3.2.3. Influence of Absorber Defect Trap Density and Energy

The photo-excited charge carriers are primarily produced within the absorber region. The existence of defects inside the absorber has a crucial impact, as they result in a nonradiative recombination process which limits the overall solar cell performance. The defect density inside the absorber perovskite films has to be alleviated to reduce carrier recombination losses [59]. Here, we study the impact of reducing the defect density inside the two sides of the absorber. Figure 15 depicts the photovoltaic parameters of the device with various defect density (*Nt*) in both n-CH3NH3SnI3 and p-CH3NH3SnI3 (*Nt* is set equal in the two layers). It is obvious that decreasing defect density beyond 1015 cm−<sup>3</sup> results in a considerable rise in the *Voc*. The *Voc* is expressed by [4,5]

$$V\_{\rm oc} = nV\_T \ln\left(1 + \frac{J\_{\rm SC}}{J\_o}\right) \tag{8}$$

where *n* is the diode ideality factor and *VT* is the thermal voltage. The reverse saturation current density, *Jo*, is determined by the recombination processes. Hence, *Voc* measures the recombination losses in the solar cell structure. As the bulk defect in absorber layers functions as nonradiative recombination centers, rising *Nt* results in increasing the probability of recombination, which causes a decline in *Voc*. Besides, one can see from Figure 15 that there is almost no impact on *Jsc* when *Nt* is less than 1015 cm−3; however, *Jsc* drops substantially with the further rising of *Nt*. This can be clarified by the dependence of the hole (electron) diffusion length *Lp* (*Ln*) on *Nt*, which is presented by,

$$L\_{n/p} = \sqrt{\frac{\mu\_{n/p} kT}{q} \frac{1}{\sigma\_{n/p} v\_{th} \mathcal{N}\_t}} \tag{9}$$

Equation (9) describes that the rise of *Nt* causes a smaller *Lp* (*Ln*). For low *Nt* values, *Lp* (*Ln*) is greater than the thickness of the absorber; therefore, *Nt* has a minor effect on *Jsc*. However, if *Nt* surpasses 1015 cm<sup>−</sup>3, *Lp* (*Ln*) is smaller than the absorber thickness and *Jsc* reduces with further rise of *Nt*. Furthermore, when *Nt* < 1015 cm−3, the PCE remains almost unaffected. However, the efficiency decreases markedly when *Nt* > 10<sup>15</sup> cm−3. Consequently, controlling the *Nt* below 1015 cm−<sup>3</sup> is essential for accomplishing higher efficiencies. At *Nt* equals 10<sup>15</sup> cm−3, an optimized conversion efficiency of 16.57% (at *Voc* = 0.896 V, *Jsc* = 25.86 mA/cm2, *FF* = 71.53%) can be obtained for the proposed HTL-free cell. The enhancement of the parameters according to reducing the trap density could be

explained in many aspects, one of which is the recombination rate, as shown in Figure S4 (see Supplementary Material).

**Figure 15.** The HTL-free configuration photovoltaic parameters with various defect density (*Nt*) in both n-CH3NH3SnI3 and p-CH3NH3SnI3.

Moreover, the influence of the trap energy position with respect to the valence band edge energy *Ev* was investigated. Figure 16 demonstrates this impact for two different values of *Nt*. The trap position is varied from 0.1 to 1.2 eV. Regarding the higher value of *Nt* (5 × <sup>10</sup><sup>17</sup> cm−3), the trap energy position has a crucial effect. Generally, the defects with low formation energy produce shallow levels. These levels are close to *Ec* or *Ev* and result in long diffusion lengths. This is clear from the figure as the long diffusion length results in a high *Voc* and, in turn, an enhancement in the overall performance is achieved. On the other hand, when the formation energy is high, the trap energy position is near the mid-gap. These levels are called deep levels and the resulting diffusion length is short, which deteriorates the performance. Regarding the lower value of *Nt* (1015 cm−3), the situation is different. The impact of the trap energy is minor and thus the cell becomes extremely immune to the defect energy position. These results imply the crucial impact of the bulk trap density. Careful manufacturing processes are needed in order to decrease the trap density to boost the cell performance for either deep or shallow levels.

**Figure 16.** Impact of bulk trap energy position relative to *Ev* on the photovoltaic parameters of the hetero/homojunction HTL-free solar cell.
