Resistance switching devices are of special importance because of their application in resistive memories (RRAM) which are promising candidates for replacing current nonvolatile memories and realize storage class memories. These devices exhibit usually memristive properties with many discrete resistance levels and implement artificial synapses. The last years, researchers have demonstrated memristive chips as accelerators in computing, following new in-memory and neuromorphic computational approaches. Many different metal oxides have been used as resistance switching materials in MIM or MIS structures. Understanding of the mechanism and the dynamics of resistance switching is very critical for the modeling and use of memristors in different applications. Here, we demonstrate the bipolar resistance switching of silicon nitride thin films using heavily doped Si and Cu as bottom and top-electrodes, respectively. Analysis of the current-voltage characteristics reveal that under space-charge limited conditions and appropriate current compliance setting, multi-level resistance operation can be achieved. Furthermore, a flexible tuning protocol for multi-level resistance switching was developed applying appropriate SET/RESET pulse sequences. Retention and random telegraph noise measurements performed at different resistance levels. The present results reveal the attractive properties of the examined devices.