Design of the solar cell does affect the mechanism of the photovoltaic action and efficiency. The structure should be optimized for efficient separation and collection of photogenerated generated charge carrier. (a) Built-in Electric field, (b) effective force field (work function difference), (c) discontinuity at an energy level at the interface, are some of the design related options implemented for better performance of the photovoltaic device. The interface at heterojunction, control voltage generation and current flow, potential variation, the electric field at either side of the junction. Perovskite configuration of FTO/TiO2/Perovskite/HTL is p-i-n type. p-i-n structures is suitable for large built-in potential across absorber layer. Built-in potential depends on the carrier density of p and n layer. The effective force field can be induced by the appropriate choice of the contacts work function. For design point of view, an HTL should be having a high hole to electron mobility ratio so that it acts as a selective contact. To gain large built-in voltage charge density should be higher in n and p region of a pin. Higher charge density will also shift the space charge layer into the intrinsic layer an advantageous situation for charge drift. Figure 2a shows the Higher builtin voltage resulting from higher density of carrier in p and n layer of pin structure. The slope of band energy level in i layer (absorber) also increases with the carrier density in p and n, as shown in figure 2a. A spike to be present at the valence band offset to lower the interfacing recombination between EV,HTM and EC,Perovskite [23,27]. The reason for the low recombination at slightly positive valence band offset is the low value of ∆. The ∆ is the energy difference EC Perovskites -EV HTL as shown in the Fig. 2. The cliff at the perovskite/HTL junction lowered the ∆ shown in figure 2b, enhancing the chances of recombination of an electron from perovskite to hole from HTL. The presence of spike at the junction increases the ∆ value shown in Fig. 2c and thus lower the chances of recombination of an electron from perovskite and hole from HTL. The high Spike value will impede hole transfer from perovskite to HTL. The slightly positive values of VBO are advantageous and their optimum value can be ascertained by simulation. Device optimization by simulation for an HTL (p layer) in p-i-n the optimizing conditions are
i) A positive VBO at the p-i junction.
ii) High hole density in p,n layer ( p+-i structure),
a) High built-in voltage
b) Lead to the higher field in absorber (i) layer.
3.1.1 HTM layer parameter
For the simulation of inorganic HTL, we inserted an interface defect layer (IDL) at HTL perovskite junction. The width and defect density of IDL is taken to be 10nm and 1017cm-3. High defect density in IDL is used to simulate the interfacial recombination caused by lattice mismatching and defect state. CZTS have bandgap tail state of multivalent defect near to conduction band and valence band. We have assumed multivalent defect of charge state {3+/2+, 2+/+, +/0} in CB at Et =1.40eV with characteristic energy of 0.05eV. Acceptor defects of charge state {0/-, -/2-, 2-/3-} at VB. The defect density of 5×1014 cm-3, capture cross section of 10-13 cm2. To model SnS defects we have used a neutral defect of density 1017cm-3. Energetic distribution of single level was .6eV above EV and capture cross section of 10-15cm2. The parameter of the CZTS, CIGS, Cu2S, Sb2S3, PbS, FeS2, SnS are taken from literature and are listed in Table 2.
These inorganic material are p-type with 2-4 order high hole density than perovskite and have a similar bandgap. Simulation is run for these sulfide as HTL in Perovskite solar cell. HTL parameter of thickness, hole density are simulated. Fig. 3 shows the dependence of inorganic HTL device performance on hole density, thickness. The hole density in the HTL is varied from 1014 to 1018 cm-3 to simulate the effect on efficiency. Efficiency rises with hole density for all HTL. As doping concentration in HTL increases, the resistivity of HTL layer reduces. This increases the VOC and FF whereas the current remains constant. Carrier (hole) concentration will affect the bend banding and potential distribution at the junction. Perovskite has a low doping thus higher doped HTL will induce banding in Perovskite absorber layer thus creating a potential distribution across perovskite layer. Higher carrier concentration will cause higher built-in voltage in the device and is favorable until limiting diffusion length at high carrier density, Auger and Radiative recombination effect supersedes. All the binary sulfides layers have shown 0.1µm optimum thickness after which efficiency becomes constant. Quaternary CZTS and CIGS have shown a 0.2µm as optimum thickness. With thickness, FF grows initially and then all the parameter becomes constant. Rau et. al. estimated critical mobility for achieving 90 % of efficiency in the solar cell [28]. The critical mobility values remain less than 1 cm2V-1s-1. The HTL material under consideration here are well know p-type material with mobilities higher than critical mobilities as required by Rau et al. The optimum value of thickness, hole density as obtained by simulations can be easily attainable in given HTL materials. These parameters are highly dependent on growth condition and stoichiometry. We have used the value of these parameter forms the experimental data reported in the literature and listed in Table 2.
3.1.2. Band diagram and IV
The band structure of all the HTL/Perovskite solar cell is simulated and shown in Fig. 4. The band alignment at the HTL/perovskite junction is observed in all structure. The CZTS, CIGS showed bending in HTL layer energy level as they have hole density of 1016 cm-3. SnS showed band bending at the back metal contact. Simulated IV curve of all the structure is shown in the Fig. 5. The junction of HTL/perovskite is changing. PbS, FeS2 are showing low efficiency of 11.1% and 10.9% due to a large negative VBO at HTL/perovskite junction. CIGS and CZTS show a moderate value of efficiency 16.5% and 18.4% respectively. They have a positive VBO of 0.25 and 0.15 eV. SnS, Cu2S, Sb2S3 are showing comparable efficiency to Spiro-MeOTAD perovskite solar cell at 20.88%, 20.6%, 20.2% respectively. The comparable efficiency of SnS could be further optimized and could replace Spiro organic HTL. The difference in electron affinity (XHTL) of the HTL layer and perovskite (XAbs) is causing the valence band offset (VBO) at the junction. For hole transport valence band offset (VBO) the alignment of the valence band level EV of HTL and EV of perovskite is important. Also at this HTL junction, an interface defect density is assumed. A 10 nm thick layer is inserted at this junction to simulate any defect density arising from electrical or mechanical dissimilarity.
3.1.3. VBO and contact optimization of HTL layer
VBO is the discontinuity in the energy level at the junction shown by a vertical line in Fig. 3. VBO is given by (EgHTM+XHTL)- (EgPerov.+ XPerov), Eg is the bandgap, X is electron affinity. The simulated band diagram of the device Inorganic HTL/Perovskite shows valence band offset. The High negative offset introduces a cliff, favorable path way for hole transport from perovskite to HTL case shown in Fig. 2b for Perovskite /SpiroMeOTAD. High positive offset (XHTL+EgHTL>XAbs+EgAbs) introduces a spike forming a barrier for hole transfer from the absorber to HTL as the shown in Fig. 2c. At zero Valence band offset make continuity at the junction. The ∆ (as shown in the figure should be large to avoid interfacial recombination between EV HTL and EC Perovskite. The positive value of VBO will be suitable to increase ∆. However large VBO will inhibit the hole transfer from absorber to HTL. The height of spike should be less than the built-in voltage in absorber. SnS show comparable efficiency to Spiro, therefore, we optimized SnS for further efficiency enhancement. The electron affinity of the HTL layer is varied to vary the VBO and the band alignment. The band alignment is simulated for positive and the negative and zero valence band offset. SnS/perovskite has a EVBO of 0.15eV shown in band diagram Fig. 4. The effect of Spike and Cliff on device performance is studied. The simulation is run for range of VBO from negative to positive value. The defect at the junction of perovskite/HTL is simulated by inserting a IDL (interface defect layer) with a defect density of 1017cm-3.
The dependence of cell efficiency on valence Band offset at interface is shown in Fig. 6. For VBO values from -0.05 to .3eV the efficiency increases and peaks at a value of 0.15eV. Interface defect density at the junction highly affects the negative valence band. Recombination current dependence on valence band offset is shown in the inset of Fig. 4. Recombination current is minimum at the slightly positive band offset region. The efficiency maximizes at VBO where recombination current is minimum. Interface defect density is assumed to be high (1017 cm-3). Recombination current depends upon the defect density at the interface. High positive VBO is detrimental for performance as simulated results shows. Slightly positive band offset of 0.05eV to 0.1eV is yielding the highest efficiency irrespective of high defect density for SnS. The reason for the low recombination current at slightly positive valence band offset is the low value of ∆. Efficiency abruptly decreases for higher VBO values as seen in the simulation Fig. 6. Interfacial recombination within the HTL/Perovskite junction can be lowered by a positive band offset. The slightly positive values of VBO are advantageous and their optimum value can be ascertained by simulation. The prominent effect of VBO is on the fillfactor of the device. Table 4 summaries the VBO resulting by variation of the electron affinity of SnS. FF maximize at the slightly positive VBO (0.1eV) the similar trend followed by efficiency.
The band diagram of SnS/perovskite in the figure shows abrupt band bending at back contact. This suggests at Schottky at the back contact with the assumed metal contact of work function 5.1eV in the simulation. The barrier at the back contact can be sorted by optimizing back contact work function. The effect of work function (ϕm) of metal contact at HTL layer is simulated for contact optimization. Fig. 7 shows the efficiency improvement with the work function (ϕm) of back contact. Simulation results show that VOC and efficiency rise initially with work function and then becomes constant for both the HTL shown in Fig. 7. This increase in VOC is due to improved built-in voltage [29,30]. We have a metal/semiconductor back contact acting as Schottky barrier for majority carrier. The barrier is required to be low to make it near ohmic. The band diagram is simulated for increasing work function values. For higher work function there is rise in energy level of the HTL at the back contact. This rise in energy level at back contact improves built-in voltage in HTL and perovskite layer. The simulated band diagram is shown work function in the inset of Fig. 7. The bending in EV and EC level at rear contact is eliminated with metal contact of high work function as shown in the simulated diagram.
The final parameters of the Perovskite with inorganic HTL layer are summarized in the Fig. 8. The inorganic HTL (CZTS, Sb2S3, Cu2S, SnS) have higher FF and SnS have higher efficiency than the standard perovskite cell with organic Spiro HTL. The VOC, FF, JSC and Efficiency are compared with Spiro-MeOTAD and the SQ limit. The SQ limit gap in VOC, JSC, FF for Spiro-MeOTAD is shown. Among them FF has the largest deficit this may be due to suboptimal band alignment at the perovskite/HTL, perovskite/ETL and the high value of series resistance and low shunt resistance values in perovskite solar cell. The efficiency of the SnS is higher than Spiro-MeOTAD. The stability of SnS and low thermal conductivity is advantageous over organic HTL like PEDOT: PSS, Spiro-MeOTAD etc. Apart from high efficiency they can provide stable encapsulation to organic-inorganic perovskite from outer moisture and temperature gradient.