Modelling and application of elastomer mesh for microwave probing

transcript

Modelling and application of elastomer mesh formicrowave probing

J. Jayabalan, B.-L. Ooi, M.S. Leong and M.K. Iyer

Abstract: A novel microwave probing application using elastomer mesh is described. It is targetedfor testing wafer level packages with very fine pitch of the order of 100 micron and large pin countsof the order of a thousand. The metallised elastomer mesh provides mechanical compliance as wellas good electrical contact. A mesh-coplanar probe is modelled by the partial element equivalentcircuit (PEEC) method. The model is verified through frequency domain measurements on aprototype test fixture.

1 Introduction

Wafer level devices need good electrical contact for makingreliable measurements especially at high frequencies whenthe circuits contain modules, such as front end RF andPLL. Contact impedance, being frequency-dependent,makes the design of test probe a challenging task. Cantilevelprobes [1] have been traditionally used for testing wafer-level devices. They are only useful for low-frequencyapplications of about 100MHz due to long lead induc-tances. Coaxial probes [2] are available with multigigahertzperformance for pitches as small as 120 micron and havebeen used for probing solder bumps. The limit on scalingdown to finer pitch makes the coaxial tips not usable as atest probe for high I/O density, fine pitch packages. Thisgap is being addressed by compliant probes for Sea o Leads(SoL) technology [3], MEMS probe [4], membrane [5–10]and Cobra [11] probe technologies. In this paper, wedescribe a novel approach based on metallised elastomermesh for microwave probing which meets the small size,high frequency and compliance requirements of wafer-levelpackages (WLP).

2 Probing considerations for WLP test: relevanceof dielectric elastomer mesh

Fine pitch WLPs with a large number of input/output pinspose tremendous test challenges at multigigahertz frequen-cies for several reasons. The test probes need to be packedwith high I/O density. They need to be mechanicallycompliant in the vertical direction to accommodatethickness variations in the wafer and interconnects. Theyalso need to be compliant in the lateral direction toaccommodate thermal expansion and contraction. At thesame time, they should offer good electrical contact forefficient signal transmission and integrity over the several

gigahertz frequency range. The signal generation anddetection point [12, 13] should be as close to the probe aspossible to minimise parasitic effects that usually corruptthe signal integrity.

The schematics connecting the elastomer probe betweenthe WLP device under test (DUT) and a PCB is shown inFig. 1. The prototype test fixture incorporates a novelconcept where a combination of a multilayer substrate andcompliant dielectric mesh interposer sheet are used indesigning a mesh-coplanar waveguide transmission struc-ture. The introduction of a multilayer PCB serves as a spacetransformer between the fine pitch of the tested device andthe large pitch of the test equipment circuits and as adistributor of a large number of signal lines between theWLP and the test circuits. The built-in compliance ofthe mesh interposer provides for the thickness variation ofthe DUT, thereby maintaining reliable electrical contactsover a wide area of square centimetres. A two-dimensionalarray of compliant mesh provides mechanical stabilitywithout breaking the device under test or the probe.

The probe metallisation lines are screen printed on theelastomer mesh as shown in Figs. 2–4. The ability tofabricate small features with the approaches that are usedfor silicon processing helps to deposit metal lines with theresolution of 40-micron line width and 100-micron pitch.The metal particles are absorbed throughout the thickness

nWLP-package

the subject of inspection

elastomer interposerhyper-SMD

(TSP)PCB

Fig. 1 Elastomer mesh interface connecting wafer-level package toPCB circuits

J. Jayabalan and B.-L. Ooi are with the Department of Electrical and ComputerEngineering, National University of Singapore, 10, Kent Ridge Crescent,Singapore 119260

M.K. Iyer is with the Institute of Microelectronics, 11, Science Park Road,Singapore

E-mail: g0203807@nus.edu.sg

r IEE, 2006

IEE Proceedings online no. 20050113

doi:10.1049/ip-map:20050113

Paper first received 28th December 2004 and in revised form 1st September 2005

IEE Proc.-Microw. Antennas Propag., Vol. 153, No. 1, February 2006 83

of the elastomer. This makes the mesh layer look like adouble-sided PCB without vias. The absence of viasmakes this probe ideal for high-frequency signal transmis-sion. The elastomer is chosen to be of low-k type tominimise signal RC delays. The PCB is made of BT resinthat is usable upto 8GHz. The elastomer mesh probestructure is shown in Fig. 4. Each probe location consists of

three fingers that correspond to ground–signal–groundplaced at a pitch of 100 microns. The probes are gold-platedto minimise the contact resistance. The thickness of themesh is 50 microns.

3 PEEC model of elastomer mesh

PEEC modelling comes from mapping the field probleminto a circuit problem [14–17]. PEEC is a delay differentialequation model that includes the delayed interaction termsamong capacitive displacement currents and the inductiveconductor currents. PEEC of a homogeneous isotropicsubstrate is extended to the case of elastomer mesh asfollows.

The Maxwell equations are represented in the form ofan electric field integral equation (EFIE) in terms of scalarand vector potentials. The scattered term for the electricfield E is

Esðr; tÞ ¼ @Aðr; tÞ@t

þrfðr; tÞ þ Jðr; tÞs

Here r is the distance vector between source and field pointsand t is time. Integrating (1) over the volume, we arrive atthe macroscopic Kirchoff’s voltage equation [16, 17]. Sincethe voltage around the closed loop is zero, we have

Jðr; tÞsþ m4p

Gðr; r0Þ @Jðr0; tdÞ@t

dv0 þr4pe0

v0Gðr; r0Þqðr0; tdÞdv0 ¼ 0 ð2Þ

where Gðr; r0Þ and td are the Green’s function and timeretardation, respectively, given by

Gðr; r0Þ ¼ 1

jr� r0j ð3Þ

td ¼ t � jr� r0jc

The lumped circuit parameters (partial inductance Lp,coefficient of potential Pp and patch resistance Rp) areextracted from the Green’s function representation of scalarand vector potentials. The partial inductance, partialpotential coefficient (reciprocal of capacitance) and resis-tance values for the 2-D geometry are obtained by [14]

Lp ¼m

Kðr; r0Þds ds0 ð5Þ

Pp ¼1

CP¼ 1

Kðr; r0Þds0 ð6Þ

Rp ¼L

sWtð7Þ

where K(r,r 0) is the Green’s function with r and r 0

representing distances, ds and ds0 area segments and l andl 0 length segments (perpendicular to the direction of currentflow) of the observation and source cells, respectively; a isthe surface area of the capacitive partition segment and L,W, t and s are the segment length (along the direction ofcurrent flow), width, thickness and bulk conductivity of themetallisation, respectively. For the case of 3-D structures,the same Green’s function kernel is used except that thesurface integrals are replaced by volume integrals.

Usually the free space homogeneous Green’s function(GF) kernel is used for extraction of partial inductances andcoefficient of potentials. But in the case of a mesh probe,it is not appropriate to use homogeneous GF alone due tothe mixture of metallic particles and polymer material. The

Fig. 2 Elastomer mesh without metallisation

Fig. 3 Elastomer mesh with metallisation

Fig. 4 Physical test sample of elastomer probe

84 IEE Proc.-Microw. Antennas Propag., Vol. 153, No. 1, February 2006

equivalent circuit for the mixture is obtained by consideringthe conduction current and displacement current usingseparate partial inductors. Otherwise, the capacitances andresistances are treated as in the standard PEEC model.The mixture of metal particles and the dielectric materialmeans that the polarisation charges and currents insidethe metallic inclusion due to dielectric mesh must beincluded to the homogeneous EFIE in order to compute thefields. This amounts to the perturbation of local electric fieldin the metal through the polarisation vector by an amountthat depends on the material permittivity and compositionof the mixture. Considering the metal particle to besurrounded by dielectric in a spherical (or cubic) symmetry,the effective local field could be represented, for isotropicmaterial, as

E ¼ E0 þ EP ¼ E0 þP

3e0nð8Þ

where n is a constant coefficient introduced to reflect thefield dependence on the material mixture composition.Table 1 summarises the value of the coefficient forcommonly encountered composition scenarios. The factor1/3e0 in the second term of (8) comes from the electricfield due to polarisation [18] of the neighbouring dielec-trics. The amplitude of the external average field is thusincreased by additional contribution from the surroundingpolarisation [19].

The static approximation (8) is valid even for oscillatorycases since the wavelength is much longer than the spacingbetween particle clusters. Thus, (8) accounts for the fieldsproduced by the dielectric medium with the metallic particleinclusions.

The PEEC model for the case of homogeneous dielectrics[15] is treated by adding and subtracting the displacementcurrent from the Maxwell’s equation as

r �H ¼ JC þ e0ðer � 1Þ @E

@tþ e0

@tð9Þ

so that the polarisation current due to the dielectrics iscombined with the conductor current to represent inductiveelements. It is noted from theMaxwell’s equation applied todielectrics that

r � ðe0E þ PÞ ¼ 0 ð10Þwhere the polarisation vector is included in the free spacedivergence term such that

P ¼ e0ðer � 1ÞE ð11ÞIn view of (8), the total electric field is split into two parts.Accordingly, (11) evolves into (12) with two terms, the firstterm being the contribution from the dielectric and thesecond term from the metal inclusion.

P ¼ e0ðer � 1ÞE0 þ e0ðee � 1ÞEP ð12Þwhere er is the relative permittivity of the bulk dielectricand ee is the effective permittivity of dielectric with metal

inclusion. The field equation (9) is then modified to

r �H ¼ JC þ e0ðer � 1Þ @E0

@tþ e0ðee � 1Þ @EP

@tþ e0

ð13ÞWith this correction, the total current in the metal–dielectricmixture is given by

Jðr; tÞ ¼ JCðr; tÞ þ e0ðer � 1Þ @E0

@tþ e0ðee � 1Þ @EP

ð14Þwhere the approximation ee ¼ ðer þ 1Þ=2 is used. Equa-tion (2) is then modified as

JCðr; tÞs

þ m4p

Gðr; r0Þ

� @JCðr0; tdÞ@t

þ e0ðer � 1Þ @2E0ðr0; tdÞ@t2

þ e0ðee � 1Þ @2EP ðr0; tdÞ@t2

�dv0

þr4pe0

Gðr; r0ÞqT ðr0; tdÞds0 ¼ 0 ð15Þ

The integral equation (15) forms the basis of the PEECmodel for dielectric mesh with metal inclusion. Thecurrent derivative of the second term forms one inductorfor a metal object, while the field derivatives form anotherinductor in series with a capacitor between adjacentnodes for a metal–dielectric mixture. When the operatingfrequency is of the order of relaxation time of the pola-rising medium, the field derivatives need to be treated asseparate inductors interacting with the corresponding timedelay.

Figure 5 shows the equivalent circuit representation of amesh cell with metal inclusion, where the interaction isgoverned by the mutual inductances as well as capacitances.The resistance element is obtained by integrating the firstterm in (15) as Z

JCðr; tÞsii

dv0 ¼ Rii ¼lii

saiið16Þ

where lii and aii are the cell length along the direction ofcurrent flow and cell cross-sectional area perpendicular tothe direction of current flow, respectively.

Table 1: Selection of constant n in (8)

Mixture coefficient, n Material composition

1 Pure dielectric

1onoN Metal–dielectric mixture

N Pure metal

k th node

i th node

RiimLiim

Riid Liid Liidj ≠ id

Vj (s)Lij

Liimj ≠ im

Vj (s)Lij

Piij ≠ iIj (s)

Pkkj ≠ kIj (s)

Fig. 5 PEEC model of a dielectric cell with metallic inclusion

For the metal cells, the inductance is calculated byintegrating the second term of (15) as

Lijm ¼m

4paiaj

Gðrj; r0iÞdv0i dvj ð17Þ

where ai and aj are the cross-sectional area of the volumecells perpendicular to the direction of current flow, i ¼ jcorresponds to the partial self inductance and i 6¼ jcorresponds to the partial mutual inductance. The inductivecouplings are represented by the voltage-controlled voltagesource summation term

VL ¼Xj 6¼i

Lij@iLjðt � tdijÞ

@t¼Xj 6¼i

LiijLjðt � tdijÞ ð18Þ

where jLj is the potential across the jth inductance cell and

tdij is the time delay according to (4) between interactionamong ith and jth cells. For dielectric cells, the inductanceterms Lijd are similar with the addition of the factore0ðer � 1Þ. If the dielectric involves the metal inclusion,there is an additional inductance term with factore0ðee � 1Þ.

For capacitance calculation of the surface cells, theintegral expression of the last term in (15) is approximatedto give the partial coefficient of potential as

@xGðrj; r0iÞqT ds0idsj

4pe0aj

Gðrþj ; r0Þ � Gðr�j ; r0Þh i

QT ds0i

¼ QT ðPþij � P�ij Þ ð19Þwhere rþj and r�j are the extremity position in the direction

of cell partition and QT ¼ ajqT is the total charge of the jthcell. In general, the coefficient of potential is represented as

Pij ¼1

4pe0aiaj

Gðrj; r0iÞds0i dsj ð20Þ

The capacitive couplings are represented by the current-controlled current source summation term

IC ¼Xj6¼i

PiiiCjðt � tdijÞ ð21Þ

where iCj is the current through the jth capacitive cell. Aseries resistance Riid is added to represent a lossy dielectric.The series capacitance is obtained from

Ci ¼e0ðei � 1Þai

lið22Þ

where li and ai are the interior dielectric cell length alongthe current direction and cross-sectional area, respectively.

4 Numerical example and results

The device under test (DUT) shown in Fig. 6 is mounted ona test fixture as shown schematically in Figs. 7 and 8. The

test fixture consists of SMA connectors to connect withcoaxial probes from measuring equipment as well aselastomer probes to connect with the DUT. The test fixturealso has one coplanar line for calibration. The calibrationmeasurement is de-embedded from the DUT measurementto remove the SMA connector and PCB parasitics. Sincethe DUT length and elastomer probe (B1mm) are muchsmaller than the fixture length (B10cm), the DUT andcalibration lines are assumed to be of equal length. Thephase errors introduced by this assumption are consideredto be negligible.

The DUT has two square pads of side 75 micronconnected by a coplanar transmission line on a high-resistivity silicon substrate. The DUT transmission line hasa length of about 1400 micron. Copper metallisation is usedfor pads and transmission lines.

Coaxial probes of 3.5-mm diameter and a probestation from Cascade Microtech along with an HP8510Cvector network analyser were used for the S parametermeasurements. A two-step calibration procedure [20] isused. As a first step, SOLT (short-open-load-through)calibration of the probes is performed prior to actualmeasurements. 201 test points were selected over afrequency range of 1–20GHz. Continuous wave RF powerlevel of�15dBm was used. This step removes the parasiticsdown to the probe tips. As a second step, to remove theeffect of the test fixture, an equivalent circuit modellingtechnique [21], developed by the authors, is adapted asfollows.

The two-port matrices for the DUT (AD) and CAL (AC)transmission line system are

AD ¼ PLMPR ð23Þ

AC ¼ PLPR ð24Þwhere PL, PR and M are the ABCD matrices of the leftSMA connector–transmission line on the test fixture andthe right SMA connector–transmission line on the testfixture and device probe–DUT, respectively.

The right-pad matrix is, by symmetry, represented interms of left-pad matrix elements as

PR ¼PLð2; 2Þ PLð1; 2ÞPLð2; 1Þ PLð1; 1Þ

� �ð25Þ

SiO2 Si

Fig. 6 Device under test layout

Fig. 7 Test fixture setup for measurement

SMA5calibration line

Fig. 8 Test fixture schematic for calibration

Pad matrix optimisation is performed by minimising thetwo-norm R of the residual matrix, where

R ¼XN

1�ReftrðPLPRÞkgReftrðACÞkg

��2

þ 1� ImftrðPLPRÞkgImftrðACÞkg

��2

ð26Þand N is the number of frequency points. The mesh matrixis obtained as

M ¼ P�1L ADP�1R ð27ÞSince the performance of the DUT is known fromindependent measurement with Cascade ACP probes, theelastomer probe performance is obtained from the collectiveperformance (27) of the DUT and elastomer probe.

Contact resistance was maintained at 0.35O throughoutthe measurement routine as evidenced by the DC measure-ment values obtained prior to and after VNAmeasurements.This shows that there is no significant contact degradation,at least within the measurement time span of 30min.However, there is found to be a slight degradation overa period of 48h to 0.5O. But this value is still acceptablefor most practical applications, such as burn-in test. Thevariation of contact resistance with the number of contactsup to 20000 cycles are within 0.5O on a larger prototypemeant for automated use, but using the same probe material.

The partial element equivalent circuit model of thecoplanar elastomer probe is obtained from the methoddescribed in Section 3 and is shown in Fig. 9. This modelof the probe is simulated in circuit solver HSPICE andcompared with the measurement results in terms ofscattering parameter S21 and S11 magnitudes.

The SMA connectors and transmission lines are de-embedded from calibration measurements. The remainingmesh probe data is compared against PEEC modelsimulation. The results of the model are in reasonableagreement with measurements in the 1–8GHz frequencyrange. The magnitude errors were less than 0.3dB forinsertion loss as shown in Fig. 10 and less than 2dB forreturn loss as shown in Fig. 11, except for some parasiticresonances due to neighbourhood interactions, which arenot modelled.

A comparison between the new probing methodologyand the existing or commercially available probes is given inTable 2. Both in terms of high-frequency operation and I/Opin density, the elastomer mesh probe offers superiorperformance. Due to ease of manufacture and robustness ofcontacts over 20000 cycles, it is also cost-effective.

5 Conclusions

A new microwave probing application based on elastomermesh for high I/O density fine-pitch wafer-level packageshas been described. The mesh provides good verticalcompliance, low contact resistance and efficient geometry

port 1 port 2

Fig. 9 Equivalent circuit of probeTime-delayed interacting current sources are represented as rectan-gular blocks, and voltage sources are represented by circles andsquare blocks

0 1 2 3 4 5 6 7 8 9

− 0.4

− 0.8

− 1.2

− 1.6

− 2.0

frequency, GHz

measurementPEEC model

Fig. 10 Insertion loss – model and measurement

0 1 2 3 4 5 6 7 8 9

− 10

− 15

− 20

− 25

− 40

− 35

− 30

frequency, GHz

measurementPEEC model

Fig. 11 Return loss – model and measurement

Table 2: Comparison of different probing technologies

Probe technology Pitch Operatingfrequency

Pincount

Cantilever/wire probe 480 micron o500MHz o500

Coaxial probe 4100 micron o3GHz o500

Membrane probe 4100 micron o3GHz o2000

New elastomermesh probe

480 micron 0–10GHz 0–10000

for high-frequency signal transmission. A mesh-coplanarprobe has been modelled by the partial element equivalentcircuit method. The effectiveness of the mesh modelling andprobing method is validated by frequency domain measure-ments in the 1–8GHz range on a wafer-level packagedevice.

6 Acknowledgments

The authors would like to gratefully acknowledge thefunding and support of the Agency for Science, Technologyand Research (ASTAR), Singapore, under grant R-265-000-112-305. They also thank Dr. Mihai, M. Sivakumarand R. Ranjan of Institute of Microelectronics and FiveIslands Corporation, Japan, in the preparation of testfixture and samples.

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Modelling and application of elastomer mesh for microwave probing

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