Another technique for the deposition of thick film pastes, that is assumed to be intro-duced in mass production in the next years, is stencil printing [1]. The advantage of stencil printing is the ability to print finer lines with higher aspect ratio [65]. For stencil printing the same equipment and pastes as for screen-printing can be used, except of the screens that are made of metal foil.
Dispensing represents a contactless method to apply a thick film paste on a sub-strate [66]. Principally, thin fingers with high aspect ratio are feasible, but the persion of homogeneous thin lines through syringes is challenging. An advanced dis-pensing method is the coextrusion technology. Here the actual paste is compressed by a sacrificial paste that is also printed on the wafers but completely burned off during firing [67, 68]. Another non-contact deposition technique is ink jet printing [69]. How-ever, these methods are predicted to stay niche products in the next years [1].
A promising candidate for future metallization technology is light induced plating (LIP) [1, 60]. Besides direct plating of nickel/copper contacts [70], a seed layer can be deposited by other techniques like,e.g., screen- or stencil printing and thickened by LIP of copper or silver [71,72]. Plated contacts principally enable high cell performance, due to low contact and line resistances (compare section 1.6.4), and the utilization of lower cost metals. However, the direct LIP technique is limited on the metallization of n-type surfaces [73].
A detailed overview of industrial relevant metallization techniques as well as techniques rather limited to lab application up to now is given in [74].
1.5 Current-voltage characteristics
In principle a silicon solar cell is a large area diode. Without illumination it shows the same current voltage characteristics as a normal diode (see figure 1.5 dark IV-curve) that can be described by Shockley’s ideal diode equation [75]. Although in the following jV-curves are presented (current density versus voltage), they will be referred to as IV-curves, as commonly done. Under illumination the dark curve is shifted into the fourth quadrant by the photocurrent density jph generated by the solar cell. The sign of this shift is caused by the direction ofjph that flows into the opposite direction as the forward biased diode. This behaviour is described by equation 1.4:
j =j0
whereV is the voltage drop across the solar cell, q the elementary charge,k the Boltz-mann constant and T the temperature in Kelvin. j0 represents the dark saturation current density of an ideal diode which is the sum of the saturation current densities of
0 100 200 300 400 500 600 700
Figure 1.5: Illuminated and dark IV-curve and the power density versus voltage of a solar cell, illustrating the IV-parameters.
base and emitter,j0b and j0e respectively:
j0 =j0b+j0e. (1.5)
Equation 1.4 accounts for radiative, Auger, Shockley-Read-Hall (SRH) and surface recombination occurring in the base and the emitter of the solar cell, leading to a diode ideality factor n = 1. To include SRH recombination in the SCR, values of n > 1 have to be assumed, or a second diode in parallel with the first one with an ideality factor n2 has to be introduced. For recombination in the SCR via defects close to the middle of the band gap n2 = 2 [76]. If further the series resistance of the solar cell RS, accounting for ohmic losses, and a parasitic shunt resistance RP are included, a solar cells IV-characteristics can be described by the commonly used two-diode-model:
j =j01 The first term in equation 1.6 describes the influence of emitter and base. The second term accounts for recombination in the space charge region. The influence of leakage currents is described by the third term. Figure 1.6 depicts the equivalent circuit diagram of a solar cell described by the two-diode-model.
In real solar cells both ideality factors depend on injection level and type of recombi-nation and can, therefore, deviate from their ideal values n1 = 1 and n2 = 2 [77].
The most important parameter to describe a solar cell’s ability to convert solar energy into electrical energy is its efficiency η which is defined as the ratio of the maximum power density that can be extracted out of the solar cell pmpp and the power density of
1.5 Current-voltage characteristics
j01 j02 RP
RS
jph
V,j
Figure 1.6: Equivalent circuit diagram of solar cell according to the two-diode-model.
the incident lightpin. η can be calculated by:
η= pmpp
pin = jmpp·Vmpp
pin (1.7)
wherejmpp andVmppare the current density and voltage at the point of maximum power output (maximum power point (mpp), see figure 1.5).
Beside the point of maximum power output, two important points in an IV-curve of a solar cell are the open-circuit voltage Voc, that is defined as the V-axis intercept of the IV-curve, and the short-circuit current density jsc, representing the j-axis intercept of the curve.
With the assumptions jph >> j0 and |jsc| = jph, the open circuit voltage Voc for an ideal diode can be calculated by equation 1.4:
Voc = kT q ln
jsc
j0
. (1.8)
Withjsc andVoc another important parameter, the fill factorFF, is defined by the ratio of the maximum power density (pmpp =jmppVmpp) and the product of jsc and Voc.
FF = jmppVmpp
jscVoc (1.9)
This is visualized in figure 1.5 by the ratio of the two rectangles.
The fill factor is significant considering losses associated with solar cell metallization, as RS and RP influence the IV-curve and therefore FF as will be discussed in section 1.6.4. Green [75] proposed an expression to determine an ideal fill factor FFid free of losses related to series resistance, shunt resistance and recombination that is only a function of Voc.
FFid = voc−ln(voc+ 0.72)
voc+ 1 (1.10)
with the ideality factor n and the normalized voltage voc >10 voc= Voc
nkTq
. (1.11)
A third fill factor that is free of series resistance effects is the pseudo fill factor pFF that can be obtained by SunsVoc measurements (compare section 2.1.2).
The two-diode-model parameters of a solar cell (j01, j02,RP and RS) can be extracted from the IV-measurements by fitting the two-diode-model to the measured curves.
For the different parameters different fitting windows are used. In figure 1.7 a semi-logarithmic plotted dark IV-curve and the approximate fitting windows for the different parameters are illustrated.
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 1E-8
1E-7 1E-6 1E-5 1E-4 1E-3 0.01 0.1
j01 j02
RP j(A/cm2 )
voltage (V)
RS
Figure 1.7:Dark IV-curve with approximate fitting windows for parametersj01,j02,RP and RS.