Musings on Cantilever Stiffness in Electron/Atomic Force Microscopes

The equation for stiffness is:
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Where a is the width, b is the thickness and l is the length. This has an effect on mass which in turn will affect resonant frequency.

However, these cancel each other’s effect on stiffness if increases simultaneously. So something else besides stiffness must be responsible for the benefits of ATM work, which is indeed the relationship between mass and resonant frequency.

However a high stiffness cantilever in Non-Contact mode ensures the attractive force between the surface and the tip do not cause the cantilever to “bend” and succumb to the attractive force.

Short and thin cantilevers made from Silicon on Oxide wafers have a low force constant which is suitable for probing, especially soft samples when working in Non-Contact/tapping mode, since excessive force is not applied to the surface being scanned.

Angular velocity can be used to obtain the Frequency:

fo0/2π

The angular velocity equation for a cantilever is:
clip_image004

From the above equation we can see that smaller values for length and thickness of the cantilever structure then the higher the frequency will be.

The intrinsic high resonance frequency is most useful in Non-contact/tapping mode, since the tip is not in contact, and the oscillation induced on the tip by the piezoelectric actuator allows the tip to “linger” a little longer closer to the surface. Lower frequency modes means the tip will spend less time at the closest point to the surface in the oscillation cycle. This ensures that effects of vibrations from the surroundings are minimised and a high image acquisition rate (due to increasing the time the tip is closest to the surface). Thermal noise is also reduced.

Fabrication of short and thin silicon cantilevers for AFM with SOI wafers

clip_image002

Sensors and Actuators A: Physical, (2006)

Step 1: Forming the handles

Stage (a) Preparation

Silicon wafers with a <1 00 > orientation (Horizontal Alignment) are used and the top most layer of Silicon will be used to form the tip.

Oxide layer is deposited between two layers of silicone and also at the top and bottom of the wafer by thermal oxidation at 1000 ⁰C.

The thermal oxide layers act as a mask at the handle side and at the top side where the tip will be defined, it also protects the silicon layer that will become the cantilever when the trenches/cleaving lines (T, C) are formed.

Stage (b) Etch Trenches

The trench lines are formed using convention lithographic techniques, by forming a photoresist on the bottom of the wafer.

Chemical hydrofluoric wet etching is used to open the sections of the oxide layer on the exposed regions of the photoresist, this etch technique cannot be used on the silicon itself as the rate of etching is too slow.

Once the oxide layers are removed from the trench pattern, then Tetra-methyl ammonium hydroxide (TMAH) wet etching is used on the Si handle layer. TMAH is better than Potassium hydroxide as KOH will destroy the oxide layer which acts as a mask here.

The etching depth is controlled by duration of the wet etch, the trenches are etched in around 12 hours and the cleaving (C) in a shorter time period to have a reduced depth as compared to the T.

Note that TMAH does not etch the oxide layer and hence this layer is left in the trench (T).

Step 2: Defining the cantilevers

Stage (c)

Conventional lithographic techniques are used to pattern the trench area of the device layer side, so that accurate alignment of the cantilever with the respect to the trench (‘T) can be achieved.

· KOH wet etching is used to etch the cantilever in a 60⁰C water bath (E)

The depth of etching is controlled by the duration and reactants used.

Stage (d)

· The cantilever mesa (M) and (E) are then etched together, a suitable photoresist and photomask is used to ensure some of the oxide layer is not etched using isotropic etching.

This stage ensures the cantilever is strong enough to withhold tensions and stress caused by spinning photoresist and other subsequent steps, thus ensuring the alignment is accurate throughout the process.

Step 3: Forming the tips and cantilevers together

Stage (e)

· KOH wet etching is used.

· The etching rate will be uniform, therefore when the (E) part of the device is totally etched off, the etch process is topped immediately. This provides the necessary sign to stop etching and will ensure a thin cantilever is left as the (M) part is thicker than the (E) part.

· Thermal oxidation can be used to sharpen the tip, reduce thickness and balance the stress in the cantilever. The above process is easily to control due to several hours needed for etching and oxidising! Therefore quantitative monitoring processes can be established during production.

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