## 1 Introduction: Recombination Processes in Perovskites
The free energy \(\mu_{oc}\) of photogenerated electron-hole pairs at the open circuit (oc) is equal to the energy splitting of the quasi-Fermi level conduction (\(F_{cb}\)) and valence (\(F_{bb}\)) bands. The trap level (\(E_{t}\)) in the mid-gap is empty from where Shockley-Read-Hall recombination of electrons (holes), \(R_{SRH,e}\) (\(R_{SRH,h}\)), occurs. Reproduced with permission from _Sci. Rep._**2017**, \(7\), 44629. Reference [6]. Figure 3 shows that the effective bulk lifetime in MAPbI3 is dominated by SRH recombination at low carrier injection levels (up to \(\Delta n\sim\) 10\({}^{15}\) cm\({}^{-3}\)). At high injection levels (up to \(\Delta n\sim\) 10\({}^{17}\) cm\({}^{-3}\)), the bulk lifetime is mainly determined by radiative recombination [3]. For perovskite solar cells under the condition of 1-sun illumination \(\Delta n\) corresponds to \(\sim\)10\({}^{16}\) cm\({}^{-3}\), resulting in relatively small Auger recombination rate constants (\(\sim\)10\({}^{-28}\) cm\({}^{6}\)/s) [7]. Clearly, perovskite materials are usually more limited by SRH recombination. Auger recombination is in general not so important. Furthermore, Auger recombination is more prominent in indirect semiconductors (such as _c_-Si) since radiative recombination is retarded as it requires interaction with phonons, while in Auger (and SRH) recombination energy and momentum is transferred. Thus, as a result of the direct bandgap and average charge-carrier concentrations, SRH recombination is the most relevant loss channel in perovskite under non-concentrated sunlight (1-sun illumination = 1000 Wm\({}^{-2}\) at AM 1.5). The observed inverse of the bulk lifetime (\(\tau_{bulk}\)) equals the sum of the reciprocal radiative lifetime (\(\tau_{rad}\)), the lifetime determined by Shockley Read Hall recombination (\(\tau_{SRH}\)) and the lifetime determined by Auger recombination (\(\tau_{Auger}\)); the inverse of the effective lifetime is also determined by the lifetime related to surface recombination (\(\tau_{surface}\)):  
\[\frac{1}{\tau_{bulk}}=\frac{1}{\tau_{rad}}+\frac{1}{\tau_{SRH}}+\frac{1}{\tau_ {Auger}}\]  
\[\frac{1}{\tau_{eff}}=\frac{1}{\tau_{bulk}}+\frac{1}{\tau_{surface}}\]  
The carrier trapping into defect states leading to SRH recombination severely limits the quasi-Fermi level splitting and hence the photovoltage of solar cells [8]. To understand the origin of SRH recombination, the density of defects but also their chemical nature, spatial and energetic distribution within the band gap is important. Section 2 will go into detail about different defects that can create electron and hole traps. Before that, we will consider the Shockley-Queisser limit to see why it is important to decrease the SRH recombination pathway. Figure 3: Relation between the charge carrier concentration, \(\Delta n\), and the different contributions to charge recombination. At low charge densities the effective bulk lifetime is mainly determined by the Shockley–Read–Hall (SRH) recombination. At higher levels, radiative charge recombination determines the bulk lifetime for p-type MAPbI3. Reproduced with permission from _Adv. Mater._**2019**, _31_, 1900428. Reference [3]. The Shockley-Queisser limit is widely used to define the theoretical maximum efficiency for single-junction solar cells [9]. The limit is defined by three important assumptions: first, it is assumed that for each incoming photon with energy greater than the band gap an electron-hole pair is produced. Secondly, electron-hole pairs with energy in excess of the band gap lose this energy via thermal relaxation. Furthermore, the Shockley-Queisser limit takes into account that a solar cell is in (thermal) equilibrium with its surroundings. Therefore, a cell under operational temperature will emit (black body) radiation. The first two assumptions relate to the spectral match and interaction of the absorber material and the incoming sunlight.