APPLIED PHYSICS LETTERS
VOLUME 83, NUMBER 7
18 AUGUST 2003
On mechanical properties of nanostructured meso-porous silicon Ch. Populaire,a) B. Remaki, V. Lysenko, and D. Barbier Laboratoire de Physique de la Matie`re, UMR-5511 CNRS, INSA de Lyon, 7, Avenue J. Capelle, Bat. Blaise Pascal, 69621 Villeurbanne Cedex, France
H. Artmann and T. Pannek Robert Bosch GmbH, FV/FLD, Postfach 10 60 50, D-70049 Stuttgart, Germany
共Received 7 April 2003; accepted 30 June 2003兲 Mechanical properties of meso-porous silicon are studied using topographic measurements and finite element simulations. Our approach is based on an original analysis of the strain at the free surface of porous silicon tub embedded in bulk Si regions allowing the determination of the Young’s modulus of the porous layers. In particular, the internal stress in the porous Si region is evaluated from the corresponding deformation of the monocrystalline Si adjacent region which mechanical parameters are well known. Moreover, a mechanical anisotropy of the columnar nanostructured porous Si is brought to the fore from the characteristic shape of the strained porous layer profile. Moderately oxidized, 70% in porosity, porous silicon patterns were investigated. Correlation of our measurements with x-ray data reported early in literature shows the macroscopic strain being close to the silicon lattice relative increase revealing an elastic deformation regime. The porous layers exhibit an unexpected low and strongly anisotropic Young’s modulus for all samples. Young’s modulus values of 1.5 and 0.44 GPa are found in parallel and perpendicular directions of the columnar structure, respectively. Finally, a phenomenological model for such a mechanical behavior taking into account porosity and percolation strength factor of the randomly arranged as-prepared and partially oxidized porous Si nanostructures is proposed. © 2003 American Institute of Physics. 关DOI: 10.1063/1.1603336兴
Nanostructure of porous silicon 共PS兲 is an object of numerous publications describing its amazing optical, electrical, thermal, and other properties. However, mechanical properties of PS are poorly studied in spite of their determining impact on integration of this nanostructured material in standard semiconductor technology procedures. Main studies on Young’s modulus and hardness of PS are summarized by Bellet1 and Duttagupta et al.,2 respectively. In general, a PS nanostructure is considered as an isotropic media from mechanical properties point of view.1–3 Such an assumption is well adapted for the case of nano-PS morphology presenting a chaotic sponge-like arrangement of nanoscale crystallites 共1–3 nm兲4 formed on lightly doped 共⬎1 ⍀ cm兲 p-type Si substrates. However, meso-PS with columnar-like arrangement of Si nanocrystallites of about 10 nm of diameter4 formed on highly doped (⬇10⫺2 ⍀ cm兲 p-type Si wafer should possess anisotropic mechanical properties. In this letter, we determine anisotropic Young’s modulus of the columnar nanostructured meso-PS by topographic measurements and finite element simulations. Patterned 100-m-thick meso-PS layers were formed on heavily doped 共0.02 ⍀ cm兲 p-type 共100兲 oriented 4 in. monocrystalline silicon substrates using a well-known anodic electrochemical dissolution process 共anodization兲5 and silicon nitride thin films as masking layers. The dissolution was performed in 20% HF 共diluted in ethanol兲 electrolyte solution. The resulting porosity of the meso-PS samples was estimated by a gravimetric measurements to be about 70%. After anodization, some samples were oxidized in dry O2 a兲
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atmosphere at 400, 500, and 550 °C during 1 h. Twodimensional 共2D兲 and three-dimensional 共3D兲 topographic scans of the samples were performed by using KLA Tencor P-10 mechanical surface profilometer. Energy dispersive x-ray fluorescence spectroscopy 共EDXRFS兲 was used to measure oxidized fraction of the meso-PS layers.6 Typical 2D and 3D topographic profiles of the partially oxidized patterned PS layers are shown on Figs. 1共a兲 and 1共b兲, respectively. Three samples were oxidized at 400, 500, and 550 °C while the last one is natively oxidized during 6 months storage in ambient air. In general, the higher oxidation temperature is, the more important layer expansion in Z direction perpendicular to the layer surface is. Oxidation induced stress appearing at the extremely large internal effective surface of the nanostructured porous layer 共several hundreds m2 per cm3 ) is assumed to be at the origin of such an important expansion.7 The surface stress appearing at the Si/SiOx interface is due to the differences of densities 共intrinsic stress兲 and thermal expansion coefficients 共thermoelastic stress兲8 of silicon and silicon oxide. Mechanical relaxation of such stresses occurs mainly toward the free space in Z direction because of the lateral squeezing of the patterned PS layers by bulk Si. For the natively oxidized samples, a Z direction strain of about 2⫻10⫺3 is found in the central part of the layer from a ratio ⌬d Z /d, where d is the porous layer thickness and ⌬d z is the layer thickness increase 共layer step height兲. This result is in good agreement with numerous x-ray diffraction measurements7 detecting relative increase of the lattice parameter ⌬a z /a in the aged meso-PS samples up to 2⫻10⫺3 compared to bulk Si. For the samples oxidized at high temperatures 共400–550 °C兲, the ⌬d z /d strain
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Appl. Phys. Lett., Vol. 83, No. 7, 18 August 2003
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FIG. 1. 共a兲 Experimental 2D profiles of native oxide 共storage during 6 months兲 and dry O2 共1 h duration兲 oxidized patterned meso-PS layers; 共b兲 experimental 3D scan performed on a sample oxidized at 550 °C; 共c兲 cross-section SEM view of patterned meso-PS layers; and 共d兲 simulated 2D profiles 共anisotropic and isotropic兲 of patterned meso-PS layer oxidized at 550 °C.
values in the range of 4⫻10⫺3 – 11⫻10⫺3 found from our macroscopic profilometer measurements are comparable to strains measured by Buttard et al.9 from lattice expansion measurements on meso-PS samples submitted to an anodic oxidation process. Such a correlation between the macroscopic and subnanoscale strains reveals the elastic nature of the interatomic distance increase after the nanoscale porosification of bulk Si and after the moderate oxidation of the formed porous nanostructures. Referring to the scanning electron microscopy 共SEM兲 picture 关Fig. 1共c兲兴 the central part of the meso-PS layer is constituted by nanoscale columns perpendicular to the sample surface. In contrast, meso-PS overetching regions 关see zoom in Fig. 1共c兲兴 corresponding to the anodization performed in bulk Si substrates beyond the masking layer are characterized by radial geometry of current lines spatial distribution and consequently, by radial pore propagation.10,11 By correlating the SEM picture and the topographic profiles 关Fig. 1共a兲兴, difference in columnar orientation clearly appeared to affect the oxidation induced macroscopic mechanical behavior of the patterned PS layers. In particular, ‘‘ear’’ shapes of the 2D topographic profiles correspond to the overetching regions as shown on Fig. 1. The higher strain in the Z direction corresponding to the overetching region can be obviously related to its less mechanical rigidity compared to the central part of PS region. In order to precisely determine Young’s modulus of the
PS layers as a function of the nano-pores orientation, the oxidation induced 2D volume expansion of the porous layers was fitted by means of ANSYS® software performing finite element analysis of the strained samples. Young’s modulus, E, and stress, , values are used as fitting parameters. Our finite element model is based on the following main assumptions: 共i兲 stress, , is considered to be homogeneously distributed in the whole PS layers; 共ii兲 a part of Z direction strain provoked by partial relaxation of lateral X – Y stress is neglected because of low Poisson’s coefficient ⫽0.0912 of the porous layers explained by the relatively high porosity value 共70%兲. First, the meso-PS layer is considered to be an isotropic and homogenous media characterized by a mean effective isotropic Young’s modulus, E. For bulk Si, E and were chosen to be 163 GPa and 0 Pa, respectively. Then, a unique possible pair (E, ) characterizing strained meso-PS layer is found to ensure the best fitting of the experimental 2D profilometer scans of the PS central part as well as of bulk Si regions. For example, E⫽1.5 GPa and ⫽11 MPa are found in such a manner for the sample oxidized at 550 °C. The similar Young’s modulus values were found for other samples oxidized at lower temperatures. Being plotted in Fig. 1共d兲, the simulated isotropic profile corresponding to this sample well fits the central part 共step height兲 of the experimentally measured 2D scans. However, typical ear
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Appl. Phys. Lett., Vol. 83, No. 7, 18 August 2003
shapes observed at the meso-PS overetching regions are not simulated in the isotropic modeling. To fit the ears at the 2D profile edges corresponding to the overetching regions with radial orientation of nanopores, an effective Young’s modulus of these zones, E eff , is assumed to be E eff⬍E储 , where E 储 ⬅E is the Young’s modulus value determined previously from isotropic simulations characterizing central part of the meso-PS samples with vertically oriented nanopores and nanocolumns. The ears form and amplitude corresponding to the sample oxidized at 550 °C are successfully fitted with E eff⫽1 GPa and the simulated 2D expansion profile 关Fig. 1共d兲兴 is very similar to the measured one 关Fig. 1共a兲兴. Moreover, 共i兲 the assumption of homogeneous stress distribution in the whole porous layer as well as 共ii兲 the Hook’s law: ⫽(⌬d 储 ,eff /d)E储,eff allow us to compare a ratio of the simulated Young’s modulus E eff /E储⫽0.67 with that of the deformations measured by profilometer ⌬d 储 /⌬d eff⫽0.73. This correlation confirms the elastic regime and the assumption of the homogeneous stress distribution in PS layer. Whereas the E 储 parameter properly characterizes mechanical properties in the direction strongly parallel to the vertical nanocolumns constituting the porous layer, the effective E eff parameter takes into account all orientations of the columns from perpendicular to parallel one. Both parameters allow us to estimate the Young’s modulus value, E⬜ , describing mechanical properties of the meso-PS layer in direction perpendicular to the to the vertical nanocolumns from the following relation: E eff⫽ 冑E⬜ E 储 .
共1兲
E⬜ is found from Eq. 共1兲 to be 0.44 GPa. The Young’s modulus anisotropy factor ⫽3.4 is calculated from the ratio E 储 /E⬜ . For all partially oxidized samples used in this work with moderate oxidized fractions ⬍0.3, the anisotropy factor remains constant meaning that the Young’s modulus values are mainly controlled by the remaining nonoxidized nanostructured silicon skeleton. Nanostructuring of bulk Si substrates by nanoscale porosification dramatically affects the silicon network rigidity characterized by Young’s modulus values at least two orders of magnitude lower compared to bulk monocrystalline Si. The similar decrease was already observed for the thermal conductivity of meso-PS.6,13 By analogy with thermal conductivity, the effective Young’s modulus of meso-PS in a first order isotropic approach, E meso-PS , can be defined as E meso-PS⫽E Si g 0 ,
共2兲
where E Si is the Young’s modulus of bulk silicon (E Si⫽163 GPa兲, ⫽(1⫺ P) is the volume fraction of the remaining silicon within the porous medium, P is the layer porosity,
and g 0 is the percolation strength interpreted as the fraction of mechanically interconnected Si nanocrystallites. For such a chaotic media, g 0 ⫽(1⫺ P) 2 can be assumed.13 Finally, the following relationship can be established for the effective PS Young’s modulus E meso-PS⫽E Si共 1⫺ P 兲 3 .
共3兲
In the case of partially oxidized samples with moderate oxidized fractions values ⬍0.3 corresponding to the monolayer sheet of relatively soft silicon oxide surrounding the Si nanocrystallites and ensuring their elastic deformation, a mechanical impact of the oxide on the mechanical rigidity of the whole meso-PS layer can be neglected. Adopting such an assumption, the Young’s modulus of the partially oxidized meso-PS layer can be estimated from Eq. 共3兲 in which P parameter should be replaced by P * accounting for Si fraction consumed by the anodization and oxidation processes and defined as following: 共 1⫺ P * 兲 ⫽ 共 1⫺ P 兲共 1⫺ 兲 .
共4兲
For example, for PS sample oxidized at 550 °C with ⫽0.26 and P⫽70%, Eqs. 共3兲 and 共4兲 give a value of E⫽1.8 GPa which is close to the value E⫽1.5 GPa determined earlier from isotropic finite element model. In conclusions, effective Young’s modulus values of the meso-PS samples are found to be about two orders of magnitude lower than the Young’s modulus of bulk monocrystalline Si substrates. Moreover, the nanostructured columnar porous layers exhibit a strong anisotropy 共factor of 3.4兲 of their mechanical properties that should be taken into consideration for further theoretical calculations, experiments, or application of this nanostructured material. A phenomenological model describing its mechanical properties is proposed. D. Bellet, in Properties of Porous Silicon, edited by L. T. Canham 共INSPEC, The IEE, London, 1997兲, p. 127. 2 S. P. Duttagupta and P. M. Fauchet, in Properties of Porous Silicon, edited by L. T. Canham 共INSPEC, The IEE, London, 1997兲, p. 132. 3 H. J. Fan, M. H. Kuok, S. C. Ng, R. Boukherroub, J.-M. Baribeau, J. W. Fraser, and D. J. Lockwood, Phys. Rev. B 65, 165330 共2002兲. 4 M. I. J. Beale, J. D. Benjamin, M. J. Uren, N. G. Chew, and A. G. Cullis, J. Cryst. Growth 73, 622 共1985兲. 5 L. Smith and S. P. Collins, J. Appl. Phys. 71, R1 共1992兲. 6 V. Lysenko, S. Perichon, B. Remaki, and D. Barbier, J. Appl. Phys. 86, 6841 共1999兲. 7 D. Buttard, G. Dolino, C. Faivre, A. Hallimaoui, F. Comin, V. Formoso, and L. Ortega, J. Appl. Phys. 85, 7105 共1999兲, and references therein. 8 J. H. Jou and L. Hsu, J. Appl. Phys. 69, 1384 共1991兲. 9 D. Buttard, D. Bellet, and G. Dolino, J. Appl. Phys. 79, 8060 共1996兲. 10 P. Steiner and W. Lang, Thin Solid Films 255, 52 共1995兲. 11 S. Perichon, Ph.D. thesis, INSA de Lyon, 2001, p. 116. 12 K. Barla, R. Herino, G. Bomchil, and J. C. Pfister, J. Cryst. Growth 68, 727 共1984兲. 13 G. Gesele, J. Linsmeier, V. Drach, J. Fricke, and R. Arens-Fischer, J. Phys. D 30, 2911 共1997兲. 1
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