IPASJ International Journal of Electrical Engineering (IIJEE)
Web Site: http://www.ipasj.org/IIJEE/IIJEE.htm
Email: editoriijee@ipasj.org
ISSN 2321-600X
A Publisher for Research Motivation........
Volume 2, Issue 9, September 2014
EFFECT OF ELECTRIC FIELD ON
BIFACIAL POLYCRISTALLINE SILICON
SOLAR CELL UNDER MULTISPECTRAL
LIGHT
Cheikh Tidiane SARR, Mouhamadou Moustapha DIONE, Idrissa GAYE, Sega gueye, Amary
THIAM, Grégoire SISSOKO
Laboratory of Semiconductors and Solar Energy, Physics Department, Faculty of Science and Technology
University Cheikh Anta Diop – Dakar – SENEGAL.
ABSTRACT
This study deals with external electric field influence on n-p-p+ polycrystalline silicon solar cell under constant multispectral
illumination. After the resolution of the continuity equation the expression of minority carrier’s density, photocurrent density
and photovoltage are presented. Through this paper, the effect of electric field on these parameters will be considered.
Keywords: Electric field – minority carrier’s density – photocurrent density – photovoltage
1. INTRODUCTION
In physics, the field effect refers to the modulation of the electrical conductivity of a material by application of an
external electric field. In a metal conductor, the electronic density that responds to applied fields is so large that an
external electric field can penetrate only a very short distance into the material. However, in a semiconductor the
electronic density is lower, and an external electric field can penetrate quite far into the material. This field penetration
alters the conductivity of the semiconductor near its surface, and is called the field effect. Many researches on solar
cells are designed to improve their performance. To do this we try to find manufacturing technology [1] or operating
conditions that minimize the effects limiting the performance of solar cells, that is to say photogenerated minority
carrier’s recombination in the bulk of the base [2] and surface, shading effects and resistive losses. One of these
researches has also been carried out in one dimension and has established the effect of an external electric field on
minority charge carriers and on electrical parameters [3]. In this work, a three-dimensional study of a polycrystalline
silicon solar cell is made. We analyze the impact of an external electric field on the minority carrier’s density,
photocurrent density and photovoltage.
2. THEORY
The polycrystalline silicon is composed of several grains of various shapes and sizes (between 1 micron and 1 mm). So
use a columnar model where the grain will be represented by a parallelepiped fig.1-a. [4] facilitate our study. In
this model it is possible to analyze the distribution of minority carrier charge in three dimensions on the grain. In this
paper, we use a fibrously oriented columnar model [5]-[6] presented below (figure.1 (1 to 3)) with the following
assumptions:
• The grains have square cross section (ax = ay = a; 0.002cm ≤ a ≤ 0.2cm) and their electrical properties are
homogeneous. We can then use the Cartesian coordinates;
• The illumination is uniform. We have a generation rate depending only on the depth in the base z.
• The grain boundaries are perpendicular to the junction and their recombination velocities independent from
generation rate under an illumination AM 1.5. So the boundary conditions of continuity equation are linear;
 The contribution of the emitter and space charge region is neglected [6], so this analysis is only developed in the
base region;
• The thickness and the base doping level Nb are 130 µm and 1017 cm-3 respectively. This type of solar cell solar cell
is called back surface field (BSF) [8].
Volume 2, Issue 9, September 2014
Page 10
IPASJ International Journal of Electrical Engineering (IIJEE)
Web Site: http://www.ipasj.org/IIJEE/IIJEE.htm
Email: editoriijee@ipasj.org
ISSN 2321-600X
A Publisher for Research Motivation........
Volume 2, Issue 9, September 2014
Figure 1: Three-dimensional model of the polycrystalline silicon solar cell.
We assume the recombination velocity at grain boundaries is the same for all plans. The phenomenon of charge carrier
generation, diffusion and conduction in the grain are related by a mathematical equation called the continuity equation:
 2 ( x, y , z )  2 ( x, y , z )  2 ( x, y , z )
 ( x, y , z )  ( x, y , z )
G( z )


 Cz


2
2
2
2
x
y
z
z
L
Dn
(1)
Where:
Cz 
n E
Dn
and L2   n Dn
Dn is the diffusion constant of excess minority carriers. τn is the lifetime of excess minority carriers. Gn(z) is a carrier
generation rate and can be written by the following expression [6]-[7]:
G(z)  n  a i e bi z
(2)
Where ai and bi are the coefficients from modelling of the generation rate overall radiation in solar spectrum to AM 1.5
and n represents the illumination level [6]-[13].
The general solution of the continuity equation (Equation 1) is given as [6]:
  x, y, z    Z jk cos(C j  x) cos(C k  y)
j
(3)
k
The factors Ck and Cj are eigen values and depend on grain size and grain boundaries’ recombination velocity only.
Inserting the (Equation 3) into (Equation 1) and replacing the expression generation by its value and taking
into account of the fact that cos(c k  x) and cos(c j  y) are orthogonal functions, we obtain a general expression for
Z kj (z) . This expression contains two constants derived using interfaces boundary conditions while the factors
Ck and Cj in (Equation 3) are determined using the grain boundaries conditions.
The boundary conditions at the n-p interface (z = 0) are:
Volume 2, Issue 9, September 2014
Page 11
IPASJ International Journal of Electrical Engineering (IIJEE)
Web Site: http://www.ipasj.org/IIJEE/IIJEE.htm
Email: editoriijee@ipasj.org
ISSN 2321-600X
A Publisher for Research Motivation........
Volume 2, Issue 9, September 2014
  x, y, z 
z

z 0
SF
  x, y, z  0 
Dn
SF is the junction recombination velocity and represents the sum of two terms:
(4)
S F  S F 0  S FJ is the external load
related to the current flow and j defines the operating point of the cell [5] SF0 is defined as the intrinsic junction
recombination velocity related to the shunt resistance, an internal load of the solar cell due to losses at the junction
level [11]-[15].
At the back side of the bifacial solar cell, we use the boundary condition for z  a :
  x, y, z 
z

zH
SB
  x, y, z  0 
Dn
(5)
SB is the back surface recombination velocity. It quantifies the rate at which excess minority carriers are lost at the back
surface of the cell [5]-[11]-[12].
A contact level of two grains in the direction (Ox) and (Oy), boundary conditions are:
  x, y, z 
x

Sgb 
a

  x   , y, z 
Dn 
2

(6)

Sgb 
a 
  x, y   , z 
Dn 
2 
(7)
a
x 
2
  x, y, z 
y
y 
a
2
Where SGB is the recombination velocity at grain boundary. With the resolution of transcendental equations we obtain
the eigen values Ck and Cj. Expressions of these equations are given by equations (8) and (9):
Sgb
a
C j tan(C j ) 
2
Dn
Sgb
a
Ck tan(Ck ) 
2
Dn
(8)
(9)
Excess minority carrier’s is function of external electric field, the grain size g, and the recombination velocity at grain
boundary SGB, at junction SF and at back surface SB.
2. 1 Photocurrent density
The photocurrent density at the junction of solar cell is obtained from the excess minority carrier’s density as follows
[5]-[12]:
qD
a2
J Ph 
a
2
a
2
   x, y, z  
 dx  dy
z
a
 z 0

  
a

2
(10)
2
19
Where D is a constant defined above and q  1.6  10 C .
2. 2 Photovoltage
By means of Boltzmann’s relation, the photovoltage VPH can be expressed as [10]:
VPH
a a


2 2
 NB

 VT  ln 1  2      x, y, z  0  dx  dy 
ni a a

 

2 2
Where VT 
(11)
k T
 0.026 V is the thermal voltage at T = 300K, ni the intrinsic carriers density and NB the
q
base doping density.
Volume 2, Issue 9, September 2014
Page 12
IPASJ International Journal of Electrical Engineering (IIJEE)
A Publisher for Research Motivation........
Volume 2, Issue 9, September 2014
Web Site: http://www.ipasj.org/IIJEE/IIJEE.htm
Email: editoriijee@ipasj.org
ISSN 2321-600X
3. RESULTS AND DISCUSSIONS
3. 1 Effect of electric field on the minority carriers’ density
5
By means of the junction recombination velocity SF, which varies from 0 to S F  1.6 10 cm / s [16].
We represent in figure 2 the evolution of the minority carrier’s density versus electric field and recombination velocity
at the back side by fixing the values of recombination velocities at junction Sf.
Figure 1: Profile of minority carriers’ density versus recombination velocity at back surface and electric field.
SF = 10cm.s-1; a = 30µm; SGB = 102cm.s-1; n =200 and z =1µm
It may be noticed when the solar cell is illuminated by front side the minority carriers density decreases with increasing
of electric field and recombination velocity at back surface SB. When we apply a polarization, the decrease of electron
diffusion flux near the junction has an important effect on the photocurrent and photovoltage. In fact, when the charge
carrier crosses the junction we note an increase of photocurrent and decrease of photovoltage. This phenomenon is
accentuated with increasing electric field. It means also solar cell electric polarization reduces carrier’s recombination
at the rear zone of the base and enhances the BSF (Back Surface Field) effect [17]. In addition to that when the
photocurrent decreases with increasing of photovoltage we note a blockage and storage of carrier that traduces the fact
that there is no passage of carriers at the junction. To determine the influence of electric field on photogenerated
carriers in the bulk of the base we plot the 3D curve in figure 3, for different values of electric field E.
a) E = 2 V.cm-1;
b) E= 6 V.cm-1
Figure 2: Effect of electric field on the photogenerated charge carriers. SF = 101 cm.s-1; SB = 103 cm.s-1 ; SGB = 102
cm.s-1; n = 200 and z = 1 µm
Volume 2, Issue 9, September 2014
Page 13
IPASJ International Journal of Electrical Engineering (IIJEE)
A Publisher for Research Motivation........
Volume 2, Issue 9, September 2014
Web Site: http://www.ipasj.org/IIJEE/IIJEE.htm
Email: editoriijee@ipasj.org
ISSN 2321-600X
For different values of electric field the concentration of minority charge carrier increases from outside to the centre of
the surface. Of course, this entails that an increase of polarization and decrease of this concentration near the junction
of solar cell which is why the charge carrier crosses junction and the diffusion phenomenon is more accentuated. In
figure 4 we present the profile of minority carriers density versus electric field and base depth.
Figure 3: Evolution of minority carriers’ density versus base depth and electric field
SF = 101 cm.s-1; SB = 103 cm.s-1; a = 30 µm; SGB = 102 cm.s-1; and n = 200
For any values of polarization, the curve analysis reveals three zones:
 A first zone near the junction, where carrier’s density gradient is positive. All carriers in that part of the curve can
be returned to the junction to participate in photocurrent. We also note that the different curves peaks move toward
the junction when electric field increases. This phenomenon is interpreted as a base depth reduction (Sissoko et al.,
1998).
 A second region corresponding to the maximum of the curve where carrier’s density gradient is zero.
 A third zone where carrier’s density gradient is negative. All carriers in that part of the curve have not the
minimum energy required to return to the base and contribute to the photocurrent, they recombine at the back side
of the solar cell.
3. 2 Impact of electric field on the photocurrent density
We plot in figure 5 the evolution of the photocurrent density versus junction recombination velocity and electric field.
Figure 4: Evolution photocurrent density versus junction recombination velocity and electric field
SB = 103cm.s-1; a = 30µm; SGB = 102cm.s-1; n =200 and z=1 µm
In this profile we observe that the photocurrent density is an increasing function electric field and junction
recombination velocity. We notice also that the photocurrent density is practically zero at low SF values (the carriers are
blocked at the junction) and the solar cell operates in this case in open circuit condition. With polarization, we find that
the current at open circuit is not zero, but rather is proportional to the bias induced field, as is the short circuit. It
therefore appears that the electric field has a great influence on the photocurrent and hence the carrier diffusion across
the junction. The photocurrent density increases quickly with junction recombination velocity to finally stabilize at
large SF values. The photocurrent is maximum and the solar cell operates in short circuit condition [18]. We present in
figure 6 a 3D curve of the photocurrent density versus electric field and recombination velocity at back surface.
Volume 2, Issue 9, September 2014
Page 14
IPASJ International Journal of Electrical Engineering (IIJEE)
A Publisher for Research Motivation........
Volume 2, Issue 9, September 2014
Web Site: http://www.ipasj.org/IIJEE/IIJEE.htm
Email: editoriijee@ipasj.org
ISSN 2321-600X
Figure 5: Profile of photocurrent density versus recombination velocity at back surface and electric field
SF = 103cm.s-1; a = 30µm; SGB = 102cm.s-1; n= 200 and z = 1 µm
We observe in figure 6 that the photocurrent density is a decreasing function of recombination velocity at back surface
SB. The decrease of photocurrent with increasing of SB is due to the reduction of the charge carrier near the
junction.When we apply a polarization, we find that the diffusion phenomenon has decreased and the recombination at
back side has increased which is why the photocurrent tends to zero.
3. 3 Influence of electric field on the photovoltage
We plot in figure 7 the 3D curve of photovoltage versus junction recombination velocity and electric field by fixing the
recombination velocities at grain boundary SGB and at back surface SB, illumination level n, grain size a and base depth
z.
Figure 6: Photovoltage versus junction recombination velocity and electric field
SB = 103cm.s-1; a =30 µm; SGB = 102cm.s-1; n =200 and z = 1 µm
It is obvious by this curve that the photovoltage is a decreasing function of junction recombination velocity and electric
field. We also note that the photovoltage is maximum for low values of SF corresponding to the open circuit condition
where the carriers are blocked at the junction and this phenomenon becomes even more pronounced as the polarization
increases. The photovoltage tends to zero for large values of junction recombination velocity where the solar cell
operates in a short circuit condition where all the charge current return to the junction. We plot in figure 8 the
evolution of photovoltage versus recombination velocity at back surface and external electric field.
Figure 7: Profile of photovoltage versus recombination at back surface and electric field
SF = 103cm.s-1; a = 30µm; SGB = 102cm.s-1; n =200 and z = 1 µm
The curve analysis reveals that the photovoltage is a decreasing function of recombination velocity at back side and as
we have previously seen a decreasing function electric field. We note that the polarization reduces the charge carrier’s
Volume 2, Issue 9, September 2014
Page 15
IPASJ International Journal of Electrical Engineering (IIJEE)
A Publisher for Research Motivation........
Volume 2, Issue 9, September 2014
Web Site: http://www.ipasj.org/IIJEE/IIJEE.htm
Email: editoriijee@ipasj.org
ISSN 2321-600X
concentration with the conduction phenomenon and in fact increases the recombination at back surface. That is why the
photovoltage decreases. We thus arrive at the conclusion, that solar cell electric polarization reduces the phenomenon
of bulk recombination in the base and enhances carrier’s migration to the junction for a possible participation in the
photocurrent.
4. CONCLUSION
In this paper, we made a three dimensional modeling of a n-p-p+ polycrystalline silicon solar cell under constant
multispectral illumination and external electric field. The resolution of the continuity equation allows us to determine
the expression of excess minority carrier’s density, photocurrent density and photovoltage. In this work, we also studied
the impact of the electric field and recombination velocities at junction and at back side on these parameters already
mentioned. It appears through this study that the electric field increases charge carrier’s mobility and facilitate their
crossing of the junction and also decreases bulk and back side recombination.
REFERENCES
[1.] Neamen, D.A Semi-conductor Physics and Devices Basic Principle. McGraw-Hill, New York. (2003).
[2.] Sinton R.A. and Swanson P.M., 1987 An optimisation study of Si Point Contact Concentration. 15th LE.E.E.
Photov. Spect. Conf. USA, pp: 1207-1208.
[3.] Zoungrana Dieng M. B., Lemrabott O.H., Toure F., Ould El Moujtaba M.A., Sow M.L. and Sissoko G External
Electric Field Influence on Charge Carriers and Electrical Parameters of Polycrystalline Silicon Solar Cell.
Research Journal of Applied Sciences, Engineering and Technology 4(17): 2967-2972 (2012).
[4.] Thongpron J., Kirtikara K., Jivacate C., 2006 Solar Energy materials and Solar Cells 90, pp: 3078-3084
[5.] Diallo H.L., Wereme A., Maïga A.S. and Sissoko G., 2008. New approach of both junction and back surface
recombination velocities in a 3D modelling study of a polycrystalline silicon solar cell. Eur. Phys. J. Appl. Phys.,
42: 203-211.
[6.] Dugas, J 3D Modelling of a reverse cell made with improved multicrystalline Silicon wafer. Solar Energ. Mater.
Solar Cells, 32: 71-88.(1994).
[7.] Sissoko, G., Museruka C., Corréa A., Gaye I. and Ndiaye A.L Light spectral effect on recombination parameters of
silicon solar cell. Renew. Energ., 3: 1487-1490 (1996).
[8.] Linda Koschier M. and al Low temperature junction and back surface field formation for photovoltaic devices. 2nd
World Conference and Exhibition on Photovoltaic Solar Energy Conversion, pp 1744-1747. (1998).
[9.] Deme M.M., Mbodji S., Ndoye S., Thiam A., Dieng A., Sissoko G. Influence of illumination incidence angle,
grain size and grain boundary recombination velocity on the facial solar cell diffusion capacitance. Rev. Energ
Renouvelables, 13(1): 109-121. (2010).
[10.] El-Adawi M.K. and Al-Nuaim I.A A method to determine the solar cell series resistances from a single I-V
characteristic curve considering its shunt resistance-new approach. Vaccum., 64: 33-36. (2002).
[11.] Dione M. M., Ly I., Diao A., Gueye S., Gueye A., Thiame M., Sissoko G Determination of the impact of the grain
size and the recombination velocity at grain boundary on the values of the electrical parameters of a bifacial
polycristallin silicon solar cell IRACST – Engineering Science and Technology: An International Journal
(ESTIJ) Vol.3, No.1, ISSN: 2250-3498, pp. 66-73 (2013)
[12.] Madougou S., Made F., Boukary M.S. and Sissoko G I-V characteristics for bifacial silicon solar cell studied
under a magnetic field. Adv. Mater. Res., 18-19: 303-312. (2007)
[13.] Mohammad, S.N An alternative method for the performance analysis of silicon solar cells. J. Appl. Phys., 61(2):
767-772. (1987)
[14.] Ahmed F. and Garg S International Centre for Theoretical Physics (ICTP), Trieste, ITALY, Internal Report.
(1986)
[15.] Mbodji, S., Mbow B., Dieng M., Barro F.I., Sissoko G A 3D model for thickness and diffusion capacitance of
emitter-base junction in a bifacial polycrystalline solar cell. Global J. Pure Appl. Sci., 16(2): 469-478. (2009).
[16.] Mbodji S., Ly I., Dione M. M., Diassé O., Sissoko G Modeling study of N+/P solar cell resistances from single I-V
characteristic curve considering the junction recombination velocity (Sf) Research Journal of Applied Journal,
Engineering and Technology Vol. 4 Issue 1 pp: 1-7 (2012).
[17.] Umesh K.M. and Jasprit S Semiconductor Device Physics and Design. Springer. (2008).
[18.] Sissoko G., Nanéma E., Corréa A., Biteye P.M., Adj M. and Ndiaye A.L Silicon Solar cell recombination
parameters determination using the illuminated I-V characteristic. Renew. Energ., 3: 1848-1851. (1998)
Volume 2, Issue 9, September 2014
Page 16