A qualitative approach to the non-sinusoidal skin and proximity effect in high frequency interconnections

Continuing component dimension shrinking, associated with the dramatically increase of the operating frequency require an improved modelling of the interconnection to include coupled electromagnetic and thermal effects. Among these, skin and proximity effects are essential in the thermal management of the package. Many electronic packages use as main signals, periodic sequence of rectangular pulses. In first part of this paper the influence of skin and proximity effects on the interconnection resistance when the current is a periodic sequence of rectangular pulses is reported. The non-sinusoidal skin effect is traditionally analysed by Fourier harmonic series. However slow convergent electromagnetic power series results. Series with accelerated convergence are used. These series are obtained by using a time-domain approach somehow similar to the transient analysis. Based on the non-sinusoidal skin depth concept, in the second part, it is presented a model for the evaluation of the increase factor of the resistance per unit length of the interconnection structures for the pulse duration / pulse repetition period ratio in the range 0.1 to 0.5. Due to the higher harmonic content of this non-sinusoidal waveform the skin depth decreases significantly compared with sinusoidal one especially for large durations of the pause between two consecutive pulses. This paper focuses to better understanding of the higher frequency, effects in modern interconnection techniques. This novel approach allows the optimization of the interconnection structures.