Nanoscale Topography of Thermally-Grown Oxide Films at ...

Journal of The Electrochemical Society, 159 (2) H79-H84 (2012) H790013-4651/2012/159(2)/H79/6/$28.00 © The Electrochemical Society

Nanoscale Topography of Thermally-Grown Oxide Filmsat Right-Angled Convex Corners of SiliconA. Fatih Sarioglu,a,z Mario Kupnik,b Srikant Vaithilingam,a and Butrus T. Khuri-Yakuba

aE. L. Ginzton Laboratory, Center for Nanoscale Science and Engineering, Stanford University,Stanford, California 94305, USAbBrandenburg University of Technology, 03046 Cottbus, Germany

The topography of a thermally grown oxide film at the right-angled convex corner of silicon is investigated. Numerical simulationsand atomic force microscopy are used to examine the top oxide surface as well as the oxide-silicon interface in the vicinity ofthe convex corner of silicon oxidized under different conditions. Our results show that under certain conditions the top surfaceof the grown oxide is not flat, but has nanoscale protrusions close to the convex corner. The effects of oxidation parameters (i.e.,temperature, duration) and high-temperature annealing on the flatness of oxide surface are presented.© 2011 The Electrochemical Society. [DOI: 10.1149/2.005202jes] All rights reserved.

Manuscript submitted September 8, 2011; revised manuscript received October 18, 2011. Published December 16, 2011.

Thermal oxidation of silicon is an indispensable and widely usedprocess in the microfabrication of semiconductor devices. Ther-mally grown oxide films form an excellent interface with siliconsurfaces, can easily be patterned and have ideal electrical and me-chanical properties. As a result, these films are commonly used asmasks, sacrificial layers or insulating layers in the semiconductorindustry.

As device sizes continue to shrink and their geometries becomemore intricate, thermal oxidation of nonplanar silicon structures be-comes increasingly important. Studies on nonplanar oxidation of sil-icon show that the oxide growth rate at highly curved regions (e.g.,sharp corners) is lower than at a planar silicon surface under identicalconditions.1–4 This reduction is attributed to changes in the oxygendiffusion rate and oxidation reaction rate at the interface due to thestress buildup in high curvature areas as a result of volume expansionduring oxide formation. The effect of stress buildup is even more pro-nounced below the oxide glass transition temperature since the stressin the oxide film cannot be relaxed by viscous flow.5–7 This nonuni-form oxidation effect has been utilized to create atomically sharp tipsused in applications such as atomic force microscopy and vacuummicroelectronics.8–10

Nonuniform oxidation at right-angled convex corners of siliconare of particular interest since these are one of the most commongeometries on silicon surfaces patterned by dry etching. Previouswork on nonuniform oxidation of convex corners focuses mainly onthe thinning of oxide films near corners or on the rounding/sharpeningof convex corners due to their impact on device performance (e.g.,subthreshold parasitic current, breakdown voltage).11, 12 The effect ofnonuniform oxidation on the topography of the top oxide surface isanother aspect of practical interest not only for device performance butalso for 3D integration and MEMS fabrication processes that involvedirect wafer bonding.13, 14

In this paper, we investigate the topography of an oxide film ther-mally grown at a right-angled convex corner of silicon by using com-puter simulations and atomic force microscopy. We observe that undercertain conditions the top oxide surface is not flat, but has nanoscaleprotrusions close to the convex corner. We investigate the effects ofoxidation parameters such as temperature and duration on the extentof the protrusion. Finally, the effect of high-temperature annealing onthe oxide film topography at a convex corner is examined. Our resultsshow that the topography variations in an oxide film can be mini-mized by appropriate choice of oxidation parameters and subsequentannealing at higher temperatures.

z E-mail: [email protected]

Simulation

We use the commercially available process simulatorTSUPREM-IV15 to model the thermal oxidation of the right-angledconvex corner of silicon in a wet ambient. The tool is intended forsimulating various microfabrication steps in two-dimensional devicecross-sections, perpendicular to the surface of the silicon wafer. Vari-ous numerical models are included in the tool for thermal oxidation.We use the model VISCOELA,15 which is based on the one describedin detail by Senez et al.16

This model fulfills all the main requirements for calculating thenanoscale topography variations of oxide films at right-angled convexcorners of silicon:

First, the dependency of diffusion and reaction rate as a function ofstress distribution is considered. The stress distribution due to volumeexpansion during oxidation; due to thermal mismatch between mate-rials; due to intrinsic strain and due to surface tension is calculated.

Second, the rheological behavior of oxide is taken into account.This is important since we model over oxidation temperatures rangingfrom 800◦C to 1100◦C, i.e. both below and above the glass transi-tion temperature (960◦C) of silicon dioxide. Up to 800◦C the oxidebehaves as elastic solid. Above 1000◦C the oxide behaves as a vis-cous liquid. Between 800◦C and 1000◦C the oxide experiences bothan elastic deformation and a steady flow process, i.e. a viscoelasticdeformation.17, 18

Third, it features adaptive gridding, which is essential for calcu-lating accurate oxide shapes.

Calculating the protrusion height H (Fig. 1c) is challenging becauseof its small order of magnitude (several tens of nm, as shown below)compared to the required model size itself (several microns). Thekey is to choose the initial grid size accordingly. The initial grid forall simulations performed in this work is the result of several testruns with various mesh sizes. We only observe meshsize-independentresults (i.e., with less than 1% variation) with an initial mesh size ofnot larger than 10 nm. However, TSUPREM-IV can only handle up to40000 nodes. Therefore, we gradually coarsen the mesh at locationsfurther away from the silicon-ambient interface, which results in a gridconfiguration as shown in Fig. 2a. Note that in this work we assumethat the trenches are deep enough that the effect of the right-angledconcave corner at the bottom of the structure can be neglected.

The output of the simulation tool for a given oxidation temperatureand duration is an oxide film cross-section as shown in Fig. 2b. Eventhough, we intentionally present a case with a relatively large protru-sion height H of approximately 30 nm extending over a distance L ofabout 7 μm, the topography variations on the top oxide surface arenot apparent (region 1 in Fig. 2b) when the figure is presented in a 1:1aspect ratio. The well known rounding of the oxide film at the cornerhowever is clearly visible (region 2 in Fig. 2b).

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H80 Journal of The Electrochemical Society, 159 (2) H79-H84 (2012)

Figure 1. Thermal oxidation of silicon convex corner (a) Silicon convex cornerbefore oxidation (b) Silicon convex corner after oxidation (c) Close-up of thetop surface of the grown oxide film showing the protrusion. H and L are definedas the protrusion height and length, respectively.

Figure 2. (a) 2D-grid for modeling the oxidation of a right-angled convexcorner of silicon with highly-nonuniform grid size, which is essential for thiswork. (b) Exemplary result of calculated oxide film topography (cross-section)for thermal oxidation in a wet ambient at 800◦C for 78 hours and 44 min.

In total, we simulate oxidation at four different temperatures(800◦C, 900◦C, 1000◦C, and 1100◦C). The temperature-dependent fit-ting parameter (VC),15 required in the model equation for calculatingthe oxide viscosity, is taken from Sutardja et al.19 For each oxidationtemperature, we simulate 30 different cases with oxide thicknessesranging from 25 nm up to 3 μm. For each case, required oxidationduration is pre-calculated using the well-known Deal-Grove model20

such that the grown oxide films are approximately identical in thick-ness at different oxidation temperatures. Then nodal coordinates atboth the oxide-air and oxide-silicon interfaces are extracted. We plotthese results using different scales in height and position axes to em-phasize small topography variations, both in the top oxide surfaceand in the oxide-silicon interface. Postprocessing these coordinatesallows us to extract the protrusion height H for all cases (oxidationtemperature and thickness).

Experimental

We etch rectangular-shaped test structures (trenches) that are60 μm-deep on a 〈100〉 silicon wafer using optical lithography anddeep reactive ion etching (DRIE). Following an RCA clean, we growoxide on the trenches in an oxidation furnace in a wet ambient atatmospheric pressure. Four samples with identical trench geometriesare oxidized at different temperatures to grow oxide films with differ-ent thicknesses. Table I gives a list of oxidation parameters togetherwith oxide film thickness measurements for these samples. The thick-nesses of the grown oxide films are measured using both spectralreflectometry and ellipsometry.

To investigate the surface profiles of the grown oxide films, weuse atomic force microscopy (AFM).21 AFM can measure the topog-raphy of a sample with sub-angstrom height resolution and nanoscalespatial resolution over tens of micrometers. Because of these capa-bilities, AFM offers several advantages for our particular problemover the other techniques that have been previously used to examineoxide film profiles over similar geometries. For example, in studies us-ing transmission electron microscopy (TEM) to image cross sections,vertical and lateral resolutions are coupled, and, therefore, high ver-tical resolution can only be obtained at high magnifications.1 This isproblematic for our specific purpose, since we are interested in obser-vations of small topographical variations (on the order of nanometers)over relatively large distances (on the order of micrometers). Opti-cal techniques on the other hand are limited by diffraction and lackthe spatial resolution required for this study. Further, silicon oxide istransparent in visible light, and, therefore, it needs to be coated witha reflective film for measurement. This is not preferred because thenon-uniformity of the coating would affect the topography under in-vestigation. Thus, AFM is the best choice for investigating small scaletopography variation in thermally-grown oxide films at right-angledconvex corners of silicon.

We measure the topographies of all samples with a commercialAFM system (Agilent 5500) using identical imaging parameters un-der ambient conditions. The AFM is operated in tapping-mode tominimize the tip/sample damage. We image a 15-μm × 15-μm areaof the top surface that includes the right-angled convex corners. Thetopography data is recorded as a 512 × 512 matrix leading to anapproximately 30 nm spatial resolution.

In our AFM measurements, we pay special attention to choos-ing the scan orientation and direction. First, the slow-axis of the

Table I. Oxidation parameters and thickness measurements forsamples.

Parameter Sample 1 Sample 2 Sample 3 Sample 4

Temperature (◦C) 800 1100 800 1100Time (hh:mm) 03:00 00:03 14:30 00:26Thickness (nm) 98 138 358 404

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Journal of The Electrochemical Society, 159 (2) H79-H84 (2012) H81

Figure 3. (a) Schematic of the AFM imaging procedure showing the scanorientation, (b) Topography image of an oxidized right-angled convex cornerof silicon.

imaging is chosen parallel to the trench edge. This minimizes theeffect of drift on the profile measurements and it is particularly impor-tant when imaging small topographical variations over large distances.Second, the scan direction is chosen such that the topography is onlyrecorded as the tip scans the top surface of the trench towards thetrench edge (Fig. 3a). This minimizes the effect of feedback error onthe measurements and is essential for accurate measurements in thevicinity of abrupt topography changes such as the right-angled convexcorner of silicon.

Recorded topography data are processed to remove artifacts and atrench profile is calculated: First, the effect of the sample tilt on themeasurements is removed using a first-order plane fit algorithm. Todo this, the top surface of the right-angled convex corner of silicon inthe image (excluding the pit) is fit to a plane. Then, by subtracting thisplane from the data, the data is leveled and a corrected image of thetrench is obtained (Fig. 3b). Next, the topography data over 40 adjacentscan lines are averaged, with the goal of reducing the noise due tosurface roughness (improved signal-to-noise ratio). The averagingdoes not affect the oxide topography measurements, because in oursamples the profile does not change along the range of the scan lines.

In order to compare the measurement results with the calculatedprofiles, we shift the AFM data to achieve a common reference forboth data sets: First, the two data sets are aligned in the verticaldirection such that the top surfaces of the trenches are level with eachother. We only consider the data points that are at least 5 μm awayfrom the right-angled convex corner of silicon and match the averageheight of these regions in simulation and AFM data. Second, the datasets are aligned in the lateral direction such that the location of thetopography peaks in the vicinity of the trench edges match. In casethere is no clear peak in the topography (e.g. 400 nm, 1100◦C), the

trench edges in the data sets are used to align the two data sets in thelateral direction.

Following the AFM measurements detailed above, the sampleswere annealed at 1100◦C for 24 hours in inert (Ar) atmosphere. TheAFM measurements are then repeated on the annealed samples to in-vestigate the effect of high-temperature annealing on the oxide surfacetopography. In addition, we analyze the oxide-silicon interface usinganother set of samples which have been prepared together with theoriginal set. The oxide films on these samples are selectively removedusing buffered oxide etch (BOE) with a short over-etching time, beforeidentical AFM measurements are repeated on the exposed interfaceof silicon, i.e., the former oxide to silicon interface.

Results and Discussion

We simulate oxidation of a right-angled convex silicon corner in awet ambient. In our simulations, we focus on oxide films less than 3μm-thick and grown at temperatures between 800◦C and 1100◦C tocover a range of applications from semiconductor devices to MEMSstructures. We calculate the oxide protrusion height, H (Fig. 1c) asa function of oxide film thickness at different temperatures (Fig. 4).Our simulation results indicate that under certain conditions thermallygrown oxide film is not flat and the protrusion can be as high as 30 nm(for 1.6 μm-thick oxide grown at 800◦C). Note that this protrusionis predicted by computer simulations based on the existing oxidationmodels.

The relationship between oxide protrusion height and the oxidefilm thickness is highly nonlinear (Fig. 4). Moreover, the protrusionheight-film thickness relation shows a similar trend at different oxida-tion temperatures of interest (800◦C-1100◦C): During the initial oxidegrowth, the protrusion height increases with the oxide film thickness inan approximately linear fashion. In this regime, the protrusion heightequals to approximately 2% of the grown oxide film thickness irre-spective of the oxidation temperature. Then, a peak protrusion heightis reached and beyond this point, the protrusion height decreases withthe oxide film thickness. Finally above a certain film thickness, theprotrusion in the oxide disappears and the surface becomes flat. Fur-ther oxidation at this point does not create a protrusion but leads toreduction in the flat top surface due to increased rounding at the con-vex corner. This should be taken into account for applications thatrequire direct wafer bonding.

Oxidation temperature is another parameter that affects the extentof protrusions of oxide films. Especially, between 900◦C and 1100◦C,the protrusion properties differ significantly (Fig. 4). The maximumprotrusion height attainable in an oxide film decreases with oxidation

Figure 4. Simulation results of oxide protrusion height, H as a function ofoxide film thickness at different oxidation temperatures that are commonlyused in practice.

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H82 Journal of The Electrochemical Society, 159 (2) H79-H84 (2012)

Figure 5. AFM topography measurements and simulations of silicon convex corners oxidized under four different conditions: (a-c) ∼100 nm-thick oxide grownat 800◦C (d-f) ∼140 nm-thick oxide grown at 1100◦C (g-i) ∼360 nm-thick oxide grown at 800◦C (j-l) ∼400 nm-thick oxide grown at 1100◦C. In all cases, largefigures (a,d,g,j) show data for both oxide surface and the oxide-silicon interface. Smaller figures on the left (b,e,h,k) show the close-ups of the oxide surface.Smaller figures on the right (c,f,i,l) show the close-ups of the oxide-silicon interface.

temperature. In oxide films grown at lower temperatures, the protru-sion height reaches its maximum value at a higher film thickness thanin oxide films grown at higher temperatures. In addition, between900◦C and 1100◦C, the oxide film thickness at which the protrusiondisappears decreases with temperature.

Our simulation results can be explained considering increased vis-cous flow of oxide films at higher oxidation temperatures. For exam-ple, the reduced protrusion height in the oxide films grown at hightemperatures can be attributed to the reconfiguration of viscous ox-ide film to minimize the intrinsic stress due to nonuniform oxidation.Likewise, negligible viscous flow below the oxide glass transition tem-perature (960◦C) leads to similar protrusion properties in the oxidefilms grown at 800◦C and 900◦C.

Using simulations, we also investigate the effect of crystal orien-tation on the surface topography of oxide films and conclude that thechange in protrusion height with the crystal direction is negligible(smaller than 3%) (Results not shown).

To quantitatively validate our simulations results, we experimen-tally investigate the topography of oxide films at right-angled convexcorners using AFM. We compare topography measurements of theoxide surface and oxide-silicon interfaces of four oxidized trenchsamples (Table I) with corresponding simulation data showing thecross sections of right-angled convex corners oxidized under respec-tive conditions for each sample (Fig. 5). Measurement and simulationdata are magnified in the vicinity of the convex corner to emphasizethe nanoscale protrusions in the oxide film and the horns at the silicon

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Journal of The Electrochemical Society, 159 (2) H79-H84 (2012) H83

Figure 6. AFM topography measurements of silicon convex corners oxidized under four different conditions before and after annealing at 1100◦C for 24hours in inert atmosphere. (a) ∼100 nm-thick oxide grown at 800◦C (b) ∼140 nm-thick oxide grown at 1100◦C (c) ∼360 nm-thick oxide grown at 800◦C(d) ∼400 nm-thick oxide grown at 1100◦C.

interface. The AFM measurement and simulation data are overlaidusing procedures described in Section 3. Slanted sidewalls in the to-pography measurements are AFM imaging artifact that occurs due totip-shape convolution. This artifact however does not create a prob-lem for the purposes of observing relatively smooth variations (e.g.,nanoscale protrusions due to oxidation) on the surface.

Topography measurements indicate that the oxide film protrudesless when grown at higher temperatures (Fig. 5). Furthermore, themeasurements agree with the simulations in that the protrusion in theoxide film increases with oxide thickness at both 800◦C and 1100◦Cas predicted by the simulations for oxide films thinner than 500 nm.However, oxidation at 800◦C leads to significantly higher protrusionheight than predicted by the simulations, whereas oxidation at 1100◦Cresults in a smoother surface than what simulations predict. Thesesuggest that the temperature dependent fitting parameter used in oursimulations must be modified accordingly to account for the effectsof oxide viscosity and stress in calculations.

There is a difference in the effect of oxidation temperature on theoxide surface and on the oxide-silicon interface: The oxide-siliconinterface profile shape changes drastically depending on the oxidationtemperature. Below oxide glass transition temperature, oxidation isretarded at the convex silicon corner and this leads to a horn in silicon(Figs. 5c and 5i). Above oxide glass transition temperature, the siliconconvex corner gets rounded (Figs. 5f and 5l). These observations arein agreement with the literature.1, 2 The oxide surface profile shape,on the other hand, does not differ significantly with the oxidation tem-

perature. In all samples we studied, oxide has nanoscale protrusionsand produces a similar surface profile although the protrusion heightchanges depending on the oxidation temperature (Figs. 5b, 5e, 5h,and 5k). Also, the topography variations due to these protrusions aresmoother and are less localized than the variations due horns at theoxide-silicon interface.

We also investigate the effect of high-temperature inert-ambientannealing on the protrusions in oxide films. We compare AFM topog-raphy measurements on oxide surfaces of each sample in Fig. 5 beforeand after the annealing process at 1100◦C (Fig. 6).

The results indicate that annealing of the oxide films at 1100◦Cin general reduces the protrusion height (Fig. 6). This is expectedsince the viscosity of oxide decreases at higher temperatures and theprotruded oxide film reflows to reduce the intrinsic stress in the film.The reduction in protrusion height is significant particularly in oxidefilms grown at lower temperatures since these films experience thehighest change in viscosity due to annealing. For example, in samplesoxidized at 800◦C, annealing reduces protrusion height close to a valuethat would be expected from a sample oxidized at 1100◦C (Figs. 6aand 6c).Also, the percentile reduction in protrusion in thin films ishigher than that of thicker oxide films grown at the same temperature(Figs. 6a and 6b). This is because the average growth rate is higher forthinner oxide films and there is less time for the film to relax duringoxidation. As a result of these two factors, the smallest change inprotrusion height occurs in thicker oxide films (e.g., 400 nm) grownat higher temperatures (e.g., 1100◦C) (Fig. 6d).

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H84 Journal of The Electrochemical Society, 159 (2) H79-H84 (2012)

Finally, note that the changes in oxide surface topography due toannealing do not necessarily imply similar changes in the profile ofthe oxide silicon interface. The annealing process alters the oxidesurface topography primarily by enhancing viscous flow of the oxidefilm at 1100◦C, above its glass transition temperature. However, thistemperature is well below the silicon melting point (1414◦C), there-fore silicon migration is negligible during annealing. Furthermore, nosilicon is consumed to chemical reactions due to inert annealing am-bient. Rather, the main affect of annealing process is on the chemicalbonding between the oxide and silicon.22, 23 Therefore, even thoughthe surface topographies of oxide films grown at different tempera-tures show a similar profile after high-temperature annealing (Figs. 6cand 6d), the topography of oxide-silicon interfaces (i.e., silicon hornsat the corners) can remain significantly different (Figs. 5i and 5l).

Conclusions

Theoretical and experimental investigation of the surface topogra-phy of thermally grown oxide films on right-angled convex cornersshow that under certain conditions the top oxide surface is not flat, buthas small-scale protrusions close to the edges. The oxidation temper-ature and duration determines the extent of these protrusions and theireffects can be understood by considering the stress in the oxide filmsand the effect of viscous flow. Our results show that the protrusions inan oxide film can be minimized by higher oxidation temperatures orsubsequent annealing at a higher temperature together with judiciouschoice of oxide film thickness. We think that nonuniform oxidation ofright-angled convex corners of silicon and its presented effects on thetopography of top oxide surface in this work is of particular interestfor applications such as 3D integration or MEMS fabrication pro-cesses that involve direct wafer bonding, in particular when denselypatterned features are present.

Acknowledgments

The authors would like to thank Hyo-Seon Yoon, Stanford Univer-sity, for her help in the oxidation and annealing steps. In addition, we

thank Dr. Peter Griffin, Stanford University, for many fruitful discus-sions. Further, we thank Prof. Roger Howe, Dr. Eric Perozziello andDr. James P. McVittie, Stanford University, for their valuable com-ments. This research was financially supported by Corporate R&DHeadquarter, Canon Inc., Tokyo, Japan, AVL List GmbH, Graz Aus-tria, and NIH grant 5R01CA134720. The fabrication for this workwas done in the Stanford Nanofabrication Facility of National Nan-otechnology Infrastructure Network.

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