A method of making an assembly can include juxtaposing a top surface of a first electrically conductive element at a first surface of a first substrate with a top surface of a second electrically conductive element at a major surface of a second substrate. One of: the top surface of the first conductive element can be recessed below the first surface, or the top surface of the second conductive element can be recessed below the major surface. Electrically conductive nanoparticles can be disposed between the top surfaces of the first and second conductive elements. The conductive nanoparticles can have long dimensions smaller than 100 nanometers. The method can also include elevating a temperature at least at interfaces of the juxtaposed first and second conductive elements to a joining temperature at which the conductive nanoparticles can cause metallurgical joints to form between the juxtaposed first and second conductive elements.

Disclosed is a bonded structure including a first microelectronic structure with a first bonding surface and a second microelectronic structure with a second bonding surface directly bonded to the first bonding surface. The first microelectronic structure includes at least one cavity a through the first bonding surface. The second microelectronic structure includes at least one protrusion extending above the second bonding surface. The at least one protrusion of the second microelectronic structure extends within the at least one cavity of the first microelectronic structure without reaching a bottom of the at least one cavity.