Theory of the Recursive Dyadic Green's Function for Inhomogeneous Ferrite Canonically Shaped Microstrip Circulators

Micro & Optical Tech Letters

2019

There has been a continuing interest in finding ways to shrink the dimensions of electronic devices, especially active devices like transistors, down to become compatible with the ever decreasing size scales, using fabrication processes such as at Intel, with the trend toward 10 nm. Eventual gate length in MOSFETs is roughly half this dimension. This had been one of the (not the only one) of interests in using ferroelectric (FE) materials in the gate of FETs, for example, when the FE material displays a negative polarization effect. Such ideas as escaping the Boltzmann tyranny have loomed large, regarding the subthreshold voltage, and have motivated this interest. It is generally understood that for stable, steady state operation of devices typical of microwave and millimeter wave electronics, no negative differential capacitance is possible with conventional thinking. However, it may be possible, perhaps in transient regions of the hysteretic curve, with strain engineering of materials, to obtain some if not all elements of the differential capacitance tensor which are negative. The analysis is based upon analyzing the physics using thermodynamic phenomenological free energy.

“…There is a fairly systematic way to find the inverse of the inverse permittivity tensor. The prescription is given by

κ^{- 1} = \frac{{((), κ^{c})}^{T}}{\det ((), κ)}

where κ c is the cofactor tensor found as

κ_{ij}^{c} = {(- 1)}^{i + j} M_{ij}^{κ}

…”

Section: Differential Capacitance Affected By Stresses and Strains Inmentioning

confidence: 99%

Ferroelectric differential capacitance affected by stresses and strains and implications for use in electronic devices

Micro & Optical Tech Letters

2019

“…Clearly, the x ij are symmetric (x ij ¼ x ji ). The deformations x ij ¼ ∂u i =∂R j and x ji ¼ ∂u j =∂R i are added together in (16), and averaged so that when inserted back into (15),…”

Section: Role Of Stresses and Strains In The Free Energy Expressionsmentioning

confidence: 99%

“…There is a fairly systematic way to find the inverse of the inverse permittivity tensor. The prescription is given by 16,17…”

Section: Capacitance Affected By Stresses and Strains In The Ferroelementioning

confidence: 99%

Physics of ferroelectric differential capacitance based upon free energy, and implications for use in electronic devices

2019

J. Adv. Dielect.

In this paper, it is shown that for stable, steady state operation of devices typical of microwave and millimeter wave electronics, no negative differential capacitance is possible with conventional thinking. However, it may be possible, with strain engineering of materials, to obtain some if not all elements of the differential capacitance tensor which are negative. Rigorous derivations are provided based upon analyzing the physics using thermodynamic phenomenological free energy. It should be emphasized that, even with strain engineering, and possible discovery of some negative capacitive elements, stable operation will not be obtained because the thermodynamics precludes it.

“…has been thoroughly presented in [14] and [15]. This capability to account for radial variations can provide new insight.…”

Section: Application Of the 2-d Recursive Green's Function Solvermentioning

confidence: 99%

Analysis of ferrite circulators by 2-D finite-element and recursive Green's function techniques

Newman

IEEE Trans. Microwave Theory Techn.

1998

Ferrite circulator operation is analyzed here by two techniques. The first employs a two-dimensional (2-D) finiteelement (FE) technique, using a publicly available FE package. We show how to adapt this code to the solution of the magnetostatic equations and solve for the distribution of internal magnetic field inside a round ferrite puck of finite thickness, and use it to verify existing approximations for the demagnetizing fields. Additionally, the 2-D FE method has also been used to calculate the RF fields and scattering parameters in circulators having noncircular shapes, as well as nonuniform material properties and bias conditions. We have also investigated the field solutions for round circulators, calculated using a recursive Green's function (RGF) technique. This technique allows for radially varying properties in the material or bias fields, and thus accommodates the nonuniform demagnetizing field distribution in finite pucks. A comparison of the results of this technique with experiment is made. We show how the impedance-matching structures attached to the circulator affect the field distributions inside, and present plots of the field distributions as a function of frequency, which provide insight into circulator operation.