The hydrothermal synthesis method was used to fabricate CdS nanoparticles. An aqueous solution of 0.025 mol cadmium acetate, 0.075 mol thiourea, 0.005 mol sodium lauryl benzenesulfate, and 0.2 mol ammonia was sealed in a Teflon-lined stainless autoclave of 50 mL, kept at 120 ° C for 2 h, and then cooled to room temperature. The precipitates were separated by high-speed centrifuge at 10 000 rpm for 5 min, and rinsed by sequential centrifugation/redispersion from/in deionized water (DI water) 5 times to remove redundant impurity completely, and finally dried in the oven at 70 ° C for 12 h. X-ray diffraction (XRD, D/max-2500, Rigaku), high resolution transmission electron microscopy (HRTEM, JEM-2100, JEOL), and X-ray photoelectron spectroscopy (XPS, PHI-5300ESCA, PHI) were used to identify the phase, particle size and chemical state of CdS, respectively. In the ALD process, the ALD system (Type: f-100, WUXI MNT MICRO AND NANOTECH CO., LTD.) was used to deposit the TiO₂ and Al₂O₃. The Tetrakis(dimethylamino)titanium (TDMAT) and trimethylaluminum (TMA) were used as metal precursors to deposit TiO₂ and Al₂O₃, respectively. Water vapor was used as the oxidant precursor. The deposition temperature was kept at 150 ° C. Each ALD cycle consisted of a 50 ms pulse of TDMAT, followed by a 20 ms pulse of H₂O for TiO₂ deposition. For Al₂O₃ deposition, each ALD cycle consisted of a 20 ms pulse of TMA, followed by a 20 ms pulse of H₂O. A 25 s purge under a constant 20 sccm flow of research-grade N₂ (g) was performed between each precursor pulse.

The photocatalytic performance was examined by degradation of methylene blue (MB). Forty milligrams of CdS powders were dispersed in MB solution (100 mL, 10 mg/L) in a water-cooling beaker, and the photocatalytic reaction temperature was kept at 25 ° C. Then it was stirred for 30 min in the dark to reach adsorption-desorption equilibrium. A xenon lamp without filter was used as a simulation sunlight source to trigger the photocatalytic reaction, and the focused intensity was ~75 mW/cm², which was measured by an irradiance meter (Model: S302-C, Thorlabs). During photodegradation of MB solution, the magnetic stirring kept running. The photodegradation was quantified by monitoring the concentration of MB at its absorption maximum (664 nm). For the photodegradation experiment, the experimental time lasted 3.5 h for 1 photocatalytic round, and then the catalyst was recycled by centrifugation and cleaned by ultrasonication in DI water. The recycled catalyst was used in the 2nd photocatalytic test. Likewise, the same method was used for the 3rd and 4th rounds of photocatalytic measurements. The same amount in weight of commercially available Degussa P25 (nanoscale TiO₂ powder; 80% anatase, 20% rutile; particle diameter: 25-30 nm), as a reference, was used to compare with the photocatalytic performance of CdS.

The x-y and x-z distributions of normalized electric field amplitude for the CdS particles were obtained with the finite element method (FEM) ^[20]. The calculation was performed with the COMSOL Multiphysics software. The CdS particle with a radius of 25 nm was illuminated by a plane wave that propagated along horizontal z-direction and polarized along vertical x-direction with a wavelength of λ  = 500 nm. The electric field amplitude of the incident plane wave was normalized to be unitary. On one side of the particle, a circular cone with a cone angle of 120° , a height of 5 nm, and the cone axis along the x-direction were digged out to form the V-shaped defect. The refractive index of CdS under the illumination wavelength of 500 nm is 2.7 + 0.7i^[21]. The results exhibited an enhancement of electric field in the vicinity of the circular cone, and the field at the outside edge of the cone was stronger than that at the inside edge.

For a semiconductor heterojunction, band bending takes place when two semiconductor materials come to contact. The bending band, i.e., quantum well/barrier, in the depletion region determines the carrier transmission between two materials. In order to quantify the carrier tunneling at the interface, one needs to solve the Schrodinger equation with a reasonable quantum well/barrier potential term, which well describes the band bending. The potential shape is essentially controlled by the materials' dielectric constant and doping concentration^[22]. In this work, we proposed a simple, accurate, and fast algorithm for numerically solving the Schrodinger equation in quantum-well/barrier structures, based on the transfer matrix method (TMM).

The TMM technique divided any arbitrary potential into numerous discrete rectangle segments. For each segment, the potential V was uniquely determined, and subsequently wave function boundary condition was applied to obtain the carrier tunneling probability through the whole arbitrary potential. In such a way, the transportation probability of excited carriers could be quantified via the TMM technique ^[23].

Specifically, for a one-dimensional steady state in this work, Schrodinger equation is expressed as,

where E and V represent the eigenvalue and the potential term, respectively. m* is the effective mass. For any shape of potentials, the TMM technique divided V into N rectangle segments, each of which could be small enough to be treated as a fixed value.

For any segments, wave function was expressed as

Where , and A_j and B_j are the coefficients of the forward and the backward wave functions, respectively.

The boundary conditions for the wave functions and the first-order of wave function derivatives between two segments were written as^[24]:

Here, m_j^* is the effective mass of the corresponding segment.

Applying the boundary conditions to Eq. (2), we obtained the coefficient relationship between any two adjunct segments:

where M_j is a 2 ×  2 matrix. With Eq. (5), we found a relation between the A and B coefficients of the outermost layers:

equation(6)

where

where   , N is the position of segment N.

Inserting M_N into Eq. (6), we simplified it as Eq. (8):

Here, B_N+1 is zero since there is no reflect wave after transferring through the potential barrier/well. Finally, the transmission coefficient T (E) was obtained as follows:

With this expression, carrier transmission probability could be determined for any shape of potentials.

The pure cubic phase of the as-prepared CdS nanoparticles was identified by XRD as shown in Fig. 1(a). TEM image exhibits the particle sizes varying from 10 to 20 nm in Fig. 1(b). The HRTEM (Fig. 1(c)) that shows the major facet of cubic CdS nanocrystal is the (111) plane with d₍₁₁₁₎ spacing of 0.33 nm owing to its low surface energy^[25].

Fig 1.

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	Fig 1. (a) XRD patterns, (b) TEM and (c) HRTEM images of as-prepared CdS nanoparticles

To examine the photocatalytic performance, CdS (40 mg) was dispersed in MB solution. In Fig. 2(a), the self-degradation of MB under irradiation was very small and can be negligible. After introducing CdS into the MB solution, high degradation efficiency of MB was observed and more than 70% MB was degraded in 60 min. The high efficiency is related to CdS's superiority of its light adsorption in the visible light range and band alignment with water redox potentials. However, after 60 min, no further catalytic activity was observed, resulting from the loss of active sites. Subsequently, the catalyst was recycled and cleaned in DI water by ultrasound, and no more obvious MB decomposition was found, and thus we concluded that the photo-corrosion indeed caused the photocatalytic failure.

Fig 2.

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	Fig 2. (a) Photodegradation of MB by CdS nanoparticles without ALD passivation; (b) S 2p and (c) Cd 3d of CdS before and after photocatalytic reactions.

To access the failure mechanism of the catalyst, XPS measurements were carried out to study the surface chemistry before and after photocatalytic reactions. An SO_x broad peak around 169 eV was identified as the S 2p core level spectra after 1 hour photocatalytic reaction, which suggests the S^2- being oxidized into SO_x ( Fig. 2(b)). Meanwhile, no detectable changes of Cd 3d core level spectra were observed before and after the photocatalytic reactions ( Fig. 2(c)), arising from the overlapping of Cd peaks between CdS and CdSO₄^[26]. Fundamentally, CdS is a natural n-type semiconductor, in aqueous environments, and valence band up-bending occurs due to the majority carriers' out-diffusion when interfacing with water^[27]. Consequently, the photo-excited holes from valence band maximum, mainly composing of S 2p orbitals ^[28], tend to transfer to the nanoparticles surface, then directly react with MB and essentially lead to the decomposition of MB pollutants. However, when soluble CdSO_x formed during the photocatalysis process, the active element S lost and the photocatalytic activity decreased. This finding is consistent with previous work on photo-corrosion ^[29]. Nevertheless, to date, there is no report to discuss about the active sites of CdS.

Without considering shape variation of the as-prepared spherical nanoparticle, the excited holes (electrons) move outward (inward), respectively, due to the band bending^[30]. In practice, the shape variation is inevitable to influence the excited charge distribution and consequently impact the active areas. In order to locate these active sites, XRD and TEM were combined to characterize the surface modification on CdS nanoparticles after photocatalysis. The CdSO₄ (200) peak emerges in XRD pattern (Fig. 3(a)) after the photocatalytic reactions since the S^2- anion is oxidized into SO₄^2- by the strong oxidizing excited holes. Surprisingly, only in the V-shaped areas of either one nanoparticle or overlapping of two particles CdSO₄ (d₂₀₀  = 0.27 nm) phase was found on surface in HRTEM images (Fig. 3(b) and (c)). On the other regions of the CdS nanoparticles, CdSO₄ was not observed. Therefore, we speculated that the active sites were located in the V-shaped areas. Similar catalytic phenomenon dependence on the V-shaped regions has been observed in NaTaO₃ catalyst^[31].

Fig 3.

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	Fig 3. (a) XRD patterns of CdS before and after photocatalytic reactions; (b) and (c) HRTEM images of the V-shaped regions of the CdS surface after photocatalytic reactions

To identify the photocatalytic active sites, we calculated the electric field distribution of CdS nanoparticle whose shape and size are analogous to those in TEM images of Fig. 1(b) and HRTEM images in Fig. 3(b) and (c). It is well known that for a spherical shape of nano-particle, the electric field of outmost shell is distributed evenly. Here, we explored the charge distribution of a sphere with V-shaped defect. According to the electromagnetic field simulation (Fig. 4), the corners of CdS display strong electromagnetic (EM) field intensity, whereas in the V-shaped areas much lower EM intensity is distributed. The majority carriers of CdS, i.e electrons, gather at the corners due to the strong build-in internal electric field between the semiconductor and solution. On the contrary, the excited holes prefer to transfer into the V-shaped regions where we find the low EM field intensity resulting from the low electron concentration and recombination rate. Under this condition, photodegradation occurs in the active V-shaped areas. This finding helps to explain why photo-corrosion takes place in the V-shaped regions (Fig. 4, W/O ALD).

Fig 4.

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	Fig 4. Distributions of normalized electric field amplitude for the CdS particle with a V-shaped defect under illumination by a plane wave and schematics of charge transfer without (W/O) and with (W/) ALD process

In order to suppress the photo-corrosion and maintain high photocatalytic efficiency, ultrathin coating passivation was performed by ALD (Fig. 4 W/ALD). Prior to ALD, we theoretically designed the ALD oxides with various thicknesses to deposit on CdS to protect the catalytic active sites. To examine how different protective layers impact the photocatalytic performance, we proposed the band alignment between CdS and TiO₂ (Al₂O₃) based on the work functions. Subsequently, we developed a code with transfer matrix method (TMM) in quantum mechanics to calculate the excited carriers' tunneling probability between two semiconductors. The tunneling probability is proportional to exp (× a) (“ U” is the barrier height, “ E” is the excited carriers energy, “ a” is the barrier width); therefore, material properties and protective layer thickness are two crucial factors to govern the tunneling probability.

To simplify the problems, we considered the step potentials rather than quadratic ones between CdS (m_e*  = 0.21 m₀, m_h*  = 0.80 m₀, m₀ is free electron mass)^[32] and oxides (TiO₂ (m_e*  = 0.0948 m₀, m_h*  = 0.1995 m₀)^[33], Al₂O₃ (m_e*  = 0.20 m₀, m_h*  = 0.25 m₀)^[34]). As shown in Fig. 5(a), band alignment between CdS and TiO₂ displays that CBM is higher than its TiO₂ counterpart, and visible light excited electrons readily transfer to TiO₂ side, whereas the holes need to overcome an energy barrier to out-diffuse. The valence band offset (VBO) between these two materials is around 1.0 eV (Fig. 5(a)), which was simplified as a square-shaped barrier. As we discussed above, the height of the barrier is determined by material property and the width could be a variable during the ALD growth process. In this work, we varied the oxide thickness from 0.1 nm to 2 nm to check how the oxide layer influences the tunneling probability. In Fig. 5(c), we found that tunneling could easily occur with the thickness less than 0.5 nm. With the increase in thickness, the tunneling probability decreases exponentially. With 2 nm thickness, the energy of 0.9 eV plus CdS band gap (2.4 eV) is needed to excite the hole carrier. Equivalently, visible light could not enable the hole diffusion. In the case of Al₂O₃/CdS, CB and VB offsets are around 3.0 eV and 3.4 eV, respectively (Fig. 5(b)). Likewise, we calculated the square-shaped barriers for these two offsets. Based on the calculations in Fig. 5(d) and (e), only thickness less than 0.2 nm could be favorable for carrier to diffuse due to the large offset. Compared to these two protective layers, the hole tunneling probability of TiO₂ is higher than Al₂O₃ due to the low VBO potential barrier in TiO₂/CdS heterostructure. In practice, band bending would occur, and the bending will slightly increase the hole tunneling probability.

Fig 5.

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	Fig 5. (a) and (b) Band alignment of CdS/TiO2 and CdS/Al2O3, respectively; (c) tunneling transmission probability of hole for CdS/TiO2; (d) and (e) tunneling transmission probability of electron and hole, respectively, for CdS/Al2O3.

Guided by the theoretical insight from TMM, the thinner protective layer provides a higher tunneling probability, and the thickness of protective layer should be less than 0.5 nm to maintain the high photocatalytic efficiency. Therefore, one cycle of ALD on these CdS nanoparticles was adopted to passivate the active regions^[35]. ALD, a self-limiting deposition technique for producing thin films, has been regarded as one promising way to precisely control film thickness and conformal grow of complex nanostructures^[18]. However, initial growth mechanism is quite complex associated with activity sites on the sample surfaces. For example, it is difficult to incubate on MoS₂ surface, but it can conformably grow uniform film after ozone pretreatment because of the surface oxygen absorbed^[36]. Therefore, the surface active sites in the V-shaped regions of CdS nanoparticles should also provide the initial sites for incubation of ALD.

Fig. 6(a) and (b) show the HRTEM images after one cycle of ALD TiO₂ and Al₂O_3, respectively. No significant grain size increase of CdS nanoparticles (10-20 nm) was observed after the ALD growth at low temperature (150 ° C)^[37]. Upon one cycle of ALD, the TiO₂ or Al₂O₃ crystalline phase could not be found in most areas from TEM results, and Ti or Al signal is below the XPS detection limit (see details in Fig. S1), attributing to less concentration of ALD oxides because of the inert cubic CdS (111) surface (d₁₁₁  = 0.33 nm), which is consistent with theoretical calculations^[24] and the lack of oxide signal from the XPS core level spectra of S 2p and Cd 3d for the as-prepared samples. But in some active areas with under-coordinated bonds, ALD layer could be formed. From Fig. 6, TiO₂ (d₁₀₁  = 0.24 nm) or Al₂O₃ (d₀₂₄  = 0.18 nm) phase was identified in the V-shaped regions of CdS nanoparticles. These crystalline phase formation could be because of the trap of precursors in the V-shaped regions and subsequently experiencing high energy beam during the TEM measurement in the specific regions. It is worth to note that only five samples out of fifty with V-shaped regions were found to have the detectable TiO₂ or Al₂O₃ phases. In other words, on most reactive V-shaped regions, crystalline phase was not observed, resulting from the self-limiting nature of ALD. This observation is consistent with the fact that Ti and Al core level signals are below the XPS detection limit after one cycle of ALD. Therefore, we assumed that the active V-shaped regions were covered with the ALD layer but only a small portion was detectable. The ultrathin ALD oxides could help to protect the active areas and thus elongate the lifetime of CdS catalyst.

Fig 6.

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	Fig 6. HRTEM images of (a) CdS/1 cycle of ALD TiO2 and (b) CdS/1 ALD cycle Al2O3

Forty milligrams of passivated samples (CdS/one ALD cycle TiO₂ or CdS/one ALD cycle Al₂O₃) were dispersed in MB solution to examine the photocatalytic performance and the catalyst lifetime.

As shown in Fig. 7(a), CdS with one ALD cycle TiO₂ shows great catalytic performance to decompose MB under illumination. As time went by from 0 min to 210 min, MB degradation was up to 90% gradually, which displayed a superior performance than the same amount of the commercially available P25. Most importantly, the catalyst lifetime was significantly improved compared with the as-prepared CdS. Furthermore, we tested three more rounds of MB degradations with 210 min per round (see Fig. 7(a)). We observed that overall degradation rate slightly reduced from round one to round four. We speculated that this performance reduction could have partly resulted from catalyst loss when recycling catalyst (left ~5 mg after 4 cycles). During the 4th round test, 50% MB pollutant can be degraded in 210 min. Interestingly, no new product was observed above the XPS detection limit after 4 rounds (14 h) of tests. In any case, the catalyst still remained active after 14 hours. In other words, the catalyst lifetime was elongated up to at least 14 times longer than that of the as-prepared CdS. One ALD cycle Al₂O₃ on CdS was also used to check catalytic performance variation in contrast to TiO₂ deposition. For the CdS/one ALD cycle Al₂O₃ sample, MB degradation was up to 65% gradually after the 1st round (Fig. 7(c)), and it showed lower efficiency compared to CdS/one ALD cycle of TiO₂ sample. This result agrees well with the TMM prediction. After the 4th round test, the catalyst still remained active for the MB degradation and new product also was not observed in XPS spectrum (Fig. 7(d)), similar to the result of CdS/one ALD cycle of TiO₂ sample. In addition, to further verify the TMM calculated results, the sample of CdS with two ALD cycles TiO₂ was also used to test the photocatalytic activity and showed the lower efficiency than CdS with one ALD cycle TiO₂ (see details in Fig. S2) due to the decrease of carrier tunneling probability when the thickness increases. Qualitatively, we believe that the TMM calculated results can provide the rational guidance to a reasonable design of protective layer for ALD passivating photo-catalyst to suppress photo-corrosion.

Fig 7.

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	Fig 7. (a) CdS/1 ALD cycle TiO2 and P25 for cyclic photo degradation MB; (b) S 2p of CdS/1cycle ALD TiO2 before and after photo catalytic reactions; (c) CdS/1ALD cycle Al2O3 for cyclic photo degradation MB; (d) S 2p of CdS/1cycle ALD Al2O3 before and after photocatalytic reactions.

In the ALD process, the V-shaped regions were partially covered with ultrathin TiO₂ or Al₂O₃, and consequently the active sites were protected. As the protective layer was conformal to V-shaped activity sites and thin enough (< ~0.5 nm), the excited holes could be tunneling through the passivation layer and react with organic pollutants (Fig. 4 W/ALD); thus, the photocatalytic efficiency was maintained. The excited electrons tend to move in the opposite directions, whereas the accumulated electrons also tend to move out by diffusion. In any case, the excited electrons do not play a role to decompose MB^[38]. To evaluate the catalytic role of carriers (electron/hole), we utilized alcohol to exhaust the supply of excited holes, and we found that MB degradation with alcohol is the same as that of the self-degradation under UV-vis light (see details in Fig. S3). This experiment confirms that the hole is the active carrier.