4 ms·
People think this is not relevant to real world problems but it actually is, albeit all the calculations aren't that relevant. Silicon substrate's resistance is
by bgnn 1y ago
People think this is not relevant to real world problems but it actually is, albeit all the calculations aren't that relevant. Silicon substrate's resistance is basically an infinitely large grid of unut resistances at the distances relevant for a local point of an IC. Note that silicon substrate is often heavily doped (p-type) and all info you get from the fab is it's resistivity (often somewhere between 1 to 100 ohm per cm). For the most advanced tech nodes its often 10 ohm/cm. If you need to develop some intuition about noise coupling via the substrate you have to think that it's a grid instead of just calculating the resustance between point A and B. We need to distribute a grid of substrate contacts to collect the noisy currents too. So the grid shows up again!
- eternauta3k 1y agoI'd argue the case you're describing is mathematically simpler precisely because it is continuous.
- Den_VR 1y agoYou’re practically describing the invention of Calculus.
- gugagore 1y agoRight, why is it a 4-connected grid instead of 8-connected, or any other topology, like a hex grid.
- bgnn 1y agoTrue, but the continuous solution is just a limit condition of tge discrete one. It doesn't make it any harder or easier, at least from what I know fron calculus. The software tools use numerical methods to solve this type of problems and they tend to divide the continuous substrate into a mesh of discrete elements to model them as lumped circuit elements so that we can represent them in a matrix and simulate the circuit using linear algebra. They often use random walk in their algorithm to find a mesh which introduces a minimum error.
- ChoGGi 1y agoMy vague understanding of photolithography is that it's hard, though I didn't realise it's bad enough to evoke an egyptian goddess. I'll see myself out.
- em3rgent0rdr 1y agoThe word used to pray to Unut is 'ohm', I believe...
- bgnn 1y agoSorry for the uncut unut units.
- fraserphysics 1y agoThe units of resistivity are ohm * cm not ohm/cm. (I worked at Fairchild a long time ago.)
- bgnn 1y agoCorrect. Sorry for the typo. I was very sleepy.