How are neutrons produced from cosmic ray particles? What are the details of how neutrons are produced as a result of cosmic ray particles hitting our planet's atmosphere?
For instance, what is the pathway that creates the highest number of neutrons from cosmic ray particles?
The article "Single event upset" states:

An SEU happens due to cosmic particles which collide with atoms in the atmosphere, creating cascades or showers of neutrons and protons. At deep sub-micrometre geometries, this affects semiconductor devices at sea level.

But it does not describe the mechanism.
The Wikipedia article on the neutron states something similar:

Cosmic radiation interacting with the Earth's atmosphere continuously generates neutrons that can be detected at the surface.

What are the processes, in detail?
 A: OK, here is something concrete and quantitative, "Guidelines for predicting single-event upsets in neutron environments":

Neutrons in the atmosphere result from cosmic-ray spallation interactions with nitrogen and oxygen nuclei. A typical reaction is a 1 GeV proton fragmenting a nitrogen necleus into lighter charged particles and simultaneoously emitting a couple of neutrons. 

Cosmic ray spallation.

From "Cosmic ray induced ionization in the atmosphere: Full modeling and practical applications":

... full numerical model, which computes the cosmic ray
  induced ionization in the entire atmosphere, from the ground
  level up to the stratosphere, all over the Globe. The model
  computations reproduce actual measurements of the
  atmospheric ionization in the full range of parameters, from
  equatorial to polar regions and from the solar minimum to
  solar maximum. A detailed numerical recipe is given in
  section 2.5 together with the precalculated tabulated
  ionization yield function (Tables 1 and 2). Using this
  method, one can easily compute the CRII for any desired
  location and conditions, instead of using, e.g., a neutron
  monitor count rate as a proxy.

It does not describe it, but the CORSIKA (Cosmic Ray Simulations for Kascade) simulation tool is used.

Google-fu: quantitative neutrons cosmic rays atmosphere
A: Between what I've learned about cosmic rays and what I can find online (example: http://www.fisica.unlp.edu.ar/~veiga/experiments.html), it seems that the primary source of neutrons in cosmic ray showers is the disintegration of the atomic nuclei that are struck by the cosmic ray or its decay products.
As you may know, cosmic rays enter the atmosphere with enormous amounts of energy, so when one strikes a nucleus, it's going to disrupt the nuclear structure. The net effect could be anything from just kicking out a single particle to shattering the entire nucleus into several pieces, as in nuclear fission - it depends on the energy of the cosmic ray and the type of atom/molecule it hits. If the cosmic ray is especially high-energy, the products of the reaction will also have high energies, and they can interact with other nuclei, repeating the same process. A wide variety of particles are produced in these interactions, including neutrons, pions, kaons, and other hadrons.
A: Spallation of air atoms' nuclei is the easiest way - there are neutrons kicked out of the nucleus directly or emmited by radioactive elements, which were activated by cosmic rays.
Also neutrons can be produced upon hadronization of quark-gluon-plasma or from electron capturing in air nuclei.
