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I'm designing a metal line in integrated cicruit which will be connected to AC voltage source in one end and transistor load in the other end. How can i calculate the inductance of the metal line (6 um lengh)? i found this equetion L = o.2 * l * (ln(2*l/w+t) + 0.223(w+t)/l + 0.5) and in another place the ther is the same equetion but insted of 0.2 * l in the begining, it is u*l/2*pi so i'm very confused.

Vova
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  • Is there a "ground plane" of some kind in near proximity to the line? (i.e. unbroken ground metallization on another layer) – The Photon Jun 06 '13 at 19:12
  • Ther is a substrate about 0.7 um beneath the wire – Vova Jun 06 '13 at 19:38
  • you should find out what your base wafer is. If yo can tell us the process we should be able to make a good guess, if not look it up. If it's an Epi wafer you're talking 0.01 ohm*cm (highly conductive) with ~ 3um of 10- 15 Ohm*cm Si on top which has ~ 3 e15 carriers/cm^3 – placeholder Jun 06 '13 at 19:54
  • It's a 0.18u process on epi wafer, but i need equetion that calculate the inductance so i can change parameters and see how they influence. – Vova Jun 06 '13 at 20:12

2 Answers2

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One doesn't typically worry about or include the inductance in the design of the metal layers in IC's (with two notable exceptions). In fact, if you look at the differential equations for signal propagation, if you include inductance they yield the wave equation, if you exclude inductance you get the diffusion equation. In Chip design we use the diffusion equation, so just concern yourself with R's and C's.

THe two exceptions? 1) bond wires 2) when you've deliberately designed an inductor into the metal layers - typically only done for RF circuits that need tank circuits.

placeholder
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  • I know it's going to be very small, but i still need to calculate it... just dont know how. – Vova Jun 06 '13 at 18:29
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If there is a nearby ground plane (like unbroken area of metallization on another layer), you could probably calculate the inductance from the approximation formulas for microstrip (if there's only one ground plane) or stripline (if the line is sandwiched between groundplanes). Be aware that you might need consider this as "buried" microstrip, if the line is not on the topmost metal layer.

If there is no nearby ground plane, then it's essentially a floating wire. If you know where the current return path is, you could use an electromagnetic structure simulator to estimate the inductance.

If you have no knowledge about where the current return path is, you will only be able to very very roughly estimate the inductance. We often estimate the inductance of bondwires as 1 nH/mm, and that approximation is probably equally good (or bad) in your situation.

The Photon
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  • for open source SW see this post http://electronics.stackexchange.com/a/68904/11861 – placeholder Jun 06 '13 at 19:22
  • Reading a little bit, I found the wirebond rule-of-thumb assumes 1 mil diameter wire. For a correction factor for different wire diameter, see here: http://www.microwaves101.com/encyclopedia/Inductance_airbridge.cfm – The Photon Jun 06 '13 at 19:27