Local Li-ion transport in amorphous silicon is studied on the nanometer scale using time domain electrochemical strain microscopy (ESM). A strong variability of ionic transport controlled by the anode surface morphology is observed. The observed relaxing and nonrelaxing response components are discussed in terms of local and global ionic transport mechanisms, thus establishing the signal formation mechanisms in ESM. This behavior is further correlated with local conductivity measurements. The implications of these studies for Si-anode batteries are discussed. The universal presence of concentration-strain coupling suggests that ESM and associated time and voltage spectroscopies can be applied to a broad range of electrochemical systems ranging from batteries to fuel cells.