Size Effect of Barium Titanate and MLCCs in the Next Generation
`
`T. Tsurumi1, T. Hoshina1,2, K. Takizawa1 and H. Kakemoto1
`1 Department of Metallurgy and Ceramics Science, Graduate School of Science and Engineering,
`Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku,Tokyo 152-8552, Japan.
`2 Research fellow of Japan Society for the Promotion of Science, Japan.
`
`Abstract - The size effect of BaTiO3 (BTO) is the most
`important issue to design the high-capacitance MLCCs in
`the next generation. In the size effect of BTO ceramics
`and powders, the maxima of the permittivity were
`observed at certain grain size and the particle size. The
`permittivity maximum in the ceramics was due to the
`domain wall contribution, while that in the powders
`related with the complex structure of the BTO powders.
`Computer simulation technique was developed to predict
`the limit of capacitance density of the multilayer ceramics
`capacitors (MLCCs) produced by the current technology.
`
`INTRODUCTION
`
`To increase the capacitance density of multilayer
`ceramics capacitors (MLCCs),
`the dielectric
`layer
`thickness in MLCCs has been continuously reduced to
`reach below 1 µm in some commercial products. The
`reduction of dielectric layer thickness demands the
`simultaneous reduction of BaTiO3 (BTO) grain size
`because 5 - 6 grains are usually necessary in one
`dielectric layer to achieve enough reliability of MLCCs
`under high DC fields. The biggest obstacle to develop
`high-capacitance MLCCs is the 'size effect' of BTO. It is
`indispensable to understand the mechanism of the size
`effect to develop MLCCs in the next generation. In this
`paper, the size effect of BTO ceramics and fine particles
`will be compared to specify what is known and what is
`unknown in this subject. The permittivity of dielectrics in
`X7R-MLCCs steeply decreases with grain size below 0.5
`µm by the size effect, which means the capacitance
`density cannot be enhanced by making ultra-thin
`dielectric layers in MLCCs, and there must be a limit of
`capacitance density
`in
`the current
`technologies of
`MLCCs. In the latter part of this paper, we try to see the
`limit of capacitance density of MLCCs using a computer
`simulation technique.
`
`SIZE EFFECT OF BTO
`
`In Fig. 1 are summarized the grain size dependences
`the permittivity of BTO ceramics
`taken from
`of
`literatures [1-3] as well as those obtained in our recent
`work. We have measured the permittivity of BTO
`ceramics fabricated from a raw powder with averaged
`particle size of 1.0 µm (Sakai Chem. BT01). The grain
`size of the ceramics was controlled by choosing sintering
`temperature. Some ceramics were sintered using a
`two-step sintering process proposed by Chen [4] to
`prevent the grain growth in the sintering. All ceramics
`made in our work had relative density above 95 %. It was
`found
`that
`the permittivity steeply
`increased with
`
`decreasing grain size beyond 1 µm. This result was
`consistent with those of Arlt et al.[1] and Kinoshita et al.
`[2] The increase of the permittivity should be cause by
`the domain wall contribution. Fig. 2 shows a wide-range
`dielectric spectrum of BTO ceramics with coarse grains
`[5]. The domain effect gave the Debye-type dielectric
`relaxation in GHz region. This domain effect was
`enhanced in the fine-grain BTO ceramics with high
`permittivity but the contribution of ionic polarization was
`the grain size. The TEM
`almost
`independent of
`
`observation revealed that the domain density increased
`with decreasing grain size. In Fig. 1, it is seen that the
`permittivity consistently decreases below the grain size of
`1.0 µm. This result can be explained by assuming that the
`grains become the mono-domain state to lose the domain
`contribution to the permittivity. However, experimental
`results clearly indicate that fine domains exist in the cores
`even below 200 nm of dielectric grains in MLCCs. This
`means that the domain contribution somehow decreases if
`the domain width becomes lower than a certain value.
`The mechanism of domain width dependence of
`permittivity is not known at present.
`Figure 3 shows the particle size dependence of
`permittivity measured for fine BTO powders [6]. The
`permittivity shows a maximum at around 140 nm but the
`mechanism to give the permittivity maximum is totally
`different from the ceramics in Fig. 1. Actually, we did not
`observe domain structures in fine BTO powders. The
`
`Fig. 1 Grain size dependence of the permittivity of
` BTO ceramics.
`
`Fig. 2 Wide-range dielectric spectrum of BTO ceramics.
`Exhibit 1017
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`grain size from 60 nm to 550 nm. Computer simulation
`software was developed to optimize the MLCC structure.
`Figure 5 shows the permittivity of dielectric layers
`with different grain size calculated using 100 SPLINE
`coefficients. It should be noted that the temperature
`stability of the permittivity was lost when the grain size
`became smaller than 120 nm because the shell part
`dominated the dielectric properties. This result is the size
`effect in real MLCCs. To obtain 47 µF in the 1608 mm
`chip size, the simulation was performed. The thickness of
`Ni internal electrodes to 0.4 µm and that of the dielectric
`layer thickness to 0.4 µm to obtain solutions. The
`software gave 427 solutions with the grain size between
`78 nm to 100 nm. The minimum number of dielectric
`layers was 899 when the grain size was 93 nm. Figure 6
`shows the permittivity vs. temperature curve of the
`MLCC designed with the grain size of 93 nm. This is the
`limit of the capacitance density as far as we use current
`technology.
`
`AC field: 300 V/mm
`
`
`
`Fig. 5 Calculated relative permittivity of dielectric
` layers with different sizes.
`
`AC-field: 350V/mm
`
`AC-field: 5V/mm
`
`Grain size: 93 nm
`DL number: 899 layers
`DL thickness: 0.4 µm
`Number of grains in one AL: 5
`
`
`
`Fig. 6 Predicted property of 47 µF MLCC with 1608
` chip size.
`
`
`
`REFERENCE
`
`1. G. Arlt, D. Hennings and G. De With, J. Appl. Phys., 58
`(1985), p.1619.
`2. K. Kinoshinata and A. Yamaji, J. Appl. Phys., 47, 371 (1976)
`3. M. H. Frey, Z. Xu, P. Han and D. A. Payne, Ferroelectrics,
`206-207 (1998), p.337.
`4. I. -Wei Chen and X. -H. Wang, Nature, 404, 168 (2000).
`5. T. Tsurumi, J. Li, T. Hoshina, H,Kakemoto, M.Nakada and J.
`Akedo, Appl. Phys. Lett., 91, 182905 (2007).
`6. T. Hoshina, H. Yasuno, S.-M. Nam, H. Kakemoto T.
`Tsurumi and S. Wada, Trans. Mater. Res. Soc. Jpn., 29
`(2004), p.1207.
`
`
`XRD profiles of powders were analyzed to determine the
`complex structure in the particles. The result of analyses
`indicated that the BTO particles consisted of three
`regions, inner tetragonal core, surface cubic layer and the
`gradient lattice strain layer (GLSL) between them as
`shown in Fig. 4. The permittivity at the GLSL must be
`higher than other parts because the GLSL is the static
`phase transition layer from cubic to tetragonal. The
`permittivity of powders was estimated by assuming
`permittivity distribution in the particles. Particle size
`dependence of the permittivity thus estimated is shown in
`Fig. 3. It was possible to simulate the particle size
`dependence of permittivity by assuming complex
`structure in the particles. The surface cubic layer has low
`permittivity and determined the total permittivity of a
`particle if the layer is thick. The result simulation
`indicated that the permittivity maximum disappears as the
`surface cubic layer becomes thick. The thickness of the
`cubic layer is determined by the defect concentration in
`the BTO powders.
`
`
`COMPUTER SIMULATION OF MLCCs
`
`
`The dielectric properties of the MLCCs with different
`grain size from 104 nm to 559 nm were measured from
`-50oC to 150oC as a function of AC-field. To predict the
`permittivity at arbitral temperature and AC-field, we have
`used the B-SPLINE interpolation software. The number
`of SPLINE coefficient to fit the permittivity is 100 for
`each grain size. A nonlinear least squares technique was
`used to predict the 100 SPLINE coefficients at arbitral
`
`
`
`
`
`Fig. 3 Particle size dependence of the permittivity of
` BTO fine particles
`
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`Fig.4 Complex structure in BTO particle.
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