Abstract. Lipa, Steven J. Experimental Characterization of Interconnects on Thin-Film Multichip Module

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2 Abstract Lipa, Steven J. Experimental Characterization of Interconnects on Thin-Film Multichip Module Substrates. (Under the direction of Dr. Michael B. Steer) Propagation characteristics of aluminum microstrip interconnects on depositied multichip module substrates using polyimide dielectric are studied. New deembedding techniques are employed, allowing separation of conductor losses from dielectric loss. The results indicate that losses due to the dielectric may exceed those that would be expected if only bulk dielectric properties are considered. Gridded and slotted ground planes are considered, as well as continuous ground planes.

3 Contents 1 Introduction Motivation : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1 2 Background Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : Determination of C : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : Conductor Loss and the determination of R : : : : : : : : : : : : : : : : : : : Dielectric Losses : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : A Brief Review of Previous Work in This Area : : : : : : : : : : : : : : : : : : : : : Deembedding Techniques : : : : : : : : : : : : : : : : : : : : : : : : : : : : : Thin-Film Interconnect Characterization : : : : : : : : : : : : : : : : : : : : : 10 3 Theoretical Approach On Determination of the RLGC Parameters : : : : : : : : : : : : : : : : : : : : : : : 15 4 Experimental Results Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : The Test Vehicle : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : Capacitance Measurements : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : Analytical determination of R : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : SParameter Measurements : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : Deembedding : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : Application of the technique to the ATT type A transmission lines : : : : : : 32 i

4 ii Experimental Analysis of ATT Type B transmission lines : : : : : : : : : : : 41 5 Conclusion Summary : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 51 A Additions to SPANA 55 A.1 spline.f : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 55 A.2 spxform.f : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 56 A.3 sprform.f : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 57 B Sample SPANA Command Files 58 B.1 Sample SPANA command le for direct dembedding : : : : : : : : : : : : : : : : : : 58 B.2 Sample SPANA command le for decascaded dembedding : : : : : : : : : : : : : : : 59 B.3 Simplied SPANA command le for RLGC parameter extraction : : : : : : : : : : : 61

5 Chapter 1 Introduction 1.1 Motivation We are now well into the era in which packaging and interconnect eects have become major limitations to the optimum performance of high-speed electronic systems. The resulting explosion in Multi-Chip-Module (MCM) research has answered many questions regarding these issues, but many more remain to be investigated. Clearly, some form of MCM technology will be at the forefront of high-speed systems technology as long as the basic building blocks we use for circuit construction retain their more-or-less two dimensional character. That is, until there is some fundamental change in the way wemake circuits, they will need to be held by something (a substrate) and they will need to be connected to each other by some sort of interconnect using some sort of insulation (the dielectric). The big questions being raised right now relate to just what form of MCM provides the best results. At the time of this writing, there are several categories of MCMs, representing a wide variety of economic, materials, and electrical advantages and disadvantages: MCM-C refers to the multilayered cored ceramic MCMs that put MCMs on the map. These were initially developed by IBM and NEC for large computers. In this technology, a large number (as many as 60) of metallization layers are sandwiched in between layers of ceramic in order to provide interconnects between silicon integrated circuits mounted (often upside-down) on top. MCM-D refers to MCMs which use Deposited polymer thin-lms for dielectrics and Deposited (sputtered) metallic conductors. A number of substrates are compatible. A special case of MCM-D uses the polymer to form waveguides for very high speed signals, resulting in what is known as an MCM-O, or Optical MCM. There are also references to MCM-C/D (D/C), a hybrid of MCM-C and MCM-D. MCM-L refers to MCMs which use printed-circuit-board substrates. The L refers to the fact that the dielectric is Laminate-based. MCM-Si refers to a Silicon substrate MCM using grown or deposited silicon dioxide as a dielectric. 1

6 2 MCM-D provides several benets from a materials standpoint when compared with the other technologies, so it will probably be popular for some time. Some of its advantages include: MCM-D provides much higher wiring density than MCM-C and MCM-L. MCM-D is inexpensive compared to MCM-C. MCM-D processing is generally simpler than MCM-C and MCM-Si. For example, the vacuum steps required for dielectrics such as silicon dioxide can be avoided. MCM-D provides a certain amount of exibility in terms of materials choices: { Polymer dielectrics allow the use of copper conductors if a barrier metal is used. { A choice of substrates is possible. Polymer dielectrics can have a low dielectric constant. Multiple layers are easier to achieve compared to other technologies. Better planarization is possible than with some technologies. Of course a major consideration in evaluating a technology is electrical performance. Therefore it is important to be able to determine the capabilities of a given technology through measurements. In the case of MCM technology this is a challenging problem for several reasons. Three of the major reasons are: 1) the dimensions of the interconnect lines and contacts are often quite small and it can be dicult to make reliable contact with them. 2) The usable bandwidth of MCMs is so large that measurements must extend well into the microwave region. 3) There are more xture parasitics to remove when evaluating the measurement data. The purpose of this work is twofold. First, to develop new techniques for characterizing MCM-D transmission lines. The propagation characteristics are the key to the performance that can be expected from an MCM. A new approach for determining this performance will be described here, which allows for a more accurate model of the transmission line. Second, to investigate the contributions of dielectric loss to the attenuation of various types of lines on MCM-Ds. Conventional wisdom says that dielectric loss is insignicant compared to conductor loss in polyimide-insulated systems. It's possible that this is a result of our previous inability to accurately measure it. In any case, the results of this work contradict conventional wisdom. We will show that it is possible to measure dielectric loss on polyimide-insulated MCM-Ds, and that its contribution to the overall attenuation of a transmission line is quite signicant.

7 Chapter 2 Background 2.1 Introduction In terms of its per-unit-length parameters, a transmission line is described by its propagation constant = p (R +!L)(G +!C) =! c p r e r e (2.1) and characteristic impedance Z C = s s R +!L r e G + =!C Z 0 r e (2.2) where! =2f, r e and r e are the eective relative permeability and permittivity respectively, f is frequency, R and L are the per-unit-length resistance and inductance of the line, and the free space impedance of the line with ideal conductors is r L0 Z 0 = = 1 C 0 C 0 c : (2.3) For non-magnetic media, and r e = R +!L!L 0 (2.4) r e = G +!C!C 0 (2.5) where L 0 and C 0 are the per-unit-length inductance and capacitance of the line in the absence of dielectric. Combining (2.2), (2.3) and (2.5) the frequency dependent characteristic impedance is related to the propagation constant by Z C (f) =; (f)! r e C 0 : (2.6) In order to accurately model the transmission line it is necessary to accurately determine the parameters R, L, G, and C. Even if an analytical approach is possible, it is necessary to verify the results experimentally. Fortunately, a great deal of eort has been focused on techniques for determining 3

8 4 some of the parameters, such as R, L, and C, because these parameters have been almost universally accepted as the most signicant. In doing this, G is assumed to be zero, but this has lead to results that are hard to explain. What is needed is a technique for determining G. In the rest of this section, some background material regarding some of the techniques used to determine parameters C and R will be covered. L will not be covered, because it turns out that some sort of time-domain or frequency domain measurement must be done in order to get all the parameters. In either case, the propagation constant of the line is available, and given, R, and C, it is possible to solve for G and L. Finally, some background information on dielectric loss mechanisms will be covered Determination of C Several approaches have been proposed for the determination of C of a transmission line from microwave measurements [1], [2] [4]. In [3] Marks and Williams use one or other of the two methods presented in [5] for determining the capacitance of a line from microwave measurements. One of these methods uses extrapolation of the microwave measurements of a line plus DC measured resistance to determine C. A second method uses microwave measurements of a terminated microwave transmission line to determine the proportionality factor in the TRL procedure and thus the capacitance of the line. Goldberg et al. [4] use the high frequency asymptotic behavior of skin eect to determine a high frequency approximate of C. Inthework of Deutsch et al., [1], direct measurement of capacitance by a capacitance meter is utilized. The following paragraphs provide a more complete description of these four main techniques: Method A.Direct Measurement While direct measurement of the line capacitance and conductance seems the obvious approach it is complicated by the test line being invariably short as limited area can generally be devoted to a single set of test structures and their relatively large probe pads. This is particularly so if a standard set of test structures is to be included as on every wafer. Two lengths of line are required to remove the capacitive and conductive eects of transitions to the line and, practically, these lines must be those used in one of the TRL-like microwave calibration procedures. Thus the lines will generally be less than a centimeter long and have capacitances of a picofarad or less. Since measurements must be made at a low enough frequency to ensure that the lines have negligible electrical length and so can be treated as lumped capacitances, the required measurements are at the limits of performance of commercial instruments. Method B.High Frequency Approximation A high frequency estimate of the line capacitance can be obtained by using the assumed frequency dependence of the per-unit-length parameters of the line [6]: C and G=! are approximately frequency independent R has a DC component, R DC, and a skin eect component, R S,which has an assumed! dependence where is around 0.5 when the skin eect is fully established L = L 0 + L int, where L int is the internal conductor inductance of the line due to current internal to the conductors and is asymptotically zero at high frequencies as then the skin eect is fully established.

9 5 Consequently and r e = R +!(L 0 + L int )!L 0 (2.7) r e = G +!C!C 0 : (2.8) Since R increases sublinearly because of the skin eect, R!L at a high frequency, f H, where L L 0 and so lim f!fh R r e (f) =1; : (2.9)!L 0 Thus where the intermediate dielectric constant r e = f!fh lim ^ r e (f) (2.10) ^ r e (f) = ; 2 (f)c 2! 2 [1 ; R=(!L 0 )] (2.11) is obtained by substituting equation 2.7 for r e in (2.1) and rearranging. Combining (2.8) and (2.11) gives C ; G = ;c2 C 0 lim 2 (f)!! 2 : (2.12) f!fh [1 ; R=(!L 0 )] Since R!L 0 at high frequencies That is C ; G ;c2 C 0 lim 2 (f)[1 +!! 2 R=(!L 0 )] : (2.13) f!fh C ;c2 C 0! 2 lim f!fh ( Re 2 (f) ; Im 2 (f) R!L 0 ) (2.14) and ( G c 2 C0 lim Im!! 2 2 (f) + Re 2 (f) ) R : (2.15) f!fh!l 0 With the frequency dependence assumed previously at high frequencies, Im 2 (f) and Re 2 (f) O(! 2 ), and R O(! ) with 0.5. Thus since Im 2 (f) is always positive andre 2 (f) is negative at high frequencies and C c2 C 0! 2 lim f!fh Re 2 (f) (2.16) G ;c 2 C0! lim! 2 f!fh Im 2 (f) : (2.17) In summary, the basic assumptions behind (2.16) and (2.17) are that the skin eect is fully established and that the skin eect resistance increases sublinearly with frequency. At suciently high a frequency and C c2 C 0! 2 Re 2 (f) (2.18) G! c 2 C0! 2 Im 2 (f) : (2.19)

10 6 Method C.Low Frequency Extrapolation (R DC Method) Williams and Marks [5] presented two methods for the determination of the capacitance of transmission lines using low frequency network parameter measurements. The rst of these methods uses the measured propagation constant : squaring (2.1) and rearranging 2 =(R DC + R S)G ;! 2 LC +!((R DC + R S)C + LG) (R DC + R S)C + LG =Im( 2 )=! : (2.20) Ignoring dielectric loss and R S, which is reasonable at low frequencies, gives 2 ) Im( C =lim f!0 R DC! : (2.21) Method D.Low Frequency Estimate (R load,dc Method) The second technique presented in [5] determines the capacitance of a line by noting that Z C is identical to the reference impedance, Z ref, of the TRL measurement procedure. For a small lumped load resistor, R load,dc,atlow frequencies [5] 1+;load 1+;load Z ref Z C = 1 ; ; load 1 ; ; Z load R load,dc : (2.22) load where ; load is the measured reection coecient of the load referred to Z ref. Substituting (2.22) in =Z C = G +!C (2.23) results in That is C G 1 ;!C C Im[]!R load,dc!r load,dc 1+;load 1 ; ; load 1+;load 1 ; ; load : (2.24) (2.25) and G Re[]!!R load,dc 1+;load 1 ; ; load : (2.26) Conductor Loss and the determination of R Of the three main loss mechanisms that lead to attenuation of the propagating signal on a transmission line, resistive losses and skin eect losses contribute to what are known as \conductor losses," or R. The next few paragraphs provide a brief background to explain the mechanisms involved and to introduce the idea of using an analytical approach to determine R.

11 7 Resistive Losses Resistive losses arise when the conductor used has a nite conductivity. While the conductivity for most metals of interest is quite high, the small dimensions (width and thickness) of the typical MCM interconnect line result in resistive losses which are not always negligible. With MCM's ranging in size up to 10 centimeters square, MCM interconnect lines can conceivably reach 18 centimeters in length. Even if the resistance of the line is only 2 per centimeter, the resistive loss of a line of this length will be very signicant. This kind of resistive loss contributes directly to the real part of the series impedance of the line, R. Skin Eect Losses In addition to the resistive losses discussed above, which eect energy at all frequencies, skin eect losses contribute to R in a frequency-dependent manner. Skin eect losses result because the eective cross-sectional area of a conductor decreases with frequency. This is due to the fact that a large part of the current ow in the conductor (63.2%) ows within a depth,, of the surface of the conductor that is given by 1 = p (2.27) f where f,, and represent the frequency of the wave, the permeability, and the conductivity of the conductor, respectively. [7] A tremendous amount of research has been done in the eld of analytically determining the frequency-dependence of the resistance of transmission lines in recent years as is evidenced in the review article by Hwang et al. [8]. Certainly any ofanumber of numerical techniques could be used to determine the free-space R of a structure as simple as a uniform transmission line. Noteworthy among current researchers in this area is Andreas Cangellaris of the University of Arizona. Dr. Cangellaris has developed a nite element/integral equation approach to analytically determining the frequency dependent inductance and resistance of complex three dimensional structures [9]. The technique has been rened to the point that accurate determination of the resistance of bends and vias in transmission lines can be made, suggesting that straight transmission lines can be handled even more accurately. 2.2 Dielectric Losses Dielectric loss is by far the most ignored of the loss mechanisms. For this reason a little more background is provided on this topic. There are two main mechanisms that give rise to dielectric loss. The dielectric can have a non-zero conductivity, leading to a loss at all frequencies. In addition, the molecules which comprise the dielectric may have mechanical resonant frequencies at or near the frequency of an applied eld. If damping forces in the dielectric cause the polarization of the dielectric to lag behind the applied eld, an increase in the loss tangent at these frequencies is possible [10]. There are several dierent polarization phenomena that come into play [11]: Elastic distortion of molecules Elastic separation of ions Alignment of polar molecules Site-jumping

12 8 The subject of dielectric loss is further complicated by the fact that the polarization and conductivity of the dielectric may depend on temperature, moisture absorption, and other environmental factors. A large amount of research has been done regarding the use of polyimide as a dielectric, [12, 13, 14, 15, 16, 17, 18], so a good deal is known about its dielectric properties. Unfortunately, most researchers have restricted their work to the realm of low frequencies. This may be in part due to the fact that some researchers [19, section 2.3] have stated that series resistive losses generally dominate the dielectric loss and therefore dielectric loss can be ignored. Some of the more signicant results of recent inquiries into the dielectric behavior of polyimide follow: In 1989, Melcher, Daben, and Arlt [14] found that water absorption by polyimide lms can reach over 3% by weight, and that the absorbed water can increase dielectric loss. Similar results have been reported by Tessier et. al. [20] in1989andwu and Denton [17] in Wu and Denton provide a table of dissipation factor (loss tangent) vs. frequency with relative humidity asa parameter. This work shows that relative humiditycanhave a tremendous eect on loss tangent at frequencies between 10 Hz and 100 khz. Unfortunately there is no data above 100 khz. The results of Tessier et. al. show that all polyimides are susceptible to this problem even though some of the more recent polyimides are to a lesser extent eected. Recent work [21, 22, 23, 24] has shown that polymer thin-lms have in-plane/out-of-plane dielectric anisotropy which can result in leaky quasi-tem mode propagation on thin-lm interconnects. In 1992, Ree, Chen, and Kirby [18] demonstrated the anisotropy of polyimide thin lms by measuring the in-plane and out-of-plane dielectric constants using a wide-angle x-ray diraction technique. 2.3 A Brief Review of Previous Work in This Area Deembedding Techniques Use of the Automatic Network Analyzer (ANA) is of paramount importance in the characterization of high speed interconnections because of the very wide bandwidths involved. Many researchers have developed techniques for optimizing the use of the ANA since its introduction in the late 1960s by R. A. Hackborn [25]. An important feature of the modern ANA is that it is often possible to eliminate measurement errors due to xturing to a very high degree. A good review of the early work in this area can be found in [26]. For the purposes of understanding the current work, it is only necessary to understand the general techniques involved and some of the more recent developments. A block diagram of an ANA measuring a two-port is shown in Fig The goal of using this type of set up is to determine the scattering parameters (S parameters) of the device under test (DUT) to a high degree of accuracy. (The usefulness of these S parameters will be considered later) The general idea of ANA calibration is to consider the imperfect ANA to consist of a perfect ANA with error-introducing two-ports (error ports) in series with the measurement ports. If the eect of the error ports on the measured S parameters is known, it may be possible to factor this out of the imperfect ANA's results to yield the measurement that a perfect ANA would see. (The error two-ports in Fig. 2.1 only include eight error terms. Four more terms are necessary for a complete two-port calibration [27], because ANA measurements are actually made in two directions.) Obviously, if a network with known S-parameters is put in place of the DUT, the

13 Figure 2.1: An ANA measuring a two-port. 9

14 10 variation of the measured S parameters from the known S-parameters will provide important clues as to the makeup of the error ports. A lot of work has been done to determine good ways to go about this. One complicating factor is that most calibration DUTs are simple impedance standards: short circuits, open circuits, and resistive loads. Building perfect shorts, opens, and resistive loads is very dicult over a very wide bandwidth. This has led to the practice of using distributed standards such as transmission lines, rst introduced by Franzen and Speciale in 1975 [28]. A number of new techniques involving distributed standards were developed in the next few years [29, 30, 31, 32],but the most popular of these was undoubtedly Engen and Hoer's TRL technique of 1979 [30], which is still in widespread use today. In 1992, Steer et al. introduced the Through-Line (TL) technique, a replacement for TRL [33]. TL is similar to TRL. The main dierence between the two is that TRL's reection standard is eliminated in TL. This is possible because TL uses the symmetry of the through measurement to determine the reection coecient of an ideal short placed at the xture reference plane. TL provides important advantages when compared with TRL: TL provides enhanced accuracy. TRL suers from inaccuracies associated with the arbitrary reection standard. Removing the reection standard eliminates this problem. TL provides better repeatablilty because fewer total measurements are required to characterize a test substrate. The steps for applying TL are: 1. Perform a calibration of the ANA by measuring an open, a short, and a resistive loadateach of the ANA's measurement ports. 2. Perform a through measurement. 3. Perform a line measurement. 4. Determine Z C (f) of the line. 5. Use these results to derive S parameters. It turns out that TL is ideal for determining the S parameters of embedded transmission lines. Two similar transmission lines (identical except in length) can be used to determine the S parameters of a section of transmission line \embedded"in the longer line. An example of the use of this technique for a microstrip line is depicted in Fig TL uses the center of the symmetrical \through"line as the location of the reference planes for the through measurement. Since the through line is symmetrical (at least in theory) and the path from the through connectors to the through reference planes is identical to the path from the line connectors to the line reference planes, it is possible to \deembed"the S parameters of the line that extends between the line reference planes using TL. The details are fully explained in [26]. As we will see in the next chapter, the technique can be adapted for use in other types of systems Thin-Film Interconnect Characterization Thin-lm interconnect has been used in MCMs since Ho et al. at IBM introduced the practice in 1982 [34]. Since that time there has been a tremendous amount of research directed at the

15 11 Figure 2.2: Example of the application of TL. materials aspects of building MCM-Ds, but not nearly as much eort directed at characterizing the interconnect. Nevertheless, there has been some activity in this area. Ho et al. presented some very limited time-domain results, as did Jensen et al. in 1984 [35]. In 1987 Lane et al. [36] characterized copper/polyimide oset striplines on a co-red ceramic substrate. They used an LCR (inductancecapacitance-resistance) meter to measure C, R, andg for their lines at 1.6 khz, and then measured the insertion loss and input impedance of their lines from 50{400 MHz using a network analyzer. The input impedance was measured twice, each time with a dierent resistive termination. These measurements yielded a \measured"attenuation and characteristic impedance. Their measured attenuation result was simply the insertion loss of the line divided by the length, and their measured characteristic impedance was found by taking advantage of the fact that the input impedance of a terminated transmission line of length l is given by: Z in = Z C Z L + Z C tanh l Z C + Z L tanh l (2.28) Where Z C is the characteristic impedance, is the propagation constant of the line, and Z L is the terminating impedance. Since Z in is known for each measurement, as well as Z L, the result is two linear equations with two unknowns (Z C and ) which can be solved easily to yield Z C. Lane et al. compared the results of these measurements with calculated values. They used 1.6 khz measurements of R, G, C, and a derived value of L calculated using L = r =c 2 C. They assumed that the dielectric constant r,was 3.5. Needless to say, the calculated results were not very close to the measured results. In 1989, Schwab et al. presented TDR data and S parameters to 9 GHz for a copper/polyimide system made by Honeywell [37]. The authors used a complex deembedding algorithm, with ve assorted standards including an open, a short, a 635 m line with an open at its end, a similar line with a short at its end, and a similar line with pads at both ends to be used as a through measurement. Unfortunately, the authors do not discuss the details of the algorithm that was used

16 12 to deembed the S parameter data. The S parameter data presented was for 3.45 cm and cm microstrips. Return loss (S 11 ) and insertion loss (S 21 )were reported. The results indicated that Honeywell was able to control the impedance of the microstrip very well (low return loss) but that there was a signicant insertion loss. Time domain measurements of a 1 GHz and 2 GHz pulse trains and a TDR output were used to demonstrate the eect of the insertion loss. Unfortunately, the authors do not mention dielectric loss, giving the impression that only the series resistive loss of the line contributes to the insertion loss. In 1990, A. Deutsch et al. published a paper [19] on measuring lossy interconnect which included a section on thin-lm interconnects. In this paper, Deutsch calculates the frequency dependence of R and L for thin-lm lines with lossy dielectrics, measures C at 1 MHz, and sets G =0. She compares simulations of the resulting model with actual TDR results using a rise time of 33.4 ps and an oscilloscope with a bandwidth of 20 GHz. The simulation waveforms shown are quite similar to the measured results. The interesting thing here is that the authors argue that the dielectric loss is negligible out to 316 GHz, yet they mention in passing that the 33.4 ps rise time excitation \can generate some dielectric loss induced dispersion." Also in 1990, Hwang et al. published experimental data on copper/polyimide and aluminum/polyimide systems. The authors used a Hewlett-Packard 8510 Network Analyzer (ANA), Cascade Microtech Probes, and a Cascade Microtech calibration substrate for calibration. The calibration substrate uses an open, a short, a through, and a 50 standard to calibrate the ANA. In addition, the authors used a variety of test structures to verify that their calibration was successful, including an open circuit stub and two attenuators. In addition to measuring the return and insertion loss, the authors calculated the attenuation constants, phase velocities and characteristic impedance for various combinations of conductor/polyimide types. The attenuation calculation was based on the formula: = 1 1 ; ln Re (S11 + S 21 ); (2.29) l (S 11 + S 21 ) ; ; where ; is the reection coecient andl is the length of the line. The reection coecient isgiven by: ;= (Z C ; Z 0 ) (2.30) (Z C + Z 0 ) where Z 0 represents the characteristic impedance of the measurement system. The technique provides fairly good results, except that resonance eects associated with the mismatch of the measurement system's characteristic impedance with the line impedance lead to rather large wavelike artifacts in the results. This is the type of measurement error that the TL deembedding technique is designed to correct. Another time-domain approach was used in 1990 by Lin et al. They studied coppernickel/polyimide microstrips on silicon substrates, using a combination TDR-TDT setup. In this case, the authors propose a lossy transmission line model that does not include a conductance term, G. The only mention of dielectric loss is that \no large loss attributable to [it] is observed."there is no explanation of how the authors arrived at this conclusion. Instead, they combine low frequency measurements of resistance and capacitance of the line with a 10 GHz measurement of the characteristic impedance of the line, and skin-eect calculations to determine model parameters. These model parameters are then used to explain the characteristics of edge transmission and reection measurements on lines of various lengths with various characteristic impedances. The authors start their analysis by converting the transmission line equations into the frequency domain via Laplace transforms. Applying a step input function to one end of the transmission line, they go on to solve for the transient response as a function of length. Using their model, the resulting time-domain

17 13 solution is: V T (t) V 0 p p = e ;Rl=2R0 t ; l LC + g (l t) t ; l LC (2.31) where R 0 is the high-frequency characteristic impedance of the line, l is the length of the line,and g \is a complicated expression describing a slow-rising pulse similar to that in an RC circuit."the authors break this into three regions: 1. a fast riseptime response represented by the rst term in (2.31) which propagates with a velocity of v =1= LC and is attenuated by the factor e ;Rl=2R0 2. a slow rising response represented by the second term 3. a DC level at which the line eventually settles A similar analysis is presented for reected pulses, resulting in a more complicated solution which can be broken into a fast rise time, a slow linear slope which in general will continue past the eventual DC settling point, a relaxation to the DC settling point, and nally establishment of the DC settling point. From the model the slope of the second segment isgiven by: and the DC level is given by: Rl 1 slope = p R 0 + Z C 2l Rl LC V 0 (2.32) DC level = 2Z C + Rl V 0 (2.33) Experimental results are provided, and it is argued that using the models discussed above with skineect adjusted parameters, it is possible to justify the general shapes of the measured waveforms, but a quantitative comparison of modeled waveforms vs. real waveforms is not presented. Finally, in 1992, Deutsch et al. presented an update to their time domain technique [38, 39, 40]. The new technique is fairly simple: Two transmission lines that are identical except for their length are used. A very short pulse 40ps is launched at one end of each line and the waveform received at the far end of each line is stored digitally. Each stored waveform is time-windowed in order to remove any reection information. Thus the stored waveforms only contain information about the forward-travelling wave. Next, the stored waveforms are numerically Fourier transformed. The ratio of the two resulting Fourier transforms yields the complex propagation constant of the line: (f) = (f)+ (f) =; 1 ln A 1 (f) l 1 + l 2 A 2 (f) + 1 (f) ; 2 (f) (2.34) l 1 ; l 2 where A 1 and 1 are the amplitude and phase of transforms of the time domain data for the line of length l 1, and A 2 and 2 are the amplitude and phase of transforms of the time domain data for the line of length l 2. The beautyofthistechnique is that it does not require anydeembedding because the eects of the xturing are the same for both measurements, and therefore cancel out. The reported results vary between the two papers in which this technique is applied to a polyimide/copper thin- lm system. The substrate used for the two papers appears to be the same type of polyimide/copper system, using stripline and oset stripline. The rst paper uses two lines which dier in length by approximately 5cm while the second paper uses two lines which dier by almost 10cm. Apparently the resolution of the measurements is increased when the dierence in the line lengths is increased. In the rst paper the authors admit to being able to measure the contribution of the dielectric loss (they report a loss tangent of 0.006), and in the later paper they are able to measure a loss tangent of The measured attenuation and phase constants do compare fairly well to the models presented

18 14 when the eect of dielectric loss is included, but the graphs of the attenuation constant have some irregularities that resemble the problems noted in the results of Lin et al. These irregularities are not addressed in the papers.

19 Chapter 3 Theoretical Approach The approach taken in the current work was based on the objectives listed in the introductory chapter and the factors and history discussed in the previous chapter. The important elements can be condensed as follows: The determination of G and its impact on the attenuation of a transmission line was of great interest. An analytic approach to determining R was assumed acceptable. A technique that exploited the TL deembedding algorithm was desirable. One of the four established methods for determining C had to be chosen. 3.1 On Determination of the RLGC Parameters The rst important decision was to determine which of the four available techniques for determining C is the best. Since no quantitative comparison was available, a comparison of the techniques was made, using experimental results and analysis. The results of the comparison are presented in the following chapter. of R. A combined nite-element/integral equation technique was chosen for the determination Having determined C and R, the problem then was to develop a technique for determining the other parameters through some sort of time- or frequency domain transmission line measurement technique. As it was desirable to verify the applicability of the TL deembedding technique to this type of problem, a frequency domain approach suggested itself. The TL deembedding technique provides the propagation constant of a transmission line,, as a byproduct. Thus, given R, C, and = p (R + j!l)(g + j!c) (3.1) it was possible to square ( 3.1) and split it into two equations in two unknowns: 2 = RG ;! 2 LC +!(RC + LG) (3.2) 15

20 16 Re ; 2 = RG ;! 2 LC (3.3) Im ; 2 =! (RC + LG) (3.4) ( 3.3) and (3.4) were combined to yield a quadratic equation for G: G 2 ; Re ; 2 G +(!C) 2 ;!C Im ; 2 =0 R R (3.5) (3.1). Thus G was determined as the solution of (3.5), and consequently L was found from The eect of R and G on signal propagation was found by separating their contributions to the attenuation constant, Re (). This was achieved by rewriting (3.1) as follows: p =! LC 1 ; R ; G 1 2 (3.6)!L!C Since R!L and G!C except at very low frequencies, it was possible to approximate the terms in parentheses in (3.6) by the rst two terms of their power series expansions. The real part of the presulting equation is an approximation of the attenuation constant = C + D where C = 1 2 R C=L is due to conductor loss and D = 1 pl=c 2 G represents the loss in the dielectric. This typeofanalysiswas used to determine the signicance of the loss due to conductance in the dielectric.

21 Chapter 4 Experimental Results 4.1 Introduction 4.2 The Test Vehicle Two MCM-D test substrates were specically designed for this work. The test substrates were made by AT&T, and represent prettymuch the current state of the art in low cost MCM-D fabrication technology. The substrates use aluminum metallization, polyimide insulation, and a silicon substrate base. Two layers of interconnect metallization are available and an aluminum ground plane is placed under all metallization. Each substrate features a variety of transmission lines and other interesting interconnection entities, such as vias, bends, etc. Two layers of metal are used with Hitachi PIX- L112 polyimide as an insulator. Only straight transmission lines were considered in the present work. The substrate shown in Figure 4.1, designated ATT type A (to dierentiate it from the second type to be described later) contains a variety of transmission lines of various widths and lengths. It is approximately 5 mm square. The lines in column A are 400 m in length, those in column B are 1 mm in length, and those in column C are 8 mm in length, all measurements being from the inside of one pad to the inside of the opposite pad. Transmission lines used in the present work were located in rows1to6. Transmission lines on row 1are10m in width and use second layer metal (SLM). A cross-section of an SLM line is shown in Figure 4.2. A longitudinal section of the same line is shown in Figure 4.3. Note that the pad structure has built-in rst layer metal so that the same structure can be used with either FLM or SLM lines. This unfortunately increases the parasitic capacitance of the pad for SLMs, which is one of the xturing eects that the TL technique is able to remove. Transmission lines on rows 2 and 3 are identical to those on row 1, except that they are 16 m and 32 m in width, respectively. Rows 4{6 contain transmission lines analogous to the lines in rows 1{3, except that FLM metallization is used. This results in a change of dimensions as indicated in Figure 4.4. Transmission lines are placed on 200 m centers, allowing each ofthe50m by50m pads that connect to a transmission line to be anked by two similar pads connected to the ground plane. Figure 4.5 is a magnied view of a section of Figure 4.1 which shows the details of the pad placement. A scanning electron microscope (SEM) photograph of a ground pad (left) and signal pad (right) cross-section is shown in Figure

22 18 Figure 4.1: ATT type A MCM-D test substrate. 4.2µm w1 =10µm w 2 =10.4µm 5µm h=10.5µm 19µm Figure 4.2: SLM transmission line cross-section. Figure 4.3: SLM transmission line longitudinal section.

23 19 10µm 4.2µm w1 =10µm w 2 =10.4µm h=5.5µm 19µm Figure 4.4: FLM transmission line cross-section. Figure 4.5: Magnied view of ATT type A pad conguration

24 20 Figure 4.6: SEM photograph of pad cross-section. A second type of test substrate was used to measure the propagation characteristics of transmission lines over gridded and slotted ground planes. This test substrate is shown in Figure 4.7. The metallization scheme, pad placement, and line lengths for the transmission lines in rows 1{3 follows the same scheme as the analogous lines on the type A substrate, except that in addition to the SLM transmission line metallization there is also a gridded ground plane made with FLM. The gridding is made up of 10 m horizontal and vertical lines separated by 10m spaces in each direction. The gridded ground plane is joined to the solid ground plane at the ground pads along each edge of the die. 4.3 Capacitance Measurements The results obtained using each of the four approaches to in-situ capacitance determination are compared in Fig. 4.8 for a typical ATT type A SLM transmission line. In Fig. 4.8 the curve labels correspond to the methods discussed in the previous section. The exception is curve C F which isa curve t to curve C assuming a p! dependence of the skin eect component of the line resistance. This curve indicates a DC intercept of 81.5 pf/m for method C. This compares favorably to the direct measurement (method A) of 82.4 pf/m. However the low frequency extrapolated value of C is dependent on the frequency range over which (2.21) is tted (see Table 4.3) owing principally to the measurement scatter and uncertainties as to the actual frequency dependent behavior of R S. The high frequency asymptotic estimation of C, method B, and the low frequency R load,dc method, curve D, also compare favorably to the other C determinations. The results are summarized in table 1. The capacitance meter used did not allow the conductive line loss to be determined, however error tolerancing establishes an upper bound on G of 30 S/m at 1 MHz. The high frequency asymptote method (B) yields a upper bound on the line conductance of 48 S/m. No indication of G could be obtained from the low frequency extrapolation methods (C and D) because

25 21 Figure 4.7: The ATT type B MCM-D test substrate Table 4.1: Capacitances determined using various measurement techniques. METHOD C Error (pf/m) (pf/m) A, Direct 1 MHz measurement B, High Frequency Asymptote 79.6 > 4.1 C, R DC method [5] 45 { 400 MHz 80.3 > { 500 MHz 81.5 > { 800 MHz 83.7 > { 1000 MHz 84.3 > { 1245 MHz 84.3 > 4.5 D, R load,dc method [5] 85 > 4.1

26 22 CAPACITANCE pf/m C F FREQUENCY C A B D MHz Figure 4.8: Capacitance approximations: A { 1 MHz capacitance measurement (method A) B { high frequency asymptotic capacitance (method B) C { measured Im( 2 )/! (method C) (C F )curve tted to C and D { capacitance calculated using microwave measurements and DC load resistance (method D).

27 23 of the scatter of the measured data. The errors of methods A, C and D will reduce as the test line lengths increase but the error of method B will change only slightly as the principal component of error is making the cross-section measurements from SEM photographs. While the four methods determine C within a 3% spread, this translates to a corresponding 3% spread in the calculation of the characteristic impedance of the line [4] and of the extracted impedances of discontinuities [41]. The direct capacitance method has the lowest error and, what is particularly important, of the four methods it is the only one traceable to capacitance standards and has a well dened error tolerance. The major diculty in assigning tolerances to the other methods is that while the extrapolations employed are theoretically sound, their error can only be estimated. Error estimates of the four methods are given in table 4.3. The accuracy of the assumptions behind the high frequency asymptotic method, method B, can be examined more closely by inspecting the asymptotic behavior of the intermediate relative permittivity, ^ r e shown in Fig Note that ^ r e is only approximately asymptotic at high REAL INTERMEDIATE RELATIVE PERMITTIVITY REAL IMAGINARY IMAGINARY INTERMEDIATE RELATIVE PERMITTIVITY FREQUENCY GHz Figure 4.9: Intermediate eective relative permittivity. frequencies. This is attributed to the eect of the high resistance of the MCM interconnect. By comparison the high frequency behaviorof^ r e was found to be asymptotic for PCB interconnects which havemuch lower resistive loss, (see [4]). The extrapolation validity errors of methods C and D are based on the observed scatter of the low frequency data. This scatter is not evident when a standard calibration substrate is used [3]. In this case the calibration structures are in coplanar waveguide so that the transition from the probe to the measurement substrate is negligible, and the dimensional tolerancing is tight. In contrast the MCM-D in-situ calibration structures used here have poor dimensional tolerances. As a result, the eect of the transition is large at 1 MHz it has a shunt capacitance of 96 ff and a series resistance of The propagation constant,, of a typical line is shown in 4.10 where the attenuation constant = Re[] and normalized =Im[]= 0 are plotted. The constant 0 =! p 0 0 is the free space propagation phase constant. Even at the highest frequencies the normalized is not constant

28 24 Table 4.2: Error estimates for calculating the total root sum squared (RSS) error of the various capacitance and conductance measurements. 1 Based on accuracy of HP4280A measuring the capacitance of the through (192 5 ff) and the line (771 9fF). 2 Based on accuracy of measuring the through ( m) and the line ( m). 3 Estimated based on the quoted accuracy of the S parameter measurements and scatter in the calculated propagation constant data. 4 Estimated based on scatter of low frequency data and dependence of extrapolated data on frequency range used. METHOD/ Line Item Notes C Error (pf/m) A, 1 MHz Capacitance measurement Capacitance measurement (Through) (192 5fF) Capacitance Measurement (Line) (771 9fF) Line length (Through) ( m) Line length (Line) ( m) TOTAL RSS ERROR 1.5 B, High Frequency Asymptote Propagation constant determination excluding line length (1 %) Line length (Through) ( m) Line length (Line) ( m) Cross Sectional Dimension 0:5m 4.0 Extrapolation validity? TOTAL RSS ERROR > 4:1 C, Low Frequency Extrapolation DC method [5] Propagation constant determination excluding line length (1 %) Line length (Through) ( m) Line length (Line) ( m) Extrapolation validity (estimated) 4 > 4.5 TOTAL RSS ERROR > 4.6 D, Low Frequency Extrapolation DC,load method [5] Propagation constant determination excluding line length (1 %) Line length (Through) ( m) Line length (Line) ( m) Fixture and extrapolation error (estimated) 5 > 4.5 TOTAL RSS ERROR > 4.6

29 25 α (NEPERS/m) FREQUENCY (GHz) β (NORMALIZED) Figure 4.10: Typical propagation constant,. indicating signicant dispersion and putting into doubt the assumed frequency independence of C. The direct capacitance measurement was used in conjunction with the 's, [4], to obtain the Z C shown in Fig The imaginary part of Z C approaches a constant at high frequencies. This is not consistent with the usually accepted view that the conductance G is negligible. As the direct capacitance technique is the simplest and probably most accurate technique of the four for determining C, this method was chosen for all subsequent work. Accordingly, a somewhat more detailed description of the technique used is appropriate, along with the results for the lines tested on the two test substrates used. The direct capacitance measurements were made using a Hewlett-Packard 4280A LCR meter. The 4280A is well suited for this measurement because it has a variable-line-length auto-zero capability. It is able to zero out the contribution of a variable length line (between 0{5m in length) including simple xturing. This is important because the 4280A measures the impedance between the center conductors of two BNC connectors. In order to measure the capacitance of a device that cannot be connected directly at the front panel of the 4280A requires two coaxial cables to extend the reach of the BNC connectors. In the case of measuring a transmission line which is only reachable by a ground-signal-ground probe, one cable center conductor must be connected to the probe's ground side, and one must be connected to the probe's signal side. Therefore an adapter is required. Figure 4.12 shows a detailed schematic view of the entire setup. All capacitance measurements were taken with a 100 mv, 1 MHz stimulus. The resulting measurements are tabulated in tables 4.3 and 4.3 these raw measurements are provided in case they are of use in some extension of this work. The nal C determinations are based on the two longest line lengths for each row on a substrate. The capacitance per unit length for a given row is simply the dierence in the capacitance measurements of the B and C column lines of that row divided by the dierence in their lengths. Table 4.3 summarizes the nal results.

30 REAL PART OF Zc (Ω) FREQUENCY A C B A B C (GHz) IMAGINARY PART OF Zc (Ω) Figure 4.11: Typical Z C. Figure 4.12: Capacitance measurement setup.

31 27 Table 4.3: ATT type A raw capacitance measurements ROW A B C 1 NA 0.192pF 0.771pF Table 4.4: ATT type B raw capacitance measurements ROW A B C pF 0.235pF 1.169pF Table 4.5: Results of direct measurement of C on ATT type A and type B transmission lines. ROW TYPE A TYPE B pF/m 133.0pF/m

32 Analytical determination of R A Scanning Electron Microscope (SEM) was used to determine the cross sectional dimensions of transmission lines on sacricial ATT type A and type B dice. The idea here was to determine the actual shape of the cross section to improve the accuracy of the combined nite element/integral equation technique used to determine R. Our hope was that the algorithm would provide a fairly accurate picture of the frequency dependence of R which we could linearly scale to make up for small dierences in the dimensions of the tested transmission lines due to photolithography errors and other processing defects. The implementation of the technique was in four steps: 1. Determination of the nominal relative cross-sectional dimensions of a line. 2. Measurement of the actual DC resistance of the line, R DC. 3. Finite element analysis of R vs.f for that line. 4. Scaling of the results of step 3 so that the DC value coincides with the specic R DC measurement for that line. Determination of the R DC of the lines was similar to the determination of C in the direct measurement technique described earlier. In this case the measured resistance of a short line was subtracted from the measured resistance of an identical (except for length) longer line right next to it. The dierence divided by the dierence in the length of the lines provides the DC resistance per unit length of the lines. The beauty of this approach was that the non-zero resistance of the measurement system (which is fairly large compared to the resistance of a 400 m long piece of aluminum) canceled out completely when the measured resistances were subtracted. In addition, the dimensional variations between two lines fabricated within microns of each other were probably not large enough to appreciably aect accuracy. The results for the ATT type A lines are shown graphically in Figure Since these lines are identical to the lines on the type B substrate, the shape of the curves was assumed to be the same, and the scaling technique was used to generate the results shown in Figures 4.14 and 4.15 based on the R DC of the type B lines. 4.5 S Parameter Measurements S parameter measurements were made using a Hewlett-Packard 8510B Automatic Network Analyzer. The test setup used is shown in Figure 4.16 Adams-Russel 7 cm exible microwave return cables and a single semi-rigid right angle bend were used to connect each of the GGB Industries Model 40 ground-signal-ground probes to the ANA ports. BNC cables were used to connect the center contacts of the bias ports to the sense inputs of a Hewlett-Packard 3457A Multimeter. This provided a DC connection to the signal path for both ports, allowing constant monitoring of the DC resistance of the transmission line under test. The DUT was supported on the vacuum chuck of a Cascade Microtech Model 42 Microwave Probe Station. The vacuum system, combined with the ability to monitor the DC resistance of the path from ANA port 1 to ANA port 2, greatly facilitated the establishment of good and consistent probe contact with the DUT. The same measurement procedure was followed for all S parameter measurements:

33 29 R (Ohms/mm) A 1A 2B 1B 2C 1C FREQUENCY (GHz) Figure 4.13: R data for ATT type A lines A R (Ohms/mm) B 2C FREQUENCY (GHz) Figure 4.14: R data for ATT type B gridded ground plane lines. 2A{ 10 m line, 2B{ 16 m line, 2C{ 32 m line

34 A R (Ohms/mm) B 2C FREQUENCY (GHz) Figure 4.15: R data for ATT type B slotted ground plane lines. 2A{ 10 m line, 2B{ 16 m line, 2C{ 32 m line Figure 4.16: S parameter measurement test setup.

35 31 1. The test setup shown in Figure 4.16 was implemented, with all SMA connectors carefully torqued to 60 N-cm. 2. The HP8510B was initialized to assure a known start-up state. 3. The measurement range was set to 45 MHz{ GHz 4. Rough ANA calibration was performed using a Cascade Microtech calibration substrate. This calibration substrate, combined with the calibration software in the HP8510B, allowed direct measurement of the pad-to-pad S-parameters. The calibration technique used requires open, short, load, and through connections, all of which are available on the Cascade Microtech calibration substrate. The isolation section of the calibration was omitted. (Basically, this section of the calibration is used to cancel out any radiative coupling between the probes. It is only accurate, however, if all the probe measurements are made with the probes at a constant relative distance from each other which is not the case here, where the lines are of variable length.) Fortunately, as explained in [33], only a rough ANA calibration was necessary at this point in the measurement. 5. The probes were placed on the pads of the transmission line to be measured. 6. The DC resistance of the signal path from ANA port 1 to ANA port 2 was noted. 7. Probe contact was optimized. Unfortunately, making contact to the contact pads was not nearly as reliable as a standard SMA connector, for instance. A few of the chronic problems: The pad geometry was not optimally matched to the probe geometry. Oxidation on the pads had to be broken by rubbing the probes on the pads The probe tips and the calibration substrate contact pads were made of soft metal, so their geometry changed with time. Position of the probes on the pads changed on every measurement because the probes were placed manually using the manipulators built into the probe station. Optimizing the contact meant carefully rubbing the probe back and forth a few times to break any oxidation on the surfaces, and good contact invariably required tapping the stage of the probe station to vibrate the probes to maximum contact. Fortunately, the DC resistance of the signal path was a very good rough guide to contact optimization, and with a little practice it became fairly easy to tell from the shape of the displayed S parameters if there was a contact problem. The quality ofthecontacts was a very important issue in getting consistently repeatable measurements. 8. The nal DC resistance of the signal path was recorded. 9. The pad-to-pad S parameter data was recorded using the IEEE-4888 interface on the HP8510B, and stored for further deembedding. In order to ensure that moisture absorption would not unduly inuence the results, special preparation of the test substrates was required as well as special storage. All substrates were baked at 423 K for one hour to drive absorbed water molecules out of the polyimide at the beginning of the project. The substrates were then stored in a dessicator until measurement. It was decided that it was unnecessary to carry out the measurements in an inert atmosphere because in general, polyimide absorbs water fairly slowly [13]. None of the substrates used for results to be reported here were out of the dessicator for more than 30 minutes at a time, and these were only subjected to a controlled environment in which the relative humidity was approximately 25%. It is possible

36 32 that absorption of atmospheric moisture had some eect on the measured results if the absorption mechanism is very fast for PIX-L112, but the results of [13] indicate that the probability of this is low. Some control wafers were subjected to the controlled environment for days at a time after dessication and subjected to repeated measurements. After several months of experiments none of the control wafers showed any change due to moisture absorption. 4.6 Deembedding Deembedding of the S parameter data of transmission lines was accomplished by the use of SPANA, a computer program developed at North Carolina State University. SPANA is an acronym for Signal Processing for Automatic Network Analysis. SPANA is capable of taking arrays of roughcalibration S parameter data and automatically applying the TL deembedding algorithm to them, and determining the S parameters of the embedded line. As a by-product, SPANA is capable of reporting (f) and Z C (f) oftheembedded line. The SPANA \dmb2"command was used for the deembedding. To rundmb2, SPANA requires the rough S parameter arrays resulting from the through (\thru") and line measurements as input, as well as the direct-measured capacitance per unit length C, and the dierence in lengths of the \thru"and \line"transmission lines as input parameters. The resulting data for (f) was processed by anewspana command \rform,"which combines this data with the analytically determined R using the analysis described in Chapter 3, to nd G and L for the embedded line. The command rform was written specically for this project and is documented in Appendix A. Once all of the RLGC parameters were known, it was possible to plot, C,andalpha D, in addition to the phase constant and the characteristic impedance Z C Application of the technique to the ATT type A transmission lines The technique was rst used to analyze the ATT type A FLM and SLM transmission lines. Figure 4.17 shows the measured G for FLM lines using the technique described above. The thicker lines, with more dielectric between them and the ground plane, showed greater conductance, as expected. Similar results, tabulated for SLM lines on the same wafer, are shown in Figure It should be noted that the same ordering is evident as in the FLM case. Plotting both sets of results on the same graph greatly lowers the resolution, but brings out a very important point very clearly, as shown in Figure The FLM lines show signicantly higher conductivity than the SLM lines. Clearly this is due to the proximity of the FLM lines to the ground plane. This suggests that it may be possible to use this data to determine the eective loss tangent for a given layer of metallization. The attenuation constant data provides another indication of this. Attenuation constant data for the FLM lines is shown in Figure 4.20 Plots of C and D for the FLM and SLM lines are shown in Figures 4.20 and Clearly D (which depends on G) makes up a signicant proportion of the attenuation of each line even though G!C. The D 's of the SLM lines coincide as they do for the FLM lines except at very low frequencies where the approximation to ( 3.6) in Chapter 3 breaks down. The dielectric loss constitutes a higher proportion of the total attenuation for the FLM lines than it does for the SLM lines which is expected since more of the elds of the FLM lines are in the dielectric. The behavior of D can be better understood by considering the relation between G and the dielectric loss tangent (tan ) of a microstrip line [42, pp. 154{155]: G=!C = k tan. Here k is a constant called the lling factor (0 k 1), that depends on the ratio of the energy in the

37 C G (Siemens/mm) B 1A FREQUENCY (GHz) Figure 4.17: Derived G versus frequency for FLM lines. 1A{10 m, 1B{16 m, 1C{32 m. G (Siemens/mm) C B A e FREQUENCY (GHz) Figure 4.18: Derived G versus frequency for SLM lines. 2A{10 m, 2B{16 m, 2C{32 m.

38 C G (Siemens/mm) B 1A 2C 2B 2A FREQUENCY (GHz) Figure 4.19: Direct comparison of G results for FLM and SLM data. ATTENUATION (db/mm) α C,1A α C,1B α C,1C α D, FREQUENCY (GHz) Figure 4.20: Attenuation constants for rst layer metal lines: C 1A, C 1B and C 1C are the conductive attenuation constants for the 10 m, 16 m and32m width lines respectively and D 1 is the eective dielectric attenuation constant.

39 ATTENUATION (db/mm) α C,2A α C,2B α C,2C α D, FREQUENCY (GHz) Figure 4.21: Attenuation constants for second layer metal lines: C 2A, C 2B and C 2C are the conductive attenuation constants for the 10 m, 16 m and 32 m width lines respectively and D 2 is the eective dielectric attenuation constant. dielectric to the total energy with k=1 indicating that the entire medium is dielectric. This relation was used to calculate the eective loss tangent for each of the lines under study. A straight-line t to the G versus f data was made for each line in the range of 2 GHz to 16 GHz yielding k tan of for 1A for 1B for 1C for 2A for 2B and for 2C. This implies aminimum eective dielectric loss tangent of as the maximum value of k is 1. The above dielectric loss tangent isunusually high for polyimide if bulk properties alone are considered. To investigate this further the dielectric loss tangent of the dielectric used was determined using a Hewlett Packard 4275A LCR meter (with 0.1 ff and 10 ns resolution) and the probing structure shown in Fig A mercury droplet was used to create a large-area capacitor using a large section on the ATT-B substrate which only has polyimide and a ground plane. Two Quater P/N A needle probes were used to make contact to the capacitor, one to the ground plane using a 50 m square surface pad and the other by immersion in the mercury droplet. The needle probes were electrically isolated from the Quater Model XYZ 500TIM micropositioners used to position them, in order to reduce the xturing capacitance that had to be zeroed out. This structure was electrically modeled by the circuit shown in Fig. 4.23, where R S is the contact resistance which must be found before the parallel RC equivalent circuit of the dielectric region between the ground plane and the bottom surface of the mercury can be determined. R S is comprised of the resistance of the probing xture, mercury contact resistance and contact resistance between the ground probe and the ground plane. R S was determined using two impedance measurements at dierent frequencies as follows. At frequency f 1 the impedance of the equivalent circuit is: Z 1 = R 1 + jx 1 = R S + 2 1=G 1+(!C=G) ; 2!C=G (4.1) 1+(!C=G) 2

40 36 Figure 4.22: Top view of low-frequency tan experiment. Figure 4.23: Circuit model for nding contact resistance R S and parallel equivalent circuit model of the dielectric between the ground plane and the bottom surface of the mercury.

41 37 and so R 1 = R S + 1=(!G 0) 1+(C=G 0 ) 2 (4.2) where it is assumed that G 0 = G=! is frequency independent. Multiplying (4.2) by f 1 and subtracting from it a similar expression at f 2 multiplied by f 2 leads to R S = f 1R 1 ; f 2 R 2 f 1 ; f 2 (4.3) Measurements were made at a number of frequencies in the range 100 khz to 10 MHz consistently yielding R S = 20 and an out-of-plane loss tangent ( G=!C) of (At 10MHz G was 3.95 S/cm 2 ) This compares favorably with measurements on similar polyimides which implied an out-of-plane loss tangent of [18]. (The in-plane loss tangent in[18]was ) It is clear, however, that the eective dielectric loss tangent of polyimide interconnects considered here far exceeds that of bulk polyimide. This excess loss could have been due to radiation resulting from dimensional irregularities, or the eect of dielectric anisotropy. To test this rst hypothesis, a sacricial ATT type-a die was painstakingly sectioned longitudinally for SEM analysis. The resulting SEM photo, shown in Figure 4.24 revealed no obvious anomalies in the vertical spacing of the line. However, dimensions could only be resolved to approximately 0.5 m due to uncertainties introduced when the sample was polished. It is doubtful that dimensional variations of that order caused the excess loss, but more research would be required to prove this. Figure 4.24: SEM photo of the longitudinal cross section of an ATT type A line. This line was meant for crosstalk testing and was chosen because it provides a longitudinal look at both SLM and FLM lines simultaneously. Having determined G, R, and C, itwas possible to determine L, using the equation L = RG ; Re ; 2! 2 : (4.4) C The resulting L data for the FLM and SLM lines are shown in Figures 4.25 and 4.26.