Probing complex heterostructures using hard X-ray photoelectron spectroscopy (HAXPES)

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Probing complex heterostructures using hard X-ray photoelectron spectroscopy (HAXPES) Banabir Pal, Sumanta Mukherjee, D.D. Sarma ∗ Solid State and Structural Chemistry Unit, Indian Institute of Science, Bengaluru 560012, Karnataka, India

a r t i c l e

i n f o

Article history: Available online xxx Keywords: Hard X-ray photoemission Buried interfaces Multilayer superlattices HAXPES Internal structure

a b s t r a c t X-ray Photoelectron Spectroscopy (XPS) plays a central role in the investigation of electronic properties as well as compositional analysis of almost every conceivable material. However, a very short inelastic mean free path (IMFP) and the limited photon flux in standard laboratory conditions render this technique very much surface sensitive. Thus, the electronic structure buried below several layers of a heterogeneous sample is not accessible with usual photoemission techniques. An obvious way to overcome this limitation is to use a considerably higher energy photon source, as this increases the IMFP of the photo-ejected electron, thereby making the technique more depth and bulk sensitive. Due to this obvious advantage, Hard X-ray Photo Electron Spectroscopy (HAXPES) is rapidly becoming an extremely powerful tool for chemical, elemental, compositional and electronic characterization of bulk systems, more so with reference to systems characterized by the presence of buried interfaces and other types of chemical heterogeneity. The relevance of such an investigative tool becomes evident when we specifically note the ever-increasing importance of heterostructures and interfaces in the context of a wide range of device applications, spanning electronic, magnetic, optical and energy applications. The interest in this nondestructive, element specific HAXPES technique has grown rapidly in the past few years; we discuss critically its extensive use in the study of depth resolved electronic properties of nanocrystals, multilayer superlattices and buried interfaces, revealing their internal structures. We specifically present a comparative discussion, with examples, on two most commonly used methods to determine internal structures of heterostructured systems using XPS. © 2015 Elsevier B.V. All rights reserved.

1. Introduction A primary objective in the broad area of materials science is to explore, investigate and understand diverse electronic properties of matter. While the traditional approach has been to search for new electronic phases in homogeneous bulk materials with new compositions or in doped materials, in recent years there has been a markedly enhanced realization that reduced dimensionality coupled with compositional heterogeneity, such as the interface of a heterostructure [1], the surface of any material, and in several examples of usually complex nanocrystals [2–4] provides the possibility of obtaining exotic properties [5] with a wide range of potential applications. The breaking of translational symmetry at the surface or at an interface makes the ground state electronic properties of a surface or an interface remarkably different from that of the bulk. There are increasing

∗ Corresponding author. Tel.: +91 80 22932945. E-mail address: [email protected] (D.D. Sarma).

number of examples where such altered properties at the interface give rise to new, exotic and emergent phases. For example, highly mobile two-dimensional electron gas (2DEG) [6], ferromagnetism [7] and superconductivity [8,9] have been observed at the interface of two diamagnetic, band insulator oxides LaAlO3 (LAO) and SrTiO3 (STO). The interface between a Mott insulator, LaTiO3 , and the band insulator, SrTiO3 , exhibits metallic ferromagnetism [10] and shows low temperature superconductivity [11]. In the atomically sharp interfaces between La2/3 Ca1/3 MnO3 (LCMO) and YBa2 Cu3 O7 (YBCO) in LCMO/YBCO superlattice heterostructures it is possible [12] to tune the critical temperature of superconductivity of the system by systematically changing the YBCO layer thickness. Phenomena like resistive switching behavior and sharp bipolar transitions [13] with the possibility of tuning the transition temperature with an external magnetic field have been observed at the interface between CoFe2 O4 (CFO) and La0.66 Sr0.34 MnO3 (LSMO). There are many other such examples in the literature where the interface between two known materials shows new and unexpected properties. Therefore, heterostructure engineering using correlated transition metal oxides has become the

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playground for discovering new physical phenomena by controlling lattice, spin, orbital and charge degrees of freedom on both sides of the interface. Understanding the origin of such remarkable properties requires layer resolved electronic and compositional information, characterizing the underlying heterogeneity responsible for these phases arising from diverse manifestations of the breaking of the translational and other symmetries near the surface/interface. In another sphere of intense activities in the recent time, researchers have developed interest in heterostructured semiconductor nanocrystals [14] due to their potential applications in electronic communications [15], sensing and imaging [16], optoelectronics [17], light-emitting diodes [18] and solar cells [19]. A wide range of electronic, optical [20] and magnetic [21] properties can be achieved just by tuning the composition and size of the nanocrystals through diverse synthetic strategies. Properties of such materials are critically dependent also on their internal structures, including the spatial dependence of the chemical composition, in addition to their sizes and shapes. This dependency on the composition profile of these nanomaterials has resulted in syntheses of core–shell, core–shell–shell, gradient core–shell and twinned heterostructured nanocrystals with complex internal structures, making it essential to understand the internal chemical structure of such nanomaterials for a comprehensive and microscopic understanding of their properties. This is important both from the fundamental point of view as well as from the point of view of technological innovations, since a proper understandings of controlling parameters for a given desirable property helps one to further tune and improve such properties for better functionalities. From the above discussion it is clear that in order to understand such a wide variety of emergent phenomena and exciting properties in heterostructured superlattices and in heterogeneous nanocrystals, it is necessary to obtain a detailed description of the compositional variation within the sample with a high degree of spatial resolution in a non-invasive manner. In this article, we show that HAXPES technique with a tunable photon energy extending to relatively high energies can provide a way to probe deep inside materials without altering its properties and yielding critical information necessary to understand the origin of such fascinating properties in a wide variety of systems.

2. Basic aspects of the HAXPES With the establishment of modern synchrotron centers, the HAXPES [22,23] technique has attracted a great deal of attention from the spectroscopic community, as evident also from the presence of a highly successful, dedicated conference series [24] to discuss various aspects of this technique. It is known that photoionization cross sections of different core levels and the valence band decrease very rapidly as a function of the photon energy, making HAXPES a demanding technique. However, the advent of state-of-the-art beamlines providing very high flux at several synchrotron sources around the globe has overcome this limitation, making HAXPES a more easily accessible technique in recent times. As pointed out in the previous section, the main advantage of performing HAXPES measurements in a synchrotron source with a tunable photon energy is in achieving adequate signals from different depths of a heterostructure. This is made possible by the fact that mean free path of photoejected electrons, detected for any photoemission spectroscopy, depends systematically on its kinetic energy which in turn is linearly dependent on the photon energy used for the photoemission process. Therefore, it is possible to vary the depth over which information is gathered in a photoemission experiment by varying the incident photon energy. Since the incident photon energy is continuously tunable at

a synchrotron source, one can tune the photoemission signal to be extremely surface sensitive by opting for a low photon energy and then systematically increase the photon energy to probe increasingly deeper layers in to the material; changes between successive spectra with an increasing photon energy then represent the composition and the electronic structure of an additional layers made progressively accessible due to the increase in the photon energy. While the description here is somewhat oversimplified and the actual analysis requires detailed modeling that often also relies on information gathered from other techniques, as described in the remaining part of this article, the essential idea of this technique is conceptually simple and has a very general applicability for a wide range of systems. Clearly, HAXPES coupled with a high brilliance synchrotron radiation source with a very high flux and state-of-the-art momentum and energy resolution will prove to be extremely powerful in understanding properties of heterostructured superlattices and heterogeneous nanocrystals. 3. Inelastic mean free path (IMFP) The direct way to enhance the probing depth in XPS is to increase the incident photon energy, consequently changing IMFP of the photoelectrons. By estimating IMFP of different elements at various photon energies, the dependence of IMFP on the kinetic energy (EK.E. ) for kinetic energy range (≥1500 eV), can be approximated as [25]  = m (EK.E. )

(1)

where the EK.E. is in the unit of electron volt (eV) and the unit of  is angstrom (Å). This empirical equation has been found to provide a reasonable estimate for a wide range of photoelectron kinetic energy beyond of hundreds of electron volts. For energies above 1500 eV to almost upto 10 keV, the best values of m and  are suggested to be 0.12 (±0.04) and 0.75 (±0.5) [26,27]. TPP and TPP-2 formula [26–30] also provide alternative ways to determine the mean free path of the photoelectron based on more detailed and accurate calculations using the equation given below: TPP =

Ep2



E

 K.E.

 

2 ˇln (EK.E. ) − C/EK.E. + D/EK.E.



(2)

where EK.E. is the photoelectron kinetic energy, EP is the free electron plasmon energy, ˇ, , C and D are different material dependent parameters characteristic of the sample. 4. Depth profiling from HAXPES While different methods of depth profiling have been developed using XPS, we describe two robust methods, namely angle dependent XPS [31] and variable energy XPS [32], which have been used quite frequently to analyze different types of geometries in recent times. As the name, angle dependent HAXPES, suggests, the XPS measurement in this case is performed with a fixed photon energy, but photoelectrons are detected with several different emission angles with respect to the surface normal [31]. On the other hand, in variable energy HAXPES [32] the sample geometry is always kept fixed, but the experiment is performed at several photon energies (see Figs. 1 and 2). It is important to mention here that apart from these two well-known methods there are several other techniques e.g. standing-wave hard X-ray photoemission spectroscopy [33,34] which can also be used in order to have a depth resolved electronic structure. In the following part, we describe the method of determining the composition profile as a function of the depth in some detail. Let us assume that we have a sample comprising of an element A. At a fixed photon energy (h), the differential intensity contribution

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Fig. 1. (a) Schematic of XPS process for a homogeneous sample. (b) Schematics of angle dependent HAXPES measurement on a heterostructured sample. The surface sensitivity increases as angle () increases.

Fig. 2. (a) and (b) Schematic of variable energy XPS measurements. The bulk sensitivity increases with an increasing photon energy as shown in the figures.

dI for a specific core level of any given element, from a volume element dV at a depth z from the surface can be expressed as dI ≈ TK.E. Ph h n exp



−z  K.E. cos 

 dV

(3)

where TK.E. is the transmission function of the analyzer, Ph is the photon flux of the source with energy h,  h is the photo-ionization cross-section of relevant photoelectrons,  is the angle of detection with respect to the surface normal of the sample, K.E. is the kinetic energy dependent mean-free-path of those photoelectrons and n is the number density of that particular element within the volume element dV. Excluding the effect of inelastic losses, the total intensity, I, can be expressed by integrating Eq. (3) over the whole sample volume as

 I=

 dI ≈ TK.E. Ph h

V

 n (x, y, z) exp

V

−z K.E. cos 

 dx dy dz

(4)

In the expression above, n(x,y,z) is number density of the element as a function of space. Most often this very general expression can be replaced by n(z), indicating a planar heterostructure with the number density of any given element being only a function of the depth from the surface of the sample. For simplicity, we assume this geometry for the subsequent discussion in this section, though consideration and analysis presented here can be easily generalized to other geometries as well, for example for spherical and cylindrical [32] geometries. Instead of one element, if the planar heterostructured sample consists of an element A up to a depth ZA and an other element B from a depth of ZA to the depth of ZB , the ratio between the total spectral intensity from the core level of A and the that of the core level of B, can be expressed as

IA = IB

  Z TK.E.(A) h(A) 0 A nA (z) exp −z/A cos dz dIA V =   Z V

dIB

TK.E.(B) h(B)

B

ZA

nB (z) exp −z/B cos dz

(5)

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where A and B are the kinetic energy dependent inelastic mean free paths of electrons detected from the specific core levels of A and B. The cross-sections are theoretically calculated quantities and the functional form of the transmission function as a function of the electron kinetic energy for a given detection system is generally known. Therefore, the experimentally obtained integrated spectral intensity I for any core level of an element at a given photon energy can be normalized to account for the cross section  and the transmission co-efficient T to express the normalized intensity, I . In terms of these normalized intensities, the expression I norm = .T for the intensity ratio in Eq. (5) can be rewritten as IAnorm IBnorm

ZA =









nA (z) exp −z/A cos dz

0 ZB



(6)

nB (z) exp −z/B cos dz

ZA

Since  is known from the detection geometry and A and B are determined by the electron kinetic energy, as discussed before, experimentally estimated normalized intensity ratios at several photon energies, can be analyzed within a least squared error approach to obtain nA (Z) and nB (Z), thereby providing a quantitative description of the internal structure of any sample. In practical terms, one is guided by physical arguments relevant to a specific sample to assume specific functional form of nA (Z) and nB (Z), to model the internal structure. The least square error fit, mentioned here, then provides quantitative estimate for the parameter values defining the model. In case of a planar heterostructure with a sharp interface, mentioned above, n (z)’s are given by nA (z) = nA

for

0 ≤ z ≤ ZA and nB (z) = nB

for

ZA ≤ z ≤ ZB

(7)

Then Eq. (6) can be expressed in a simplified form as IAnorm IBnorm

ZA =

0 ZB



ZA









exp −z/B cos dz



A = B

≈



exp −z/A cos dz

A exp B





1 − exp −ZA /A cos 





exp −ZA /B cos  − exp −ZB /B cos 



ZA B cos 



(for ZB  ZA and B )

− exp

 Z 1 A cos 

B

−

1 A



(8)

 (9)

Since planar heterostructue are often formed by depositing a thin layer of a different substance (containing the element “A”) on top of a bulk substrate (containing the element “B”) it becomes straight forward to use Eq. (9), representing ZB → ∞ limit, to extract the only unknown, namely the thickness (ZA ) of the overlayer. This approach can be easily generalized to describe more complex heterostructures, e.g. a heterostructure with mixed interface between element A and B instead of having a sharp interface, distinguished by different variation of the number densities of elements A and B within the heterostructure represented by suitable modifications in Eq. (7). For such complex situations with more number of unknown parameters characterizing the internal structure, it is necessary to carry out HAXPES experiments at multiple photon energies to reliably estimate parameters during the complex internal structure from the least-squared-error approach. It can be easily seen from Eqs. (6) and (8) or (9) that the intensity ratio between the core level of element A and that of element B can be varied either by varying the angle  or by varying the mean free paths, by changing the photon energy. We have illustrated these two ways of changing the intensity ratio between core levels of element A and element B in Figs. 1 and 2.

It is evident from Fig. 1b that an increase in the detection angle  with respect to the sample surface normal, will increase the “effective” thickness of the overlayer as seen from the detector, which in turn will increase the intensity contribution from the core level of sample A. Therefore, the intensity ratio, IA /IB , estimated at a particular h is expected to increase with an increase in the detection angle  thereby providing estimates of ZA and ZB for any given sample according to the above equations. This forms the basis of obtaining depth resolved information in a quantitative manner from an angledependent XPS study. On the other hand, variable energy XPS relies on changing the mean free path by changing the kinetic energy of the photoelectrons (Eqs. (1) and (2)) keeping the sample geometry fixed, as illustrated schematically in Figs. 2a and b. With an increase in the photon energy the IMFP of the electron increases making the intensity ratio increasingly bulk sensitive. A large number of scientific groups have used HAXPES to probe layer resolved compositional and electronic structure variations in planar hetrostructures and complex heterogeneous nanocrystals. For example Sing et al. [35] performed angle dependent HAXPES measurement in the LaAlO3 –SrTiO3 thin films and estimated the Ti3+ concentration at the interface. They also calculated the carrier density as a function of the LaAlO3 layer thickness. In another investigation, Paul et al. [36] used energy dependent HAXPES to evaluate thickness of the interface in a Fe3 O4 –GaAs bilayer sample which is a promising material for spintronics applications. Beni et al. [37] used a similar approach to estimate layer resolved compositional variation in complex Al–Cr–Fe metallic alloy systems. Mukherjee et al. [38] used a similar methodology to estimate thickness of the CoFeB and MgO layer in CoFeB/MgO/CoFeB magnetic tunnel junctions (MTJs) to resolve an outstanding controversy [39], establishing that boron did not diffuse beyond one or two atomic planes at the interface in a suitably formed device structure. In one of the early applications to investigate heterogeneous nanocrystals with x-ray photoelectron spectroscopy (XPS), White et al. [40] demonstrated that PES can qualitatively differentiate between a core shell structure and a homogeneous alloy structure. With the help of XPS, Alivisatos et al. [41] provided evidence of surface bonding of TOPO with Cd atoms only for CdSe nanocrystals, suggesting an unpassivated nature of the surface Se atoms, thereby providing a qualitative description of the surface structure of such nanocrystals. Some of the earliest synchrotron based XPS measurements [42,43] on CdS nanocrystals have concluded that the thiol capping agents stabilizes the S atom in the CdS nanocrystals and it is a better capping agent. The first step toward a quantitative determination of the structure of nanocrystals, based on energy dependent XPS measurement was reported by Nanda et al. [44] using Al K-alpha and Mg K-alpha X-ray sources. From the variation of intensities of distinct S species at these two photon energy Ref. [44] provided the easiest quantitative description of the complex internal structure of thiol capped CdS nanocrystals. A similar analysis was also reported for ZnS nanocrystals in Ref. [32]. Following a similar approach Borchert et al. [45] analyzed ZnS nanocrystals covered with TOP/TOPO as capping agent as well as more complex systems like CdS/HgS/CdS quantum dot quantum well structure and CdS/HgS/CdS/HgS/CdS double quantum well structure. From their studies they concluded that a reliable analysis is possible for structures like CdS/HgS/CdS, when the innermost core and outermost radius could be obtained from independent TEM measurements. However, Santra et al. [46] used the multiple photon energies, available from a synchrotron source to show that reliable quantitative description of the internal structure of complex heterostructured nanocrystals can be deduced based on the variation in the intensity ratios of different core level spectra as a function of the photon energy. Subsequently, several other such investigations to obtain quantitative description of internal structures of a variety of nanocrystals have been reported [3,47] in the literature.

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Since both energy dependent and angle dependent XPS are nowadays widely used to understand the layer resolved electronic and compositional structure in planar heterostructures and in complex nanocrystals, it is worthwhile to discuss the consequences of experimental uncertainties in such quantitative analysis for a better appreciation of the limits of applicability of these otherwise powerful techniques. In order to illustrate the error analysis, we simulate the case of a planar heterostructure consisting of a 6 unit cell overlayer of LaTiO3 (LTO) with a thickness of 2.4 nm on top of a SrTiO3 (STO) substrate. In passing we note that this is not a hypothetical case, since this system specifically has attracted much attention in the recent time due to interesting properties of a suspected 2-dimensional electron gas forming at the interface. Since Ti is in 3+ and in 4+ oxidation states in LaTiO3 and SrTiO3 , respectively, this system provides a particularly favorable case to determine the internal structure by monitoring only the Ti 2p spectral region with distinct Ti3+ and Ti4+ signals in HAXPES. In this case, the cross sections, transmission functions and the mean free path are essentially the same for both signal, leading to a great simplification that the experimentally obtained intensity ratio is also the normalized intensity ratio and Eq. (9) has A = B = , leading to I3+ = exp I4+



d . cos 



−1

(10)

with d being the overlayer thickness. Thus, given any  (determined by the photon energy and the binding energy of the Ti 2p spectrum) and  (given by the experimental geometry) the intensity ratio observed in the experiment is directly determined  by the overlayer thickness, d. In Fig. 3a, we show how I3+ /I4+ vary as a function of the angle  for a few values of the photon energy, as in a typical angle dependent HAXPES experiment. It is clear that there is little sensitivity of the intensity ratio on  for smaller values of , suggesting that angle dependent HAXPES approach should cover a wide range of angles in order to accurately determine the overlayer thickness. Fig. 3a also suggests that higher photon energies make angle dependent HAXPES rather insensitive, as suggested by the flatness of the plots in the figure for h > 4.5 keV. This would apparently suggest that it is better to work with a low photon energy to extract reliable information from such experiments. However, this would be an erroneous conclusion arising from one effect that we have not discussed so far, namely the noise level in the real, experimentally obtained signal that limits the accurate determination of the experimental intensity ratio itself, thereby introducing errors in estimating the overlayer thickness. It is easy to anticipate that there would be an optimal photon energy for a given heterostructured sample. For example, if h is too small, there will be negligible signal from the substrate, making the denominator susceptible to the noise in the spectra and thereby limiting the reliability of the intensity ratio and consequently the reliability of the estimated overlayer thickness d. In the opposite limit of a very high photon energy, the contribution of the overlayer appearing in the numerator of the intensity ratio becomes vanishingly small, thereby making the intensity ratio highly uncertain due to the intrinsic noise in the overlayer spectral feature. These limiting considerations for very low and very high photon energies make it obvious that there is an optimal choice of the photon energy for HAXPES investigation of the internal structure. In order to investigate this point further, we take a realistic example of LaTiO3 /SrTiO3 heterostructure mentioned above and estimate the background intensity, B, obtained in a typical experiment with h = 3600 eV and I3+ and I4+ . We consider that determination of individual intensities, I3+ and I4+ , are uncertain due to the presence of noise in the spectra, with the noise being proportional to the square root of the total signals, namely, (B + I3+ ) and (B + I4+ ), respectively. We estimate the

Fig. 3. (a) Variation of I3+ /I4+ intensity from a hypothetical LaTiO3 /SrTiO3 heterostructure as a function of the angle  for a few values of the photon energy. (b) Estimated error in calculating the overlayer thickness as a function of the photon energy for different overlayer thicknesses due to the presence of finite noise level on recorded spectra. (c) Optimal choice of  as a function of the overlayer thickness, d for different measurement angles. Inset in (c) shows the optimal  as a function of effective thickness of the overlayer for all different measurement angles.

maximum error in obtaining the intensity ratio,











I3+ /I4+ , by



evaluating I3+ + n3+ /I4+ − n4+ and I3+ − n3+ /I4+ + n4+ , where n3+ and n4+ are the estimated noise levels. While we have the correct d value for infinitely accurate I3+ and I4+ , we may have an easy estimate of the error bar, d, on d due to the spectral noise by evaluating dmax from I3+ + n3+ /I4+ − n4+ and dmin from





I3+ − n3+ /I4+ + n4+ . We have plotted thus estimated error in estimating the overlayer thickness as a percentage of thickness in Fig. 3b as a function of the photon energy for different overlayer

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thickness and at a fixed angle,  of 5◦ . Clearly, the uncertainty in obtaining the overlayer thickness shows a minimum at a particular photon energy, defining the optimum h for a HAXPES investigation. It is to be noted here that the relevant expression, Eq. (10), does not involve the photon energy directly and the influence of the photon energy in this case appears entirely through the value of  that indirectly depends on h. For the sake of simplicity here, we have used  to be given by the often-used expression with m =  = 0.5 in Eq. (1) and a Ti 2p binding energy of 462 eV. Thus the optimal photon energy defined by the minima of the plots in Fig. 3b can be readily converted into an optimal choice of  for each overlayer thickness, d, for which plots are shown in Fig. 3b. We have plotted this optimal  as a function of the overlayer thickness, d, in Fig. 3c; the result shows a remarkable linear dependence. We have carried out similar analyses for another two fixed values of , namely 40◦ and 60◦ , and resulting optimal ’s are also plotted in Fig. 3c. Since the electron path length through the overlayer is not d, but d/cos  (see Fig. 1b), we show plots of optimal ’s as a function of d/cos  in the inset of Fig. 3c. It shows a remarkable collapse of all optimum values of  onto a nearly 45◦ straight line as a function of the effective electron path length through the overlayer. Thus, this simple analysis brings forth an important conclusion that HAXPES experiments are best performed with the photon energy so chosen as to make the mean free paths of the photoelectrons approximately equal to the effective length-scale of the relevant internal structure being probed in any given heterostructured sample.

5. Applications in two different systems The interface between CFO and LSMO shows [13] resistive switching (RS) behavior and a bipolar transition (at 300 K); interestingly, the switching voltage which can be tuned sensitively by the application of a small magnetic field. A cross-sectional TEM image of the heterostructure, showing growth of CFO on top of LSMO, discernable from the contrast difference of the two layers, is presented in Fig. 4a. The estimated [13] thickness, d, of the CFO layer is 6.5 (±0.5) nm. Both angle dependent as well as energy dispersive XPS were performed [48] on this heterostructure with the photon energy varying between 4000 eV and 6000 eV. Recoil energy corrected C 1s spectra were used for calibration of the photon energies in all these experiments. A Shirley function is used for the background correction in all cases. The background corrected photoelectron spectra of Co 2p, Fe 2p and Mn 2p with h = 4800 eV are shown in Fig. 4b for  = 5◦ and 60◦ . The spectra were normalized at the maximum of the Fe 2p spectra for a facile comparison. It is evident in the figure that Co 2p and Fe 2p spectra remain essentially the same in terms of spectral feature, as well as relative intensities independent of , showing that Co and Fe have the same spatial distributions in this heterostructure. This clearly establishes that there is no diffusion of Co relative to Fe, retaining the integrity of the CFO layer as desired for this device structure. The relative intensity of the Mn 2p spectra, on the other hand, increases upon changing the detector angle from 60◦ to 5◦ . Since decreasing  increases the bulk sensitivity, the increase in the Mn intensity relative to Fe and Co is a reflection of the fact that LSMO is the layer beneath CFO in this heterostructure. For a quantitative determination of the thickness it is necessary to correct the experimental intensity ratios with respect to in earlier cross-sections and the transmission function explained   sections. Thus corrected as “normalized” intensity ratios IFe /IMn



Fig. 4. (a) Transmission electron microscope image of a CoFe2 O4 /La0.66 Sr0.34 MnO3 heterostructure showing an average thickness of 6.5 (±0.5) nm. [Reproduced with permission from Applied Physics Letters 100, 2012, 172412 (Ref. 13). Copyright 2012, AIP Publishing LLC.] (b) Angle dependent HAXPES measurements at two different photon energies for the same sample. (c) Variable energy HAXPES data for the same sample at different photon energies.



and IFe /ICo are shown in the inset to Fig. 4b for the two values of . We used these intensity ratios to calculate the thickness, d, of the CFO layer using Eq. (9) and found it to be 8 (±2.8) nm. This is in Please cite this article in press as: B. Pal, et al., Probing complex heterostructures using hard X-ray photoelectron spectroscopy (HAXPES), J. Electron Spectrosc. Relat. Phenom. (2015), http://dx.doi.org/10.1016/j.elspec.2015.06.005

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fair argument with the thickness of the CFO layer estimated from TEM, namely 6.5 nm. High energy photoelectron spectroscopy was also performed on the same heterostructure at a fixed detection angle () of 5◦ at three different photon energies of 4000 eV, 4800 eV and 5900 eV. The background corrected Co 2p, Fe 2p and Mn 2p photoelectron spectra recorded at these three photon energies are shown in Fig. 4c. The spectra are again normalized at the maximum of the Fe 2p spectral intensity for an easy comparison. As should indeed be expected, relative intensities of Co 2p and Fe 2p spectra are basically independent of the photon energy, while the Mn 2p spectral intensity increases systematically with the increase of the photon energy. The  cross-section   corrected experimental intensity ratios IFe /IMn and IFe /ICo are shown in the inset to Fig. 4c. We have





used Eq. (9) to describe the photon energy dependence of IFe /IMn within the least squared error method to estimate the thickness of the top CFO layer. The best fit shown as the blue line in the inset to Fig. 4c was obtained with a CFO thickness of 6.8 (±2.0) nm in very good agreement with the result of cross-sectional TEM (Fig. 4a). As mentioned earlier, photon energy dependent photoelectron spectroscopy has additional advantages for structures other than planar geometries, for example, for internal structure determination of spherical nanocrystals [46,49]. Clearly most commonly encountered spherical nanocrystals cannot be probed meaningfully by changing the angle of detection, since its symmetry ensures the intensities to be insensitive to the angle. In order to use the photon energy dependent method for spherical nanocrystals, it is more convenient to perform the integration mentioned in Eq. (4) in a spherical polar geometry [46]. While the details of the method can be found in [32], we demonstrate the use of this approach by presenting briefly HAXPES results on spherical Zn1-x Cdx Se1-y Sy nanocrystals. While the nature of the alloying at the cation (Zn/Cd)

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and anion (S/Se) sites were unknown for this sample, the overall size of the nanocrystal was determined to be 5.0 ± 0.7 nm from TEM analysis. Experimental S 2p and Se 2p core level spectra recorded at different photon energies between 1487 eV and 4000 eV from ZnCdSeS nanocrystals are shown in Figs. 5a and b as black filled circles. All the spectra were decomposed to obtain the intensities of S 2p and Se 3p components separately, as shown  in the figures. The cross-section normalized intensity ratios ISe /IS are shown in Fig.  5c.The increase in the cross-section corrected intensity ratio ISe /IS with increasing photon energy suggests that Se is present toward the core of these nanocrystals. The internal structure obtainedfrom the  simulation of the crosssection corrected intensity ratio ISe /IS is shown schematically in Fig. 5d. The structure consists of a pure CdSe core of radius 1 (±0.1) nm and a homogeneous alloyed shell of ZnCdS of thickness 0.7 (±0.1) nm. There is a mixed layer in between these two layers, where the number density of Cd and Se decreases continuously from the nominal values of pure CdSe, reaching the concentration corresponds to ZnCdS, at the outer layer of the nanocrystals. The variations of the number densities (n) across the radius r of the nanocrystals for Zn, Cd, S and Se  are shown  in Fig. 5d.  The best fit to the intensity ratios between ISe /IS and ICd /IZn are shown as shaded regions in Fig. 5c with the width of the shade represent 10% error in the estimated parameter values. In conclusion, we have described two closely related methods to determine internal structures of heterostructures with typical dimension of a few tens of nm using HAXPES. We have illustrated the methodology with applications to planar or thin film heterostructures and to spherical nanocrystals geometry. We have also shown that these methods are most accurate when the photon energy is so chosen as to make the mean free path of the photoelectron comparable to length scale of the phenomenon being probed.

Fig. 5. (a) and (b) Show core level photoelectron spectra of Se 3p and S 2p at four different photon energies. (c) Photoemission cross-section corrected intensity ratios between different core levels, ISe /IS and ICd /IZn , are shown as filled circles and filled diamonds, respectively. The shaded regions in this figure represent the expected variations in the intensity ratio for the structure shown in (d), with the width of these regions representing the typical uncertainties. (d) Schematic representation of the internal structure of Zn1-x Cdx Se1-y Sy nanocrystals obtained from the analysis of the cross-section corrected experimental intensity ratio.

Please cite this article in press as: B. Pal, et al., Probing complex heterostructures using hard X-ray photoelectron spectroscopy (HAXPES), J. Electron Spectrosc. Relat. Phenom. (2015), http://dx.doi.org/10.1016/j.elspec.2015.06.005

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Please cite this article in press as: B. Pal, et al., Probing complex heterostructures using hard X-ray photoelectron spectroscopy (HAXPES), J. Electron Spectrosc. Relat. Phenom. (2015), http://dx.doi.org/10.1016/j.elspec.2015.06.005