## 3 Results and Discussion  
### The Performance of Solution-Processed Perovskite PDs  
CsPbBr\({}_{3}\) perovskite polycrystalline films were prepared by a two-step solution method proposed by our group previously [30]. The SEM image in Figure 3a is the morphology of the perovskite films, showing their compact and uniform features with a grain size close to 1 \(\upmu\)m. The CsPbBr\({}_{3}\) perovskite film was further characterized with a PL spectrum as shown in Figure 3b. The sole PL peak in the spectrum indicates the pure phase of CsPbBr\({}_{3}\) perovskite, and the peak location at 525 nm is consistent with its bandgap of about 2.3 eV [32]. Perovskite PDs were fabricated based on high-quality film with a device figuration of ITO/SnO\({}_{2}\)/CsPbBr\({}_{3}\)/P3 HT/Carbon, as shown in Figure 4a. The I-V characteristic curves of the PDs were measured with or without the illumination of 480 nm light, as shown in Figure 4a. When the PD is operated in self-power mode (photovoltaic mode), the photocurrent is 6.5 \(\times\) 10\({}^{-6}\) A and the dark current is as low as 6.7 \(\times\) 10\({}^{-12}\) A, resulting in an on/off ratio of about 10\({}^{6}\). Pinholes in the perovskite layer can cause serious current leakage, resulting a high dark current. Such a low dark current of our PDs is attributed to the high-quality CsPbBr\({}_{3}\) films, which are comparable to the commercial silicon PDs with same active area. Figure 2: The working mechanism of state machine for (**a**) transition; (**b**) reception. There are several key parameters in evaluating the performance of PDs. Noise current is one of the crucial parameters of PDs, which generally consists of shot noise (\(i_{shot}\)) and thermal noise (\(i_{thermal}\)), that can be expressed as follows [33]:  
\[i_{shot} = \sqrt{2 eI_{dark}B}, \tag{1}\]  
Figure 4: (**a**) I–V characteristics of the perovskite PDs with and without illumination. The insert is the schematic and optical image of the fabricated CsPbBr\({}_{3}\) PD. (**b**) The measured noise current spectra of the instrument and CsPbBr\({}_{3}\) perovskite PDs at the photovoltaic mode, (**c**) Responsivity (in green) and specific detectivity (in blue) spectrum of perovskite PDs. (**d**) Transient response of perovskite PDs with different sensitive areas under the illumination of a 488 nm laser at a frequency of 100 kHz. Figure 3: (**a**) SEM image; (**b**) steady-state photoluminescence spectra of the solution processed CsPbBr\({}_{3}\) perovskite films. \[i_{thermal}=\sqrt{\frac{4k_{B}TB}{R_{es}}}, \tag{2}\]  
\[i_{n}=\sqrt{i_{shot}^{2}+i_{thermal}^{2}}, \tag{3}\]  
where \(e\) is the elementary charge, \(I_{dark}\) is the dark current, and \(B\) is the bandwidth, \(k_{B}\) is the Boltzmann constant, \(T\) is the absolute temperature, and \(R_{es}\) is the resistance of the PDs, which can be calculated from the I-V curve at 0 V as \(1.78\times 10^{7}\)\(\Omega\). The shot noise and the thermal noise calculated from Equations (1) and (2) are about \(1.5\times 10^{-15}\) A Hz\({}^{-1/2}\) and \(3.1\times 10^{-14}\) A Hz\({}^{-1/2}\), respectively. Since the thermal noise is an order of magnitude higher than the shot noise, indication of the noise current of these perovskite PDs is dominated by thermal noise. The noise current was also estimated by extracting from the fast Fourier transform of the dark current, monitored for 200 s, as shown in Figure 4b. The measured noise current (\(4.3\times 10^{-14}\) A Hz\({}^{-1/2}\)) is close to the calculated thermal noise. Responsivity (\(R\)) and specific detectivity (\(D^{*}\)) are also key figure-of-merit parameters of PDs. \(R\), indicating how efficiently the detector converts the optical signal to an electrical signal, is the ratio of photocurrent to incident-light intensity. \(D^{*}\) characterizes the ability to detect how weak the light is, determined by the responsivity and the noise.