## 1 Introduction  
Copper foam is a new multifunctional material with plenty of connected or unconnected pores that are evenly distributed in the copper matrix. Owing to its excellent electrical conductivity, thermal conductivity, and large specific surface area, it is widely used in electrode materials [1], catalyst [2], and enhanced heat transfer [3; 4; 5; 6; 7; 8]. There are many methods for modifying copper foam, and some scholars have studied the modification of copper foam structure. Currently, the modification methods of copper foam mainly include anodizing [9], electrochemical corrosion [10], surface oxidation [11; 12], and chemical bath deposition [13] methods. [PERSON] et al. [9] have used anodization to successfully prepare CuO nanowires, nanosheets, and flower-like nanostructures that are supported on copper foam to obtain an additive-free and binder-free supercapacitor conductive electrode. CuO nanosheets have a nearly vertical orientation on the copper foam substrate, and they are composed of interconnected nanoparticles. [PERSON] et al. [10] have prepared a cactus-like CdS-Cu\({}_{9}\)S\({}_{5}\) structure on copper foam by electrochemical corrosion and hydrothermal methods; the obtained material is a highly efficient catalyst for the photochemical decomposition of water. Owing to its unique cactus-shaped structure, it can provide abundant surface catalytic active sites and many charge transfer channels, which enhances the photo-induced carrier transport and separation during the photoelectrochemical process. To improve the thermal performance, [PERSON] et al. [14] modified the deciduous structure and micro-flower structure on the surface of copper foam using surface oxidation and chemical modification methods to change its wettability, and they studied its pool boiling mechanism. Their results showed that the micro-nanostructure size of the superhydrophilic sample was smaller than that of the superhydrophobic sample, which produced higher contact area and allowed liquid to better penetrate the gap. To our knowledge, most sediments were mainly CuO and Cu(OH)\({}_{2}\). There is little research on the modification of the pure copper multi-level structure on the copper foam surface by electrodeposition, and there are no studies reporting the effect of experimental parameters on the deposited structure. [PERSON] et al. [15] used a simple constant current electrodeposition route, and grass-shaped Ni/Cu nanosheet arrays were successfully grown on copper foam. Their experiments showed that the as-deposited grass-like Ni/Cu nanosheet array had excellent electrocatalytic activity and was used for a hydrogen evolution reaction. At the same time, a modified copper foam catalyst also showed high durability. [PERSON] et al. [16] have deposited a three-dimensional porous copper film directly on Cu foam by an electrodeposition method using hydrogen bubbles as a dynamic template. The electrocatalytic activity of hydrazine electrooxidation was tested by linear scanning voltammetry, chronoamperometry, and electrochemical impedance spectroscopy. The authors suggest that the improvement of the electrocatalytic performance of hydrazine electrooxidation was mainly due to the high pore structure of the Cu/Cu foam electrode, which provided a larger surface area and allowed the electrolyte to more easily enter the surface of electrocataly. There have been many studies on the modification of smooth copper surfaces by electrodeposition. [PERSON] et al. [17] have studied the morphology of copper deposits obtained under overpotentials belonging to the plateau of the limiting diffusion current density and at higher overpotentials. Copper dendrites form at the overpotential that belongs to the limit diffusion current density plateau. The copper dendrite shape depends on the overpotential of electrodeposition. At higher overpotentials (800 mV and 1000 mV) and greater current density values, porous and very dispersed copper deposits were obtained. [PERSON] et al.