Evaluation of electrical performance of solar photovoltaic cells

Electricity from sunlight is a truly "green" and cheap energy source, but requires an energy conversion system based on photovoltaic (PV) cells and storage devices (such as batteries). PV or solar cells are increasingly used in outdoor lighting, and even in the home and industry; they can be made using the same processes used to manufacture semiconductor devices. The function of a solar cell is very simple: it absorbs photons of sunlight and releases electrons. When a load is connected to the solar cell, an electric current is generated.

Electrical characterization of PV cells and materials requires a variety of electrical measurements. These tests can be performed on cells during R&D or as part of the cell manufacturing process. These tests include current vs. voltage (IV), capacitance vs. voltage (CV), capacitance vs. frequency (Cf), and pulsed IV tests. Many common parameters can be extracted from these electrical test results, such as output current, maximum output power, doping density, conversion efficiency, resistivity, and Hall voltage.

PV cells are made from a variety of light-absorbing materials, including crystalline and amorphous silicon, thin films made from cadmium telluride (CdTe) and copper indium gallium selenide (CIGS) materials, and organic/polymer-based materials.

The equivalent circuit model of a PV cell (see Figure 1) provides insight into how this device works. An ideal PV cell can be modeled as a photosensitive current source in parallel with a diode. Photons from the light source are absorbed by the solar cell material. If the energy of the photons is higher than the energy band of the cell material, electrons are excited into the conduction band. If an external load is connected to the output of the PV cell, current is generated.

PV Cell/Photon Hυ/Load

Figure 1. The equivalent circuit of a photovoltaic cell consisting of a series resistor (RS), a shunt resistor (rsh), and a light-driven current source.

Due to material defects and ohmic losses in the cell substrate material and its metal leads and contacts, the PV cell model must represent these losses in terms of series resistance (RS) and shunt resistance (rsh), respectively. Series resistance is a critical parameter because it limits the maximum available power (PMAX) and short-circuit current (ISC) of the PV cell.

The series resistance (rs) of a PV cell is a function of the metal contact resistance on the cell, ohmic losses on the front surface of the cell, impurity concentration, and junction depth. Ideally, the series resistance should be zero. The shunt resistance represents the losses due to surface leakage or lattice defects along the cell edge. Ideally, the shunt resistance should be infinite.

To extract the important test parameters of photovoltaic cells, various electrical measurements are required. These measurements usually include DC current and voltage, capacitance, and pulse IV.

Electricity from sunlight is a truly "green" and cheap energy source, but requires an energy conversion system based on photovoltaic (PV) cells and storage devices (such as batteries). PV or solar cells are increasingly used in outdoor lighting, and even in the home and industry; they can be made using the same processes used to manufacture semiconductor devices. The function of a solar cell is very simple: it absorbs photons of sunlight and releases electrons. When a load is connected to the solar cell, an electric current is generated.

Electrical characterization of PV cells and materials requires a variety of electrical measurements. These tests can be performed on cells during R&D or as part of the cell manufacturing process. These tests include current vs. voltage (IV), capacitance vs. voltage (CV), capacitance vs. frequency (Cf), and pulsed IV tests. Many common parameters can be extracted from these electrical test results, such as output current, maximum output power, doping density, conversion efficiency, resistivity, and Hall voltage.

PV cells are made from a variety of light-absorbing materials, including crystalline and amorphous silicon, thin films made from cadmium telluride (CdTe) and copper indium gallium selenide (CIGS) materials, and organic/polymer-based materials.

The equivalent circuit model of a PV cell (see Figure 1) provides insight into how this device works. An ideal PV cell can be modeled as a photosensitive current source in parallel with a diode. Photons from the light source are absorbed by the solar cell material. If the energy of the photons is higher than the energy band of the cell material, electrons are excited into the conduction band. If an external load is connected to the output of the PV cell, current is generated.

PV Cell/Photon Hυ/Load

Figure 1. The equivalent circuit of a photovoltaic cell consisting of a series resistor (RS), a shunt resistor (rsh), and a light-driven current source.

Due to material defects and ohmic losses in the cell substrate material and its metal leads and contacts, the PV cell model must represent these losses in terms of series resistance (RS) and shunt resistance (rsh), respectively. Series resistance is a critical parameter because it limits the maximum available power (PMAX) and short-circuit current (ISC) of the PV cell.

The series resistance (rs) of a PV cell is a function of the metal contact resistance on the cell, ohmic losses on the front surface of the cell, impurity concentration, and junction depth. Ideally, the series resistance should be zero. The shunt resistance represents the losses due to surface leakage or lattice defects along the cell edge. Ideally, the shunt resistance should be infinite.

To extract the important test parameters of photovoltaic cells, various electrical measurements are required. These measurements usually include DC current and voltage, capacitance, and pulse IV.

DC current-voltage (IV) measurement (provides V measurement I)

PV cells can be evaluated using a DC IV curve, which typically shows the current produced by a solar cell as a function of voltage (see Figure 2). The maximum power (PMAX) that the cell can produce occurs at the maximum current (IMAX) and voltage (VMAX) points, and the area under the curve represents the maximum output power that the cell can produce at different voltages. This IV curve can be generated using basic measurement tools such as an ammeter and voltage source, or instruments that integrate source and measurement capabilities such as a digital source meter or source measure unit (SMU). To meet the needs of this type of application, the test equipment must be able to source voltage and sink current over the range available for PV cell measurements, while providing analysis capabilities to accurately measure current and voltage. A simplified measurement configuration is shown in Figure 2.

Battery current (mA) / Maximum power area / Battery voltage

Figure 2. This curve shows the typical forward-biased characteristics of a PV cell, where maximum power (PMAX) occurs at the intersection of maximum current (IMAX) and maximum voltage (VMAX).

Solar Cells

Figure 3. A typical system for measuring the IV curve of a solar cell consists of a current source and a voltmeter.

The measurement system should support four-wire measurement mode. Using four-wire measurement technology can solve the problem of lead resistance affecting measurement accuracy. For example, one pair of test leads can be used to provide a voltage source, and the other pair of leads can be used to measure the current flowing through the battery. It is important to place the test leads as close to the battery as possible.

A true DC IV curve of an illuminated silicon solar cell measured with an SMU is shown in Figure 4. Since the SMU can sink current, the curve passes through the fourth quadrant and allows the device to source power.

Figure 4. This typical IV curve for a forward-biased (illuminated) PV cell shows how output current rises rapidly with increasing voltage.

Other data that can be derived from a PV cell's DC IV curve characterize its overall efficiency -- how quickly it converts light energy into electrical energy -- which can be defined by a number of parameters, including its energy conversion efficiency, maximum power performance, and fill factor. The maximum power point is the product of the maximum cell current and voltage, where the cell's power output is at its highest.

Fill factor (FF) is a way to compare the IV characteristics of a PV cell to the IV characteristics of an ideal cell. Ideally, it should be equal to 1, but in real PV cells, it is generally less than 1. It is actually equal to the maximum power generated by the solar cell (PMAX=IMAXVMAX) divided by the power generated by the ideal PV cell. The fill factor is defined as follows:

FF=IMAXVMAX/(ISCVOC)

Where IMAX = current at maximum output power, VMAX = voltage at maximum output power, ISC = short-circuit current, and VOC = open-circuit voltage.

The conversion efficiency is the ratio of the maximum output power (PMAX) of the photovoltaic cell to the input power (PIN), that is:

h=PMAX/PIN

IV measurements of PV cells can be made in either forward bias (under illumination) or reverse bias (in darkness). Forward bias measurements are made with controlled illumination of the PV cell, where the energy from the illumination represents the input power to the cell. The cell is swept with a range of applied voltages and the current produced by the cell is measured. Typically, the voltage applied to the PV cell is swept from 0V to the open circuit voltage (VOC) of the cell. At 0V, the current should be equal to the short circuit current (ISC). When the voltage is VOC, the current should be zero. In the model shown in Figure 1, ISC is approximately equal to the load current (IL).

The series resistance (rs) of a PV cell can be found from at least two forward-biased IV curves measured at different light intensities. The light intensity is not important, because it is the ratio of the change in voltage to the change in current, the slope of the curve, that is meaningful in all cases. Remember that the slope of the curve varies greatly from the beginning to the end, and the data we are interested in appears in the far-forward region of the curve, where the curve begins to show linear characteristics. At this point, the inverse of the change in current as a function of voltage gives the value of the series resistance:

rs=ΔV/ΔI

The measurements discussed so far in this article have been made on PV cells exposed to luminous output power, i.e., under forward bias conditions. However, certain characteristics of PV devices, such as shunt resistance (rsh) and leakage current, are obtained when the PV cell is shielded from light, i.e., under reverse bias conditions. For these IV curves, the measurements are made in a dark room, and the output current is measured and plotted against the applied voltage from a starting voltage of 0V to the point where the PV cell begins to break down. The slope of the PV cell's reverse bias IV curve can also be used to determine the magnitude of the shunt resistance (see Figure 5). From the linear region of the curve, the shunt resistance can be calculated as follows:

rsh=ΔVReverseBias/ΔIReverseBias

V reverse bias/linear region for estimating rsh/ΔI reverse bias/ΔV reverse bias/logI reverse bias

Figure 5. The slope of a PV cell's reverse-biased IV curve provides the shunt resistance of a PV cell.

In addition to performing these measurements without any light source, the PV cells should be properly shielded and low-noise cables should be used in the test configuration.

Capacitance measurement

Similar to IV measurements, capacitance measurements are used to characterize solar cells. Depending on the cell parameter that needs to be measured, the capacitance can be measured as a function of DC voltage, frequency, time, or AC voltage. For example, measuring the capacitance of a PV cell as a function of voltage can help us study the doping concentration of the cell or the built-in voltage of a semiconductor junction. Capacitance-frequency sweeps can provide information for finding charge traps in the depletion region of the PV substrate. The capacitance of a cell is directly related to the area of ​​the device, so a device with a larger area to measure will have a larger capacitance.

CV measurements measure the capacitance of the cell under test as a function of the applied DC voltage. As with IV measurements, capacitance measurements use a four-wire technique to compensate for lead resistance. The cell must maintain a four-wire connection. The test setup should include a shielded coaxial cable with the shield connected as close to the PV cell as possible to minimize cable errors. Correction techniques based on open and short circuit measurements can reduce the effect of cable capacitance on measurement accuracy. CV measurements can be made in both forward and reverse bias conditions. A typical curve of capacitance versus sweep voltage in reverse bias (see Figure 6) shows a rapid increase in capacitance when sweeping toward the breakdown voltage.

Figure 6. Typical curve of PV cell capacitance versus voltage.

Another capacitance-based measurement is drive level capacitance profiling (DLCP), which can be used on some thin-film solar cells (e.g. CIGS) to determine the relationship between PV cell defect density and depth. This measurement involves applying a swept peak-to-peak AC voltage and varying the DC voltage while making capacitance measurements. The two voltages must be adjusted so that the total applied voltage (AC + DC) remains constant even while sweeping the AC voltage. In this way, the exposed charge density in a certain area within the material will remain constant, and we can obtain the defect density as a function of distance.

Resistivity and Hall voltage measurement

The resistivity of PV cell materials can be measured using a four-pin probe method3 by sourcing current and measuring the voltage, using either a four-point collinear probing technique or the Van der Pauw method.

When using the four-point collinear detection technique for measurement, two of the probes are used to connect the current source and the other two probes are used to measure the voltage drop on the photovoltaic material. When the thickness of the PV material is known, the volume resistivity (ρ) can be calculated according to the following formula:

ρ=(π/ln2)(V/I)(tk)

Where ρ = volume resistivity in Ωcm, V = measured voltage in V, I = source current in A, t = sample thickness in cm, and k = correction factor that depends on the ratio of probe to wafer diameter and the ratio of wafer thickness to probe spacing.

Another technique for measuring the resistivity of PV materials is the Van der Pauw method, which uses four small contacts around a plate to apply current and measure the resulting voltage. The plate to be tested can be a PV material sample of uniform thickness and any shape.

The Van der Pauw resistivity measurement method requires measuring eight voltages. Measurements V1 to V8 are made around the perimeter of the material sample, as shown in Figure 7.

Figure 7. Common methods for measuring Vanderbilt resistivity

The two resistivity values ​​can be calculated using the above 8 measurement results according to the following formula:

ρA=(π/ln2)(fAts)[(V1–V2+V3–V4)/4I]
ρB=(π/ln2)(fBts)[(V5–V6+V7–V8)/4I]

Where ρA and ρB are the two volume resistivity values, ts = sample thickness in cm, V1–V8 are the measured voltages in V, I = the current flowing through the photovoltaic material sample in A, and fA and fB are geometric coefficients based on the sample symmetry that are related to the two resistance ratios QA and QB as follows:

QA=(V1–V2)/(V3–V4)
QB=(V5–V6)/(V7–V8)

When the values ​​of ρA and ρB are known, the average resistivity (ρAVG) can be calculated according to the following formula:

ρAVG=(ρA+ρB)/2

Errors in high resistivity measurements can come from many sources, including electrostatic interference, leakage current, temperature, and carrier injection. Electrostatic interference is generated when a charged object is brought near the sample. To minimize these effects, the sample should be properly shielded from external charges. This shield can be made of conductive material and should be properly grounded by connecting the shield to the low potential terminal of the measurement instrument. Low-noise shielded cables should also be used for voltage measurements. Leakage currents can affect the measurement accuracy of high-resistance samples. Leakage currents come from cables, probes, and test fixtures and can be minimized by using high-quality insulators, minimizing moisture, and enabling guarded measurements, including the use of triaxial cables.

Pulsed IV Measurement

In addition to DC IV and capacitance measurements, pulsed IV measurements can also be used to derive certain parameters of solar cells. In particular, pulsed IV measurements have been very useful in determining the effects of conversion efficiency, minimum carrier lifetime, and cell capacitance.

All of the PV measurements detailed in this article can be quickly and easily performed using an automated test system designed for semiconductor characterization, such as the 4200-SCS Semiconductor Characterization System from Keithley Instruments.4 The system can source and sink current using four-pin probing and supports software-controlled current, voltage, and capacitance measurements. The system can be configured with a variety of source and measure modules to perform continuous and pulsed IV and CV measurements to obtain some important PV cell parameters. For example, the system can be connected to a PV cell using a 4225-PMU module for a pulsed IV sweep (see Figure 8)5. In addition to sourcing a pulsed voltage, the PMU can also sink current to measure the output current of the solar cell, as shown in Figure 9. The 4200-SCS system supports a variety of hardware modules and software measurement function libraries.

Solar cell/SMA coaxial line connection common end

Figure 8. The 4225-PMU module can be used for pulsed IV measurements on PV cells.

Figure 9. Plotted representation of pulsed IV measurement on a silicon PV cell