  This review discusses detector physics and Monte Carlo techniques for
cryogenic, radiation detectors that utilize combined phonon and ionization
readout. A general review of cryogenic phonon and charge transport is provided
along with specific details of the Cryogenic Dark Matter Search detector
instrumentation. In particular this review covers quasidiffusive phonon
transport, which includes phonon focusing, anharmonic decay and isotope
scattering. The interaction of phonons in the detector surface is discussed
along with the downconversion of phonons in superconducting films. The charge
transport physics include a mass tensor which results from the crystal band
structure and is modeled with a Herring Vogt transformation. Charge scattering
processes involve the creation of Neganov-Luke phonons. Transition-edge-sensor
(TES) simulations include a full electric circuit description and all thermal
processes including Joule heating, cooling to the substrate and thermal
diffusion within the TES, the latter of which is necessary to model
normal-superconducting phase separation. Relevant numerical constants are
provided for these physical processes in germanium, silicon, aluminum and
tungsten. Random number sampling methods including inverse cumulative
distribution function (CDF) and rejection techniques are reviewed. To improve
the efficiency of charge transport modeling, an additional second order inverse
CDF method is developed here along with an efficient barycentric coordinate
sampling method of electric fields. Results are provided in a manner that is
convenient for use in Monte Carlo and references are provided for validation of
these models.
