HFSS15: Surface Roughness Model: Huray

Because surface roughness can increase conductor power losses more than two times, HFSS includes an advanced surface roughness model based on the visible features of copper conductors used in circuit fabrication. For instance, the magnified surface of copper appears as an irregular collection of nodules. The Huray model of the physical effects calls for three parameters:

A_f, the area of a unit cell

N, the number of nodules per cell (modeled as spheres).

a, the radius of a typical nodule.

These relate to the two user specified parameters in the Finite Conductivity Boundary dialog as follows:

Nodule radius, a

Hall-Huray Surface Ratio = 4 * PI *a^2*N/A_f

The equations

(1)

(2)

where

(3)

Introducing

(4)

The actual calculation implemented is:

(5)

The dialog accepts two parameters: a and sr. The simplified model uses a=0.5 um, sr= 2.9

References:

1. P.G. Huray, S.G. Pytel, S.H. Hall, F. Oluwafemi, R.I. Mellitz, D. Hua, and P. Ye, “Fundamentals of a 3-D “Snowball” Model for Surface Roughness Power Losses”, 11th Annual IEEE SPI Proceedings, May 13 – 16, 2007.

2. S.H. Hall, S.G. Pytel, P.G. Huray, D. Hua, A. Moonshiram, G. Brist, and E. Sijercic, “Multi-GHz, Causal Transmission Line Modeling Methodology with a Hemispherical Surface Roughness Approach”, IEEE Transactions on Microwave Theory and Techniques, December 2007 pp 2614 – 2624.

3. S.G. Pytel, P.G. Huray, A. Moonshiram, S.H. Hall, R.I. Mellitz, G. Brist, F. Oluwafemi, H.M. Meyer, L. Walker, and M. Garland, “Analysis of Copper Treatments and the Effects on Signal Propagation”, 58th Annual IEEE ECTC, May 26 – 30, 2008, pp 1144 – 1149.

4. S.G. Pytel, “Multi-gigabit data signaling rates for PWBs including dielectric losses and effects of surface roughness”, PhD. Dissertation, University of South Carolina, 2007.

5. P.G. Huray, O. Oluwafemi, J. Loyer, E. Bogatin, and X. Ye; "Impact of Copper Surface Texture on Loss: A Model That Works", DesignCon 2010, February 1 - 4, 2010.