In the following, several “crosstalk maps” [115] are presented that given an overview over the magnitudes of single and summed crosstalk terms at many location on a TSV array.
These maps use colored squares where the coordinate in the diagram refers to the location of a port and the corresponding via in the array. The color of each square corresponds to the level of a certain crosstalk measure, e.g. the magnitude of far-end crosstalk form a central via of the array. The rounded level value indBis also printed on each square. These crosstalk maps are depicted in Figures 6.13, 6.14, and 6.15. The array for which all these maps are computed is based on a pattern of 3×3 vias. The vias at two opposite corners of this pattern are assigned as ground vias. By replicating this pattern 4 times along both coordinates, a total array size of 144 vias (112 signal vias and 32 ground vias) is obtained.
First, in Fig. 6.13a, the individual single-ended crosstalk terms (magnitudes of scattering paramters) of all vias in the array from a via at one of the central positions in the array are shown. Due to the symmetry, these are also the levels of (far-end) crosstalk at the via ports at these locations from the central via. As can be observed in Fig. 6.13a, the levels depend mainly on the distance between the vias and the number and locations of ground vias close to the locations of both the emitting and receiving via. In the next step, three vias near the array center are viewed as aggressor channels. In Fig. 6.13b these channels are marked with the letter “S”. Fig. 6.13b also shows the PSXT from these three channels at the other vias in the array. The level of this PSXT is then dependent on a larger number of different distances to aggressor vias and ground vias than the single crosstalk contribution in Fig. 6.13a. Next, the PSXT is computed for every via. Each single-ended channel that is attributed to a signal via is viewed as both an aggressor and victim of crosstalk. This is depicted in Fig. 6.13c. As can be seen, the PSXT is generally higher when vias have more signal vias and fewer ground vias close to them. The before crosstalk maps give an insight of an expected order of magnitude at the frequency of50 GHz. In the next step, a weighting as in (6.6) is used to obtain the corresponding results for a digital signal which is a train of trapezoidal-shape pulses with5 psrise time and a full width at half maximum (FWHM) of 25 ps. The results for this WPSXT are depicted in Fig. 6.13d. The lowest crosstalk can be observed again at locations close to two ground vias. The highest crosstalk is observed at locations near the array rim. Except at positions near the array rim (here the two rows of vias closest two it) the PSXT and WPSXT is the same for the same positions in the3×3 pattern. Results for the case with a finite size of the substrate and the plane metallizations are also considered and depicted in Fig. 6.14a. An influence of the finite metallizations, i.e. a relevant difference to the case with infinite planes, can only be observed at the two rows of vias nearest to the array rim. In the present example the vias in the upper right
6.4 Total Uncorrelated Crosstalk in Large Arrays
Signal via Ground via
z
dvias
tsi tox rb
ra metal
silicon
Power Sums of Far-End Crosstalk:
x z y
Figure 6.12: Silicon interposer structure consisting of a metal-clad substrate. The metal parts of cladding and via barrels are electrically isolated from the silicon substrate by silicon dioxide layers. The reference planes are at the outer planes of the metallizations. The top left part of the image shows a top view of the array, the right part shows corresponding levels of total far-end crosstalk on channels assigned to signal vias. Typical dimensions are: via barrel radiusrb= 15µm, antipad radiusra = 30µm, pitchdvias= 200µm, silicon substrate thickness tsi= 100µm, and silicon dioxide thicknesstox= 1µm. Figure and text taken from [14].
and lower left corner have the largest (average) distance to the ground vias and therefore show the highest PSXT levels.
Next, also an example for differential channels is investigated. These are obtained from the previously presented single-ended results by the methods discussed in Appendix G.3 and presented in Figs. 6.15a and 6.15b. As before, the single scattering parameters are mainly influenced (in magnitude) by the distance of the aggressor channels to the victim channels.
For the WPSXT in 6.15b it can be observed that the levels of this differential crosstalk are between13 dBand25 dBlower than the corresponding single-ended results. The levels are between about −65 dB for those ports with more ground vias in close vicinity and about
−55 dBfor via pairs with another via pair close to them.
G G G G
Figure 6.13: Crosstalk results for a setup with infinite planes, a pitch of 200µm, an oxide thickness of 1µm, a silicon layer thickness of 100µm, and a silicon conductivity of 10 S/m. Ground Vias are marked with the letter “G”. Numbers indicate the respective levels in dB of far-end crosstalk. Different color maps are used for encoding the levels in order the magnify the difference within each map. (a) single-ended far-end crosstalk at 50 GHz to or from the channel assigned to the central via marked with the letter “S” (b) power summation of 3 aggressors which are each marked with the letter “S” (c) single-ended power sum of crosstalk (PSXT) at 50 GHz (d) total uncorrelated crosstalk (WPSXT) for the signal with 20 ps rise time and 100 psFWHM. Figure and text taken from [14]. (continues in Fig. 6.14)
6.4 Total Uncorrelated Crosstalk in Large Arrays
Figure 6.14: (continued from Fig. 6.13) (a) single-ended WPSXT as before but with finite planes with edges at200µmdistance to array border (centers of outermost vias) (b) labeling of positions referred to in Fig. 6.16. Figure and text taken from [14].
G G G G
-130 -129 -113 -107 -115 -122
-142 -133 -118 -137
Figure 6.15: Setup as in Figs. 6.13/6.14 but single-ended channels combined to differential channels (a) far-end crosstalk in dB at 50 GHz between the differential channels created from pairs of adjacent vias to or from the central channel marked with the letter “S” (b) corresponding differential WPSXT for the signal with20 ps rise time with finite planes with edges at200µmdistance to array border. Figure and text taken from [14].
Pitch (µm)
100 150 200 250 300
WPSXT(dB)
Silicon thickness (µm)
50 100 150
Oxide thickness (µm)
0.5 1 1.5 2
Norm. distance to plane border
0 2 4 6 8 10
Figure 6.16:WPSXT as function of several varied parameters with the default parameter set being that of Fig. 6.13d. The default parameters are marked with gray vertical dashed lines.
Except for the variation of signal and ground via assignment, the various lines give the values at the positions marked in Fig. 6.14f and the blue dashed lines give linear or logarithmic fits for position 1 where the highest crosstalk is observed. Parameter studies of (a) pitch, (b) silicon substrate thickness, (c) silicon conductivity, (d) oxide thickness, (e) pulse length, (f) distance of the plane border for the case of finite planes normalized to the pitch of200µm. (continued in Fig. 6.17) Figures adapted and text taken from [14].