Investigation of Porosity and Fractal Properties of the Sintered Metal and Semiconductor Layers in the MDS Capacitor Structure

MDS capacitor (metal – dielectric – semiconductor) is a structure in which metal plate is represented by compact bulk-porous pellets of niobium sintered powder, and semiconductor plate – by pyrolytic layer of MnO2 . In the present paper we report the results of investigation of microporosity of sintered Nb and pyrolytic MnO2 and also the fractal properties of semiconductor layer.


Introduction
MDS capacitor (metal -dielectric -semiconductor) are structures in which metal plate is represented by compact bulk-porous pellets of niobium sintered powder, and semiconductor plate is produced by pyrolytic layer of MnO 2, are widely used in microelectronics [1].Capacity of such bulk-conduction capacitors (BCC) mostly depends on porosity of the sintered pellets.Indeed [2], the main attribute of niobium powder sintered pellets, which also verifies their application in BCC, is bulk porosity being formed at powder sintering.Such attribute contributes to extension of effective surface of the sintered pellet S up to the value which exceeds greatly their visible surface.BCC capacity C increases in direct proportion to S growth (as to the standard formula for electric capacitor: С = / S d ε , where ε -dielectric permeability, and d -thickness of dielectric ).
At the same time [3], the specific feature of pyrolytic formation of MnO 2 is water steam release, which results in generation of cavities in a semiconductor (see pyrolysis reaction (1) (1) Herewith, stability range of MDS structure is mainly determined by the amount of water contained in manganese dioxide, which ensure compaction of contacts between BCC layers due to packing of cavities in MnO 2 , i.e. depends on open porosity of pyrolytic layer.
From the very moment when the fractal theory has originated in its current form [4,5], it has been noticed proximity of fractal and porous systems.Applying to the considered structures we [6,7] have defined and investigated fractality of niobium porous sintered pellets.It is consistently to assume that porous layers of MnO 2 also posses fractal properties.
At the same time, considering the fact that our investigation has been done by small-angle X-ray scattering (SAXS) method, we've also been interested in studying of possible changes in scattering mechanism (surface -volume) at transformation from sintered pellets to pyrolytic layers.Taking all this into account the investigations of microporosity of sintered niobium powder and MnO 2 pyrolytic layer as well as fractal properties of manganese dioxide are presented in this article.

Experimental procedure
Compact pellets has been obtained according to [8] by vacuum sintering of niobium powder.In the present work submicroporosity were investigated by small-angle X-ray scattering (SAXS) and Hg porosimetry method.SAXS technique was described in [9].The experimental technique of Hg porosimetry was reported in [10]."Carlo Erba Strumentazione 2000" Hg porosimeter was used ).MnO 2 porous layer have been prepared by the thermal deposition (pyrolysis ) of Mn(NO 3 ) 2 under the temperature T= 570 K. Surface microrelief of MnO 2 were investigated by OLYMPUS SZX12 optical microscope.

Results and discussion
The SAXS technique has assisted in the determination of mean-square dimensions (2R) of submicropores (SMP).Due to the found polymodality of SMP, their conditional subdivision into four dimensional fractions was performed.The highest contribution to the submicropore volumetric concentration is made by the SMP with mean-square dimension of 2 R = 15 nm, and so that total SMP concentration is 71% ( Tab.I ).
The asymptotic nature of the SAXS indicatrices is very similar to the law: I(s) ~ s -4 (where I is SAXS intensity, and s is a wave vector).Such dependence [11] affirms the equiaxial shape of submicropores.Similar values of integral parameters of indicatrices, associated with the SMP specific volume, "shadow area", and dimensions are also in favor of such assumption: V n 1/3 = 25 nm; f 1/2 = 20 nm; l n = 15 nm, respectively.

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At the same time, the Hg porometry method demonstrates hysteresis at the dependence graph between the overall volume of mercury-filled SMPs, and mercury pressure (Fig. 1), thus indicating the presence of SMP flattening and generation of a bottleneck that inhibits mercury yield.The work allows to conclude that submicropore shapes depend on the powder sizeby transfer to more highly dispersed powder, it is occurred relevant transfer from the"rod" shape, when two dimensions considerably exceed the third one (V n 1/3 ≈ f n 1/2 ›› l n ) to deformed equiaxial volume, respectively.
The morphology, concentration and size distribution of MnO 2 have been investigated by SAXS.The observed SMPs were in the range 0,1≤2R≤100nm.We've analyzed the following values: type of angular distribution; asymptotics and the integral parameters of the dispersion indices of SAXS related to the typical size l n; the typical volume V n and the typical SMP shadow area f n .The mean square size of the SMP has been determined by the tangent technique described in by Kratky [12].
Since the size distribution appeared to be polymodal, we've divided the pores into four groups, according to their size: 2R≤1nm; 1nm≤2R≤4nm; 4nm≤2R≤8nm; 8nm≤2R≤50nm.1,5x10 -3 2x10 7  1,5x10 3 ______________________________________________________________________ The absence of noticeable anisotropy of SAXS shows the character of the dispersion indices which asymptotically comply with the Porod law I(s)~s -4 (where I(s) is the intensity of X-ray and s is a diffraction vector).One can assume that scattering SMPs have no domineering orientation, and they are more equiaxial than macro-and micropores.However, some differences in the integral parameters l n = 5nm; V n 1/3 = =5nm and f 1/2 =13nm allows us to conclude that SMP axes are quite equal.Absolute values of these are close to the values calculated by the Guinier technique based on another way of averaging pore sizes.This affirms that most SMPs have more or less equal axes, unlike macropores.

Tab. II. Characteristics of submicropores in
As it can be seen from the Tab.II the major contribution to the SMP volume concentration is made by submicropores not exceeding 8 nm -mostly from the range of 1≤ 2R ≤ 8nm.The total share of the SMPs in the MnO 2 film is about 9.8 % which conforms to the known value [13].
It should be noticed that, unlike macro-and micropores, some equiaxial SMPs are closed and filled with gas.Their formation results from both clustering oxygen vacancies shaped in MnO 2 films and the fact that solidifying rate during the pyrolysis largely exceeds gas emission rate.A part of the emitted gas is therefore trapped in the SMPs.The invariant curve of the dispersion indices ( Fig. 2) reflects the distribution pattern of SMP over their volumes.Here, one can see several maxima; this confirms that the distribution is polymodal, i.e.SMP exists in several typical sizes.This can be a result of (i) peculiarities in the process of pore formation involving gases and crystals or (ii) the process where clustering of oxygen vacancies and continuous gas evacuation in bubbles is accompanied by the growth of the 1atter.Some bubbles burst before solidifying as a result of internal pressure, but some solidify and remain in the layer.It is quite natural that families of arising, growing and bursting bubbles are described by different distribution.The developed surface microrelief of MnO 2 films (Fig. 3) contributes to interesting investigation of the fractal properties of this compound.
As it is known [14] in order to describe X-ray scattering by a porous solid even in the Porod region, the well known q -4 law must be modified.The appropriate theory was developed by Wong [15] and the main formula of this theory for scattering of surface is as follows: 6 ( ) ~D I q const q − × (2) Here I(q) -is the SAXS intensity and D is the surface fractal dimension.Calculation of I(q) -q dependencies allows to determine to which area of the object corresponds information on dispersion [5].In case when the index value lg ( ) / lg I q q α = −∂ ∂ is in the range of 3 -4, the dispersion is affected by the surface area of the object and measurement results allows to determine fractal dimension of the surface D = 6 -α ( for three-dimensional object 2 D ≤ ≤ 3).In case when α ≤ 3, dispersion is caused with the full volume of the object, which dimension is D = α .
In our case the scattered intensity/wave vector relationship (Fig. 3) shows the fractal behavior.Indeed, on the graph, the coefficient of the curved part of the slope, which can be closely approximated by the line, α (Fig. 4) is: α = 2.87.Consequently, considering the abovementioned the present situation contributes to dispersion with full volume of the covering while fractal dimension of MnO 2 is determined as D=α =2.87.
The received value is very close to the value of fractal dimension of sintered niobium (D (Nb) = 2.81) calculated in [6].At the present time the authors can hardly say whether it is a simple coincidence or is related to special features of the structures' formation.At least, it shall be pointed that as it has been shown in [14] in case of sintered niobium fractal dispersion is caused due to the surface of the object.

Conclusions
According to our analysis the major contribution to the sintered niobium powder microporosity is made by SMP with the mean -square size of 2R = 15nm, while the total concentration of SMP in the compact pellets is about 71%.We have noticed that the submicropore shapes depend on the powder size, by transfer to more highly dispersed powder.The relevant transfer from the "rod" shape occurs when two dimensions considerably exceed the third one (V n 1/3 ≈ f n 1/2 ›› l n ).The major contribution to the SMP volume concentration is made by submicropores which are not exceeding 8 nm.The total share of SMP in the MnO 2 film is about 9,8%.The curve of SAXS invariant for the MnO 2 has several maxima, which confirms that the distribution is polymodal, i.e.SMPs exist in several typical sizes.We have found that MnO 2 layers are fractal structures with the value of fractal dimension of D = 2,87, which is close to that calculated for niobium pellets.
SMPs in the niobium sintered compact structures MnO 2 .