preparation.
[21]
[22]
[23]
[24]
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[2] R. B. Campbell and D. L. Meier, “The fabrication and testing of
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[3] B. Ross, “Survey of literature on minority carrier lifetimes in silicon
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[5] M. A. Green, A. W. Blakers, S . R. Wenham, S. Narayanan, M. R.
Willison, M. Taouk, and T. Spitalak, “Improvements in silicon solar
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[7] A. Rohatgi and P. Rai-Choudhury, “An approach toward 20-percentefficient silicon solar cells,” IEEE Trans. Electron Devices, vol. ED33, pp. 1, 1986.
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[lo] D. K. Bhattacharya, A. Mansingh, and P. Swarup, “Determination
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Daniel L. Meier (M’80) received the B.S. degree
in physics from St. Vincent College in 1969, the
M.S. degree in physics from Carnegie-Mellon
University in 1971, and the Ph.D. degree in solidstate physics from Carnegie-Mellon University in
1975. His Ph.D. dissertation dealt with magnetic
phase transitions in electrically insulating crystals
at very low temperatures and in high magnetic
fields.
From 1975 until 1980, he was employed as a
Research Physicist at Carnegie-Mellon where he
worked on problems associated with extracting energy from the temperature gradient in the ocean (OTEC). In 1980, he joined Westinghouse as a
Senior Engineer where he has contributed to the design, fabrication, and
characterization of semiconductor devices, particularly silicon solar cells.
In addition to making an expenmental study of semiconductor contacts, he
has investigated the effects of low-energy hydrogen ion implantation on
dendritic web silicon solar cells, and has camed out a study of the electncal
activity of defects in web solar cells. Recent research interests include the
study of radiation damage in GaAs and InP solar cells. He has authored or
co-authored over 30 technical papers.
Dr. Meier is a member of the IEEE Electron Devices Society.
*
Jeong-Mo Hwang (S’84-M’85) was born in Korea. He received the B.E. degree in electronics
engineering from Pusan National University,
Pusan, Korea, in 1974, the M.S. degree in electrical engineering from the Korea Advanced Institute of Science, Seoul, Korea, in 1976, and the
Ph.D. degree in electrical engineering from Arizona State University, Tempe, in 1986. His doctoral research was on oxygen-related defects in
silicon, with an emphasis on their formation and
their influence on electrical properties of material.
T
1
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79
MEIER et al. : EFFECT OF DOPING DENSITY AND INJECTION LEVEL
From 1976 to 1979, he was with the Central Research Laboratory of
Gold Star Company, Seoul, where he was involved in microprocessor-based
system design. From 1979 to 1980, he taught undergraduate courses at the
Electronics Engineering Department of Kyungpook National University,
Daegu, Korea. In 1986, after finishing his Ph.D. work, he joined the Westinghouse R&D Center, Pittsburgh, PA, where he has been involved in the
modeling of bifacial solar cells and the characterization of charge-coupled
devices to investigate process-induced bulk and surface traps. His current
research interests are concerned with the optical and electrical characterization of silicon-on-insulator (SOI) structures, particularly, SO1 formed by
high-dose oxygen implantation (SIMOX), to investigate defects in both silicon overlayer and buried oxide.
Dr. Hwang is a member of Sigma Xi and Phi Kappa Phi.
Robert B. Campbell received the B.Sc. degree
from Carnegie-Mellon University in 1951 and the
Ph.D. degree from Temple University in 1959
After several years of research in precipitating
ferromagnetic systems, he spent a number of years
studying the growth of silicon carbide and device
fabrication from this high-temperature semiconductor material. He was a member of an intemational committee on silicon carbide research. For
the last ten years, he has been involved in the research and development of photovoltaic cells from
dendritic web silicon. He is currently Manager, Photovoltaic Process Development, at the Advanced Energy Systems Division of Westinghouse
1
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