### Photocurrent and photovoltage

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The illumination characteristics of silicon solar cells are shown in Figure 1. It can be seen from the figure that the short-circuit current increases linearly with the increase of light intensity, the open-circuit voltage increases exponentially with the increase of light intensity, and tends to be saturated under strong light. The I-U characteristic curves of solar cells under different irradiance are shown in Figure 2.

1. Photocurrent Assuming that all photogenerated carriers generated in the solar cell can be collected, the photocurrent density J_{L} is

In the formula, Φ(λ) is the number of photons with wavelength λ and bandwidth dλ projected onto the solar cell per unit area; Q is the quantum yield, that is, the probability that a photon with energy greater than E_{g} generates a pair of photogenerated carriers, which can usually be considered as Q≈1; R(λ) is the spectral reflectance of incident light; α(λ) is the spectral absorption coefficient; H is the thickness of the cell; dx is the thin layer in the cell at x from the cell surface; G_{L}(x) is the generation rate of photogenerated carriers at x.

Photogenerated carriers can be generated in the N region, depletion region and P region of the solar cell, and these photogenerated carriers can form photocurrent through the depletion region. When calculating the photogenerated current, various factors such as the generation and recombination of carriers, diffusion and drift in each region must be considered. The photocurrent formation process in the solar cell is shown in Figure 3.

The photocurrent in the top region is mainly generated by short-wave light, accounting for about 5% to 12% of the total photocurrent; the photocurrent in the space charge region accounts for about 2% to 5%; the photocurrent in the base region is mainly generated by long-wave light, accounting for about 90%.

2. When the short-circuit current is illuminated and the solar cell is short-circuited, the PN junction is in a zero-bias state. At this time, the short-circuit current density J_{SC} is equal to the photo-generated current density J_{L}, and the short-circuit current density J_{SC} is proportional to the incident light intensity Φ, as shown in Figure 1.

J_{SC}=J_{L}∞Φ (1.2)

3. Photovoltage Under the light, the voltage generated at both ends of the solar cell is the photovoltage. in the open state, the carriers generated by the illumination are separated by the built-in electric field to form a photocurrent flowing from the N region to the P region, while the open circuit voltage U_{OC} appearing at both ends of the solar cell generates a forward junction current JD flowing from the P region to the N region. Under steady illumination, the photocurrent JL and the forward junction current JD are numerically equal (J_{L}=J_{D}).

Since, in general, J_{L}/J_{D}>>1, there are:

It can be seen that U_{OC} increases with the increase of J_{L} and decreases with the increase of J_{0}. As the curve factor A increases, the reverse saturation current density J_{0} also increases, so U_{OC} does not increase with the increase of the factor A.

When ignoring the effect of the recombination current in the depletion region, the reverse saturation current density is

U_{D} is the maximum PN junction voltage, and eU_{D} is equal to the PN junction barrier height. According to formula (1.5) and formula (1.4), when A=1 and J_{L}/J_{D}>>1, substitute formula (1.5) into formula (1.4), we can get

It can be seen from equation (1.6) that when the temperature is low and the light intensity is high, the open circuit voltage U_{C} is close to U_{D}. Therefore, the greater the doping concentration on both sides of the PN junction, the greater the open circuit voltage.