# Terahertz Single-Pixel Imaging Improved by Using Silicon Wafer with SiO\({}_{2}\) Passivation
## 3 THz Photomodulation Experiments  
To investigate the effects of the SiO\({}_{2}\) passivation thickness, various thicknesses were prepared. This was achieved by etching the double-sided passivated silicon wafer, where the thickness of each SiO\({}_{2}\) layer was measured to be 287 nm. The passivated silicon wafer was first cut into small pieces of the same size, and was then etched by using 40% potassium hydroxide solution with different duration time. The thickness of the SiO\({}_{2}\) layer was measured by a film thickness meter. Table 1 summarizes the obtained SiO\({}_{2}\) thicknesses of each side (both sides have the same thickness). The THz time-domain signal transmitted through the sample under CW laser illumination \(E_{\text{samp}}(t)\) was collected. As a reference, the THz time-domain signal without any modulator \(E_{\text{ref}}(t)\) was collected. The THz transmittance is then calculated by [23],  
\[T_{\text{on}}(\omega)=\frac{E_{\text{samp}}(\omega)}{E_{\text{ref}}(\omega)}\,, \tag{5}\]  
where \(\omega\) is the frequency of the transmitted THz wave, \(E_{\text{samp}}(\omega)\) and \(E_{\text{ref}}(\omega)\) are the Fourier transform of \(E_{\text{samp}}(t)\) and \(E_{\text{ref}}(t)\), respectively. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline Sample & S1 & S2 & S3 & S4 & S5 & S6 & S7 & S8 & S9 \\ \hline Thickness (nm) & 0 & 21 & 109 & 140 & 148 & 180 & 216 & 247 & 287 \\ \hline \end{tabular}
\end{table} 
Table 1: As-fabricated silicon wafer with different SiO\({}_{2}\) passivation thicknesses. Figure 2a shows that as the SiO\({}_{2}\) thickness increases from 0 nm to 148 nm, the transmittance of the THz field decreases from about 55% to 7%. Further increasing the SiO\({}_{2}\) thickness results in increased transmittance: for the thickness of 287 nm, the transmittance is 30%. To evaluate the modulation efficiency of different samples, we make use of the modulation factor (MF), which is defined as the change of the integrated transmitted THz power under the illumination [24],  
\[\text{MF}\equiv\frac{\int T_{\text{off}}(\omega)\;\text{d}\omega-\int T_{\text {on}}(\omega)\;\text{d}\omega}{\int T_{\text{off}}(\omega)\;\text{d}\omega}\,. \tag{6}\]  
Here, \(T_{\text{off}}(\omega)\) and \(T_{\text{on}}(\omega)\) are the transmitted powers when the laser is off and on, respectively. Figure 2b shows that all the MFs for different SiO\({}_{2}\) thicknesses increase with the CW laser power, where \"0 nm\" implies the bare silicon wafer. This is because the carrier density in the semiconductor is proportional to the optical power of the laser beam and is modulated through photodoping [25]. Strikingly, for laser power of 330 mW the maximum MF of 0.9 is achieved by sample S5 with SiO\({}_{2}\) thickness of 148 nm; this value is three times of that for the bare silicon (MF \(=\) 0.3 for sample S1). Figure 3a shows that as the SiO\({}_{2}\) thickness increases, the MFs for different CW laser powers first increase and then decrease, exhibiting maximum values around the SiO\({}_{2}\) thickness of 148 nm. To understand the physics origin for the terahertz photomodulation performance, we measured the optical reflectivity of the CW laser by the as-fabricated samples. In experiments, the optical reflectivity was obtained by dividing the power reflected from the sample by that from a gold mirror. Figure 3b shows that as the SiO\({}_{2}\) thickness increases, the optical reflectivity first decreases from about  
Figure 3: (**a**) THz modulation factor versus SiO\({}_{2}\) thickness under the illumination of different CW laser powers. (**b**) Calculated (blue curve) and measured (red dots) optical reflectivity of the CW laser versus SiO\({}_{2}\) thickness. Figure 2: (**a**) THz transmittance for different SiO\({}_{2}\) thicknesses. (**b**) Modulation factor versus CW laser power. 30% to about 6%, and then increases again to 30%. The smallest optical reflectivity of 6% is achieved for SiO\({}_{2}\) thickness of 147 nm.