Abstract

In the research field of novel solar cells and LEDs it is very common to use off-the-shelf glass substrates with a pre-added electrode layer to deposit the pixels onto. The contacting pads of this pre-added layer are often not metalized during the production process and hence introduce a large electric resistance when contacted. Furthermore, multi-pixel samples often share this electrode (common electrode) and hence increase the total current running through this one contact. The effects of both constellations are investigated in this paper as well as the influence of shunted pixels on a characterized neighboring pixel sharing a common electrode. It is shown by simulation and confirmed by measurements that a large contact resistance flattens the current-voltage (IV) curve of a measured device. This results in wrong maximum-power-point (MPP) and open-voltage circuit (Voc) values in the case of illuminated solar cells. Shunted neighbors in a common-electrode design will in addition shift the IV-curves to the right and falsify the results even more. The short-circuit current (Isc) of illuminated solar cells is only affected at large current levels and results are not presented here. The limitations of non-metalized contact pads and the employment of common electrode designs are found in the accuracy of measured MPP and Voc of a pixel. Possibilities to circumvent these issues are the metallization of all contact pads with an appropriate material like gold or silver and the avoidance to use a common electrode in multi-pixel designs

Introduction

The R&D community in the field of novel solar cells and LEDs commonly fabricates small-area samples with multiple pixels sharing a common electrode (CE). Off-the-shelf glass substrates with (prestructured) ITO layer or other transparent electrode make the sample production faster and more reliable. The pixel hence will have a CE on ITO level as scribing of the ITO to create individual pixels is an extra step in the production that not every lab can do. In addition, metalizing the contacting pads to reduce the contact resistance might only be done for the counter electrodes and not for the ITO contact pads. This leaves the CE to be ITO only having a much larger contacting resistance than its counterparts. The drawback of a large contacting resistance (Rc) is covered in the first part of this white paper (section 3). The second part discusses the different measurement modes for IV curves and includes further non-idealities like shunted pixels (sections 4 to 12). The third part will show some actual measurements with faked contacting resistance and shunts (section 13). The influence of Rc is shown exemplarily in the changes of the current-voltage (IV) curve of an ideal diode (e.g. an LED) and a simple model of a solar cell. The measuring device (e.g. a Fluxim instrument like Litos or Litos Lite) is simulated1 with an ideal voltage source and a measurement resistor Rm, which is used to determine the current flowing through a single pixel. Two measuring methods are compared as they are currently implemented in our systems. Sequential refers to applying a ramped voltage to a single pixel at a time while the other pixels remain on ground (0V) potential. Parallel refers to the simultaneous appliance of the exact same (this is an ideal, non-realistic case) ramped voltage to all pixels.

Influence of Rc on single pixel measurement

We start with an ideal circuit of a diode attached to a voltage source Vsource (Figure 1). The current is determined by measuring the voltage drop over the shunt Rm1. Ramping of the voltage from 0V to 2V and plotting the resulting IV-curve of the device under test (DUT) will allow a good visual comparison of the different cases using this diode IV-curve as a reference.

Figure 1: Top) shows a simplified circuit for a single pixel sample with a voltage source (Vsource = Vs), a shunt for voltage drop to current conversion (Rm1) and the device under test (DUT1), which is represented by an ideal pn-diode. The voltage source is ramped up from 0V to 2V to measure a current-voltage curve (IV-curve) of the DUT. Bottom) The voltage VDUT1 is shown in the second graph to highlight the voltage loss over Rm1.

Introducing a contact resistance Rc (Figure 2) with an unknown value between the contact pad and the contacting pin, e.g. a spring-loaded gold pin, will lead to an additional, unknown voltage drop reducing the voltage seen by the DUT1. This additional voltage drop leads to an erroneous voltage reading and can only be corrected with a 4-point measurement. For simplicity, the non-common electrode contacting resistance Rc1 is fixed to 1Ω throughout the paper and only Rc2 of the CE is varied. All references to Rc are linked to the latter, unless otherwise stated. Measuring the so modified DUT voltage at VDUT1 against ground (GND) will overestimate the actual voltage drop 𝑉̃ 𝐷𝑈𝑇1 over the DUT. The measured value is

where I is equal to the measured voltage drop VRm1 across Rm1 and divided by Rm1, 𝑉̃ 𝐷𝑈𝑇 is the actual voltage drop over the pixel and RC1, RC2 represent the contact resistance on both ends of the DUT. The IV-curve with this ‘modified’ and overestimated 𝑉𝐷𝑈𝑇1 is showing a flattening with increasing Rc. This flattening can be explained by the current I being inversely proportional to the load seen by 𝑉𝐷𝑈𝑇1 as shown by the simplified Ohm’s law

simplified Ohm's Law

with Rload being the sum of both contact resistances RC1 and RC2 as well as the voltage-dependent resistance of DUT1. Knowing the exact value of Rc would allow a correction of the measured voltage and thus of the IV-curve as the current is known. Unfortunately, Rc depends on various factors like metallization type and quality of the contacts, possible corrosion, humidity, contact pressure, etc. and is hence difficult to determine. A true 4-point measurement would help but can often not be realized due to mechanical constraints, costs and time limitations.

Figure 2: IV-curve of an ideal diode with contacting resistances on both ends where Rc1 = 1Ω and Rc2 is varied. Rc flattens the IVcurves and falsifies the results. A realistic Rc is expected to be in the range of 3 – 10

What about multiple independent pixels?

The influence of neighboring pixels on the pixel under measurement in a multi-pixel design can be avoided, if all pixels are electrically separated, that is, have no common electrode (we ignore lateral charge travelling and other effects). This would be the case for cleanly scribed pixels produced on a common transparent electrode. However, deviations from pixel to pixel could be seen even under the assumption of perfectly identical pixel characteristics as Rc might not be equal for each pixel contact.

Adding a common electrode to a multi-pixel design

In a sample design with multiple pixels sharing a common electrode, the pixel-to-pixel influence can become severe with increasing forward currents and Rc. The worst case is a sample with a single or multiple shunted pixels, as will be shown later. Sequential or parallel measuring of IV-curves will lead to slightly different results as the currents through the individual pixels are summed up at the CE, but the CE contacting resistance remains the same independently of the measurement method used (we assume one contact pin per pixel with the same Rc value for all contacts to the CE pad). Figure 3 shows the circuit for a sequential IV measurement. The passive pixel (DUT2) would ideally be electrically floating but is instead tied to GND potential as it is the case with our current instruments.

Figure 3: IV-curve of DUT1 for sequential IV measurement of a CE sample with two pixels.

Comparing the sequential IV measurement for a CE sample (Figure 3) to a non-CE sample (Figure 2) shows a very slight shift of the curves towards smaller voltages (towards left) for the former. This is easily explained by the parallel circuit of the two return contact resistances Rc2 = Rc4 which, in this case, would result in half the value seen by the rest of the circuit. The voltage drop over the resulting Rc is

assuming equal contacting resistances and no reverse current flowing through DUT2. A parallel IV measurement (Figure 4) on the contrary leads to the same results as seen in section 3 with just a single pixel. This can be explained by the halving of the total Rc while doubling the current flowing through Rc as each pixel contributes equally as long as the source voltage and the contact resistance on the Vs side are exactly(!) the same (Rc2 = Rc4, I1(t) = I2(t)). The assumption of the exact same contacting resistance for all pixels is surely not very realistic but serves the purpose.

Figure 4: IV-curve of DUT1 for parallel IV measurement of a CE sample with two pixels. For simplicity, both pixels are connected to the same voltage source

What if a pixel of a sample with common electrode (CE) is shunted?

Having a shunted pixel on a CE sample will further distort the resulting IV-curve. Figure 5 shows the circuit assuming a DUT2 pixel shunt of 1Ω.

Figure 5: IV curve of DUT1 for parallel measurement with shunted pixel DUT2 on a CE sample. x-axis of the plot is cut on the right side.

The effect of the shunt is not very pronounced for low contacting resistances (<1Ω) but shows a large shifting of the curves to the right while slightly flattening them even more. This constitutes the worst case for a passive DUT like a diode or an LED.

What happens with a solar cell and lights on?

The situation gets more complicated for a solar cell as it produces a photocurrent when illuminated. This behavior can be modelled by adding a current source parallel to the diode as shown in Figure 6 (see Figure 1 for comparison with the dark IV-curve). The solar cell is simulated with an arbitrarily chosen photocurrent of 1mA.

Figure 6: IV curve of a simple solar cell model in the dark and illuminated.

The first case (Figure 7 to Figure 10) is again the sequential measuring of the IV-curve for increasing Rc values. Maximum power point (MPP) and open-circuit voltage (Voc) are shown in the legends of the following graphs for a better comparison of the Rc effects on photovoltaic (PV) devices.

Figure 7: Single PV pixel with a photocurrent of 1mA. The MPP is shifted towards smaller values while Voc remains practically the same for increasing Rc values. See Figure 2 for comparison with the dark IV-curve.

Figure 8: IV-curve of DUT1 for sequential measurement of modelled solar cells. The MPP is decreasing with increasing Rc as seen before (values are about the same) but in addition Voc decreases with increasing Rc. See Figure 3 for comparison with the dark IV-curve.

Figure 9: IV-curve of DUT1 for sequential measurement with shunted DUT2 with Rs = 1Ω. The small shunt value decreases Rc (parallel circuit of the second pixel to Rc2 and Rc4) and ‘improves’ the bad contact. The MPP value deviations are reduced for such a small Rs. The photocurrent of DUT2 has practically no influence on the IV-curve for such low shunts.

Figure 10: IV-curve of DUT1 for sequential measurement with shunted DUT2 with Rs = 100Ω. While the MPP deviates again more than for lower shunt values, also the flattening is more pronounced but not as bad as in the example without a shunt (Figure 8). Its again the shunt that ‘improves’ the contacting resistance Rc.

Figure 11 to Figure 13 show the results for the parallel IV-method, which again is worse than the sequential method for larger Rc values (direct comparison between sequential and parallel method is shown in section 8).

Figure 11: IV-curve of DUT1 for parallel measurement of a PV sample. See Figure 4 for comparison with the dark IV-curve. The MPP values are almost equal to the sequential case (Figure 8) even though the curves’ flattening is much more pronounced.

Shunting the second pixel (Figure 12) shifts the DUT1 curves of higher Rc to the right while the flattening remains the same. The shift to the right is due to the additional current flowing through the second pixel shunt (DUT2 is not yet conductive). This current increases the voltage drop across Rc leading to a higher potential of the CE. This higher potential lowers the voltage across DUT1, which hence is starting to conduct only at a larger Vs value.

Figure 12: IV-curve of DUT1 for parallel measurement with shunted DUT2 with Rs = 1Ω. The circuit fakes an increasing MPP and unrealistic Voc for larger Rc values. x-axis is cut on the right side.

Figure 13 shows the same circuit but with a less severe pixel shunt of 100Ω. The shift to the left is now less pronounced as the additional current through the shunt is smaller compared to a low shunt value.

Figure 13: IV-curve of DUT1 for parallel measurement with shunted DUT2 with Rs = 100Ω. Also, a larger shunt will fake an increased MPP and Voc and is giving the IV-curve a slight kink downwards. The effect is however less pronounced the larger the shunt value.

Is sequential better than parallel?

Comparing the sequential with the parallel simulation of an IV-curve measurement (Figure 14) seems to show a more accurate result for the sequential method as the IV-curves are less flattened with increasing Rc. However, the accuracy is very similar for low Rc values (<1Ω) and worsens for increasing contacting resistance values to unusable results. In fact, both methods fail for larger Rc as MPP and Voc deviate substantially from the ideal case.

Figure 14: IV-curve of DUT1 for sequential (top) and parallel (bottom) IV measurement.

Let’s compare the different measuring methods for fixed Rc values

Figure 15 to Figure 18 compare the sequential and parallel method for dark (top) and illuminated (bottom) pixels for a fixed Rc. First, let’s compare the IV curves for the best case with Rc = 0.001Ω where all variants of Rc show the same result.

Figure 15: Comparing IV curves with Rc = 0.001Ω for dark (top) and illuminated (bottom) cases. The deviation from the ideal pixel is due to the additional anode-contact resistor of 1Ω.

Next, Rc is increased to 1Ω, which is a somewhat more realistic case. The curves start to deviate from the single pixel curve for the sequential (ends up closer to ideal case but still worse than with Rc << 1Ω) and the shunted case. A parallel measurement with the conditions described above (exact same contacting resistances and currents) does show the same result as the single pixel case and overlaps the curve.

Figure 16: Comparing IV curves with Rc = 1Ω for dark (top) and illuminated (bottom) cases

Figure 17 shows the comparison for devices with Rc = 10Ω. The deviations are even more pronounced. It is important to note that, if the IV curve of any multi-pixel parallel case is overlapping with the single pixel case (orange curve) in the following examples, it is because of the selected measurement conditions. It does not indicate that the multipixel measurement is as correct as the single pixel.

Figure 17: Comparing IV curves with Rc = 10Ω for dark (top) and illuminated (bottom) cases.

The last case shown here is with Rc = 50Ω because larger Rc values will give even more unusable results for any device configuration.

Figure 18: Comparing IV curves with Rc = 50Ω for dark (top) and illuminated (bottom) cases.

How does the IV curve of the shunted pixel behave?

The DUT2 IV curves (Figure 19) for increasing Rc will result in exactly the same curve(s) as for DUT1 (see Figure 8), if DUT2 is not shunted and a parallel IV measurement is performed.

Figure 19: Parallel IV curves of DUT2 under light with varying Rc.

The dark case for shunted DUT2 for the sequential and parallel case are shown in Figure 20 and Figure 21.

Figure 20: Sequential dark IV curves of DUT2 with shunt resistor of 1Ω (top) and 100Ω (bottom).

Figure 21: Parallel dark IV curves of DUT2 with shunt resistor of 1Ω (top) and 100Ω (bottom).

Illuminating and shunting DUT2 with 1Ω or 100Ω in sequential mode results in IV-curves shown in Figure 22.

Figure 22: Sequential IV curves of DUT2 with shunt resistor of 1Ω (top) and 100Ω (bottom).

Illuminating and shunting DUT2 with 1Ω or 100Ω in parallel mode is shown in Figure 23.

Figure 23: Parallel IV curves of DUT2 with shunt resistor of 1Ω (top) and 100Ω (bottom)

What about stressing measurements?

Pixels will influence each other as soon as a common electrode and a contacting resistance are present as seen in the simulated IV-curves above (section 5). This is also observed for stressing measurements of one or several pixels of such a sample. The current through a pixel will change as soon as the current through another pixel changes and hence the measurements of V(t) and I(t) will no longer be neighbor-independent. The effect becomes more prominent the larger the contacting resistance is. Also shunted pixels will introduce a difference between the measured voltage over a given pixel and the actual voltage over a DUT leading to an over- or underestimated maximum power point tracking for instance.

Summary of simulated cases

The effects on IV-measurements for multi-pixel samples without and with common electrode are investigated. In addition, the influence of shunted pixels is shown. The conclusion drawn from the above results emphasizes the importance of small contacting resistances (<1Ω) to reduce the influence on measurement results. Increased contact resistances will shift the measured currents and voltages and produce wrong results in open-circuit voltage (VOC) and maximum-power-point (MPP) estimations (even in the case of single pixel samples). Only short-circuit current (ISC) values are not affected. Shunted pixels, which are not excluded properly through e.g. being electrically disconnected from the measuring circuit, will distort the measurements even more. It is highly recommended to metallize all contacts of a sample with a high conducting material like gold or silver, clean the contacting pins properly and replace them when worn. To increase the accuracy of the measurement and minimize the influence of neighboring pixels, pads of shunted pixels should be isolated from the others by masking them with tape to prevent contact with the measuring instrument as long as the instrument does not allow for electrical disconnection of the pixel.

Real measurements

A set of measurements has been performed with a test PCB (Figure 24) to verify the simulations shown above. The test PCB is equipped with small solar cells (D1 to D6) of type PDB-C152SM (1206 SMD) and a resistor Rc to simulate the padto-pin resistance as well as a shunt resistor Rs. Both Rc and Rs are varied and used in different combinations to verify the findings seen in the simulations. Note that the curves are not directly comparable as the devices (D) used to have slightly different characteristics (present intrinsic serial and parallel resistance), six instead of two devices are employed, and the values for the resistors do not match the ones in the simulation. Nonetheless, the simulation results from above are shown below for a comparison of the overall tendencies.

Figure 24: Circuit of test PCB with six solar cells and options for shunting a single pixel (Rs) as well as modifying the pad-to-pin resistance (Rc).

Dark IV measurements

The dark IV curve of pixel D1 (shown as a representative of all pixels) for a parallel measurement is shown in Figure 25. Flattening of the curves with increasing Rc as seen in the simulation Figure 26 can be observed. The more extreme flattening in the measurement compared to the simulation can be explained by the different characteristics of the PV cell.

Figure 25: Increasing Rc for IV curves measured in parallel mode. No pixels are shunted (Rs = ∞Ω).

Figure 26: Simulation of increasing Rc for IV curves in parallel mode. No pixels are shunted (Rs = ∞Ω).

The effects of a shunted neighboring pixel on a measured pixel are shown in Figure 27. The shift to the right can again be observed as also seen in the simulation Figure 28. Values should not directly be compared to the simulation.

Figure 27: Effects of shunting a pixel on the IV curves.

Figure 28: Simulation of the effect of a neighboring shunted pixel.

Figure 29 compares the sequential and parallel measuring methods for the dark case. The behavior can be compared to Figure 30 of the simulation. The sequential measurement will lead to results closer to the ideal case with Rc = 0Ω compared to a parallel measurement with a contacting resistance and a shunt will mainly influence the parallel measurement by shifting the curve to the right.

Figure 29: Comparing parallel and sequential measurements.

Figure 30: Simulation of sequential and parallel method.

Light IV measurements

Figure 31 to Figure 33 show the illuminated PV cells with various combinations of Rs, Rc and measurement methods (see legend for details). Sequential measurements are plotted as dashed lines for better identification. The figures show only the region of interest. Comparing the results with the simulation Figure 32 show similar tendencies above 0.68V but they do not match around VOC. A reason could again be the intrinsic serial and parallel resistance in the measured devices.

Figure 31: IV curve of pixel 1 under illumination. Compared are sequential and parallel measurements with and without contact resistance Rc.

Figure 32: Simulation of sequential and parallel method under illuminated conditions without a shunt.

The next figure Figure 33 shows the IV-curves of pixel 1 when pixel 2 is shunted with 10Ω. The tendencies can again be seen in the simulated curves in Figure 34. Even the curve (red) for the sequential method with Rc and a shunted neighbor shows the same crossing of the Rc-free curves (blue, orange, green) in both the measurement and simulation. It is not very apparent in the measurement though.

Figure 33: IV curves of pixel 1 under illumination with shunted pixel 2. Compared are sequential and parallel measurements with and without added contact resistance Rc.

Figure 34: Simulation of sequential and parallel method under illuminated conditions a shunt of 1Ω.

Conclusion of measurements

The measurements with sequential and parallel methods as well as artificial contact resistance and shunts show nicely the expected behavior seen in the simulations