Current-voltage characteristics of Si p-i-n negative resistance diodes doped with Au atoms were studied under different conditions of fabrication of the samples. When the p-i-n diode was fabricated by the use of Si wafer whose original resistivity is relatively low, or when the cross section of the diode is large, it was found that the threshold current becomes larger than the holding current in the ON-state. It was also found that a constant voltage region was observed in the ON-state. The cross section of a filamentary current path just after its formation was about 10-4_??_10-3cm2. It was seen that samples with cross sections smaller than this value shows no constant voltage region. Based on Lampert and Ridley theories, models displaying these features were proposed and qualitative agreement between the models and experimental results was obtained.