The basic physics is very simple.
One needs to know a few basic things:
Minority carrier injection - if a p-n junction is biased in the forward direction (i.e. p-type semiconductor is positive with respect to n-type), electrons overcome the potential barrier (in the depletion region of p-n junction), and thus they are injected into p-type semiconductor. In p-type material, electrons are minority carriers, have a long life time (allowing them to travel hundreds and thousands microns, laterally). Minority carriers (electrons) either recombine, or collected (extracted) by n-wells or n+ regions (which act as potential well for electrons). Minority carriers recombine quickly (short lifetime) in heavily doped regions. Their transport is diffusion (also affected by built-in electric field from non-uniform doping), same as in bipolar transistors (in the base).
The same things happen with holes in n-type doped semiconductor (they recombine in n+ regions, and are collected by p-wells and p+ regions).
Now, referring to your drawings, if, for example, one of the n+ regions in NMOSFET is biased negatively with respect to the substrate, it will inject electrons into the substrate.
The electrons will diffuse out, until they get sucked out by n+ well.
They will lower the local potential of the n-well at the places where they are entering the n-well. This will drive them (through drift mechanism) towards n+ regions, until they are extracted from the silicon into interconnects.
Also, positive local bias of the n-well will (may) change the potential of the PMOS body - so that will act as a forward bias for p+-n-well junctions in PMOSFET.
The holes will be injected into n-well, diffuse through it, until they are extracted (or recombined) into p-substrate - then they will drift into p+ regions.
The positive biasing of the p-substrate near n+ regions will enhance electron injection - so that the positive feedback can happen, and the current may be increasing indefinitely until silicon or metal melting destroys the chip.
The guardrings help intercept the diffusion of the minority carriers - and either block their diffusion by extracting them (electrons - into n+ regions, holes - into p+ regions), or by increasing the potential barrier and decreasing their lifetime, or through some other mechanism (for example, active guard rings - that establish an electric field opposing the flow of minority carriers). Also some other techniques may be used to block the minority carrier injection or reducing the lifetime - like deep trenches, heavily doped substrates, SOI substrates, etc.
There are some good books describing latchup in detail, for example:
S. Voldman, "Latchup"
M.D.Ker at al, "Transient induced latchup..."
R.Troutman, ""CMOS latchup..."
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Max
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