## 2 Theory of ADETAM  
The theoretical formulation of the ADETAM, which is an averaging procedure for coherent simulation results to consider the incoherent characteristics in a mixed coherent-incoherent multiplayer, can be applied to both planar and non-planar structures. For convenience, we derive the theoretical formulation of the ADETAM in a planar mixed coherent-incoherent thin-film multilayer structure shown in Figure 1.  
We assume that multiple incoherent layers, representing millimeter-order front encapsulation layers, lie in front of the coherent multilayer structure, which can range from a transparent conducting oxide (TCO) top contact to a metal back contact. The mixed coherent-incoherent multilayer is assumed to be sandwiched between a semi-infinite transparent ambient medium on the left (\(j=0\)) and the right (\(j=n+1\)). The multiple incoherent layers (\(j=1\), \(\cdots\), \(m\)) are assumed to be transparent and the remaining coherent layers (\(j=m+1\), \(\cdots\), \(n\)) can be either transparent and absorptive. All the layers are assumed to be  
Figure 1: Schematic diagram of a planar mixed coherent-incoherent thin-film multilayer structure. The multiple incoherent layers (\(j=1\), \(\cdots\), \(m\)) are assumed to be transparent and the remaining coherent layers (\(j=m+1\), \(\cdots\), \(n\)) can be either transparent or absorptive. To optically model random phase variations in the incoherent layers, each incoherent layer (\(v=1\), \(\cdots\), \(m\)) is divided into an initial layer of the original thickness \(d_{v}\) and an additional phase-shift layer of the equispaced phase thickness \(b_{v}\). A plane wave is obliquely incident from the semi-infinite transparent ambient on the left (\(j=0\)) with the incidence angle \(\theta_{0}\). The directions of the s- and p-polarized light are orthogonal to or parallel to the plane of incidence. isotropic and homogeneous with planar and parallel interfaces. When the thickness of each layer is \(d_{j}\), the corresponding complex refractive index is denoted by \(\widetilde{n}_{j}=n_{j}+ik_{j}\), where \(n_{j}\) indicates the refractive index and \(\kappa_{j}\) represents the extinction coefficient, respectively. To optically model random phase variations in the incoherent layers, each incoherent layer (\(v=1,\,\cdots,\,m\)) is divided into an initial layer of the original thickness \(d_{v}\) and an additional phase-shift layer of the equispaced phase thickness \(b_{v}\)[21]. We assume that a plane wave, which has the optical intensity of \(I_{0}\) at the wavelength of \(\lambda\), is obliquely incident from the semi-infinite transparent ambient on the left (\(j=0\)) with the incidence angle \(\theta_{0}\). According to the [PERSON]'s law, the refraction angle of each layer is determined by \(\sin\theta_{j}=(n_{0}/\widetilde{n}_{j})\sin\theta_{0}\) and \(k_{0}=2\pi/\lambda\) is the magnitude of the wave number in the ambient (\(j=0\)). When the light propagating from the left to the right denotes a positive direction, the light propagation in the positive and negative directions are expressed as \(+\) and \(-\) superscripts. The directions of the s- and p-polarized light are orthogonal to or parallel to the plane of incidence. According to the TMM, the s(p)-polarized electric field amplitudes on the interface between the right boundary of the layer \(j\) and the left boundary of the layer \(k\) (\(j<k\)) are described by an interface matrix that is given by  
\[\left[ \begin{array}{c}E_{jR}^{+s(p)}\\ E_{jR}^{-s(p)}\end{array} \right]=\Gamma_{jk}^{s(p)}\left[ \begin{array}{c}E_{ kL}^{+s(p)}\\ E_{kL}^{-s(p)}\end{array} \right]=\frac{1}{\textit{{f}}_{jk}^{s(p)}}\left[ \begin{array}{cc}1&r_{jk}^{s(p)}\\ r_{jk}^{s(p)}&1\end{array} \right]\left[ \begin{array}{c}E_{kL}^{+s(p)}\\ E_{kL}^{-s(p)}\end{array} \right] \tag{1}\]  
where \(r_{jk}^{s(p)}\) and \(r_{jk}^{s(p)}\) are the s(p)-polarized complex Fresnel reflection and transmission coefficients at the interface from the layer \(j\) to the layer \(k\)[15].