The theoretical framework of the neutrino electron excitation at low energies including the screening effect in semiconductor detectors is developed for the first time, both in the Standard Model of particle physics and in the presence of the neutrino magnetic moment. We apply the framework of the non-relativistic effective theory on the neutrino electron scattering and explore the contribution of the screening effect of semiconductors to the neutrino electron excitation based on the linear response theory. We calculate the corresponding numerical results with the popular silicon and germanium targets and show that excitation rates from the neutrino magnetic moment are dramatically enhanced by the screening effect and the sensitivity can be significantly improved to the level of 10−13μB, much better than the current best limits from the laboratory and astrophysical probes.