rough-metal-surface propagation loss modeling
TRANSCRIPT
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
2Henning Braunisch – Rough Surface ModelingAugust 5, 2010
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
3Henning Braunisch – Rough Surface ModelingAugust 5, 2010
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
4Henning Braunisch – Rough Surface ModelingAugust 5, 2010
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:
5Henning Braunisch – Rough Surface ModelingAugust 5, 2010
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
6Henning Braunisch – Rough Surface ModelingAugust 5, 2010
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
7Henning Braunisch – Rough Surface ModelingAugust 5, 2010
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).
8Henning Braunisch – Rough Surface ModelingAugust 5, 2010
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
9Henning Braunisch – Rough Surface ModelingAugust 5, 2010
Sample preparation
Need to expose rough copper surfaces on processed samples
Example: Organic package substrate
Laser milling Reactive ion etching
10Henning Braunisch – Rough Surface ModelingAugust 5, 2010
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
11Henning Braunisch – Rough Surface ModelingAugust 5, 2010
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 ,
12Henning Braunisch – Rough Surface ModelingAugust 5, 2010
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
13Henning Braunisch – Rough Surface ModelingAugust 5, 2010
Extracted power spectral density
Largest spatial frequency corresponds to sampling of just below 50 nm
14Henning Braunisch – Rough Surface ModelingAugust 5, 2010
Attenuation enhancement factor
In this particular case, SPM result and Hammerstad-Bekkadal fit are relatively close
15Henning Braunisch – Rough Surface ModelingAugust 5, 2010
Correlation
Good agreement observed
Conductor loss only
Smooth-line loss
Rough-line loss
Example:
10 Gb/s
f0
fu
16Henning Braunisch – Rough Surface ModelingAugust 5, 2010
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
17Henning Braunisch – Rough Surface ModelingAugust 5, 2010
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