Mechanics and Tribology of MEMS Materials - prod.sandia.gov ...

2.2 Critical Flaw Size Evaluation
To evaluate the critical flaw size distribution, data from 127 tensile samples were pooled.
The mean strength was 2.95 GPa with a standard deviation of 0.41 GPa. These samples covered
a range of reported strengths of 1.76 to 3.81 GPa. A histogram of the strength values is shown in
the left graph of Figure 2.3.
The critical flaw size was found by assuming a value for fracture toughness of 1.2
MPa.m 1/2 [2.1], a Fq of 1.1 (this factor ranges from 1.04 to 1.14 for small cracks) and a
relationship between the mean stress, S, the flaw size, a, and the fracture toughness, K, of:
K = (2 . Fθ . S/π) . (π . a) 1/2
The flaw sizes calculated are shown in the right graph of Figure 2.3. The mean flaw size
is 115 nm with a standard deviation of 38 nm. As can be seen from the graph, the flaw sizes do
not follow a normal distribution, but rather indicate the median size falls in the range of 75 to 85
nm, with no flaws smaller than 65 nm associated with the measured fracture strength. The tail of
the distribution has five samples (out of 127) that had calculated flaw sizes larger than 185 nm
(189, 209, 214, 246, 303 nm).
For comparison, the strength of polysilicon produced in the MUMPS process, and released
under various conditions by the end-user, had a mean reported strength of 1.55 GPa with a range
of strength from 1.3 to 1.8 GPa [2.2]. Thus, the calculated mean flaw size would be 389 nm,
with a range of 289 to 553 nm, representing a significantly larger mean flaw than in Sandia’s
polycrystalline silicon.
Count
16
14
12
10
8
6
4
2
0
1.6 2 2.4 2.8 3.2 3.6 4
Fracture Strength (GPa)
27
Count
35
30
25
20
15
10
5
0
25 75 125 175 225 275 325
Flaw size (nm)
Fig. 2.3. Observed failure strength histogram (left) and calculated flaw size histogram (right).