Measuring the inductance of a micron feature size gold coil

[ubergewehr273]

TL;DR

How do I experimentally measure the inductance of a gold coil patterned on a glass substrate? The feature size is of the order of a few microns.

Hi all,

I recently fabricated a bunch of gold coils patterned onto a glass substrate and am in need of measuring the inductance of these samples. Since the feature size is in microns, I can't exactly use an RLC meter.

At the moment, I'm trying to build an LCR series circuit with a PCB and trying to see if at a fixed resonant frequency (which we define) and a fixed capacitance that we use, we observe resonance at said frequency thus determining the inductance experimentally. Previously I simulated the design of the coil in COMSOL and computed the inductance, and thus using the LC resonance approach. Unfortunately, my initial measurements yielded a lot of noise in the data when making the measurements using a vector network analyzer. That's probably because I didn't make my PCB designs robust and neglected a lot of connections (had to resort to using copper wires and silver epoxy to make connections, resulting in a frankensteinesque style of a circuit).

Is there a more direct way to measure the inductance? or a more alternate and robust approach to measuring it?

Thanks in advance!

 

[Baluncore]

TL;DR Summary: How do I experimentally measure the inductance of a gold coil patterned on a glass substrate? The feature size is of the order of a few microns.

Is there a more direct way to measure the inductance?

Probably not. No matter what you do, the inductance of the leads and the capacitance to the substrate will confound your measurements. At those dimensions, everything is a transmission line, even the conductor you use to fabricate your inductance.

Consider, for example, a regular transmission line, with a known characteristic impedance. Place your inductor(s) in series, as a lump, part way along that line. You can then do frequency or time domain reflectometry to study the step change in impedance, then from that compute the change in inductance per unity length.

Computation of the inductance will be more reliable than measurement of inductance. If you require a critical inductance for some special purpose, then that will also give you a way to measure the inductance. If you cannot make that inductance measurement by substitution, then the particular value of the inductance is not really critical, and you may find yourself chasing your tail, rather than finishing the project.

Why do you need an inductor?
If the circuit is being designed for a narrow frequency band, then an inductor can be fabricated from a short transmission line of computed length and impedance. The same goes for filters, where an array of TLs will give you a transfer function, the same as a lumped filter.

 

[ubergewehr273]

Consider, for example, a regular transmission line, with a known characteristic impedance. Place your inductor(s) in series, as a lump, part way along that line. You can then do frequency or time domain reflectometry to study the step change in impedance, then from that compute the change in inductance per unity length.

Hi, thanks for this! How would I proceed in measuring the inductance using frequency domain reflectometry? I understand that one-way would be to basically build an LCR series circuit with proper impedance matching with respect to the source transmission line and to measure the reflectance at the resonant frequency. But what I'm confused about is how I could proceed in determining the inductance in this fashion.

 

[Baluncore]

How would I proceed in measuring the inductance using frequency domain reflectometry?

You would need to study transmission lines and reflectometry first.

Building an LCR series circuit will not help you. The inductor will have some capacitance, the capacitor will have some inductance and the resistor will have both inductance and capacitance. Sum zero reactance will be at a meaningless frequency.

Why does a particular numerical inductance value have such importance?
In what critical circuit would such an inductor be required?

 

[DaveE]

Why does a particular numerical inductance value have such importance?

Yes, this.

Maybe you would be better off with more of a trial and error approach using the application's performance as the metric, whatever that is. Can you just make a test bed with a few different versions and see which works best? The measurement is difficult and there are likely questions about the value, or meaning, of that data anyway, even if it's "good" data.

As @Baluncore said, at this scale (OK, maybe any scale), it's not just an inductor.

 

[TonyStewart]

This micron size is not useful for testing with your <10GHz VNA, but if you had this bandwidthnd you had all the ports required for Open / Short / Load / Thru calibration on the PCB board, then it could be measured.

I would suggest using methods for testing X-RAY properties of materials and lookup the paramagnetic properties of gold under X-band RADAR, X-RAYs, Gamma etc.

As you may have computed, a single turn at 1 micron gold might be around 2 pH which is 50 ohms at 4 Terrahertz.

https://www.wikiwand.com/en/Electron_paramagnetic_resonance
http://www.spring8.or.jp/en/news_publications/press_release/2012/120123_2/