AP_06_4.vp

1 Solar cells
A solar cell, or photovoltaic cell, is a semiconductor device

consisting of a large-area P-N junction diode, which in the
presence of sunlight is capable of generating usable electrical
energy. This conversion is called the photovoltaic effect.
When light strikes the P-N junction of a semi-conductor the
absorbed photon energy releases an electron from the P-type
region and moves it to the N-type, creating a hole in the
valence band and producing a current. The main criteria for
the selected solar cell are efficiency and costs. These define
the performance and availability, and they can vary greatly.
This paper deals with problems of efficiency influenced
by imperfections of crystal lattices, and the applicability of
the basic diagnostic method used for determining such
imperfections.

Free charge carriers generated by impacting light (known
as excess carriers) move in all directions from their place of
origin. An important quantity defining the range of a gen-
erated charge carrier is its lifetime, i.e., the time that passes
before an electron meets a hole and recombines. However, as
electrons and holes reach the boundary of the P-N junction,
they are rapidly swept by the electric field of this junction,
either to the P-side (in the case of holes) or to the N-side
(in the case of electrons), generating voltage on the outer
electrodes.

The basic means for lowering carrier lifetimes are lattice
vibrations (phonons) and impurities or, generally speaking,
lattice impurities. As lattice vibrations depend only on crystal
structure and temperature, which are fixed for a specific semi-
conductor material and usage, we will be concerned here with
lattice impurities and their effect on the lifetime of charge
carriers.

2 Problems of carrier trapping and
recombination
Every physical system attempts to achieve so-called ther-

mal equilibrium as soon as possible, as do excess carriers. In
the case of silicon, which is widely used in photovoltaic appli-
cations, the way to achieve thermal equilibrium, is either by
Auger recombination or by capturing free charge carriers on
energy levels that lie in the band that separates the conduc-
tion and valence band (the forbidden band, or the band gap).

These energy levels can originate either from an imper-
fection of the crystal lattice (e.g., dislocation) or from foreign
atoms in some positions of the lattice, or even from complex
crystal defects induced, for example, by radiation.

These imperfections strongly influence the electron and
hole transport through the bulk of the semiconductor device.
They can act either as a trap, where an electron or a hole is
trapped on this level for a certain time, or as a genera-
tion-recombination (G-R) center, where one charge carrier
annihilates with a carrier with the opposite charge.

3 Dark forward I-V characteristics of
solar cells
When conducted under different temperatures, this

method provides many parameters of a solar cell, e.g., the
temperature dependence of the shunt resistance and diode
factor, the energy and concentration of the dominant recom-
bination center, the lifetime of the charge carriers.

The measuring apparatus works with a current source
with a range of 0 to 100 mA. The temperature range is from
approximately 20 °C to 150 °C. The process itself is controlled
by a computer via a serial bus RS232, and the data (values of
voltage and current) is stored on the hard drive.

The dark current of forward biased solar cell IDF can be
expressed by the formula

I A J e
V R I

A J e
V R I

DF
S

�
��

�

�
�

01
1

exp

�

�2
1

kT
V R I

R
�

�
��

�

�
�

�
� �

� S

P
,

(1)

where A stands for the area of the sample, J01 is diffusion
current density, J02 is generation-recombination current den-
sity, �1 and �2 are the diode factors, RS is the series resistance,
RP is the shunt resistance, e is the electric charge, and k is the
Bolzmann constant. The series resistance of large-area solar
cells is small and can be negligible.

The plotted graph of I-V characteristics is divided into
three regions:
1. in the range 0–40 mV, the influence of shunt resistance

dominates and can be calculated; the current through the
cell can be expressed by:

Acta Polytechnica Vol. 46 No. 4/2006

Measurement of Solar Cell Parameters
with Dark Forward I-V Characteristics

J. Salinger

The grade of a solar cell depends mainly on the quality of the starting material. During the production of this material, many impurities are
left in the bulk material and form defect levels in the band-gap, which act as generation-recombination centers or charge carrier traps. These
levels influence the efficiency of solar cells. Therefore knowledge of the parameters of these levels, e.g., energy position, capture cross section
and concentration, is very useful for solar cell engineering. In this paper emphasis is placed on a simple and fast method for obtaining these
parameters, namely measurements of dark characteristics. Preliminary results are introduced, together with the difficulties and limits of this
method.

Keywords: Solar cell, lattice imperfections, lifetime, dark I-V characteristics.

I
V
RDF P

� . (2)

2. in the range 40–300 mV, the generation-recombination
compound of the total current predominates, so it can be
expressed by:

I A J
e V
kT

V
RDF P

�
�

�
��

�

�
�

�
� �02

2
1exp

�
. (3)

3. above 300 mV, the first term in the expression of the total
current (diffusion compound) is dominant, so, by the
curve fitting method, the diffusion saturation current and
the diffusion diode factor can be extracted.

4. Extracting the cell parameters
The generation-recombination current density J02 can be

expressed by:

J
e n di

02 �
�sc

. (4)

This means that the density J02 is inversely proportional to
the lifetime of the charge carriers in the space charge region,
for which in the case of a single trapping level the following
formula can be obtained:

� � �sc p0 n0� �
��

�
�

�

�
�

��

�
�

�

�
exp exp

W W
kT

t i t i . (5)

Here, �p0 and �n0 stand for the lifetime of the minority
carriers in an N-type semiconductor or a P-type semi-conduc-
tor, respectively, Wt is the energy level of the G-R center (or
trap), and Wi is the intrinsic Fermi level [1]. With the knowl-
edge of these lifetimes and the capture cross sections the G-R
center concentration Nt can also be extracted. Thus, to obtain
the maximum parameters of the solar cell band gap structure,
we are interested in the second region of the plotted graph.

Problems can arise from the fact that only a single recom-
bination level can be extracted from this measurement. If
there are, for example, two deep levels of approximately the
same concentration, however, the standard extracting tech-
nique will lead to incorrect values of deep level energy.

To evaluate a large number of parameters, curve fitting is
used. While linear dependence can be fitted without prob-
lems, fitting exponential dependence can be difficult, and the
results may vary strongly with different initial conditions.
These complex conditions may cause errors when simple fit-
ting techniques are applied to them. For example, non-linear
dependence of the diode factor on temperature is observed.

5 Parameters of G-R centers from I-V
measurement
Monocrystalline silicon samples fabricated by the Czoch-

ralsky grown method were used in the measurements. The
dimensions were 102×102 mm, and each sample represented
one batch.

Figs. 1, 2 and 3 show the temperature dependence of
shunt resistance Rp, diode factor �2 and G-R current I02,
respectively.

For maximum efficiency of a solar cell, the highest shunt
resistance is needed. The measured resistances are shown in
Fig. 1. The values of the shunt resistance at the highest tem-

peratures were always lower than at room temperature (RT),
but some differences were found:

26 © Czech Technical University Publishing House http://ctn.cvut.cz/ap/

Acta Polytechnica Vol. 46 No. 4/2006

Fig: 1: Temperature dependence of shunt resistance RP of sam-
ples #1942-02 (�), #20 (�) and LE2 (�)

Fig. 2: Temperature dependence of diode factor �2 of the sam-
ples #1942-02, #20 and LE2

Fig. 3: Temperature dependence of G-R current I02 of samples
#1942-02, #20 and LE2

1. variation of more than one order between samples (e.g.
#1942-02 and LE2) at RT.

2. samples such as #1942-02 showed a small initial increase
in the shunt resistance before a final decrease.

Diode factor �2 showed a decrease with temperature
growth (Fig. 2). In some cases, however, this dependence was
not very clearly confirmed (e.g., sample #20). Diode factors
�2 have to be extracted, so that the G-R current density I02 can
be evaluated more precisely.

The hyperbolic logarithm of the G-R current density as a
function of temperature is shown in Fig. 3. The dependence is
almost linear. For the lowest trapping/generation effect, this
dependence should be weak. This is shown in Fig. 3 for sam-
ple LE2, thus confirming its quality from the shunt resistance
measurement.

The preceding extracted parameters and the obtained
dependences were used for evaluating the energy levels of the
G-R centers and their densities and the lifetime of the excess
charge carriers in the space charge region. These parameters
are shown in Tables 1 and 2 for each sample.

Comparing values of the deep energy levels with mea-
sured efficiencies, we can evaluate the influence of these
levels. The samples of series LE# have almost the same levels
and lifetimes, and also their efficiencies are similar. The same
can be said about samples 1942-02 and 1940-24. Although
the deep energy levels in these two batches are different, their
influences are nearly identical. On the other hand, samples
#10, 20 and 22 show some inhomogeneities in the deep level
energy and the lifetime in the space-charge region. In sample
1x-0883 a very deep level was found and the lowest efficien-
cy was measured. Other parameters of the measured solar
cells, e.g., surface recombination velocity and series resis-
tance, need to be determined for a more precise evaluation of
the influence of deep level influence on efficiency.

Determining the formers of the deep levels, the most
probable lattice imperfections creating deep levels in the
range from 0.2 to 0.37 eV below the conduction band (or
above the valence band), are bounded with boron, carbon and
oxygen atoms, e.g. BiCs �0.29 eV, Bi �0.37 eV and BiOi
�0.20 eV [2]. Here ‘�’ means energy above the valence band
and ‘�‘ means below the conduction band. The deep levels
found in samples #10, 20 and 22 may have been caused
by some special treatment of these samples, e.g. electron

bombardment, which induces vacancy-related defects like VO
�0.18 eV, or carbon related defects like CiCs �0.11 eV [1, 3].

Of course there may be some other explanation in each
sample of electrical behavior, namely the inherence of two or
more energy levels deep within the band gap. This simple
technique cannot give the exact parameters of these centers,
for reasons mentioned above.

6 Conclusion
A proper characterization of the charge carrier lifetime

and the extracting parameters of G-R centers is very useful for
solar cell utilization. and will play a key role in their future de-
velopment. Although the method of dark forward character-
istics has some limitations. as mentioned in the text, this
method is very fast, non-destructive and simple, and can be
used together with other methods as a diagnostic tool in the
development and production of solar cells.

7 Acknowledgments
Research described in the paper was supervised by prof.

V. Benda, FEE CTU in Prague, Department of Electrical
Technology.

References
[1] Tran Hung Quan: Diagnostics of Large Area Crystalline So-

lar Cells. 2003
[2] Adey, J., Jones, R., Briddon, P. R., Goss, J. P.: Optical

and Electrical Activity of Boron Interstitial Defects in Si.
J. Phys.: Condens. Matter, Vol. 15 (2003) S2851–S2858 PII

[3] Schroder, D. K.: Semiconductor Material and Device Char-
acterization. John Wiley & Sons. Inc., New York, 1990

Ing. Jan Salinger
e-mail: salinj1@feld.cvut.cz

Department of Electrical Technology

Czech Technical University in Prague
Faculty of Electrical Engineering
Technická 2
166 27 Praha, Czech Republic

Acta Polytechnica Vol. 46 No. 4/2006

sample# �Wt [eV] Wt1 [eV] Wt2 [eV]

10 0.438 0.122 0.998

20 0.373 0.187 0.933

22 0.341 0.219 0.901

1942-02 0.351 0.209 0.911

1940-24 0.360 0.200 0.920

1x-0883 0.201 0.359 0.761

LE1 0.248 0.312 0.808

LE2 0.212 0.348 0.772

LE5 0.224 0.336 0.784

Table 1: Possible energy levels found in selected samples

sample# �sc (295 K) [s] efficiency [%]

10 2.05×10�8 14.29

20 8.00×10�8 13.43

22 1.83×10�8 14.11

1942-02 1.53×10�8 14.27

1940-24 1.63×10�8 14.15

1x-0883 2.90×10�8 7.44

LE1 1.50×10�8 14.58

LE2 1.10×10�8 14.57

LE5 1.50×10�8 15.03

Table 2: Lifetime of minority charge carriers in the space charge
region. and the solar cell efficiencies of the measured
sample