Article pubs.acs.org/Langmuir
Repulsive van der Waals Forces Self-Limit Native Oxide Growth Christian Bohling and Wolfgang Sigmund* Department of Materials Science and Engineering, University of Florida, 225 Rhines Hall, Gainesville, Florida 32611, United States ABSTRACT: Silicon is one of the most studied materials, yet questions remain unanswered about its unusual property of growing a self-limiting native oxide that attains its final thickness in a matter of hours yet months later has not grown further. For the first time, we have explored this selflimiting growth in terms of repulsive van der Waals (vdW) forces generated by the combination of material properties inherent to the system. These repulsive forces represent an energy barrier preventing additional oxidizing chemicals, mainly oxygen and water, from adsorbing on the surface as well as hindering diffusion of those that do adsorb toward the interface. We have also proven that this native oxide can be increased in thickness at room temperature and without reactive species by changing the oxidation environment to one predicted by theory to result in attractive vdW forces, thus allowing oxygen/water to interact with the surface more freely.
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However, the predicted growth of the oxide film, using diffusion data from Kajihara et al.,12 is shown in Figure 1, where the predicted final thickness after 1 year is an order of magnitude larger than the measured self-limited thickness. Therefore, while the Cabrera−Mott theory may indeed help to explain the high oxidation rates of growing oxide films, literature values for diffusion constants suggest that the decline in magnitude of a generated voltage potential between surface and unoxidized material is not the sole cause for the selflimiting growth behavior of native oxides. This leads to the question of what additional factors may be causing the cessation of growth in this system. We hypothesize that the self-limiting behavior can be attributed, at least in part, to the effects of repulsive van der Waals (vdW) forces.
INTRODUCTION Silicon is one of the most studied materials of the modern age and is used extensively in the electronics that we use every day. Silicon oxide is used as a dielectric material in the semiconductor industry and is typically grown by surface oxidation of silicon wafers using any of several techniques, including elevated temperature, steam, ozone, plasma, etc.1−8 The Deal− Grove2 model is perhaps the most common means of predicting silicon oxide growth at elevated temperatures; however, it does not apply to temperatures lower than 500 °C. A native silicon oxide film will also grow on the surface of a silicon wafer if left exposed to air. This native oxide is selflimiting in nature, with the final thickness dependent upon relative humidity. In dry pure oxygen, the film will only grow to ∼1 nm, whereas in humid air, the film will grow to ∼2 nm.9,10 In both cases, this final thickness is reached in a matter of hours, with no additional growth occurring even 1 year beyond the original deposition. Perhaps the most well-known theory describing this self-limiting phenomenon is given by Cabrera and Mott.11 Their oxidation theory hypothesizes that, for an oxide that grows in a layer-by-layer fashion, as oxygen begins to adsorb on the pristine metal surface, it can dissociate into atomic oxygen. This dissociation causes the oxygen atoms to behave as low-energy traps at the surface, resulting in the generation of a voltage potential drop between the underlying material and surface. The density of these traps at the surface is such that they can create fields of large strength that, even for a film of >5 nm in thickness, may approach ∼107 V/cm.11 This potential drop lowers the activation energy of ion diffusion through the oxide layer, allowing growth to proceed even at ambient temperatures, where normal diffusion proceeds very slowly. As the oxide film becomes thicker, the field strength decreases accordingly, subsequently limiting the described effect on the activation energy of diffusion and eventually resulting in negligible growth. © XXXX American Chemical Society
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THEORY vdW forces derive from the natural fluctuations of the molecular dipoles inherent to all materials. These fluctuations impart change in neighboring dipoles as well as with this mutual oscillation, resulting in the generation of interaction forces between materials in close proximity. vdW interaction forces are nearly always attractive in nature, but by satisfying certain conditions, the system can result in repulsion between materials as well. The interaction forces between materials are found by calculating the Hamaker constant for the system.13 Hamaker’s method of deriving the Hamaker constant has been modified by Lifshitz,14 Parsegian and Ninham,15 and Hough and White16 to simplify calculation from a sum of all individual molecular interactions at all frequencies to the interaction between continuous phases characterized by their frequency-dependent Received: January 21, 2015 Revised: April 6, 2015
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DOI: 10.1021/acs.langmuir.5b00251 Langmuir XXXX, XXX, XXX−XXX
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Figure 1. Predicted silicon oxide thickness at room temperature versuss time if the native oxide film growth was solely diffusion-limited.
Figure 2. Hamaker constant versus oxide thickness for silicon−silicon oxide−contacting material systems.
corresponding material at a given imaginary frequency, iξm, h is Planck’s constant, CUV and CIR are the absorption strengths of the given material in the UV and IR regions, and ωUV and ωIR are the corresponding frequencies of absorption for those absorption strength values, respectively. These equations show by inspection that certain combinations of materials will result in a repulsive interaction between materials. When the condition ε1 ≤ ε2 ≤ ε3 or ε1 ≥ ε2 ≥ ε3 is met, in other words, when the dielectric response fucntion (DRF) of the intervening medium lies between those of the other two phases, the preceding equations give a negative Hamaker constant, indicating repulsion of the contacting material from the surface. Repulsive vdW forces are responsible for several natural phenomena, including the climbing of liquid helium up the walls of containers and the spreading of alkanes across the surface of water.17,18 The majority of documented repulsive vdW interactions have been measured using the colloid probe technique for atomic force microscopy to measure forces between a particle and surface through a liquid-intervening medium.19−28 In the case of the silicon native oxide system, the surface native oxide acts as the intervening medium between silicon and contacting material. By examination of the DRFs of silicon and silicon oxide, the system is predicted to repel any material
dielectric constants derived from absorption and relaxation at infrared (IR) and ultraviolet (UV) wavelengths only, because of these frequencies being the dominant contributors. The resulting equations are as follows for deriving the Hamaker constant, A132, describing a system where a particle, material 2, contacts a surface, material 1, through an intervening medium, material 3: A132
3kT = 2
Δ13 =
∞
∞
∑ ′∑ m=0
(Δ13Δ23)s s3
s=1
ε1(iξm) − ε3(iξm) , ε1(iξm) + ε3(iξm)
(1)
Δ23 =
ε2(iξm) − ε3(iξm) ε2(iξm) + ε3(iξm) (2)
2
iξm = m
4π kT h
(3)
C IR
ε(iξm) = 1 + 1+
2
( ) ξm ωIR
C UV
+ 1+
2
( ) ξm ωUV
(4)
where the prime designation in eq 1 indicates that the first term, m = 0, is multiplied by 0.5, T is the temperature in kelvin, k is the Boltzmann constant, ε is the dielectric constant of the B
DOI: 10.1021/acs.langmuir.5b00251 Langmuir XXXX, XXX, XXX−XXX
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Figure 3. Difference between the kinetic energy (E) of an oxygen molecule and the interaction potential of the oxygen molecule−native (2 nm thick) silicon oxide−silicon system (W), where the oxygen molecule is 0.5 nm from the silicon−silicon oxide interface.
in the presence of water will achieve greater thicknesses than that of a film grown in dry air alone but will still self-limit because of the magnitude of repulsion increasing as growth continues. As discussed previously, because the scattering probability from the surface of the native oxide is not 100%, we must also address those oxygen molecules that do adsorb onto the surface and manage to diffuse into the silicon oxide lattice. Here, we treat the oxygen molecule as a particle within the intervening medium, silicon oxide, interacting with a surface, the underlying silicon, and calculate the interaction potential between these phases with the following equation, where W is the interaction potential, A is the Hamaker constant, R is the particle radius, and D is the distance between the particle and surface:
possessing a DRF below that of silicon oxide, theoretically resulting in the repulsion of both oxygen and water from the surface. It is also important to note that an oxygen/water molecule within the silicon oxide layer is not only repelled from the silicon−silicon oxide interface, i.e., a silicon−silicon oxide− oxygen molecule system, but also attracted back toward the silicon oxide−air interface. To calculate Hamaker constants for the silicon−silicon oxide system, we must turn to the Tabor−Winterton approximation29 because of the lack of data in the literature on the variation in dielectric properties of silicon oxide at multiple frequencies as the oxide film thickness increases during the native oxidation process. This change as the oxide grows is a result of the properties of the first monolayer of silicon oxide closely resembling that of bulk silicon, with the properties of the film trending toward that of bulk silicon oxide as thickness increases. The Tabor−Winterton approximation uses refractive indices at a single wavelength to estimate the Hamaker constant. This calculated constant is not as accurate as the described Lifshitz method but will serve to identify the attractive/repulsive nature of the system and give a general idea of how the magnitude of the interaction force changes as the thickness of the native oxide increases from zero. The Tabor−Winterton approximation equation is as follows: A132 ≈
W = −AR /6D
(6)
To find the kinetic energy of an oxygen molecule, we approximate using eq 7, which gives the kinetic energy of an ideal gas and where E is the kinetic energy, T is the temperature, and kB is the Boltzmann constant. E=
3hυe 3kT ⎛ ε1 − ε3 ⎞⎛ ε2 − ε3 ⎞ ⎜ ⎟⎜ ⎟+ 4 ⎝ ε1 + ε3 ⎠⎝ ε2 + ε3 ⎠ 8 2
5TkB 2
(7)
By comparison of the interaction potential of the 2-fold vdW system, both repulsion from the silicon oxide−silicon interface and attraction back toward the surface, to the kinetic energy of the oxygen molecule at varying temperatures, as shown in Figure 3, we see that the repulsive energy of the system is greater in magnitude than that of the kinetic energy of the oxygen molecule at low temperatures. This repulsion within the silicon oxide lattice represents an energy barrier against diffusion, inhibiting further growth of the oxide layer. To summarize, even if an oxygen molecule does adsorb onto the surface, it is energetically unfavorable to continue diffusion toward the interface. However, as the temperature is increased, the energy of the oxygen molecules begins to overcome the energy of repulsion away from the interface and diffusion becomes less and less inhibited. In the same vein as this repulsive force representing a diffusion barrier to oxygen that does adsorb onto the silicon oxide surface, the system, again theoretically, also works in reverse, meaning that the combination of air/water and silicon oxide should repel silicon from the silicon−silicon oxide interface, creating an energy barrier against the diffusion of
(n12 − n32)(n2 2 − n32) n1 + n3 n2 + n3 ( n1 + n3 + n2 + n3 ) (5)
where T is the temperature (K), k is the Boltzmann constant, ε is the static dielectric constant of the corresponding material, h is Planck’s constant, υe is the plasma frequency (3 × 1015 Hz),30 and n is the refractive index of the corresponding material at a single wavelength. Using refractive index versus oxide thickness data from Kalnitsky et al.,31 Figure 2 shows the change in magnitude of the repulsive Hamaker constant versus oxide thickness for the silicon−silicon oxide−air system. Also shown is the Hamaker constant versus thickness data for the silicon−silicon oxide− water system. We can see from these two curves that the magnitude of the repulsive Hamaker constant for water as a contacting material is less than that of air at all thicknesses. This may provide an explanation for why a native oxide film grown C
DOI: 10.1021/acs.langmuir.5b00251 Langmuir XXXX, XXX, XXX−XXX
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Figure 4. Hamaker constant versus oxide thickness for silicon−silicon oxide−contacting material systems.
Figure 5. Thickness versus time for samples submerged in oxygenated diiodomethane and samples left in open air.
than both, the continued growth of the native oxide should be less hindered. Additionally, as the oxide thickness increases, the system becomes attractive, which may indicate that the native oxide will continue with unlimited growth, eventually slowed by diffusion of oxygen between the surface and silicon−silicon oxide interface, and not reach a hard limit as in the cases of air and water.
silicon moving toward the surface to create a fresh, unoxidized layer. We have also used Tabor−Winterton approximation to search for a liquid for which the predicted interaction between contacting material and silicon−silicon oxide combination is even less repulsive, with this contacting liquid ideally having an attractive interaction with the surface. Air/oxygen is partially soluble in all liquids, and oxygenating a liquid will not result in a significant deviation from its bulk, unoxygenated properties. Therefore, by choosing a liquid that provides an attractive vdW force for the system, we can make predictions for a system by which we can “force” contact between dissolved oxygen and the surface. To achieve this, a liquid must be found that has a dielectric response function (DRF) between that of silicon and silicon oxide for the majority of the frequency range used for calculation. Only a few liquids meet these criteria, with diiodomethane having the properties best suited for this work.32 Additionally, by changing the contacting material, we can reduce or even remove the vdW force for attraction of oxidizing compounds back toward the surface. As seen in Figure 4, until ∼3 nm of oxide thickness is reached, diiodomethane is repelled from the surface but, more importantly, is less repelled than both air and water at these thicknesses. Because a native oxide is still formed upon exposure to air and water and diiodomethane is less repelled
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EXPERIMENTAL SECTION
We have tested these predictions by exposing silicon wafer samples to diiodomethane, which was either oxygenated by agitation or oxygenated and hydrated by agitating with small amounts of water, for an extended period of time. Samples were tested in two orientations: floating on top of a bulk volume of diiodomethane polished side down or adding diiodomethane on top of a sample to sit as a thin film. As a control, samples were also left exposed to air for the same duration. All samples were etched in hydrofluoric acid prior to the experiment and were allowed to regrow a fresh native oxide before continued growth was attempted. The native oxide thickness for all samples was between 17 and 19 Å at the start of recording; therefore, some additional growth is expected for control samples that self-limit at ∼21 Å. Measurements were taken in 5 day increments to give the oxide layer enough time to grow in the greatly reduced oxygen concentration present in a liquid environment compared to that of open air. All measured thicknesses were normalized to the original native oxide thickness of that individual sample; therefore, any change D
DOI: 10.1021/acs.langmuir.5b00251 Langmuir XXXX, XXX, XXX−XXX
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Langmuir in thickness is represented as a departure from zero. The results of this experiment are shown in Figure 5, with each data point representing the average value of thickness measurements for multiple samples of each designation.
diffusion, which increases as the distance from the interface decreases. In air, the described repulsion persists as the temperature is raised; however, increasing the temperature also increases the energy of the interaction, improving the probability of adsorption as well as increasing the number of collisions per time increment between oxygen and the surface because of the increased motion of gas molecules with an elevated temperature.
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RESULTS As seen, exposing the silicon wafers to oxygenated/oxygenated + hydrated diiodomethane has allowed the native oxide layer to grow beyond the self-limiting thickness seen when samples are left in ambient air. Differences in film growth between “floating” and “thin film” samples can be attributed to the large difference in volume of diiodomethane used in the respective samples. The floating samples rested atop a large volume of diiodomethane and, as such, had access to a larger volume of dissolved oxygen. It should be noted that, as in the growth of a native oxide film in dry versus moist air, the presence of water aids the oxidation process. No growth is seen for those samples left in air for the duration once the normal self-limiting thickness was achieved. Variations in the measured thickness for those samples left in open air are attributed to sources of error, such as change in the thickness of the adsorbed water film present on all solid materials in an atmosphere of varying ambient humidity. To verify the final thickness recorded by ellipsometry for a control sample and floating sample in diiodomethane with dissolved air and water, the sample with greatest growth, transmission electron microscopy (TEM) images were taken and image analysis was conducted to directly measure the surface oxide thickness at regular intervals. As measured by TEM, the diiodomethane-exposed sample possesses a surface oxide film ∼5 Å, on average, thicker than that of the corresponding control sample compared to a difference of ∼6 Å as shown by the ellipsometry measurements above. The agreement between the two measurements verifies that an increase of ∼25% in oxide thickness has actually occurred for this system. A statistical analysis on results from both methods of thickness measurement was also conducted to confirm that any increase in thickness was not due to random measurement error. This analysis showed with high confidence, >99.99% probability, that the thickness increase is due to changing the oxidation environment, oxygenated/hydrated diiodomethane versus air, as opposed to being due to random error. The standard deviation in ellipsometry thickness measurements was less than 0.5 Å for each sample and for TEM measurements was less than 0.25 Å for each sample. While the oxide layer growth seen in these experiments is only measured in angstroms, any growth at all flies directly in the face of the currently accepted theory on the self-limitation of native oxides, especially when considering the fact that the oxidizing compounds used, oxygen and water, are practically insoluble in diiodomethane. Because of the growth achieved by simply changing the ambient environment of the silicon wafer, we conclude that the self-limiting nature of silicon native oxide is not due to a “diffusion barrier” at the silicon−silicon oxide interface arising as the oxide reaches ∼2 nm in thickness, as claimed by the Cabrera−Mott theory. Instead, the decline in growth is, at least in part, due to surface forces preventing oxidizing compounds, most commonly oxygen and water, from interacting with the surface and scattering away as a result. Because these compounds have no dwell time on the surface, there is extremely limited uptake of oxidizing material that would lead to further growth. Those molecules that do make it into the material also encounter an energy barrier against
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CONCLUSION If improvements can be made to the growth rates observed in this experiment, this work could prove greatly beneficial to the semiconductor industry in terms of being able to grow a silicon oxide film between the thicknesses of 2−20 nm. Current thermal growth technology remains largely limited in this thickness range because of uneven growth rates across samples as a result of minor fluctuations in the temperature dependent upon the sample location in the furnace. Additionally, growth in this thickness range remains difficult to predict because it proceeds much more quickly than the Deal−Grove model allows, hence the thickness limitation for the model stated by the authors.2 This concept could also be applied to other materials with a continuous native oxide, including aluminum and titanium, if a suitable oxidizer carrier is found. Additionally, we have shown for the first time that a repulsive vdW effect is seen in a system of solid materials, instead of requiring the liquid-intervening medium used in all previously reported instances of repulsive vdW forces. Expanding this science could lead to improvements in barrier technology and corrosion resistance. By coating metals with a system of silicon−silicon oxide, instead of the more common solely silicon oxide coatings, or another more suitable combination, we may be able to protect the underlying surface with a protective film combination that not only dramatically inhibits undesirable compounds from interacting with the surface but also prevents their eventual diffusion by repelling them away from the underlying interface. There are also possibilities for development of energy-efficient equipment for processes such as room-temperature air separation and “distillation” by nature of one compound being more repelled from a surface than another, removing the heating requirement currently seen in these technologies.
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AUTHOR INFORMATION
Corresponding Author
*Telephone: 352-846-3343. Fax: 352-392-7219. E-mail: [email protected]fl.edu. Notes
The authors declare no competing financial interest.
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REFERENCES
(1) Kakiuchi, H.; Ohmi, H.; Harada, M.; Watanabe, H.; Yasutake, K. Formation of silicon dioxide layers at low temperatures (150−400 °C) by atmospheric pressure plasma oxidation of silicon. Sci. Technol. Adv. Mater. 2007, 8, 137−141. (2) Deal, B. E.; Grove, A. S. General relationship for the thermal oxidation of silicon. J. Appl. Phys. 1965, 36, 3770. (3) Ligenza, J. R. Silicon oxidation in an oxygen plasma excited by microwaves. J. Appl. Phys. 1965, 36, 2703. (4) Pliskin, W. A.; Lehman, H. S. Structural evaluation of silicon oxide films. J. Electrochem. Soc. 1965, 112, 1013−1019. (5) Deal, B. E. The oxidation of silicon in dry oxygen, wet oxygen, and steam. J. Electrochem. Soc. 1963, 110, 527−533. E
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Langmuir (6) Kazor, A.; Boyd, I. W. Ozone-induced rapid low temperature oxidation of silicon. Appl. Phys. Lett. 1993, 63, 2517−2519. (7) Cui, Z.; Madsen, J. M.; Takoudis, C. G. Rapid thermal oxidation of silicon in ozone. J. Appl. Phys. 2000, 87, 8181−8186. (8) Xu, J.; Choyke, W. J.; Yates, J. T. Enhanced silicon oxide film growth on Si (100) using electron impact. J. Appl. Phys. 1997, 82, 6289. (9) Raider, S. I.; Flitsch, R.; Palmer, M. J. Oxide growth on etched silicon in air at room temperature. J. Electrochem. Soc. 1975, 122, 413− 418. (10) Morita, M.; Ohmi, T.; Hasegawa, E.; Kawakami, M.; Ohwada, M. Growth of native oxide on a silicon surface. J. Appl. Phys. 1990, 68, 1272−1281. (11) Cabrera, N.; Mott, N. F. Theory of the oxidation of metals. Rep. Prog. Phys. 1949, 12, 163−184. (12) Kajihara, K.; Miura, T.; Kamioka, H.; Hirano, M.; Skuja, L.; Hosono, H. Surface dissolution and diffusion of oxygen molecules in SiO2 glass. J. Ceram. Soc. Japan 2004, 112, 559−562. (13) Hamaker, H. C. The London−van der Waals attraction between spherical particles. Physica 1937, 4, 1058−1072. (14) Lifshitz, E. M. The theory of molecular attractive forces between solids. J. Exp. Theor. Phys. 1955, 29, 94−110. (15) Parsegian, V. A.; Ninham, B. W. Temperature dependent van der Waals forces. Biophys. J. 1970, 10, 664−674. (16) Hough, D.; White, L. The calculation of Hamaker constants from Liftshitz theory with applications to wetting phenomena. Adv. Colloid Interface Sci. 1980, 14, 3−41. (17) Israelachvili, J. N. Intermolecular and Surface Forces, 2nd ed.; Academic Press: San Diego, CA, 1992. (18) Dzyaloshinskii, I. E.; Lifshitz, E. M.; Pitaevskii, L. P. The general theory of van der Waals forces. Adv. Phys. 1961, 10, 165−209. (19) Bohling, C. D.; Sigmund, W. M. Predicting and measuring repulsive van der Waals forces for a Teflon AF−solvent−α-alumina system. Colloids Surf., A 2014, 462, 137−146. (20) Woan, K. V.; Sigmund, W. M. Force interactions of porous silica glass microspheres against mirror-polished stainless steel in nonaqueous solvents. Langmuir 2011, 27, 5377−5385. (21) Lee, S.; Sigmund, W. M. AFM study of repulsive van der Waals forces between Teflon AF thin films and silica or alumina. Colloids Surf., A 2002, 204, 43−50. (22) Lee, S.; Sigmund, W. Repulsive van der Waals forces for silica and alumina. J. Colloid Interface Sci. 2001, 243, 365−369. (23) Feiler, A.; Bergström, L.; Rutland, M. Superlubricity using repulsive van der Waals forces. Langmuir 2008, 24, 2274−2276. (24) Munday, J. N.; Capasso, F.; Parsegian, V. A. Measured longrange repulsive Casimir−Lifshitz forces. Nature 2009, 457, 170−173. (25) Milling, A.; Mulvaney, P.; Larson, I. Direct measurement of repulsive van der Waals interactions using an atomic force microscope. J. Colloid Interface Sci. 1996, 180, 460−465. (26) Bowen, W. R.; Hilal, N.; Lovitt, R. W.; Wright, C. J. An atomic force microscopy study of the adhesion of a silica sphere to a silica surfaceEffects of surface cleaning. Colloids Surf., A 1999, 157, 117− 125. (27) Meurk, A.; Luckham, P. F.; Bergström, L. Direct measurement of repulsive and attractive van der Waals forces between inorganic materials. Langmuir 1997, 13, 3896−3899. (28) Matope, S.; Rabinovich, Y. I.; Van der Merwe, A. F. van der Waals interactions between silica spheres and metallic thin films created by e-beam evaporation. Colloids Surf., A 2012, 411, 87−93. (29) Tabor, D.; Winterton, R. H. S. The direct measurement of normal and retarded van der Waals forces. Proc. R. Soc. A 1969, 312, 435−450. (30) Butt, H.-J.; Kappl, M. Surface and Interfacial Forces; John Wiley & Sons: Hoboken, NJ, 2009. (31) Kalnitsky, A.; Tay, S. P.; Ellul, J. P.; Chongsawangvirod, S.; Andrews, J. W.; Irene, E. A. Measurements and modeling of thin silicon dioxide films on silicon. J. Electrochem. Soc. 1990, 137, 234− 238.
(32) Drummond, C. J.; Chan, D. Y. C. van der Waals interaction, surface free energies, and contact angles: Dispersive polymers and liquids. Langmuir 1997, 7463, 3890−3895.
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DOI: 10.1021/acs.langmuir.5b00251 Langmuir XXXX, XXX, XXX−XXX
Repulsive van der Waals Forces Self-Limit Native Oxide Growth Christian Bohling and Wolfgang Sigmund* Department of Materials Science and Engineering, University of Florida, 225 Rhines Hall, Gainesville, Florida 32611, United States ABSTRACT: Silicon is one of the most studied materials, yet questions remain unanswered about its unusual property of growing a self-limiting native oxide that attains its final thickness in a matter of hours yet months later has not grown further. For the first time, we have explored this selflimiting growth in terms of repulsive van der Waals (vdW) forces generated by the combination of material properties inherent to the system. These repulsive forces represent an energy barrier preventing additional oxidizing chemicals, mainly oxygen and water, from adsorbing on the surface as well as hindering diffusion of those that do adsorb toward the interface. We have also proven that this native oxide can be increased in thickness at room temperature and without reactive species by changing the oxidation environment to one predicted by theory to result in attractive vdW forces, thus allowing oxygen/water to interact with the surface more freely.
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However, the predicted growth of the oxide film, using diffusion data from Kajihara et al.,12 is shown in Figure 1, where the predicted final thickness after 1 year is an order of magnitude larger than the measured self-limited thickness. Therefore, while the Cabrera−Mott theory may indeed help to explain the high oxidation rates of growing oxide films, literature values for diffusion constants suggest that the decline in magnitude of a generated voltage potential between surface and unoxidized material is not the sole cause for the selflimiting growth behavior of native oxides. This leads to the question of what additional factors may be causing the cessation of growth in this system. We hypothesize that the self-limiting behavior can be attributed, at least in part, to the effects of repulsive van der Waals (vdW) forces.
INTRODUCTION Silicon is one of the most studied materials of the modern age and is used extensively in the electronics that we use every day. Silicon oxide is used as a dielectric material in the semiconductor industry and is typically grown by surface oxidation of silicon wafers using any of several techniques, including elevated temperature, steam, ozone, plasma, etc.1−8 The Deal− Grove2 model is perhaps the most common means of predicting silicon oxide growth at elevated temperatures; however, it does not apply to temperatures lower than 500 °C. A native silicon oxide film will also grow on the surface of a silicon wafer if left exposed to air. This native oxide is selflimiting in nature, with the final thickness dependent upon relative humidity. In dry pure oxygen, the film will only grow to ∼1 nm, whereas in humid air, the film will grow to ∼2 nm.9,10 In both cases, this final thickness is reached in a matter of hours, with no additional growth occurring even 1 year beyond the original deposition. Perhaps the most well-known theory describing this self-limiting phenomenon is given by Cabrera and Mott.11 Their oxidation theory hypothesizes that, for an oxide that grows in a layer-by-layer fashion, as oxygen begins to adsorb on the pristine metal surface, it can dissociate into atomic oxygen. This dissociation causes the oxygen atoms to behave as low-energy traps at the surface, resulting in the generation of a voltage potential drop between the underlying material and surface. The density of these traps at the surface is such that they can create fields of large strength that, even for a film of >5 nm in thickness, may approach ∼107 V/cm.11 This potential drop lowers the activation energy of ion diffusion through the oxide layer, allowing growth to proceed even at ambient temperatures, where normal diffusion proceeds very slowly. As the oxide film becomes thicker, the field strength decreases accordingly, subsequently limiting the described effect on the activation energy of diffusion and eventually resulting in negligible growth. © XXXX American Chemical Society
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THEORY vdW forces derive from the natural fluctuations of the molecular dipoles inherent to all materials. These fluctuations impart change in neighboring dipoles as well as with this mutual oscillation, resulting in the generation of interaction forces between materials in close proximity. vdW interaction forces are nearly always attractive in nature, but by satisfying certain conditions, the system can result in repulsion between materials as well. The interaction forces between materials are found by calculating the Hamaker constant for the system.13 Hamaker’s method of deriving the Hamaker constant has been modified by Lifshitz,14 Parsegian and Ninham,15 and Hough and White16 to simplify calculation from a sum of all individual molecular interactions at all frequencies to the interaction between continuous phases characterized by their frequency-dependent Received: January 21, 2015 Revised: April 6, 2015
A
DOI: 10.1021/acs.langmuir.5b00251 Langmuir XXXX, XXX, XXX−XXX
Article
Langmuir
Figure 1. Predicted silicon oxide thickness at room temperature versuss time if the native oxide film growth was solely diffusion-limited.
Figure 2. Hamaker constant versus oxide thickness for silicon−silicon oxide−contacting material systems.
corresponding material at a given imaginary frequency, iξm, h is Planck’s constant, CUV and CIR are the absorption strengths of the given material in the UV and IR regions, and ωUV and ωIR are the corresponding frequencies of absorption for those absorption strength values, respectively. These equations show by inspection that certain combinations of materials will result in a repulsive interaction between materials. When the condition ε1 ≤ ε2 ≤ ε3 or ε1 ≥ ε2 ≥ ε3 is met, in other words, when the dielectric response fucntion (DRF) of the intervening medium lies between those of the other two phases, the preceding equations give a negative Hamaker constant, indicating repulsion of the contacting material from the surface. Repulsive vdW forces are responsible for several natural phenomena, including the climbing of liquid helium up the walls of containers and the spreading of alkanes across the surface of water.17,18 The majority of documented repulsive vdW interactions have been measured using the colloid probe technique for atomic force microscopy to measure forces between a particle and surface through a liquid-intervening medium.19−28 In the case of the silicon native oxide system, the surface native oxide acts as the intervening medium between silicon and contacting material. By examination of the DRFs of silicon and silicon oxide, the system is predicted to repel any material
dielectric constants derived from absorption and relaxation at infrared (IR) and ultraviolet (UV) wavelengths only, because of these frequencies being the dominant contributors. The resulting equations are as follows for deriving the Hamaker constant, A132, describing a system where a particle, material 2, contacts a surface, material 1, through an intervening medium, material 3: A132
3kT = 2
Δ13 =
∞
∞
∑ ′∑ m=0
(Δ13Δ23)s s3
s=1
ε1(iξm) − ε3(iξm) , ε1(iξm) + ε3(iξm)
(1)
Δ23 =
ε2(iξm) − ε3(iξm) ε2(iξm) + ε3(iξm) (2)
2
iξm = m
4π kT h
(3)
C IR
ε(iξm) = 1 + 1+
2
( ) ξm ωIR
C UV
+ 1+
2
( ) ξm ωUV
(4)
where the prime designation in eq 1 indicates that the first term, m = 0, is multiplied by 0.5, T is the temperature in kelvin, k is the Boltzmann constant, ε is the dielectric constant of the B
DOI: 10.1021/acs.langmuir.5b00251 Langmuir XXXX, XXX, XXX−XXX
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Figure 3. Difference between the kinetic energy (E) of an oxygen molecule and the interaction potential of the oxygen molecule−native (2 nm thick) silicon oxide−silicon system (W), where the oxygen molecule is 0.5 nm from the silicon−silicon oxide interface.
in the presence of water will achieve greater thicknesses than that of a film grown in dry air alone but will still self-limit because of the magnitude of repulsion increasing as growth continues. As discussed previously, because the scattering probability from the surface of the native oxide is not 100%, we must also address those oxygen molecules that do adsorb onto the surface and manage to diffuse into the silicon oxide lattice. Here, we treat the oxygen molecule as a particle within the intervening medium, silicon oxide, interacting with a surface, the underlying silicon, and calculate the interaction potential between these phases with the following equation, where W is the interaction potential, A is the Hamaker constant, R is the particle radius, and D is the distance between the particle and surface:
possessing a DRF below that of silicon oxide, theoretically resulting in the repulsion of both oxygen and water from the surface. It is also important to note that an oxygen/water molecule within the silicon oxide layer is not only repelled from the silicon−silicon oxide interface, i.e., a silicon−silicon oxide− oxygen molecule system, but also attracted back toward the silicon oxide−air interface. To calculate Hamaker constants for the silicon−silicon oxide system, we must turn to the Tabor−Winterton approximation29 because of the lack of data in the literature on the variation in dielectric properties of silicon oxide at multiple frequencies as the oxide film thickness increases during the native oxidation process. This change as the oxide grows is a result of the properties of the first monolayer of silicon oxide closely resembling that of bulk silicon, with the properties of the film trending toward that of bulk silicon oxide as thickness increases. The Tabor−Winterton approximation uses refractive indices at a single wavelength to estimate the Hamaker constant. This calculated constant is not as accurate as the described Lifshitz method but will serve to identify the attractive/repulsive nature of the system and give a general idea of how the magnitude of the interaction force changes as the thickness of the native oxide increases from zero. The Tabor−Winterton approximation equation is as follows: A132 ≈
W = −AR /6D
(6)
To find the kinetic energy of an oxygen molecule, we approximate using eq 7, which gives the kinetic energy of an ideal gas and where E is the kinetic energy, T is the temperature, and kB is the Boltzmann constant. E=
3hυe 3kT ⎛ ε1 − ε3 ⎞⎛ ε2 − ε3 ⎞ ⎜ ⎟⎜ ⎟+ 4 ⎝ ε1 + ε3 ⎠⎝ ε2 + ε3 ⎠ 8 2
5TkB 2
(7)
By comparison of the interaction potential of the 2-fold vdW system, both repulsion from the silicon oxide−silicon interface and attraction back toward the surface, to the kinetic energy of the oxygen molecule at varying temperatures, as shown in Figure 3, we see that the repulsive energy of the system is greater in magnitude than that of the kinetic energy of the oxygen molecule at low temperatures. This repulsion within the silicon oxide lattice represents an energy barrier against diffusion, inhibiting further growth of the oxide layer. To summarize, even if an oxygen molecule does adsorb onto the surface, it is energetically unfavorable to continue diffusion toward the interface. However, as the temperature is increased, the energy of the oxygen molecules begins to overcome the energy of repulsion away from the interface and diffusion becomes less and less inhibited. In the same vein as this repulsive force representing a diffusion barrier to oxygen that does adsorb onto the silicon oxide surface, the system, again theoretically, also works in reverse, meaning that the combination of air/water and silicon oxide should repel silicon from the silicon−silicon oxide interface, creating an energy barrier against the diffusion of
(n12 − n32)(n2 2 − n32) n1 + n3 n2 + n3 ( n1 + n3 + n2 + n3 ) (5)
where T is the temperature (K), k is the Boltzmann constant, ε is the static dielectric constant of the corresponding material, h is Planck’s constant, υe is the plasma frequency (3 × 1015 Hz),30 and n is the refractive index of the corresponding material at a single wavelength. Using refractive index versus oxide thickness data from Kalnitsky et al.,31 Figure 2 shows the change in magnitude of the repulsive Hamaker constant versus oxide thickness for the silicon−silicon oxide−air system. Also shown is the Hamaker constant versus thickness data for the silicon−silicon oxide− water system. We can see from these two curves that the magnitude of the repulsive Hamaker constant for water as a contacting material is less than that of air at all thicknesses. This may provide an explanation for why a native oxide film grown C
DOI: 10.1021/acs.langmuir.5b00251 Langmuir XXXX, XXX, XXX−XXX
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Langmuir
Figure 4. Hamaker constant versus oxide thickness for silicon−silicon oxide−contacting material systems.
Figure 5. Thickness versus time for samples submerged in oxygenated diiodomethane and samples left in open air.
than both, the continued growth of the native oxide should be less hindered. Additionally, as the oxide thickness increases, the system becomes attractive, which may indicate that the native oxide will continue with unlimited growth, eventually slowed by diffusion of oxygen between the surface and silicon−silicon oxide interface, and not reach a hard limit as in the cases of air and water.
silicon moving toward the surface to create a fresh, unoxidized layer. We have also used Tabor−Winterton approximation to search for a liquid for which the predicted interaction between contacting material and silicon−silicon oxide combination is even less repulsive, with this contacting liquid ideally having an attractive interaction with the surface. Air/oxygen is partially soluble in all liquids, and oxygenating a liquid will not result in a significant deviation from its bulk, unoxygenated properties. Therefore, by choosing a liquid that provides an attractive vdW force for the system, we can make predictions for a system by which we can “force” contact between dissolved oxygen and the surface. To achieve this, a liquid must be found that has a dielectric response function (DRF) between that of silicon and silicon oxide for the majority of the frequency range used for calculation. Only a few liquids meet these criteria, with diiodomethane having the properties best suited for this work.32 Additionally, by changing the contacting material, we can reduce or even remove the vdW force for attraction of oxidizing compounds back toward the surface. As seen in Figure 4, until ∼3 nm of oxide thickness is reached, diiodomethane is repelled from the surface but, more importantly, is less repelled than both air and water at these thicknesses. Because a native oxide is still formed upon exposure to air and water and diiodomethane is less repelled
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EXPERIMENTAL SECTION
We have tested these predictions by exposing silicon wafer samples to diiodomethane, which was either oxygenated by agitation or oxygenated and hydrated by agitating with small amounts of water, for an extended period of time. Samples were tested in two orientations: floating on top of a bulk volume of diiodomethane polished side down or adding diiodomethane on top of a sample to sit as a thin film. As a control, samples were also left exposed to air for the same duration. All samples were etched in hydrofluoric acid prior to the experiment and were allowed to regrow a fresh native oxide before continued growth was attempted. The native oxide thickness for all samples was between 17 and 19 Å at the start of recording; therefore, some additional growth is expected for control samples that self-limit at ∼21 Å. Measurements were taken in 5 day increments to give the oxide layer enough time to grow in the greatly reduced oxygen concentration present in a liquid environment compared to that of open air. All measured thicknesses were normalized to the original native oxide thickness of that individual sample; therefore, any change D
DOI: 10.1021/acs.langmuir.5b00251 Langmuir XXXX, XXX, XXX−XXX
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Langmuir in thickness is represented as a departure from zero. The results of this experiment are shown in Figure 5, with each data point representing the average value of thickness measurements for multiple samples of each designation.
diffusion, which increases as the distance from the interface decreases. In air, the described repulsion persists as the temperature is raised; however, increasing the temperature also increases the energy of the interaction, improving the probability of adsorption as well as increasing the number of collisions per time increment between oxygen and the surface because of the increased motion of gas molecules with an elevated temperature.
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RESULTS As seen, exposing the silicon wafers to oxygenated/oxygenated + hydrated diiodomethane has allowed the native oxide layer to grow beyond the self-limiting thickness seen when samples are left in ambient air. Differences in film growth between “floating” and “thin film” samples can be attributed to the large difference in volume of diiodomethane used in the respective samples. The floating samples rested atop a large volume of diiodomethane and, as such, had access to a larger volume of dissolved oxygen. It should be noted that, as in the growth of a native oxide film in dry versus moist air, the presence of water aids the oxidation process. No growth is seen for those samples left in air for the duration once the normal self-limiting thickness was achieved. Variations in the measured thickness for those samples left in open air are attributed to sources of error, such as change in the thickness of the adsorbed water film present on all solid materials in an atmosphere of varying ambient humidity. To verify the final thickness recorded by ellipsometry for a control sample and floating sample in diiodomethane with dissolved air and water, the sample with greatest growth, transmission electron microscopy (TEM) images were taken and image analysis was conducted to directly measure the surface oxide thickness at regular intervals. As measured by TEM, the diiodomethane-exposed sample possesses a surface oxide film ∼5 Å, on average, thicker than that of the corresponding control sample compared to a difference of ∼6 Å as shown by the ellipsometry measurements above. The agreement between the two measurements verifies that an increase of ∼25% in oxide thickness has actually occurred for this system. A statistical analysis on results from both methods of thickness measurement was also conducted to confirm that any increase in thickness was not due to random measurement error. This analysis showed with high confidence, >99.99% probability, that the thickness increase is due to changing the oxidation environment, oxygenated/hydrated diiodomethane versus air, as opposed to being due to random error. The standard deviation in ellipsometry thickness measurements was less than 0.5 Å for each sample and for TEM measurements was less than 0.25 Å for each sample. While the oxide layer growth seen in these experiments is only measured in angstroms, any growth at all flies directly in the face of the currently accepted theory on the self-limitation of native oxides, especially when considering the fact that the oxidizing compounds used, oxygen and water, are practically insoluble in diiodomethane. Because of the growth achieved by simply changing the ambient environment of the silicon wafer, we conclude that the self-limiting nature of silicon native oxide is not due to a “diffusion barrier” at the silicon−silicon oxide interface arising as the oxide reaches ∼2 nm in thickness, as claimed by the Cabrera−Mott theory. Instead, the decline in growth is, at least in part, due to surface forces preventing oxidizing compounds, most commonly oxygen and water, from interacting with the surface and scattering away as a result. Because these compounds have no dwell time on the surface, there is extremely limited uptake of oxidizing material that would lead to further growth. Those molecules that do make it into the material also encounter an energy barrier against
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CONCLUSION If improvements can be made to the growth rates observed in this experiment, this work could prove greatly beneficial to the semiconductor industry in terms of being able to grow a silicon oxide film between the thicknesses of 2−20 nm. Current thermal growth technology remains largely limited in this thickness range because of uneven growth rates across samples as a result of minor fluctuations in the temperature dependent upon the sample location in the furnace. Additionally, growth in this thickness range remains difficult to predict because it proceeds much more quickly than the Deal−Grove model allows, hence the thickness limitation for the model stated by the authors.2 This concept could also be applied to other materials with a continuous native oxide, including aluminum and titanium, if a suitable oxidizer carrier is found. Additionally, we have shown for the first time that a repulsive vdW effect is seen in a system of solid materials, instead of requiring the liquid-intervening medium used in all previously reported instances of repulsive vdW forces. Expanding this science could lead to improvements in barrier technology and corrosion resistance. By coating metals with a system of silicon−silicon oxide, instead of the more common solely silicon oxide coatings, or another more suitable combination, we may be able to protect the underlying surface with a protective film combination that not only dramatically inhibits undesirable compounds from interacting with the surface but also prevents their eventual diffusion by repelling them away from the underlying interface. There are also possibilities for development of energy-efficient equipment for processes such as room-temperature air separation and “distillation” by nature of one compound being more repelled from a surface than another, removing the heating requirement currently seen in these technologies.
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AUTHOR INFORMATION
Corresponding Author
*Telephone: 352-846-3343. Fax: 352-392-7219. E-mail: [email protected]fl.edu. Notes
The authors declare no competing financial interest.
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REFERENCES
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