Physical properties of filaments in Cu/HfO2/Pt conducting-bridge memory (CB-RAM) were investigated basing on direct observation by conducting atomic force microscopy (C-AFM) and energy dispersive X-ray spectroscopy (EDS), R-T characteristics until liquid nitrogen temperature, and I-V characteristics both in air and in vacuum. As a result, physical picture of filaments in Cu/HfO2/Pt structures was revealed. Filaments consist of Cu containing large residual resistance and the cross-sectional area of the filament, S
fila, was roughly proportional to set voltage, V
set, even when current compliance was kept constant. Interestingly, resistivities of filaments are same among all the filaments in different samples and are invariant even after repetitive switching that changes resistance of the filaments. Cu/HfO2/Pt obeyed the universal relation that reset current, I
reset, is proportional to the inverse of resistance in a low resistance state, 1/R
LRS, which is known to be applicable to oxygen-migration-based resistive switching memories such as Pt/NiO/Pt. Considering the invariance of resistivity of the filament, this suggests the fact that I
reset is decided dominantly by S
fila. In addition, it was suggested that moisture is necessary for dissolution and migration of Cu to form filaments.