JES I ON P AT THE S -S OLUTION I NTERFACE Surface States- and Field-Effects at GaAs(100) Electrodes in Sodium Dodecyl Sulfate Acid Solution

Sodium dodecyl sulfate (SDS) effects at the electriﬁed p- and n-GaAs(100)/H 2 SO 4 interfaces were investigated by EIS, XPS and AFM. XPS data revealed that under the open circuit conditions, SDS adsorption on GaAs(100) results in a protective overlayer which prevents the further oxidation in air of both types of semiconductor surfaces. The dopant nature is, however, decisive for the way of bonding the surfactant molecule to the surface. At the p-doped substrate, SDS adsorbs mainly at As sites by its hydrocarbon tail and by the anion head to the Ga sites at the n-doped one. Although the surfactant behaves as a dipole under the applied potential control, the dopant type plays a key role in the SDS interaction with GaAs(100) electrodes too. EIS data evidenced that SDS interaction with n-GaAs(100) electrode brings a pronounced decrease of the capacitive contribution of the surface states and a shift of the ﬂatband potential to less negative values, unlike the p-doped one, where no signiﬁcant change in its electronic properties was observed. These results were rationalized in terms of surface states- and ﬁeld-effects operating at the electriﬁed interfaces under discussion. ©

The importance of the surface/interface states in controlling the behavior of the electrified semiconductor/electrolyte is well recognized since the pioneer works of Green 1,2 postulated that changes produced by an externally applied field are entirely experienced in the semiconductor space charge region only when density of the surface/interface states is negligible. Originating in lattice defects and vacancies and/or electron acceptor/donor adsorbed species, they are mainly tributary to surface pretreatment 3 and crystallographic orientation. 4,5 There is, however, evidence that dopants play as well a role in the surface/interface density distribution and energy at GaAs electrodes. We observed that the nature of the majority carriers plays a decisive role in controlling the surface state-and field-effects exerted on the second harmonic generation process at GaAs(111)A/solution interface. 6 Plieth et al. 7 noticed that H 2 O 2 shifted the flatband potential of p-GaAs(100) but did not influence that of n-GaAs(100) electrode and assigned this fact to the different energetic position of their surface states with respect to the Fermi level. Hens and Gomes 8 also reported that the most plausible reaction mechanism for the reduction process Fe 3+ /Fe 2+ occurring at n-GaAs electrode but not at p-GaAs electrode involves transfer of conduction band electrons through surface states.
The distinct electrochemical behavior of the p-and n-GaAs(100) electrodes covered with L-cysteine-thiolate observed in sulfuric acid solutions 9,10 pointed as well to different dopant-induced surface states as being involved in. Dopants were found to play a key role in driving the particular bonding of this organic molecule, preponderant on As sites at p-doped, and on Ga sites at the n-doped substrate, as the XPS data revealed. 9 Analysis of the impedance spectra of the Zndoped and the Si-doped GaAs(100) electrodes brought evidence that chemical bonding is closely related with the surface states within the semiconductor bandgap having energetic positions similar to that associated with the antisite defects. The preferential bonding of Lcysteine on As-sites observed at p-GaAs(100) was thus correlated with the higher density of missing Ga or the As Ga -antisite defect observed at about 0.9 eV below the bottom of the conduction band at the bare electrode. STM investigations revealed indeed that dopant atoms and antisite defects have a close relationship. [11][12][13] This conclusion was strengthened by the experiments performed in sodium dodecyl sulfate (SDS) solutions 10 which showed that anionic surfactant is involved in a chemical bond only with the Ga atoms available on L-cysteinecoated GaAs(100) electrodes, observed to be in a higher amount at the p-doped electrode.
Our investigations pointed out so far that dopants exert a notable influence on the distribution of the antisite defect-related surface states within the GaAs(100) bandgap. Given that such electronic states may control the weight of the surface Ga and As atoms, which keep their chemical individuality when they interact with the species in solution, it is of interest to investigate the dopant effects on other chemical interactions. SDS is certainly a good candidate in this respect as long as this surfactant forms a chemical bond only with Ga atoms, as XPS data 10 revealed.
Chemisorbed species may induce surface states within the semiconductor bandgap which could alter the semiconductor surface/interface states population. This is why chemical modification of the GaAs surface proved to be one of the most efficient methods to improve its electronic properties. A large variety of atoms and ions, such as hydrogen, 14 chlorine, 15 sulfur, 16 oxygen, 17,18 or organic molecules 19 was proposed so far. Of the latter ones, self-assembled monolayers of thiols, 20 attracted particularly high attention. There is, however, by our knowledge, a class of chemical compounds with notorious self-assembling properties which has never been used in this respect: surfactants.
Surfactants have many advantages: high adsorptive efficiency, low price, low toxicity, and easy handling. Their ability to adsorb on semiconducting substrates has been hitherto scarcely utilized only to influence either the morphology of the growing films 21 or their adsorptive properties. 22,23 The interaction of surfactants with solid surfaces depends on their bulk concentration. Bellow a critical value, known as critical micelle concentration (CMC), adsorption is driven primarily by the surfactant-surface interactions yielding individually adsorbed surfactant molecules with low density. Above CMC, interactions between the surfactant molecules themselves tend to control the adsorption process and surface aggregates named hemi-micelles (the adsorbed equivalent of micelles) begin to form until the saturation coverage is reached. The dynamic equilibrium between the individual surfactant molecules in the bulk solution and the hemi-micelle on the solid substrate is closely controlled by the electrostatic interactions between the electrolyte ions and the polar heads. At the electrified metal/electrolyte interfaces, the applied potential becomes, however, the decisive factor for controlling the surfactant adsorption and aggregation processes. [24][25][26] At electrified semiconductor/ electrolyte interfaces, there are no such reports so far. Therefore, investigations on the interaction of surfactants with GaAs electrodes may also bring information concerning other potential factors involved in the potentialdriven changes in the short-ranged and long-ranged interactions operating in the surfactant adlayers.
With this end in view, we studied the effects of SDS, a typical anionic surfactant, on the electrochemical behavior of the p-and n-GaAs(100) electrodes in an electrolyte with a common anion (H 2 SO 4 ) by combining Electrochemical Impedance Spectroscopy (EIS), X-ray Photoelectron Spectroscopy (XPS) and Atomic Force Microscopy (AFM) investigations. It is the aim of this paper to present these results.

Experimental
EIS investigations were performed in a three-compartment electrochemical cell having a saturated calomel electrode (SCE) as a reference electrode and a platinum foil as a counter electrode. The working electrodes were prepared from Zn doped (p = 1 ÷ 1.1 × 10 19 cm −3 ) and Si doped (n = 1.2 ÷ 4 × 10 18 cm −3 ) GaAs(100) wafers (supplied by AXT Company (GEO Semiconductor (UK) Ltd. and Wafer Technology Ltd. (UK), respectively) mounted on Teflon holders with the rear part and the edges sealed by epoxy resin. Back ohmic contacts to the sample were provided by alloying with Au-Zn alloy (p-doped) and Au-Ge-Ni alloy (n-doped) using the thermal evaporation technique. The GaAs electrodes were previously degreased in acetone, washed with deionized water (Direct-Q 3UV System, Millipore) and etched in a mixture were purchased from Sigma-Aldrich and used without further purification. Experiments were conducted in well deaerated solutions, in dark and at room temperature, with an IM6 Zahner frequency analyzer. Impedance spectra recorded by applying a sinusoid signal with 10 mV amplitude in a frequency interval from 0.3 to 3 × 10 5 Hz were fitted using the ZView software (Scribner Associates Inc., Southern Pines, N. C.). The impedance scans were performed in a potential range where no faradaic process takes place, by holding the working electrode at the preset cathodic/anodic end potential followed by successive positive/negative increments of 50 mV until the preset anodic/cathodic end potential was reached.
AFM measurements were carried out in non-contact mode with an XE-100 from Park Systems using sharp tips (<8 nm tip radius) of PPP-NCHR type from NanosensorsTM. The Image Processing Program (XEI -v.1.8.0) developed by Park Systems was used to represent the AFM micrographs in the enhanced color view mode.
The fractal analysis of the AFM images was carried out with the height correlation function method, 27 more suitable for short range correlations, and the variable length scale method 28 more efficient at long range correlations, which were previously described. 9 A SPECS spectrometer equipped with a monochromatized Al Kαanode radiation source operated at 400 W was used for the XPS investigations. The wide survey and detail spectra were taken at pressures lower than 2 × 10 −9 mbar with pass energy of 100 eV and 10 eV, respectively. The binding energy scale was referenced to the C1s peak at 285.00 eV. Peaks were resolved with the SDP v7.0 software (XPS International) and assigned by considering reliable literature reports. The spectra were fitted using Voigt peak profiles and either a linear or a Shirley background depending on the background shape. Figure 1 illustrates the SDS effects on the impedance spectra taken for p-GaAs(100) (Figure 1a) and n-GaAs(100) (Figure 1b) electrodes in 1N H 2 SO 4 solution at a potential (0 V) close to their values of the open circuit potential (OCP). One may easily observe that changes are more pronounced at the n-doped electrode than at the p-doped one. The anionic surfactant brings the real and the imaginary components of the interfacial impedance of the two types of electrode to similar values despite the large difference found in the simple acid solution given by their different doping levels.

EIS.-
More information concerning the influence exerted by the surfactant at the electrified interfaces under discussion was provided by the analysis of the impedance spectra carried out with a conventional 5elements model circuit, [29][30][31][32][33] which is the simplest way to describe the response of the semiconductor surface/interface having time constants within the frequency range.
As seen in Figure 2, SDS exerts no visible influence on the capacitive contributions of the semiconductor space charge region (C SC ) and the surface states (C SS ) controlling the electrochemical behavior of the p-GaAs(100) electrode but it brings important changes in the potential distribution at the n-GaAs(100) electrode giving rise to a pronounced decrease of Css concomitant with an increase of Csc. The electrochemical behavior of the two types of GaAs(100) electrodes in 1N H 2 SO 4 solution is tributary to the surface states located within their bandgap. Both the p-and the n-GaAs(100) electrodes exhibit deviations from linearity of the Mott-Schottky plot (black plots in Figure 2) as often reported. 34 This is usually considered to be the result of the potential-dependent charging of their surface states. [34][35][36] The profiles of the surface state density at the Fermi level, N SS (ε F ) estimated from the EIS data 9,30 shown in Figure 3, reveal the presence of one important group of electronic states centered at about 0.7 eV for the n-doped electrode, and at 0.9 eV below the edge of the con- duction band (E C,S ) for the p-doped electrode, in good agreement with the previous findings. 6,9,37 Similar deep surface states, observed in photo-and thermalemission experiments 38 as well by pulsed field effect measurements, 39 capacitance deep-level transient spectroscopy, 40 transient spectroscopy and paramagnetic resonance investigations 41,42 have been assigned to the so called antisite defects. The upper level found at E C,S -0.7 eV, associated with an As deficit, Ga As antisite (a Ga atom on an As site), and identified as the main electron trap in n-GaAs 43 has an acceptor character. The lower one, located at E C,S -0.9 eV, associated with a missing Ga defect, As Ga antisite (an As atom on a Ga site), and considered 44 responsible for the Fermi-level pinning position on p-type samples, has a donor character.
SDS adsorption of the n-GaAs(100) electrode causes a considerable decrease in the capacitive contribution of the surface states as well as a shift of the Mott-Schottky plot resulting in an apparent less negative flatband potential, E FB , during both the direct and reverse potential scan. Such effects point to an electronic interaction of the surfactant and the acceptor-like surface states observed at E C,S -0.7 eV at the n-GaAs(100) electrode in H 2 SO 4 solution having a negative impact on the latter ones. As lower density of the acceptor-type of surface states is associated with lower surface bending at n-GaAs, 45 the disappearance of the surface states grouped at the middle of the bandgap of the n-GaAs(100) electrode and the lower band bending suggested by the less negative E FB give a solid support to this assumption.
By contrast, the SDS interaction with the p-GaAs(100) electrode does not influence the electrical charging of the surface states located at E C,S -0.9 eV. Their donor character and/or their energetic position may explain why they cannot be involved in an electronic interaction with the anion head of the surfactant. One may therefore conclude that SDS bonding to GaAs(100) substrate is dependent on the dopant nature. More information in this respect was provided by the XPS analysis of the chemical composition of these samples at different steps of the experiments. XPS.-The XPS investigations on the p-and n-GaAs(100) samples removed from the SDS acid solution before and after the EIS investigations, rinsed with water and dried in air, revealed significant differences between the two types of substrate. The presence of -OSO 3 − functional group of the SDS in the S-2p core level region (BE = 168.9/170.1 ± 0.1 eV), 46.47 observed at p-and n-GaAs(100) samples after 1 hour contact with SDS acid solution ( Figure 4) proves that surfactant is adsorbed on the semiconducting substrate regardless the dopant nature. SDS interacts, however, quite distinctly with the shallow As and Ga atoms of the two substrates. At p-GaAs(100), one may observe only a prevention of the surface oxidation. As seen in Figure 4, both the profile of the strong core level lines of the substrate, As-3d and Ga-3d, and the details of the secondary ones, As-2p 3/2 and Ga-2p 3/2 (red lines), show much lower amounts of As-O (BE = 1325.4 ± 0.2 eV; BE = 2.73 ± 0.2 eV) [48][49][50][51] and Ga-O (BE = 1118.9 ± 0.2 eV; BE = 1.2 ± 0.1 eV) 48-51 species in comparison with those corresponding to the sample taken off the simple acid solution (black lines). At n-GaAs(100), a new surface species in the Ga-2p 3/2 spectral region, with BE = 1120.0 ± 0.3 eV; BE = 2.0 ± 0.1 eV replaces completely the Ga-O species, meaning that SDS and Ga atoms are involved in a strong chemisorption bond. As this species does not appear in the Ga-2p 3/2 spectral region observed at p-GaAs(100) substrate, one may conclude that SDS adsorbs in this latter case only at As sites, and without chemical bonding. This is in a very good agreement with the results of the EIS investigations, which pointed out that the near-surface region of the n-doped electrode is expected to be Ga rich, due to the high density of GaAs antisite defects, whereas at the p-doped one, it should be As rich, due to the prevailing As Ga antisite defects. 43 As any dipole, the surfactant molecule should tend to align itself with the applied electric field. Electrochemical bias is thus expected to influence SDS interaction with p-and n-GaAs(100) electrodes. The S-2p core level region presented in Figure 5 illustrates the impact of the applied potential for the two types of electrodes emersed from the SDS solution at the end of the cathodic (−0.6 V) and anodic (0.1 V) potential scans. Data in Figure 5 reveal an enhancement of the SDS adsorption at the end of the cathodic potential scan (−0.6 V) at both types of electrode, as expected. The dipole pointed into the surface clearly gives preferentiality to the interaction of the sulfate head with the shallow Ga atoms. The increase in intensity of the -OSO 3 − core-level line is related with the additional involvement of the Ga atoms at p-GaAs(100), evidenced by the shoulder appearing at higher binding energies in the profile of the Ga-3s core level line. At n-GaAs(100), the much higher amount of adsorbed SDS under the negative bias, is clearly due to a higher coverage of the Ga atoms, indicated by the concomitant decrease in intensity of the Ga-3s core level line.
The preponderant involvement of the Ga atoms in the SDS adsorption of the n-GaAs(100) surface is also manifest in the profile of the Ga-2p 3/2 core level lines at −0.6 V (Figure 6 (top)). One may see that the weight of the Ga-bound SDS species is much higher at n-GaAs(100) than at p-GaAs(100). By comparing these data with the corresponding ones recorded under the same bias conditions for the electrodes taken off simple acid solutions (black lines in Figure 6) it is clear that SDS adsorption suppresses completely the oxidation in air of the Ga atoms and inhibits it in a lower extent that of the As atoms. A somewhat similar effect is found at the anodic end of the potential window (0.1 V) in Figure 6 (bottom). The anodic oxidation as well as  the possible further oxidation in air of the GaAs(100) surface is highly inhibited by the SDS adsorption. This outcome is more pronounced at the p-doped electrode, where the As-O species have not only a much lower weight but also a lower chemical shift, BE, of 1.97 ± 0.02 eV instead of that observed when SDS is not present, which obviously represents a lower oxidation state. Similar values previously observed were assigned either to As-S bond (1.45-2.0 eV) 52 or to As-O (1.92 eV). 53 Taking into account that the -OSO 3 − is a stable species and there is no other S 2− source in the solution, the second hypothesis is more plausible. One may, therefore, conclude that the positive bias yields an augmentation of the SDS species adsorbed by the hydrocarbon tail on the As sites, particularly at p-GaAs(100).
There is another important difference between the SDS effects observed at the two types of GaAs(100) electrodes, which should be commented. This concerns the changes in the binding energies of the Ga-2p 3/2 and As-2p 3/2 core level noticed only at the n-doped samples. As one may see in Figure 4 and Figure 6, there is a clear shift of about 0.5 eV of their binding energies to higher values, no matter the conditions of the SDS adsorption, at open circuit or under the electrochemical bias. This should be a consequence of the changes brought about by the SDS adsorption in the population of electronic states within the bandgap resulting in a decrease of the band bending. Similar BE shifts to higher energies were also observed for both Ga-2p 3/2 and As-2p 3/2 core level lines at thiolate 51 -and S-passivated 54

GaAs surfaces and interpreted as an adsorption-induced decrease in the band bending.
Changes in the populations of the surface states located at the n-doped substrate should be related with the SDS bonding on Gasites. The bonding and the antibonding levels of the chemisorbed species may act as adsorbate-induced surface states of donor and acceptor type, respectively. 14,15,45 The quenching of the acceptor-like surface states within the n-GaAs(100) bandgap might be due to the close vicinity of the donor-like HOMO levels of the new formed surface species. Similar electron levels should be also introduced within the bandgap at the p-doped electrode by the Ga-bound SDS species formed on their surface under the applied potential control. However, since such fully occupied donor-like electron levels are electrically neutral, they cannot entail changes either in the position of the flatband potential or the binding energy of the substrate corelevels. One may, therefore, conclude that the nature of the surface states localized within the GaAs(100) bandgap, closely related with the dopant type, plays the key role in driving its interaction with SDS.
AFM.-SDS interaction with GaAs(100) brings changes not only in the surface chemistry but also in the surface morphology of the semiconductor substrate. AFM images illustrated in Figure 7 show that SDS adsorption results in significant agglomerations of surfactant molecules on p-GaAs(100, where the adsorbed molecules build large and compact aggregates, whereas changes at the n-doped substrate are rather insignificant. The adsorbed ionic surfactants cannot yield uniform layers either on hydrophobic or hydrophilic substrates because of the spontaneous curvature resulting in the repulsive inter-head interactions. However, linear aggregates (cylindrical or half-cylindrical) lying down on metal 55,56 and non-metal 57,58 substrates have been often reported. The tail (hydrocarbon) group interacts mainly with the hydrophobic surfaces giving rise to hemi-micelle above the CMC which provides a basis for half-cylindrical aggregates whereas the head (sulfate) group prefers the oppositely charged hydrophilic substrates resulting in aggregates structures which depend on the density of the electrostatically bound head groups. 14,57 Individual anionic species obviously coexist with micelles in the SDS solutions with a concentration of 40 mM, considerably higher than CMC of SDS in 1N H 2 SO 4 solution which is 0.8 mM as documented in the literature. 59 p-GaAs(100) surface sets its OCP in H 2 SO 4 at about 0.3 V bellow its flatband potential (0.34 V). Due to the inborn negative charge of the depletion layer, the specific adsorption of the anionic head of the surfactant at Ga sites is not really a concurrent with the adsorption of the surfactant tail on the prevailing As Ga antisite defects as the EIS and XPS measurements revealed. The XPS data presented above evidences that SDS interacts mainly by its tail with the As sites at p-doped sample and the low weight of the oxidized species suggests the possibility of their self-organization as hemi-micelles. Therefore, one may assume that the compact surface structures observed at p-GaAs(100) may represent linear aggregates formed by species oriented with the hydrocarbon tail to the surface. This assumption is further supported the short-range and long-range correlations operating between the surface species pointed out by the fractal analysis of these images.
Fractal analysis is a method suited to describe irregular forms and shapes because it assigns a number, the fractal dimension, to every structure, describing how irregular, porous, agglomerate is. The main property of the fractal objects is the self-similarity, the property of the object to look the same at different scales. If in mathematics, self-similarity is obeyed toward infinity, in nature, the fractal objects are self-similar in a narrow range, the self-similarity range, a domain where the self-similarity is obeyed. Self-similarity has a very simple mathematical description: N(r/R) ∼ (r/R)-D, where N(r/R) is the number of boxes of size r which cover the object of linear size R and D is the fractal dimension. 60,61 At molecular scale, irregularities and defects on surfaces of the most materials are self-similar, in other words fractals. 62 Such surfaces are described by fractal dimensions found to be in the range 2 < D < 3; low values (close to D = 2.0) indicate smoothness, a plane surface, meanwhile high values(close to D = 3) indicate highly irregular surfaces.
Fractal analysis of the images taken for the SDS-covered p-GaAs(100) indicates a self-similar surface structure with a low value of the fractal dimension, D = 2.23 ± 0.02 /2.33 ± 0.02, and large self-similarity limits, (5-800 nm) as seen in Figure 8. Having no correspondent on the bare surface, this might be associated with the compact aggregates formed by the species oriented with the hydrocarbon tail to the surface. The other self-similar surface structure observed on the SDS covered p-GaAs(100), with D = 2.40 ± 0.05 is comparable with that noticed at the bare substrate (D = 2.45 ± 0.02). The self-similar surface structure with D = 2.76 ± 0.02, observed at the bare p-GaAs(100), which is not anymore present at the SDS covered substrate, may represent the oxidized species.
On the other hand, anionic surfactants are expected to adsorb readily by electrostatic interactions on positively charged surfaces. The positive charge of the near-surface layer formed at the n-doped substrate under the depletion condition existing at OCP ∼ 0 V is thus very favorable for such an interaction. XPS data discussed above confirm that SDS interacts mainly by its anion head with the Ga-sites at n-GaAs(100). The intrinsic repulsive inter-head interactions should restrain the local aggregates. In good agreement with these assumptions, the fractal analysis presented in Figure 8 evidences that the SDS species adsorbed at n-GaAs(100) substrate, rather conserves than changes the fractal behavior observed in simple acid solution. Both methods point to only one self-similar surface structure with a fractal dimension of 2.32/2.38, found by the correlation function method (1) and 2.40/2.45, by the variable scale method (2), respectively, at the two different window scales, 2 × 2 μm 2 and 8 × 8 μm 2 . This is very close to that of 2.27/2.38 observed at the n-GaAs(100) sample removed from simple acid solution. The similar values of D found at small and large scales indicate that the shortand the long-range correlations operate between the same types of surface species. This seems to be in all probability the individual adsorbed molecule since the same D value is observed at the bare substrate. The surface structure with the higher fractal dimension (D = 2.50/2.64) observed only at the bare substrate, is most probably due to the surface oxides. Its disappearance along with the significantly higher self-similarity range of the surface structure associated with the SDS adsorbed species than that found at the bare surfaces is a further proof of the good protection against the surface oxidation.
The successive steps applied during the anodic and cathodic potential scans bring important changes in the surface morphology as well as in the self-organization of the surfactant molecules on the surface of the two types of electrode, as expected.
The interfacial aggregation of the SDS molecules depends on the electrochemical bias because of the inherent interaction between the anionic surfactant and the applied electric field. Potential-driven phase changes of surfactant adlayers on electrode surfaces are often reported in literature. [63][64][65] The aspect of the surface aggregates of the adsorbed species as well as their fractal behavior looks rather distinct at p-and n-GaAs(100) electrodes, at both ends of the potential window, as one may see in Figure 9 and Figure 10. The fractal analysis points to a mixture of self-similar surface structures at both substrates reflecting the distinct effects of the applied field on the prevailing adsorbed species on each of them. Under the negative bias, at the p-doped electrode, there is a large variety of fractal dimensions, ranging from 2.15 to 2.84, with different values found by the two methods at both scale windows. At the n-doped electrode there are, however, only 3 superposed selfsimilar surface structures in the two scale windows with quite similar D values (2.18 ± 0.02, 2.45 ± 0.05 and 2.76 ± 0.02), and large selfsimilarity limits suggesting a homogeneous and ordered surfactant overlayer. The observed differences reflect the field effects exerted on the surfactant dipole distinctly bound at the types of electrode. The negative bias is expected to promote the hemi-micelles disaggregation at p-GaAs(100) by the negative impact on the strong dipoles formed by the Na + and SO 4 2− entities and to enhance concurrently the headdown orientation of the dodecyl sulfate anions at both electrodes. This effect may explain why there are more self-similar structures with short ranged and long ranged correlations at the p-doped electrode contrasting with the high scale self-similar comportment observed at the n-doped one, at the end of the negative (cathodic) potential scan.
A comparable high scale self-similar behavior was found at the pdoped electrode under the positive bias. As seen in Figure 10, there are 4 superposed fractal structures with fractal dimensions of 2.13/2.22, (20-500 nm) 2.43/2.45 (100-200 nm), 2.58/2.60 (500-1000 nm) and 2.80/2.81 (800-1500 nm) and large self-similarity limits. As only the latter one (D = 2.80/2.81) could not be observed in the 2 × 2 μm 2 image because of its large scale comportment, one may estimate that the surfactant overlayer is homogeneous and well-ordered under the anodic bias. This is supposed to be due to the head-up orientation of the anionic surfactant promoted by the applied field favoring bonding by its hydrocarbon tail to the As atoms.
On the other hand, the fractal behavior of the n-doped electrode resembles closely to that noticed at open circuit ( Figure 8) except for it is less homogeneous, as the different values of D estimated at the two scale windows suggest. The comparable fractal properties is  certainly due to the fact that the applied potential is close to the OCP value, which is around 0.05 V. Structural inhomogeneity may be the effect of the double sequence of potential-induced changes into the surfactant orientation during the (first) cathodic and the (subsequent) anodic potential scans. A similar effect could also contribute to the partial disorder found at p-GaAs(100) at the end of the (first) anodic and the (subsequent) cathodic potential scan.
By comparing the results of the fractal analysis for the adsorption morphologies observed at the two substrates under electrochemical bias to that found at open cell conditions, one may conclude that the applied field plays also an important role in the surfactant behavior at GaAs(100)/solution interface. This is because the SDS molecule behaves as a dipole under the applied potential control and tends to align itself with the electric field as we also reported elsewhere. 10 Due to its alignment with the applied field, under the negative bias, the surfactant has the sulfate head oriented toward the surface and, according to the XPS data, it interacts preferentially with Ga atoms. The more ordered SDS film formed on n-GaAs(100) surface should be thus related with the higher amount of the Ga-bound SDS species indicated by the XPS data. Under the positive bias, the head-up orientation of surfactant dipole entailed by the applied field is expected to favor the interaction of the hydrocarbon tail with the shallow As atoms. Under such circumstances, the adsorption of SDS is enhanced at the p-doped electrode, where there EIS data point to a surface excess of As atoms. The efficient protection against the surface oxidation pointed out by the XPS data ( Figure 6) as well as the fractal comportment over large domains ( Figure 10) provides a strong support in this respect.

Conclusions
We examined the role of the surface states-and the field-effects in the SDS interaction with the electrified p-and n-GaAs(100)/H 2 SO 4 interface by coupling EIS, XPS and AFM investigations. XPS results showed a relatively good protection against the surface oxidation in air at both substrates in the absence of the electrochemical bias. The nature of the dopant is, however, decisive for the way of bonding the surfactant molecule to the surface. Changes in the spectral region of the substrate core level lines evidenced that SDS is mainly adsorbed by its hydrocarbon tail on As sites, at the p-doped substrate, and chemisorbed through its anion head on Ga sites, at the n-doped one. AFM images and their fractal analysis pointed also toward distinct features of the adsorbed species at the two substrates. SDS molecules adsorbed at p-GaAs(100) build large and compact aggregates characterized by a selfsimilar surface structure with low values of D and large self-similarity limits, which suggest hemi-micelles formation. At n-GaAs(100), the surfactant yields islands of variable dimensions. The fractal properties of the overlayer similar to those found at the bare substrate implies they are due to the individually adsorbed species.
Although the surfactant molecule behaves as a dipole under the applied potential control, favoring the SDS adsorption by its anion head under the cathodic bias and by its hydrocarbon moiety under the anodic bias, both EIS and XPS investigations revealed the key role of the dopant in this interaction. EIS data revealed that SDS caused a pronounced decrease of the capacitive contribution of the surface states at the n-doped electrode accompanied by a positive shift of the flatband potential but no significant change at the p-doped one. This is closely related with the distinct nature of the emergent surface states within the semiconductor band gap: acceptor-like in n-GaAs(100), associated with Ga As antisite defects, and donor-like in p-GaAs(100), associated with As Ga antisite defects.
The lower band bending suggested by the positive shift of the flatband potential and the BE shifts to higher values for the substrate core-level lines along with the disappearance of the surface states located at E C,S -0.7 eV pointed out remarkable changes in the electronic properties of n-GaAs(100). These results suggest that interaction of SDS with n-doped GaAs substrate might become a promising tool to improve both the electronic properties of the semiconductor and its protection against the surface oxidation in air.