# The basic characteristics of solar cells: output power/fill factor/photoelectric conversion efficiency

Solar cell output power and fill factor
The output power of the solar battery is equal to the product of the current and voltage flowing through the battery, that is, according to the power definition formula P=UI, set P as a different constant, and substitute U and I to output the volt-ampere characteristic curve in the solar battery. Make a series of equal power curves (as shown in Figure 1). Among these equal power curves, only the one that is tangent to the output volt-ampere characteristic curve of the solar cell. The bar is the maximum output power of the solar cell under the current irradiance. This tangent point is called the optimal operating point M. The intersection drawn from the origin The straight line at point M is the optimal load line, the calculated optimal resistance value Rm of the load, the current value corresponding to point M is the optimal output current Im, and the corresponding voltage value is the optimal output voltage Um. From Im and Um The obtained rectangular geometric area is also the largest area that can be covered by the characteristic curve, which is called the optimal output power or maximum output power Pm of the solar cell. It can also be obtained by the following formula:
Pm=ImUm = FFIscUoc
In the formula, FF is the fill factor of the solar cell, sometimes also called the curve factor. In order to be more helpful to accurately calculate the maximum power point, the P-U curve as shown in Figure 2 can also be drawn according to the volt-ampere characteristic curve.

The fill factor of a solar cell is an important parameter to evaluate the performance of the solar cell and determines the output characteristics of the solar cell. The higher the fill factor, the closer the output characteristic is to a rectangle, and the higher the photoelectric conversion efficiency of the solar cell. The fill factor FF is less than 1. There are many factors that affect the fill factor. It is not only related to internal parameters such as the PN junction curve constant A, parallel resistance RSH, and series resistance Rs of the battery material, but also related to external conditions such as solar cell operating temperature T and irradiance. .

It can also be seen in the graph of the solar cell volt-ampere characteristic curve that the more square the volt-ampere characteristic curve is, the larger the curve factor FF will be. At this time, the corresponding solar cell output characteristics will be better, and the photoelectric conversion efficiency of the cell will be higher. For conventional silicon solar cells, FF is generally between 0.75 and 0.8. The parallel resistance RSH and series resistance Rs of the solar cell have a great influence on the fill factor. The short-circuit current will drop more and the fill factor will also decrease: the smaller the parallel resistance, the greater the shunt current.
The more the open circuit voltage drops, the more the fill factor decreases (as shown in Figure 3).

Photoelectric conversion efficiency
The photoelectric conversion efficiency of a solar cell refers to the percentage of the maximum output electric power of the light-receiving single solar cell to the total optical power radiated to the geometric area of ​​the light-receiving plane of the cell, namely

In the formula, Pm is the maximum output power of the solar cell; Pm is the input power of the light. illumination
The input power can be calculated by the following formula

In the formula, Aall is the total area of ​​the solar cell exposed to light; F(λ) is the photon flux density of the spectrum with wavelength λ; h is Planck’s constant; C is the speed of light. The calculation of Pm is as mentioned above, so the photoelectric conversion efficiency of the solar cell can be expressed by the following formula

Among them, the short-circuit current of the solar cell can also be calculated by the following formula
Isc =9ηeN(Eg)
In the formula, ηe is the collection efficiency or quantum efficiency, that is, the ratio of the number of electron-hole pairs generated and collected by each photon to the number of generated electron-hole pairs (the value is less than 1); N(Eg) is the energy The photon flow exceeding the forbidden band width Eg.

It can be seen from the above calculation that the short-circuit current is proportional to ηe and N(Eg). The photoelectric conversion efficiency η of the solar cell is also a function of ηe, N(Eg) and the fill factor FF. There are many factors that affect the photoelectric conversion efficiency of solar cells. There are six main types of losses that affect the efficiency of solar cells during the entire photoelectric conversion process.
①The solar cell chooses the wavelength of sunlight. Different wavelengths of sunlight have different penetrating capabilities. Only photons that enter the battery material and have an energy greater than the band gap Eg can generate electron-hole pairs. This process consumes approximately 25% of solar radiation energy.
②The reflection of light on the surface of the solar cell causes the loss of solar radiant energy. Using a better anti-reflection process, the radiant light will also lose about 10%.
③The loss of photons inside the solar cell. The photons with energy greater than Eg reach the inside of the semiconductor, but due to recombination and lifetime, all of them cannot be generated into useful electron-hole pairs. This process will cost approximately 60%.
④ The maximum operating voltage of solar cells is generally about 60% of the open circuit voltage, so full power output cannot be achieved.
⑤ Due to the influence of the series resistance Rs and the parallel resistance RSH, the output efficiency is often reduced by about 5%.
⑥Filling factor FF is usually 0,75~0.8.

The actual photoelectric conversion efficiency of the solar cell is combined and deducted from the above-mentioned parts of the loss, and converted into the total efficiency. Therefore, the actual efficiency of solar cells produced by conventional processes is about 18%-22%. Even by improving the technological means and processes of battery production, the actual efficiency of solar cells can only reach about 20%. Solar cells made of different materials have different photoelectric conversion efficiencies due to different internal band gap widths and different responses to light of various wavelengths. Calculations show that under the condition of air quality AM1.5, the upper limit of the photoelectric conversion efficiency of silicon-type solar cells is 33%, and the upper limit of the current commercial silicon-type solar cells is 25%, so there is a certain potential for development.