Leakage currents of polysilicon TFT's (thin film transistors) were reduced significantly by a two-step annealing technique which utilized low-temperature crystallization of amorphous films and a reduction of trap states by a high-temperature process. Two-step annealing formed polysilicon films with larger grains and lower electron spin densities. Trap state densities obtained from TFT on-currents correlated strongly with the leakage currents of the TFT's.