Lab Manual: Atomic Force Microscopy (AFM)
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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
- Work with a TA or Instructor.
- Learn the signal paths and connections of the system.
- Practice aligning the AFM optics.
- Learn how to calibrate the AFM to extract useful physical data.
- Measure the vibrational noise floor in the AFM system.
- Use the AFM to record the vibrational noise spectrum of a cantilever probe (Experiment ##)
Extended AFM work
- Image several different samples with the AFM and measure physical dimensions of imaged features.
- Use the AFM to measure the elastic modulus and surface adhesion force of several different samples.
- 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 $m, respectively.
Major operational steps
Power-on
For our AFMs to run, you must turn on three things: (1) the detection laser, (2) the photodetector, and (3) piezo-driver power supply. The photodetector has a battery that provides reverse bias, and the others have dedicated power supplies (refer to Figure 1 for where these switches are located). When you finish using the AFM, don't forget to turn off the three switches you turned on at the beginning.
Signal connections and data flow
The first key step to using the instrument is properly connecting all of the components together. Figure 7 will help to guide you. The AFM itself requires two signal inputs (Xin and Yin) to drive the piezo actuator, which connect to the electronics board on the back of the headplate. They are provided by the computer's analog signal outputs (NI-USB6212 DAQ channels AO0 and AO1, respectively). The computer also needs to read these two signals in, together with the AFM signal output, so these become the three DAQ inputs, AI1, AI2, and AI0, respectively.
The output from the AFM's photodetector is a current signal, proportional to the brightness of the laser spot, that needs to be converted to a voltage (a 100 k$ \Omega $ resistor to ground is sufficient). It's good to be able to amplify and offset this voltage at our convenience, so we run this signal through a Tektronix AM502 amplifier before it enters the DAQ.
Finally, during calibration, it's very useful to watch the detector signal as a function of stage movement in realtime, on the oscilloscope screen, so we run those signals to the scope as well.
Laser alignment and diffractive modes
To get a cantilever position readout, the laser needs to be well focused on the interdigitated fingers of the cantilever. Use the white light source and stereo-microscope to look at the cantilever in its holder. The laser spot should be visible as a red dot (there may be other reflections or scattered laser light, but the spot itself is a small bright dot). Adjust its position using the knobs on the kinematic laser mount, until it hits the interdigitated fingers (use the cantilever schematics in Figures 5 and 6 as a reference).
When the laser is focused in approximately the right position, the white "screen" around the slit on the photodetector will allow you to see the diffraction pattern coming out of the beam splitter. Observe the spot pattern on this screen while adjusting the laser position until you see several evenly spaced "modes." Make sure you aren't misled by reflections from other parts of the apparatus — some may look similar to the diffraction pattern, but aren't what you're looking for.
When you see the proper diffraction pattern is on the detector, adjust the detector's position such that only one mode passes through the slit. Typically the 0th mode gives the largest difference between bright and dark.
Sample loading and positioning
When changing or inserting a sample disk, the 3-axis stage must be lowered far enough for the disk to clear the bottom opening of the cantilever mount, as shown in the figures above. This requires a large travel distance, so exercise caution when bringing the sample back up to the cantilever, and take care not to crash the tip.
Correctly mounting a sample in the AFM is a key part of obtaining quality images. Our samples are always mounted on disks, which are magnetically held to the piezo actuator offset post. The AFM can image only a small area near the center of the opening in the metal cantilever holder, so be sure that the area of interest for imaging ends up there. This must be done by moving the stage because of the way the x-y scanning is accomplished, as described below.
The area of interest must be directly over the center of the offest post, and the offset post must be over the center of the piezo disc, which is clamped to the stage. It is critical to reposition the offset post as nearly centered as possible on the piezo disk, to ensure true horizontal motion in the x-y plane. Centering the sample disk at the top of the offset post is not critical; rather, it is the area of interest that must be centered at the top of the post for as little z deflection as possible during scanning. For instance, in figure 8(b) above the sample disk is visibly off-center, which is not necessarily a problem.
Engaging the tip
The process of bringing the probe tip to the sample surface so we can scan images and measure forces is called "engaging." The aim is to get the tip in close proximity so it is just barely coming into contact, and bending only slightly. If the probe does not touch the surface, it is obviously useless, but if it's bent too much against the surface it can damage the sample or simply push through soft features and report topologies lower than actual.
Before engaging, start the piezo z-modulation scan in the matlab software (see Sec. 3.3.3). Be sure the mode switch on the AFM electronics board is flipped down to "force spec. mode," and make sure to turn on the piezo power supply. Carefully bring the tip near the surface, first turning the red motor knob by hand, then very slowly with the joystick. When you make contact, you will see the modes on the photodetector fluctuate in brightness. Because of the device geometry, only the central long cantilever with the tip will make contact with the sample surface.
Calibration and biasing
At this point, it's worth pausing to review the definition of calibration, as well as the distinction between sensitivity and resolution — terms which will often used frequently in this context, but whose accurate meaning isn't always made explicit. Be sure you're clear on the differences between them.
Calibration - finding the relationship between the output of your instrument to the physical quantity you are measuring like distance or force; in our case, relating the mode brightness measured by the photodiode to cantilever tip de°ections
Sensitivity - a numerical expression for the calibration, the "slope" of a transducer output e.g. mV/N, W/ºA, or in our case nm/V
Resolution - the minimal measurement or change in signal that an instrument can detect; depends completely on the noise and the frequency and bandwidth of the measurement
It's a good idea to run a calibration before performing any measurement, because they varies from AFM to AFM, and may be thrown o® by drifts or disturbances. We calibrate our AFM in force spectroscopy (or z-modulation) mode, in which the sample is only moved straight up and down (see Section 3.3.3 for details).
Watching the AFM signal on the oscilloscope in x-y mode, (with detector output on the y-axis, and the stage actuation signal on the x-axis) you should see something like the plots shown in Figure 9: a °at line that breaks into a sin2 function at a certain x-value (whether it starts upward or downward depends on the mode you choose). The °at line is the cantilever out of contact, and the oscillating section is the cantilever bending, after making contact with the sample.
If necessary, use the o®set on the voltage ampli¯er to position the sin2 so that it is centered around zero. Then, set the out-of-contact bias point by moving the position of the laser focus on the ¯ngers until the °at section of your force spec. curve is approximately at zero volts, halfway between the maximum and minimum, as in Figure 9(c).