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Nanodimensional effect at planar inductance with “conducting film inside current ring”technology 
 


Authors 
 Sapogin V.G. 
 Prokopenko N.N. 
 Ivanov Y.I. 
 Bugakova A.V. 
Date of publication 
 2016 

Abstract 
 ABSTRACT
The planar inductances, being realized at insulating base as multiturns circular, spiral, square and more complex geometric forms, for example, orthogonal spirals, are widely used in modern devices of communication and telecommunications, in structures “systemonchip” and “systeminpackage”.
The inductances, fabricated as planar spiral, loaded at adjacent to spiral semiconducting film with patterned shield, have been suggested in [8][10]. The frequency dependences, measured in these works, show that inductance of planar spiral can has as positive so negative values.
Such inductance has been named as dynamic planar one in papers [2][5]. There original methods of calculation of inductance’s frequency characteristics have been proposed.
PURPOSE
This paper has deal with research of frequencyindependent planar inductance. The paper object is to suggest the method of calculation of frequencyindependent microscopic positive planar inductance (PPI) for its creation over breakthrough “conducting film inside current ring”technology. The realization of this technology permits to increase surface density of inductance till limit value of 10 H/m2.
METHODS
The construction of inductance suggested uses the known singleturn topology of its creation [1]. To form frequencyindependent vortex current’s inductance the additional thin film, which has the known conductivity, is introduced into internal domain of current ring. The thin film has no electric contact with the turn.
The inductance of construction is summed from two components: the inductance of current ring and flux inductance, which calculation has been represented in the paper.
To calculate frequencyindependent inductance of conducting film, the system of differential equations, consisting of two Maxwell’s equations, differential form of Ohm’s law and relationship between the current and the flux, determining the inductance, is used.
We suppose that thin film (solid, conducting, nonmagnetic) is in external homogeneous variable magnetic field, which has the single component, coinciding with film’s axis. Under such orientation the variable magnetic field will generate in thin film the vortex electric field, the strength of which will has the single axial component. For the first time the experimental proof of existence of such probable vortex electric field’s orientation has been obtained under creation of betatrons – inductive accelerators of electrons [6].
We get radial distribution of vortex electric field from the first Maxwell’s equation over original magnetic field. The density of Foucault currents has the same distribution in space in homogeneous conducting medium. The scales of strength and density of vortex current have been obtained under calculation.
We find the value of current, induced all over thin film, over the law of distribution of Foucault currents’ density by calculation of flux integrals. The density of vortex Foucault currents creates selfmagnetic field in the space of thin film. This magnetic field of substance reply on external influence has the single projection, coinciding with film’s axis, for original orientation of vortex currents in cylindrical system of coordinate. The direction of projection of magnetic field’s reply over all film’s points is opposite to the direction of external magnetic field. This is the main reason of diamagnetism, being manifested by Foucault currents.
The distribution of substance reply’s magnetic field is calculated by integration of second Maxwell’s equation, written in cylindrical system of coordinate, and inductive properties of thin film are investigated.
Further we find flux inductance. It represents by itself the coefficient of proportionality between total average magnetic flux, which crosses the conducting film over halfperiod, and the current, which appears in the film over the same period. The total average magnetic flux is summed from the flux of external magnetic field and the flux of substance reply’s magnetic field. The flux of external magnetic field vanishes under averaging over halfperiod, but the flux of substance reply’s magnetic field depends on phase relationships and can be as positive so negative value.
RESULTS
The calculation show that average flux inductance of thin film over halfperiod does not depend on the frequency and can be as positive so negative one. It is important that flux inductance depends on geometric dimensions of film only, but its operational frequency depends on film’s conductivity and locates in the band, being determined by the scale of frequency.
The suggested construction and computation of PPI with “conducting film inside conducting ring”technology have significant advantages. They give capability to realize microscopic integral inductance, which value depends on thickness and radius of additional film only. Its positive contribution in total inductance permits appreciably to increase the inductance, being obtained under classic singleturn decision at the same square.
The operational band of frequencies of inductance suggested can be “moved” in given band by the choice of resistivity of additional thin film’s material.
DISCUSSION
The experiments with planar spiral inductor of 170 um radius, have been carried out in [7]. It has been loaded at thin conducting layers of CuAl. Under their total width of 400 nm, layers have formed positive frequencyindependent vortex current’s inductance. The theory suggested explains the existence of such inductance by dimensions of layer, i.e., by nanodimensional effect.
The estimates, executed over calculation relationships, point out at that nanodimensional effect discovered permits from 7 till 50 times to increase the values of planar inductance at the square of 100ő100 um2 in one layer. It is substantially more than the value of maximal inductance, obtained in traditional CMOStechnologies [12].
It is also shown in experiments [7] that laminated film with total width more than 1 um can manifest itself as frequencydependent inductance, which vanishes at two characteristic frequencies, that is validated by theory, developed in [11].
Nulls of inductance divide whole frequency band into three parts. At lowfrequency interval the inductance of cylindrical multilayers film – positive value, decreasing with growth of frequency (paramagnetic properties of Foucault currents are manifested). At midband frequency interval the inductance is negative (natural diamagnetic properties of Foucault currents are manifested). At this interval the minimal value of inductance is achieved at defined frequency. At highfrequency interval the inductance is positive (again paramagnetic properties of Foucault currents are manifested) and practically is independent of frequency. In accordance with suggested in [11] theory the cutoff frequency in dynamic inductance is absent. The correctness of such assertion requires experimental check. 
Keywords 
 positive planar inductance (PPI), cylindrical film, current ring, nanodimensional effect, “conducting film inside current ring”technology. 
Library reference 
 Sapogin V.G., Prokopenko N.N., Ivanov Y.I., Bugakova A.V. Nanodimensional effect at planar inductance with “conducting film inside current ring”technology // Problems of Perspective Micro and Nanoelectronic Systems Development  2016. Proceedings / edited by A. Stempkovsky, Moscow, IPPM RAS, 2016. Part 3. P. 114119. 
URL of paper 
 http://www.mesconference.ru/data/year2016/pdf/D043.pdf 

