3.6.4 Materials selection for cantilevers
Table 1 shows some of the physical and mechanical properties of materials that can be deposited and etched in thin-film form. One of the consequences of manufacturing these materials in thin-film form is that properties that in the bulk material can be determined to within a few per cent are much less easy to measure, and appear in some cases to be very different from the bulk material. The variation in measured values can be attributed in part to small variations in the processes used in creating and depositing the materials, in part to the sheer difficulty of conducting tests on samples of such small dimensions, and in part to the statistical variation in the measured values of those properties in which the ‘weakest link’ in the material sample has a dominant influence on the value obtained. For instance, the ultimate tensile strength of a sample of material depends on the length and nature of the largest defect. In a sample that is less than a millimetre in all its dimensions, defects are small in number and the statistics of large populations do not apply. This results in there being a large spread in measured values from sample to sample.
The lack of accurately determined material properties is a difficult challenge in MEMS; it makes the whole exercise much more risky than (to generalise shamelessly) conventional, macroscale engineering. The issue of process control lies right at the heart of micro and nano technologies – not being able to measure material properties accurately is one thing, but failing to produce the same material from run to run or wafer to wafer has the potential to make matters considerably worse. Being on the wrong curve on Figure 4 may result in a sensor with characteristics quite different from what was expected or, in the worst case, no sensor at all, as the component made from the rogue material fails under its own tension after being released.
However, we have to start somewhere and Table 1 shows some values that can be used for initial design calculations.
Table 1 Physical properties of thin-film materials for AFM cantilevers
|Young's modulus / GPa||Poisson's ratio||Density / kg m−3||Electrical resistivity / Ω m||Thermal conductivity / Wm−1 K−1||Temperature coefficient of expansion / µm m−1 K−1|
|Single-crystal silicon||125–180||0.23||2330||1 × 10−6−100 (dopant dependent)||157||2.6|
|Polycrystalline silicon||160||0.22||2330||always higher than single crystal Si for a given dopant concentration||34||2–2.8|
|Thermal silicon dioxide||70||0.17||2240||1 × 1013||1.4||0.35|
|3C-silicon carbide||400||0.25||3300||1–1 × 104 (dopant dependent)||360–490||4|
|LPCVD silicon nitride||250–290||0.23–0.27||3300||1 × 1014||15–30||1.6|
|PECVD silicon nitride||160||0.25||2500||1 × 1010||16–33||1.5|
|DLC (diamond-like carbon)||800–1000||0.22||1800–2800||>1 × 1011||400–1000||1|
|Aluminium||70||0.33||2710||2.7 × 10−8||156||24|
|Platinum||147||0.39||21 500||11 × 10−8||69||9|
|Gold||70 (bulk); 35–44 (e-plated)||0.42||19 300||5–10 × 10−8||298||19–26|
|Nickel||180||0.31||8900||1.4 × 10−7||92||13|
It seems that there are two conflicting requirements for the cantilevers: on the one hand, a high resonant frequency is desirable, implying a high value for E; on the other, a low stiffness is wanted, for which a low value of E would make matters easier. For the density of the material, the decision is more straightforward: a low-density material is needed for a high resonant frequency and, since density does not play a direct part in the stiffness of the cantilever, there is no conflict here.
One of the materials listed must have a combination of E and ρ that is better suited to the job than any of the others, but what is the surest way of knowing which this is? The answer lies in the merit index, a number that expresses the suitability of a material for the particular purpose to which it is to be put. The merit index is obtained by a suitable mathematical combination of all the relevant material properties.