Nickel Characterization for Interconnect Analysis Yuriy Shlepnev #1, Scott McMorrow*2

# Simberian Inc. 3030 S Torrey Pines Dr., Las Vegas, NV, 89146, USA

1 shlepnev@simberian.com * Teraspeed Consulting Group LLC

121 North River Drive, Narragansett, RI, 02882, USA 2 scott@teraspeed.com

Abstract—Landau-Lifshits model of ferromagnetic metal

permeability is proposed in the paper for broad-band characterization of nickel in PCB/packaging interconnects made of copper plated with nickel and gold (ENIG finish). Unknown parameters of the plated nickel are identified with the measured generalized modal S-parameters of nickel-plated microstrip line segment and electromagnetic analysis of the same segment with multi-layered conductor interior model. The model predicts dispersive frequency dependency of nickel permeability with a resonance between 2 and 3 GHz. The resonance produces an anomaly in the insertion loss and group delay consistent with the experimental data.

I. INTRODUCTION Electroless nickel/immersion gold (ENIG) interconnect

finish is widely used over the last few years as a lead-free alternative to protect copper PCB and packaging interconnects from oxidation. ENIG finish produces a clean surface suitable for soldering for a long period of time. A layer of gold preserves interconnects from oxidation and may reduce signal attenuation at high frequencies. Nickel serves as a barrier preventing inter-diffusion of gold into copper. Appropriate modelling of the nickel layer on such boards is important for accurate prediction of signal degradation effects. Electrical characterization of nickel for analysis of microwave and digital signal propagation in interconnects with ENIG finish is the subject of this paper.

Nickel is a ferromagnetic metal with relatively large resistivity and non-unit frequency-dependent relative permeability [1]-[2]. A good review of nickel characterization is provided in [3]. Nickel is probably the most mysterious metal widely used in electronics. DC resistivity of pure nickel, reported by different authors, ranges from 4 to 5 of resistivity of copper [3]. It was also observed that the resistivity of the nickel layer can be 3-10 time of pure nickel [4]. Reports on the permeability of nickel are even more confusing – from 1 to 600 at DC and from 1 to 20 at RF/microwave frequencies [3]. The differences in outcome can be explained by the differences in the samples, process impurities and differences in investigation techniques. Thus nickel must be characterized only in the context of a particular manufacturing technology and for a particular application. Here, we will focus on ENIG finish technology and interconnects for multi-gigabit or microwave signals with the electromagnetic fields transverse to the wave propagation direction.

A relatively thick layer of gold (1-5 µm) on top of nickel electrically shields the nickel layer at microwave frequencies and reduces the signal degradation due to the large resistance and ferromagnetic properties of the nickel [5]. Effect of nickel can be safely neglected in these cases. In low-cost PCBs/packages the thickness of gold layer is usually below 0.1-0.2 µm. This is smaller than the current skin depth in gold at microwave frequencies (skin depth for gold is about 1.4 µm at 3 GHz and about 0.78 µm at 10 GHz). Anomalies in the insertion loss or attenuation at frequencies from 2 to 4 GHz due to ENIG finish with thin gold layer were observed earlier [5]-[7]. Though, the authors were not able to accurately reproduce such behaviour in simulations with simplified conductive or non-dispersive permeability models for nickel. ENIG plating model was constructed in [4] as an increase in total resistivity of the finished conductor. Ferromagnetic properties of nickel were neglected which led to large discrepancies between the model and measurements. Electromagnetic models with non-dispersive permeability of nickel were used in [5], [6] and did not reproduce the observed anomaly in insertion loss. In [3] it was suggested to use second order Debye permeability model for nickel, but parameters of the model were not identified and it was not verified with measurements.

In this paper we start from experimental observation of the anomaly in insertion loss and group delay in interconnects plated with nickel and gold. The resonance can be observed on both original S-parameters and reflection-less generalized modal S-parameters. Next, we build an electromagnetic model of plated interconnects with the physics-based dispersive Landau-Lifshits (L-L) permeability model [8], to characterize the nickel layer. The model is based on the theory of moving boundaries between uniformly magnetized layers and predicts a resonance at the microwave frequency band. Assuming frequency-dependent properties of dielectrics, and other conductors and interconnect geometry are known, we will adjust parameters of L-L model of nickel in the computed model to match the measured generalized modal S-parameters. The derived permeability model can be used for reliable prediction of interconnect behaviour for that particular manufacturing technology over the frequency range where the measured and computed S-parameters were matched.

Note that thin layers of electroplated nickel are also used in micro-electro mechanical structures (MEMS) and in micro-fabricated filters operating at RF/microwave frequencies [3].

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Though, to our knowledge and according to the author of [3] there were no reports on anomalies in the insertion loss and group delay. The reason may be either a difference in behaviour of different types of nickel alloys (electroless plated nickel may contain 7-11% of phosphorous and some other impurities) or because RF/microwave structures are typically investigated only over relatively narrow frequency band.

Accurate and reliable modelling of nickel in ENIG finished interconnects can improve electrical predictability and usefulness of this technology, eliminate uncertainties in the analysis of signals in interconnects, and promote its use for multi-gigabit digital and RF/microwave applications.

II. RESONANCE IN ENIG-FINISHED INTERCONNECTS A test board with multiple strip and microstrip structures

has been developed and built for a material identification project following the methodology suggested in [9]. Multiple test fixtures with straight 100 mm and 150 mm segments of single-ended and differential strip and microstrip lines were placed on the board for the material identification. Each structure was equipped with low-reflection 2.92 mm connector launches. There was no solder mask on the board and ENIG finish with 1-6 um layer of nickel and 0.05 um layer of gold was used to prevent oxidation. S-parameters for all structures on the board were measured with VNA from 10 MHz to 40 GHz.

Fig. 1. Anomalies in insertion loss anomaly (top) and in group delay (bottom) for microstrip structure with 100 mm and 150 mm segments (a fragment of the model is shown here – actual data acquired up to 40 GHz).

Structures with the strip line segments were successfully used to identify parameters of the wideband Debye (Djordjevic-Sarkar) model for the substrate dielectric. Measured S-parameters for all structures with the microstrip line segments had some anomalies in the insertion loss and in group delay around 3 GHz as shown for two structures in Fig. 1.

This increase in insertion loss cannot be simply explained by an increase in loss due to reflection – the reflection parameters are well below -20 dB at those frequencies as illustrated by Fig. 2 for multiple structures with single-ended microstrip lines. All samples measured consistently show the same insertion loss and group delay anomaly. We observed the same anomaly in structures with differential microstrip segments.

Fig. 2. Magnitudes of S-parameters for 3 test structures with 100 mm microstrip line segments and for 4 test structures with 150 mm segments.

Originally the authors believed that “hooks” in insertion loss and group delay pointed to a potential resonance in the printed circuit board, the straight line segment, or in the measurement launch into the trace. The line was evaluated for discontinuities at about a 30 mm interval that could cause the resonance (half wavelength in microstrip line). All other potential sources of resonance phenomena were investigated in the printed circuit board and the measurement apparatus. No discontinuities or structural resonances were discovered, and relatively homogeneous dielectric was used.

Increase in the attenuation around 3 GHz in ENIG-finished interconnects was earlier observed in [5] (see Fig. 13), [6] (see Fig. 10) and in [7] (see Fig. 3). Though, none of the authors reported an anomaly in group delay. Looking at just the insertion loss, the effect may be attributed to re-distribution of currents inside the multi-layered strip with a layer of nickel with higher resistivity [4]. We have not been able to reproduce this effect in simulations using just large resistivity and simple non-dispersive permeability models of the nickel layer. Our observation of variation in both insertion loss and group delay indicate resonance, which cannot be explained by a redistribution current theory. After all possible simple explanations of the phenomena were ruled out, we came to the conclusion that the effect can be attributed to physical resonance behaviour of the nickel layer and started further

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investigation. After further research of the literature, we finally decided to use a resonant physics-based ferromagnetic metal model suggested by Landau and Lifshits (L-L) in [8].

III. LANDAU-LIFSHITS MODEL Landau and Lifshits have proposed a theory of the

dispersion of magnetic permeability in ferromagnetic materials in their seminal paper in 1935 [8]. Assuming that the ferromagnetic material has uniformly magnetized layers and the boundaries between the layers with the opposite magnetization are moving due to the external magnetic field they derived formulas for magnetic permeability in a harmonic electromagnetic field parallel and perpendicular to the axis of easiest magnetization. The expression for the relative magnetic permeability in the transverse electromagnetic field can be written as follows:

( )2

02 2

0 2h l hf i f

f i f fγµ µ µ µ

γ+ ⋅ ⋅

= + − ⋅+ ⋅ ⋅ −

(1)

where f is frequency in Hz; lµ is permeability at low

frequencies; hµ is permeability at high frequencies; 0f is resonance or proper frequency in Hz; γ is damping coefficient in Hz. For convenience, the damping coefficient can be normalized to the proper frequency. Note that Landau and Lifshits estimated that the permeability of pure deformed nickel may have proper frequency or resonance at about 15 GHz. To our knowledge, there are no data neither confirming nor rejecting the estimation. The model (1) can be combined with the first order Debye model to describe nickel behaviour at lower frequencies and model the transition from large permeability observed at DC to smaller values at RF frequencies [1]-[3]. Additional terms to describe transition to unit permeability at very high frequencies can be also used to extend the model bandwidth. Alternatively to (1), the second order Lorentzian model can be used to approximate the permeability with the resonant behaviour.

In this paper we will use the L-L model to simulate nickel layer in ENIG-finished interconnects. Unknown parameters of the model (1) will be identified with the measured S-parameters by generalized modal S-parameters method [9]. To do this we have to compute generalized modal S-parameters of the plated line segment and adjust the parameters in model (1) to match them with the measured GMS-parameters.

IV. MODEL OF PLATED MICROSTRIP SEGMENT To start the identification of the nickel permeability model

(1), we first build an electromagnetic model of the line segment with the multilayered conductor as shown on the cross-section view in Fig. 3.

Fig. 3. Cross-section of microstrip line for electromagnetic analysis.

To our knowledge, one of the first computational models for microstrip line with multilayered conductor was constructed on the basis of Trefftz’s method in [10]. Here we will use a hybrid technique based on the method of lines extended for planar 3D structures in [11] and combined with the Trefftz finite elements [12] to simulate the conductor interior. Trefftz elements use plane-wave solutions of Maxwell’s equations in the element media as the intra-element basis functions. In our case, admittance or scattering parameters of a single element can be defined following [11] with the plane wave complex propagation constant and characteristic impedance for the intra-metal elements defined as:

0

0

2ik i fZ ik

π σ µ µσ

≈ ⋅ ⋅ ⋅ ⋅

≈ (2)

where σ is the metal conductivity; 0µ is permeability of vacuum, µ is relative permeability of metal (unit for Cu and Ag and defined by (1) for Ni).

Because element size does not have to be smaller or even compatible with the skin layer depth, we can use just three layers of elements to simulate the conductor interior as shown in Fig. 4.

Fig. 4. Trefftz finite element model of the three-layer conductor (elements have different size along the Z-axis).

One layer of elements simulate copper, one layer is for nickel and one for gold. The elements are connected together first and then connected to the grid Green’s matrix built with the method of lines. The surface impedance of the conductor is adjusted to simulate the rough conductor surface. With this hybrid technique we compute admittance parameters for two segments of microstrip line and extract complex propagation constant, characteristic impedance and complex impedance and admittance per unit length following procedure suggested in [13]. The algorithm described here was implemented in the electromagnetic signal integrity software Simbeor 2011 [14].

Finally, after the complex propagation constant Γ for the plated microstrip line has been found, the generalized modal S-matrix of the line segment with length dL can be computed as:

( )( )

0 expexp 0

dLSg dL−Γ ⋅ = −Γ ⋅

(3)

Matrix Sg is normalized to the complex characteristic impedance of the microstrip line and does not have reflection. In case of coupled or multi-conductor line such matrix has zero modal transformation terms [9]. Due to absence of reflections and modal transformations and simplicity of the transmission term, the GMS-matrix (3) is ideally suitable for

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the material parameters identification purpose. No computational models of probes or launches are required.

V. MODEL IDENTIFICATION WITH GMS-PARAMETERS The material identification procedure used here is described

in detail in [9]. To start the identification, we first convert regular measured S-parameters of the structures with 100 mm and 150 mm microstrip segments shown in Fig. 1 into the reflection-less generalized modal parameters (3) of 50 mm line segment. Technically, assuming identities of the cross-sections and launches, we extract S-parameters of the line segment with the length equal to the length difference of the test fixtures. The extracted S-matrix is normalized to the unknown characteristic impedance of the microstrip line and thus has exactly zero reflection. The results are shown with blue lines in Fig. 5 and Fig. 6. We can clearly see that the anomaly in the generalized insertion loss and group delay is similar to the original S-parameters. At the anomaly frequencies the losses come both from conductor and dielectric. At lower frequencies the conductor losses are dominant and at higher frequencies the dielectric losses dominate.

The dielectric parameters were identified with the strip line structures without plating, and did not show any peculiarities around 3 GHz. This is clear evidence of the nickel plating effect (gold is a regular metal and the layer is too thin to have any effect on the electrical properties of the structure). Note that the generalized parameters appear noisy at frequencies above 20 GHz. This is mostly due to non-identities of the launches and non-identities of the cross-sections in the two structures used to extract GMS-parameters. Some results on sensitivity of GMS-parameters to non-identity of the test fixtures are reported in [15].

Fig. 5. Magnitude of measured (blue) and computed (red) generalized transmission of 50 mm microstrip segment with ENIG finish.

Fig. 6. Measured (blue) and computed (red line with +) generalized group delay (top graph) and phase (bottom graph) for 50 mm microstrip segment with ENIG finish.

The next step in the identification procedure is to build the computational model of the same 50 mm section of microstrip line as described in section IV. To do this, we need to define the dimensions of the microstrip line. The board was cross-sectioned at multiple locations and photographed as shown in Fig. 7. As we can see the microstrip is not actually rectangular as in the model shown in Fig. 3. The strip is approximated as rectangular with strip width 69 um and total thickness 10-12 um. RMS roughness for the bottom side of the microstrip is defined as 0.6-1.2 um with roughness factor 2.5. RMS roughness value 0.2 um with roughness factor 2 was used for all other surfaces. Ni layer thickness is defined as 1-6 um and Au layer as 0.05 um. Dielectric thickness of substrate is 30 um and dielectric is identified as the wideband Debye model (also known as Djordjevic-Sarkar model) with dielectric constant 3.x and loss tangent 0.01x at 1 GHz (the model reproduces causal decline in dielectric constant and slight increase in loss tangent with frequency). The top layer copper fill is spaced 600 um away.

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Fig. 7. Micro-photograph of the microstrip line cross-section with ENIG finish. Layer of nickel is thicker at the edges of the strip.

At this point we have all data necessary to compute the GMS-parameters (3) of 50 mm microstrip line segment. The only unknowns are parameters of the nickel permeability defined in (1). We first simulated structure with total strip thickness 12 um and Ni layer 6 um with roughness 0.6 um. Approximately knowing the position of resonance, we first define the proper frequency 0f as 2.6 GHz. Then we adjust

lµ to 6.0 and hµ to 2.0 and resistivity relative to resistivity of copper to 6.0 (absolute conductivity σ about 1.0e7 S/m) to match GMS-parameters at high and low frequencies. After that we adjust the damping coefficient γ to 00.18 f⋅ and match the shape of resonance on the insertion loss and group delay curves. This model produced acceptable accuracy at the resonant frequency and above. Though, below the resonance the match was no so good. After adjustment of geometry to another corner case with total strip thickness 10 um, Ni layer thickness 1 um and roughness 1.2 um we repeated the identification procedure and have got the following parameters of the model: 0 2.5f GHz= , 5.7lµ = , 1.4hµ = ,

=1.55e7 S / mNiσ , 00.22 fγ = ⋅ . GMS-parameters of this numerical model are plotted (red lines) with the measured data (blue lines) on the graphs in Fig. 5 and Fig. 6. Some discrepancies in GMS-parameters can be explained by substantial differences in the cross-sections of simulated and actual microstrip lines. As we can see from Fig. 7, the actual trace is not rectangular and not trapezoidal either. The thickness of plating layers also varied between the samples and over the surface of the microstrip. Complex permittivity of the nickel with the identified parameters is plotted in Fig. 8.

Finally, we computed S-parameters of the original test structures with the connectors and launches and compared them with the originally measured data as shown in Fig. 9. Considering the differences in the computed and actual geometry of the microstrip line cross-section, we cannot expect ideal match of the computed and measured S-parameters. Though, the model produces acceptable correspondence with the measurements for this particular board and can be used to design interconnects for multi-gigabit signals using this board fabrication process with ENIG plating and the constructed models of dielectric and nickel.

Fig. 8. A possible L-L model for permeability of nickel in ENIG-finished microstrip line: 0 2.5f GHz= , 5.7lµ = , 1.4hµ = ,

=1.55e7 S / mNiσ , 00.22 fγ = ⋅

Fig. 9. Measured (solid lines) and computed (stars and circles) insertion

loss (top graph) and group delay (bottom graph) of the test fixtures with 100 mm and 150 mm ENIG-finished microstrip segments.

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Fig. 10. Measured (top) and modelled (bottom) eye diagrams for 5 Gbps

signal in test structure with 150 mm microstrip line segment.

Taking into account dispersive properties of nickel is important for analysis of multi-gigabit signals in plated interconnects. Though, the most visible effect of nickel may be expected for 5 Gbps data rate with the main frequency harmonic at 2.5 GHz (at the resonance of nickel). The constructed model produces good correspondence with the experimental results as shown in Fig. 10 for 5 Gbps signal. We have also observed good correspondence between measured and simulated eyes for signals with data rates from 3.125 Gbps to 12 Gbps.

A hybrid model that includes a Debye term for lower frequencies in addition to the resonant L-L term for the microwave frequencies may be needed to produce better match of computed and measured data. Further investigation of a structure with more defined geometry of cross-section or numerical model better reproducing the cross-section geometry may be needed to build more accurate and universal model for nickel.

VI. CONCLUSION Resonant behavior of interconnects made of copper plated

with nickel and gold (ENIG finish) has been reported in the paper. It was shown that resonance between 2 and 3 GHz is visible on measured insertion loss as well as on group delay

graphs and cannot be simply explained. The resonance has been attributed to ferromagnetic properties of the nickel layer. Landau-Lifshits (L-L) ferromagnetic metal model is proposed for simulation of the nickel layer in the multi-layered conductor. An electromagnetic model of copper microstrip line segment plated with Ni and Au has been constructed. Parameters of the L-L model are identified by matching measured and computed generalized modal S-parameters of the nickel-plated microstrip line segment. It was observed that the choice of the parameters in the L-L model (1) is not unique and does not produce perfect match simultaneously at high and low frequencies. Though, it reproduces the experimentally observed resonance in insertion loss and group delay with acceptable accuracy. The model may be specific to this particular case and cannot be considered as a universal model for nickel in ENIG finish.

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[14] Simbeor 2011 Electromagnetic Signal Integrity Software, www.simberian.com

[15] Sensitivity of PCB Material Identification with GMS-Parameters to Variations in Test Fixtures, Simberian’s App Note #2010_03, http://simberian.com/AppNotes.php

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