EXPERIMENTAL AND THEORETICAL CHARACTERIZATION OF THICK AND THIN FILMS FOR MICROWAVE USES ON 99 . 6 % ALUMINA SUBSTRATES

In a previous paper,1 we showed, with a microwave quality factor (Q) measurement, that in the X band and with alumina substrates, thick film losses are not worse than thin film losses when the inks are screened then etched, and when they have copper oxide as adhesive layer and gold or copper as metal powder.


INTRODUCTION
A large part of MIC technology is concerned with materials: the properties of metalliza.tions, as well as substrates, are of particular importance.
The classical method used to characterize these metallizations is to determine their losses by a microwave quality factor (Q) measurement.This method is relatively complex and tedious, so we have worked out an easier method which gives good agreement with the theory.

CHARACTERIZATION METHODS
As we give some formulas in this section, we define here the symbols which will be used.

TanS:
Xg, o: guided and free space wavelength Q: F, C: frequency and light velocity e: substrate dielectric constant OtD: eef: substrate effective dielectric a, a L: constant substrate loss tangent /ao, Co: free space permeability and permittivity q: dielectric filling factor Zo: free space impedance unloaded quality factor free space losses dielectric substrate losses ground plane and line losses Re, RL: ground plane and line skin resistance PG, PL: ground plane and line resistivity w,t: h: width and thickness line dielectric substrate thickness 2.1 Classical characterization method.The design of MIC's requires the measurements of losses by the mean of an unloaded Q' measurement.This method has been described in an earlier paper, Q is related to the losses by the following equation" Q r/o'Xg [1]   with x Xo/(eo.,)/ C/Fo(eoO m [21 This method is complex (requiring sophisticated equipment) and tedious (it requires a photo etching of the pattern, and we have instabilities during the measurements at high frequencies).
2.2 An easier characterization method.
Because of the disadvantages of the microwave Q' measurements, we have developed an easier method which is based upon a D.C. resistivity measurement.
2.2 a. Theory.The losses in MIC'S are generally divided into two parts: 1) the dielectric losses, and 2) the ohmic losses, which are themselves divided in two parts" the ground plane and line losses.

DISCUSSION
From equations [10] and [15], tables I and II, and figure 1, it can be seen theoretically and experimentally that: 1) the losses are dependent upon the resistivity, and 2) the ground plane resistivity cannot be neglected.
3.1 Evaluation and characterization of MIC'S by a resistivity measurement.
It is of great interest to know if this simple method permits not only a comparison between different metallizations (evaluation), but also constitutes a characterization method, and consequently a means of determining the absolute value of losses, such as the Q measurement.
We have seen that, with figure 1, we give the theoretical and experimental curves Q f(o).If we take into account the only ohmic losses (table I), we can see that there is a divergence between theoretical and experimental Q; this difference increases when the resistivity decreases.
O Theoretical Q (ohmic losses only) Theoretical Q (total losses) Frittless gold ink (2)__ %" (4) Thick film Mixed gold ink .+4).\ (5) (6)(7)(8)  The influence of the ground plane resistivity on the measured and theoretical Q is displayed in table II.TABLE II Ground plane resistivity influence on measured and theoretical Q.The line pattern is etched; 2.79. 10 .cm is a frittless gold ink resistivity" 32.4.10 s2.cm is a fritted silver-palladium To obtain a good agreement, we must introduce the dielectric losses CtD, and a correcting factor K which takes into account the surface roughness of the substrate.At 10 GHz, with tan/i 2.10-4, and qe/ee --0.9375 ,2 we have: tXD 0.513.10 - Np/cm from equation [3], and K -- 1.05. s The table III presents the total theoretical losses (aD, a6, CtL, and surface roughness losses) and Q for different resistivities.
From table III, we can see that the dielectric losses cannot be neglected for the lower resistivities, but the greater the resistivity is, the more aD can be neglected.This explains the divergence between theoretical (if only computed with ohmic losses) and experimental Q (see figure 1).
If we take into account the total losses, we can see from figure 1, that there is a very good agreement between theory and practice, and that consequently the resistivity measurement is a characterization method of MIC's as suitable as the Q measurement.For a lower cost, it would be attractive to use a ground plane metallization such as silver- palladium which is about ten to fifteen times less expensive than gold.Unfortunately, the results show that the ohmic losses are very much higher than when we have gold as ground plane and conductor line.So, if we compute t6 versus aL with equations [10]   and 15] for the experimental resistivities used (see table II), we have cz6 --0.16 aL for a 2.79 #2.cm frittless gold conductor line and ground plane, and tG --0.56 aL when the gold ground plane is substituted by silver-palladium.As we can see in table IV, we have a good agreement between theory and measurements if we take into account the total losses (OtD, OtG, Ot L and surface roughness losses).

3. 2
Influence of the ground plane.

TABLE IIl Total
theoretical losses and Q for some resistivities