A template having tapered openings can be employed to enable injection of underfill material through gaps having a width less than a lateral dimension of an injector needle for the underfill material. Each tapered opening has a first lateral dimension on an upper side and a second lateral dimension on a lower side. Compliant material portions can be employed to accommodate variations in distance between the template and stacked semiconductor chips and/or an injector head. Optionally, another head can be employed to apply compressed gas to push out the underfill material after the underfill material is applied to the gaps. Multiple injector heads can be employed to simultaneously inject the underfill material at different sites. An adhesive layer can be substituted for the at least one lower compliant material portion.