A copper conductor in a certain high-speed integrated circuit has an approximately rectangular cross section with height h=50 nm and width w=25 nm . The highest frequency of interest is f=30 GHz and the operating temperature is T = 100 °C Is skin effect significant? If not, at what frequency

Question

A copper conductor in a certain high-speed integrated circuit has an approximately rectangular cross section with height h=50 nm and width w=25 nm . The highest frequency of interest is f=30 GHz and the operating temperature is [latex] T=100^{\circ} C [/latex] . Is skin effect significant? If not, at what frequency would skin effect become significant?

Accepted Answer

The resistivity of copper at [latex] 100^{\circ} C [/latex] is

[latex] \begin{aligned} ho_{100} & \cong ho_{25}\left[1+\alpha_{25}\left(100^{\circ} C -25^{\circ} C ight) ight] \\& \cong(1.71 \mu \Omega cm )\left[1+\left(4138 imes 10^{-6} ight)(75) ight] \\& \cong 2.24 \mu \Omega cm .\end{aligned} [/latex]

The skin depth at 30 GHz is

[latex]\begin{aligned} \delta &=d \sqrt{\frac{ ho /(1 \mu \Omega cm )}{f /(1 MHz )}} \ & \cong(50.33 \mu m ) \sqrt{\frac{2.24}{30 imes 10^{3}}} \cong 435 nm ,\end{aligned} [/latex]

which is much larger than the largest dimension of the conductor, so skin effect is insignificant. For skin effect to be significant, the skin depth must be on the order of the largest dimension. The corresponding frequency is

[latex] \begin{aligned} (50.33 \mu m ) \sqrt{\frac{2.24}{f / 1 MHz }} \cong 50 nm \ & \Rightarrow f \cong 2.27 THz ,\end{aligned}[/latex]

which lies in the infrared region of the electromagnetic spectrum.

Question 2.15: A copper conductor in a certain high-speed integrated circui...

Related Answered Questions

A copper wire is heated from 25ºC to 100ºC. What is the percent increase in resistivity? ...

Verified Answer:

A calculation indicates that a resistor having resistance R=61.7kΩ is needed in a certain circuit. Refer to Table 2.1 and give the nearest standard value from each series. ...

Verified Answer:

Verified Answer:

Verified Answer: