Supporting information
A non-destructive method to measure the mechanical properties of
ultrathin film prepared by atomic layer deposition
Qinglin Zhang1,2, Xingcheng Xiao1, a), Yang-Tse Cheng2 and Mark W. Verbrugge1
1General
2Department
Motors Global Research and Development Center, Warren, Michigan, 48090, USA
of Chemical and Materials Engineering, University of Kentucky, Lexington, Kentucky, 40506-0046, USA
Table S1. Young’s modulus obtained from [110] direction of N-type (100) silicon wafer by LAW measurements
C11
Young’s modulus (GPa)
165.57 ± 0.08
C12
C44
63.52 ± 0.13
79.52 ± 0.02
The depth of SAW is proportional to the wave length: the higher frequency is, the smaller
penetrated depth of the SAW. The phase velocity (SAW velocity, 𝑐) depends on frequency (𝑓), and the
relation between 𝑐 and 𝑓 is termed dispersion. The phase velocity is defined as:
𝑐 = 𝑐(𝐸, 𝐸 ′ , 𝑣, 𝑣 ′ , 𝜌, 𝜌′ , 𝑑, 𝑓𝑘 )
𝐸 is the modulus of substrate, 𝐸 ′ is the modulus of film; 𝑣 is the Poisson’s ratio of substrate, 𝑣 ′ is the
Poisson's ratio of film; 𝜌 is the density of substrate, 𝜌′ is the density of film; 𝑑 is the film thickness, and
𝑓𝑘 is the frequency along k direction. Si wafers were used as substrate. Film density and thickness are
determined independently with x-ray reflectivity (XRR) and electron probe microanalysis (EPMA)
Alumina film’s Poisson’s ratio was assumed to be 0.21. (Young’s modulus is not sensitive with Poisson’s
ratio by this method.) The fitting process is completed with commercial fitting program (LAW Analyzer),
based on the principle of minimizing the least-square errors:
∑[𝑐(𝑓𝑘 ) − 𝑐(𝐸, 𝐸 ′ , 𝑣, 𝑣 ′ , 𝜌, 𝜌′ , 𝑑, 𝑓𝑘 )]2 → 𝑚𝑖𝑛
𝑘
𝑐(𝑓𝑘 ) is the measured curve and 𝑐(𝐸, 𝐸 ′ , 𝑣, 𝑣 ′ , 𝜌, 𝜌′ , 𝑑, 𝑓𝑘 ) is the theory curve. 1
Table S2. Area density measurements of the alumina coating as determined by EPMA quantitative measurements
and GMRFILM thin film modeling program using scanning mode (30 μm area).
Position
1
2
3
4
5
6
7
8
9
10
Average
Std. dev.
1
Area density
(μg/cm2)
11.9
11.7
11.7
11.6
12.0
12.1
11.6
11.7
11.7
11.6
11.8
0.2
D Schneider, Th Witke, Th Schwarz, B Schöneich, and B Schultrich, Surface and Coatings
Technology 126 (2), 136 (2000);
Dieter Schneider and Thomas Schwarz, Surface and
Coatings Technology 91 (1), 136 (1997);
Dieter Schneider, Thomas Schwarz, Hans-Joachim
Scheibe, and Michael Panzner, Thin Solid Films 295 (1), 107 (1997);
HJ Bauer and Warren
P Mason, Physical Acoustics: Principles and Methods. (Academic Press, 1965).