ap-4-10.dvi Acta Polytechnica Vol. 50 No. 4/2010 Conductivity Measurements of Silverpastes M. Dirix, O. Koch Abstract Thedevelopmentof three-dimensional printedcircuit boards requires researchonnewmaterialswhich caneasily bedeformed. Conducting pastes are well suited for deformation even after they are applied to the dielectric carrier. This paper deals with measurements of the electrical conductivity of these conducting pastes. Two different conductivity measurement techniques are explainedandcarried out. The resultingmeasurements giveanoverviewof the conductivityof severalmeasured samples. Keywords: conductivity, conducting pastes, 3d circuits. 1 Introduction Currentprinted circuit board(PCB)production is still mostly based on thewell-known concept of laminating andphoto-etching. During the laminatingprocess, the whole surface of the dielectric carrier is covered with a conducting material such as copper. Then the con- ductingmaterial is coveredwith aphotosensitive poly- mer and exposed to a light projection of the desired circuit. Afterwashing, only thedesiredcircuit surfaces are coveredwith the polymer. Using ahighly corrosive etching fluid, the conducting material not covered by the polymer is removed, leaving only the circuit. The disadvantages of this method are on the one hand the use of conducting material that will be dis- carded. This is costly. On the other hand, the lam- inating process uses high pressure to bond the con- ductor with the dielectric carrier. This bonding can therefore only be applied to hard flat surfaces, such as standard dielectric carriers. These flat surface PCBs are ill-suited for deformation, which limits their ap- plication in the growing market for 3D shaped circuit boards. Oneway to solve this problem is to useMolded In- terconnectDevicematerials in combinationwithLaser Direct Structuring (LDS) [1]. InMID-LDS, the dielec- tric carrier is preformed into the desired shape. Then the surface of the dielectric carrier is covered with an organic metal complex. The organic metal complex can be activated using a laser beam. The activated surface is roughened, and the organicmetal complex is separated into metal atoms and organic ligands. This makes the activated surface suited for copper coating with a strong grip. After cleaning, the copper coating is then built up on the activated areas using a current- free copper bath. Another approach is to use thin flexible dielectric carriers together with a moldable conductor, such as conducting pastes. In this approach, the conductor is first applied to the surface of the dielectric carrier us- ing a printing technique like that used for ink printers. The shape of the applied circuit has to take into ac- count the desired form of the circuit after deforming. The dielectric carrier together with the conductor are then deformed into the desired shape. The advantages clearly lie in the straightforward processing steps. Most conducting pastes consist of conducting ma- terial dissolved in an epoxy, polyamide or acrylate ad- hesive. After applying thepaste, thematerial isheated in order to thoroughly bond the conductor to the car- rier and remove the solvent from the conducting struc- ture. The resulting conducting structure is studied for its conductivity and usability for high frequent PCB designs. This paper presents two methods for mea- suring the electrical conductivity of such conducting pastes. 2 Microstrip T-resonator measurement structure The microstrip T-resonator is a two-port resonator which consists of a 50Ω microstrip line with a par- allel quarter wavelength resonating line [2]. Figure 1 shows the layout of the T-resonator used here. The open-endedquarterwavelength transmission line stub, resonates at odd integermultiples of the quarterwave- length frequency. The first resonance can be deter- mined by calculating the length of the quarter wave- length stub, as follows Lel = nc 4f √ ref f (1) where n is the order of the resonance (here n = 1), c is the speed of light, f is frequency, ref f is the effec- tive dielectric constant for the dielectric carrier that is used. The line length of the quarterwavelength stub is calculated to have the primary resonance at 500MHz. In order to get the first resonance as accurately as possibly at 500 MHz, corrections must be applied for open-end and T-junction effects. These effects where 19 Acta Polytechnica Vol. 50 No. 4/2010 compensatedwith the use of Agilent ADS commercial software. The accurate designing makes it possible to have data points at the desired frequencies. ����������������������� ����������������������� ����������������������� ����������������������� ����������������������� ����������������������� ����������������������� ����������������������� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� quarter wavelength stub port 1 port 2 Fig. 1: Basic layout of the T-Resonator measurement structure The T-resonator operates like a notch filter with a resonant null in the resonance frequencies. A network analyser (NWA) is used to measure the transmission of the two-port network. From the measurement it is possible to determine the loaded quality factor QL by finding the resonance frequencies and the correspond- ing 3 dB bandwidths BW3dB. The loaded quality fac- tor is the calculated as QL = f BW3dB (2) The loaded quality factor is influenced by the 50Ω test set of the NWA. In order to compensate, the un- loaded quality factor Q0 has to be extracted Q0 = QL√ 1−2 ·10−(LA/10) (3) where LA is the insertion loss in dB at the resonance. The unloaded quality factor Q0 comprises the three main loss effects, namely conductor, dielectric and ra- diation losses [3]. Q−10 = Q −1 c + Q −1 d + Q −1 r (4) where Qc is the quality factor due to conductor losses, that we want to derive, Qd is the quality factor due to dielectric losses, and Qr is the quality factor due to radiation losses. The T-resonator is first implemented using aknownconductor, copper, anda referencemea- surement is carried out. For copper, the attenuation due to conductor loss can be obtained with [4] αc = Rs Z0W (5) where Rs = √ ωμ0 2σ is the surface resistivity of the con- ductor. Using (5), the quality factor due to conductor losses can be calculated as Qc(copper)= β 2α (6) Now it is possible to derive the sum quality factor of both other losses from the measurement with Q−1ref(copper)= Q −1 0 − Q −1 c (7) It is assumedhere that the losses due to the dielec- tric carrier and radiation are equal for the reference measurement with the copper conductor and for the measurements carriedoutusing the conductingpastes, if the samedielectric carrier is usedand thedimensions of the resonator are equal. The surface resistivity Rs and further the electrical conductivity σ canbederived by calculating equations (7), (6) and (5) backwards for the measured sample. There is limited accuracy, due to the relatively small quality factor and the assumption that the di- electric and radiation losses are equal for the copper and for the samples. Only assumptions can be made about the global locationof the electrical conductivity. 3 Surface resistance measurements by means of a dielectric resonator The methods described in this section are based on the findings of J. Krupa [5]. The measurements are performed using a dielectric resonator, manufactured by QWED. In a completely closed resonator, the un- loaded quality factor comprises only the quality fac- tor due to conductor losses Qc and the quality factor due to dielectric losses Qd. The unloaded quality of a resonator which is completely filled with a dielectric material can then be described as Q−10 = Rss Asup + Rsm Amet + pe tanδ (8) where Asup and Amet are geometrical factors for the conducting surfaces of the resonator, the former for the surface of the sample and the latter for the lat- eral metal parts of the resonator. Rss and Rsm are the corresponding surface resistance values for sample and metal. pe is the fraction of the electrical energy stored in the dielectricmaterial, and tanδ is its dielec- tric loss tangent value. Although equation (8) is valid for any of the res- onator modes, only the T E0ρφ modes are considered for the conductivitymeasurements. The T E0ρφ modes are chosenbecause theyhaveboth axial symmetryand ohmic contact between the surface of the sample, and the lateral metal conductor has no influence on the quality factor of the resonance. This lack of influence results in high reproducibility for experiments using the same pair of samples. For the measurements, the T E010, T E011 and T E012 modes are used to determine the electrical conductivity of the sample. In order to eleminate the surface resistance of the lateral metal conductor in (8), first a measurement is made using samples of the samematerial as themetal. 20 Acta Polytechnica Vol. 50 No. 4/2010 Using the measured unloaded quality factor as a ref- erence Q0ref it is possible to write (8) as Rss =AsupQ − 0 1− A2sup Asup + Amet Q−10ref − pe tanδ A−1sup + A −1 met (9) With equation (9) it is now possible to determine the surface resistance of the sample, and from this to derive the electrical conductivity. The accuracy of the measurement depends on measuring the unloaded quality factor, the uncertainty of the dielectric loss tangent value and the values of the geometrical fac- tors. The former is resolved by adjusting both the coupling loops to have a maximal transmission S21 of −40dB, which results in a maximum error for Q0 of 1%. Both the other values are provided by the manu- facturer. The accuracy of the measurement using the dielectric resonator relies on the assumption that the conductor deposit is bulk. The deposited conductor is only assumed to be bulk if its thickness is at least 3δ, where δ = 1√ πf κμ [6]. If the deposited conduc- tor is thinner, the electromagnetic field can in part penetrate through the conductor into the carrier. The dielectric losses of the carrier will then have an effect on the quality factor of the measurment. For samples with a minimum of 3δ, the maximum accuracy, tak- ing into account the error of Q0, is 2% for the surface resistance and 5% for electrical conductivity. 4 Measurements The T-resonator structure is implemented using a Rogers RTDuroid 5880 laminate. Figure 2 shows the resulting resonator structure, a copper structure on the left and a structure with a sample conducting paste on the right. The reference sample in copper was created using a photo-etching technique. In or- der to check for connectivity errors, the T-resonator sample structures were created once using a copper conductor with a quarter wavelength stub printed on top using the conducting paste, and in the other case both transmission line and quarter wavelength stub were printed using the conducting paste. For these measurements it has to be taken into account that the laminate was possibly unsuited for the prepara- tion and for the heating steps required for applying the conducting pastes, resulting in higher inaccuracy of the measurements. Figure 3 presents the resulting transmission measurements. Two resonant points can be seen, one at approximately 500 MHz and one at 1.5 GHz. Several samples with different pastes were then measured, and the results can be found in Ta- ble 1. Fig. 2: The T-Resonator Structure Fig. 3: Transmission measurement of the T-Resonator Structure Table 1: Electrical conductivity measurements using the T-resonator structure Sample σ [S/m] @500 MHz σ [S/m] @1.5 GHz 01 3E6 3E6 03 2E6 3E6 07 2E6 3E6 08 3E6 4E6 The dielectric resonator uses samples with surface dimensions of approximately 9.5 cm times 9.5 cm on both the top side and thebottomside of the resonator. Using the dielectric resonator, the copper samples are first measured as a reference. The copper samples are laminated surfacesofRogersRTDuroid35μminthick- ness. The actual samples are squares of conducting pastes printed on a dielectric carrier with an approx- imated thickness of 10μm, which was the current de- positing limit. This is less than the formerly defined 3δ that is needed for the assumption of a bulk con- ductor. However, considering the high reproducibility of the measurements, and taking into account that all samples use the same carrier and have the same de- positet thickness, it is still possible to make a qualita- tive evaluationof thedifferencesbetween themeasured samples. The resulting conductivitymeasurementsare shown in table 2. 21 Acta Polytechnica Vol. 50 No. 4/2010 Table 2: Electrical conductivity measurements using the dielectric resonator Sample σ [S/m] σ σ @1.6 GHz @2.1 GHz @2.7 GHz Copper 5.53E7 5.35E7 5.65E7 07120902 5.89E+006 5.61E+006 5.43E+006 07120910 5.35E+006 4.98E+006 5.50E+006 07120913 4.42E+006 4.35E+006 4.48E+006 07120914 4.45E+006 4.47E+006 4.73E+006 07120915 4.40E+006 4.63E+006 4.62E+006 07120916 4.35E+006 4.68E+006 4.63E+006 07120917 5.50E+006 5.72E+006 5.67E+006 07120918 5.50E+006 5.50E+006 5.50E+006 5 Conclusion A T-resonator structure for measuring electrical con- ductivity has been realised for 500 MHz and 1.5 GHz. Further, a dielectric resonator has been evaluated and acquired for accurate measurements at 1.6 GHz, 2.0 GHz and 2.7 GHz. Taking into account the accu- racy of themeasurements it is possible tomake a qual- itative evaluation of the different conducting pastes. Theelectrical conductivities of the sample conduct- ing pastes were measured using the T-resonator and the dielectric resonator. The conductivity of the con- ducting pastes has been shown to be approximately 10%of the electrical conductivity of copper. Although the conductor losses for the conducting pastes will be larger than in the case of copper, they are still usable for designing high frequent circuits. Acknowledgement The researchdescribed in this paperwas supervisedby Prof. D. Heberling, Institute of High Frequency Tech- nology, RWTH Aachen University. References [1] Orlob, C., Kornek, D., Preihs, S., Rolfes, I.: Com- parison ofmethods for broadband electromagnetic characterisation of Molded Interconnect Device materials.Advances inRadio Science, 2009, vol.7, p. 11–15. [2] Lätti, K. P., Heinola, J. M., Kettunen, M., Ström, J. P., Silventoinen, P.: A Novel Strip Line Test Method for Relative Permittivity and Dissi- pationFactor of PrintedCircuit BoardSubstrates. URSI/IEEE XXIX Convention on Radio Science, 2004, p. 71–74. [3] Amey, D. I., Curilla, J. P.: Microwave properties of ceramic materials. Du Pont Electronics, 1991, p. 267–272. [4] Pozar,D.M.: Microwave Engineering. 3th ed.Wi- ley, 2005. [5] Krupka, J., Klinger, M., Kuhn, M., Baranyak, A., Stiller, M.: Surface Resistance Measurements of HTS Films by Means of Sapphire Dielectric Res- onators. IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, 1993, vol. 3, No. 3, p. 3043–3047. [6] Krupka, J., Derzakowski, K., Zychowicz, T., Givot, B. L., Egbert, W. C., David, M. M.: Mea- surements of the surface resistance and conduc- tivity of thin conductive films at frequencies near 1 GHz employing the dielectric resonator tech- nique. Personal Communication. About the authors Marc DIRIX was born in Geleen, the Netherlands in 1980. He received his Dipl.-Ing degree in Electri- cal Engineering from RWTH Aachen University, Ger- many, in 2009. Currently, he is a research assistant at the Institute of HighFrequencyTechnology atRWTH AachenUniversity,where he isworking towards a doc- toral degree (PhD).His research interests includemea- surement of high frequent properties of newmaterials. Olivier KOCH was born in Dortmund, Germany in 1977. He receivedhisDipl.-Ingdegree inElectricalEn- gineering fromRWTHAachenUniversity,Germany, in 2004. Currently, he is a research assistant at the Insti- tute of High Frequency Technology at RWTH Aachen University, where he is working towards a doctoral de- gree (PhD). His research interests include Power Am- plifiers and MIMO systems. M. Dirix O. Koch E-mail: marc@ihf.rwth-aachen.de, koch@ihf.rwth-aachen.de Institute of High Frequency Technology RWTH Aachen University Melatener Strasse 25, 52074 Aachen, Germany 22