Free Space Microwave Characterization of Silicon Wafers for Microelectronic Applications

2005 ◽  
Vol 2 (2) ◽  
pp. 35
Author(s):  
Zaiki Awang ◽  
Deepak Kumar Ghodgaonkar ◽  
Noor Hasimah Baba
Keyword(s):  
Complex Permittivity ◽  
Free Space ◽  
Normal Incidence ◽  
Silicon Wafers ◽  
Reflection And Transmission Coefficients ◽  
Frequency Range ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Quarter Wave ◽  
Mode Transitions

A contactless and non-destructive microwave method has been developed to characterize silicon semiconductor wafers from reflection and transmission measurements made at normal incidence using MNDT. The measurement system consists of a pair of spot-focusing horn lens antenna, mode transitions, coaxial cables and a vector network analyzer (VNA). In this method, the free-space reflection and transmission coefficients, S11 and S21 are measured for silicon wafers sandwiched between two Teflon plates of 5mm thickness which act as a quarter-wave transformer at mid-band. The actual reflection and transmission coefficients, S11 and S21 of the silicon wafers are then calculated from the measured S11 and S21 using ABCD matrix transformation in which the complex permittivity and thickness of the Teflon plates are known. From the complex permittivity, the resistivity and conductivity can be obtained. Results for p-type and n-type doped silicon wafers are reported in the frequency range of 11 – 12.5 GHz. The dielectric constant of silicon wafer obtained by this method agrees well with that measured in the same frequency range by other conventional methods.

scholarly journals Estimation of S-parameters and dielectric permittivity of quartz ceramics samples in millimeter waveband

Doklady BGUIR ◽  
2021 ◽  
Vol 19 (7) ◽  
pp. 65-71
Author(s):  
N. A. Pevneva ◽  
D. A. Kondrashov ◽  
A. L. Gurskii ◽  
A. V. Gusinsky
Keyword(s):  
Dielectric Constant ◽  
Dielectric Permittivity ◽  
Ceramic Materials ◽  
Reflection And Transmission Coefficients ◽  
Frequency Range ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Higher Order Modes ◽  
S Parameters ◽  
The Fourier Transform

A modified Nicholson – Ross – Weir method was used to determine complex parameters and dielectric permittivity of ceramic materials in the range 78.33–118.1 GHz. The measuring equipment is a meter of complex reflection and transmission coefficients, a waveguide measuring canal with a special measuring cell, consisting of two irregular waveguides and a waveguide chamber between them, which provides insignificant influence of higher-order modes. The dependences of the amplitude and phase of the reflection and transmission coefficients on frequency were obtained experimentally for fluoroplastic and three ceramic samples in the frequency range 78.33–118.1 GHz. The obtained S-parameters are processed according to an algorithm that includes their averaging based on the Fourier transform in order to obtain the values of the dielectric permittivity. Fluoroplastic was used as a reference material with a known dielectric constant. The dielectric constant of fluoroplastic has a stable value of 2.1 in the above mentioned frequency range. The dielectric constant of sample No. 1 varies from 3.6 to 2.5 at the boundaries of the range, sample No. 2 – from 3.7 to 2.1, sample No. 3 – from 2.9 to 1.5. The experimental data are in satisfactory agreement with the literature data for other frequencies taking into account the limits set by the measurement uncertainty.

Amplitude‐variation‐with‐angle behavior of self‐similar interfaces

Geophysics ◽  
1999 ◽  
Vol 64 (6) ◽  
pp. 1928-1938 ◽  
Author(s):  
Kees Wapenaar
Keyword(s):  
Normal Incidence ◽  
Reflection And Transmission Coefficients ◽  
Well Logs ◽  
Amplitude Variation ◽  
Reflection And Transmission ◽  
Velocity Function ◽  
Transmission Coefficients ◽  
Step Functions ◽  
Self Similar ◽  
Amplitude Variation With Angle

Amplitude‐variation‐with‐angle (AVA) analysis is generally based on the assumption that the medium parameters behave as step functions of the depth coordinate z, at least in a finite region around the interface. However, outliers observed in well logs often behave quite differently from step functions. In this paper, outliers in the acoustic propagation velocity are parameterized by functions of the form [Formula: see text]. The wavelet transform of this function reveals properties similar to those of several outliers in real well logs. Moreover, this function is self‐similar, according to [Formula: see text], for β > 0. Analytical expressions are derived for the acoustic normal incidence reflection and transmission coefficients for this type of velocity function. For oblique incidence, no explicit solutions are available. However, by exploiting the self‐similarity property of the velocity function, it turns out that the acoustic angle‐dependent and frequency‐dependent reflection and transmission coefficients are self‐similar as well. To be more specific, these coefficients appear to be constant along curves described by [Formula: see text], where p is the raypath parameter and ω the angular frequency. The singularity exponent α that is reflected in these curves may prove to be a useful indicator in seismic characterization.

Tunable and Self-Sensing Microwave Composite Materials Incorporating Ferromagnetic Microwires

2008 ◽  
Vol 54 ◽  
pp. 201-210 ◽  
Author(s):  
Dmitriy Makhnovskiy ◽  
Arkadi Zhukov ◽  
V. Zhukova ◽  
J. Gonzalez
Keyword(s):  
Magnetic Field ◽  
Composite Materials ◽  
External Magnetic Field ◽  
Resonance Frequency ◽  
Free Space ◽  
Effective Permittivity ◽  
Stress Sensitivity ◽  
Reflection And Transmission Coefficients ◽  
Reflection And Transmission ◽  
Transmission Coefficients

New types of stress sensitive and magnetic field tunable microwave composite materials are discussed where embedded short ferromagnetic microwire inclusions are used as controllable radiative elements. The dc external magnetic field is applied to the whole composite structure. And, the local stress is transferred to the individual microwires through the accommodating composite matrix. The spatial and angular distributions of microwires can be random, partly ordered, or completely ordered. For a wide frequency range, the free-space microwave response of a wire-filled composite can be characterized by a complex effective permittivity with resonance frequency dispersion. The latter depends on the conductive and magnetic properties of the microwire inclusions that contribute to the ac microwire magnetoimpedance (MI). In the vicinity of the so-called antenna resonance frequency, which is defined by the length of microwires and matrix dielectric constant, any variations in the MI of the microwires will result in large changes of the effective permittivity, and hence the reflection and transmission coefficients for an incident microwave. The field or stress dependence of the effective permittivity arises from the corresponding field or stress sensitivity of the MI in the ferromagnetic microwires with induced circumferential or helical magnetic anisotropy, respectively. The strong field tunable effect in the proposed composite materials can be utilized to introduce reconfigurable microwave properties in coatings, absorbers, and randomizers, and also in new media such as microwave metamaterials and bandgap wire structures. A maximum field tunability of 30 dB was achieved for free-space transmission measurements when the external magnetic field changed from zero to ~40 Oe. The stress sensitivity of reflection and transmission coefficients opens up new possibilities for the distant non-destructive testing and evaluation of composite materials both in the laboratory environment and large scale applications. The stress tunability of transmission coefficient may reach up to 5-8 dB within the elastic limit. The reflection coefficient usually demonstrates less tunability in both cases (field and stress dependent) and may require a multilayer structure to achieve better results, but it is always strong enough for the stress sensing applications.

scholarly journals Approximate reflection coefficients for a thin VTI layer

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. C1-C11 ◽  
Author(s):  
Qi Hao ◽  
Alexey Stovas
Keyword(s):  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
Normal Incidence ◽  
Reflection And Transmission Coefficients ◽  
Reflection Coefficients ◽  
Angle Of Incidence ◽  
Isotropic Layer ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
P And Sv Waves

We have developed an approximate method to derive simple expressions for the reflection coefficients of P- and SV-waves for a thin transversely isotropic layer with a vertical symmetry axis (VTI) embedded in a homogeneous VTI background. The layer thickness is assumed to be much smaller than the wavelengths of P- and SV-waves inside. The exact reflection and transmission coefficients are derived by the propagator matrix method. In the case of normal incidence, the exact reflection and transmission coefficients are expressed in terms of the impedances of vertically propagating P- and S-waves. For subcritical incidence, the approximate reflection coefficients are expressed in terms of the contrast in the VTI parameters between the layer and the background. Numerical examples are designed to analyze the reflection coefficients at normal and oblique incidence and investigate the influence of transverse isotropy on the reflection coefficients. Despite giving numerical errors, the approximate formulas are sufficiently simple to qualitatively analyze the variation of the reflection coefficients with the angle of incidence.

scholarly journals ELECTROMAGNETIC RADIATION REFLECTION AND TRANSMISSION CHARACTERISTICS OF TWO-LAYER STRUCTURES BASED ON TRANSITION METAL OXIDES

Doklady BGUIR ◽  
2019 ◽  
pp. 93-100
Author(s):  
O. V. Boiprav ◽  
N. V. Bogush ◽  
L. M. Lynkou
Keyword(s):  
Surface Layer ◽  
Transition Metal ◽  
Metal Oxides ◽  
Electromagnetic Radiation ◽  
Transition Metal Oxides ◽  
Reflection And Transmission Coefficients ◽  
Frequency Range ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Layer Structures

The aim of the work, the results of which are presented in the framework of the article, was to study the of electromagnetic radiation interaction laws in the frequency range 0.7…17 GHz with two-layer structures, the surface layer of which was made using powdered titanium dioxide, and the inner layer was made using a powder material based on oxide ferric iron. The thickness of the layers of the studied structures varied from 0.3 to 1 cm. To achieve this goal, theobjectives associated with the development of a methodology for the manufacture of multilayer structures based on composite materials containing transition metal oxides, as well as with the measurement of such structures samples electromagnetic radiation reflection and transmission coefficients in the frequency range 0.7...17 GHz. These measurements were carried out using a panoramic meter of reflection and transmission coefficients SNA 0.01–17. Based on the obtained measurement results, it was shown that in the frequency range 0.7…2 GHz, the lowest values of electromagnetic radiation reflection coefficient, reaching –20 dB, are characterized by structures whose surface layer thickness is 1 cm, and in the range 2 ... 17 GHz – structures, thickness the surface layer of which is 0.5 or 1 cm (depending on the thickness of the inner layer). The values of electromagnetic radiation transmission coefficient in the frequency range of 0.7...17 GHz of such structures reach –23 dB. Based on the results of the study, it is proposed to use the considered structures in the process of creating shielded rooms or improving the latter (for example, in cases, when it's necessary to reduce the level of passive interference in rooms shielded with metal materials).

Reflection and Transmission Coefficients of Plane Waves in Magnetoelectroelastic Layered Structures

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
J. Y. Chen ◽  
H. L. Chen ◽  
E. Pan
Keyword(s):  
Piezoelectric Materials ◽  
Plane Waves ◽  
Layered Structures ◽  
Organic Glass ◽  
Reflection And Transmission Coefficients ◽  
Material Structure ◽  
Layered System ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Novel Material

Reflection and transmission coefficients of plane waves with oblique incidence to a multilayered system of piezomagnetic and/or piezoelectric materials are investigated in this paper. The general Christoffel equation is derived from the coupled constitutive and balance equations, which is further employed to solve the elastic displacements and electric and magnetic potentials. Based on these solutions, the reflection and transmission coefficients in the corresponding layered structures are subsequently obtained by virtue of the propagator matrix method. Two layered examples are selected to verify and illustrate our solutions. One is the purely elastic layered system composed of aluminum and organic glass materials. The other layered system is composed of the novel magnetoelectroelastic material and the organic glass. Numerical results are presented to demonstrate the variation of the reflection and transmission coefficients with different incident angles, frequencies, and boundary conditions, which could be useful to nondestructive evaluation of this novel material structure based on wave propagations.

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