A vacuum carrier can be employed to provide a partial vacuum on a back side surface of a substrate thereby holding the substrate flat against a rigid surface of the carrier throughout the duration of a bonding process. The magnitude of vacuum can be optimized to limit the warping of the substrate during and after bonding with another substrate, and to limit the mechanical stress induced in the solder balls during cooling. The vacuum carrier can include a base plate, a seal plate with at least one opening configured to accommodate at least one substrate, and vacuum seal elements configured to create a vacuum environment that pushes the substrate against the base plate when the vacuum carrier is under vacuum. The configuration of the vacuum carrier is chosen to avoid distortion of the substrate due to the vacuum seal elements, while allowing adjustment of the magnitude of the partial vacuum.