Surface-directed spinodal decomposition in the pseudobinary alloy (HfO_2)_x(SiO_2)_{1-x}
J. Liu, X. Wu, W. N. Lennard, D. Landheer, M. W. C. Dharma-Wardana
aa r X i v : . [ c ond - m a t . m t r l - s c i ] S e p Surface-directed spinodal decomposition in the pseudobinaryalloy (HfO ) x (SiO ) − x J. Liu, X. Wu, W. N. Lennard, D. Landheer, and M. W. C. Dharma-Wardana Department of Physics and Astronomy,University of Western Ontario, London, Ontario, Canada N6A 3K7 Institute for Microstructural Sciences,National Research Council of Canada,Ottawa, Ontario, Canada K1A 0R6 (Dated: November 12, 2018)
Abstract
Hf silicate films (HfO ) . (SiO ) . with thicknesses in the range 4-20 nm were grown on siliconsubstrate by atomic layer deposition at 350 ◦ C. Hf distributions in as-grown and 800 ◦ C annealedfilms were investigated by high resolution transmission electron microscopy (HRTEM), angle-resolved x-ray photoelectron spectroscopy (ARXPS) and medium energy ion scattering (MEIS).HRTEM images show a layered structure in films thinner than 8 nm. The ARXPS data also re-veal a non-uniform distribution of Hf throughout the film depth. Diffusion of SiO to the filmsurface after a longer time anneal was observed by MEIS. All these observations provide evidencefor surface-directed spinodal decomposition in the pseudobinary (HfO ) x (SiO ) − x alloy system. PACS numbers: 68.37.Og, 64.75.St, 05.70.Fh . INTRODUCTION When an initially homogeneous binary mixture is rapidly quenched into an unstable statebelow the critical temperature, phase separation occurs via diffusion which results in a com-position fluctuation throughout the system. In the bulk mixture where the interfacial andelastic energies can be neglected, the composition fluctuation results in a random isotropicmicrostructure comprised of phase regions enriched in either component.[1, 2] The single-phase domains then grow with time corresponding to the coarsening of the phase separatedstructure.[3] This phenomenon has been referred to as spinodal decomposition (SD). In thinfilms where the translational and rotational symmetries are broken due to the presence ofinterfaces or free surfaces, spinodal decomposition may interact with wetting phenomena re-sulting in a very different structure at the film boundaries compared to the bulk behaviour,which has been recognized as surface-directed spinodal decomposition (SDSD).[4–8] Exper-iments [4–6] and simulations [7, 8] have shown that in SDSD, a composition wave normalto the film surface forms at the surface due to the preferential attraction of the surfaceto one of the two components. This wave then propagates into the film bulk and decaysbecause of thermal noise.[9] Most experimental studies in SDSD have been carried out inpolymer mixtures [4–6] where the associated phase diagrams can be tailored and a smallself-diffusion coefficient slows the SD dynamics. While it is predicted that SD could occurin any two-component system whose phase diagram shows a miscibility gap, such as theZrO -SiO , HfO -SiO , La O -SiO or Y O -SiO systems,[10] observations of SDSD in thinsolid films have not yet been reported by other groups.As the size of complementary metal oxide semiconductor (CMOS) transistors rapidlyshrinks, the thickness of the traditional gate dielectrics, i.e., SiO and SiO x N y , enters into asub-nanometer regime.[11] In this thickness range, the increase of direct tunneling currentthrough the gate oxide raises significant power consumption and device reliability issues.In order to reduce the gate leakage current, materials (so called high- κ ) with dielectricconstants larger than SiO have been widely investigated so that a thick dielectric layercould be used as a gate insulator to improve transistor performance.[12, 13] Pseudobinaryalloys (ZrO ) x (SiO ) − x and especially (HfO ) x (SiO ) − x , have been considered as the mostpromising candidates to replace SiO and SiO x N y in CMOS technology due to their thermalstability on Si and moderately high dielectric constants.[14] Amorphous thin films are suit-2ble for CMOS transistors since grain boundaries in polycrystalline structures can introduceconducting paths.[15] However, phase separation has been reported in (ZrO ) x (SiO ) − x and(HfO ) x (SiO ) − x systems with x = 0.15 − or HfO .[16, 17] Kim and McIntyre [10] calcu-lated the metastable extensions of the miscibility gap and spinodal for the ZrO -SiO systembased on available phase diagrams and predicted that, upon rapid thermal annealing at con-ventional device processing temperatures, the (ZrO ) x (SiO ) − x system with a compositionin the spinodal (x=0.1 − ) x (SiO ) − x film/Si substrate interface on SD and predicted a composition wave nor-mal to the substrate surface which decays when propagating into the bulk of the film. Itis expected that the (HfO ) x (SiO ) − x system would experience the same phase separationduring annealing due to the similarity of the chemical properties of Hf and Zr silicates.Previously, we reported cross-sectional high resolution transmission electron microscopy(HRTEM) and high angle annular dark field scanning transmission electron microscopy(HAADF-STEM) images that showed SDSD in (HfO ) . (SiO ) . films which were grownby atomic layer deposition (ALD) at 350 ◦ C and annealed at 800 ◦ C.[19] Here we present moreexperimental evidence of SDSD in these films, i.e., the line intensity profiles extracted fromthe cross-sectional HRTEM images, the angle-resolved x-ray photoelectron spectroscopy(ARXPS) Hf 4f peaks, medium energy ion scattering (MEIS) measurements and plan-viewHRTEM images that show a layered structure for the (HfO ) . (SiO ) . films and thegrowth of the composition wave during a longer time annealing. II. EXPERIMENTS (HfO ) . (SiO ) . thin films were grown on p -type Si(100) substrates by ALD using theprecursors tetrakis(diethylamido)hafnium and tris(2-methyl-2-butoxy)silanol. The detailedgrowth procedure has been described previously.[18] ALD utilizes the self-limiting reactionmechanism between gaseous precursors and the surface species to produce a thin film oneatomic layer at a time.[20] During a growth cycle, each precursor was introduced separatelyinto the deposition chamber. Alternate precursor pulses were separated by an inert gas purgestep. The precursor pulse cycles were repeated until the desired film thickness was achieved.3rior to deposition, the substrate was heated to 500 ◦ C for 300 s in an O environmentto oxidize the H-terminated surface. In situ x-ray photoelectron spectroscopy (XPS) datashowed that the oxidation process resulted in a < ◦ C.An ex situ rapid thermal anneal (RTA) was subsequently performed in N at 800 ◦ C for 6s. In order to investigate the Hf depth profiles in both the as-grown and annealed films, h i cross-sectional transmission electron microscope (TEM) samples were prepared usingstandard dimpling and ion milling procedures and subsequently characterized by HRTEMand HAADF-STEM in a JEOL JEM-2100F TEM operating at 200 kV. The HRTEM andHAADF-STEM images are referred to as bright field (BF) and dark field (DF) images,respectively. The film composition variation with depth was also investigated by ARXPSusing monochromatic Al K α x rays. The MEIS technique was also used to study Hf profilesin the as-grown and annealed thin films. MEIS experiments were performed using incident95 keV hydrogen ions wherein a double alignment (channeling/blocking) geometry ( h i in and h i out ) was employed to collect the scattered ions in a two-dimensional detector. Theequipment description and experimental setup are described in detail in Kim et al .[21] III. RESULTS AND DISCUSSION
Figure 1(a) shows the BF image of a 5 nm as-grown film. The darker area near thesurface indicates a region of higher Hf concentration relative to the brighter area close tothe substrate. The upper inset of Fig. 1(a) shows the DF image of the 5 nm film. Thecontrast in the DF image is reversed relative to the BF image such that the DF image ismore sensitive to the atomic number of the constituent atoms. Both images confirm theHf-rich top region and the Hf-deficient (i.e., Si-rich) bottom region of the film. The lowerinset of Fig. 1(a) shows the line intensity profile integrated over the width of the rectangleshown in the BF image. This profile represents the Hf distribution in the direction normalto the substrate surface. A lower intensity region corresponds to a higher Hf concentration.The line intensity profile clearly shows a wave-like Hf distribution throughout the film. The5 nm film separates into two layers with the layer closer to the substrate Si-rich and thelayer closer to the surface Hf-rich. The TEM images of thinner as-grown films (4 nm) showa similar structure, see Fig. 1(b). 4
IG. 1: BF images of as-grown films: (a) 5 nm; (b) 4 nm; (c) 6.4 nm; (d) 12 nm. The upper insetsshow the corresponding DF images and the lower insets show the line intensity profiles integratedover the width of rectangles in the BF images.
Figure 1(c) shows the BF and DF images and the line intensity profile of a 6.4 nm as-grown film. The 6.4 nm as-grown film is comprised of four layers starting from the substrate:Si-rich, Hf-rich, Si-rich and Hf-rich layers. The line intensity profile for this film [Fig. 1(c),lower inset] shows that the Hf-rich layer closer to the substrate has a lower Hf concentrationthan the Hf-rich layer closer to the film surface. The Hf concentration difference in thesetwo layers cannot be resolved in the DF image [Fig. 1(c), upper inset].5s the film thickness increases to 12 nm, the layered structure can hardly be identified inthe BF image [Fig. 1(d)]. The line intensity profile [Fig. 1(d), lower inset] shows that thereare Hf-rich layers close to both the surface and interface. The DF image of this film [Fig.1(d), upper inset] shows that there is a Si-rich layer on the substrate. This layer is followedby a Hf-rich layer. In the center of the film, Hf-rich clusters are mixed with Si-rich clusters.The distances of the centers of the first Hf-rich layers from the substrates for the 4 nm, 5nm, 6.4 nm and 12 nm films are 2.8, 3.5, 1.7 and 1.4 nm, respectively. It can be concludedthat as the film thickens beyond 5 nm in the film deposition process, some of the Hf atomsin the Hf-rich layer closer to the film surface diffuse towards the substrate. As alreadyspecified, the interface Si thermal oxide is < since its thickness is toolarge, i.e., significantly > θ ,of 75 ◦ and 45 ◦ for the 5 nm film before and after RTA. The Si 2p / peak from the substrateat 99.3 eV is used as a reference. The binding energies and intensities of the Si 2p peaksfrom the film for both photoelectron takeoff angles barely changed before and after RTA[Fig. 3(a)]. The BE of the Hf 4f / peak for the as-grown film shifts to higher energy by0.27 eV as θ increases from 45 ◦ to 75 ◦ , indicating a higher Si concentration in the film layercloser to the substrate since the ARXPS signal is more surface sensitive at lower θ anda higher Hf concentration in Hf silicate films results in a shift of BE to lower energy.[22]This observation is in accord with the HRTEM images of Fig. 1(a). The intensity of theHf 4f peak at θ = 45 ◦ decreases after RTA, suggesting a diffusion of Hf atoms towards thesubstrate which results in an increase of Hf concentration in the film layer closer to thesubstrate, and therefore a shift (0.14 eV) of the Hf 4f peak to lower BE at θ = 75 ◦ afterRTA. The area of the O 1s peak corresponding to the Si − O − Hf bond component [Fig. 3(c),6
IG. 2: BF images of (a) 5 nm; (b) 6.4 nm; (c) 8 nm and (d) 12 nm films after RTA. The upperinsets show the corresponding DF images and the lower insets show the line intensity profilesintegrated over the width of rectangles in the BF images. as-grown 45 ◦ ] also decreases after RTA, which is in agreement with the observed decrease ofthe Hf 4f peak intensity at θ = 45 ◦ after RTA.Figure 2(b) shows the BF and DF images and the line intensity profile for the 6.4 nmfilm after RTA. Comparing Fig. 2(b) to Fig. 1(c), it can be concluded that after RTA, someof the Hf atoms in the Hf-rich layer closer to the film surface diffuse to the Hf-rich layer7
06 104 102 100 as-grown 45 RTA 45 as-grown 75 RTA 75
Binding Energy (eV) I n t en s i t y ( a r b . un i t s ) (a) 22 21 20 19 18 17Hf 4f (b)Hf 4f
536 534 532 530(c)Si-O-C Si-O-SiSi-O-Hf
FIG. 3: (Color online) ARXPS peaks for the 5 nm film before and after RTA at θ = 45 ◦ and 75 ◦ :(a) Si 2p; (b) Hf 4f; (c) O 1s. closer to the substrate and the distance between the first Hf-rich layer and the substratedecreases. After RTA, the 6.4 nm film separates into three layers: a Si-rich layer sandwichedbetween two Hf-rich layers. It is believed that the 0.5 nm thick interface layer in Fig. 2(b)is Si thermal oxide formed during the substrate oxidation process before film deposition.Figures 2(c) shows the BF and DF images and the corresponding line intensity profilefor a film after RTA. This film is 7 nm thick after RTA − − and it consists of four layers starting from the substrate: Si-rich, Hf-rich,Si-rich and Hf-rich layers.The layered structure can hardly be identified in the BF image of the 12 nm film afterRTA [Fig. 2(d)]. The line intensity profile of this film [Fig. 2(d), lower inset] shows that theHf concentration near the surface and interface is slightly higher than that in the film. TheDF image of this film [Fig. 2(d), upper inset] shows that there is a Si-rich layer close to thesubstrate, which is followed by a Hf-rich layer. Above these two layers, Hf-rich domains aremixed with Si-rich domains.The above shown TEM images strongly suggest that the structure of these(HfO ) . (SiO ) . films is caused by SDSD. A composition wave normal to the substratesurface is observed. If the composition wavelength, λ C , is defined as the distance betweenthe centers of two successive Hf-rich layers, then λ C measured from the TEM images [Figs.2(b) and 2(c)] is ∼ λ C ), a layered structureis observed via TEM throughout the entire film: the surface layer is Hf rich and the layerclosest to the interface Si oxide can be Si rich or Hf rich depending on the film thickness.8f the film thickness is λ C or 2 λ C , the layer closest to the interface is Si rich. If the filmthickness is 1.5 λ C , the layer closest to the interface is Hf rich. This result is rather sur-prising because the (HfO ) . (SiO ) . films were grown on a very thin layer of Si thermaloxide. The Si-rich component in these films should have a lower interface energy with theinterfacial Si thermal oxide layer. Therefore, it was to be expected that the film layer closestto the interface should always be a Si-rich layer. As the film thickens to > λ C , a Si-richlayer followed by a Hf-rich layer is observed at the film/Si interface [Fig. 2(d)] and there isno continuous Hf-rich layer in the center of the film, indicating a tendency for decay of thecomposition wave.To further study the effect of film thickness on the film structure, dilute HF (0.4%) wasused to etch back the 6.4 and 12 nm films. Before etching, the (HfO ) . (SiO ) . filmswere subjected to the usual RTA process to reduce the etching rate [23] and to achieve thelayered structure shown in Fig. 2(b) for the 6.4 nm film. After etching, the RTA step wasrepeated. Spectroscopic ellipsometry was used to monitor the etching rate, (i.e., the filmthickness was measured after every 4 s etch). For the 6.4 nm film, XPS was also used tomeasure film thickness [24] before and after etching.Figure 4(a) shows the BF and DF images and the line intensity profile for the 6.4 nmfilm after RTA, HF etch and RTA. A layer of 2 nm film was removed after the HF etch, i.e.,the top Hf-rich layer in Fig. 2(b) was removed. The Hf-rich layer closest to the substratein Fig. 2(b) has diffused to the top of the film after the HF etch and following the secondRTA, resulting in a structure similar to that in Fig. 2(a), which corresponds to a 5 nm film(annealed) on a Si substrate. The thickness of the film after RTA shown in Fig. 4(a) is 1 nmgreater than expected after HF etching, which can likely be explained by oxidation of theSi substrate during the annealing process via water molecules absorbed in the film duringthe HF etching process.Figure 4(b) shows the BF image and the corresponding line intensity profile for the 12nm film after RTA, HF etch (removing ∼ formed after HF etching and the second RTA. The lineintensity profile shown in the lower inset of Fig. 4(b) reveals a wave-like distribution of Hfatoms in the direction perpendicular to the substrate surface. The predominantly layeredstructure, which was not observed for the 12 nm film [Figs. 1(d) and 2(d)], appears whenthe film thickness is reduced to a value in the region of < ∼ λ C .9 IG. 4: BF images of (a) 6.4 nm, and (b) 12 nm films after RTA, HF etch and RTA. The upperinset in (a) shows the corresponding DF image and the lower insets in (a) and (b) show the lineintensity profiles integrated over the width of rectangles in the BF images.
According to the theory and simulation of SDSD, the single-phase domain, and thereforethe composition wavelength in thin films, will increase as the annealing time increases, whichcorresponds to a coarsening of the phase separated structures.[7, 10] In order to search forthis phenomenon in Hf silicate films, longer time anneals were performed for the 6.4 nm and12 nm films. Figure 5(a) shows the BF and DF images and the line intensity profile for the6.4 nm film after a 600 s anneal at 800 ◦ C in N . Only one Hf-rich layer and one Si-rich layerare observed indicating a growth of single-phase regions during a longer time anneal. Thethickness of this film has increased by ∼ impurity in N to the interface where oxidation of thesubstrate occurs.[25]The plan-view BF images presented in Figs. 6(a) and 6(b) show the 6.4 nm film afterRTA and 600 s anneal at 800 ◦ C in N , respectively. These images also indicate a growth ofeither the Hf-rich or Si-rich domains (i.e., either the dark or the bright areas) in the planeof the film during a longer time anneal.Figure 7 shows the Hf 4f ARXPS peaks (at θ = 45 ◦ and 75 ◦ ) for the 6.4 nm as-grownfilm, and for the same film after RTA and 600 s anneal at 800 ◦ C in N . For the as-grown10 IG. 5: BF images of (a) 6.4 nm, and (b) 12 nm films after a 600 s anneal at 800 ◦ C in N . Theupper insets show the corresponding DF images and the lower inset in (a) shows the line intensityprofile integrated over the width of rectangle in the BF image. Some of the crystalline HfO regionsare encircled. and RTA films from the surface to 4 nm depth, the 6.4 nm film [Figs. 1(c) and 2(b)] has asimilar structure as the 5 nm film [Figs. 1(a) and 2(a)]: i.e., a Hf-rich layer near the surfacefollowed by a Si-rich layer. The number of photoelectrons that escape from the film decreasesexponentially with depth. The contribution to the XPS peak from the Hf-rich layer closestto the substrate [Figs. 1(c) and 2(b)] is negligible compared with the contribution fromthe layers above. It is therefore not surprising that Hf 4f peaks from the 6.4 nm film havesimilar shifts as those peaks from the 5 nm film when θ changes from 45 ◦ to 75 ◦ before andafter RTA. For the as-grown film, the Hf 4f / peak shifts to higher energy by 0.23 eV as θ increases from 45 ◦ to 75 ◦ . At θ = 75 ◦ , the Hf 4f / peak shifts 0.08 eV to lower energyafter RTA compared with the as-grown film. After a 600 s anneal, the Hf 4f / peaks shiftto a higher BE for both θ = 45 ◦ and 75 ◦ , indicating that the Hf-rich phase in the film aftera longer time anneal has a lower Hf concentration than that in the as-grown film or in the11 IG. 6: Plan-view BF images of the 6.4 nm film after (a) RTA and (b) 600 s anneal at 800 ◦ C inN . film after RTA. However, the Hf 4f / peak after 600 s anneal shifts to higher BE by 0.15eV as θ increases from 45 ◦ to 75 ◦ , still indicating a higher Hf concentration in the film layercloser to the surface, which is in agreement with the TEM image [Fig. 5(a)]. The intensitiesof these Hf peaks cannot be compared directly because they are not aligned to a reference.
22 21 20 19 18 17 as-grown 45 RTA 45 600 s anneal 45 as-grown 75 RTA 75 600 s anneal 75 I n t en s i t y ( a r b . un i t s ) Binding energy (eV)
FIG. 7: (Color online) ARXPS Hf 4f peaks for the 6.4 nm as-grown film, and for the same filmafter RTA and 600 s anneal at 800 ◦ C in N . Figure 5(b) shows the BF and DF images for the 12 nm films after a 600 s anneal at 800 ◦ Cin N . Comparing to the film thickness after RTA [Fig. 2(d)], it can be concluded that a ∼ , i.e., almost all the Si-rich layer close to the substratein Fig. 5(b), has grown during the 600 s anneal. HfO crystallites were observed in thisfilm indicating that nucleation and growth of HfO occurred after spinodal decompositionduring the annealing process. The DF image of this film [Fig. 5(b), upper inset] is similarto Fig. 2(d): there is a Si-rich layer on the substrate with a ∼ crystallites arenot observed for films thinner than 12 nm even after an anneal at 800 ◦ C in N for 600 s,which is not surprising since the onset of crystallization of HfO in Hf silicate films dependson both film composition [26] and thickness.[27]In the nucleation and growth mechanism, for a nucleus to be stable with respect to furthergrowth, it must reach a critical size. Smaller nuclei are unstable and may dissolve becauseof surface energy effects and their large surface to volume ratio.[28] Therefore the nucleationand growth process is suppressed in thinner films and a higher temperature is needed forcrystallization to occur.[27] In contrast, HfO crystallites with dimension of 5 − ◦ C. FIG. 8: BF images of a 20 nm as-grown films. Some of the crystalline HfO regions are encircled. From those cross section TEM images, e.g., Figs. 1, 2, 4 and 5, it seems that the film layerclosest to the surface is always a Hf-rich layer. However, if a Si-rich layer is on the surface,it is difficult to resolve this layer from the glue that is used to prepare the TEM sample. Inorder to examine the film composition as a function of film depth, Hf/(Hf+Si) values wereextracted from ARXPS measurements and the results are presented in Table I for various θ values. The Hf concentration, which is proportional to the Hf/(Hf+Si) ratio, decreasestowards the surface for all films (therefore implying an increase in the Si concentration).Comparing the Hf concentration in the as-grown and annealed films at θ = 10 ◦ , more SiO is observed to diffuse to the film surface during annealing which suggests a wetting of the13lm surface by the SiO -rich component. Previously, simulation results showed that the Si-rich phase contains >
98 mol% SiO in the (ZrO ) x (SiO ) − x system after phase separationduring 900 ◦ C anneals.[10] Assuming that the Si-rich phase in the (HfO ) . (SiO ) . filmsis pure SiO , then the thickness of the surface layer of the films can be estimated. Theescape depth ( λ e ) of Si 2p photoelectrons excited by Al Kα x rays in SiO is 3 nm,[24]which should be a reasonable estimate as well for Hf silicate films. The sampling depth thenvaries from 9 nm (3 λ e ) at θ = 90 ◦ to 1.6 nm at θ = 10 ◦ . Assuming that the film compositiondetermined at θ = 75 ◦ corresponds to the average composition, then the thickness of thesurface SiO layer is estimated to be ∼ − − . TABLE I: Hf concentration extracted from ARXPS peak intensities. θ is the photoelectron takeoffangle. Hf/(Hf+Si)Film thickness θ (nm) Film description 75 ◦ ◦ ◦ MEIS measurements were also performed to study the film composition and the Hf depthprofile for the 6.4 nm film. Figure 9 shows the MEIS spectra for the 6.4 nm as-grown filmand for the same film after RTA and a 600 s anneal at 800 ◦ C in N . The MEIS spectra arealigned to the O edge. As can be seen, the Si edges of the three spectra are also aligned.The Hf edge shifts slightly to lower energy after RTA, indicating a diffusion of the HfO component to the substrate or a diffusion of SiO to the film surface. After a 600 s anneal,the Hf edge shifts to lower energy by 120 eV. If the density of the surface SiO layer isassumed to be 2.2 g/cm , then this energy shift corresponds to a diffusion of 0.35 nm SiO to the film surface during the 600 s anneal process. This result is in good agreement with14he estimate of the surface SiO layer thicknesses from ARXPS data and confirms that thefilm surface is wetted by the SiO layer after anneal. Compared to the as-grown film, the Siand O peaks are obviously wider after a 600 s anneal, which is due to the oxidation of thesubstrate by O impurities in N , as mentioned earlier. The slight increase of the O and Siareas after RTA probably results from the same process. It should be pointed out that theMEIS technique measures absolute areal density (i.e., the product ρ t, ρ is the film densityand t is the film thickness) for the atomic constituents of a film. Therefore, MEIS cannotdetermine the film thickness without a knowledge (or assumption) of the film density. TheMEIS data are unable to resolve the layered structures shown in Figs. 1(c) and 2(b), sincethe ion beam extent in any direction (0.1 − FIG. 9: (Color online) MEIS spectra of the 6.4 nm film: as-grown, after RTA and after 600 sanneal at 800 ◦ C in N . The film compositions (Table I) calculated from the ARXPS peak intensities show thatthe 5 nm as-grown film has the same Hf concentration at θ = 45 ◦ and 75 ◦ . However, Fig. 3(b)shows that the Hf 4f peaks of this film shift to higher energy as θ increases from 45 ◦ to 75 ◦ ,indicating a lower Hf concentration in the film layer closer to the substrate. This apparentdiscrepancy can be explained using a simplified schematic for the Hf concentration gradientacross the film depth as shown in Fig. 10. Layer 1 is SiO and Layer 2 (Hf x Si − x O ) has ahigher Hf concentration than Layer 3 (Hf y Si − y O ), i.e., x > y . The average composition ofLayers 1 and 2 is the same as the composition of Layer 3. When the XPS measurements aretaken at θ = 45 ◦ , most of the signal intensity comes from Layers 1 and 2. As θ increases to75 ◦ , the contribution of photoelectrons excited in Layer 3 increases significantly; thereforethe Hf 4f peak will shift to higher energy since Layer 3 has a lower Hf concentration than15ayer 2. However, the film composition calculated from the XPS peak intensities will notchange since Layer 3 has the average composition of Layer 1 and 2. The layered structureshown in Fig. 10 agrees with the HRTEM image shown in Fig. 1(a). FIG. 10: Schematic showing the layered structure for the 5 nm film.
Using grazing-incidence small angle x-ray scattering (GISAXS), Stemmer et al. [17]observed interference peaks in the horizontal cuts of their two-dimensional GISAXS intensitydistribution, which correspond to a Hf concentration fluctuation in the plane of the film with λ C -values of 5 nm in the 4 nm (HfO ) x (SiO ) − x films ( x = 0.4) after 1000 ◦ C annealing. Thisobservation was confirmed by their plan-view TEM image, which showed interconnected Hf-rich and Si-rich regions. However, these authors did not try to interpret vertical cuts of theirGISAXS data but still concluded that their observations were inconsistent with SDSD. Incontrast, the TEM images reported here always show a layered structure for post-annealedfilms of thickness < -SiO systems. In effect, when the region availablefor phase separation is a 2-dimensional film in the x − y plane with a restricted thickness w in the z direction, the w parameter controls the ensuing structure. This can be understoodby looking at the free-energy of the system which consists of species i = 1 , , · · · with crys-tal structures iν, iµ, · · · . The free energy consists of a configurational energy E ( c ν , c µ , · · · )based on the possible crystal structures c ν , c µ , · · · and an entropy component S ( c ν , c µ , · · · ).Thus the total free energy can be written as F ( c ν , c µ , · · · ) = E ( c ν , c µ , · · · ) − T S ( c ν , c µ , · · · ) , where T is the temperature. The free energy analysis gives the equilibrium state and becomesstrictly valid if the spinodal structures are the ground state of the system. If such structures16esult from a kinetic process (i.e., if they are metastable structures), the free energies must bereplaced by energies corresponding to quasi-stationary states. However, the present analysisis adequate to understand the observed effects.In a thick film containing two species (e.g., SiO and HfO ), the energetically favourabletotal nanostructure is made up of the bulk crystal structures which we denote by c b and c b . Here, if species 1 is HfO , then c b (i.e., the bulk HfO structure of large grains) is themonoclinic structure.[29] If the second material is Si the bulk structure is cubic, while in thecase of SiO we may take it to be the crystalobite structure or some modification thereof,as needed for surface films.[30] We need to consider the situation where both Si atoms andHf atoms may compete for bonding with O atoms. If thin films are formed on a substrate,then we have to deal with possible spinodals based on the bulk structures and the crystalstructures manifested by vanishingly thin films. Let us denote the crystal structures foundin vanishingly thin films by c f and c f . The thinnest HfO films tend to form orthorhombicstructures,[29] while the structure of very thin SiO layers on Si substrates tend to be quasi-crystalline or amorphous modifications of the crystalobite structures.[30]When the thickness w of the film is extremely small, e.g., less than a nanometer, bondsinvolving only a single binary species are possible in the x − y plane but the z directionthickness w would only allow a monolayer or two of a single (binary) species such as HfO .Our experiments show the formation of a Hf-rich surface layer whose structure can be inter-preted starting from an orthorhombic disposition of the Hf-O bonds but taking account oftheir termination at the surface. When the thickness w of the deposited layer is increased,inner layers face competition, forcing them towards the bulk crystal structure c b , which inthis case is monoclinic. A similar competitive process involving the crystal structures ofspecies 2, i.e., SiO , also occurs. Bonds may also be formed between the common element(oxygen) with Hf or Si. However, there is not enough volume in a thin film to achieve thefull configurational entropy of each species by full phase separation. Thus a compromise isachieved by SDSD. This compromise itself depends on the film thickness, partly because thelimiting structures c ib and c if are different in each species. Other factors which may comeinto play are effects associated with crystal growth kinetics (i.e., non-equilibrium effects).However, such effects are, in our view, unimportant in this problem as the effects can beexplained via a model which assumes local thermodynamic equilibrium.The validity of the above picture is evident on a qualitative basis. A more detailed17uantitative evaluation is not considered here since simulation of SiO /HfO structures usingfirst principles density functional methods[30] or tight-binding methods[31] is beyond thescope of the present study. IV. CONCLUSIONS
Surface-directed spinodal decomposition in Hf silicate films during the film growth andannealing process can be envisioned from the above observations. In the as-grown film,there is always a very thin layer of SiO ( ∼ monolayer of SiO ) at the film surface. Beneaththis layer is a Hf-rich layer. When the film thickness is < > λ C , the film separates into three layers after RTA: aSi-rich layer sandwiched between two Hf-rich layers. If the film thickness is ∼ λ C , the filmhas a four-layer structure starting from the substrate surface: Si-rich, Hf-rich, Si-rich andHf-rich. As the thickness increases to > λ C , the film loses its layered structure in the centerof the film. After a longer time anneal, the layered structure coarsens and the compositionwave grows. Crystallization of HfO was observed in a 12 nm film after 600 s anneal at800 ◦ C and in a 20 nm as-grown film, indicating that nucleation and growth of HfO followsspinodal decomposition during the annealing or film deposition process.The configurations in as-grown and annealed (HfO ) . (SiO ) . films are qualitativelyin agreement with the theory of SDSD, i.e., composition waves were observed normal tothe film surface. The observation that the composition of the film layer in contact withthe substrate can be affected by film thickness has never been predicted by any SDSDsimulation. Presumably, theoretical studies of SDSD could be modified to accommodatethese experimental results. At this time, it is difficult to study SDSD in (HfO ) . (SiO ) . films to determine whether the composition wave obeys the growth law, i.e., λ C ∼ t / ,[6]because: (i) TEM is a qualitative technique concerning atomic composition; (ii) SD in oxidesystems is not easily controlled since the process occurs during the film deposition process;(iii) an alternative kinetic process, viz., nucleation and growth, can impede SD during thelate stages of phase separation; and (iv) any O impurity in the annealing N ambient may18lso diffuse through the film and oxidize the substrate. Although GISAXS is a powerfultool to characterize composition fluctuations in thin films,[17, 32] caution has to be takenwhen using this technique to study SDSD in Hf silicate films since HfO crystallizes at arelatively low temperature in thick films, as seen in the 20 nm as-grown film. While SDSDin the (HfO ) . (SiO ) . thin films has been confirmed, the composition range for which(HfO ) x (SiO ) − x films experience SD and the resultant compositions of the phase-separateddomains are still open questions.The present observation of SDSD in (HfO ) x (SiO ) − x films may present significant deviceperformance and reliability challenges for high- κ gate dielectric applications of pseudobinaryalloy systems such as ZrO -SiO , Y O -SiO , La O -SiO , etc.,[10] and have effects on thinfilm applications for any two-component system whose phase diagram shows a miscibilitygap. The ALD growth mechanism for two-component films could also be influenced bySDSD if the film surface is preferentially attracted to one of the two components. Acknowledgments
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