Mechanism of Copper Foil Roughness Impact on High-Frequency Signal Transmission

Mechanism of Copper Foil Roughness Impact on High-Frequency Signal Transmission

High-frequency signal transmission (>1 GHz) is highly sensitive to conductor suRFace properties. Copper foil roughness significantly affects signal integrity (SI) and insertion loss by altering current distribution under the skin effect, increasing surface scattering, and enhancing dielectric loss. The mechanisms are analyzed as follows:

I. Skin Effect and Current Path Distortion

1. Skin Depth (δ) vs. Frequency:

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   • $\rho$: Copper resistivity (1.68×10⁻⁸ Ω·m), $f$: Frequency, $\mu$: Permeability.

   • At 10 GHz, δ≈0.66μm, concentrating current near the surface.

2. Prolonged Current Paths:

   • Roughness peaks/valleys (Rz=3–5μm) force current to follow contoured paths, increasing effective resistance (Rac​):

     

     Rq​: Root-mean-square roughness.

II. Surface Scattering and Dielectric Coupling

1. Electromagnetic Scattering:

   • Non-specular reflections (diffuse scattering) cause phase distortion and attenuation.

   • At 28 GHz, scattering loss can exceed 30% of total insertion loss.

2. Dielectric Loss Enhancement:

   • Micro-voids at copper-dielectric interfaces (e.g., FR4, Rogers) localize electric fields, increasing polarization loss (higher Df).

III. Roughness Quantification and Loss Models

1. Hammerstad Model:

   

   • Modifies conductor loss based on roughness.

2. Huray Snowball Model:

   • Models roughness as spherical nodules (radius $r$) to calculate effective surface area:

     

   • Accurately predicts mmWave (30–100 GHz) losses.

IV. High-Frequency Performance Examples

V. Mitigation Strategies

1. Copper Foil Selection:

   • Hyper Very Low Profile (HVLP, Rz≤1.5μm) for >10 GHz applications.

   • Reverse-Treated Foil (RTF) to minimize oxidation and roughness variation.

2. Surface Treatments:

   • Chemical polishing or plasma cleaning to achieve Ra≤0.3μm.

   • Smooth coatings (e.g., graphene) to fill micro-voids.

3. Design Compensation:

   • Pre-emphasis/equalization based on roughness models.

   • Optimize stack-up to reduce coupling between high-speed layers and rough copper.

VI. Validation Methods

1. Roughness Measurement:

   • White-light interferometry (3D profile, Ra/Rz).

   • Atomic force microscopy (AFM) for nanoscale resolution.

2. High-Frequency Testing:

   • Vector network analyzer (VNA) for S-parameters (S11/S21).

   • Time-domain reflectometry (TDR) for impedance continuity.

VII. Standards and Trends

• IPC-4562A: Defines copper roughness grades (e.g., HVLP, RTF).

• IEEE P370: Standard for high-frequency interconnect testing.

• Trends: Nanoscale smooth copper (Rz<0.5μm) + low-Dk/Df dielectrics for 112 Gbps PAM4 and THz applications.