Stress values in layers of some thin-film materials and substrate parameters (auxiliary information for stress-target specification)

In Table 1, we collected substrate parameters (Young's modulus \(E\) and Poisson's ratio \(\nu\)) necessary for calculations using Stoney formula.

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Table 1.

Substrate Young's modulus \(E\) [GPa] Poisson's ratio \(\nu\) [a.u.] Data source
Fused Silica 74 0.17
CaF2 75.8 0.29
 ZnS 87.6 0.3
BaF2 53.07 0.31

Ge 102.7 0.2
KBr 26.8 0.3
Sapphire 400 0.29 
Silicon 131 0.22
YAG 280 0.24
ZnSe 70.3 0.3

In Table 2, we collected reference data for some typical thin-film materials*. Using these values you can calculate target parameters: open stress target calculator.

Table 2.

Layer material Deposition method Stress, MPa Data source
SiO2     Radio frequency magnetron sputtering -220**

G. N. Strauss, Mechanical Stress in Optical Coatings, In: Kaiser N., Pulker H.K. (eds) Optical Interference Coatings. Springer Series in Optical Sciences, vol 88. Springer, Berlin, Heidelberg

Reactive advanced plasma source ion plating -300
Plasma enhanced chemical vapor deposition -75
Ion-beam assisted deposition -1255
E-beam evaporation -160
TiO2     Reactive evaporation  -260
 Mid-frequency magnetron sputtering  -700
 Reactive ion plating  -275
 Ion beam assisted deposition  -540
 Al2O3    Radio frequency magnetron sputtering  -250
 Reactive evaporation +100
 Reactive ion plating  -210
Ta2O5  Radio frequency magnetron sputtering -275
Reactive ion plating -200
Nb2O5 Direct current magnetron sputtering -175
Ge E-beam evaporation (120°C)    -50

T. Amotchkina et al, Characterization of e-beam evaporated Ge, YbF3, ZnS, and LaF3 thin films for laser-oriented coatings, Applied Optics Vol. 59, pp. A40-A47 (2020)

ZnS -400
YbF3 140
LaF3 380

*) In the case, when in the literature source an interval of stress values was given, an average value is presented in Table 1.

**) Compressive stress - negative sign, tensile stress - positive sign.

Important. Please note, that stresses in thin-films are strongly dependent on deposition process and process parameters (see, for example, [1], [2]). It is recommended to estimate stress values of your processes.