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King Saud University, Electrical Engineering Department,
PO Box 800, Riyadh 11421, Saudi Arabia
Phone: +(966) 1 467 6751 Fax: +(966) 1 467 6757 E-mail: roshdy@ksu. edu.sa
Abstract. The current-voltage characteristics of solar cells, under illumination and in the dark, represent a very important tool for characterizing the performance of the solar cell.
The PC-ID computer program has been used to analyze the deviation of the dark current - voltage characteristics of p n junction silicon solar cellspom the ideal two-diode model behavior of the cell, namely the appearance of “humps
” in the I-V characteristics.
The effects of the surface recombination velociq, the minority carrier Ifetimes in the base and emitter regions of the solar cell, as well as the temperature dependence of the I-V characteristics have been modeled using PC-ID.
It is shown that the
“ humps
“ in the I-V characteristics arise as a result of recombination within the space-charge region of the solar cell, and occur when conditions for recombination are different fiom the simple assumptions of the Shockley-Read-Hall theov.
The voltage-current characteristics of solar cells is a very important technique for the characterization of solar cells. It gives a good idea about the cell’s parameters and junction characteristics. Different models have been used for the solar cell to describe its experimentally observed behavior. The most popular model for the silicon p-n junction solar cell is the two-diode model [ voltage by :
, in which the cell current is described as a function of cell
Where
101 and Ioz are saturation currents, al and az are the ideality factors for the two diodes, respectively; R, and
Kh are the series and shunt resistances of the cell, IL is the light- generated current, and k is the Boltzmann’s constant. In this equation the terms represent the cell’s diffusion current , , respectively [2]. The analysis of the I-V curves for commercial silicon solar cells showed that the value of az deviates from the theoretically assumed value of 2 , and that by choosing az f 2 the I-V curves could be fitted very well.
The I-V characteristics of some high-efficiency Si solar cells showed however an additional “hump” or shoulder
the lower voltage range ( about 0.1 to 0.5 V) which could not be fitted by varying the value of diode ideality factor, az [ 11.

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The Sah-Noyce-Scockley theory was traditionally used for expressing the recombination currents in Si p-n junctions [3]. In this theory certain assumptions were made in the development of the junction recombination currents. The diode was assumed to be symmetrically doped , the trap level was assumed to be in the middle of the energy gap (E, =
Ei) and the capture cross sections for electrons and holes , c, and cp , equal. These assumptions are not always correct in real world situations, and this leads to the inability of the two-diode model to explain the anomalies in the Si solar cell characteristics,
I-V
In some silicon solar cells it was noticed that the dark current-voltage characteristics displayed an anomalous behavior from ideal two-diode model behavior, showing “humps” in
’ certain regions of the characteristics [4].
In this paper, the PC-1D computer program [ 5 ] is used to analyze the deviation of the dark current
- voltage characteristics of pn junction silicon solar cells from the ideal two- diode model behavior. The effects of the surface recombination velocity the minority carrier lifetimes in the base - and emitter regions of the solar cell, as well as the temperature dependence of the I-V characteristics are modeled using PC-1D. The results show a very good fit with experimental results.
The
cell modeling program PC-ID was used to simulate different physical conditions of the silicon solar cell, and predict the observed measurements. In order to account for imperfections in the cell we assume a thin defected layer is present within the solar cell, and study the effect of varying the position of this defected layer on the solar cell characteristics. Figure (1) shows the structure of the Si solar cell structure modeled. The cell parameters were as follows : cell thickness = 200 ,U m ,junction depth, xj = 0.7 ,U m , = 1 x 10l6 emitter doping: Gaussian profile n-diffusion with a surface concentration of 3 x
cmJ, front surface recombination velocity, Sf = 0 cm-’ ,
= 300
OK.
AR coating was considered. No recombination centers were assumed to be present except at surfaces.
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Figure (2) shows the effect of the minority carrier lifetime in the n- and p-regions on the solar cell’s dark I-V characteristics, both with gap-centered traps and off-center traps. The effect of traps is more pronounced in the case of low quality material (low lifetimes).
Fig. (3) shows the effect of varying the minority carrier lifetime on the dark I-V characteristics. The effect of different minority carrier lifetimes in the n- and p-regions is studied. It is clear from simulation that the effect of eo the solar cell is more pronounced than that of ZC,, , and is dominant at lower base

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> 0.45 V). It is also clear from the figure that “humps” show up in the dark I-V characteristics of the cell under unsymmetrical conditions o f e o and g , assumptions of symmetry of the Shockley-Read-Hall theory [3].
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Figure (4) shows the effect of changes in the trap level, E, -
, on the dark I-V characteristics. We compare trap levels exactly at mid-gap to those at 8kT (0.207 eV) from the middle of the energy gap, both for bulk and rear surface traps. It is noticed from PC-1D simulation that bulk trap levels are the ones that control the dark I-V characteristics, being more detrimental when they are exactly at the center if the energy bandgap.
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Figure (5) shows the effect of changes in the surface recombination velocity on the dark I-V characteristics. Using PC-1D we varied the surface recombination velocity, S,, from
1 to 10,000 c d s , with everything else the same. As is clear from the figure, higher surface recombination velocities resulted in larger dark current.
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Figure (6) shows the temperature dependence of the solar cell dark I-V characteristic temperatures lower (240K) than room temperature. Also the extent of the “hump’ effect increases as temperature increases.
Figure (7) shows the effect of varying temperature on the spectral response of the silicon solar cell in figure (6). It is clear that the effect of temperature is more pronounced on the dark I-V characteristics than it is on the spectral response of the cell.
Figure (8) shows the effect of varying the cell thickness on the dark I-V characteristics, while figures (9) and (IO) show the effect of varying the surface recombination velocity on the dark I-V characteristics for the cells of two different thickness,
10 P m a n d . 200)Uk The effect of the surface recombination velocity is greater on the thinner than the thicker cell.
current
The
of the dark
- voltage characteristics of pn junction silicon solar cells from the ideal two-diode model behavior. The effects of the surface recombination velocity, the minority carrier lifetimes in the base - and emitter regions of the solar cell, as well as the temperature dependence of the I-V characteristics have been studied.
It is shown that the
“ humps
“ in the I-V characteristics arise as a result of recombination within the space-charge region of the solar cell, and occur when conditions for recombination are different from the simple assumptions of the Shockley-Read-Hall theory.

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R. J Stirn,
“
Junction Characteristics of Silicon solar Cells,” IEEE Photovoltaic
Specialists’ Conference, pp. 72-82, 1972.
H. J. Moller, “Semiconductors for Solar Cells,”, Artech House, Boston, 1993.
C . T: Sah, R. N. Noyce, and W. Shockley,
“
Carrier Generation and Recombination
P-N Junctions and P-N Junction Characteristics,
“
Proc. of the IRE, 1228
-
1243,
1957.
J. Beier, and B. Voss,
“
Humps in Dark I-V-Curves
-
Analysis and Explanation,”
Proc. IEEE 231d PVSC, Louisville, KY, pp. 321
-
326, May 1993.
PClD
1997.
Version 4.5 for Windows, University of New South Wales, Sydney, Australia, n+-emitter
F==l p-base
1 E 4
1 E-1
1 E-2
Fig. (1) Structure of p-n junction silicon solar cell modeled
1 E-4
1 E-5
1 E-6
1 E-7
1 E-8
1 E 9
1 E - 1 0
0.0 0.1
J
......
~
I.... -1 ,I.........,
0.2
1 I
.......
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0.3 0.4
Voltage (V)
-.I
0.5
1
..... A.-.. .J
0 . 6
1
0.7
Fig. (2) Effect of minority-carrier lifetimes on the dark I-V characteristics

Fig. (3) Effect of varying the minority carrier lifetime in the n- and p-regions on the dark I-V characteristics.
. .. .
. .
......... I.OE+l y.
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1.OE-1
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1 .OE9
1 .OE-4
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1 .OE-6
1 .OE-7
1.OE-8
0.0 0.2 0.4
Voltage (Volts)
0.6 0.8
Fig. (4) Effect of trap level on dark I-V characteristics

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1 .OE-1
1 .OE-2
1 .OE3
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1 .OE-8
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0.0 0.2 0.4
Voltage (Volts)
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Fig. (5) Effect of varying surface recombination velocity on the dark I-V characteristics of the solar cell
1 .OE-7
1 .OE-8
1 . O S 3 i i
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0.2 0.4
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Fig. (6) on the dark I-V characteristics

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Fig. (7) Effect of temperature on the spectral response
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(8) Effect of cell thickness on the dark I-V characteristics

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Fig. (9) Effect of surface recombination velocity on the dark I-V characteristics: thin cell (cell thickness = 10 pm) c c
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Fig. (10) Effect of surface recombination velocity on the dark I-V cell (cell thickness = 200 pm)