Internal Stress Prediction and Measurement of Mid-Infrared Multilayer Thin Films

We present an experimental method for evaluating interfacial force per width and predicting internal stress in mid-infrared band-pass filters (MIR-BPF). The interfacial force per width between the two kinds of thin-film materials was obtained by experimental measurement values, and the residual stress of the multilayer thin films was predicted by the modified Ennos formula. A dual electron beam evaporation system combined with ion-assisted deposition was used to fabricate mid-infrared band-pass filters. The interfacial forces per width for Ge/SiO₂ and SiO₂/Ge were 124.9 N/m and 127.6 N/m, respectively. The difference between the measured stress and predicted stress in the 23-layer MIR-BPF was below 0.059 GPa. The residual stresses of the four-layer film, as well as the 20-layer and 23-layer mid-infrared band-pass filter, were predicted by adding the interface stress to the modified Ennos formula. In the four-layer film, the difference between the predicted value and the measured stress of the HL (high-low refractive index) and LH (low-high refractive index) stacks were -0.384 GPa for (HL)² and -0.436 GPa for (LH)², respectively. The predicted stress and the measured stress of the 20-layer mid-infrared filter were -0.316 GPa and -0.250 GPa. The predicted stress and the measured stress of the 23-layer mid-infrared filter were -0.257 GPa and -0.198 GPa, respectively.