Interfacial engineering to modulate surface dipoles, work functions and dielectric confinement of halide perovskites

Abstract

The interfacial properties between perovskite photoactive and charge transport layers are critical for device performance and operational stability. Therefore, an accurate theoretical description of the link between surface dipoles and work functions is of scientific and practical interest. We show that for a CsPbBr₃ perovskite surface functionalized by dipolar ligand molecules, the interplay between surface dipoles, charge transfers, and local strain effects leads to upward or downward shifts of the valence level. We further demonstrate that the contribution of individual molecular entities to the surface dipoles and electric susceptibilities are essentially additive. Finally, we compare our results to those predicted from conventional classical approaches based on a capacitor model that links the induced vacuum level shift and the molecular dipole moment. Our findings identify recipes to fine-tune materials work functions that provide valuable insights into the interfacial engineering of this family of semiconductors.

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Introduction

Metal halide perovskites have received remarkable attention in the scientific community because they represent a promising class of semiconductors for optoelectronics, with simple, easy and cheap fabrication processes.¹ Attractive properties, such as tunable band gap,² long carrier diffusion length,³ ambipolar charge transport,⁴ high defect tolerance⁵ have led to various and promising applications in the field of optoelectronic devices, such as solar cells,⁶ photodetectors,⁷ light emitting diodes⁸ and lasers.⁹ It is now common knowledge that “interfaces” are central to the performances of all these devices.¹⁰ The interface materials having an energetically favorable alignment between the photoactive layer and the charge transport layers provide efficient operation.¹¹ For instance, suitable alignments with hole transport layer and the electron transport layer aid to enhance the performance of solar cells by effectively transporting the charge carriers towards the electrode layers. On the other hand, proper alignment is also required to facilitate carrier injection towards the photoactive layer for LEDs. Therefore, it is of great interest in the field of surface and interface engineering to develop methods that can effectively tailor the energy levels of the materials. Nowadays, surface functionalization has already proved successful in fine tuning the energy level alignments between the various materials composing the device. Surface functionalization directly affects the surface dipoles that subsequently influence the work function or the energy levels of the material at the interface.^11,12 In this regard, the widely used method to achieve a desired interface energetics is to tune the energy levels by introducing specific molecules having significant dipole moment with the correct orientation.^13–16

Assessment of the impact of interface functionalization on band alignment requires detailed knowledge about its nature and composition. But, a proper characterization of interfaces is challenging in thin-films because of the presence of harsh surfaces and the difficulty to control their morphologies during the fabrication process. In addition, implementation of classical characterization techniques such as Ultraviolet Photoelectron Spectroscopy (UPS) may be difficult because molecules may tend to detach in an ultra-high vacuum region.¹³ Therefore, to ascertain meaningful conclusions, various experimental techniques need to be combined, such as Kelvin probe (KP), Kelvin probe force microscopy (KPFM), Ambient Pressure Photoemission Spectroscopy (APS) and cyclic voltammetry (CV).^13,17,18 Theoretical investigations taking into account the atomistic description of surfaces and interfaces may thus provide interesting guidance for experimental work and future developments.

Regarding the theoretical approaches, some empirical models have been developed in the past, targeting mainly monolayers and metal-oxides. For example, Demchak and Fort,¹⁹ developed an empirical model to inspect monolayers at water–air interfaces, which was later on applied to explore ultrathin layers consisting of dipolar molecules and a capacitor model. More recently, Leung et al.²⁰ demonstrated the relationship between surface dipole density and work function, and its strong dependence on the substrate's orientation, along with adsorbate-induced charge transfer. Zheng et al.²¹ used a similar approach to tune the work function of γ-CsSnI₃ as a function of surface dipoles and ligand layer coverage. Recently, some of us further extended the scope of such approaches with a theoretical framework that allows bridging results from atomistic ab initio calculations and classical simulation approaches for multilayered thin film devices.²²

Surface functionalization and/or passivation has already been well explored experimentally for metal halide perovskites. For instance, molecules such as mercaptobenzimidazole with –NO₂ and –OCH₃ groups are employed to modify the perovskite (CH₃NH₃PbI_3−xCl_x)/electron transport layer interface, leading to enhanced power conversion efficiency (PCE) and stability.²³ Recently, J. Duan et al. regulated the side group of an aniline molecule based on the same functional groups on CsPbBr₃ perovskite solar cells.²⁴ In addition, recent theoretical studies proposed phenylethylammonium (PEA⁺) and its halogen derivatives (XPEA⁺) to passivate the surface of γ-CsSnI₃,²¹ and DMSO and (2,4,6-trimethylphenyl) phosphonic acid (TMPPA) molecules to passivate the surfaces of both CsPbI₃ and MAPbI₃ slabs.²² Notably, the aforementioned studies mainly focused on only one kind of molecules or side group regulated dipolar passivating molecules. Hence, there are not many reports that bring a comparative discussion on the effect of various ligands and their surface coverage to fine tune the work function of the perovskites.

In this work, we further exploit the semi-classical approach recently developed by some of us to tailor the surface dipole and work function of CsPbBr₃.²² This perovskite material has recently shown great promises not only for light emitting devices, such as deep blue²⁵ and single photon emitters,²⁶ but also radiation-detectors^27,28 and can be synthesized in various forms, namely single crystals,^28–30 thin films,³¹ nanoplatelets,^25,32 colloidal quantum dots³³ and superlattices.^34,35 Ligands under consideration are phosphonate, oleate, DMSO, anilinium, anilinium –NO₂, anilinium –OCH₃, and three different alkylammonium ligands [primary dodecylammonium (DA), secondary didodecylammonium (DDA), and quaternary dimethyldidodecylammonium (DMDDA)]. This specific set of ligands has been chosen based on their use in the synthesis of perovskite materials and nanocrystals, either as capping ligands and/or as passivation agents.^36–40 Aniline derivatives were added given the available data on work function shifts,²⁴ which motivated us to further explore their charge state and orientation. We thoroughly investigate the influence of each specific ligand on the work function and discuss the microscopic origin of the induced changes in terms of surface and interface dipoles. The impact of surface coverage is inspected. Additivity of surface and interface dipoles as well as electric susceptibilities are also discussed. Finally, we compare our results to those predicted using the conventional empirical approach based on a capacitor model and emphasize its validity in the context of halide perovskites.

Results and discussion

Interplay between surface dipole density and work function

In this section, we briefly summarize the methodology that will be used to investigate the relationship between surface/interface dipoles and work functions.^20,41 The method is based on a semi classical approach (classical physics combined with density functional theory (DFT) calculations) that has been introduced in more details in a previous work.²² Fig. S3† provides information about the various conventions used in this work.

Relation between the polarization density and the charge density. We start by inspecting the electrodynamics that relates the displacement electric field (D) with the polarization density (P).

D = ε₀E + P (1)

By considering Gauss’ law, the polarization density is related to the bound charge density (ρ_b):

−∇·P = ρ_b. (2)

The surface is modeled with a perovskite slab oriented perpendicular to the z-axis with the layer of molecular dipoles deposited at the surface (see ESI, Fig. S3†). The interaction between surface and molecules leads to the additivity of two dipoles: (i) the intrinsic dipole of the ligands or molecules (vide infra) and (ii) the dipole ascribed to the interaction between the molecules and surface. The net interaction eventually leads to a shift in perovskite surface energetics. The slab structure is built in such a way that the dipole density is vanishing in the middle bulk like region of the slab (z = z₀ = 0, considered as the origin) while it is also vanishing in the middle of the vacuum region (at ).

We consider the planar averaged charge density along z (ρ_b(z)) concomitant with the density profile of the polarization density along the z axis (P_z)

The weighted integral of the charge density between z₀ and can be computed from a DFT simulation of the slab

where P_b(z) = zρ_b(z). Using integration by parts, this quantity is identified as the surface dipole density (p):

In order to get some insight into the various contributions close to the surface, a polarization density profile can be extracted by a partial integration of the weighted charge density (see Leung et al.²⁰) or P_b(z) can be represented directly as in the work of Traoré et al.²²

Relation between surface dipole density and work function. In order to bridge our approach with the work of Leung et al.,²⁰ we use the numerical implementation of the surface dipole density (from eqn (4)) and combine it with Poisson's equation (−ε₀∇²V = ρ_b), a detailed derivation is given in ref. 22, to obtain

The work function ϕ is given by eV(c/2) − eV(z₀) (Fig. S3†), leading to

It is possible in the case of DFT calculations performed on semiconductors at T = 0 K (ref. 22) to directly relate the work function to the energy at the top of the valence band (E^abs_v, Fig. S3†). Therefore eqn (7) can be written as

and its variation readswhere E^abs_v in Joule (J) and p surface dipole density in C m⁻¹. This work function definition in the theoretical work by Leung et al.²⁰ allows computing the electrostatic potential step for an electron to escape the material through a dipolar surface. Notice that the experimental definition of the work function is related to the position of the Fermi level (Fig. S3†), which may depend on various aspects including the sample temperature and carrier doping (vide infra). Eqn (9) provides a relationship between a shift in the valence energies (ΔE^abs_v) and a change in surface dipole density (Δp). Therefore, from the aforementioned methodology, the change in surface properties due to surface functionalization via dipolar molecules can be discussed using the polarization density profiles. In our work, we further validate the robustness of the DFT based methodology by comparing the ΔE^abs_v computed directly from the change of surface dipole density (Δp) (from eqn (9)) to the shift in the valence energies determined from the variations of the Hartree potential alignments (ΔE^abs_v) (for definition, see Fig. S3(d) and ESI text I.4†).

Investigated ligands

Fig. 1 shows various ligands or molecules that have been considered in this work. The names of the following are 5-carbon chain phosphonic acid (pentylphosphonic acid (C₅H₁₃O₃P)), 5-carbon chain oleic acid (pentanoic acid), commonly known as valeric acid (C₅H₁₀O₂), dimethyl sulfoxide (DMSO) ((CH₃)₂SO), aniline (C₆H₅NH₂) and its derivatives such as p-nitroaniline (aniline –NO₂ (C₆H₆N₂O₂)), p-methoxyaniline or p-anisidine (C₅H₉NO) (aniline –OCH₃).

Fig. 1 Molecules and their Hirshfeld charge analysis to show the direction of the dipole moment (a) phosphonate (b) oleate (c) DMSO (d) anilinium (e) anilinium –OCH₃ (f) anilinium –NO₂. Alkylammonium ligands are taken from classical MD simulation snapshots of ref. 42: (g) primary dodecylammonium (DA) (h) secondary didodecylammonium (DDA), and (i) quaternary dimethyldidodecylammonium (DMDDA). The Red (blue) region corresponds to excess electronic charge (electron deficiency). Black arrows show the direction of the dipole moments (see Fig. S3† for sign convention).

Note that for Pentanoic acid and Pentylphosphonic acid, we consider their conjugate base i.e. Pentanoate (C₅H₉O₂⁻) and Hydrogen phosphonate (C₅H₁₂O₃P⁻). For aniline, nitroaniline, and methoxyaniline (see ESI, Fig. S4†), the corresponding conjugate acids are anilinium (C₆H₅NH₃⁺), methoxyanilinium (C₅H₁₀NO⁺) and nitroanilinium (C₆H₇N₂O₂⁺). For the sake of simplicity, we refer to the considered molecules as phosphonate, oleate, DMSO, anilinium, anilinium –OCH₃ and anilinium –NO₂.

In addition, we consider three different alkylammonium ligands i.e. primary dodecylammonium (DA), secondary didodecylammonium (DDA), and quaternary dimethyldidodecylammonium (DMDDA). Note that, these ligands are taken from equilibrated snapshots of classical molecular dynamics (MD) simulations, so that dynamic effects are reflected in the alkyl chain of the molecules.⁴²

As a first step, the distribution of charges in the molecules is shown via Hirshfeld charge analysis. The red (blue) region corresponds to a more negative charge (more positive charge) (see Fig. 1). Convention used for the dipole moment direction is from negative to positive charge (Fig. S3(a)†). We calculate the dipole moments of the optimized molecular structures. See Table 1 for a comparison with available experimental or theoretical data from the literature.

Table 1 Computed molecular dipole moments (PBE) compared to previous works. Subscript e and t correspond to experimental and theoretical reported values

Molecules	μ (D) (calculated)	μ (D) (previous works)
Phosphonic acid	1.40	1.56e (ref. 43)
Oleic acid	1.59	1.50e (ref. 44)−1.61e (ref. 45)
DMSO	3.79	3.90e (ref. 46)
Aniline	1.70	1.97t (ref. 24)
Aniline –NO2	7.44	7.56t (ref. 24)
Aniline –OCH3	1.61	1.38t (ref. 24)

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Molecules such as phosphonate, oleate, and DMSO act as Lewis bases (electron donating), while anilinium and its derivatives act as Lewis acids with a tendency to withdraw electrons. It is worth noting that there is a relation between the electron-withdrawing/donating nature of molecules and the shift in valence levels. Lewis acid/base interactions with the surface involve charge transfer, i.e. directly associated with the surface dipole density, which can be quantified using eqn (3)–(5). The surface dipole density, in turn, has an impact on the valence energy, as described by eqn (8) and (9).

Among all molecules, aniline –NO₂ presents the strongest dipole. The dipole moment of the charged molecules such as DA, DDA and DMDDA, with respect to their center of mass as the origin, are calculated as 25.45 D, 19.84 D and 16.84 D, respectively. These values are consistent with the trend obtained for amines in the literature.⁴⁷ Notably, values of charged molecules are origin dependent.

Surface–ligand interaction to tune surface dipole density and work function

Firstly, we test the robustness of our methodology by inspecting slabs of CsPbBr₃ without functionalization of the surfaces. We construct a CsPbBr₃ slab from its pseudo-cubic structure²⁷ so as to avoid issues related to symmetry breaking (see ESI for detailed discussion, Fig. S1c†). We consider the CsBr terminated surface, which appears to be more stable as compared to PbBr₂ terminated one.⁴⁸ We confirm this by comparing the surface energies of the CsBr and PbBr₂ terminated surfaces (see ESI, section V†).

Thus, we mainly proceed with the CsBr terminated surface of CsPbBr₃, considering a slab having 8 octahedra layers (for convergence see ESI, section I†) to study the effect of surface functionalization. To compare various approaches for the work function shifts, charge density, polarization density profiles, surface dipole densities and Hartree potential alignments are computed.

Negative surface dipole variation by surface functionalization. In many reports, molecules are shown to functionalize the surface by coordinating to lead, ascribed to the commonly observed halide vacancies in experiments.^49,50 For that purpose, phosphonic acid ligand is chosen as a good example,^39,51,52 as it is already known for its strong binding with metal ions, such as Pb in PbSe quantum dots.⁵³ Consistently with previously reported modeling strategies,^51,54 we remove a H atom from the phosphonic molecule (–OH end) and form a phosphonate anion. Then, we substitute a bromine (Br) atom (outer terminal) by the oxygen atom (O) of the phosphonate anion. This ensures the charge neutrality of the whole system. Note that, the pristine surface of the considered slab being terminated by four Br atoms, the concentration values of 25%, 50%, 75% and 100% correspond to substitutions of 1 Br, 2 Br, 3 Br and 4 Br atoms with phosphonate anions, respectively. The optimized structures of the pristine CsBr terminated CsPbBr₃ slab and that with phosphonate molecules attached to the slab are shown in Fig. 2(a). The latter is illustrated for a molecular coverage of 50%. The shaded portion shows the outer layers that are relaxed in our methodology and the middle layers are kept fixed such that they mimic the structure of bulk CsPbBr₃Fig. 2(a). A computation of the Hartree potential profile can be used to analyze the valence energy of a pristine CsPbBr₃ slab (Fig. S3(d)†). We observe a successive increase in the valence energies (E^abs_v) or an upward shift of the valence levels (see Fig. 2(b)) with increasing molecular coverage. The corresponding values are summarized in Table 2.

Fig. 2 (a) CsPbBr₃ CsBr terminated slabs without (top) and with (bottom) phosphonate ligands attached to the surface. The later is illustrated for 50% molecular coverage. (b) Valence energies for 0% to 100% surface coverage. (c) Polarization density profiles for 0% and 50% molecular coverage (for other concentrations see ESI, Fig. S7†). The integration of these polarization profiles result in the surface dipole densities (Table 2). (d) Variation of the electronic charge density upon functionalization with phosphonate for 50% molecular coverage. For clarity, only one side of the symmetric slab is shown. Orange and turquoise color represent electronic depletion and accumulation region, respectively, and the arrow indicates the net dipole direction. (e) Relation between the change in surface dipole density and the molecular coverage. (f) Relation between the change in the valence energies and the molecular coverage. The valence energy values are computed from the Hartree potential profiles.

Table 2 Valence energies (E^abs_v) and surface dipole densities (p) computed at the PBE + SOC level of theory for different molecules and molecular coverage changing from 0% to 100% for CsBr terminated CsPbBr₃ slabs. Change in surface dipole densities (Δp). Shifts of valence levels obtained from the difference of surface dipole density (ΔE^abs_v using eqn (9)) and computed from the Hartree potential alignment [HP] ΔE^abs_v (Fig. S3(d)†)

	E ^absv (eV)	ΔE^absv [HP] (eV)	p × 10^−11 (C m^−1)	Δp × 10^−11 (C m^−1)	ΔE^absv (eV) [eqn (9)]
CsPbBr 3 slab with phosphonate concentration
Pristine	−4.87	—	+3.50	—	—
25% phosphonate	−4.73	+0.14	+3.30	−0.20	+0.23
50% phosphonate	−4.60	+0.27	+3.20	−0.30	+0.34
75% phosphonate	−4.49	+0.38	+3.08	−0.42	+0.47
100% phosphonate	−4.45	+0.42	+3.00	−0.50	+0.56
CsPbBr 3 slab with oleate concentration
Pristine	−4.87	—	+3.50	—	—
25% oleate	−4.63	+0.24	+3.20	−0.30	+0.34
50% oleate	−4.37	+0.50	+2.96	−0.54	+0.61
75% oleate	−4.20	+0.67	+2.83	−0.67	+0.76
100% oleate	−4.16	+0.71	+2.77	−0.73	+0.83
CsPbBr 3 slab with DMSO concentration
Pristine	−4.87	—	+3.50	—	—
25% DMSO	−4.52	+0.35	+3.14	−0.36	+0.41
50% DMSO	−4.14	+0.73	+2.80	−0.70	+0.79
75% DMSO	−3.82	+1.05	+2.53	−0.97	+1.10
100% DMSO	−3.31	+1.56	+2.07	−1.43	+1.62

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To understand the microscopic origin of these shifts, we compute their polarization density profiles (P_b(z)) shown in Fig. 2(c) and analyze the surface and interface dipoles. There are few worthy points that can be highlighted from these polarization profiles (P_b(z)): (i) the surface dipoles counteract each other on both sides of the structure as expected from the symmetry of the slab, (ii) the dipole vanishes in the middle of the slab, (iii) by integrating the area under the peaks of the profiles (P_b(z)) from the center of the slab to the middle of the vacuum (eqn (5)), the surface dipole density (p) can be determined. The computed values of surface dipole densities and the change in surface dipole densities (Δp) for different concentrations (0–100%) are given in Table 2. From Fig. 2, we attribute the increase of E^abs_v for phosphonate to the decrease in surface dipole density induced by surface functionalization. The decrease in surface dipole density can be further explained as a result of electron transfer from the phosphonate to the outer perovskite layer, yielding a dipole direction away from the surface (see Fig. 2(d)). We examine this in more depth by looking into the interplay of octahedral tilting in the surface layer and contraction or expansion of PbBr bond lengths at the surface (see ESI, section VII†). We observe from Table S5† that when we compare 25% concentration to other concentrations (50%, 75% and 100%), the surface layers are more distorted with smaller in-plane Pb–Br–Pb angles and much larger out of plane delta (δ (ref. 55)) octahedra tilt angles. It is well known that octahedral tilting significantly influence the electronic properties.^56,57 Larger deviations from 180° in Pb–Br–Pb bond angle result in deeper valence levels. This indicates that surface relaxation addtionally impacts the dipole density at the surface, which in turn influence the valence energy. Our conclusion from the aforesaid discussion is that by varying the surface coverage with phosphonate, the work function can be tuned by several meVs with a valence level shifted upwards with increasing coverage.

Next, we extend our discussion to the oleic acid and DMSO molecules, generally used as a surfactant to fabricate colloidal quantum dots.^58–60 The details regarding how these molecules are attached on the surface⁵⁰ are given in ESI (section VIII†). The calculated E^abs_v and surface dipole density values for various concentrations are given in Table 2. The increase in E^abs_v or upward shift in valence level for oleate anions and DMSO are induced by the reduction of surface dipole density as a result of charge transfer from the molecule to the outer perovskite layer (see ESI, section VIII†). Between 75% and 100% concentration of phosphonate and oleate anions, there is only a minor change in the E^abs_v values (∼0.04 eV). It is due to the steric hindrance of bulky molecules (phosphonate and oleate) that impedes the relaxation of the surface (ESI, section VII†), which is not observed with DMSO. For lower surface coverages, the changes in surface dipole density (Δp) and the shift in the valence energies (ΔE^abs_v) as a function of molecular coverage for phosphonate anions are linear (see Fig. 2(e) and (f)). The linearity relationship also holds for oleate anions and DMSO (ESI, Fig. S12†). Noteworthy, the ΔE^abs_v obtained from Hartree potential alignment are in agreement with ΔE^abs_v computed using eqn (9) (see Table 2).

To sum up the aforementioned results, all the studied cases show an upwards shift of the valence level with an increase in the concentration of molecules on the surface. The observed trend is DMSO > oleate > phosphonate in effectively tuning the E^abs_v energies. These molecules may also act as potential passivating agents as they do not present any molecular states in between their perovskite-based band edges (ESI, Fig. S13†).

Limitation of the computational methodology. Choy and collaborators have reported their work based on mercaptobenzimidazole interface molecules and demonstrated that the defect passivation (halide vacancies) as well as tuning of energy levels can be achieved via modulating the functional groups, such as nitryl (–NO₂) and methoxyl (–OCH₃) groups.²³ Notably, these groups have opposite effects on the solar cell performance, owing to their different electronegativities. –NO₂ and –OCH₃ functional groups act as electron withdrawing and electron donating groups, respectively. Recently J. Duan et al.²⁴ have performed experimental studies by regulating the side group of an aniline molecule based on the same functional groups. Following this, we compute the valence energies and surface dipole densities as a function of molecular coverage for the cations on a CsPbBr₃ surface, and discuss our results in light of the available experimental data.²⁴ We first consider anilinium and its derivatives, where the –NH₃⁺ group substitutes a Cs-atom of the outer layer of the CsPbBr₃ surface (Fig. 3a). At a given concentration, (Fig. 3(c) in a horizontal direction) the following trend for E^abs_v is observed: anilinium –NO₂ < anilinium < anilinium –OCH₃. This trend does not match the experimental trend reported for the valence bands derived from UPS spectra analysis²⁴ (see Fig. 3(b) and ESI, Fig. S15†). The comparison is not improved when considering neutral molecules with NH₂ group pointing towards the surface (ESI section XII†), as assumed in the original report.²⁴ Interestingly, with the NO₂ group pointing towards the perovskite surface (ESI section XIII†), the valence levels undergoes an upward shift. But, at the smallest computed coverage (25%), this shift is predicted to be huge, whereas the experimental one is about 0.1 eV.²⁴ Actually, experiments evidence a sizeable shift of the Fermi level with respect to the vacuum that points towards a p-doped semiconductor. This effect is not captured by the present simulations. Besides, from the computed band structures of anilinium derivatives (ESI, Fig. S14†), no in-gap molecular states are found, which confirms that they may act as potential passivating agents.

Fig. 3 (a) CsPbBr₃ CsBr terminated slabs without (top) and with anilinium, anilinium –OCH₃ and anilinium –NO₂ ligands on the surface. The NH₃⁺ group is placed at a Cs-vacancy of the outer layers on each side of the surface (see zoom view) and is illustrated for 50% molecular coverage. (b) Experimental valence energies (top, green)²⁴ and (c–f) computed E^abs_v for pristine (orange) and for (c) 25%, (d) 50%, (e) 75%, and (f) 100% surface coverage (blue).

Comparison between primary, secondary and quaternary alkylammonium ligands

Recently alkylammonium ligands, particularly DMDDA halides, have attracted considerable interest in obtaining purifiable and stable colloids.^40,61,62 In light of this, we applied the present methodology to a comparison between three different alkylammonium ligands namely DA, DDA and DMDDA. We have used extracted orientations of long alkyl chain of ligands from classical MD simulations.⁴² Notably, solid-state NMR spectroscopy confirmed that CsPbBr₃ QDs are CsBr terminated with alkylammonium ligands, partially substituting Cs cations at the surface.⁶³ Thus, we substitute Cs⁺ with the alkylammonium ligand, replacing the cesium by the nitrogen of NH₃⁺, NH₂⁺ and N⁺ groups corresponding to DA, DDA and DMDDA molecules, respectively (Fig. 4(a)). The computed E^abs_v values for DA, DDA and DMDDA are given in Table 3. As previously demonstrated, the observed trend is related to the change in surface dipole density values (Δp) obtained by integrating the area under the peak of (P_b(z)) shown in Fig. 4(c). We obtain small differences between the three alkylammonium ligands, including small structural distorsions of the octahedra at the surface (Table S9†). Still, experimental values may change more significantly, depending on various aspects such as surface doping, molecular coverage, molecular orientations and induced lattice strain at the surface.

Fig. 4 (a) CsPbBr₃ CsBr terminated slabs without (top) and with DA, DDA and DMDDA ligands on the surface for a coverage of 11%. Corresponding (b) valence energies and (c) polarization density profiles.

Table 3 Valence energies (E^abs_v) and change in surface dipole densities (Δp) computed at the PBE + SOC level of theory for DA, DDA and DMDDA at CsBr terminated CsPbBr₃ slabs. Shifts of valence levels obtained from the difference of surface dipole density (ΔE^abs_v using eqn (9)) and computed from the Hartree potential alignment [HP] ΔE^abs_v (Fig. S3(d)†)

	E ^absv (eV)	ΔE^absv [HP] (eV)	Δp × 10^−11 (C m^−1)	ΔE^absv (eV) [eqn (9)]
Pristine	−4.87	—	—	—
DA	−4.75	+0.12	−0.18	+0.20
DDA	−4.65	+0.22	−0.25	+0.28
DMDDA	−4.58	+0.29	−0.32	+0.36

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Additivity of surface dipole densities and electric susceptibilities

Hitherto, we have investigated different ligands on the CsPbBr₃ surface, resulting in positive or negative surface dipole density variations. The increase/decrease in the valence energies is directly linked to the dipole density of the individual components comprising the whole structure.²² Hence, it is interesting to disentangle the individual role of each entity at the interface. We illustrate this decomposition by considering two cases (i) DMSO and (ii) Aniline –NO₂ on a CsBr terminated CsPbBr₃ surface. Fig. 5(a) and (b) present the polarization density profiles (P_b(z)) of one side of the symmetric slab computed for the pristine perovskite (CsBr slab), the distorted pristine (distortion in the outer layer of the slab due to Cs vacancies), the isolated molecule, and the whole structure. The addition of P_b(z) profiles of the distorted pristine (top panel) and the isolated molecule (middle panel) reproduce the P_b(z) profile of the whole structure (bottom panel). From these P_b(z) profiles, we notice that at the interface, the DMSO molecule counteracts the pristine perovskite (Fig. 5(a)), resulting in a net reduction of the surface dipole density, that subsequently lowers the work function, leading to the upwards shift of the valence level. On the contrary, aniline –NO₂ molecule (anilinium –NO₂ is shown in ESI, Fig. S20(a)†) allows to significantly increase the surface dipole density (Fig. 5(b)), with an opposite effect on the valence energy and work function.

Fig. 5 Additivity of surface dipoles densities illustrated with the plot of the polarization density profiles (P_b(z)) computed for (a) DMSO and (b) aniline –NO₂ ligands on a CsBr terminated CsPbBr₃ surface. A zoom view is shown as inset for isolated molecules. Additivity of electric susceptibilities illustrated with the plot of the position dependent high frequency dielectric profiles (ε_∞(z)) computed for (c) aniline –NO₂ ligand on a CsBr terminated CsPbBr₃ surface. Here, the –NH₂ group of aniline –NO₂ is pointing towards the surface.

Fig. 5(a) and (b) present the polarization density profiles (P_b(z)) of one side of the symmetric slab computed for the pristine perovskite (CsBr slab), the distorted pristine (distortion in the outer layer of the slab due to Cs vacancies), the isolated molecule, and the whole structure. The addition of P_b(z) profiles of the distorted pristine (top panel) and the isolated molecule (middle panel) reproduce the P_b(z) profile of the whole structure (bottom panel). From these P_b(z) profiles, we notice that at the interface, the DMSO molecule counteracts the pristine perovskite (Fig. 5(a)), resulting in a net reduction of the surface dipole density, that subsequently lowers the work function, leading to the upwards shift of the valence level. On the contrary, aniline –NO₂ molecule (anilinium –NO₂ is shown in ESI, Fig. S20(a)†) allows to significantly increase the surface dipole density (Fig. 5(b)), with an opposite effect on the valence energy and work function.

We may inspect also the different contributions to the dielectric constant profile. Notably, the interfacial contribution to the dielectric constant profile has already been investigated in the literature using state-of-the-art first-principles approaches.^64–66 We use the same method to also show the additivity of the contributions to the electric susceptibility at the surface functionalized by molecular ligands. For that purpose, we compute the position dependent high frequency dielectric profile along the stacking axis (z) for aniline –NO₂ and DMSO (see ESI, Fig. S20(b)†) attached on the perovskite surface. Generally, organic molecules have a smaller dielectric constant than the inorganic perovskites. Here, we notice that the bulk dielectric constant i.e. 4.70, in fair agreement with earlier work,⁴⁹ is nicely captured at the center of the pristine slab. The variation in from ε_r1 = 4.70 at the center of the dielectric constant profile (pristine distorted) to ε_r2 = 1.32 (at the position of the isolated molecule) illustrates the presence of dielectric confinement effects (see Fig. 5(c), bottom panel). The dielectric constant profiles of the whole structures (bottom panel) are reasonably well decomposed into their individual counterparts (top and middle panel), using the following equation:⁶⁷

ε^{whole structure}_∞(z) = ε^{pristine distorted}_∞(z) + ε^{isolated molecule}_∞(z) − 1 (10)

demonstrating the additivity of the electric susceptibilities. The position dependent high frequency dielectric profiles of the molecules investigated in the present work are given in ESI (Fig. S21†), with the values lying between 1–1.5.

Revisiting the classical capacitor model for molecular functionalization of halide perovskite surfaces

We end up by revisiting the conventional classical approach based on a capacitor model.^19,68,69 This approach has been widely used in the context of deposition of molecules on Au metal surfaces⁷⁰ or TiO₂ surfaces.^71,72 Within this model, the work function at the surface is modulated by −eΔV, so that Δϕ = −eΔV. The expression for Δϕ is computed from the Poisson's equation, given by:where N_s, μ, θ, ε_r and ε₀ are number of dipoles per unit area, dipole moment, tilt angle between dipole and surface normal (see Fig. S3(a)†), dielectric constant and permittivity of free space, respectively. Eqn (11) gives an attractive description of the effect of molecular dipoles on the device properties, including molecular orientation and surface coverage. However, this formula depends on the arbitrary choice of the dielectric permittivity, as already reported for the case of monolayers at water–air interface.⁶⁸ Two possible values of ε_r can be reasonably considered: (i) ε_r1 of perovskite material, and (ii) the effective dielectric constant ε_r2 at the position of the molecules (Fig. 5(c) and ESI, Fig. S20†). Combining DFT computed dipole moment values (μ) of the isolated free molecules from Table 1, with dipole moment orientations extracted from the optimized functionalized surfaces and Δϕ (Δϕ = −ΔE^abs_v) derived from the Hartree potential approach, we obtain the effective dielectric constants ε_r reported in Table 4. It appears that the dielectric constant at the position of the molecules is closest to the effective dielectric constant needed for an approximate capacitor model. Still, differences between ε_r2 and ε_r are sizeable. In addition, the dipole orientation also significantly deviates from the ideal situation where θ = 0. Therefore, our semi-classical approach allows recovering the trends already captured by a simple capacitor model but further provides atomistic information at the interface, with atomistic insight on the interplay between surface dipoles, surface relaxation and charge transfer that directly affects the work function.

Table 4 Effective dielectric constant (ε_r) computed using eqn (11). Δϕ is the change in work function (Δϕ = −ΔE^abs_v) computed using the Hartree potential approach. μ is the dipole moment value computed from DFT calculations (Table 1). θ is the tilt angle between the dipole and the surface normal. ε_r1 and ε_r2 are the dielectric constant of perovskite materials, and the effective dielectric constant at the position of the molecules (Fig. S21†), respectively

Molecules	Δϕ = −ΔE^absv	μ (D)	θ (°)	μ cos θ (D)		ε r1	ε r2
Pentylphosphonic acid (phosphonate)	−0.14	1.40	8.20	1.38	2.53	4.7	1.19
Pentanoic acid (oleate)	−0.24	1.59	20.69	1.49	1.59	4.7	1.15
DMSO	−0.35	3.79	52	2.33	1.71	4.7	1.12
Aniline	+0.40	1.70	171.96	−1.68	1.08	4.7	1.22
Aniline –OCH3	+0.23	1.61	174.49	−1.60	1.78	4.7	1.27
Aniline –NO2	+1.61	7.44	173.76	−7.39	1.18	4.7	1.32

---

Conclusions

In summary, we present a methodology that links the change in surface dipole density to the work function using the classical Maxwell's equation and the output from first-principles calculations. Using CsPbBr₃ slabs, we illustrate how surface functionalization via tuning the dipole and geometry of ligands effectively controls the work function, with information down to the atomic level. The valence level shifts can be rationalized based on the detailed knowledge of surface dipoles, surface dipole densities, charge transfer as well as local strain effects at the interface as a result of surface–ligand interaction. We observe a continuous decrease in the surface dipole densities correlated with upwards shift of the valence level for DMSO, oleate and phosphonate ligands. A similar behavior is observed for primary, secondary and quaternary alkylammonium ligands, with comparable small changes for all three. Influence of chemical engineering of the surface is further illustrated considering aniline/anilinium and their nitro and methoxy derivatives. Our approach predicts a downward shift of the valence levels that is not experimentally observed, highlighting the limitations of the considered defect and dopant-free surface models. Comparison of results obtained within the present framework with those predicted from the classical capacitor model exemplifies the rather arbitrary choice needed for the effective dielectric constant needed in the later. Overall, our computational strategy provides a useful approach to design and fine tune the energetics of surfaces and interfaces for optimized optoelectronic devices, well beyond the specific case of metal halide perovskites.

Computational details

DFT calculations are performed on basis set of finite-range of numerical atomic orbitals implemented in SIESTA code.^73,74 We use van der Waals density functional with C09 exchange⁷⁵ within the van derWaals DF2 flavor to describe the exchange–correlation term for optimizing the atomic positions of the structures. We use a modified version of the SIESTA software “master-post-4.1-251” to include DF2 flavor. This tuning has been suggested to improveC09 based geometry optimization over that with the original DF1 flavor.⁷⁶ The structures are fully relaxed using the fast inertial relaxation engine (FIRE) algorithm⁷⁷ until the structure satisfies the following relaxation criteria (i) the two consecutive ionic steps have an energy difference less than 10⁻⁴ eV, and (ii) the maximum forces acting on each atom are less than 0.02 eV Å⁻¹. The single point calculations are performed using the generalized gradient approximation⁷⁸ (GGA with PBE) functional including spin–orbit coupling⁷⁹ on top of vdwDF2-C09 optimized structures. To correct the band gaps, Slater half occupation technique,^80–82 known as DFT-½ i.e. PBE-½ is used (see ESI, section I.3†). We take a polarized double-zeta basis set with an energy shift of 50 meV for bulk CsPbBr₃. To describe accurately the properties of the surfaces, we include orbitals with weight in the vacuum region, known as diffuse orbitals:⁸³ diffuse orbitals (5s, 5p, 5d) for Br atom on the top of two atomic layers on both sides of the slab with 30% diffuse orbital size or cutoff radii. A real space mesh grid energy cutoff of 350 Ry is used for our calculations. For the high-frequency dielectric constant profiles calculations, an electric field of 0.025 eV Å⁻¹ is applied along the [001] direction. A detailed discussion for the computational details is given in ESI, section I.† Note that, to reduce the computational burden, we consider a converged five carbons chain length for oleate and phosphonate (see section IV of the ESI for details†).

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

Authors acknowledge funding from the European Union's Horizon 2020 program, through an Innovation Action under Grant Agreement No. 861985 (PeroCUBE) and through a FET Open research and innovation action under the Grant Agreement No. 899141 (PoLLoC). J. E. acknowledges the financial support from the Institut Universitaire de France. This work was granted access to the HPC resources of TGCC under the allocations 2021-A0110907682 and 2022-A0110907682 made by GENCI. Authors are grateful to Maksym Kovalenko and Andriy Stelmakh for useful discussions and providing the MD snapshots.

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Footnote

† Electronic supplementary information (ESI) available: Computational details; definition and convention; investigated ligands; convergence of carbon chain length for the molecules on a CsPbBr₃ surface; surface energies of CsBr and PbBr₂ terminated slabs; polarization density profile for phosphonate anion on a CsPbBr₃ surface; surface relaxation effect on valence levels; detailed results for oleate anion and DMSO molecule on a CsPbBr₃ surface; band structure of CsPbBr₃ slabs with phosphonate, oleate, DMSO, aniline, aniline –OCH₃ and aniline –NO₂ (two orientations) as well as anilinium and its derivatives; experimental valence energy positions of aniline, aniline –OCH₃ and aniline –NO₂-treated CsPbBr₃ reported in the literature for perovskite films; additional results on the additivity of surface dipole densities and electric susceptibilities; computed position dependent high frequency dielectric profiles and dielectric constants at the position of the molecules. See DOI: https://doi.org/10.1039/d3nr01126g

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