I designed and investigated a pi-conjugation-extended dinaphthocarbazole phosphonic acid as a hole-selective layer for inverted perovskite solar cells. In my approach, the functional terminal unit of a conventional carbazole-based self-assembled monolayer is replaced by a larger dinaphthocarbazole framework. This single structural change simultaneously modifies the molecular dipole, the frontier orbital distribution, the interfacial energy alignment, the substrate wettability, the molecular packing motif, and the nucleation landscape for the perovskite absorber. The resulting self-assembled monolayer enables inverted perovskite solar cells with a power conversion efficiency of 24.32%, accompanied by improved thermal stability and operational stability relative to a reference carbazole-based device. I describe here the molecular rationale, synthesis, computational analysis, surface chemistry, crystallization control, device physics, and stability behavior in a unified mechanistic picture. The central finding is that extending pi-conjugation in the hole-selective layer is not merely an electronic modification; it is a coupled molecular, interfacial, and morphological design strategy for high-performance perovskite solar cells.
1. Introduction and Motivation
Inverted perovskite solar cells have advanced rapidly because of their simple device architecture, low-temperature processability, compatibility with tandem integration, and steadily increasing certified efficiencies. In an inverted p-i-n perovskite solar cell, the hole-selective layer is one of the most influential interfaces in the entire stack. It determines hole extraction, electron blocking, substrate work function, perovskite nucleation, and long-term interfacial stability. Self-assembled monolayers have therefore become a central class of hole-selective materials for high-efficiency inverted perovskite solar cells. A typical self-assembled monolayer contains an anchoring group, a linker group, and a terminal functional group. Phosphonic acid anchoring groups are especially effective because they can condense with surface hydroxyl groups on indium tin oxide to form robust In-O-P and Sn-O-P bonds. The terminal group controls the surface dipole and energy level alignment, while the linker influences molecular orientation, packing density, and charge transport.
Carbazole-based self-assembled monolayers, particularly 4PACZ, have become benchmark hole-selective layers in inverted perovskite solar cells. Their electron-rich carbazole unit provides favorable hole transport, and their phosphonic acid group anchors strongly to transparent conductive oxides. However, 4PACZ has two well-known limitations. First, its molecular dipole is modest, so the work function shift of the indium tin oxide substrate is limited. This weakens the energy level alignment between the substrate and the perovskite, leading to interfacial energy loss and reduced open-circuit voltage. Second, the planar carbazole core promotes molecular aggregation through pi-pi stacking. Aggregation can produce incomplete substrate coverage, nonuniform surface potential, and poor film homogeneity, all of which degrade the performance and stability of perovskite solar cells. These issues motivate molecular designs that increase the dipole moment without sacrificing processability and that suppress strong pi-pi stacking without eliminating charge transport.
I reasoned that a pi-extended polycyclic aromatic terminal group could address both limitations at once. A larger conjugated framework can delocalize charge, increase the molecular dipole, and strengthen electron donation to the perovskite interface. At the same time, if the extended framework is nonplanar, it can frustrate close pi-pi stacking and promote uniform monolayer formation. Dinaphthocarbazole is an attractive candidate because it extends the carbazole skeleton with two fused naphthalene units. The resulting core is more electron-rich and more polarizable than carbazole, but it also contains an intrinsic intramolecular dihedral angle that breaks perfect planarity. I therefore selected a dinaphthocarbazole phosphonic acid, abbreviated here as 4PADNC, and compared it directly with 4PACZ in inverted perovskite solar cells. The comparison reveals how pi-conjugation extension influences molecular dipole, work function, surface homogeneity, perovskite crystallization, charge extraction, nonradiative recombination, and device stability.
The general performance metric of a perovskite solar cell is the power conversion efficiency:
$$ \mathrm{PCE} = \frac{V_{\mathrm{OC}} J_{\mathrm{SC}} \mathrm{FF}}{P_{\mathrm{in}}} $$
Here, \(V_{\mathrm{OC}}\) is the open-circuit voltage, \(J_{\mathrm{SC}}\) is the short-circuit current density, \(\mathrm{FF}\) is the fill factor, and \(P_{\mathrm{in}}\) is the incident optical power density. Because the absorber bandgap fixes the maximum attainable current to a first approximation, improvements in \(V_{\mathrm{OC}}\) and \(\mathrm{FF}\) are often the most direct route to higher efficiency in perovskite solar cells. Both parameters are strongly controlled by interfacial nonradiative recombination and charge extraction. I therefore focused on how a pi-extended hole-selective layer changes the interfacial boundary conditions of inverted perovskite solar cells.
2. Molecular Design and Computational Analysis
I compared 4PACZ and 4PADNC at the molecular level using density functional theory. The most important descriptors are the molecular dipole moment, the electrostatic surface potential, the frontier orbital energies, and the intramolecular dihedral angle. The calculated dipole moment of 4PADNC is 3.01 D, whereas 4PACZ has a dipole moment of 1.89 D. This increase is substantial and directly relevant to the work function of indium tin oxide. A larger dipole oriented at the substrate interface produces a stronger interfacial potential shift, which can deepen the effective Fermi level and improve energy alignment with the perovskite. The electrostatic surface potential of 4PADNC also shows a more concentrated charge distribution on the terminal dinaphthocarbazole unit than that of 4PACZ. I interpret this as evidence for stronger local electron density at the interface, which can promote better contact and more efficient charge transfer with the perovskite.
Another key structural parameter is the intramolecular dihedral angle. The dinaphthocarbazole core of 4PADNC exhibits a dihedral angle of approximately 34.62 degrees. This nonplanar geometry contrasts with the relatively planar carbazole core of 4PACZ. The nonplanarity is beneficial because it weakens intermolecular pi-pi stacking. Strong pi-pi stacking can drive aggregation and island formation on the substrate, but moderate suppression of stacking allows the molecules to spread more uniformly. The result is a denser and more homogeneous self-assembled monolayer. I note that this does not eliminate intermolecular electronic coupling; instead, it balances packing density and surface uniformity. The extended pi-system still supports hole transport, while the twisted core prevents excessive crystallite-like aggregation.
The frontier orbital energies further support the design. The highest occupied molecular orbital of 4PACZ is calculated to be -5.87 eV, while that of 4PADNC is -5.23 eV. These values are consistent with cyclic voltammetry measurements. The shallower highest occupied molecular orbital of 4PADNC is beneficial for hole extraction because it reduces the energetic barrier between the perovskite valence band and the hole-selective layer. The lowest unoccupied molecular orbital is also shifted, but the primary hole-selective function is governed by the valence band alignment and the substrate work function.
| Property | 4PACZ | 4PADNC | Implication for perovskite solar cells |
|---|---|---|---|
| Terminal unit | Carbazole | Dinaphthocarbazole | Extended pi-conjugation and stronger electron donation |
| Calculated dipole moment | 1.89 D | 3.01 D | Larger work function shift and improved energy alignment |
| Intramolecular dihedral angle | Near planar | 34.62 degrees | Suppressed pi-pi stacking and more uniform monolayer |
| Calculated HOMO | -5.87 eV | -5.23 eV | Lower hole extraction barrier |
| Calculated LUMO | Not limiting for hole selectivity | Not limiting for hole selectivity | Electron blocking remains favorable |
| Electrostatic potential | Moderate concentration | Higher and more concentrated | Stronger interfacial contact and charge transfer |
I also considered the adsorption energy of the self-assembled monolayer on the perovskite (100) surface. The adsorption energy can be written as:
$$ E_{\mathrm{ads}} = E_{\mathrm{total}} – E_{\mathrm{surface}} – E_{\mathrm{molecule}} $$
Using this definition, 4PADNC gives an adsorption energy of -4.45 eV, whereas 4PACZ gives -3.87 eV. The more negative value for 4PADNC indicates stronger interaction with the perovskite surface. Stronger adsorption is not always beneficial if it disrupts film growth, but here the interaction promotes more intimate contact and passivates buried interface defects. In my view, the extended pi-system provides additional van der Waals and electrostatic interactions that stabilize the interface without creating a covalent trap. This stronger adsorption is one reason the perovskite film grows with larger grains and fewer buried voids.
3. Synthesis and Molecular Characterization
I synthesized 4PADNC through a convergent route beginning from 2-aminoanthracene. The first step forms the dinaphthocarbazole core through a rhodium-catalyzed oxidative cyclization in hexafluoroisopropanol. The product, 8H-dinaphtho[2,3-c:2′,3′-g]carbazole, is obtained as a brown solid. I then alkylated the core with 1,4-dibromobutane under phase-transfer conditions to install a bromobutyl linker. The bromo intermediate undergoes Michaelis-Arbuzov reaction with triethyl phosphite to give the diethyl phosphonate ester. Finally, trimethylsilyl bromide is used to cleave the ethyl groups and generate the phosphonic acid. The overall sequence is modular, and each intermediate is purified by column chromatography. The final product is a pale green solid with good thermal stability.
| Step | Reaction type | Key reagent | Product | Role in final perovskite solar cells |
|---|---|---|---|---|
| 1 | Oxidative cyclization | 2-Aminoanthracene, Rh/C, HFIP | Dinaphthocarbazole core | Provides extended pi-conjugated terminal unit |
| 2 | N-Alkylation | 1,4-Dibromobutane, KOH | Bromobutyl-substituted core | Installs flexible linker |
| 3 | Michaelis-Arbuzov | Triethyl phosphite | Diethyl phosphonate ester | Introduces phosphonic acid precursor |
| 4 | Silyl dealkylation | Trimethylsilyl bromide | Phosphonic acid | Enables anchoring to indium tin oxide |
I characterized the final molecule by nuclear magnetic resonance spectroscopy and mass spectrometry. The proton nuclear magnetic resonance spectrum shows aromatic signals from the dinaphthocarbazole core in the region from 7.52 to 9.79 ppm, while the aliphatic linker protons appear between 1.52 and 4.74 ppm. The carbon nuclear magnetic resonance spectrum displays core carbon signals from 113.96 to 136.00 ppm and side-chain carbon signals from 21.20 to 43.11 ppm. The phosphorus nuclear magnetic resonance spectrum shows a single signal at 25.28 ppm, confirming one phosphorus environment. Mass spectrometry gives a molecular ion peak consistent with the expected molecular weight. Thermogravimetric analysis shows a 10% weight-loss temperature of 347 degrees Celsius, which is high enough for the annealing steps used during perovskite solar cells fabrication. This thermal stability is important because the hole-selective layer must survive the crystallization and annealing of the perovskite absorber.
The synthetic route also matters for reproducibility. The use of a bromobutyl linker and a phosphonic acid anchor follows the design logic of many high-performing self-assembled monolayers for perovskite solar cells. The difference is the extended aromatic terminal group. I found that the extended core does not compromise solubility in the dimethylformamide and ethanol mixture used for spin coating. This is essential because self-assembled monolayers must be deposited as dilute solutions to avoid multilayer formation. The resulting monolayer is thin enough to avoid parasitic absorption but dense enough to modify the substrate work function.
4. Anchoring, Surface Chemistry, and Monolayer Morphology
I verified anchoring of the self-assembled monolayers on indium tin oxide using X-ray photoelectron spectroscopy. After deposition of either 4PACZ or 4PADNC, a clear phosphorus 2p signal appears. This confirms that the phosphonic acid group is present at the surface. I also observe shifts in the indium 3d and tin 3d binding energies toward higher values. These shifts indicate strong electronic interaction between the phosphonic acid and the metal oxide surface. The most likely anchoring chemistry involves dehydration condensation between the P-OH groups of the phosphonic acid and surface In-OH or Sn-OH groups, forming In-O-P and Sn-O-P bonds. This covalent anchoring is a key reason self-assembled monolayers remain stable during perovskite solar cells operation.
I used nanoscale Fourier transform infrared spectroscopy to map the spatial distribution of the phosphonic acid groups. The infrared feature associated with the phosphorus-oxygen double bond appears in the 1100 to 1300 cm^{-1} range. For 4PACZ, I observe pronounced clustering and aggregation. For 4PADNC, the signal is significantly more uniform across the indium tin oxide surface. The improved uniformity is consistent with the larger intramolecular dihedral angle and the reduced pi-pi stacking tendency. A uniform monolayer is important because it avoids uncovered regions that can cause direct contact between the perovskite and the transparent conducting oxide, which would increase nonradiative recombination and degrade the fill factor in perovskite solar cells.
Kelvin probe force microscopy provides further evidence. The contact potential difference of bare indium tin oxide is about -96 mV. After 4PACZ deposition, it becomes -264 mV. After 4PADNC deposition, it becomes -350 mV. A more negative contact potential difference corresponds to a higher work function and a deeper Fermi level. I therefore conclude that 4PADNC shifts the substrate energetics more strongly than 4PACZ. The 4PADNC surface also shows a narrower distribution of contact potential difference values. This narrower distribution indicates better surface potential uniformity, which is desirable for uniform perovskite nucleation and consistent hole extraction across the device area. In contrast, the broader distribution for 4PACZ suggests phase separation or uneven molecular packing, which can produce local variations in energy alignment.
| Surface parameter | Indium tin oxide | 4PACZ/indium tin oxide | 4PADNC/indium tin oxide |
|---|---|---|---|
| Contact potential difference | -96 mV | -264 mV | -350 mV |
| Work function trend | Reference | Moderate increase | Stronger increase |
| Surface potential uniformity | Broad | Broad and irregular | Narrow and uniform |
| Phosphorus signal | Absent | Present | Present |
| Indium and tin binding energy shift | Reference | Shifted to higher energy | Shifted to higher energy |
| Nanoscale infrared uniformity | Not applicable | Clustered | Uniform |
I also measured the conductivity of the self-assembled monolayers using conductive atomic force microscopy. The average current for 4PADNC is 0.555 nA, compared with 0.257 nA for 4PACZ. This indicates that 4PADNC is more conductive and supports faster charge transfer. I fabricated hole-only devices with a simple indium tin oxide/self-assembled monolayer/silver structure. The 4PADNC device exhibits ohmic behavior and a higher conductivity of 7.18 x 10^{-4} mS cm^{-1}, compared with 5.69 x 10^{-4} mS cm^{-1} for 4PACZ. These results show that the extended pi-system improves hole selectivity and transport without introducing a significant injection barrier. For perovskite solar cells, this means that the hole-selective layer can extract carriers more efficiently while still blocking electrons.
Wettability of the substrate by the perovskite precursor solution is another critical factor. The contact angle of the perovskite precursor solution on 4PACZ is 34.21 degrees, while on 4PADNC it is 28.54 degrees. The lower contact angle on 4PADNC indicates better wetting. Better wetting promotes uniform nucleation and suppresses dewetting, which is important for large-area perovskite solar cells. I attribute this improvement to the more uniform monolayer and the stronger interfacial interaction between the extended pi-system and the polar precursor solution. The combination of good wetting, strong anchoring, and high surface potential uniformity creates a favorable substrate for high-quality perovskite film growth.
5. Energy Level Alignment and Hole Selectivity
I determined the energy level alignment of the perovskite and the self-assembled monolayer-modified substrates using ultraviolet photoelectron spectroscopy and high-resolution synchrotron radiation photoelectron spectroscopy. The perovskite work function is 4.58 eV. After 4PACZ modification, the indium tin oxide work function is 4.50 eV. After 4PADNC modification, it is 4.62 eV. This difference is important because it changes the hole extraction barrier. I estimate the hole extraction barrier as:
$$ \Delta E_h = E_{\mathrm{VB,perovskite}} – E_{\mathrm{WF,HSL}} $$
For the 4PACZ system, the barrier increases to about 1.02 eV, which promotes unfavorable band bending for hole extraction. For the 4PADNC system, the barrier decreases to about 0.90 eV. A lower hole extraction barrier reduces interfacial energy loss and improves both open-circuit voltage and fill factor in perovskite solar cells. I also measured the valence band edge. The 4PADNC/indium tin oxide valence band is -5.43 eV, while the 4PACZ/indium tin oxide valence band is -5.64 eV. The perovskite valence band is -5.52 eV. Therefore, the 4PADNC valence band lies closer to the perovskite valence band, which reduces the energy offset and facilitates hole transfer.
The energy difference between the valence band and the Fermi level provides additional information about p-type character. For 4PADNC, this difference is 0.81 eV. For 4PACZ, it is 1.14 eV. A smaller valence band to Fermi level separation indicates stronger p-type character, which favors hole selectivity and hole transport. I therefore conclude that the extended pi-conjugation of 4PADNC increases the electron-rich character of the terminal group, shifts the molecular dipole, deepens the substrate Fermi level, and improves the energetic match with the perovskite absorber. In inverted perovskite solar cells, this combination directly reduces the voltage deficit and improves charge collection.
| Energy parameter | 4PACZ system | 4PADNC system | Perovskite reference |
|---|---|---|---|
| Substrate work function after monolayer | 4.50 eV | 4.62 eV | 4.58 eV |
| Valence band edge of monolayer-modified substrate | -5.64 eV | -5.43 eV | -5.52 eV |
| Hole extraction barrier | 1.02 eV | 0.90 eV | Not applicable |
| Valence band to Fermi level difference | 1.14 eV | 0.81 eV | Not applicable |
| p-type character | Weaker | Stronger | Not applicable |
The alignment can also be discussed in terms of the open-circuit voltage loss. The detailed balance limit gives:
$$ E_g = q V_{\mathrm{OC}} + \Delta E_{\mathrm{loss}} $$
where \(E_g\) is the absorber bandgap and \(\Delta E_{\mathrm{loss}}\) includes radiative and nonradiative losses. A lower hole extraction barrier and reduced interfacial recombination reduce the nonradiative component of \(\Delta E_{\mathrm{loss}}\). In my devices, the 4PADNC-based perovskite solar cells achieve a higher open-circuit voltage than the 4PACZ reference, consistent with improved energy alignment and reduced interfacial recombination. The shallower highest occupied molecular orbital of 4PADNC and the deeper substrate work function work together to reduce the energetic mismatch at the hole-selective interface.
6. Perovskite Film Growth and Crystallization
The substrate controls the initial stages of perovskite nucleation and crystal growth. I therefore examined the morphology and crystallinity of perovskite films deposited on 4PACZ and 4PADNC. Cross-sectional scanning electron microscopy shows that the perovskite film on 4PACZ contains more vertical grain boundaries. Vertical grain boundaries can impede charge transport and create recombination pathways. In contrast, the perovskite film on 4PADNC exhibits larger grains and fewer vertical boundaries. Top-view scanning electron microscopy gives average grain sizes of 386 nm on 4PACZ and 439 nm on 4PADNC. Larger grains reduce the total grain boundary area and therefore reduce nonradiative recombination in perovskite solar cells.
Atomic force microscopy shows that the root-mean-square roughness of the perovskite film on 4PACZ is 20.42 nm, while on 4PADNC it is 17.73 nm. The smoother surface on 4PADNC indicates more uniform film growth. I also examined the buried interface by peeling the perovskite film with ultraviolet-curable adhesive. The buried interface on 4PACZ contains many pores and cracks, whereas the buried interface on 4PADNC is dense and uniform with no obvious voids. This is a strong indication that the extended pi-conjugated monolayer promotes dense nucleation and suppresses void formation at the bottom interface. For inverted perovskite solar cells, a dense buried interface is critical because it directly controls hole extraction and shunt pathways.
Grazing-incidence X-ray diffraction confirms the improved crystallinity. The diffraction ring at approximately 10 nm^{-1} corresponds to the (100) plane of the perovskite. The film on 4PADNC shows a sharper and more intense ring than the film on 4PACZ. Radial integration gives a full width at half maximum of 0.1911 for the 4PADNC film, compared with 0.2406 for the 4PACZ film. A smaller full width at half maximum indicates larger coherent crystalline domains and better crystallinity. I attribute this to the combined effects of improved wetting, stronger adsorption energy, and more uniform surface potential. The extended pi-system also provides a favorable interface for the growth of the perovskite (100) plane, which is known to be beneficial for charge transport in perovskite solar cells.
| Film property | Perovskite on 4PACZ | Perovskite on 4PADNC |
|---|---|---|
| Precursor contact angle | 34.21 degrees | 28.54 degrees |
| Average grain size | 386 nm | 439 nm |
| Root-mean-square roughness | 20.42 nm | 17.73 nm |
| Buried interface morphology | Pores and cracks | Dense and uniform |
| (100) diffraction full width at half maximum | 0.2406 | 0.1911 |
| Vertical grain boundaries | More | Fewer |
The adsorption energy calculations provide a molecular explanation for the improved film growth. The more negative adsorption energy of 4PADNC means that the perovskite precursors interact more strongly with the monolayer surface. This can slow down nucleation and promote ordered crystal growth, resulting in larger grains. I emphasize that the stronger interaction does not lead to excessive pinning because the nonplanar core and flexible linker allow the monolayer to accommodate the perovskite lattice. The net effect is a better-defined buried interface with fewer defects, which is exactly what is needed for high-performance perovskite solar cells.
7. Photovoltaic Performance of Inverted Perovskite Solar Cells
I fabricated inverted perovskite solar cells with the architecture indium tin oxide/self-assembled monolayer/perovskite/C60/BCP/silver. The 4PACZ reference device achieves a power conversion efficiency of 22.89%, with an open-circuit voltage of 1.138 V, a short-circuit current density of 25.20 mA cm^{-2}, and a fill factor of 79.81%. The 4PADNC device achieves a power conversion efficiency of 24.32%, with an open-circuit voltage of 1.159 V, a short-circuit current density of 25.38 mA cm^{-2}, and a fill factor of 82.69%. The efficiency improvement is therefore driven mainly by simultaneous gains in open-circuit voltage and fill factor, with a small contribution from short-circuit current density. This is consistent with reduced interfacial recombination and improved charge extraction.
| Device | \(V_{\mathrm{OC}}\) (V) | \(J_{\mathrm{SC}}\) (mA cm^{-2}) | FF (%) | PCE (%) | Integrated \(J_{\mathrm{SC}}\) (mA cm^{-2}) |
|---|---|---|---|---|---|
| 4PACZ reference | 1.138 | 25.20 | 79.81 | 22.89 | 24.34 |
| 4PADNC target | 1.159 | 25.38 | 82.69 | 24.32 | 24.56 |
External quantum efficiency measurements give integrated photocurrents of 24.34 mA cm^{-2} for 4PACZ and 24.56 mA cm^{-2} for 4PADNC. These values agree well with the current-voltage measurements, confirming that the photocurrent enhancement is real and not an artifact of spectral mismatch. Under continuous one-sun illumination at the maximum power point, the 4PADNC device maintains a stabilized efficiency of 23.92% over 300 seconds. Statistical analysis over 30 independent devices shows excellent reproducibility. The fill factor and power conversion efficiency distributions are narrower for 4PADNC than for 4PACZ, indicating that the improved surface uniformity translates into device-level consistency. This reproducibility is important for the scalable manufacturing of perovskite solar cells.
I also analyzed the diode behavior of the devices. The ideality factor is extracted from the light-intensity dependence of the open-circuit voltage:
$$ n = \frac{q}{k_B T} \frac{dV_{\mathrm{OC}}}{d \ln I} $$
Here, \(q\) is the elementary charge, \(k_B\) is the Boltzmann constant, \(T\) is temperature, and \(I\) is light intensity. The 4PADNC device gives an ideality factor of 1.12, while the 4PACZ device gives 1.34. A lower ideality factor indicates reduced trap-assisted nonradiative recombination. I also examined the short-circuit current density as a function of light intensity:
$$ J_{\mathrm{SC}} \propto I^{\alpha} $$
The exponent \(\alpha\) is closer to unity for the 4PADNC device, which indicates more balanced charge transport and reduced bimolecular recombination. Together, the lower ideality factor and the near-unity exponent explain the improved fill factor and open-circuit voltage in the 4PADNC-based perovskite solar cells.
8. Charge Carrier Dynamics and Recombination
I studied charge carrier dynamics using transient absorption spectroscopy, steady-state photoluminescence, and time-resolved photoluminescence. In transient absorption spectroscopy, all samples show a ground-state bleach peak at about 770 nm. The bleach recovery reflects the competition between recombination and hole transfer to the self-assembled monolayer. The 4PADNC/perovskite sample shows stronger bleach quenching than the 4PACZ/perovskite sample over the 5000 ps time scale. Fitting the decay kinetics gives lifetimes of 1745.46 ps for 4PACZ/perovskite and 942.66 ps for 4PADNC/perovskite. The shorter lifetime for 4PADNC indicates faster hole extraction, which is consistent with the lower hole extraction barrier and higher conductivity.
Steady-state photoluminescence shows the same trend. The perovskite film on 4PADNC has the weakest photoluminescence intensity, meaning that nonradiative recombination and radiative recombination are both more effectively quenched by hole transfer. Time-resolved photoluminescence gives an average carrier lifetime of 1433.92 ns for 4PACZ and 1149.64 ns for 4PADNC. I calculated the average lifetime using the standard double-exponential expression:
$$ \tau_{\mathrm{ave}} = \frac{A_1 \tau_1^2 + A_2 \tau_2^2}{A_1 \tau_1 + A_2 \tau_2} $$
The shorter average lifetime for 4PADNC is not a sign of poor quality; rather, it reflects more efficient charge transfer at the interface. In perovskite solar cells, fast extraction competes with recombination, so a shorter lifetime in the presence of a hole-selective layer usually indicates improved hole collection.
I also measured the Urbach energy from the absorption onset:
$$ \alpha(E) = \alpha_0 \exp\left(\frac{E – E_0}{E_u}\right) $$
The Urbach energy reflects energetic disorder and structural quality. The 4PADNC/perovskite sample has the lowest Urbach energy of 43.38 meV, indicating reduced disorder and fewer tail states. Photoluminescence quantum yield is 2.21% for 4PADNC and 1.49% for 4PACZ. The corresponding quasi-Fermi level splitting values are 1.181 eV for 4PADNC and 1.169 eV for 4PACZ. A higher quasi-Fermi level splitting directly supports a higher open-circuit voltage. I therefore conclude that 4PADNC both improves charge extraction and reduces nonradiative recombination, two effects that are often difficult to achieve simultaneously in perovskite solar cells.
| Charge dynamics parameter | 4PACZ | 4PADNC |
|---|---|---|
| Transient absorption lifetime | 1745.46 ps | 942.66 ps |
| Time-resolved photoluminescence average lifetime | 1433.92 ns | 1149.64 ns |
| Urbach energy | Higher | 43.38 meV |
| Photoluminescence quantum yield | 1.49% | 2.21% |
| Quasi-Fermi level splitting | 1.169 eV | 1.181 eV |
| Ideality factor | 1.34 | 1.12 |
I used space-charge-limited current measurements to estimate the trap density. The trap-filled limit voltage is related to the trap density by:
$$ N_{\mathrm{trap}} = \frac{2 \epsilon \epsilon_0 V_{\mathrm{TFL}}}{q L^2} $$
Here, \(\epsilon\) is the relative permittivity, \(\epsilon_0\) is the vacuum permittivity, \(V_{\mathrm{TFL}}\) is the trap-filled limit voltage, \(q\) is the elementary charge, and \(L\) is the film thickness. The 4PADNC device gives a trap density of \(1.92 \times 10^{15} \mathrm{cm^{-3}}\), while the 4PACZ device gives \(2.15 \times 10^{15} \mathrm{cm^{-3}}\). The lower trap density in the 4PADNC device confirms better defect passivation at the buried interface. Electrochemical impedance spectroscopy shows that the recombination resistance increases from 789.1 ohm for 4PACZ to 1559.8 ohm for 4PADNC, while the series resistance decreases from 31.8 ohm to 23.2 ohm. The higher recombination resistance and lower series resistance explain the improved fill factor and open-circuit voltage.
Transient photovoltage and transient photocurrent measurements provide additional insight. The recombination lifetime under open-circuit conditions is 2.41 microseconds for 4PACZ and 4.43 microseconds for 4PADNC. The longer recombination lifetime for 4PADNC indicates better passivation and reduced nonradiative recombination. The charge extraction time is 0.95 microseconds for 4PACZ and 0.47 microseconds for 4PADNC. The faster extraction time confirms that the pi-extended monolayer improves hole transport and reduces interfacial charging. In my view, the combination of faster extraction and slower recombination is the key device-level advantage of 4PADNC in inverted perovskite solar cells.
9. Stability of Perovskite Solar Cells
Stability is as important as efficiency for perovskite solar cells. 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 hours, while the 4PACZ device retains only 68.5%. I also performed thermal stability testing at 85 degrees Celsius in nitrogen. After 600 hours, the 4PADNC device retains 91.5% of its initial efficiency, compared with 74.4% for the 4PACZ device. These improvements are substantial and are consistent with the structural and interfacial properties discussed above.
| Stability test | 4PACZ retention | 4PADNC retention | Condition |
|---|---|---|---|
| Operational stability | 68.5% after 1000 h | 90.2% after 1000 h | Unencapsulated, nitrogen, 100 mW cm^{-2} light-emitting diode |
| Thermal stability | 74.4% after 600 h | 91.5% after 600 h | Unencapsulated, nitrogen, 85 degrees Celsius |
I attribute the improved stability to several factors. First, the denser and more uniform self-assembled monolayer reduces direct contact between the perovskite and the indium tin oxide surface, which suppresses interfacial degradation. Second, the larger perovskite grains and reduced vertical grain boundaries limit ion migration and moisture ingress along grain boundaries. Third, the buried interface is dense and free of voids, so delamination and shunt formation are less likely. Fourth, the stronger adsorption energy of 4PADNC stabilizes the interface against thermal stress. Fifth, the reduced trap density lowers the driving force for nonradiative recombination and local heating. Together, these effects produce more robust inverted perovskite solar cells.
I also note that the thermal stability of the molecule itself is high. The 10% weight-loss temperature of 4PADNC is 347 degrees Celsius, which is well above the annealing temperatures used during device fabrication and above the operating temperatures encountered in accelerated aging tests. This molecular thermal stability ensures that the hole-selective layer does not decompose during perovskite annealing or long-term operation. The phosphonic acid anchoring group also forms strong In-O-P and Sn-O-P bonds, which resist displacement by perovskite precursors and degradation products. For perovskite solar cells, this combination of molecular and interfacial stability is essential for commercial viability.
10. Mechanistic Summary
The mechanistic picture that emerges from my investigation is that pi-conjugation extension changes the hole-selective layer in four coupled ways. First, it increases the molecular dipole moment from 1.89 D to 3.01 D. This larger dipole shifts the indium tin oxide work function from 4.50 eV to 4.62 eV, reducing the hole extraction barrier from 1.02 eV to 0.90 eV. Second, it introduces a nonplanar dinaphthocarbazole core with a dihedral angle of 34.62 degrees. This nonplanarity suppresses excessive pi-pi stacking, leading to a more uniform monolayer with narrower surface potential distribution. Third, it strengthens the adsorption energy on the perovskite (100) surface from -3.87 eV to -4.45 eV. This stronger interaction promotes dense nucleation, larger grains, and a void-free buried interface. Fourth, it enhances the p-type character of the monolayer and increases its conductivity, which improves hole extraction and reduces nonradiative recombination.
These four effects explain the device improvements. The open-circuit voltage increases from 1.138 V to 1.159 V because the energy level alignment is improved and nonradiative recombination is suppressed. The fill factor increases from 79.81% to 82.69% because series resistance decreases and recombination resistance increases. The short-circuit current density increases slightly from 25.20 mA cm^{-2} to 25.38 mA cm^{-2} because the perovskite film has larger grains, fewer grain boundaries, and a smoother surface. The overall power conversion efficiency increases from 22.89% to 24.32%. In my analysis, no single factor dominates; rather, the molecular design couples electronic, surface, and morphological improvements in a way that is well suited to inverted perovskite solar cells.
| Design feature | Molecular consequence | Interfacial consequence | Device consequence in perovskite solar cells |
|---|---|---|---|
| Extended pi-conjugation | Larger dipole and shallower HOMO | Better work function shift and lower hole barrier | Higher \(V_{\mathrm{OC}}\) and improved hole extraction |
| Nonplanar dinaphthocarbazole core | Reduced pi-pi stacking | More uniform monolayer and narrower surface potential | Better reproducibility and higher fill factor |
| Stronger adsorption | More negative adsorption energy | Dense buried interface and fewer voids | Larger grains and reduced nonradiative recombination |
| Higher conductivity | Improved hole transport | Lower series resistance | Higher fill factor and faster extraction |
| Robust phosphonic acid anchoring | Strong In-O-P and Sn-O-P bonds | Stable interface under thermal stress | Improved thermal and operational stability |
I can express the fill factor improvement in terms of the diode parameters. For a solar cell, the fill factor is approximately:
$$ \mathrm{FF} = \frac{P_{\mathrm{max}}}{V_{\mathrm{OC}} J_{\mathrm{SC}}} $$
and the maximum power point is determined by the balance between charge extraction and recombination. When the series resistance decreases and the recombination resistance increases, the current-voltage curve becomes more square, which increases the fill factor. The 4PADNC device shows exactly this behavior: lower series resistance, higher recombination resistance, lower ideality factor, and faster extraction. These are all signatures of an improved hole-selective contact in perovskite solar cells.
11. Broader Implications for Perovskite Solar Cells
The results of my study suggest that polycyclic aromatic hydrocarbon terminal groups are a promising direction for self-assembled monolayers in perovskite solar cells. The conventional carbazole unit is planar and relatively small, which limits both dipole moment and surface uniformity. Extending the pi-system to dinaphthocarbazole increases the dipole and electron density, while the intrinsic twist suppresses aggregation. This combination is difficult to achieve with simple substituent engineering. Adding electron-withdrawing groups can increase the dipole, but it can also change the frontier orbital energies in undesirable ways. Adding bulky substituents can suppress aggregation, but it can reduce packing density and charge transport. The dinaphthocarbazole strategy avoids these trade-offs by using an extended, electron-rich, nonplanar aromatic core.
I also emphasize that the self-assembled monolayer is not a passive interfacial layer. It actively participates in perovskite nucleation, crystal orientation, defect passivation, and charge extraction. Therefore, the design of hole-selective layers for perovskite solar cells should consider molecular electronics, surface science, and crystallization kinetics together. In my work, the extended pi-conjugation improves all three. The larger dipole improves the electronic boundary condition, the nonplanar core improves the surface boundary condition, and the stronger adsorption improves the crystallization boundary condition. This integrated design philosophy can be extended to other anchoring groups, linkers, and terminal units for perovskite solar cells and related optoelectronic devices.
For future work, I would explore several directions. First, the length and flexibility of the alkyl linker could be varied to tune packing density and charge transport. Second, different polycyclic aromatic cores could be compared to separate the effects of dipole, conjugation length, and nonplanarity. Third, the monolayer could be combined with surface passivation treatments to further reduce interfacial defects. Fourth, large-area deposition methods such as slot-die coating and blade coating should be tested to evaluate scalability. Fifth, long-term stability under damp heat and full-spectrum illumination should be evaluated to assess commercial readiness. These studies would help translate the molecular design principles demonstrated here into practical perovskite solar cells modules.
12. Conclusion
I have shown that a pi-conjugation-extended dinaphthocarbazole phosphonic acid self-assembled monolayer, 4PADNC, functions as an excellent hole-selective layer for inverted perovskite solar cells. The extended dinaphthocarbazole core increases the molecular dipole moment from 1.89 D to 3.01 D, shifts the indium tin oxide work function to 4.62 eV, and reduces the hole extraction barrier to 0.90 eV. The nonplanar core with a 34.62-degree dihedral angle suppresses pi-pi stacking and produces a more uniform monolayer with narrower surface potential distribution. The stronger adsorption energy on the perovskite (100) surface promotes dense nucleation, larger grains, a smoother surface, and a void-free buried interface. These improvements lead to faster hole extraction, lower trap density, higher recombination resistance, lower series resistance, and reduced nonradiative recombination. The resulting inverted perovskite solar cells achieve a power conversion efficiency of 24.32%, compared with 22.89% for the 4PACZ reference, along with improved thermal stability and operational stability. I conclude that extending pi-conjugation in hole-selective self-assembled monolayers is a powerful strategy for advancing the efficiency and stability of perovskite solar cells.
| Overall comparison | 4PACZ reference | 4PADNC target |
|---|---|---|
| Best PCE | 22.89% | 24.32% |
| \(V_{\mathrm{OC}}\) | 1.138 V | 1.159 V |
| \(J_{\mathrm{SC}}\) | 25.20 mA cm^{-2} | 25.38 mA cm^{-2} |
| FF | 79.81% | 82.69% |
| Integrated \(J_{\mathrm{SC}}\) | 24.34 mA cm^{-2} | 24.56 mA cm^{-2} |
| Operational stability after 1000 h | 68.5% | 90.2% |
| Thermal stability after 600 h at 85 degrees Celsius | 74.4% | 91.5% |
| Hole extraction barrier | 1.02 eV | 0.90 eV |
| Trap density | \(2.15 \times 10^{15} \mathrm{cm^{-3}}\) | \(1.92 \times 10^{15} \mathrm{cm^{-3}}\) |
| Recombination resistance | 789.1 ohm | 1559.8 ohm |
| Series resistance | 31.8 ohm | 23.2 ohm |
In summary, my study establishes a clear structure-property-performance relationship for pi-extended dinaphthocarbazole phosphonic acid in inverted perovskite solar cells. The molecular design simultaneously addresses dipole strength, molecular packing, surface uniformity, interfacial adsorption, charge extraction, and defect passivation. The result is a high-efficiency and stable perovskite solar cells platform that benefits from a more favorable hole-selective contact. I believe this approach provides a useful blueprint for the next generation of self-assembled monolayers for perovskite solar cells and other thin-film photovoltaic technologies.