## 2 Generation Mechanism of Electroluminescence Polarization Characteristics
### Polarization Characteristic Generation  
In the production process of solar cells, silicon wafers usually need to be solidified. During the curing process, residual stress is usually introduced into the wafer and makes the crystal anisotropic; subsequently, plastic deformation will occur at a high temperature, which leads to the formation and movement of crystal defects such as dislocations. As a result, the quantum mechanical effect at the dislocation core gives the electroluminescence polarization characteristics, especially at the regions with high dislocation density, where the polarization direction is consistent with the dislocation direction.  
According to the principle of quantum mechanics, the radiation recombination of photovoltaic cells depends on the wave function of the carrier, and the electroluminescence intensity I is positively correlated with the probability R of optical transition at the defect. According to the Bloch theorem, the wave function at the crystal defect can be reduced to the spatially related conduction \(|u_{c}\rangle\) and valence \(\langle u_{v}|\) Bloch bands [10]. Thus, for an anisotropic semiconductor, the probability of optical transition can be formalized as the emission of linearly polarized photons including the polarization vector [10]; that is, the luminous intensity can be expressed as:  
\[I\propto K\left|\langle u_{v}|\stackrel{{\rightarrow}}{{e}}\cdot \hat{p}|u_{c}\rangle\right|^{2} \tag{4}\]  
where \(\stackrel{{\rightarrow}}{{e}}\) is photon; \(K\) and \(\hat{p}\) is the overlap of the envelope describing the electron and hole; and \(\hat{p}\) is the momentum operator.  
Linearly polarized \(\overrightarrow{p}\) can be decomposed into a parallel component \(\overrightarrow{e_{\parallel}}\) and a perpendicular component \(\overrightarrow{e_{\perp}}\) to the incident plane. By time integrating \(\overrightarrow{e_{\parallel}}\) and \(\overrightarrow{e_{\perp}}\), the parallel \(I_{//}\) and vertical components \(I_{\perp}\) of the outgoing light can be obtained:  
\[\left\{\begin{array}{l}I_{//}=\varepsilon_{//}I\\ I_{\perp}=\varepsilon_{\perp}I\end{array}\right. \tag{5}\]  
where, \(\varepsilon_{//}\) and \(\varepsilon_{\perp}\) are the emissivity of the parallel component and the vertical component of the outgoing light.  
The emissivity is mainly affected by the type of target material, surface roughness, physical and chemical nature, and material thickness. Defects and doping are the determining factors of carrier type, concentration, transmission, and non-radiative recombination of photogenerated carriers in semiconductors. There are many kinds of defects, concentrations, and anisotropy in the crystal structure of solar cells, which makes the emissivity of the parallel component and the vertical component of the light emitted from the defect area unequal. Research shows that the electroluminescence from the defect area of solar cells shows a high degree of polarization, especially from a high dislocation area [11]. On the other hand, the etching of silicon-based solar cells makes the surface uneven to form a strong diffuse reflection, which also causes the emissivity of the parallel and vertical components of the outgoing light are unequal [17]. For PV panels, from top to bottom, they comprise glass, EVA, a solar cell, and a backplane and aluminum frame sealed together by lamination. When photons are emitted from the PN junction, they need to pass through two layers of structure (EVA, glass) to refract. The emission conditions are different under different voltages and different emission angles, so the polarization characteristics are related to the forward bias and emission angle. The degree and angle of polarization can be written as:  
\[\left\{\begin{array}{l}DOP=\left|\frac{I_{//}-I_{\perp}}{I_{//}+I_{\perp}} \right|=\left|\frac{\varepsilon_{//}-\varepsilon_{\perp}}{\varepsilon_{//}+ \varepsilon_{\perp}}\right|\\ AOP=\arctan\left(\frac{I_{//}}{I_{\perp}}\right)==\arctan\left(\frac{ \varepsilon_{//}}{\varepsilon_{\perp}}\right)\end{array}\right. \tag{6}\]