Can really small transistors be modeled as in undergrad textbooks?

Question

Most undergrad textbooks on microelectronics (those covering semiconductors, diodes, BJT's, FET's, etc.) that I have laid my hands on discuss semiconductor concepts such as charge carries, drift, recombination, among others, to explain why transistors behave the way they do, and then present mathematical models for how different types of transistors work (e.g. IV curves) in order to analyse circuits involving them.

My question is, can state-of-the-art transistors such as those in modern CPU's be modeled by similar formulas? Given that modern transistors based on 7 nm technology can be only a few atoms in size (~30), do the same concepts apply, or do you really need PhD-level knowledge to even begin to understand how they actually work?

I've seen from other sources how ASIC foundries will share pspice models of the transistors that they can handle to customers and that they tend to be extremely complicated with dozens if not hundreds of parameters, so I got curious about this.

Answer 1

My question is, can state-of-the-art transistors such as those in modern CPU's be modeled by similar formulas?

Yes

You need to understand what a model is.

A model is a description of a subset of the behaviours of something, that is sufficiently accurate for some stated purpose.

That is why you have different levels of model for the same thing, you have different purposes for using the model.

One model of a bipolar transistor is a IBE-dependent CE current source. This is enough for many purposes, crudely biassing a transistor for instance, or understanding a logic gate.

However, you need a more accurate model for building an amplifier, or a high speed logic gate. This is why you have Ebers-Moll, Gummel-Poon, behavioural SPICE models, measured S_parameters, and a few more besides.

Each is as simple as possible, while being good enough for the job in hand. None captures the entire range of behaviour shown by a real life transistor.