Rough-Metal-Surface Propagation Loss Modeling

1Henning Braunisch – Rough Surface ModelingAugust 5, 2010

Rough-Metal-Surface

Propagation Loss Modeling

Henning Braunisch*, Xiaoxiong Gu†,Alejandra Camacho-Bragado*, and Leung Tsang†

*Intel CorporationComponents Research

Chandler, Arizona, USA

†University of WashingtonDepartment of Electrical Engineering

Seattle, Washington, USA

IEEE Waves & Devices Phoenix Chapter Seminar Series


Outline

• Introduction

• Attenuation enhancement factor

• Small-perturbation method

• Effective conductivity

• Estimation of power spectral density

• Quantitative 3-D surface imaging methods

• Sample preparation

• Correlation of theory and experiment

• Impact on multi-Gb/s signaling

• Conclusions


Introduction

Off-chip interconnect structures often exhibit rough metal surfaces with RMS roughness Rq in the order of microns• As deposited or deliberately roughened to enhance adhesion

At 5 GHz, skin depth into a smooth conductor made of non-ideal copper based on classical electrodynamics is about 1 µm• Impact on wave propagation is non-negligible

Cross-section of flex-circuit with rough trace over rough ground plane

75 µm


Attenuation enhancement factor

Smooth-conductor propagation loss multiplied by correction factor due to surface roughness

frough often approximated by Hammerstad-Bekkadal (1975) fit• Based on modeled data published by Morgan in 1949

• Depends on only single roughness parameter, Rq

dcf rough(1)

2

rough 4.1arctan2

1s

qRf

(2)

fs

1 (3)

Hammerstad-Bekkadal:

Corrected attenuation constant:

Skin depth:


Small-perturbation method

Developed at University of Washington

Random rough surface characterized by its power spectral density, W(kx,ky)

frough obtained by straightforward numerical integration

(4)

(5)

(6)

PSD normalization:

3-D SPM to second order:

Isotropic random rough surface:

22

22

2

rough

j2Re),(

221 yx

s

yxyx

ss

qkkkkWdkdk

Rf

),(2

yxyxq kkWdkdkR

0

2

22

2

rough

j2Re)(

421

kkWkdk

Rf

sss

q


Effective conductivity

Concept of effective conductivity can be used to model structures with multiple roughness types• Applicable to 2-D and 3-D field solvers

Effective conductivity is frequency dependent• High-frequency approximation

(7) 2

rough

roughf

Given metal conductivity :

De-smear

CZ etch

Bulk Cu

Multi-roughness modeling examplefor a package trace


Estimation of power spectral density

• Fast algorithm for isotropic random rough surfaces

• Process single image instead of hundreds

• Given surface height profile h(x,y):

1. Utilizing 1-D fast Fourier transform (FFT), average the squared magnitude spectra along all lines in the x and y directions of the sampled surface height function.

2. Take an inverse FFT to obtain an estimate of the correlation function of the isotropic rough surface.

3. Obtain the PSD estimate by computing a Fourier-Bessel transform of order zero (also known as Bessel or Hankel transform).


Quantitative 3-D surface imaging methods

• Optical interferometry• Relatively poor, diffraction limited lateral resolution of typically

350 nm

• Height maps with partially missing data can be problematic for the Fourier methods employed in this work

• Scanning probe microscopy• Atomic force microscopy (AFM)

• Good lateral resolution

• Limited z range

• Scanning electron microscopy (SEM)• Stereopairs obtained at different tilt angles

• Requires well characterized, high-resolution SEM stage


Sample preparation

Need to expose rough copper surfaces on processed samples

Example: Organic package substrate

Laser milling Reactive ion etching


Correlation of theory and experiment

• Outline:

1. Measure and de-embed propagation loss of rough line

2. Expose and image rough surface quantitatively

3. Extract power spectral density of rough surface

4. Calculate attenuation enhancement factor

5. Model smooth line and separate conductor and dielectric loss

6. Calculate model based rough-line attenuation constant

7. Compare measured and predicted rough-line losses


De-embedding using two-line method

Yields propagation constant of transmission line without approximations

Does not yield characteristic impedance Zc

2

1111

2

21

2

21

21211 2sech

1j

baba

ba

SSSS

SS

(8)

Zc ,


Surface imaging using AFM

Reasonable qualitative agreement between AFM and SEM images

Pseudocolor plot ofAFM data

3-D rendering ofAFM data

SEM image for qualitative comparison


Extracted power spectral density

Largest spatial frequency corresponds to sampling of just below 50 nm


Attenuation enhancement factor

In this particular case, SPM result and Hammerstad-Bekkadal fit are relatively close


Correlation

Good agreement observed

Conductor loss only

Smooth-line loss

Rough-line loss

Example:

10 Gb/s

f0

fu


Impact on multi-Gb/s signaling

• For example, signaling rate of 10 Gb/s corresponds to:• Fundamental frequency of f0 = 5 GHz

• Highest frequency of interest fu = 1.5 f0 = 7.5 GHz

• As shown by data on previous slide, impact due to surface roughness is similar to that of dielectric loss

• Many high-speed channels are primarily return loss (reflection) and cross-talk limited• Smoother lines and lower dielectric loss could still lead to somewhat

improved system performance

• Packages and board contribute to (largely additive) insertion loss

• Should improve contributions in a balanced approach

• Optimized low-loss or long channels can be significantly impacted

• Clear need for accurate predictive capability


Conclusions

• Developed new methodology for the modeling of interconnect surface roughness impact on signaling• Good agreement with measurements for a package substrate

• Applications in:• Interconnect design, especially when insertion loss becomes limiting, for

example on long channels

• Package-level and board-level substrate process technology development

• Current and future work:• Modeling and correlation with measurements for different substrate

types

• Imaging metrology refinement• Blind spots in interferometry

• Testing of a new AFM scanner

• Multi-roughness modeling using effective conductivity

• Advanced theoretical and numerical work at University of Washington

Rough-Metal-Surface Propagation Loss Modeling

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