A bonded structure is disclosed. The bonded structure can include a first element that has a first bonding surface. The bonded structure can further include a second element that has a second bonding surface. The first and second bonding surfaces are bonded to one another along a bonding interface. The bonded structure can also include an integrated device that is coupled to or formed with the first element or the second element. The bonded structure can further include a channel that is disposed along the bonding interface around the integrated device to define an effectively closed profile The bonded structure can also include a getter material that is disposed in the channel. The getter material is configured to reduce the diffusion of gas into an interior region of the bonded structure.