Daily and annual modulation rate of low mass dark matter in silicon detectors

Low threshold detectors with single-electron excitation sensitivity to nuclear recoil events in solid-state detectors are also sensitive to the crystalline structure of the target and, therefore, to the recoil direction via the anisotropic energy threshold for defect creation in the detector material. We investigate this effect and the resulting daily and annual modulation of the observable event rate for dark matter mass range from 0.2 to 5 GeV/c$^{2}$ in a silicon detector. We show that the directional dependence of the threshold energy and the motion of the laboratory result in modulation of the event rate which can be utilized to enhance the sensitivity of the experiment. We demonstrate that the spin-independent interaction rate in silicon is significant for both high and low dark matter masses. For low-mass dark matter, we show that the average interaction rate in silicon is larger than germanium, making silicon an important target for identifying dark matter from backgrounds. We find 8 and 12 hours periodicity in the time series of event rates for silicon detector due to the 45-degree symmetry in the silicon crystal structure.