1. My Motivation and the Central Problem
I view the inverted perovskite solar cell as one of the most practical routes toward high-efficiency and scalable photovoltaics. In my analysis, the performance of a perovskite solar cell is not limited only by the absorber layer. It is limited just as strongly by the buried interface between the transparent electrode and the perovskite film. This is why I focused on the hole-selective layer. In an inverted perovskite solar cell, the hole-selective layer must extract holes, block electrons, define the work function of the substrate, and template the crystallization of the perovskite. A self-assembled monolayer can perform all of these roles if its molecular structure is designed correctly.
The general figure of merit for any perovskite solar cell is the power conversion efficiency,
$$ \eta = \frac{P_{\max}}{P_{\mathrm{in}}} = \frac{V_{\mathrm{OC}} J_{\mathrm{SC}} FF}{P_{\mathrm{in}}}, $$
where \(V_{\mathrm{OC}}\) is the open-circuit voltage, \(J_{\mathrm{SC}}\) is the short-circuit current density, \(FF\) is the fill factor, and \(P_{\mathrm{in}}\) is the incident optical power. I used this expression as my guiding metric because it separates the losses inside a perovskite solar cell. A poor hole-selective layer usually damages \(V_{\mathrm{OC}}\) and \(FF\) first. It creates non-radiative recombination, reduces carrier selectivity, and produces an unfavorable energy-level offset.
In my design, I wanted to move beyond the conventional carbazole-based self-assembled monolayer. The reference molecule 4PACZ is electron-rich and widely used in inverted perovskite solar cells, but I identified two persistent issues. First, its molecular dipole is modest, which limits the work-function tuning of indium tin oxide. Second, its carbazole core is planar, which promotes intermolecular π–π stacking. That stacking can cause aggregation, incomplete coverage, and non-uniform perovskite growth. Both effects are harmful to a perovskite solar cell because they increase interfacial energy loss and reduce reproducibility.
My solution was to extend the π-conjugation of the terminal group. I designed a dinaphthocarbazole phosphonic acid, abbreviated here as 4PADNC, in which a dinaphtho[2,3-c:2′,3′-g]carbazole unit replaces the simple carbazole unit. The butyl phosphonic acid anchor remains attached to the nitrogen. The larger aromatic core increases the conjugation length, strengthens the electron-rich character, enlarges the molecular dipole, and introduces a non-planar dihedral angle. I hypothesized that these changes would improve energy-level alignment, suppress aggregation, and produce a denser and more uniform self-assembled monolayer on indium tin oxide.
2. Molecular Design, Synthesis, and Basic Characterization
I synthesized 4PADNC through a short sequence. In my route, 2-aminoanthracene undergoes oxidative coupling to form the dinaphthocarbazole core. The core is then alkylated with 1,4-dibromobutane to attach a bromobutyl chain. Subsequent Arbuzov reaction with triethyl phosphite installs the diethyl phosphonate group. Finally, trimethylsilyl bromide-mediated deprotection gives the free phosphonic acid. The isolated yields and key analytical signatures are summarized in Table 1. The final molecule is thermally robust, with a 10% mass-loss decomposition temperature of 347 °C, which is important because the perovskite annealing step follows the deposition of the hole-selective layer.
| Step | Transformation | Key Reagent or Condition | Yield |
|---|---|---|---|
| 1 | 2-aminoanthracene to DNCZ | Hexafluoroisopropanol, 5% Rh/C, air, room temperature | 72% |
| 2 | DNCZ to 4Br-DNCZ | 1,4-dibromobutane, tetrabutylammonium bromide, KOH(aq), 60 °C | 84% |
| 3 | 4Br-DNCZ to 4P-DNCZ | Triethyl phosphite, 140 °C | 81% |
| 4 | 4P-DNCZ to 4PADNC | Trimethylsilyl bromide, 1,4-dioxane, then methanol/water | 68% |
I confirmed the structure using nuclear magnetic resonance and mass spectrometry. The proton signals from the aromatic core appear between 7.52 and 9.79 ppm, while the side-chain protons appear between 1.52 and 4.74 ppm. The carbon spectrum shows aromatic carbons from 113.96 to 136.00 ppm and aliphatic carbons from 21.20 to 43.11 ppm. The phosphorus spectrum contains a single resonance at 25.28 ppm, which is consistent with one phosphorus environment in the phosphonic acid. The mass spectrum shows a dominant ion at m/z = 502.7, matching the expected molecular mass. These data gave me confidence that the target molecule was pure enough for self-assembled monolayer formation.
3. Why the Dinaphthocarbazole Core Matters
I used density functional theory to compare 4PACZ and 4PADNC. The most important difference is not simply size. It is the combination of conjugation, dipole, and geometry. The dinaphthocarbazole unit extends the π-system and shifts electron density toward the terminal aromatic core. In the electrostatic surface potential, 4PADNC shows a more concentrated charge distribution near the terminal group. This is favorable for interfacial contact with the perovskite because it can strengthen the local interaction and assist charge transfer.
The dipole moment is a central design parameter. I calculated the gas-phase molecular dipole,
$$ \mu = \left| \sum_i q_i \mathbf{r}_i \right|, $$
and obtained 3.01 D for 4PADNC versus 1.89 D for 4PACZ. A larger dipole at the electrode interface can shift the effective work function more strongly. In a perovskite solar cell, that shift directly affects the built-in field and the selectivity of hole extraction. I also found that the dinaphthocarbazole core is not planar. The intramolecular dihedral angle is about 34.62°. This non-planar geometry weakens π–π stacking and helps prevent molecular aggregation. The planar carbazole unit in 4PACZ lacks this geometric penalty for stacking, which explains why it can form clustered regions on indium tin oxide.
I summarize the key molecular descriptors in Table 2.
| Descriptor | 4PACZ | 4PADNC | My Interpretation |
|---|---|---|---|
| Terminal aromatic core | Carbazole | Dinaphthocarbazole | Extended π-conjugation in 4PADNC |
| Molecular dipole moment (D) | 1.89 | 3.01 | Stronger work-function tuning |
| Intramolecular dihedral angle | Near planar | 34.62° | Suppressed π–π stacking |
| Calculated HOMO (eV) | −5.87 | −5.23 | More shallow HOMO, better alignment |
| Adsorption energy on perovskite (eV) | −3.87 | −4.45 | Stronger interfacial binding |
| Thermal decomposition onset | Not the focus here | 347 °C | Compatible with device annealing |
4. Anchoring on Indium Tin Oxide and Monolayer Uniformity
I verified the anchoring chemistry with X-ray photoelectron spectroscopy. After depositing either 4PACZ or 4PADNC on indium tin oxide, a clear phosphorus signal appears. This confirms that the phosphonic acid group reaches the oxide surface. I also observed that the indium and tin core levels shift to higher binding energy after monolayer deposition. This shift indicates a strong electronic interaction between the phosphonic acid and the oxide. The accepted mechanism is dehydration condensation between the P–OH groups and surface In–OH or Sn–OH groups, forming In–O–P and Sn–O–P linkages.
The anchoring reaction can be represented in a simplified form as
$$ \mathrm{In\!-\!OH} + \mathrm{HO\!-\!P} \rightarrow \mathrm{In\!-\!O\!-\!P} + \mathrm{H_2O}, $$
$$ \mathrm{Sn\!-\!OH} + \mathrm{HO\!-\!P} \rightarrow \mathrm{Sn\!-\!O\!-\!P} + \mathrm{H_2O}. $$
This covalent anchoring is essential for a stable self-assembled monolayer in a perovskite solar cell. If the molecule only physisorbs, it can desorb during perovskite processing or device operation. The phosphorus signal and the core-level shifts convinced me that the monolayer is chemically bound rather than merely coated.
I then used nanoscale infrared spectroscopy to map the spatial distribution of the monolayers. I selected the vibrational region associated with the phosphorus-oxygen bond. The 4PACZ film shows clear clustered regions. In contrast, the 4PADNC film is much more uniform across the indium tin oxide surface. I attribute this to the larger dihedral angle and weaker intermolecular stacking in 4PADNC. A uniform monolayer is critical for a perovskite solar cell because it ensures uniform surface energy, uniform work function, and uniform nucleation sites for the perovskite.
I summarize the anchoring and uniformity observations in Table 3.
| Characterization | Observation for 4PACZ | Observation for 4PADNC | Meaning for the perovskite solar cell |
|---|---|---|---|
| P 2p XPS | Phosphorus signal detected | Phosphorus signal detected | Successful phosphonic acid anchoring |
| In 3d and Sn 3d XPS | Shift to higher binding energy | Shift to higher binding energy | Strong oxide–phosphonate interaction |
| Nano-FTIR mapping | Clusters and aggregation | Uniform coverage | More homogeneous substrate for perovskite growth |
| Contact angle with precursor | 34.21° | 28.54° | Improved wetting and spreading |
5. Energy-Level Alignment and Work-Function Tuning
Energy-level alignment is where I expected the extended conjugation to pay off most clearly. I combined ultraviolet photoelectron spectroscopy, synchrotron radiation photoelectron spectroscopy, and Kelvin probe force microscopy to map the relevant energy levels. The perovskite work function is 4.58 eV. After 4PACZ treatment, the indium tin oxide work function becomes 4.50 eV. After 4PADNC treatment, it becomes 4.62 eV. The deeper work function for 4PADNC is closer to the perovskite, which reduces the barrier for hole extraction.
I define the hole extraction barrier as
$$ \Delta E_{\mathrm{h}} = E_{\mathrm{VB, perovskite}} – E_{\mathrm{F, substrate}}, $$
where \(E_{\mathrm{VB, perovskite}}\) is the valence-band edge of the perovskite and \(E_{\mathrm{F, substrate}}\) is the Fermi level of the treated substrate. In my measurements, the 4PACZ system gives \(\Delta E_{\mathrm{h}} = 1.02\) eV, while the 4PADNC system gives \(\Delta E_{\mathrm{h}} = 0.90\) eV. The smaller barrier means less energy loss and more efficient hole extraction. This is a direct benefit for the open-circuit voltage and fill factor of the perovskite solar cell.
I also compared the valence-band positions. The 4PACZ-treated indium tin oxide has a valence band at −5.64 eV, while the 4PADNC-treated surface has a valence band at −5.43 eV. The perovskite valence band is at −5.52 eV. Therefore, 4PADNC is better matched to the perovskite. The energy difference is smaller, so the interfacial hole transfer is more favorable. In addition, the energy difference between the valence band and the Fermi level is 0.81 eV for 4PADNC and 1.14 eV for 4PACZ. This indicates stronger p-type character for 4PADNC, which supports hole selectivity.
Kelvin probe force microscopy gave a consistent picture. The contact potential difference values are −96 mV for bare indium tin oxide, −264 mV for 4PACZ-treated indium tin oxide, and −350 mV for 4PADNC-treated indium tin oxide. A more negative contact potential difference corresponds to a higher work function in this context. The 4PADNC surface also shows a narrower contact potential difference distribution, which means the surface potential is more uniform. This uniformity is important for a perovskite solar cell because it prevents local patches of poor extraction or poor nucleation.
I summarize the energy-level parameters in Table 4.
| Parameter | Bare ITO | ITO/4PACZ | ITO/4PADNC | Perovskite |
|---|---|---|---|---|
| Work function (eV) | Reference | 4.50 | 4.62 | 4.58 |
| Contact potential difference (mV) | −96 | −264 | −350 | Not applicable |
| Valence-band edge (eV) | Not applicable | −5.64 | −5.43 | −5.52 |
| Fermi-level to valence-band separation (eV) | Not applicable | 1.14 | 0.81 | Not applicable |
| Hole extraction barrier (eV) | Not applicable | 1.02 | 0.90 | Not applicable |
6. Electrical Conductivity and Hole Selectivity
I used conductive atomic force microscopy to probe local electrical conductivity. The average current for 4PADNC on indium tin oxide is 0.555 nA, compared with 0.257 nA for 4PACZ. This means the 4PADNC monolayer is more conductive and can transfer charge more effectively. I also fabricated hole-only devices with an indium tin oxide/self-assembled monolayer/silver structure. The 4PADNC device shows more Ohmic behavior and a higher conductivity. The measured conductivity increases from \(5.69 \times 10^{-4}\) mS cm\(^{-1}\) for 4PACZ to \(7.18 \times 10^{-4}\) mS cm\(^{-1}\) for 4PADNC. This supports the conclusion that 4PADNC has stronger hole selectivity and better hole transport.
The relationship between conductivity and device performance can be expressed through the series resistance and fill factor. In an ideal diode-like solar cell, the fill factor is sensitive to series resistance,
$$ FF \approx FF_0 \left(1 – \frac{R_s J_{\mathrm{SC}}}{V_{\mathrm{OC}}}\right), $$
where \(FF_0\) is the ideal fill factor and \(R_s\) is the series resistance. Therefore, a more conductive hole-selective layer can reduce \(R_s\) and increase \(FF\). I observed exactly this trend in my devices.
I summarize the electrical properties in Table 5.
| Measurement | 4PACZ | 4PADNC | Expected effect |
|---|---|---|---|
| Average c-AFM current (nA) | 0.257 | 0.555 | Higher local conductivity |
| Hole-only conductivity (mS cm\(^{-1}\)) | \(5.69 \times 10^{-4}\) | \(7.18 \times 10^{-4}\) | Improved hole transport |
| Series resistance in final device (Ω) | 31.8 | 23.2 | Lower resistive loss |
| Recombination resistance (Ω) | 789.1 | 1559.8 | Suppressed recombination |
7. Substrate Wetting and Perovskite Film Growth
A hole-selective layer is also a growth template. I measured the contact angle of the perovskite precursor solution on the treated substrates. The 4PACZ surface gives a contact angle of 34.21°, while the 4PADNC surface gives 28.54°. The lower contact angle means better wetting and more uniform spreading of the precursor solution. This is beneficial for forming a compact and pinhole-free perovskite film. A perovskite solar cell depends on this buried interface because voids and cracks at the bottom of the film cause shunting and non-radiative recombination.
I examined cross-sectional scanning electron microscopy. The perovskite grown on 4PACZ contains more vertical grain boundaries. These boundaries can impede charge transport and create recombination pathways. The perovskite grown on 4PADNC has larger grains and fewer vertical boundaries. Top-view scanning electron microscopy gives average grain sizes of 386 nm for 4PACZ and 439 nm for 4PADNC. Atomic force microscopy gives a root-mean-square roughness of 20.42 nm for the 4PACZ-based film and 17.73 nm for the 4PADNC-based film. The smoother and more uniform film is consistent with better substrate wetting and stronger interfacial binding.
I also studied the buried interface by peeling the perovskite film with an ultraviolet-curable adhesive. The 4PACZ substrate shows many pores and cracks at the buried surface. The 4PADNC substrate shows a dense and uniform buried surface with no obvious pores. This is one of the strongest pieces of evidence that the extended dinaphthocarbazole core improves perovskite growth at the bottom interface.
I summarize the morphology and crystallization data in Table 6.
| Property | Perovskite on 4PACZ/ITO | Perovskite on 4PADNC/ITO | Benefit for perovskite solar cell |
|---|---|---|---|
| Precursor contact angle | 34.21° | 28.54° | Improved wetting |
| Average grain size (nm) | 386 | 439 | Fewer grain boundaries |
| RMS roughness (nm) | 20.42 | 17.73 | Smoother perovskite surface |
| Buried interface morphology | Pores and cracks | Dense and uniform | Reduced shunting and recombination |
| GIXRD FWHM for (100) | 0.2406 | 0.1911 | Higher crystallinity |
8. Crystallinity and Preferred Orientation
I used grazing-incidence X-ray diffraction to evaluate crystallinity and orientation. The diffraction ring at \(q = 10\) nm\(^{-1}\) corresponds to the (100) plane of the perovskite. The 4PADNC-based film shows a sharper and more intense (100) ring. Radial integration confirms a stronger and narrower (100) peak. The full width at half maximum is 0.1911 for 4PADNC and 0.2406 for 4PACZ. According to the Scherrer relation,
$$ D = \frac{K \lambda}{\beta \cos\theta}, $$
where \(D\) is the crystallite size, \(K\) is the shape factor, \(\lambda\) is the X-ray wavelength, \(\beta\) is the full width at half maximum, and \(\theta\) is the diffraction angle. A smaller \(\beta\) implies a larger coherent domain size. Therefore, the 4PADNC substrate produces a more crystalline perovskite film with larger coherent domains. This is exactly what I wanted for a high-performance perovskite solar cell because larger grains and fewer boundaries reduce non-radiative recombination.
I also performed density functional theory calculations of the adsorption energy between the self-assembled monolayer and the perovskite (100) surface. I used
$$ E_{\mathrm{ads}} = E_{\mathrm{SAM/perovskite}} – E_{\mathrm{SAM}} – E_{\mathrm{perovskite}}. $$
The calculated adsorption energy is −3.87 eV for 4PACZ and −4.45 eV for 4PADNC. The more negative value for 4PADNC indicates stronger binding. Stronger binding can passivate the buried interface and guide oriented perovskite growth. This helps explain the improved crystallinity, reduced defects, and better device stability.
9. Device Fabrication and Photovoltaic Performance
I fabricated inverted perovskite solar cells with the structure indium tin oxide/self-assembled monolayer/perovskite/C60/BCP/silver. The perovskite composition was \(\mathrm{Cs}_{0.05}\mathrm{MA}_{0.10}\mathrm{FA}_{0.85}\mathrm{PbI}_3\). The self-assembled monolayer was deposited from a dimethylformamide/ethanol mixture, annealed, and then covered with the perovskite. The top contact consisted of C60, BCP, and silver. I used the same procedure for both 4PACZ and 4PADNC so that the comparison would be fair.
The best 4PACZ control device gives a power conversion efficiency of 22.89%, with \(V_{\mathrm{OC}} = 1.138\) V, \(J_{\mathrm{SC}} = 25.20\) mA cm\(^{-2}\), and \(FF = 79.81\%\). The best 4PADNC device gives 24.32%, with \(V_{\mathrm{OC}} = 1.159\) V, \(J_{\mathrm{SC}} = 25.38\) mA cm\(^{-2}\), and \(FF = 82.69\%\). The improvement is distributed across all three parameters, which is a strong sign that the hole-selective layer improves both energetics and transport. The external quantum efficiency spectra integrate to 24.34 mA cm\(^{-2}\) for 4PACZ and 24.56 mA cm\(^{-2}\) for 4PADNC, in good agreement with the \(J\)–\(V\) curves. A steady-state power output measurement at the maximum power point gives 23.92% over 300 s for the 4PADNC device.
I summarize the photovoltaic parameters in Table 7.
| Device | \(V_{\mathrm{OC}}\) (V) | \(J_{\mathrm{SC}}\) (mA cm\(^{-2}\)) | \(FF\) (%) | PCE (%) | Integrated \(J_{\mathrm{SC}}\) (mA cm\(^{-2}\)) |
|---|---|---|---|---|---|
| 4PACZ control | 1.138 | 25.20 | 79.81 | 22.89 | 24.34 |
| 4PADNC target | 1.159 | 25.38 | 82.69 | 24.32 | 24.56 |
| Improvement | +0.021 | +0.18 | +2.88 | +1.43 | +0.22 |
The statistical distribution across 30 devices confirms that the improvement is reproducible. The fill factor and efficiency distributions are narrower for 4PADNC, which indicates better process uniformity. This is consistent with the more uniform monolayer and more uniform surface potential measured earlier. In my view, reproducibility is just as important as the champion efficiency for a perovskite solar cell because it determines whether a molecular design can be scaled.
10. Stability of the Perovskite Solar Cell
I tested unencapsulated devices in a nitrogen glove box. Under continuous light-emitting-diode illumination at 100 mW cm\(^{-2}\), the 4PADNC device retains 90.2% of its initial efficiency after 1000 h. The 4PACZ control retains only 68.5%. I also performed thermal stability testing at 85 °C in nitrogen. After 600 h, the 4PADNC device retains 91.5% of its initial efficiency, while the control retains 74.4%. These results show that the extended dinaphthocarbazole core improves not only efficiency but also long-term stability.
I attribute the stability improvement to several factors. The denser and more uniform monolayer provides better substrate coverage. The stronger adsorption energy improves interfacial adhesion. The larger perovskite grains and lower defect density reduce internal degradation pathways. The buried interface is more compact and has fewer pores, so moisture and ion migration are less likely to initiate degradation. For a perovskite solar cell, these interfacial factors often determine the difference between a laboratory result and a durable device.
I summarize the stability data in Table 8.
| Stress Test | 4PACZ Retention | 4PADNC Retention | Condition |
|---|---|---|---|
| Operational stability | 68.5% after 1000 h | 90.2% after 1000 h | Unencapsulated, N2, 100 mW cm\(^{-2}\) LED |
| Thermal stability | 74.4% after 600 h | 91.5% after 600 h | Unencapsulated, N2, 85 °C |
| Steady-state power | Reference | 23.92% over 300 s | Maximum power point tracking |
11. Charge-Carrier Dynamics at the Buried Interface
I used transient absorption spectroscopy to follow the ground-state bleach at 770 nm. The bleach decays as holes transfer from the perovskite to the hole-selective layer. The 4PADNC/perovskite sample shows stronger bleach quenching on the 5000 ps time scale. Fitting the decay gives a lifetime of 1745.46 ps for 4PACZ/perovskite and 942.66 ps for 4PADNC/perovskite. The shorter lifetime for 4PADNC indicates faster hole extraction. This is exactly what I expected from the improved energy alignment and higher conductivity.
I also measured steady-state photoluminescence and time-resolved photoluminescence. The 4PADNC sample shows the weakest photoluminescence intensity, which means the most efficient quenching by hole extraction. The average carrier lifetime from a double-exponential fit is 1433.92 ns for 4PACZ and 1149.64 ns for 4PADNC. I calculated the average lifetime using
$$ \tau_{\mathrm{ave}} = \frac{A_1 \tau_1^2 + A_2 \tau_2^2}{A_1 \tau_1 + A_2 \tau_2}, $$
where \(A_i\) and \(\tau_i\) are the amplitudes and lifetimes of the fitted components. The shorter average lifetime in the 4PADNC system confirms more efficient charge transfer and reduced recombination loss.
I used the Urbach energy to evaluate the energetic disorder of the perovskite film. The 4PADNC/perovskite sample gives the lowest Urbach energy, 43.38 meV. A lower Urbach energy indicates a sharper absorption edge and fewer tail states. This helps reduce voltage loss in the perovskite solar cell. Photoluminescence quantum yield increases from 1.49% for 4PACZ to 2.21% for 4PADNC. The corresponding quasi-Fermi-level splitting values are 1.169 eV for 4PACZ and 1.181 eV for 4PADNC. The higher quasi-Fermi-level splitting directly supports the higher open-circuit voltage.
I summarize the charge-carrier dynamics in Table 9.
| Parameter | 4PACZ System | 4PADNC System | Physical Meaning |
|---|---|---|---|
| TAS lifetime (ps) | 1745.46 | 942.66 | Faster hole extraction |
| TRPL average lifetime (ns) | 1433.92 | 1149.64 | More efficient interfacial transfer |
| Urbach energy (meV) | Higher | 43.38 | Lower energetic disorder |
| PLQY (%) | 1.49 | 2.21 | Suppressed non-radiative recombination |
| QFLS (eV) | 1.169 | 1.181 | Higher attainable \(V_{\mathrm{OC}}\) |
| TPV recombination lifetime (µs) | 2.41 | 4.43 | Longer effective lifetime |
| TPC extraction time (µs) | 0.95 | 0.47 | Faster charge extraction |
| Ideality factor | 1.34 | 1.12 | Reduced trap-assisted recombination |
12. Defect Density and Recombination Analysis
I used space-charge-limited current measurements to estimate the trap density. The trap-filled limit voltage \(V_{\mathrm{TFL}}\) is related to the trap density by
$$ N_{\mathrm{trap}} = \frac{2 \varepsilon \varepsilon_0 V_{\mathrm{TFL}}}{q L^2}, $$
where \(\varepsilon\) is the relative permittivity, \(\varepsilon_0\) is the vacuum permittivity, \(q\) is the elementary charge, and \(L\) is the film thickness. I obtained \(V_{\mathrm{TFL}} = 0.196\) V for 4PACZ and \(V_{\mathrm{TFL}} = 0.219\) V for 4PADNC. The calculated trap density is \(2.15 \times 10^{15}\) cm\(^{-3}\) for 4PACZ and \(1.92 \times 10^{15}\) cm\(^{-3}\) for 4PADNC. The lower trap density in the 4PADNC device confirms better buried-interface passivation and higher perovskite film quality.
I also analyzed the light-intensity dependence of the open-circuit voltage. The ideality factor is
$$ n = \frac{q}{k_B T} \frac{dV_{\mathrm{OC}}}{d\ln I}. $$
The 4PADNC device gives \(n = 1.12\), while the 4PACZ device gives \(n = 1.34\). A lower ideality factor means less trap-assisted Shockley–Read–Hall recombination. I also examined the short-circuit current density as a function of light intensity,
$$ J_{\mathrm{SC}} \propto I^{\alpha}. $$
The 4PADNC device has an exponent closer to unity, which indicates better charge transport and less bimolecular recombination. These two results explain the higher fill factor and open-circuit voltage in the 4PADNC perovskite solar cell.
13. Impedance, Transient Photovoltage, and Transient Photocurrent
I used electrochemical impedance spectroscopy to separate the recombination and series resistances. The recombination resistance increases from 789.1 Ω for the control to 1559.8 Ω for 4PADNC. The series resistance decreases from 31.8 Ω to 23.2 Ω. A higher recombination resistance means that charge carriers live longer before recombining. A lower series resistance means that charge carriers are collected more efficiently. Together, these changes improve both \(V_{\mathrm{OC}}\) and \(FF\).
I also performed transient photovoltage and transient photocurrent measurements. The transient photovoltage decay gives a recombination lifetime of 2.41 µs for 4PACZ and 4.43 µs for 4PADNC. The transient photocurrent rise gives an extraction time of 0.95 µs for 4PACZ and 0.47 µs for 4PADNC. The longer recombination lifetime and shorter extraction time in the 4PADNC device are ideal for a perovskite solar cell because they allow carriers to be collected before they recombine. This is a direct kinetic explanation for the efficiency improvement.
I summarize the defect and recombination parameters in Table 10.
| Parameter | 4PACZ | 4PADNC | Effect on perovskite solar cell |
|---|---|---|---|
| \(V_{\mathrm{TFL}}\) (V) | 0.196 | 0.219 | Lower trap density |
| \(N_{\mathrm{trap}}\) (cm\(^{-3}\)) | \(2.15 \times 10^{15}\) | \(1.92 \times 10^{15}\) | Reduced non-radiative recombination |
| Ideality factor | 1.34 | 1.12 | Less trap-assisted recombination |
| \(R_{\mathrm{rec}}\) (Ω) | 789.1 | 1559.8 | Better carrier retention |
| \(R_s\) (Ω) | 31.8 | 23.2 | Lower resistive loss |
| TPV lifetime (µs) | 2.41 | 4.43 | Longer effective lifetime |
| TPC extraction time (µs) | 0.95 | 0.47 | Faster extraction |
14. Mechanistic Picture
From my perspective, the mechanism can be summarized in five connected steps. First, the phosphonic acid anchor binds covalently to indium tin oxide, forming In–O–P and Sn–O–P linkages. Second, the extended dinaphthocarbazole core raises the molecular dipole to 3.01 D, which shifts the substrate work function to 4.62 eV and aligns the Fermi level more favorably with the perovskite. Third, the non-planar dihedral angle of 34.62° suppresses π–π stacking, giving a denser and more uniform monolayer. Fourth, the more uniform and more wettable substrate produces a perovskite film with larger grains, fewer vertical grain boundaries, lower roughness, and higher crystallinity. Fifth, the improved energy alignment, higher conductivity, lower trap density, and faster hole extraction reduce non-radiative recombination and increase \(V_{\mathrm{OC}}\), \(J_{\mathrm{SC}}\), and \(FF\) simultaneously.
I can express the interfacial charge-transfer rate in a simplified kinetic form as
$$ k_{\mathrm{CT}} \propto \exp\left(-\frac{\Delta E_{\mathrm{h}}}{k_B T}\right), $$
where \(\Delta E_{\mathrm{h}}\) is the hole extraction barrier. A smaller barrier for 4PADNC increases the charge-transfer rate. This is consistent with the shorter transient absorption lifetime, shorter transient photoluminescence lifetime, and shorter transient photocurrent extraction time. I can also express the recombination loss through the diode equation,
$$ V_{\mathrm{OC}} = \frac{n k_B T}{q} \ln\left(\frac{J_{\mathrm{SC}}}{J_0} + 1\right), $$
where \(J_0\) is the reverse saturation current density. A lower ideality factor and lower trap density reduce \(J_0\), which increases \(V_{\mathrm{OC}}\). This explains why the 4PADNC perovskite solar cell reaches 1.159 V while the control reaches 1.138 V.
15. Comparison of Molecular Design Strategies
I have considered several possible strategies for improving hole-selective layers in perovskite solar cells. One strategy is to add electron-withdrawing substituents to increase the dipole. This can shift the work function, but it may also change the frontier orbital energies and disrupt the alignment with the perovskite. Another strategy is to introduce steric groups to suppress aggregation. This can improve uniformity, but it may reduce packing density and charge transport. My dinaphthocarbazole design combines several advantages in one molecule: extended conjugation, a larger dipole, a non-planar core, strong anchoring, and good thermal stability. This combination is why I believe it is a useful design principle for future perovskite solar cell interfaces.
I summarize the comparison of design strategies in Table 11.
| Strategy | Potential Benefit | Possible Drawback | My Approach with 4PADNC |
|---|---|---|---|
| Electron-withdrawing substituents | Larger dipole, work-function tuning | Frontier orbital shifts, synthesis complexity | Avoided; conjugation extended instead |
| Steric bulk | Suppressed aggregation | Reduced packing and transport | Intrinsic non-planar DNC core |
| Longer alkyl chain | Better solubility and film formation | Poorer charge transport | Kept butyl anchor for compact monolayer |
| Extended π-conjugation | Stronger dipole and better transport | Possible stacking if planar | Balanced by 34.62° dihedral angle |
| Phosphonic acid anchor | Covalent binding to ITO | Requires careful processing | Confirmed In–O–P and Sn–O–P bonding |
16. Broader Implications for Perovskite Solar Cell Technology
The results convinced me that molecular geometry is just as important as molecular energy levels in a hole-selective layer. A molecule can have a good highest occupied molecular orbital, but if it aggregates on the electrode, the effective surface energy and work function become non-uniform. That non-uniformity creates local barriers and local recombination centers. In a perovskite solar cell, these local defects can dominate the device performance even if the average properties look good. The dinaphthocarbazole core solves this problem by combining a large dipole with a non-planar shape.
I also believe the concept can be generalized. Many self-assembled monolayers for perovskite solar cells use planar aromatic terminals. Replacing them with partially twisted polycyclic aromatic hydrocarbons could improve coverage without sacrificing conjugation. The key is to maintain a strong anchor, a suitable dipole, and a frontier orbital that matches the perovskite. Future work could explore different polycyclic cores, different linker lengths, and different anchoring groups. I would also like to test these monolayers in wider-bandgap perovskites for tandem perovskite solar cells, where interfacial energy alignment is even more critical.
Another important implication is stability. The 4PADNC device retains more than 90% of its initial efficiency after 1000 h of operation and after 600 h at 85 °C. This is a meaningful improvement over the control. The enhanced stability comes from the stronger buried interface, the denser monolayer, and the higher-quality perovskite film. In my view, interface engineering for perovskite solar cells must address both efficiency and durability. A molecule that improves efficiency but degrades quickly is not a practical solution. The dinaphthocarbazole phosphonic acid improves both.
17. Quantitative Summary and Derived Relations
I can summarize the device improvement using the diode parameters. The open-circuit voltage gain can be written as
$$ \Delta V_{\mathrm{OC}} = \frac{n_2 k_B T}{q} \ln\left(\frac{J_{\mathrm{SC},2}}{J_{0,2}}\right) – \frac{n_1 k_B T}{q} \ln\left(\frac{J_{\mathrm{SC},1}}{J_{0,1}}\right). $$
Because the short-circuit current density changes only slightly, most of the \(V_{\mathrm{OC}}\) gain comes from the reduction in \(J_0\) and the lower ideality factor. The fill factor gain can be related to the series and shunt resistances through
$$ FF = \frac{V_{\mathrm{MPP}} J_{\mathrm{MPP}}}{V_{\mathrm{OC}} J_{\mathrm{SC}}}, $$
where \(V_{\mathrm{MPP}}\) and \(J_{\mathrm{MPP}}\) are the voltage and current density at the maximum power point. I observed a fill factor increase from 79.81% to 82.69%, which is consistent with the lower series resistance and higher recombination resistance.
I also used the integrated external quantum efficiency to cross-check the short-circuit current density,
$$ J_{\mathrm{SC}} = q \int \mathrm{EQE}(\lambda) \Phi_{\mathrm{AM1.5G}}(\lambda) d\lambda, $$
where \(\Phi_{\mathrm{AM1.5G}}\) is the photon flux of the AM1.5G spectrum. The integrated values of 24.34 and 24.56 mA cm\(^{-2}\) agree well with the \(J\)–\(V\) results. This agreement confirms that the efficiency improvement is not an artifact of spectral mismatch or measurement error.
18. Experimental Details in My Workflow
I cleaned indium tin oxide substrates by sequential sonication in deionized water, detergent, deionized water, acetone, and isopropanol. Each step lasted 15 min. I then treated the substrates with ultraviolet-ozone for 15 min. The hole-selective layer was spin-coated from a 0.5 mg mL\(^{-1}\) solution in dimethylformamide/ethanol (1:4 by volume) at 3000 rpm for 30 s and annealed at 100 °C for 10 min. The perovskite precursor was prepared by dissolving CsI, MAI, FAI, and PbI2 in dimethylformamide/dimethyl sulfoxide (4:1 by volume) to give the target composition. The solution was stirred for 1 h at room temperature. The perovskite film was deposited by a two-step spin-coating process: 1000 rpm for 10 s and 5000 rpm for 30 s. During the second step, 180 µL of chlorobenzene was dropped 10 s before the end. The film was annealed at 100 °C for 30 min. A 0.3 mg mL\(^{-1}\) solution of a passivating molecule in isopropanol was spin-coated at 5000 rpm for 30 s and annealed at 100 °C for 10 min. Finally, C60 (25 nm), BCP (6 nm), and silver (100 nm) were thermally evaporated under high vacuum.
I summarize the fabrication conditions in Table 12.
| Step | Condition | Purpose |
|---|---|---|
| ITO cleaning | Water, detergent, water, acetone, isopropanol; 15 min each | Remove contaminants |
| UV-ozone | 15 min | Activate oxide surface |
| SAM deposition | 0.5 mg mL\(^{-1}\), DMF/ethanol 1:4, 3000 rpm, 30 s | Form hole-selective monolayer |
| SAM annealing | 100 °C, 10 min | Promote condensation and anchoring |
| Perovskite deposition | 1000 rpm 10 s; 5000 rpm 30 s; chlorobenzene drop | Form dense absorber layer |
| Perovskite annealing | 100 °C, 30 min | Improve crystallization |
| Passivation | 0.3 mg mL\(^{-1}\), 5000 rpm, 30 s, 100 °C 10 min | Reduce surface defects |
| Top contact | C60 25 nm; BCP 6 nm; Ag 100 nm | Electron transport and electrode |
19. What I Learned from the Data
The most important lesson I learned is that a hole-selective layer in a perovskite solar cell should be evaluated as an integrated interfacial system. The molecular dipole, the frontier orbital energy, the packing geometry, the anchoring chemistry, the wetting behavior, and the crystallization template all interact. A change in one property can affect the others. In this work, the extended dinaphthocarbazole core improves the dipole and the energy alignment, while the non-planar geometry prevents the aggregation that would otherwise ruin the uniformity. The phosphonic acid anchor ensures strong binding to indium tin oxide. The butyl linker provides enough flexibility for self-assembly without insulating the interface. The result is a more uniform monolayer, a better perovskite film, a more efficient device, and a more stable device.
I also learned that the buried interface controls more than just hole extraction. It controls perovskite nucleation, grain growth, grain boundary formation, and defect density. The 4PADNC substrate gives larger grains and fewer vertical boundaries. This reduces non-radiative recombination and improves charge transport. The lower Urbach energy and higher photoluminescence quantum yield confirm that the perovskite film itself is better. Therefore, the performance improvement is not only an interface effect. It is also an absorber-quality effect induced by the interface.
20. Conclusion and Outlook
I designed, synthesized, and characterized a π-conjugation-extended dinaphthocarbazole phosphonic acid as a hole-selective layer for inverted perovskite solar cells. The molecule has a large dipole moment of 3.01 D, a non-planar core with a 34.62° dihedral angle, a deep work function of 4.62 eV on indium tin oxide, and a strong adsorption energy of −4.45 eV on the perovskite surface. It forms a dense and uniform self-assembled monolayer, improves perovskite wetting and crystallization, and reduces interfacial energy loss. The resulting perovskite solar cell achieves 24.32% power conversion efficiency, compared with 22.89% for the control. It also retains 90.2% of its initial efficiency after 1000 h of operation and 91.5% after 600 h at 85 °C.
I believe this work provides a clear molecular design rule for hole-selective layers in perovskite solar cells. Extending π-conjugation increases the dipole and improves transport. Introducing a non-planar core suppresses aggregation and improves coverage. Keeping a strong phosphonic acid anchor ensures stable binding. Combining these features in one molecule gives a better buried interface, a better perovskite film, and a better perovskite solar cell. In future work, I would like to apply this strategy to other polycyclic aromatic cores and to tandem perovskite solar cells, where precise interfacial energy alignment and long-term stability are essential.
21. Consolidated Quantitative Comparison
| Category | Metric | 4PACZ | 4PADNC | Change |
|---|---|---|---|---|
| Molecular | Dipole moment (D) | 1.89 | 3.01 | +1.12 |
| Molecular | Dihedral angle (°) | Planar | 34.62 | Non-planar |
| Energy | Work function on ITO (eV) | 4.50 | 4.62 | +0.12 |
| Energy | Hole extraction barrier (eV) | 1.02 | 0.90 | −0.12 |
| Energy | Valence-band edge (eV) | −5.64 | −5.43 | +0.21 |
| Morphology | Contact angle (°) | 34.21 | 28.54 | −5.67 |
| Morphology | Grain size (nm) | 386 | 439 | +53 |
| Morphology | RMS roughness (nm) | 20.42 | 17.73 | −2.69 |
| Crystallinity | GIXRD FWHM | 0.2406 | 0.1911 | −0.0495 |
| Device | \(V_{\mathrm{OC}}\) (V) | 1.138 | 1.159 | +0.021 |
| Device | \(J_{\mathrm{SC}}\) (mA cm\(^{-2}\)) | 25.20 | 25.38 | +0.18 |
| Device | \(FF\) (%) | 79.81 | 82.69 | +2.88 |
| Device | PCE (%) | 22.89 | 24.32 | +1.43 |
| Dynamics | TAS lifetime (ps) | 1745.46 | 942.66 | −802.80 |
| Dynamics | TRPL lifetime (ns) | 1433.92 | 1149.64 | −284.28 |
| Dynamics | PLQY (%) | 1.49 | 2.21 | +0.72 |
| Recombination | Ideality factor | 1.34 | 1.12 | −0.22 |
| Recombination | Trap density (cm\(^{-3}\)) | \(2.15 \times 10^{15}\) | \(1.92 \times 10^{15}\) | −0.23 × 10\(^{15}\) |
| Stability | 1000 h operational retention (%) | 68.5 | 90.2 | +21.7 |
| Stability | 600 h thermal retention (%) | 74.4 | 91.5 | +17.1 |
This consolidated table captures the full arc of my investigation. It starts from molecular structure, moves through interface energetics and morphology, then connects to charge-carrier dynamics, device parameters, and stability. The table also shows that the improvement is not isolated to one measurement. It appears consistently across independent techniques. That consistency is the strongest evidence that the dinaphthocarbazole phosphonic acid is an effective hole-selective layer for inverted perovskite solar cells.
22. Final Perspective
I remain optimistic about the role of molecular interface design in the future of perovskite solar cells. The perovskite absorber itself is already excellent. Many remaining losses occur at interfaces. A well-designed self-assembled monolayer can reduce those losses, improve film growth, and extend device lifetime. The dinaphthocarbazole phosphonic acid demonstrates that a single molecular change can improve efficiency, reproducibility, and stability at the same time. I hope this work encourages further exploration of extended polycyclic aromatic systems for hole-selective layers and other interfacial layers in perovskite solar cells. The combination of strong anchoring, large dipole, non-planar geometry, and extended conjugation is a powerful design platform for the next generation of perovskite solar cell interfaces.