Very broad low frequency dielectric data of a surface stabilized ferroelectric liquid crystal (SSFLC) sample in the frequency(ω) domain was analyzed by use of the Tikhonov regularization method to derive three distinctive modes of relaxation in time (τ) domain as corresponding to the X-mode, D-mode, and L-mode. The mode dependence on the probe field strength was studied in detail for two different cases of surface treatments: one with the indium tin oxide (ITO ) coating only and the other with polyimide dressing and rubbing alignment on top of the ITO coating. Origins of the three relaxation modes were discussed on the basis of the observed effects of the different surface treatments, probe field strength, and probing frequency. In addition, we have studied temperature dependent behaviors of two low frequency dielectricrelaxation modes; space charge accumulation and X-mode, observed in a sample of surface-stabilzed ferroelectric liquid crystal(SSFLC). From Cole-Cole plot studies a separate temperature dependence of dielectric strength △ε and relaxation frequency $\omega_r$ for the two low frequency modes was obtained and found to follow an Arrhenius relation in the respective asymptotic regions far from the phase transition temperatures.
From the Arrhenius plots we could obtain the activation energies of △U = 0.42 eV for space charge accumulation and 0.13 eV for X-mode deformation respectively. Temperature dependence of rotational viscosity in the SmC* phase was also found to be in conformity with the temperature dependence derived from the X-mode parameters in the effective Debye relaxation regime.