## 3 \(V_{oc}\) Losses Analysis
### \(V_{oc}\) Loss Due to Surface Recombination  
#### 3.2.1 SRV on a Passivated n type Surface  
There is a 1-2 \(\upmu\)m 5 \(\times\) 10\({}^{17}\) cm\({}^{-3}\) or 1 \(\times\) 10\({}^{18}\) cm\({}^{-3}\) n type FSF layer in this UTSi solar cell, and this layer is mostly etched away during the shallow texturing process [5]. The front surface of the textured UTSi solar cell is mainly an n (5 \(\times\) 10\({}^{15}\) cm\({}^{-3}\)) surface with a partially remaining n\({}^{+}\) (5 \(\times\) 10\({}^{17}\) cm\({}^{-3}\) or  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Steps** & \(J_{\theta}\) **Components** & \(J_{\theta}\) **Value (A/cm\({}^{2}\))** & \(V_{oc}\) **(mV)** \\ \hline – & \(J_{0b}\) & 4.73 \(\times\) 10\({}^{-15}\) & – \\ – & \(J_{0e}\) & 3.03 \(\times\) 10\({}^{-17}\) & – \\
1 & \(J_{0b}+J_{0e}\) & 4.76 \(\times\) 10\({}^{-15}\) & 767.0 \\ \hline \hline \end{tabular}
\end{table}
Table 1: \(J_{0}\) components, values and their corresponding \(V_{oc}\) values when SRV is 0 cm/s. \(J_{0e}\) is the reverse saturation current density in the emitter, \(J_{0b}\) is the reverse saturation current density in the base and FSF layer.  
1 \(\times\) 10\({}^{18}\) cm\({}^{-3}\)) surface. The front surface is passivated by silicon oxynitride (SiO\({}_{\text{x}}\)N\({}_{\text{y}}\)) [9]. This section tests the surface recombination in the SiO\({}_{\text{x}}\)N\({}_{\text{y}}\) passivated n type surfaces. Two groups of test samples were designed, as shown in Figure 2: group A1 with n (5 \(\times\) 10\({}^{15}\) cm\({}^{-3}\)) epitaxial surfaces and group B1 with n\({}^{+}\) (5 \(\times\) 10\({}^{17}\) cm\({}^{-3}\)) surfaces. Float-zone (FZ) substrates were chosen because they have negligible bulk recombination and provide an ideal substrate for epitaxial growth. In this way, their lifetime or implied \(V_{oc}\) values are not limited by bulk but by surfaces. These FZ substrates were from the same wafer and these samples were processed along with control samples to eliminate extrane variables. After SiO\({}_{\text{x}}\)N\({}_{\text{y}}\) deposition, these samples were annealed at 400 \({}^{\circ}\)C for 10 min to activate surface passivation [9]. Their implied \(V_{oc}\) (\(iV_{oc}\)) and lifetime were measured by a Sinton lifetime tester [10]. An \(iV_{oc}\) of 718 mV and effective lifetime of 1085 \(\upmu\)s were obtained in the sample with 18 \(\upmu\)m 5 \(\times\) 10\({}^{15}\) cm\({}^{-3}\) n type silicon epitaxial layers, while an \(iV_{oc}\) of 696 mV and lifetime of 556 \(\upmu\)s were measured in the sample with 1 \(\upmu\)m heavily doped 1 \(\times\) 10\({}^{18}\) cm\({}^{-3}\) n\({}^{+}\) epitaxial layers. To calculate the SRV of both surfaces, the equation \(\frac{1}{\tau_{off}}=\frac{1}{\tau_{bulk}}+\frac{2\times S}{W}\) is used, where \(\tau_{\text{eff}}\) is the effective lifetime measured, \(S\) is the SRV, \(W\) is the thickness of silicon, \(\tau_{\text{bulk}}\) is the bulk lifetime of the FZ wafer. In this calculation, the intrinsic bulk lifetime of the FZ wafer, 1.8 \(\times\) 10\({}^{4}\)\(\upmu\)s, was estimated using an online program PV Lighthouse [11]. Intrinsic bulk lifetime eliminates the effect of Shockley-Read-Hall recombination and leads to conservative values for the SRV. SRV values for the 5 \(\times\) 10\({}^{15}\) cm\({}^{-3}\) surface and 1 \(\times\) 10\({}^{18}\) cm\({}^{-3}\) surface are 13 cm/s and 26 cm/s, respectively.  
\begin{table}
\begin{tabular}{c c c c} \hline
**ID** & \(iV_{oc}\) **(mV)** & **Lifetime (\(\upmu\)s)** & **SRV (cm/s)** \\ \hline Group A1 & 718 & 1085 & 13 \\ Group B1 & 696 & 556 & 26 \\ \hline \end{tabular}
\end{table}
Table 2: \(iV_{oc}\) and \(J_{0}\) components for samples in Figure 2.  
Figure 2: Control sample and two groups of test samples for n and n\({}^{+}\) epitaxial layers and their passivation.