Temperature dependencies of silicon whiskers' resistance doped with boron to concentration of 5 x 10(18) cm(-3) and modifed nickel where measured in temperature range 4.2 - 70K by impedance spectroscopy method. Received results are shown on frequency dependence of crystal conductance at cryogenic temperature in frequency range up to 250 kHz. Is investigated the features of frequency dependence of active resistance Si whiskers which allowed to get important information about transfer mechanism, which is realized in investigated samples at low temperature. Significant influence of nickel doping on transport properties of the silicon crystals is shown, which manifests in polarization processes at low temperatures. Conductivity of microcrystal on the measurement with a alternating current, are explained by the mechanism of carrying charge carriers on the twice-occupied states. The Mott law of hopping conductivity is realized in silicon microcrystals doped with boron and nickel. The polarization relaxation time of charge carriers was calculated t = 7 x 10(-4) s