*4.1. Through-Thickness Stress Gradients in Sputtered Al1*−*xScxN films*

*4.1. Through-Thickness Stress Gradients in Sputtered Al1−xScxN films*  During film growth, stresses due to lattice mismatch, intrinsic strains and microstructure produces tensile and compressive stresses. The average stress of a sputtered Al1−xScxN film is strongly correlated to the value of the chamber pressure during deposition [3]. At 25 sccm process gas flow, the sputtering chamber will be at a near constant pressure of 1.09 × 10−3 mbar. At 25 sccm pure N2 flow, when Al0.68Sc0.32N is deposited to a final thickness of 500 nm, the average stress within the film will be approximately 137 MPa. The average film stress vs. thickness for Al0.68Sc0.32N films deposited under 25 sccm pure N2 flow using the process conditions in Table 1 is provided in Figure 2a. The average film stress is a strong function of the final film thickness due to the through-thickness stress gradient of the films. The through-thickness stress gradient can be modeled using Equation (2) in conjunction with the data in in Figure 2a where α is 41.12, β is 6.6522, and γ is 0.2194. α is determined using a linear fit of the measured average stress versus flow data shown in Figure 2b. In Figure 2a, the stress starts highly compressive and becomes more tensile as the thickness of the film increases. At lower film thicknesses, the microstructure of the film continuously changes and the grain size increases with increasing During film growth, stresses due to lattice mismatch, intrinsic strains and microstructure produces tensile and compressive stresses. The average stress of a sputtered Al1−xScxN film is strongly correlated to the value of the chamber pressure during deposition [3]. At 25 sccm process gas flow, the sputtering chamber will be at a near constant pressure of 1.09 <sup>×</sup> <sup>10</sup>−<sup>3</sup> mbar. At 25 sccm pure N<sup>2</sup> flow, when Al0.68Sc0.32N is deposited to a final thickness of 500 nm, the average stress within the film will be approximately 137 MPa. The average film stress vs. thickness for Al0.68Sc0.32N films deposited under 25 sccm pure N<sup>2</sup> flow using the process conditions in Table 1 is provided in Figure 2a. The average film stress is a strong function of the final film thickness due to the through-thickness stress gradient of the films. The through-thickness stress gradient can be modeled using Equation (2) in conjunction with the data in in Figure 2a where α is 41.12, β is 6.6522, and γ is 0.2194. α is determined using a linear fit of the measured average stress versus flow data shown in Figure 2b. In Figure 2a, the stress starts highly compressive and becomes more tensile as the thickness of the film increases. At lower film thicknesses, the microstructure of the film continuously changes and the grain size increases with increasing film thickness. As the thickness increases, the columnar growth of the film is more stable causing the throughthickness stress gradient to reduce and the average film stress to asymptote towards a constant value with further increases in thickness. These trends are clearly observable in Figure 2a.

film thickness. As the thickness increases, the columnar growth of the film is more stable

25 sccm.

causing the through-thickness stress gradient to reduce and the average film stress to as-

**Figure 2.** Average stress plots of PVD deposited Al0.68Sc0.32N films with (**a**) Average stress versus thickness plot at a constant 25 sccm N2 flow and (**b**) Average stress versus flow for 500 nm Al0.68Sc0.32N with pure N2 flow from 20-30 sccm [3]. **Figure 2.** Average stress plots of PVD deposited Al0.68Sc0.32N films with (**a**) Average stress versus thickness plot at a constant 25 sccm N<sup>2</sup> flow and (**b**) Average stress versus flow for 500 nm Al0.68Sc0.32N with pure N<sup>2</sup> flow from 20–30 sccm [3].
