The thermal resistance of the first-level Cu dissipation substrate (R Cu) with different Cu thickness is investigated in this work. Using the "constant-forward-voltage" method, the thermal resistances of the first-level Cu dissipation substrates (R Cu) were measured against different Cu thickness. In the initial increase in the Cu thickness (up to 0.6 mm), R Cu decreases with the Cu thickness. As the Cu thickness over 0.6 mm, R Cu starts to slightly increase with the Cu thickness. The thermal resistance (R Cu) of the Cu substrate is composed of the z-direction thermal resistance (R z) and the two-dimensional horizontal spreading resistance (R s). The initial decrease in R Cu should attribute to the decrease in R s with the Cu thickness. After the initial increase in R Cu, the R Cu would increase and be dominated by the R z increase with the Cu thickness. Intriguingly, a minimum R Cu value occurs at the Cu thickness of about 0.6 mm. Also, in this paper, we discuss the possible inaccuracy factors of the "constant-forward-voltage" method.