Channeling in direct dark matter detection II: channeling fraction in Si and Ge crystals

The channeling of the ion recoiling after a collision with a WIMP changes the ionization signal in direct detection experiments, producing a larger signal than otherwise expected. We give estimates of the fraction of channeled recoiling ions in Si and Ge crystals using analytic models produced since the 1960's and 70's to describe channeling and blocking effects. We used data obtained to avoid channeling in the implantation of dopants in Si crystals to test our models.