Photovoltaic (PV) cells, also called solar cells, convert light directly to electricity. Fabricated from a wide variety of materials and processing methods, these devices are used for terrestrial power generation as well as commercial, military, and research space power applications.
In these applications, during R&D and in production, characterization of PV cell electrical performance often is required. This involves measuring cell I-V characteristics.
A PV cell may be represented by the equivalent circuit model shown in Figure 1, consisting of a photon current source, IL; a diode; a series resistance, rs, and a shunt resistance, rsh. The rs represents the ohmic losses on the front surface of the cell; the rsh is the loss due to diode leakage currents.
The conversion efficiency, h, is defined in Equation 1:
h = ––– (1)
where: Pin = the power input to the cell defined as the total radiant energy incident on the surface of the cell.
Pm = the maximum power point which is the product of Im and Vm, the cell current and voltage where the power output of the cell is the greatest (Figure 2).
The fill factor (FF), Equation 2, is a figure of merit for the cell, indicating how far the cell I-V characteristics deviate from those of an ideal diode.
FF = ––––– (2)
The FF is the ratio of the areas of the two rectangles bounded by the products ImVm and IscVoc, also shown in Figure 2 where Voc is the open-circuit voltage and Isc is the short-circuit current. The greater the value of rs and the lower rsh, the lower the value of FF, which always is less than 1.0.
These and other critical performance parameters, especially the cell’s equivalent rsh and rs, must be determined under carefully controlled test conditions. During I-V measurements, the cell must be maintained at a constant temperature and requires a light source with constant intensity and a known spectral distribution.
For cells used in space and terrestrial applications, the intensity and spectral distribution of the source should closely approximate the sun. High accuracy in Isc, Voc, and FF measurements using a secondary source is achieved with data corrections based on measurements made with standard cells under reference levels of illumination, such as those obtained in high-altitude balloons and aircraft.
Forward Bias I-V
Measurements under controlled illumination are used to generate the forward biased I-V curve between the two points (V1 = 0, I1 = Isc) and (V2 = Voc, I2 = 0). The parameters Voc and Isc can be directly determined from the curve, then Im, Vm, Pm, FF, and h can be easily calculated using Equations 1 and 2. In actual practice, Im and Vm are determined as a result of iteratively maximizing Pm (all the I-V point pairs in the I-V curve), which then provides the product Im Vm in Equation 2.
Several methods have been developed to estimate rsh and rs from the I-V characteristics of the cell under varying levels of illumination. Each method has limitations that depend on the type of cell under investigation and operating conditions, such as temperature and light intensity.
An early method providing good results in rs derivation is based on I-V curve measurements at two or more light intensities. For the simplest case, two light intensities are used to find short-circuit currents, Isc1 and Isc2, by using a current D I below Isc, where In = Isc – D I is chosen on both I-V curves. The currents I1 = Isc1 – D I and I2 = Isc2 – D I correspond to voltages V1 and V2 and rs then is given by
The technique also may be extended to multiple points using more than two light intensities, generating a line whose slope gives the series resistance according to
The method is illustrated in Figure 3.
Reverse Bias I-V
The reverse-bias test is performed in the dark between 0 V and the level where breakdown begins to occur. Figure 4 illustrates the typical reverse-bias response of a PV cell, including the linear region used to estimate rsh.
Test System and Configuration
Depending on the test environment, PV cell I-V measurements might be made with manually operated power supplies and DMMs or with PC-controlled source-measure units (SMUs) connected to cells through an automated switching system. Manual instruments are suitable for R&D. Automated instruments are prevalent in production environments where multiple devices connect to the SMU through a scanner.
Figure 5 is a basic equipment configuration for generating forward-bias I-V curves, using an SMU and four-wire connections to the cell to minimize measurement lead-resistance errors. A solar simulator provides appropriate illumination for the cell. A cooled, vacuum hold-down chuck secures the cell and provides isothermal test conditions.
The rs of a PV cell is low, typically less than 1 W for cells designed for operation at 1× sun intensity (approximately 135.7 mW/cm2) and less than 0.1 W for concentrator cells. The rs of concentrator cells must be low to minimize I2R losses, because these cells are designed to operate at intensities of several hundred to several thousand suns. Since the rs of the cell is relatively low, a four-wire connection to the cell contacts is required to make accurate I-V measurements.
If currents to be measured under these conditions are greater than 1 µA, an unguarded, four-wire configuration using Kelvin contact probes provides accurate measurements. For test currents less than 1 µA, stray leakage currents in cables and fixturing may create errors and noise in the measurements.
Two methods are available to reduce or eliminate these errors. The first requires high-resistance materials when constructing the test fixture and keeping the fixture free of contaminants.
The second method employs built-in guard circuitry found in some SMUs. This method, illustrated in Figure 6, avoids the hassle of finding special fixture materials and taking extraordinary precautions in fixture and PV cell handling.
In Figure 6, the V-W guard output of the SMU is a low-impedance source at nearly the same potential as the high-impedance point, Hi (output). Guarding ensures that the contact-probe housing remains isolated from the circuit.
Although the probe housing is constructed of insulating materials, contamination could cause a breakdown in resistance and introduce measurable stray currents. The guard plate under the probe, at approximately the same potential as the probe on the top contact of the cell, ensures that no current flows through the probe housing, so the measured current is only that flowing through the cell.
Source current specifications for the SMU depend on PV cell characteristics. Most solar cells require an instrument that can source/sink currents between 1 A and 3 A for short-circuit tests. A few cells may need less, but think about future requirements before selecting a lower rated instrument (Table 1).
Other characteristics of the SMU should include current measurement accuracy of less than 1%, low source noise levels, measurement input impedance of 109 W or higher, and voltage measurement repeatability around 0.02%. An SMU with these specifications is a cost-effective alternative to using an expensive, high-wattage programmable power supply with a separate DMM.
Some solar cell assemblies use multiple PV cells in series. When testing these, make sure the SMU has adequate voltage ranges and resolution for the I-V measurements. For example, 10-mV resolution on a 2-V range is adequate to generate the I-V curve of any single junction cell. A 20-V range with 100-mV resolution might be required for multi-junction cells and small arrays. For reverse-bias, dark condition I-V measurements, a 1-mA minimum current range with about 10-pA resolution should be sufficient for most cells.
About the Author
Roland Lowe is an applications engineering manager at Keithley Instruments. He has eight years of experience in ATE system design and construction, including active component test systems. Previously, Mr. Lowe was with NASA Lewis Research Center. He received a B.S.E.E. degree from Rensselaer Polytechnic Institute and an M.S.E.E. degree from Cleveland State University. Keithley Instruments, 28775 Aurora Rd., Cleveland, OH 44139, (800) 552-1115.
1. SMU: Keithley Model 2420 Digital SourceMeter® or equivalent*
2. PC with an IEEE 488.2 interface card
3. Source illumination (solar simulator)
4. Temperature-controlled hold down chuck/test fixture
5. IEEE 488 interface cable
6. Test leads (four-wire) and two-point, adjustable contact probes
* Primary criteria are sufficient forward bias current capacity and adequate resolution for reverse-bias dark-current measurements (frequently as small as 1 nA and possibly as low as 10 fA).
Copyright 1998 Nelson Publishing Inc.