Materials Characterization Using A Structure Based On Microstrip Line

Lamia Zarral Laboratory of Instrumentation Scientific

Institute of electronic Department of electronic, ,FERHAT Abbess University,

Setif, Algeria lamia_zarral@yahoo.fr

Fabien NDAGIJIMANA Laboratory of INPEG Minatec

Institute of Microelectronic, Electromagnetic and Photonic Department Of Microelectronic, Joseph FOURIER

University Grenoble, France fabien@minatec.inpg.fr

Abstract— The considerable evolution of microelectronics has highlighted the need for new dielectric materials of high permittivity (high-k). Because of their high permittivity, these materials can also be very good candidates for other microwave applications, especially if their dielectric losses are low. A new application of miniature antennas performed on these high-k materials and designed a new concept of interconnections without son. Proper use of these materials requires a knowledge of their dielectric properties. To do so, a rigorous characterization of these materials has been established [35], and we used to characterize our materials. We present in this section a technique for extracting the permittivity and permeability of high-k materials from measurements of planar transmission lines.

Keywords- Electric characterization – transmission-line – coaxial probe – complex permittivity – thin layer dielectric – multilayer materials – semiconductor materials

I. INTRODUCTION Transmission lines are modeling tools most commonly

used in the fields of circuits and systems in telecommunications include, for example, microstrip lines [Liu03], the two-wire lines with ADSL, the interconnections in microelectronics [Gri04] and more recently in power electronics, including the modeling of new filters used in input stages and output of power supplies [Wyk04] [Wyk08] [1]. The considerable evolution of microelectronics HAS Highlighted the Need for new dielectric materials of high permittivity (high-k). Because of their high permittivity, these materials can also be very good candidates for other microwave applications, especially if their dielectric losses are low. A new application of miniature antennas performed on these high-k materials will be a new concept of wireless interconnections.

Proper use of these materials requires acknowledge of their dielectric properties. To do so, a rigorous characterization of these materials has been established [2], and used to characterize our materials.

We present in this section a technique for extracting the permittivity and permeability of high-k materials from measurements of planar transmission lines.

II. PRINCIPLE OF THE METHOD OF EXTRACTION

The purpose of determining the effective permittivity is to estimate the impedance characteristic lines. The effective permittivity is a factor influencing their characteristics: length of the antenna resonance and characteristic impedance for the lines [3]. The use of Two transmission line techniques permitted to proper discontinuity effects Occurring in the connector Areas. Also this method HAS-been applied successfully to a microstrip configuration with FR-4 substrate. Using SMA connector, loss tangent has-been inferior to 10-2 Measured up to 14GHz, and relative permittivity has-been Measured with an error of 3% up to 18GHz (4) The principle of the proposed method is shown schematically in Figure 1.

Figure 1. Schematic of the proposed extraction method.

The measurements were performed with the vector analyzer 8720, which provides the [S] parameters of the structure to be characterized. Moreover, the formulas linking the [S] matrix and the secondary

constants of a transmission line is the basis of our method [7].

The principle is based on measuring the S parameters of a planar line deposited on the substrate to be characterized. In addition to the measurement of the line on the substrate, a second measurement of vacuum line is needed (figure2) [5]. This method can also estimate the dielectric and magnetic losses angle in the substrate. This method is very rigorous [6], but in our case we used anstead of strip "w" a central conductor of an internal diameter d = 3mm, and an external diameter D = 4mm. There are many wave guides with, non rectangular sections. The most used have circular or elliptical sections. Their study is similar to the guide of rectangular section and results are similar, although mathematically it is more laborious. We show that all these guides have a cutoff frequency, since their cross section contains only one conductor. We obtain an approximative value of this frequency from the dispersion relation, by replacing the cutoff wavelength

c by the diameter D given by [7]:

)( 222

2cz

r

kkc +=ε

ω

With : Dk

cc

πλπ 22 ≈=

Dcetf

ckf

rr

c21min21

minmin 22 επεπ

ω==

Then:

For D = 10cm, operating in air

( )1≈rε , .3min GHzf =

III. PARAMETERS EXTRACTION Moreover, the formulas linking the [S] matrix and

the secondary constants of a transmission line is the basis of our method.

Moreover, the formulas linking the matrix [S] and the constants a secondary transmission line is the basis of our method [7].

∗∗

∗∗∗ =

00 c

cR Z

Zγγμ

∗∗

∗∗∗ =

c

cR Z

Z

0

0

γγε

( )1ln1 2 −±= ∗∗∗ AAl

γ

( )( )∗

∗∗∗∗∗

⋅++−

=12

12212211

211

SSSSSA

( )( )( )( ) ∗∗∗∗

∗∗∗∗∗

−−−+++

=12212211

12212211

1111

50SSSSSSSS

Zc

Where ∗γ and

∗cZ (resp.

∗∗00 cetZγ ) is the propagation

constant and characteristic impedance of the line. l: is the length of the line.

To characterize the material being placed directly in the structure, these constants are obtained by the following relations [8]:

( )( )( )( ) ∗∗∗∗

∗∗∗∗∗

−−−+++

=12212211

12212211

1111

SSSSSSSS

ZZ nc

( )( )⎟⎟⎠

⎞⎜⎜⎝

⎛⋅

+−+=⋅ ∗

∗∗∗∗−

21

211222111

211cosh

SSSSSlγ

To extract the effective permittivity and permeability, we used the following relations [9]:

∗∗

∗∗∗ =

matair

airmateff Z

Zγγε ∗∗

∗∗∗ =

airair

matmateff Z

Zγγμ

Our study focuses only on the dielectric properties, so we take only the equations for the relative permittivity. To the equations we have so far, we must add the equations that relate the effective permittivity to the relative permittivity.

Given that: then we can show that:

Knowing that: 2/1

1211−

⎟⎠⎞

⎜⎝⎛ +=⇒≥

Wha

hW

Then we can show that:

aaeff

r +−+

=1

1.2 εε

By inference, we have:

aaeff

r +−+

=1

1.2)Re(

'εε et

aeff

r +=

1.2

)Im("ε

ε

'

"

r

reTan

εεδ =

With these equations we will build a program in Matlab, which will help us find the curves of the results of this method.

Figure 2. Rreal and imaginary part of relative permittivity of Teflon This curve shows that ε” is nul, this implies that losses are zero.

IV. CONCLUSION Our method is used for characterization in guided space.

It was made, using a microstrip line, but with a central conductor with an outer diameter, D = 4 mm and an internal diameter d = 3mm. This method is easy to perform and also economical , with great advantage and a good percentage of errors in permittivity. After the results of S type parameter that shows the state of the electromagnetic wave transmission through different materials, the extraction was done using mathematical derived from the theoretical study. These equations were put into a program in Matlab to display the curves of the results of the relative permittivity of each material.

References [1] A. Rumeau, "Behavioral Modeling in electrical engineering under-representation diffusive: Methods and Applications", PhD thesis, University of Toulouse III - Paul Sabatier, France, November 23, 2009.

[2] M. Kadi, J. Dansou, F. Ndagijimana, "Hybrid solution for interconnection without son by miniature antennas for multichip support", OHD - Calais - France, September: 2003. [3] H. M. BARAKAT, "Radio Frequency Device millimeters Objects Communicating Smart Dust ", PhD thesis, University Joseph Fourier-Grenoble I, France, January 18, 2008. [4] M. Moukanda, F. Ndagijimana, J. Chilo, P. Saguet “ Effet des discontinuités et de la conductivité d’une monture coaxiale pour la caractérisation des matériaux ”, Grenoble, France

[5] J. Lescot, B. Boyer, J. Haidar, F. Ndagijimana. "Characterization of homogeneous isotropic materials," LEMO, Grenoble, France.

[6] C. Kittel "Introduction to solid state physics."

[7] JA Edminister "Electromagnetism", 1985.

[8] A. Moliton "Applications of electromagnetism in material media", Edition Hermes, June-2004

[9] M. Moukanda, F. Ndagijimana, J. Chilo, P. Saguet "Effect of discontinuities and the conductivity of a coaxial mount for materials characterization", Grenoble, France

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

x 109

0

0.5

1

1.5

2

2.5

Frequence - [Hz]

Rée

l et

Imag

inai

re d

e E

psilo

n r

imag Er

réel Er