Al2O3

Mass transport and thermal stability of TiN/Al2O3/InGaAs nanofilms O. Ceballos-Sanchez, A. Sanchez-Martinez, M. O. Vazquez-Lepe, T. Duong, R. Arroyave et al. Citation: J. Appl. Phys. 112, 053527 (2012); doi: 10.1063/1.4751435 View online: http://dx.doi.org/10.1063/1.4751435 View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v112/i5 Published by the American Institute of Physics.

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JOURNAL OF APPLIED PHYSICS 112, 053527 (2012)

Mass transport and thermal stability of TiN/Al2O3/InGaAs nanofilms O. Ceballos-Sanchez,1 A. Sanchez-Martinez,1 M. O. Vazquez-Lepe,1 T. Duong,2 ~a,3 and A. Herrera-Gomez1 R. Arroyave,2 F. Espinosa-Magan 1

CINVESTAV-Unidad Queretaro, Queretaro, Qro. 76230, Mexico Department of Mechanical Engineering, Texas A&M University, College Station, Texas 77843-3123, USA 3 Centro de Investigaci on en Materiales Avanzados, Chihuahua, Chihuahua 31109, Mexico 2

(Received 16 February 2012; accepted 9 August 2012; published online 13 September 2012) The structure of TiN/Al2O3 nanofilms grown on InxGa1-xAs substrates was studied with angleresolved x-ray photoelectron spectroscopy (ARXPS), high resolution transmission electron microscopy (HRTEM), and density functional theory calculations. From the ARXPS studies, it was possible to characterize in detail the composition and distribution of the various layers constituting the nanofilms; the results were consistent with HRTEM micrographs. The analysis of the ARXPS data showed that annealing causes diffusion of indium atoms from the substrate into the titanium layer. It also allowed for establishing that the thickness and composition of the C 2012 American Institute of Physics. dielectric layers remain stable under thermal treatments. V [http://dx.doi.org/10.1063/1.4751435] I. INTRODUCTION

III-V compounds, in particular InGaAs, are candidates to replace Si as the semiconductor in complementary metal-oxide-semiconductor (CMOS) devices.1–3 Some problems associated with III-V semiconductors are the instability of the substrate surface under treatments prior to the growth of the dielectric and the difficulty of finding thermodynamically stable dielectrics, which also passivate the interface.4 There is evidence of the removal of native oxides and the passivation of the high-k/III-V interfaces when Al2O3, HfO2, and ZrO2 are grown by atomic layer deposition (ALD).5–8 However, the high temperatures required for activation of some dopants in the device induce structural changes that degrade electrical properties.9–11 These changes might include the formation of native oxides, defects, and atomic interdiffusion.8 A proper characterization of the structural alterations associated with the degradation of electrical properties is important for understanding failure mechanisms. The discussion in the literature about the structural changes induced by annealing these types of nanofilms is not very extensive. Some qualitative results, mainly for hafnia as the dielectric, could be found in some references.12–15 In this paper, we report a quantitative study of the structure of TiN/Al2O3 nanofilms grown on InxGa1-xAs and of the structural changes caused by annealing at 500 C for 2 min and at 700 C for 10 s. Through angle resolved x-ray photoelectron spectroscopy (ARXPS), it was possible to determine the structure of the films and to discriminate changes induced by annealing. The experiments provided evidence that In diffuses upward to the TiN layer from the InxGa1-xAs substrate. Interestingly, the similar diffusive phenomenon was not detected for the rest of the substrate elements. To explain this transport phenomenon, ab initio studies using density functional theory (DFT) were carried out. II. EXPERIMENTAL AND DFT CALCULATIONS DETAILS

The three TiN/Al2O3/InGaAs samples employed for this study were grown on InxGa1-xAs substrates previously 0021-8979/2012/112(5)/053527/10/$30.00

cleaned with dilute HF solution (H2O: HF ¼ 100:1) for 1 min. Al2O3 was deposited by ALD using trimethylaluminum and ozone as oxidizer with a target thickness of 3 nm. To complete the MOS structure, the samples were capped with thin enough TiN layers to allow XPS studies of the substrate and dielectric layer while maintaining adequate thickness to protect the dielectric layer from desorption during annealing. One piece was annealed at 500 C for 120 s (representative of a “gate last” process) and another at 700 C for 10 s (representative of a “gate first” process). High resolution transmission electron microscopy (HRTEM) images were acquired with a JEOL JEM-2200FS instrument for the sample annealed at 500 C for 120 s (gate-last) sample. A focused ion beam (FIB) instrument model JEOL JEM-9320FIB was employed for TEM sample preparation. Gold and tin were evaporated to protect the surface of the samples. The ARXPS data were obtained in a ThermoFisher-VG instrument equipped with a monochromatic Al Ka1 (1486.7 eV) x-ray source (model XR5) and a hemispherical electron analyzer with seven channeltrons (model XPS110). The high-resolution spectra were collected at seven different angles employing 15 eV pass energy and 0.05-0.1 eV energy step for all relevant core levels (As 3d, In 3d5/2, Ga 3d, Al 2p, O 1s, N 1s, Ti 3p, and C 1s). The take-off angle, defined as the angle between the surface and the hemispherical analyzer input lens axis, was controlled by tilting the sample. Data collection was done employing between 20 and 60 scans. The fitting of the XPS spectra was accomplished using Voigt functions; the branching ratios and spin-orbit splittings employed were chosen from either known values or directly determined from the peak fitting process. The center and width of each peak were obtained by fitting all the angles simultaneously, and allowing these parameters to vary freely.16 The simultaneous peak fitting method was crucial to robustly assess the parameters for entangled peaks.17 The spectra were shift corrected by assigning the bulk As 3d5/2 peak a binding energy of 40.6 eV and shifting the rest of the regions accordingly. The background was treated in an active

112, 053527-1

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way as described in Ref. 18. The assessment of the structure of the films (thickness and composition of each layer) was made employing the multilayer model (MLM).19 The MLM is robust against data noise for a number of reasons. It is parametric and the number of output parameters does not exceed the maximum number allowed for a robust analysis, as described in Ref. 20 (the output information does not exceed the input information, so the solutions can be stable). In addition, it allows for iterative convergence (typically taking no more than four iterations) to self-consistency. This is possible since the parameters, such as the effective attenuation lengths and the atomic density, can be input into the analysis according to the composition of each layer that is found at each iteration. The MLM is encompassed in the software XPSGEOMETRYV,21 which also accounts for the extra angular dependence incorporated by the geometrical factors R

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of the XPS instrument as the sample is tilted to change the photoelectron take-off angle. These factors include the manipulator’s axis of rotation, the size and shape of the spectrometer analysis volume, and x-ray beam.22 In this way, it is not necessary to normalize the spectra, greatly improving the robustness of the method against noise. Generation and transport energies for mobile impurities were carried out within the framework of DFT23 implemented via the Vienna ab initio simulation package (VASP).24,25 Particularly, the exchange-correlation term was approximated using the generalized gradient approximation (GGA) in the form of PW9126 and coupled with projected augmented-wave (PAW) pseudopotentials.27 The electronic configurations of In, Ga, and As are: [Kr]5s24d105p1, [Ar]4s2 3d104p1, and [Ar]4s23d104p3, respectively. The Brillouin zone integrations were performed using a Monkhorst-Pack

FIG. 1. Angle resolved XPS spectra (dots) and fits (lines) for the TiN/Al2O3/InGaAs untreated sample.

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mesh28 with 5000 k-points per reciprocal atom. Full relaxations were realized by using the Methfessel-Paxton smearing method of order one29 and a final self-consistent static calculation with the tetrahedron smearing method with Blochl corrections.30 A cutoff energy of 350 eV and 520 eV was set for the substrate and alumina calculation, respectively, and the spin polarizations were taken into account. III. EXPERIMENTAL RESULTS AND ANALYSIS

Figure 1 shows the ARXPS data for the core levels of the TiN/Al2O3/InGaAs unannealed nanofilm. Through simultaneous data peak-fitting, it was possible to discriminate the chemical components associated with the oxidation state of each element contained in the sample. The peak composition for some of the elements is presented, although some others are described in the following figures. As shown in Figure 1(a), the As 3d spectra include the contribution from Ti 3p photoelectrons. The As 3d spectra were fitted with two doublets associated with arsenic in InGaAs at 40.6 eV and elemental arsenic at 41.2 eV.31 It has been reported that the presence of elemental arsenic contributes to leakage current, large values for equivalent oxide thickness (EOT), and hysteresis.14,32 As expected from exposure to the environment, the TiN layer underwent oxidation becoming a combination of titanium nitride, oxynitride, and oxide. The Ti 3p region was fitted with three doublets associated with titanium in TiN, TiO2, and TiON. The Al 2p spectra (Figure 1(b)) were fitted with one doublet associated with Al3þ at 74.3 eV. The O 1s and N 1s regions were associated with O-Ti, O-Al, TiO-N and with N-Ti and Ti-O-N bonds, respectively. The components for oxygen in Al2O3 (531.4 eV) and nitrogen in TiN (397 eV) were clearly identified. Figure 1(e) shows the Ga 3d and In 4d regions. For some samples, it was difficult to deconvolve (peak-fit) the Ga 3d signal since it overlaps with the In 4d peak. Nevertheless, it was possible to identify the doublets associated with gallium in InGaAs (at 19.0 eV) and in Ga-O bonds (Ga3þ, at 20.1 eV).3 The In 4d region was fitted with two doublets associated with indium in InGaAs and in In-O bonds. The In 3d5/2 spectra (Figure 1(f)) were fitted with two singlets associated

with indium in InGaAs at 444.4 eV and In3þ at 445.2 eV. Table I shows the parameters employed for the peak-fitting, it includes the spin orbit splitting, the Gaussian and Lorentzian widths, branching ratios, and positions. The fixed parameters are the branching ratios and the Lorentzian widths. The symbols in Figure 2 correspond to the electron takeoff angular dependence of the intensity of the peaks shown in Figure 1. The assessment of the structure of the film was done from the analysis of this dependence employing the MLM.19 The results of the analysis are shown in Figure 3, which illustrates the thickness and compositions of the various layers constituting the films together with the associated uncertainties. The lines in Figure 2 correspond to the theoretical prediction of the angular dependence of the peak intensities in accordance with the physical model shown in Figure 3(a). The angular dependence of the intensity of the Al 2p peak (Figure 2(a)) matches that for the O 1s peak at 531.4 eV (Figure 2(c)), i.e., they are located in the same space region. Their binding energy and composition (Al2O3 6 0.25) are consistent with alumina. The angular dependence of As-bulk and elemental arsenic was reproduced with great precision by treating them as such, with the elemental As located at the interface. The amount of elemental As corresponds to slightly over one monolayer. The dependence for C 1s and N 1s is shown in Figure 2(b). According to its behavior, the C 1s component is consistent with adventitious carbon located at the top surface.33 The amount of spurious surface carbon is ˚ , slightly above 1 ML if the atomic density equivalent to 2.6 A of graphite is employed. The dependence of the N 1s peak area at 397 eV (Figure 2(b)) is compatible with the behavior of the Ti 3p peak area at 34.6 eV (Figure 2(d)); they form stoichiometric TiN. The angular dependence of the Ti 3p and N 1s peaks is consistent with a location on top of the dielectric. Figure 2(e) shows the take-off angle dependence of the Ga-bulk and Ga3þ peaks. Although not as closely as other components, the Ga take-off angle behavior was reproduced robustly enough to conclude that the gallium oxide is located at the oxide/semiconductor interface contributing roughly 0.35 ML. Figure 2(f) shows the take-off angle dependence of the In 3d5/2 peak area for substrate indium (444.4 eV) and

TABLE I. Fitting parameters for the As 3d, Ga 3d, In 3d, Al 2p, Ti 3p, and N 1s core level spectra. All energies in eV. Core level As 3d As 3d Ga 3d Ga 3d In 4d In 3d5/2 In 3d5/2 In 3d5/2 Al 2 p Ti 3 p Ti 3 p Ti 3 p N 1s O 1s

Chemical state

Spin-orbit splitting

Gaussian width

Lorentzian width

Binding energy

As bulk As-As Ga bulk Ga2O3 In bulk In bulk In2O3 In2O5 Al2O3 TiN TiON TiOx TiN Al2O3

0.70 0.70 0.44 0.44 0.84 … … … 0.50 0.14 0.14 0.14 … …

0.60 0.60 0.51 0.72 0.57 0.58 1.1 1.1 1.27 2.44 2.44 2.44 0.94 1.44

0.14 0.14 0.18 0.18 0.14 0.32 0.32 0.32 0.27 0.08 0.08 0.08 0.30 0.25

40.61 41.2 19 20.10 17.1 444.40 445.20 446.10 74.30 34.65 36.72 39.18 397 531.40

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FIG. 2. Take-off angle dependence of the peak areas for the TiN/Al2O3/InGaAs untreated sample. The solid lines correspond to theoretical behavior generated according to the physical model shown in Figure 3(a).

In-O (445.2 eV). As can be seen, the model reproduced the experimental data quite accurately. Table II shows the values of the parameters employed in the analysis, including the cross section and asymmetric fac-

tor employed to calculate the differential cross section34 (considering the effect of the monochromator35) and the effective attenuation length36 for the photoelectrons as they travel through the various layers.

FIG. 3. Multilayer physical model for the TiN/Al2O3/InGaAs samples with different heat treatments.

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TABLE II. Parameters employed in the film structure analysis. ˚ )c Effective attenuation length (A Core level Ga 3d As 3d In 3d5/2 Al 2p Ti 3p N 1s O 1s C 1s

Asymmetry factor(b)a

Total cross section (r)a

1.00 1.05 1.20 0.95 1.35 2.00 2.00 2.00

0.015 0.025 0.309 0.007 0.011 0.024 0.040 0.013

4p

dr b dX

0.011 0.019 0.233 0.005 0.007 0.014 0.023 0.008

InGaAs

As-As

Al2O3

TiN

TiO2

C

27.26 26.94 20.46 26.37 27.25 21.68 19.42 23.57

24.62 24.33 18.53 23.82 24.62 19.66 17.63 21.36

31.21 30.84 23.48 30.21 31.15 24.80 22.26 26.93

23.50 23.22 17.65 22.74 23.45 18.63 16.70 20.25

26.47 26.15 19.91 25.62 26.40 20.99 18.83 22.79

35.35 34.92 26.75 34.26 35.15 27.91 25.12 30.24

a

From Ref. 35. From Ref. 34. c From Ref. 36. b

Similar structural analysis was carried out for the rest of the samples. The ARXPS data for the 700 C for the 10 s sample are shown in Figure 4, and the corresponding take-off angle dependence in Figure 5. The lines are the theoretical prediction in accordance to the physical model shown in Figure 3(c). A HRTEM micrograph for the 500 C for 120 s sample is shown in Figure 6. The bright first layer on top of the

crystalline substrate can be associated to the alumina layer. Its thickness, slightly larger than 2 nm, is consistent with the physical model presented in Figure 3(b) (the TiN-TiON layers cannot be resolved probably due to a reaction with the Sn deposited for protection during FIB sample preparation). The uncertainties shown in Figure 3 were inherited from the uncertainties of the area of the peaks. The latter were

FIG. 4. Angle resolved XPS spectra (dots) and fits (lines) for the TiN/Al2O3/InGaAs sample annealed at 700 C/10 s.

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FIG. 5. Take-off angle dependence of the peak areas for the TiN/Al2O3/InGaAs sample annealed at 700 C for 10 s. The solid lines correspond to theoretical behavior generated according to the physical model shown in Figure 3(c).

calculated through the covariant matrix method37 (the covariant method is encompassed in the software employed for peak-fitting16). The uncertainty of the thickness and composition of each layer was done employing the worst-case scenario, in which the uncertainties of the peak areas combine to yield the largest variations from the averaged values, and the uncertainty propagates in the most significant way. The

FIG. 6. Cross section HRTEM micrograph for the TiN/Al2O3/InGaAs sample annealed at 500 C for 120 s. The alumina layer can be clearly distinguished.

uncertainties of the peak areas were added to some peaks and subtracted from others and new self-consistent physical models were created. The uncertainties shown in Figure 3 reflect the largest differences found among the various models created within the range of area values allowed by their uncertainties. The uncertainty for the composition of the alumina is larger than the rest because the O 1s signal at 531.4 eV, associated to oxygen in alumina, also has a contribution from oxygen in surface hydroxyls.38 The center value was calculated differently, by the best fit to the take-off angle dependence shown in Figure 2(c). Its uncertainty was calculated by doubling the error (x2 ) to the best fit. The titanium layer is constituted by TiN and TiON at different percentages depending of the annealing temperature, and is rich in anions for all the three samples. The angular dependence of the Ti 3p and N 1s peaks is consistent with a location on top of the dielectric for all samples. The As0 remained roughly constant as well as the high-k dielectric. The spurious carbon layer is larger for the annealed samples. A comparison of some of the components for the different sample treatments is shown in Figure 7. As a consequence of annealing at 500 C, there is an increase in the In 3d5/2 peak at 445.2 eV associated to In3þ (Figure 7(a)). A peak associated with In5þ (445.9 eV) appears for the sample treated at 700 C. In accordance with the changes observed in the In 3d5/2 spectra, the In 4d region shows an increment in the peak associated with In3þ (at 17.8 eV) and the

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FIG. 7. Comparison of the core level XPS spectra of (a) In 3d5/2, (b) Ga 3 d, In 4d, (c) As 3d, Ti 3 p, and (d) Al 2 p under the different heat treatments. The intensities of the signals from the substrate (In, As, and Ga in InGaAs) are about the same for all three samples, slightly larger for the 500 C/120 s sample because the dielectric layer is thinner (see Figure 3). The In 3d5/2 spectra clearly show the growth of the In3þ component with annealing and the appearance of a component associated with In5þ at 700 C. The rest of the peaks show very little changes suggesting that the structure is stable. There is no chemical shift observed in the Al 2 p signal.

appearance of a component at 18.4 eV associated with In5þ for the sample treated at 700 C (Figure 7(b)). Note that both the In 3d5/2 and In 4d spectra exhibit a contribution associated with In-O bonds that increase with annealing. The Ga 3d, As 3d, and In 3d signals from the substrate remain approximately constant. Because the XPS signal does not show overlapping with other peaks, the In 3d5/2 core level was employed for the structural analysis of the films. Figure 7(c) exhibits changes in the Ti 3p region related to the relative concentrations for the TiN, TiON, and TiOx components. In contrast, the elemental arsenic remains stable under annealing (Figure 7(c)). In the same way, the Al 2p spectra remain stable (Figure 7(d)). The shape of the O 1s XPS spectra (not shown) varies for the samples treated at 500 C/120 s and 700 C/10 s, reflecting the changes in the Ti layer. IV. DISCUSSION A. Indium diffusion

For the unannealed alumina sample, the analysis of the take-off angle dependence of the In3þ component indicates that it is located at the oxide/semiconductor interface. For the heat treated samples, the analysis shows significant changes in the distribution of indium in In-O bonds (In3þ and In5þ). Figure 8 shows the take-off angle dependence of the In3þ peaks area for the (a) unannealed and (b) heat treated at 700 C for 10 s. It also shows the predicted behavior generated under various scenarios for the distribution of indium in In-O bonds. As expected for the unannealed sample, the scenario that closely reproduces the In3þ take-off angle dependence corresponds to a location at the oxide/semiconductor interface. The contribution of this component is roughly 0.15 ML. However, for the heat treated samples, the angular dependence clearly suggests a different location. In the case of the sample treated at 700 C for 10 s, it is clear that the experimental data are not at all consistent with the scenario in which the indium in In-O

bonds is located at the oxide/semiconductor interface (compare the experimental data, points, with curve 1 in Figure 8(b)). The location at which the model accurately reproduces the experimental data for indium is that in which it is distributed all the way into the Ti layers (curve 2 in Figure 8(b)). According to this analysis, the amount of indium diffused to the metallic layer is equivalent to 0.16 ML for the sample treated at 500 C for 120 s and 0.73 ML for the sample treated at 700 C for 10 s. The latter considered the contribution of both oxidation states of the indium (In3þ and In 5þ) since their take-off angular dependence is similar to each other, suggesting that they share the same depth distribution. This reveals the diffusion of indium atoms through the alumina layer from the oxide/semiconductor interface to the metallic layer. The excess of anions in the titanium layer (mentioned above) suggests that it can offer pinning sites for the arriving indium atoms. This is compatible to the oxidized states of the diffused In (In3þ and In5þ).39 Figure 8(c) shows the take-off angle dependence of the peak intensity of Ga 3d in Ga-O bonds (Ga3þ) for both the unannealed and heat treated at 700 C samples. It also shows lines for a scenario for each sample in which the Ga is located in the Ti layers. The lack of compatibility between the experimental data and the theoretical prediction under this scenario shows that Ga is not diffusing into the Ti layer as in the case of indium. Another argument against Ga diffusion is that the intensity of the Ga 3d peak associated to Ga3þ is about the same for all three samples. The diffusion of gallium into a shallower location would have significantly increased the peak intensity for the annealed samples, as in the case if indium. (compare the scale of Figures 8(a) and 8(b)). This is in accordance with the report of Suh et al.,12 which shows energy dispersive spectroscopy data suggesting that the diffusion of Ga in TiN/HfO2/ InGaAs structures is prevented by the addition of an interfacial alumina layer.

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FIG. 8. The experimental take-off angle dependence of the In 3d5/2 and Ga 3d peak areas associated with In-O and Ga-O bonds (symbols) are compared with the theoretical behavior (lines) under different scenarios of the distribution of Inþ and Gaþ. (a) For the unannealed TiN/Al2O3/InGaAs sample, the scenario corresponding to Inþ at the interface clearly reproduced the experimental behavior. (b) However, when the TiN/Al2O3/InGaAs sample is heat treated the distribution of the Inþ that best reproduces the experimental data is that in which it is located at the metallic layer. (c) The peak intensity and take-off angle dependence of the Ga3þ component is roughly the same for all three samples. Their behavior is incompatible with diffusion into the TiN layer or into the alumina layer. This is patent by comparing the experimental data (dots) with the expected theoretical dependence assuming that the atoms are located in the Ti layer (lines).

B. Calculation of the activation energy for the diffusion of In

The assessment of the Arrhenius activation energy of the diffusion in the dielectric is of technological importance and could provide a clue about the transport mechanism. By considering that the mechanisms governing the diffusion of In is the same at both annealing temperatures (500 C and

J. Appl. Phys. 112, 053527 (2012)

700 C), it is possible to obtain an approximate value of the transport activation energy. To calculate the flux, it was assumed that In pins when it reaches the Ti layer, becoming immobile. Therefore, the concentration of mobile indium in the Ti layer is zero, so the gradient of the In concentration in the dielectric is simply C=d. C is the concentration of free (mobile) indium at the dielectric/substrate interface and d is the thickness of the dielectric layer. Using Fick’s law and neglecting transient effects, the flux J is equal to DC/d. Both D and C depend on the temperature and an activation energy could be associated to each factor: D ¼ D0 expðEA =kTÞand C ¼ C0 expðEC =kTÞ, where EA is the activation energy for the transport in the dielectric, EC is the activation energy governing the concentration of mobile indium at the interface, k is the Boltzmann constant, and T the annealing temperature. The total activation energy, ET¼ EC þ EA , that quantitatively describes the difference in mass transport between both temperatures (500 and 700 C) is 1.29 eV. This was calculated from the ratio of the experimentally determined fluxes at both temperatures for each type of sample (see Sec. IV A). The concentration of mobile In at the interface is affected by two thermally activated processes, the formation of mobile indium in the substrate (with a corresponding activation energy EG ) and its transport inside the substrate to the interface (with a corresponding activation energy ES ). Therefore, EC ¼ EG þ ES . These last two energies can be determined more reliably than those involving the transport through alumina.40 Within the framework of DFT,23 the calculations of formation and activation energies, as implemented via VASP,24,25 were systematically carried out as hereby described. The study started by first considering a perfect supercell of 54 atoms modeling the bulk substrate with periodic boundary conditions. The cell was fully relaxed to minimize its interaction forces and total energies as well as to optimize its shape. The exchange and correlation energies were assessed using GGA in the form of PW9126 coupling with the PAW pseudopotentials27 with a cutoff energy of 350 eV. The Brillouin zone integrations were performed using a Monkhorst-Pack mesh28 with 5000 k-points per reciprocal atom. The full relaxations were realized by the Methfessel-Paxton smearing method of order one followed by a final self-consistent static calculation with the tetrahedron smearing method using Blochl corrections.30 The relaxed system was then perturbed so that one single atom (In or Ga) leaves its equilibrium lattice site to a nearest interstitial position, forming at the same time both

TABLE III. Energy to generate an interstitial In and Ga from a lattice position, leaving behind a vacancy in InxGa1-xAs. ESC-D is the total free energy of the supercell with one defect, ESC is the total free energy of the perfect supercell, ED is the free energy of a single defect atom within a box, and EG is the formation energy. Impurity (tetra) In Ga

ESC-D (eV)

ESC (eV)

ED (eV)

EG. (eV)

212.720607 212.345230

212.99098 212.99098

0.16997896 0.203546

0.4403 0.8493

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TABLE IV. Activation energies for mobile impurities in InxGa1-xAs; where Einit and ESaddle are the total free energies of the system at the initial and saddle states, respectively. Mechanism

Impurity (tetra)

Einit (eV)

ESaddle (eV)

ES (eV)

Interstitial

In Ga In Ga

202.25911 204.35976 200.56673 199.78123

202.04056 204.050235 197.76109 197.80964

0.21855 0.309525 2.80564 1.97159

Vacancy

vacancy and interstitial defects. The pre-analysis, using the 41 AFLOW package, indicated the tetrahedron as the largest interstitial site within the substrate. Total energy of the newly created defect system was then evaluated by relaxing the system using the same configurations as above. The formation energy was calculated by subtracting the energy of the perfect supercell and of the defect alone from that of the supercell with defects:42 EG ¼ ESCD ESC ED . The energy of a single In (Ga) interstitial defect was calculated using the common atom-in-a-box method; it was assumed that the energy of a single vacancy defect is zero as this would be the result of empty-box simulation. The calculation results are shown in Table III. It can be seen that the formation energy of indium is almost a half of that of gallium, indicating that indium defects can be generated much easier than gallium defects inside the substrate. The mobility of generated vacancy and interstitial defects were then studied by carrying out the calculations of activation energies. In the current work, this task was fulfilled by the so-called nudged elastic band (NEB) method. The NEB is a method for finding minimum energy paths (MEP) between known initial and final states; along the reaction path lays a saddle point at which the reaction energy is highest. Within the scope of this study, the initial and final states are two nearest interstitial positions (e.g., A-site and B-site) and the reaction path is the diffusion path along which impurity atom moves from interstitial A to interstitial B. The activation energy is defined as the energy of the saddle point, i.e., the highest energy along MEP. Here, the applied NEB code, which was well integrated into VASP, was implemented by J onsson’s and Henkelman’s groups.43–46 The code works by optimizing along the diffusion path a number of intermediate “images,” which are linearly interpolated between A-site and B-site as a guess for MEP. Each image finds its position with balancing force perpendicular to the band while maintaining equal spacing to neighboring images. This constrained optimization is done by adding artificial spring forces between images to keep them spaced along the path. The activation energies for the substrate were calculated using a 55-atom (53-atom) supercell for interstitial (vacancy) diffusion; the results of the calculation are shown in Table IV. TABLE V. Activation energies of mobile impurities in alumina. Mechanism

Impurity (tetra)

Interstitial

In Ga As

Einit (eV)

ESaddle (eV)

EID (eV)

593.02679 653.97138 595.89643

580.32935 640.05 581.47231

12.69744 13.92138 14.42412

FIG. 9. Electron localization functions and charge densities of interstitial arsenic vs. interstitial indium within the alumina layer. Arsernic shows four strong bonds versus two bonds of indium.

According to the data listed in Table IV, interstitial impurities are much more mobile than vacancies within the substrate. The mobility of interstitial can also be signified by its dominant available sites as compared to vacancy sites, suggesting an interstitial diffusion mechanism inside the bulk substrate. From the DFT calculations, a possible explanation of why indium diffuses, but not gallium, is the availability of mobile indium in the substrate surface. Although seemingly counterintuitive since indium is a larger atom, the interstitial diffusion activation energy is larger for gallium (0.31 eV vs 0.22 eV for In). In addition, the energy for the formation of interstitial is also larger for gallium (0.85 eV vs 0.44 eV for In). The relative Arrhenius exponential factor is 0.002 smaller for Ga at 700 C (at lower temperatures, the relative Arrhenius factor is even larger). This would make the transport of gallium undetectable for many techniques, including XPS. The specific transport mechanism of indium in alumina is unknown. However, by combining the activation energies for the formation of a mobile indium atom (0.44 eV) and its diffusion inside the substrate (0.22 eV) with the experimentally found total activation energy (1.29 eV), it can be stated that the activation energy is approximately EA ¼ 0:63EV ð¼ 1:29EV 0:22EV 0:44EVÞ. An effort was made to study the mobility of indium and gallium within bulk alumina using the NEB method. An 80-atom supercell was employed and the largest interstitial, estimated by the AFLOW code, is octahedron. It was assumed that there is no ionic defect and the diffusion occurred as an electric-neutral impurity (In or Ga) transporting from one interstitial to another. The calculated activation energies for the bulk alumina using NEB are shown in Table V. From Table V, diffusion of electric-neutral impurities through bulk alumina can be discarded since the calculations indicate a much larger value (12.69 eV) than the estimated value of EA (0.63 eV). Even though, the calculations did

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interestingly point out the diffusing dominance of the largest atom In over the smallest atom As (and the in-between Ga) within the oxide layer, as reasonably explained by bonding strength through the electronic localization function (ELF) and charge density analysis (see Figure 9). From the results in Ref. 40, grain-boundary transport can also be discarded. Other unexplored possibility is transport through no compact (porous) alumina. V. CONCLUSIONS

The structure of TiN/Al2O3 nanofilms on InGaAs was determined in detail employing high resolution ARXPS. This allowed a quantitative determination of the mass transport phenomena caused by annealing. It was found that the indium diffuses through the dielectric layer and pins at the metallic layer. The activation energy for the transport of indium in alumina was assessed. In contrast, no observation of As or Ga diffusion through the dielectric was made, which is consistent with the DFT calculations of the activation energy for the availability of mobile atoms at the interface. The dielectric layer remained stable with the thermal treatments, as well as the metallic As layer located at the interface. ACKNOWLEDGMENTS

This work was supported in part by CONACyT Project CB-2007-01#80285 and by TAMU-CONACyT Projects 2008-031 and 2011-026. The technical support of Alfredo Mu~ noz, Oscar Solıs, Carlos Ornelas, and Cesar Leyva for the preparation and measurement of the TEM samples is greatly appreciated. R. A. and T. D. would like to acknowledge the Texas A&M Supercomputing Facility and the Texas Advanced Computing Center for the computational resources provided to perform the DFT calculations. 1

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