1. Study of C–V characteristics in thin n+
-p-p+
silicon solar cells and induced
junction n-p-p+
cell structures
Sanjai Kumar, Vikash Sareen, Neha Batra, P.K. Singh n
National Physical Laboratory, Dr. K.S. Krishnan Road, New Delhi 110012, India
a r t i c l e i n f o
Article history:
Received 29 June 2009
Received in revised form
23 February 2010
Accepted 16 March 2010
Available online 27 April 2010
Keywords:
Silicon solar cell
Induced structure
Impedance spectrum
Capacitance–voltage
a b s t r a c t
Capacitance–voltage (C–V) measurements were carried out on conventional n+
-p-p+
structure based
silicon solar cells (SSC) of different thicknesses (40–300 mm) and on induced junction n+
-p-p+
structures (IJS) under dark at room temperature. The capacitance is determined from the best fit of the
measured data. It is shown that the capacitance under reverse and forward bias condition can be
divided into two distinct regions, which are correlated to the quality of the junction and effectiveness
of back surface field (BSF). It is found that the IJS has shallow junction and better BSF than the
conventional solar cells.
& 2010 Elsevier B.V. All rights reserved.
1. Introduction
Capacitance–voltage (C-V) measurements are important for
the study of semiconductor devices and solar cells. Generally
capacitance is measured in the reversed bias (Mott-Schottky)
condition to determine barrier potential and doping
concentration. But vital information about the device can be
obtained by measuring capacitance in both reverse and forward
bias conditions, where it is referred as transition (Ct) and diffusion
(Cd) capacitances, respectively. Transition capacitance is caused
by the separation of charges in the space charge region and is
given by [1,2]
Ct ¼
dQ
dVa

9. ¼
b
VbiÀVað Þ1=2
ð1Þ
where Va is the applied voltage, Vbi is the junction voltage and b is
a constant. The value of the junction voltage depends on the
doping levels of the two regions and is defined as
Vbi ¼
kT
e
ln
NaNd
n2
i
" #
, b ¼ A
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
eNe0er
2
r
,
1
N
¼
1
Na
þ
1
Nd
where A is the device area, Na and Nd are the doping concentration
in p and n regions, respectively. er and eo are the relative
permittivity of material and that of free space. ni is the intrinsic
concentration, e is electronic charge, k is the Boltzmann constant
and T is the temperature. It is clear from Eq. (1) that a plot of 1/C2
versus Va should be a straight line in the case of one-sided abrupt
junction. The slope of the straight line gives the impurity
concentration and it is extrapolation of the line to 1/C2
¼0 gives
the value of Vbi.
On the other hand, under forward bias, diffusion capacitance is
defined as [3,4].
Cd ¼
te
2kT
I0exp
eVa
nkT
for ot51 ð2Þ
where t is minority carrier lifetime of the material, I0 is reverse
saturation current, o is angular frequency and n is diode ideality
factor.
It is obvious from Eq. (2) that Cd is directly related to the
carrier lifetime, reverse saturation current and is proportional to
the term exp(eVa/nKT). Therefore, Cd (at low frequencies under
forward bias) is especially important to get information about a
number of parameters related with p–n junction. Eq. (2) can be
rewritten as
lnðCdÞ ¼ ln
te
2kT
I0
þ
e
nkT
Va ð3Þ
Hence, plot of Cd on logarithmic scale with Va has linear
dependence from which information about the minority carrier
lifetime and diode ideality factor (n) of the device can be deduced.
In this paper we report C–V measurements on induced
junction n-p-p+
and conventional n+
-p-p+
silicon solar cells of
different thicknesses. Capacitance of the device is deduced from
the complex plane impedance spectrum described by the
ARTICLE IN PRESS
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journal homepage: www.elsevier.com/locate/solmat
Solar Energy Materials Solar Cells
0927-0248/$ - see front matter 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.solmat.2010.03.019
n
Corresponding author. Tel.: +91 11 45608588; Fax: +91 1145609310
E-mail address: pksingh@nplindia.org (P. K. Singh).
Solar Energy Materials Solar Cells 94 (2010) 1469–1472

10. ARTICLE IN PRESS
following relation.
ZðoÞ ¼ Rs þ
Xm
i ¼ 1
Ri
1þðoRiCiÞ2
þj
Xm
i ¼ 1
oCiR2
i
1þðoRiCiÞ2
ð4Þ
where m is the number of RC network operative in the device and
ti ¼RiCi. In the present case maximum m¼3 is considered wherein
t1, t2 and t3 are the time constants, which correspond to the two
interfaces and the bulk. Rs represents the series resistance and the
second and third terms on right hand side of eq. (4) are real (Z ’)
and imaginary (Z ’’) components of Z. The value of Z ’ between
lower and upper frequency bounds has contributions of various
resistive components. A good fitting of the experimental data
could be obtained using the above relation involving a single RC
network (n¼1) under reverse bias condition. On the other hand, a
more complicated RC circuit consisting a number of RC networks
connected in series is required under forward bias as well as to
zero bias conditions as will be shown later.
2. Experimental details
In the present study, both side chemically–mechanically
polished p-type 3 O cm resistivity /100S CZ silicon wafers were
used. The minority carrier lifetime in the wafers was measured by
using microwave detected photoconductive decay (m-PCD) sys-
tem from Semilab (Model WT2000 PV) prior to the device
formation. The effective carrier lifetime in the material was found
5–6 ms (without surface passivation). In order to make devices of
different thicknesses, thinning of the wafers to the desired
thickness was done by chemical etching. The silicon solar cells
of different thicknesses were fabricated by a process protocol, the
important steps of which are given below.
Thinning of wafer: in 20% NaOH solution at 90 1C for different
time durations to get desired thickness.
Wafer cleaning: by RCA process.
Junction formation: by phosphorous solid diffusion source at
850 1C for 60 min.
BSF formation: by depositing thin aluminum. Annealing at
750 1C for 30 min. followed by removal of extra Al from the
back side.
Back contact: 2 mm thick layer of Al by thermal deposition.
Front contact: deposition Ti/Pd/Ag thin films using a shadow
mask and contact sintering in forming gas.
On the other hand, the induced (n-p-p+) structure based cells
were formed by deposition of semitransparent layers of low and
high work function metals, i.e., aluminum of thickness $1000 ˚A
on one and $300 A thick palladium on the other side of the
silicon wafers. The two metal films create inversion and
accumulation layers on p-type silicon, respectively, thereby
resulting in n-front and p+
-back regions as described in Ref. [5].
Therefore, n-p-p+ structure is formed without involving any high
temperature process step.
The C–V measurements on induced junction n-p-p+ structure (IJS)
and silicon solar cells (SSC) of different thicknesses were carried out
by using a system consisting of frequency response analyzer (FRA,
Solartron Model 1260), electro–chemical interface (ECI, Solartron
Model 1287A); a computer with a data acquisition and Z-plot
software [6]. All the measurements were carried out in dark at 300 K.
3. Results and discussion
The solar cells of different thicknesses (300, 150, 100 and
40 mm) were fabricated in the same batch using the process
protocol described in the preceding section. No surface texture or
antireflection coating was given to reduce reflection losses.
The material and device parameters are listed in Table 1.
The characteristics of a reference silicon solar cell used for the
calibration are also given in the same table.
The impedance spectra (in complex plane) of silicon solar
cells of different thicknesses under dark at zero bias condition
are shown in Fig. 1. As the measured impedance spectra have the
shape of nearly perfect semicircles indicating that each device
has a single time (t¼RC) constant and the data can be fitted into
a single RC network lumped to a series resistance (Rs) of the
device. The values of the resistances and capacitances are
determined by curve fitting using Z-plot software [6] and the
deduced values are listed in Table 2. The impedance
measurements on all samples were carried out under reverse
and forward bias conditions. Impedance curves for cells of
different thicknesses under reverse bias at À0.5 V and forward
bias at open circuit voltage (Voc value is determined by I-V
characteristics at AM1.5 and are given in Table 1) are shown in
the insets of Fig. 1. The values of the series resistances (Rs)
obtained from the shift of the impedance curves on the real axis
are found quite close to the values (0.4–0.6 O) deduced from the
illuminated I–V characteristics and also by using the procedure
defined in [7].
The best fit values (with experimental data) of capacitance
at different bias voltages (in forward and reversed bias
conditions) are determined for the cells of different thicknesses.
The ln(C) vs V curves are plotted in Fig. 2 which can be divided
into two distinct regions, i.e., one for À1.0oVa r0.2 V and the
other for Va 40.2V. In the region 1, i.e., under reverse and low
forward bias, the capacitance is predominantly governed by the
transition capacitance and is representative of junction
properties. The slope of the curves is found practically the
same (i.e., $0.4 mF/V cm2
). This is indicative of fact that all the
cells have almost the same junction depth (xj) as expected in
the devices processed in the same batch. The inset of Fig. 2
shows 1/C2
–V curves for all the cells (under forward bias)
wherein the slopes and their intersections on the abscissa give
the doping density (Nd) and Vbi respectivily. The Nd values are
found in the range of 6.8–7.6 Â 1015
cm-3
and the values of
Vbi À2 kT/q are between 0.52 and 0.54 eV, which corresponds to
Vbi ¼0.57–0.59 eV. As expected the difference in these
parameters is not significant.
Region 2, i.e., under forward bias (Va 40.2 V) the capacitance
is dominantly diffusion capacitance that increases exponen-
tially with bias voltage. It is clear from Fig. 2 that the slope
increases rapidly with the reduction in thickness. It can be
utilized for the determination of diode ideality factor and which
is found to be 2.4 in the $300 mm cell and close to 1 in thin
solar cells.
Fig. 3 represents the impedance spectrum of a secondary
reference silicon solar cell of efficiency 10.2% (Voc¼0.58 V,
Jsc¼28.6 mA/cm2
, FF¼0.61) at zero bias and at different forward
bias (insets) up to the open circuit voltage. It is clear from the
curves that all the measured data could be fitted into single
semicircle and the deduced R and C values at zero bias are given in
Table 2. Under forward bias at Voc, impedance values could be
influenced by inductance of the device.
Fig. 4 shows the impedance spectra for the induced junction
structure measured under zero (main figure), À0.5 V reverse
and+0.5 V forward bias conditions (insets). The best fit R and C
values under dark at zero bias are given in Table 2. Under forward
bias, the impedance data (right side inset of Fig. 4) could be fitted
only with a combination of three series connected RC networks
rather than with a single RC network. It is known that the high
frequency end of the spectra represents the bulk [8], hence by
S. Kumar et al. / Solar Energy Materials Solar Cells 94 (2010) 1469–14721470

11. ARTICLE IN PRESS
using the different RC combinations, the bulk and interface
capacitance can be separated out [9].
Fig. 5 shows ln(C) vs. V curves of the IJS along with the results
obtained on 40 mm thick n+
-p-p+
structure silicon solar cell and
the secondary reference silicon solar cell. The value of Ct is less
in the case of IJS compared to conventional silicon solar cell
structures, which is indicative of high barrier height and shallow
junction (xj).
On the other hand, larger value of Cd in the thinner sample is a
direct manifestation of the effectiveness and quality of back
surface field. Its value is still higher in IJS which shows the
effectiveness and superiority of BSF in such structures. The value
of the diode factor is found$1.4 in IJS structure.
4. Conclusions
The impedance spectroscopy technique is used to measure the
capacitance of silicon solar cells of different thicknesses and of
Table 1
The details of the wafers used and the device parameters obtained on the fabricated solar cells of different thicknesses (device area¼18.25 cm2
) and secondary reference
(device area¼4 cm2
) solar cell.
Sample Type Resistivity
(X cm)
Initial wafer
thickness (lm)
Wafer thickness
after etching (lm)
Sheet resistivity
(X/) (Front/back)
Voc (V) Jsc (mA/cm2
) FF g (%)
S-1 p $3.0 310 29575 36.06/18.14 0.571 26.20 0.58 8.67
S-2 p $3.0 315 14575 36.70/18.78 0.569 25.84 0.57 8.38
S-3 p $3.0 308 9575 36.24/17.76 0.566 24.13 0.55 7.64
S-4 p $3.0 312 4575 35.18/17.44 0.562 23.52 0.56 7.63
Reference cell p – – – – 0.588 28.55 0.61 10.20
Fig. 1. Impedance spectra of the solar cells of different (300, 150, 100 and 40 mm)
thicknesses at zero bias and insets show spectra under reverse (Vr ¼ À0.5 V) and
forward (Vf ¼Voc) bias under dark. The points are the experimental data and the
lines are the best fit curves.
Table 2
The best fitted values of R, C and Rs for silicon solar cells of different thicknesses
(300, 150, 100 and 40 mm), secondary reference solar cell along with induced
n-p-p+
junction structure at zero bias under dark. The values in the braces [ ]
represents the % error in the fitting.
Sample Rs (X) R (KX) C (lF)
S-1 0.79[2.73] 1.69[0.27] 0.58[0.26]
S-2 0.78[2.82] 0.99[0.27] 0.59[0.28]
S-3 0.70[1.64] 0.73[1.54] 0.78[1.69]
S-4 0.59[1.33] 278.10[1.16] 0.79[1.08]
Reference cell 0.63[1.00] 2.13[1.81] 0.24[1.21]
IJS 40.8[3.42] 241.10[0.55] 0.016[0.47]
Fig. 2. ln(C) vs. V curves for 300, 150, 100 and 40 mm thick n+
-p-p+
structure
based silicon solar cells along with the best fit lines. The inset shows the CÀ2
vs. V
curves for the cells.
Fig. 3. Impedance spectra of the reference solar cell at different forward (Vf ¼0.0,
0.2, 0.4 and 0.58 V) bias condition under dark. The points are the experimental
data and the lines are the best fit curves.
S. Kumar et al. / Solar Energy Materials Solar Cells 94 (2010) 1469–1472 1471

12. ARTICLE IN PRESS
induced junction based devices. It has been shown that the
capacitance associated with different biasing can be utilized to
gather information related with device and the material. It is
found that thin silicon solar cells show better back surface field
effect compared to the thick silicon solar cell. The induced
junction based n-p-p+
structure can be created by depositing the
different work function metals on the two sides of silicon wafer
(without any heat treatment) and which has an effective back
surface field and shallow junction as compared to conventional
silicon solar cells.
Acknowledgements
We thank Dr. V. Kumar, Director, NPL for his support and one
of the authors S.K. acknowledges the financial support provided
by MNRE, Government of India. The work is supported by CSIR
Supra Institutional project (Grant no. SIP17).
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Fig. 4. Impedance spectra of an induced junction based device under dark and at
reverse (À0.5 V) and forward (+0.5 V) bias conditions. In forward bias the
different theoretical curves obtained with different combinations of RC networks
are presented. The curve C#1 is for the three RC circuits in series. The curve C#2
and C#3 (overlapped) give the value obtained by one and three RC networks in
parallel, respectively. The overlapped curves C#4 and C#5 correspond to two RCs
in series and two parallel RC with one RC series networks, respectively.
Fig. 5. ln(C) vs. V data for induced n-p-p+
junction structure with 40 mm
thick n+
-p-p+
structure based silicon solar cell and secondary reference solar cell
along with the best fit lines.
S. Kumar et al. / Solar Energy Materials Solar Cells 94 (2010) 1469–14721472