  Context. The YORP effect is the thermal torque generated by radiation from
the surface of an asteroid. The effect is sensitive to surface topology,
including small-scale roughness, boulders, and craters.
  Aims: The aim of this paper is to develop a computationally efficient
semi-analytical model for the crater-induced YORP (CYORP) effect that can be
used to investigate the functional dependence of this effect.
  Methods. This study obtains the temperature field in a crater over a
rotational period in the form of a Fourier series, accounting for the effects
of self-sheltering, self-radiation, and self-scattering.
  Results. We obtain the temperature field of a crater, accounting for the
thermal inertia, crater shape, and crater location. We then find that the CYORP
effect is negligible when the depth-to-diameter ratio is smaller than 0.05. In
this case, it is reasonable to assume a convex shape for YORP calculations.
Varying the thermal conductivity yields a consistent value of approximately
0.01 for the spin component of the CYORP coefficient, while the obliquity
component is inversely related to thermal inertia, declining from 0.004 in
basalt to 0.001 in metal. For a z-axis symmetric shape, the CYORP spin
component vanishes, while the obliquity component persists. Our model confirms
that the total YORP torque is damped by a few tens of percent by uniformly
distributed small-scale surface roughness. Furthermore, for the first time, we
calculate the change in the YORP torque at each impact on the surface of an
asteroid explicitly and compute the resulting stochastic spin evolution more
precisely.
  Conclusions. The semi-analytical method that we developed, which benefits
from fast computation, offers new perspectives for future investigations of the
YORP modeling of real asteroids and for the complete rotational and orbital
evolution of asteroids accounting for collisions.
