# Analysis of the Optical Properties of Screen-Printed  and Aerosol-Printed and Plated Fingers of Silicon Solar Cells

Authors: R. Woehl; M. Hörteis; S. W. Glunz
Journal: Advances in OptoElectronics
 (2008)

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## Abstract

One main efficiency loss in industrial solar cells is the shading of the cell caused by the metal front side contacts. With the aerosol-printing technique plus an additional light-induced plating (LIP) step, not only is the geometrical contact width narrowed compared to screen-printed contacts but also the shape of the finger changes. In this work, the effective shading of different finger types is analysed with two different measurement methods. The essential parameter for characterising the finger is the effective width which can be reduced drastically compared to the geometrical width due to total internal reflection at the glass-air layer and the reflection from the roundish edges of the contact fingers into the cell. This parameter was determined with different methods. It could be shown that for aerosol-printed fingers the effective (optical) width is only 38% of its geometrical width, while for standard screen-printed fingers it is 47%. The measured values are compared to a theoretical model for an aerosol-printed and plated finger and are in good agreement.


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## Body

## 1. Introduction

Conventional  silicon solar cells produced in the industry possess, in
addition to busbars, many metal fingers on the front side of silicon solar cells.
The fingers should conduct the current with as little resistance loss as
possible which leads to a necessary minimum of cross-section of the finger.
Since at the same time the metal fingers cause shading losses, the aim is to produce
fine lines with a high aspect ratio (ratio of height to width).One route Fraunhofer ISE follows is to use a two-step metallisation
technique. In the first step, the   seed layer is created which forms a good
mechanical and electrical contact to the silicon surface. In this work the seed
layer is printed with an aerosol printer from the company   Optomec (Saint Paul, Minn, USA). The specially prepared ink is sprayed into an
aerosol (for details see [1, 2]) and is directed to the printing
head. This head consists of 10 identical nozzles in a row. The so-called sheath
gas flow focuses the aerosol and avoids that the aerosol gets in contact with
the inner surface of the nozzle. The seed layer has a width of about 50 μm.
After printing, the cell has to be fired at a temperature of 800C°.The second step is the light-induced plating (LIP). During this process,
the fingers are thickened about 20μm with silver in order to receive good line
conductivity. In the configuration, the whole solar cell is placed into a
silver bath. The rear side must be contacted and the front side illuminated. Due
to the photovoltaic effect, the potential on the front surface becomes negative
so that the silver ions are deposited on the front contacts. With the LIP
method, high-efficiency solar cells of over 23% can be achieved [3] and industrial inline processing
can be used [4].With this technique about 70μm wide contacts on a monocrystalline,
textured surface with an antireflection coating (ARC) were achieved (see Figure 1).Figure 1
Cross-section of an aerosol-printed and plated finger exhibiting a geometrical width of 72μm. The seed layer width was approximately 50 μm and the plated silver about 20 μm.Compared to a standard screen-printed contact (see Figure2), it clearly has the advantage of a smaller geometrical
width (72 μm compared to 130 μm). Furthermore, the two contact fingers differ
in their shape, which should influence their reflection properties. Especially
for the aerosol-printed finger light could be reflected directly or via total
internal reflection at the module glass-air interface onto the active area of
the cell, thus reducing the effective shading of the finger.Figure 2
Cross-section of a screen-printed finger exhibiting a geometrical width of 130μm.Blakers [5, 6] and Stuckings and Blakers  [7] have already analysed this effect
for contact fingers with a seed layer width of 3.5–8 μm and  postplated silver using measurement of the global short-circuit current and
global reflection. They have observed a great reduction of the effective
optical width of the contacts to about a third of the geometrical width.The main motivation of this paper is to analyse if the contact fingers
fabricated with the industrial feasible aerosol jet printing technology will
also show such a dramatic reduction and to compare the optical performance of
these fingers with the standard industrial screen-printed contacts. To achieve
this goal, we have used the methods suggested by Stuckings and Blakers in
addition to locally resolved measurements of the reflection.


## 2. Theoretical Considerations

For the calculation of shading  losses of the solar cell, the determining
factor for the fingers is not the geometrical width, but the effective (optical)
width. It is the  fraction of the geometrical (measured) width that actually
shades the solar cell. The effective width can be significantly smaller than
the geometrical width because light can be reflected from the finger to the  cell
and therefore contribute to the power generation.Blakers [5, 6] has calculated the effective
shading of a roughly half-circular encapsulated finger to be 36%. The nearly
optimum half-circled shape was achieved by a very narrow seed layer and a
subsequent silver electroplating step. He compared this value with jsc measurements of cells covered with isopropanol and found excellent agreement.
Stuckings and Blakers  [7] also calculated the theoretical
effective width of a half-circular encapsulated finger and found a similar
value of 34%. He compared this value to reflection measurements and determined
experimental values between 30% and 35% which is in good agreement with the
theoretical value. In this work, on the one hand, the finger structures are
quite different from the previously investigated ones due to the wider seed
layer and, on the other hand, the striking question is if the aerosol-printed
fingers are beneficial compared to the screen-printed ones.Assuming that the light hits the finger perpendicular to the
encapsulated cell (see Figure3), there are three different cases for the light to be
reflected:(I)
direct reflection onto the silicon
surface;(II)
total reflection can occur at the
boundary layer glass air;(III)
the light can be reflected out of
the module. For cases I and II, the light can contribute to current generation and
therefore reduces the effective width. In order to determine the lateral
x-position for the simple case of a half-circular shaped finger, where total
reflection occurs, the refractive index of the glass has to be measured. In the
wavelength range of 600–1000 nm, a value
of nglass=1.528±0.007 was determined. With the
refractive index for air nair=1 and Snells law (1)α=arcsin(nairnglass),the critical angle for total reflection is α=40.9°. The (upper) angle β is the half of the alternate
angle of α, β=20.4°. This angle can be found as
well between the silicon and the tangent of the half circle. The gradient of
the tangent is −tan(β)=−0.37 and can be set equal with the derivation of the equation of a
half circle (f(x)=1−x2) (2)f′(x)=−x1−x2=−0.37. If the origin is set at the middle of the circle, it follows that the light
hitting the finger at a position −0.35>x>0.35 (assuming
a unit circle) total reflection occurs. The situation changes to case I at a
tangent smaller than −1 with an x-position of 0.71. Thus the fraction of the
area of a half-circled finger can be assigned: I = 29.3%, II = 35.8%, and III =
34.9%.Figure 3
Three different cases for the reflection of the light from the finger. The pottant between the silicon and glass is not illustrated because it has about the same refractive index as the glass and therefore no influence on the optics.For the aerosol-printed and plated finger, however, the cross-section
looks slightly different. As can be seen in Figure1, the flanks are indeed similar to a quarter circle,
but the finger has a 30 μm wide middle section due to wider seed layer.
Therefore, the model was extended with an additional 4th part describing this
middle section (see Figure 4). This shifts the area fractions to I = 16.7%, II =
20.5%, III = 19.9%, and IV = 42.9%.Figure 4
Sketch for the aerosol-printed and plated finger with the four areas that have different reflection properties.Area IV is assumed to be a lambertian emitter, that is, in each angle
the same amount of light is reflected. The waviness in the micrometer range and
also the rough microstructure of the plated silver make the assumption reasonable
(see Figure5).Figure 5
Microstructure of the plated silver surface.Light that is reflected from the metal, with an angle>40.9°, hits
the glass-air interface   100% and is reflected back to the silicon. In order to
calculate the part of the reflected light at smaller angles, the light is
divided into two halves: one is s-polarised and the other half is p-polarised [8]. For the varying angle of incidence φ Snell’s law of refraction is applied (3)Rref=(η0−η1η0+η1)2   with η0,1=H/E the optical admittance and the index
0 for air and 1 for glass. Figure 6 shows that for small angles the reflection is smaller
than 5% and just before α=40.9° increases rapidly.Figure 6
Simulated data for the reflection at the interface glass-air.The effective width EW illustrates the fraction of the absorption and
the loss of reflection of a finger   and is 100% minus the light that reaches the
silicon. The amount of light that reaches the silicon is 100% minus the losses
of area III (LIII) and IV (LIV) multiplied by the reflection
of the silver (4)EW=100%−(100%−LIII−LIV)⋅RAg. The fraction of the angle of the light being reflected out of the module
is (5)dα=12π∫02πdφ∫0αdϑsinϑ=[−cosϑ]0α=0.245   with φ, ϑ the spherical coordinates.With the data of Figure6, that about 96% of the light with an angle <α  leaves the module and that 42.9%
of the covered area of the finger is IV, it results (6)LIV=0.245⋅0.429⋅96%.Because of the rough microstructure, not all of the light of area III
leaves the module directly. Half of it is assumed to behave like a lambertian surface
so that (7)LIII=0.623⋅0.199⋅96%.In this model, multiple reflections between finger and the interface are
neglected as well as the absorption within the glass layer. The measurement for
the reflection of the plated silver between 600 nm and 1000 nm is shown in Section
3 and is RAg=83.7%.The effective width EW of an aerosol-printed and plated finger with an encapsulated
glass layer above then results in EW = 34.7% (of the geometrical width).


## 3. Cell Preparation

For the experiment, fourp-type Cz-silicon textured wafers with
industrial emitter (60 Ohm/sq) and Al-BSF were processed with different fingers
(see Table 2). Two cells received a 50 μm wide seed layer with the aerosol printer.
Afterwards, the fingers were thickened of about 20 μm by LIP. These two cells differed
in their finger spacing: one cell had a line spacing of 1.955 mm (Awd); the
small spacing was half of it (Asd). The two screen-printed cells are identical,
though one was plated additionally, which is the reason why the geometrical
width is greater. The finger widths are based on microscope measurements. After
LIP, the cells were encapsulated into a module using EVA.


## 4. Global Measurement

At this measurement, as proposed by Stuckings and Blakers  [7], a 0.5 cm wide and 1 cm high area
is illuminated with a wavelength dependent spectrum between 600 nm and 1000 nm
and the reflection is measured. The encapsulated cells have been measured including
5 horizontal adjusted fingers in the measurement area. For the sample Asd, 10 fingers
were included. In Figure 7, the wavelength-dependent reflection Rref for the four cell types is plotted. Additionally, the following samples were
studied: one sample without metal, one completely covered with screen-printed
silver, and one completely of plated silver. As expected, the reflection increases
with the covered metal fraction. Comparing the completely covered samples, it
can be concluded that the plated silver reflects more light than the screen-printed
silver.Figure 7
Reflection curves of the global measurement of the four processed cells of Table2 and additionally one cell without metal, one completely covered with screen-printed silver and one with completely plated silver.The optical loss (OL) of a metal finger can be calculated by using the
following equation, according to the method of Stuckings and Blakers   [7]: (8)OL=Rref(cell)−Rref(withoutmetal)Aref+αabsAabs.Optical loss is the reflection of a
cell minus the reflection without metal plus the absorption of the silver
finger αabs. αabs equals 100%−Rref (completely
screen-printed silver), respectively, Rref (completely plated
silver). The reflections are weighted with the covered areas Aref and  Aabs, which are determined from the microscope pictures.
Schematically, the calculation is clarified in Figure 8.Figure 8
Drawing for clarifying the optical loss OL: the reflection signal of the sample without metal is subtracted and the absorption of the silver is added to the reflection signal of each of the four cells.The data for the optical loss are plotted in Figure9, showing how much light is lost by each type of area.Figure 9
Curves for the optical loss OL for the four different cell types that are calculated according to (8).Regarding the fraction of the optical loss to the reflection of a flat
finger that reflects all the light or differently expressed the fraction of OL
to the fraction of the finger coveragepGW, we receive the effective width (9)EW=OLpGW. This is shown in Figure 10. The effective widths of all fingers are clearly
under 60%, which means that just up to 60% of the finger area are effectively
shading the cell and at least 40% of the light striking the finger are still
producing current (see Figure
3). Furthermore, the effective widths for the aerosol-printed
cells are much smaller than for the screen-printed fingers. Averaging the data,
the aerosol-printed and plated cells have an effective width of 36%, the
screen-printed finger 42%, and the additionally plated screen-printed finger an
EW of 50%.Figure 10
Effective width EW for the four different cells (see Table2) with an error of the finger width of 4 μm and a measurement signal of 2%.


## 5. Lbic Measurement

Usually, the LBIC method is used to measure the spatially resolved IQE
by scanning a cell with a laser beam [9]. In this experiment, the laser beam
with a wavelength of 833 nm and a diameter of 6 μm was scanning a finger (of
the four different cells above) 10 times with a displacement of 3.1 μm, while
measuring the reflection. The data of two fingers are shown in Figures 11 and 12. Comparing them, the screen-printed
finger looks wider than the aerosol-printed finger and has a higher maximal
reflection. But since the geometrical widths are different their optical
behaviour is uncertain.Figure 11
Locally resolved reflection signal using an LBIC setup of a screen-printed nonplated finger.Figure 12
Locally resolved reflection signal using a LBIC setup of an aerosol-printed and plated finger.In order to compare the
data with the measurement setup above, the following procedure was applied. The
10 scans were averaged and the signal was integrated and divided by GW. The
loss by reflection is shown in Figure13. Beside the loss by reflection, the loss by
absorption of the silver has to be included because not 100%−lossofreflection is the amount of light that reaches the silicon. The amount is only αin=(100%−lossofreflection)⋅RAg. So the effective width is EW=100%−αin, which is plotted in Figure 13.Figure 13
Loss by reflection and effective width EW for the LBIC measurement of the four differently processed cells.The trend observed for this data is the same as for the global method.
The aerosol-printed cells are optically narrower than the screen-printed cells.
The aerosol-printed cells have an EW of 43% (average of Awd and Asd) and the
screen-printed as well as the one with LIP has an EW of 52%.


## 6. Conclusion

The effective reflection of different types of metal fingers, produced
by industrial feasible technologies, has been analysed by theory and
experiment. The theory showed that the effective shading area is significantly
smaller than the geometrical one for a metallised front side finger. The
calculated theoretical value for the aerosol-printed finger is in good
agreement with the measurements (see Table1). The small deviation probably
occurs because of the assumption of the lambertian emitter of the surface. Both
measurement techniques (the global and the locally resolved one) showed that
the effective width EW for a finger is between a third and about half of the
geometrical width. In both cases, the aerosol-printed plus plated finger has
not only a smaller geometrical finger width than the screen-printed ones but
also a smaller effective (optical) finger width. Averaging the values for the
aerosol-printed cells the effective width is 38%, which is slightly higher than
the values Blakers [5, 6] (36%) and Stuckings and Blakers   [7] (30–35%) received for contacts with
a very narrow seed layer and electroplating. This is due to the wider flat
middle part of the aerosol-printed fingers and therefore these results are in
good agreement.Table 1
Calculated and measured effective
widths for the three different methods for the aerosol and screen-printed
cells. The screen-printed column includes the mean value for the screen-printed
and the one with a plated step.
MethodAerosol-printingScreen-printingTheoretical value34.5—Global measurement36.041.9LBIC measurement42.852.3Table 2
Explanation of the four different
cells that have been processed.
AbbreviationExplanationGeometrical
finger width
GW [μm]Fraction of
finger coverage ofthe global measurement areapGW [%]AwdAerosol-printed
cell with wide line distance65±4.93.25AsdAerosol-printed
cell with small line distance70.6±4.47.06SScreen-printed
cell124.8±4.36.24S + LIPScreen-printed
cell +LIP135.8±3.96.79



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*Source: 759340-2008-09-16.xml*