Mechanically pre-biased shadow mask and method of formation

A shadow mask that includes:

• a substrate that defines a first plane, the substrate including a cavity;
• and
• a composite layer that is disposed on the substrate, the composite layer having a first region that is disposed over the cavity and defines a membrane having a first lateral dimension, wherein the first region includes an aperture pattern comprising at least one aperture that extends completely through the membrane, and wherein the composite layer comprises a plurality of layers that includes:
• (1) a first layer that comprises a first material, the first layer having a first thickness and a first residual stress, wherein the first layer is characterized by a fracture stress that is based on the first lateral dimension, and wherein the first residual stress is greater than the fracture stress;
• and
• (2) a second layer that comprises a second material, the second layer having a second thickness and a second residual stress, wherein the second residual stress at least partially compensates the first residual stress such that the composite layer is characterized by an effective residual stress that is lower than the fracture stress;
• wherein the first and second layers are in intimate physical contact such that neither of the first and second layers can move independently of the other;
• wherein the first residual stress and second residual stress collectively define a stress gradient in the composite layer that is at least partially directed along a first direction that is normal to the first plane.