A capacitor structure can include a parallel connection of a plurality of trench capacitors. First nodes of the plurality of trench capacitors are electrically tied to provide a first node of the capacitor structure. Second nodes of the plurality of trench capacitors are electrically tied together through at least one programmable electrical connection at a second node of the capacitor structure. Each programmable electrical connection can include at least one of a programmable electrical fuse and a field effect transistor, and can disconnect a corresponding trench capacitor temporarily or permanently. The total capacitance of the capacitor structure can be tuned by programming, temporarily or permanently, the at least one programmable electrical connection.