## Combinatorial flux adder for determining photovoltaic cell nonlinearity

In the solar cell measurement field, there have been reports of two kinds of nonlinearity verification methods. One involves performing irradiance-mode spectral response measurements as a function of light bias (LB) current . The second method includes a simple flux addition method using a dual light source approach. The measurement from the first technique requires the use of complicated optics and an elaborate setup and reliance on the use of a calibrated reference photodetector whose linearity response over the low light conditions of the modulated monochromatic beam has is previously verified by another method. Additionally, this method can be time consuming especially when the light bias current needs to vary over many orders of magnitude. The second method based on comparing the ratio of added photocurrents obtained from two light sources, such as tungsten sources or two LEDs to their combined two-source output, can reveal device nonlinearity, but does not provide any insight on the actual nonlinear relationship.

This new NIST novel invention resolves these issues. It consists of two LED lamps (can be extended to sets of LED lamps of many different colors) that are remotely controlled by two LED drivers that supply certain amounts of current, first to each LED separately (singular currents), and then a combination of these unique currents to both LEDs at the same time (combination currents). A solar cell is placed in the path of the light flux generated by these LEDs. The cell can be illuminated by the LEDs in free space or through a medium such as a light pipe, ensuring maximum excitation. For each supplied current, a short circuit current signal is recorded from the solar cell. The LEDs are pulsed, for better stability, and the photogenerated current from the cell is an AC current that is first converted to voltage using a transimpedance preamplifier with a gain. This voltage is then measured by a lock-in amplifier. A lock-in amplifier only measures AC signals of a certain frequency (the pulsed frequency of the LED supplied current), therefore, the signal to noise ratio is very high. The objective is to use the measured solar cell signals and calculate the incident fluxes, taking advantage of the physical property that flux is an additive quantity. This is achieved by constructing an over determined linear system of equations, based on an Nth degree polynomial model for the relationship between signals and fluxes. These equations are solved using linear least squares fit, to solve for unknown fluxes and the degree coefficients. If the relationship between the generated signals and the incident fluxes is linear, then no higher order terms above 1 are required. However, for nonlinear devices, it may be necessary to solve for 4th or 5th degree polynomial terms. Generally, the quantity of interest is the ratio of signal to flux, r, vs. signal. If r is fixed as a function of signal, the cell is considered linear. However, there are many types of solar cell devices that show a changing r, indicative of nonlinear behavior. From a fundamental physics perspective, knowledge of this non-linear relationship can be useful in understanding or modeling charge carrier recombination phenomena or the role of defects on device performance. From a practical measurement perspective, reference solar cells or detectors that are used to measure the output of other test cells or modules are typically required to have a linear short circuit current output with irradiance over the range of interest. Since the plane of incidence irradiance level is set and monitored using linear short circuit current measurements of a reference cell, it is imperative that such devices have a linear output with irradiance, particularly over the standard reporting conditions. If the reference cell is not linear and no other substitute cells are available, then the irradiance measurements can be corrected based on knowing the mathematical relationship between the signal and the flux.

The aspects of this invention that are new are: 1. The two selected LEDs are first pulsed individually (creating singular fluxes), and then pulsed together in a combinatorial fashion, 2. The combination fluxes can be as many as desired, but more combinations provide a better fit outcome. This approach allows for the implementation of a very simple algorithm and the singular and combinatorial signals are simply recorded in a spreadsheet without the need for de-convoluting one from another, 3. The lock-in based technique provides for great signal to noise detection, 4. To take advantage of all the flux the LEDs can generate or to improve light mixing when using many LEDs, the light from both LEDs (or both LED sets) can first be coupled into a light pipe, which can then direct the mixed light to the solar cell location, 5. The data is analyzed within the framework of a polynomial-form, overdetermined linear system of equations of up to Nth degree to solve for the unscaled ratios of signal-to-flux. The goodness of the fit is determined by considering the residuals and their pattern, and 6. The unscaled ratios can be scaled based on a known flux measurement using a previously calibrated detector.

The figure below (100) is a combinatorial flux adder in the second singular period. The elements are: driver (102), light emitters (104 and 106), second light (110), photovoltaic cell (112), first control signal (114), second control signal (116), second photon flux (122), and photovoltaic output (132).

The invention is a light emitting diode (LED)-based system utilizing a combinatorial flux addition method to investigate the nonlinear relationship between incident irradiance flux and the short circuit current signal in solar cells. The magnitude of the light flux is controlled by supplied currents to two LEDs in pulsed mode and within a combinatorial algorithm. The data is then analyzed by means of an overdetermined linear system of equations derived from an appropriately chosen Nth degree polynomial representing the relationship between the measured signals and the unknown incident fluxes. The flux values and the polynomial coefficients are then determined by a linear least squares method to obtain the best fit. The technique can be applied to any solar cell, under either a monochromatic or broadband spectrum.

Does not require the use of complicated optics and an elaborate setup

Behrang Hamadani, Andrew Shore, Howard Yoon