Lab Manual: Atomic Force Microscopy (AFM)

AFM Apparatus

Objectives and learning goals

• Learn function of the 20.309 AFM and the relationships between its components.
• Understand how to extract quantitative information from this tool.
• Use the AFM to estimate the value of a fundamental physical constant.
• Possibly to take images, probe sample stiffness, and/or perform protein pulling.
• Analyze sources of uncertainty and noise in the system that limit the accuracy of measurements.

Roadmap scenarios and milestones

The AFM can be used both for A basic "mini-lab" homework problem, and also for more involved projects. This section will outline the mini-lab and provide one possible outline for extended, for instance as a final project. You are encouraged to devise much more creative uses for the AFM in final projects and beyond.

AFM mini-lab

1. Work with a TA or Instructor.
2. Learn the signal paths and connections of the system.
3. Practice aligning the AFM optics.
4. Learn how to calibrate the AFM to extract useful physical data.
5. Measure the vibrational noise floor in the AFM system.
6. Use the AFM to record the vibrational noise spectrum of a cantilever probe (Experiment ##)

Extended AFM work

1. Image several different samples with the AFM and measure physical dimensions of imaged features.
2. Use the AFM to measure the elastic modulus and surface adhesion force of several different samples.
3. Use the AFM and a gold-coated tip to pull and unravel proteins to determine their structures.

The 20.309 AFM System

This section describes the various components of the AFM you will use in the lab, and particularly how they differ in operation from a commercial AFM. In lecture we will discuss the operational principles of a commercial AFM. You may also ¯nd it helpful to review some of the References in Section 8 at the end of this module.

Hardware

A photo of our AFM setup is provided in Figure 1 for you to refer to as you learn about the instrument. Start by physically examining the setup and identifying all the parts described below.

Motion control system

To be useful for imaging, an AFM needs to scan its probe over the sample surface. Our microscopes are designed with a fixed probe and a movable sample (also true of some commercial AFM systems). Whenever we talk about moving the tip relative to the sample, in 20.309 we will always only move the sample. The sample is actuated for scanning and force spectroscopy measurements by a simple piezo disk, shown in Figure 2. The piezo disk is controlled from the matlab scanning software, which is described in Section 3.3.

For vertical motion along the z-axis, there are three regimes of motion:

Manual (coarse): Turning the knob on the red picomotor with your hand (clockwise moves the stage up).

Piezo-disk (fine): Actuating the piezo disk over a few hundred nanometers using the matlab software. For x- and y-axis positioning (in the sample plane), coarse movements are accomplished with the stage micrometers, and fine (several nm) movements are also attained using the piezo disk.

Optical system

Our microscopes use a somewhat different optical readout from a standard AFM to sense cantilever deflection. Rather than detecting the position of a laser beam that reflects off the back surface of the cantilever, we measure the intensity of a diffracted beam. To do this, a diode laser with wavelength $ \lambda $ = 635 nm is focused onto the interdigitated (ID) finger structure, and we observe the brightness of one of the reflected spots (referred to as "modes") using a photodiode. This gives us information about the displacement of one set of fingers relative to the other — this is useful if one set is attached to the cantilever and the other to some reference surface.

As the cantilever deflects, and the out-of-plane spacing between the ID fingers changes, the reflected diffractive modes change their brightness, as shown in Figure 3. However, a complication of using this system is the non-linear output characteristic of the mode intensities. As the out-of-plane deflection of the fingers increases, each mode grows alternately brighter and dimmer. The intensity $ I $ of odd order modes vs. finger deflection $ \Delta $z has the form

$ I \propto sin^2 \left( \frac{2\pi}{\lambda}\Delta z \right) $,

and for odd modes, the sine is replaced by a cosine. The plot in Figure 4(a) shows graphically the intensity of two adjacent modes as a function of displacement.

This nonlinearity makes the sensor's sensitivity depend critically on the operating point along this curve at which a measurement is done. To make useful measurements, the ID interferometer therefore needs to be biased to a spot on the $ sin^2 $ curve where the function's slope is greatest midway between the maximum and minimum, as sketched in Figure 4(b).

Due to residual strain in the silicon nitride from which the cantilevers are fabricated, the relative planar alignment of the two finger sets varies slightly over the area of the grating. This variation is typically a few hundred nanometers in the lateral direction. Therefore, the bias point of the detector's output can be adjusted along the $ sin^2 $ curve by moving the incident laser spot side to side on the diffraction grating.

Cantilever probes for imaging

A few words about probe breakage: you will break at least a few probes — this is a normal part of learning to use the tool. We have a large, but not infinite supply of replacement probes. The cost of an individual AFM probe is not large, and the greater problem with breaking them is the time lost to replacing the probe and realigning the laser.

Exercise caution when moving the sample up and down, but don't let this prevent you from getting comfortable moving the sample around. Under most conditions, the cantilevers are surprisingly flexible and robust. They are most often broken by running them into the sample (especially sideways) — avoid "crashing" the tip into the surface, or worse bumping the stage into the die or fluid cell. Makesure you're familiar with the motion control system (Sec. 3.1.1).

The probes we use for imaging are shown in Figure 5 with relevant dimensions. The central beam has a tip at its end, which scans the surface. The shorter side beams to either side have no tips and remain out of contact. The side beams provide a reference against which the deflection of the central beam is measured; the ID grating on either side may be used. When calibrating the detector output to relate voltage to tip deflection, remember to include a correction factor to account for the ID finger position far away from the tip.

Cantilevers for thermal noise measurements

For noise measurement purposes, we'd like a clean vibrational noise spectrum, which is best achieved using a matched pair of identical cantilevers. The configuration with a central long beam and reference side-beams has extra resonance peaks in the spectrum that make it harder to interpret. With the geometry shown in Figure 6 the beams have identical spectra which overlap and reinforce each other. Using a pair of identical beams also helps to minimize any common drift effects from air movements or thermal gradients.

There are two sizes of cantilever pairs available. For the long devices, L = 350 $ \mu $m and the finger grating starts 140 $ \mu $m and ends 250 $ \mu $m from the cantilever base. For the short devices, L = 275 $ \mu $m, and the finger gratings begin 93 $ \mu $m and end 175 $ \mu $m from the base. The width and thickness of all of the cantilevers is b = 50 $ \mu $m and h = 0.8 $ \mu $m, respectively.

Major operational steps

Power-on

For our AFMs to run, you must turn on three things: (1) the detection laser, (2) the photodetector, and (3) piezo-driver power supply. The photodetector has a battery that provides reverse bias, and the others have dedicated power supplies (refer to Figure 1 for where these switches are located). When you finish using the AFM, don't forget to turn off the three switches you turned on at the beginning.