[silizium]

The full optical wave is contained in the dielectric conductor. This conductor needs it's minimum cross section such that the wave can propagate. If it is too small then the wave can not propagate. Also there is a maximum cross section if you want single mode operation.

You get to this result if you take the electromagntic wave equation - a partial differential equation - and solve that for your transmission line configuration.

The proper analogy in the realm of electrical waveguides is the hollow waveguide. The hollow waveguide supports TE- and TM-modes but not TEM modes just like a dielectric conductor. The size is also a function of the dielectric constant ε.

What we mostly use are TEM waveguides like microstrips or coaxial cables. The difference between electrical waveguides that supports TEM modes and waveguides that supports TE/TM modes is that the former has two independent potential planes and the latter only one. Also TEM waveguides do not have a lower cutoff frequency. A TEM wave with any frequency can propagate on any microstrip configuration.

This is not true for TE/TM waves.

What's important to understand is that for microstrips/coaxial cables the power isn't transferred in the metal but in the space (dielectric) around the metal - see Poynting vector. So what happens if you have a second conductor in that space? You get crosstalk! So TEM transmission lines do not contain the wave like hollow waveguides or optical fibers (edit: ok coaxial cables do, microstrips don't)

Now the question, how big is the microstrip? Is it just the width of the signal conductor? No, it is not.

Edit: The width of the metal lines in a chip is given by the current it must carry - current density requirement, electro-migration issues. Power lines are wide because they have to supply power to the circuit but logic traces in CMOS technology only carry negligible amount of current. In circuits like RF power amplifiers with bipolar transistors the trace width is much larger because it has to carry a much larger current. But again, microstrip lines do not have a lower cutoff frequency.