### Efficiency and characteristics of solar cells

**1. Efficiency of solar cells**

The photoelectric conversion efficiency n of a solar cell is the ratio of the output electrical power to the incident light power when the solar cell is illuminated by light, referred to as cell efficiency, which can be expressed as

where A_{i} is the area of the solar cell; P_{in} is the incident light power per unit area.

If the shaded grid line area is deducted from the total area, the cell efficiency under the effective area A_{a} can be obtained.

There are various losses in the photoelectric conversion process of solar cells:

1) optical loss. Reflection loss on the cell surface; the long-wave loss caused by the transmission of light with a wavelength greater than 1.1 μm (hv<E_{g}) through the battery;

After a photon with hv>E_{g} excites photogenerated carriers, the excess energy cannot be utilized, resulting in short-wave loss.

2) electrical losses. Photogenerated hole-electron pairs recombine in vivo and on the surface, as well as through other recombination centers; when the photo-generated carriers are separated by the PN junction, the losses in the junction region include the loss of phonons and microplasma effects; the loss of junction current due to minority carrier recombination, and the loss caused by the height of the potential barrier; series and parallel resistance losses.

In order to improve the photoelectric conversion efficiency, various losses must be reduced as much as possible.

**2. Crystalline silicon solar cell efficiency limit**

Some researchers have proposed the concept of optimal cell structure and its efficiency limit. Assume that all avoidable losses are eliminated, i.e., reflection losses are completely eliminated, and incident light is maximally absorbed by ideal light trapping techniques; SRH and surface recombination are assumed to be avoided except Auger recombination; the ideal contact electrode has neither shading nor series resistance loss; there are no transfer losses in the substrate, and the carrier distribution in the substrate is so uniform that at a given voltage, carrier recombination can be minimized. In order to minimize Auger recombination and free carrier absorption, the optimal cells are fabricated with intrinsic semiconductor silicon material with a thickness of about 80 μm. After comprehensive treatment of carrier recombination and light absorption, the results show that the efficiency of single crystal silicon solar cells can be close to 29% under the conditions of a solar light intensity, AM1.5 and 25℃.

**3. Spectral characteristics of silicon solar cells**

The spectral characteristic of a solar cell refers to the magnitude of the short-circuit current of the solar cell when the light of different wavelengths per unit radiant flux irradiates the solar cell, which is usually represented by a characteristic curve, which is called the spectral response SR (λ). The spectral response of solar cells can be divided into relative spectral response and absolute spectral response, as shown in Figure 1.

The spectral properties of solar cells can also be expressed in terms of quantum efficiency. The quantum efficiency of solar cells can be divided into external quantum efficiency EQE (λ) and internal quantum efficiency IQE (λ).

The external quantum efficiency of a solar cell is defined as: the ratio of the number of photo-generated carriers that are generated inside the cell and contribute to the short-circuit current by light with a wavelength of λ to the number of photons incident on the cell surface, which is：

EQE(λ)=I_{sc}(λ)/eΦ(λ) (1-3)

In the formula, e is the amount of electrons; Φ(λ) is the photon flux with the wavelength incident on the surface of the battery.

The internal quantum efficiency of a solar cell is defined as the ratio of the number of photogenerated carriers that are generated inside the cell by light with a wavelength of λ and contribute to the short-circuit current to the number of photons incident inside the cell, that is, the number of photons deducted from the reflection loss on the surface of the battery can be expressed as

In the formula, R(λ) is the reflectivity of the cell surface to the light of wavelength λ; T(λ) is the transmittance. Usually, the transmittance T(λ) can be neglected.

The internal quantum efficiency of a solar cell is always greater than its external quantum efficiency.

**4. Temperature and illumination characteristics of silicon solar cells**

Figure 2 shows the temperature characteristics of a silicon solar cell. Because the change rate of the forbidden band width of silicon with temperature is about -0.003eV/°C, the change of the open circuit voltage U_{OC} is about -2mV/°C. The short-circuit current I_{sc} increases slightly with increasing temperature. Under the same light, the output power of the battery decreases with the increase of temperature, and the power decreases by 0.35%~0.45% for every 1℃ increase.

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