Fabrication and surface stochastic analysis of enhanced photoelectrochemical activity of a tuneable MoS 2 – CdS thin ﬁ lm heterojunction †

A very simple and well-controlled procedure was employed to prepare CdS nanoparticle/few-layer MoS 2 nanosheet/Indium tin oxide (ITO) thin ﬁ lm heterostructures. To tune and fabricate the CdS/MoS 2 ( t )/ITO thin ﬁ lms with various surface topographies, ﬁ rst electrophoretic deposition (EPD) was used to deposit MoS 2 nanosheets on the ITO substrate under an optimized applied potential di ﬀ erence (8 V) for di ﬀ erent deposition times ( t ) of 30, 60, 120 and 240 s. Then, CdS nanoparticles were deposited via a successive ion layer adsorption and reaction (SILAR) technique. The highest photo-current density of 285 m A cm (cid:1) 2 was measured for the CdS/MoS 2 (60 s)/ITO sample, which was about 2.3 times higher than the value obtained for bare CdS/ITO. The photo-enhancement mechanism of the CdS/MoS 2 ( t )/ITO heterostructures was described using a stochastic model. The results show that the CdS/MoS 2 (60 s)/ITO electrode exhibits the highest roughness exponent (2 a ¼ 0.67) with the smoothest nanometric ﬂ uctuations, resulting in the best wetting properties, and thus, the highest interaction between the electrolyte and the sample surface, leading to the highest PEC activity. On the other hand, the samples with small a possess rough and nanometric-jagged ﬂ uctuations. The air trapping inside these microscopic surface ﬂ uctuations reduces the wettability as well as surface interaction between the sample and the electrolyte, resulting in low photo-current density. data analysis, contact angle measurements and electrochemical impedance spectroscopy measurements, it was shown that the samples with the higher roughness exponents have a smoother surface in nanometric scale resulting in a better wettability (lower contact angle) and higher photo-current density. On the other hand, the layers formed with small a values, have very rough and nanometric-jagged  uctuations which cause air trapping and reduce the wettability of the surface leading to the photo-current density reduction. Our stochastic investigation results provide very useful information to manipulate the surface topographic properties which in  uence the PEC performance of various photo-active thin  lms.


Introduction
In recent years, accompanying the fascinating properties of graphene and its booming development, rapidly growing research interest and scientic attention has been focused on the other ultrathin 2D crystals. In particular, there is at present an increasing interest in transition metal dichalcogenides (TMDs) due to their potential for a wide range of applications. [1][2][3] TMDs have the general formula of X-M-X (M is a transition metal such as Mo, W, Ti, V, and X is a chalcogen such as S and Se), in which two hexagonally-arranged X planes are separated by the same hexagonal metal plane. Inside each X-M-X layer, the atoms are bonded together covalently and adjacent layers stack over each other via weak van der Waals force. 4 This weak interlayer force allows to easily exfoliating the bulk TMDs into atomically thick 2D nanosheets. These 2D crystals can improve the intrinsic properties of their bulk form and introduce a completely new and fascinating range of properties.
It has been reported that MoS 2 low dimensional nanostructures exhibit photo-responsivity due to their suitable band gap for solar spectrum absorption (MoS 2 mono-layer is a direct band gap semiconductor with energy band gap of E g $1.9 eV (ref. 15)) and photocatalytic stability against photocorrosion. 16,17 many studies have reported the photocatalytic activity of MoS 2 nanostructures toward water pollutant degradation, 18,19 photocatalytic hydrogen production 20,21 and photoelectrochemical activity, 17 indicating promising potentials of MoS 2 2Dnanosheets for solar energy harvesting and conversion.
Among various photo-active materials, CdS has been the subject of many interests because of its low cost and simple preparation methods for various applications. 19,22 More importantly, CdS has a narrow direct band gap with E g ¼ 2.4 eV, 23 making it a well-known photo-active material under visible light. However, bare CdS suffers from low photocatalytic activity and low stability under sunlight irradiation. To overcome these drawbacks, noble metal co-catalysts such as Pt, Pd, and Au are oen used to improve its catalytic activity and stability. 24,25 But, using noble metal co-catalyst is limited due to their high cost and scarcity. So, it is very interesting to nd a low cost but effective alternative co-catalyst to improve CdS visible photoactivity and its stability against photocorrosion.
Recently, MoS 2 nanostructures have been shown as a promising low cost co-catalyst to enhance CdS photocatalytic activity toward hydrogen production. [25][26][27][28] Zong et al. have experimentally conrmed that photocatalytic activity of MoS 2 -loaded CdS is even higher than that of Pt/CdS under the same reaction conditions. 25,29 Chen et al. have also obtained H 2 evolution rate up to 1315 mmol h À1 using the MoS 2 /CdS photocatalyst which was much higher than 488 mmol h À1 reported for Pt/CdS photocatalyst. 26 Although many fascinating photocatalytic results have been reported for MoS 2 -CdS hetero-structure, but, low-cost, easy and safe preparation method to obtain MoS 2 -CdS thin lms and their photoelectrochemical (PEC) performance has been rarely investigated, and the PEC property of the MoS 2 -CdS thin lm is still in its infancy. Specially, to the best of our knowledge, the effect of MoS 2 -CdS thin lm topography on its PEC performance has not been reported, yet.
We have demonstrated in our recent reports that investigation of surface topography from a stochastic point of view, provides very useful information to understand various properties of prepared thin lms such as eld emission property 30 and photoelectrochemical performance. 31,32 Herein, for the rst time, we have carefully explored the correlation between stochastic topographic properties and PEC performance of CdS/MoS 2 /ITO thin lms. To do that, we have employed a facile, well-controlled, completely safe and straight forward procedure to prepare CdS/MoS 2 thin lms on indium tin oxide (ITO) substrate with tuneable surface topographies. At the end, a mechanism was suggested based on the surface stochastic analysis and the contact angle (CA) measurements. The proposed model can provide a guidance to prepare the CdS/MoS 2 /ITO thin lm with specic surface topography and proper wettability leading to the highest PEC performance toward hydrogen production under sunlight irradiation.

Materials
Deionized water puried with Milli-Q System (Millipore, Billerica, MA, USA) was used during all preparation procedures. All other materials were commercially provided and used without any further purication. These are including: absolute ethanol (Rionlon Chemical Reagent Inc., China), indium tin oxide (ITO) sheets (

Few-layer MoS 2 solution preparation
Based on our previous report, 33 mixed-solvent strategy was used to prepare few-layer MoS 2 solution. In brief, 250 mg of bulk MoS 2 was dispersed into 50 mL mixed water : ethanol solution with the volume fraction of water/ethanol ¼ 55/45. Aer 30 min stirring, the solution was sonicated for 15 h in a common bath sonicator. The sonicated solution was maintained in room condition for 48 h. Then the 2/3 of the supernatant of the solution was collected and centrifuged at 3800 rpm for 45 min.

Thin lm preparation
Electrophoretic deposition method was employed to deposit MoS 2 nanosheets. Two pre-cleaned ITO sheets were placed in parallel manner with distance of 15 mm inside the few-layer MoS 2 solution. The optimized electrical potential of 8 V was applied between these two ITO electrodes for different deposition times (t) namely 30, 60, 120, and 240 s. Aer preparation of MoS 2 (t)/ITO thin lms, the CdS nanoparticles were deposited on the layers via successive ion layer adsorption and reaction (SILAR) method. The layers were immersed into 50 mM Cd(NO 3 ) 2 and then in 50 mM Na 2 S aqueous solutions for 20 s. These two immersion steps were named as a SILAR cycle. The samples were rinsed with DI water between each immersion step. 20 SILAR cycles were repeated to obtain CdS/MoS 2 (t)/ITO thin lms.

Photoelectrochemical measurements
The PEC results were obtained by using a three-electrode setup connected to a CHI 660D electrochemical workstation (Shanghai Chenhua Instrument Co., China). In this setup, the synthesized CdS/MoS 2 (t)/ITO thin lms were used as working electrode, a saturated calomel electrode (SCE) as the reference electrode and a platinum wire as the counter electrode. All the electrodes were put into 50 mM Na 2 S aqueous solution as electrolyte and 0.1 V bias voltage was applied during all PEC tests. The same electrolyte was also used to carry out the electrochemical impedance spectroscopy (EIS) measurements with the AC voltage amplitude of 5 mV and the voltage frequency ranging from 100 kHz to 1 Hz. The EIS data were obtained under 3 W Xe lamp irradiation.

Material characterization
Atomic force microscopy AFM (Agilent SPM 5500, USA) in tapping-mode was used to identify the MoS 2 nanosheets lateral size and thickness and the results were analysed by "WSxM 5.0 Develop 7.0" soware. 34 Surface topographies of the layers were investigated under the same conditions reported in our previous works. 30,31,35 PGENERAL T6 spectrophotometer was utilized to obtain the UV-visible absorption spectra of the samples. To study nanostructure morphology and chemical composition of the prepared thin lms, Tecnai-G2-F30 (USA) high resolution transmission electron microscope (HRTEM) was employed. Raman microscopy (Invia Renishaw, UK, exciting laser wavelength of 514.5 nm) was also used to identify the composition of the samples. Si Raman peak at 520 cm À1 was the reference for Raman spectra calibration.

Surface stochastic analysis
Surface stochastic analysis was used for better understanding of the surface topography effects on PEC activities of the samples. Most common concepts for stochastic study of a surface (two dimensional substrate of size L Â L) are the mean height of growing lm h, its surface roughness W and roughness exponent a dened by the following expressions: 36 where t andx are the deposition time and lateral coordinate, respectively. The averaging over different realizations of the sample position is represented by notation of h.i. Surface structure function, S(r), is used to measure the roughness exponent of a surface. This function depends on the length scale of Dx ¼r and is dened as: 35 Height-height correlation function for a stationary surface, C(r), is related to the surface structure function as follows: C(r) is dened by the correlation length h and the roughness exponent a (Hurst exponent) as is shown below: 35 Replacing eqn (5) into (4) and expand it for small r, the second order structure function S(r) scales with r as following: 35 The roughness exponent a normally ranges between 0 and 1 (0 < a < 1), and it is dened within the context of a microscopic limit (L / 0). According to eqn (5), for times much larger than saturation time, smaller roughness exponent corresponds to a very rough and jagged surface (high microscopic uctuation). On the other hand, a surface with the larger roughness exponent possesses a smoother texture. 30,37 More information and detailed discussions about these parameters can be found elsewhere. 36 These concepts will be used to correlate the variation of surface roughness and topography of the deposited thin lms and generated photo-current densities from the CdS/ MoS 2 (t)/ITO thin lms during PEC process.  15 C and D excitonic peaks located at 450 and 400 nm are related to interband transitions from the occupied dz 2 orbital to unoccupied dxy, x 2 À y 2 and dxz, yz orbitals. 17 It is clear that absorption of MoS 2 nanosheets increases from 800 to 400 nm (visible solar region) and decrease in UV region (400 to 200 nm), which indicates that MoS 2 akes are very good candidates for photovoltaic and photocatalytic application in visible region of solar spectrum. In the photovoltaic related studies, sun light transmission is also an important parameter which determines the output photocurrent density of the materials. Therefore the corresponding UV-visible transmittance of the obtained MoS 2 solution has been depicted in Fig. S1 of ESI. † The absorption spectrum and light-brownish colour of the exfoliated solution ( Fig. 1 inset) are in good agreement with standard UV-visible absorption spectrum for 2H-MoS 2 semiconducting phase, 17,38 indicating that no crystal change occurred during our proposed preparation procedure.

Exfoliated MoS 2 nanosheets
AFM analysis was also employed to explore the dimensions of the nal MoS 2 akes. A 2D-AFM image has been shown in Fig. 2a and height proles of some selected akes have been also plotted. As it can be seen, there is a distribution of akes sizes between about 30 and 150 nm. The thicknesses of akes have also a distribution between about 1 and 15 nm. It is well known that the akes with the same size and thickness cannot  be obtained by sonication-exfoliation methods and the nal products have a distribution in thickness and size. [39][40][41] Herein, the MoS 2 nanosheets obtained via mixed-solvent strategy (a type of sonication-exfoliation methods) show the same behaviour too. The average thickness and lateral dimension of the akes were measured to be $5 and $60 nm, respectively.
It was reported that a monolayer MoS 2 prepared via chemical exfoliation methods is about 0.8-1.2 nm thick. 15,42 Based on these ndings, it is estimated that the prepared MoS 2 akes contain 6 layers in average. It is worth to note that there are also many single-layer nanosheets in the nal solution. The population of these single-layer akes can be increased via higher speed centrifugation and appropriate ltrations.
The dimensions of the akes were also investigated through direct observation via TEM analysis. The TEM image (Fig. 2b) clearly shows the MoS 2 nanosheets with an average of 60 nm in lateral size, conrming our AFM results. These results indicate that our utilized method can be manipulated to obtain both few-layer and single-layer MoS 2 nanosheets.

CdS/MoS 2 (t)/ITO thin lms
Aer deposition of MoS 2 akes on the ITO substrate by EPD technique at various deposition times followed by CdS loading via SILAR method, the obtained CdS/MoS 2 (t)/ITO layers were analysed by UV-visible transmission spectroscopy. Fig. 3 shows the UV-visible transmittance spectra of the thin lms. As it can be seen, all of the CdS/MoS 2 (t)/ITO thin lms have lower transmittance than the bare CdS/ITO as it was expected. The CdS/ITO thin lm has an absorption edge at $500 nm. The bulk CdS thin lm exhibits an absorption edge at 520 nm. 43 Thus, the observed blue-shi indicates that the obtained CdS/ITO thin lm contains CdS nanostructures with the average dimension of $10 nm. 43,44 A second absorption edge appears at $680 nm in the CdS/MoS 2 (t)/ITO thin lm which it is absent in the bare CdS/ITO layer. This absorption edge is related to peak A as excitonic transition in 2H-MoS 2 layer, as discussed before (see Section 3.1 and Fig. 1). Inspecting the Fig. 3 indicates that the addition of MoS 2 few-layer nanosheets to the CdS/ITO thin lm, increases the light intensity absorption and also extends the absorption edge from 500 nm to $700 nm, which are in favour of CdS thin lm photo-activity enhancement under visible light. Similar observations have been also reported elsewhere for CdS-MoS 2 (ref. 45) and CdS-WS 2 heterostructures. 46 Raman spectroscopy was employed to determine the crystal phase composition of the nal obtained thin lms. Fig. 4a shows the Raman spectrum of the CdS/MoS 2 (60 s)/ITO thin lm. Two obvious Raman peaks at 300 and 600 cm À1 are related to two characteristic CdS longitudinal optical (LO) phonon modes named 1LO and 2LO, respectively. 47,48 The 1LO phonon peak for a single crystal of bulk CdS has been reported at peak position of 305 cm À1 , while it has been observed at $300 cm À1 for CdS nanostructures. 49,50 The observed red shi of the 1LO Raman peak in the CdS/ MoS 2 (t)/ITO thin lms compared with the bulk CdS is due to the phonon connement effect 49 and this observation is consistent with other reports for 1LO peak in CdS nanoparticles (d $ 4-10 nm). 47,51 It is well known that there are four active rst-order Raman modes observed in bulk 2H-MoS 2 Raman spectra, namely, E 1g (286 cm À1 ), E 1 2g (383 cm À1 ), A 1g (407.5 cm À1 ), and E 1 2g (32 cm À1 ). 52,53 The E 1g mode is forbidden in the back scattering conguration. The E 2 2g mode cannot be accessible for conventional Raman apparatuses due to the constraint of Rayleigh line rejection lter (>100 cm À1 ). 54 Thus, the MoS 2 Raman spectrum is dominated by E 1 2g and A 1g modes. These two peaks are clearly observable at 383.5 and 407.2 cm À1 , indicating the presence of 2H-MoS 2 few layers in the nal thin lms.
Li et al. have reported that Raman frequencies of E 1 2g and A 1g peaks vary monotonically with the layer number of ultrathin MoS 2 akes and can be used as reliable features to identify the  MoS 2 layer number. 54 Using A 1g peak position, the following exponential tting model can be used to estimate the average number of layers: where N is the number of layers, c the tting parameter and u bulk ¼ 407.5 cm À1 , u 1L ¼ 403 cm À1 and u A 1g are bulk, monolayer and measured A 1g peak position of MoS 2 , respectively. Aer tting the model to the data reported for various MoS 2 thicknesses, 53-55 c ¼ 0.508 was obtained. Inserting this parameter into the exponential tting model, the average number of layers for u A 1g (N) ¼ 407.2 cm À1 was estimated to be $6 layers. The obtained thickness of MoS 2 nanosheets is in agreement with the AFM observations. Raman mapping is a powerful technique to characterize the uniformity of the 2D materials and it helps to understand the large scale quality and uniformity of the nal products surfaces.  Fig. S2 † that the ITO electrode surface has been completely covered with deposited materials (MoS 2 and CdS) with nearly the same thickness in large scale. As it was mentioned before (Fig. 2a related discussions), the sonication-exfoliation methods cannot provide 2D materials with exactly the same thicknesses and sizes. 2D akes obtained by these methods have a distribution in both thickness and lateral dimension. 39,40,56 Thus, it was expectable that the obtained Raman mapping images for our synthesized samples do not have the same colour in different sample area. The AFM results also conrm that the akes do not have the same size and thickness (Fig. 2a).
In addition of Raman mapping, SEM analysis was also used to monitor surface morphology changes and to conrm if the MoS 2 and CdS can completely cover whole ITO surface with acceptable uniform deposition thickness. The obtained SEM images of bare ITO, MoS 2 /ITO, CdS/ITO and CdS/MoS 2 (60 s)/ ITO electrodes have been shown as Fig. S3 (ESI †). The obtained SEM images conrm that the materials have been deposited uniformly on ITO surface for all of the electrodes, which is in consistent with Raman mapping results.
TEM analysis was used to clearly verify the formation of atomic-heterojunction between the CdS nanoparticles and MoS 2 nanosheets. The CdS/MoS 2 (60 s)/ITO electrode was razed carefully with a keen knife and sonicated in DI water for 30 min. The resulted suspension was dropped on carbon-coated Cu grid and subjected to TEM analysis. The results have been shown in Fig. 4b and c. Fig. 4b shows that the CdS nanoparticles with an average diameter of $10 nm have been deposited on the MoS 2 sheets, conrming Raman and UV-visible absorption results.
The measured sizes of the deposited CdS nanoparticles are also in good agreement with our previous reports on CdS nanoparticles obtained via SILAR methods. 43,44 The hexagonal arrangement of atoms in MoS 2 nanosheets as well as the CdS (112) planes can be clearly observed in Fig. 4c. Therefore, Raman and TEM results strongly conrm that we have successfully fabricated CdS-MoS 2 atomic hetero-junction, using our simple combined procedure without any crystal changes and any oxidation.
To evaluate and compare photoelectrochemical activity of the different CdS/MoS 2 (t)/ITO thin lm heterostructures, the photo-current densities (J) generated by the samples under similar photo-irradiation condition (500 W Xe lamp light with intensity of 55 mW cm À2 ) were measured. The results have been presented in Fig. 5 and Table 1. Fig. 5 shows the measured J as a function of irradiation time (J-t curve). It was found that all the CdS/MoS 2 (t)/ITO thin lms except CdS/MoS 2 (240 s)/ITO have higher photo-current densities as compared with the bare CdS/ITO layer (125 mA cm À2 ). The sample prepared with 30 s of MoS 2 deposition shows a higher J value (197 mA cm À2 ) as compared to the bare CdS/ITO. Further increasing MoS 2 deposition time to 60 s, results in increase of J up to 285 mA cm À2 . This is about 2.3 times greater than the value for the bare CdS/ITO thin lm.
The results show that charge separation and transfer condition is improved when CdS makes an appropriate junction with MoS 2 nanosheets. It can be understood more clearly by measuring and comparing the rise times and fall times of the as-prepared CdS/MoS 2 (60 s)/ITO structure and traditional CdS/ ITO layers. The rise time is dened as the time that the photocurrent reaches to 90% of its stable value from dark current value upon light irradiation and the fall time is known as the time needed for the current value to drop to 10% aer the light was turned off. 57 Accordingly, the rise and fall times of the CdS/MoS 2 (60 s)/ITO and the CdS/ITO was measured and the results have been shown and compared in Fig. S4. † Rise times were determined to be 180 AE 10 and 210 AE 10 ms and the fall times were obtained to be 300 AE 10 and 380 AE 10 ms for the CdS/MoS 2 (60 s)/ITO and the CdS/ITO, respectively. The shorter rise and fall times for the CdS-MoS 2 sample show that the photo-sensitivity of CdS layer has been improved when a junction is made with MoS 2 nanosheets, which is very bene-cial for many applications such as photo-detectors and sensors. [58][59][60] Fig . 5 The measured photo-current density versus irradiation time of the various CdS/MoS 2 (t)/ITO thin films prepared with different EPD time.

Photo-enhancement mechanism
There are some reports discussing on the photo-activity of the CdS-MoS 2 heterojunction, and some reasons have been explained for photo-activity enhancement of CdS aer junction forming with MoS 2 . 25,27,61 Herein, for the rst time, we have investigated the PEC performance of the CdS/MoS 2 (t)/ITO thin lms from surface stochastical and topographical point of view, accompanying with other important factors concerning. One of the most important factors inuencing the photo-current density of a layer is its charge transfer resistance (R ct ). This parameter was evaluated by using electrochemical impedance spectroscopy (EIS) measurements with amplitude of 5 mV and frequencies ranging from 100 kHz to 1 Hz.
The Nyquist plots for the synthesized samples were obtained under 3 W Xe lamp light photo-irradiation, and the results have been shown in Fig. 6 aer compensation of the solution resistance. The R ct values are extracted by tting the Nyquist plots data with equivalent Randles circuit via Z view soware, and the obtained values have been listed in Table 1. As it can be seen, deposition of MoS 2 nanosheets initially reduced the charge transfer resistance of the CdS/ITO thin lms. But, increasing the EPD time resulted in increase in the MoS 2 loading, and consequently, the R ct in the CdS/MoS 2 (t)/ITO thin lms was increased as it was expected. Therefore, lower R ct in some CdS/MoS 2 (t)/ITO thin lms (t ¼ 30 and 60 s) as compared with CdS/ITO layer is a good reason for the obtained higher photo-current density. Concerning only R ct , the CdS/MoS 2 (60 s)/ITO (with higher R ct ) should exhibit a lower photo-current density than the CdS/ MoS 2 (30 s)/ITO sample. But we have observed an opposite situation. Therefore, charge transfer resistance is not the only decisive factor inuencing the photo-activity of the CdS/ MoS 2 (t)/ITO thin lms.
Thin lms with higher surface area are benecial for higher photo-current generation as they have more active sites upon light harvesting and as a result, more reactions sites. The root mean square (rms) surface roughness (W) and surface area ratio (A r ) are useful parameters to compare the surface area of the layers. These two parameters have been evaluated and presented in Table 1 for the samples, based on our AFM data analysis.
2D-like structure of few-layer MoS 2 has very high surface area. So, it is expected that MoS 2 deposition increases the surface area of CdS layer and all the CdS/MoS 2 (t)/ITO thin lms have more surface area as compared with the CdS/ITO sample. The obtained highest photo-current density (J) for the highest surface roughness (W) is logical and well accepted. The CdS/ MoS 2 (60 s)/ITO and the CdS/MoS 2 (120 s)/ITO samples have nearly the same value of W in the range of our data error bar (AE0.5 nm), but the former photo-current density is much higher that the latter one. The obtained higher R ct for the CdS/ MoS 2 (120 s)/ITO is one of the reasons for its lower J. Concerning only R ct , when charge transfer resistance of the CdS/MoS 2 (60 s)/ ITO increased from 1467 U to 2155 U in the CdS/MoS 2 (120 s)/ ITO, the J should be decreased from 285 to 194 mA cm À2 . But the obtained J for the CdS/MoS 2 (120 s)/ITO is 177 mA cm À2 . This means that increasing R ct cannot be responsible for such signicant photo-current reduction.
To understand the other reasons, a better criterion than W, namely the surface area ratio (A r ) of the samples should be compared. This parameter has been evaluated for the samples and reported in Table 1.
The A r values show more unusual results. The CdS/ MoS 2 (120 s)/ITO layer has higher A r than the CdS/MoS 2 (60 s)/ ITO but its photo-current density has a lower value. So, another scenario should be considered for the PEC performance of the synthesized samples. The W and A r are representations of macroscopic surface properties of the samples. To better understand the thin lm properties, some microscopic surface parameters should be evaluated. Based on our previous studies, 30,31 Hurst exponent (a) which is obtained based on stochastic analysis can provide very useful information to understand microscopic properties of a surfaces. Surface structure function, S(r), is calculated according to eqn (3) using raw AFM data. To do that, various places of the samples with area of 2 mm Â 2 mm and resolution of 256 Â 256 pixels were scanned by the AFM tip to obtain the h(x) for each pixel. The used AFM instruments and conditions were similar to our previous works. 30,31,35 The obtained S(r) spectra have been plotted as a function of r in Fig. S5. † The plots show that the structure functions of the samples become saturated in large r values (more than 100 nm). For small r, we can scale S(r) with r to calculate the corresponding Hurst exponent a (eqn (6)). The obtained a for various CdS/MoS 2 (t)/ITO thin lms have been listed in Table 1. As it can be seen, MoS 2 nanosheets deposition resulted in increasing a to reach its highest value (2a ¼ 0.67) for the CdS/MoS 2 (60 s)/ITO. Aer that, the roughness exponent decreased and reached approximately to its saturated value for samples prepared with 120 and 240 s EPD. The stochastic analysis data show that the highest photo-current density is related to the samples with the greatest roughness exponent. As discussed before, two samples of the CdS/MoS 2 (60 s)/ITO and the CdS/MoS 2 (120 s)/ITO have almost the same W, and thus R ct cannot be responsible for this signicant difference between the photo-current densities of these samples. Thus, it seems that the microscopic parameter of a, is playing an important role in the PEC performance of the layers.
Based on the above discussions, the mechanism of enhanced PEC activity of the samples can be proposed as following: (i) interface state effect plays an important role in the heterojunction properties, and makes a crucial effect on photovoltaic, photocatalytic and photoelectrochemical properties of CdS/MoS 2 (t)/ITO thin lms. The nature and properties of the materials interface inuence on charge separation and transport and consequently on photo-current density (J) of the photo-active materials. (ii) On the other hand, surface morphology and topography can also inuence on the samples photo-activity. Therefore, J can be assumed as a function of interface states and morphology of the samples.
The interface states inuence on charge resistance (R ct ) and the morphology makes effect on contact angle (q) as well as wettability of the thin lms surfaces. The q can be described as a function of macroscopic uctuation (which is concerned by surface roughness (W)) and microscopic uctuation (donated by Hurst exponent (a)). Therefore it can be written: The effects of R ct (due to interface states) have been explored and discussed via EIS measurements ( Fig. 6 and its related discussions). Aer that, the effect of surface morphology of the samples, namely W and a, should be investigated. Based on discussions mentioned about W, for the samples with the same R ct and W, the photo-current density is a function of Hurst exponent (a): Therefore, in the following we have discussed about relation between J and a.
One of key factors inuencing on the photo-current density of a sample is its degree of wettability during the PEC tests. A better wettability causes superior atomically contact and thus charge transfer and exchange is facilitated between the sample surfaces and the solution resulting in a higher photo-current density. The higher Hurst exponent means that the surface is smoother and the lower one represents a very rough and jagged surface (high microscopic uctuation). 36 Very high microscopic uctuations (meaning small a) may prevent the atomic contact between solution and the sample surfaces during PEC test. It is possible that air molecules to be trapped inside the microscopic jagged sites of the surface and reduce the wettability of the samples. 62 To examine this issue, wettability of the prepared thin lms were evaluated via contact angle (CA) measurements. The obtained angles q have been listed in Table 1.
The macroscopic parameter W, microscopic parameter a and corresponding CA pictures for various CdS/MoS 2 (t)/ITO thin lms have been illustrated together in Fig. S6. † As it can be seen, among all of the samples prepared with various EPD times, the sample possessing the highest roughness exponent, exhibits the lowest contact angle and better wettability. The obtained CA results conrm our discussion, and the results can be explained by a simple mechanism illustrated in Fig. 7.
According to the proposed mechanism for the CdS/MoS 2 (t)/ ITO surfaces, (the resistance (R) and macroscopic uctuations (W) were assumed constant), as the roughness exponent (a) increases, the microscopic uctuations decreases resulting in a smoother surface in nanometric scale, the smaller contact angle and nally the larger surface contact between the electrolyte and the sample surface.
This situation facilitates the photo-generated charge transfer into the electrolyte and as a result, the photo-current density reaches to a greater value. On the other hand, the samples with smaller Hurst exponent (a) have rough and nanometric jagged uctuations more than others.
Air molecules trapped into these microscopic uctuations decrease the surface contact between the electrolyte and the sample surface. 62 The increase of the contact angle in this situation further supports our proposed mechanism. It was shown that the CdS/MoS 2 (60 s)/ITO has generated the highest current density (285 mA cm À2 ) as compared to other samples. On the other hand, analysed AFM data show that this sample has the greatest Hurst exponent a (0.67) and contact angle measurements show that the minimum water contact angle belongs to the CdS/MoS 2 (60 s)/ITO thin lm.
To be more assure about the air trapping, the photo-current density of the CdS/MoS 2 (60 s)/ITO was measured under long time photo-irradiation. If the air trapping is occurred, the air molecules can be detrapped gradually during long time irradiation leading to increase microscopic contact surface between the samples and the electrolyte, resulting in photocurrent density enhancement. The results have been shown in Fig. S7. † As it can be seen, the generated photo-current density increases gradually during continuous photo-irradiation, which can be a sign of air detrapping. All of these obtained results are fully agreed with our proposed model.

Conclusions
We have reported a facile and well-controlled procedure to prepare CdS/MoS 2 (t)/ITO thin lm heterostructures with enhanced photo-current densities as compared with the bare CdS/ITO thin lm. Our utilized experimental procedure allowed us to easily tune and prepare thin lm heterojunctions with various surface topographies. To understand the role of surface parameters inuencing the generated photo-current densities of the samples, the macroscopic (surface roughness W and surface area A r ) as well as microscopic surface properties (Hurst exponent a) were investigated, and we have found a correlation between these two scales using stochastic AFM observations.
According to the stochastic data analysis, contact angle measurements and electrochemical impedance spectroscopy measurements, it was shown that the samples with the higher roughness exponents have a smoother surface in nanometric scale resulting in a better wettability (lower contact angle) and higher photo-current density. On the other hand, the layers formed with small a values, have very rough and nanometricjagged uctuations which cause air trapping and reduce the wettability of the surface leading to the photo-current density reduction. Our stochastic investigation results provide very useful information to manipulate the surface topographic properties which inuence the PEC performance of various photo-active thin lms.