Intermodulation Electrostatic Force Microscopy

The Intermodulation measurement concept can be applied to Electrostatic Force Microscopy (EFM), were a force on the cantilever is induced by a voltage applied between the tip and sample. We call this method ImEFM™, and its implementation requires the synchronous multi-port capability of the Multifrequency Lockin Amplifier (MLA™). Two output ports are used with ImEFM™, one port driving the tip-sample voltage at a low frequency and the other port driving the cantilever via the shaker piezo near the cantilever resonance frequency. The tip-surface capacitance gradient is a nonlinear function of the tip-surface separation, and this nonlinearity causes intermodulation or frequency mixing between the electrostatic drive and the mechanical drive. Measuring 4 intermodulation products near resonance and taking ratios of their amplitudes, we extract the contact potential difference between the tip and surface. The theory of the method and its validation was given by Borgani et al. [Borgani-2014]. Here we describe the user interface in the AFM Software Suite.

ImEFM™ requires a conducting cantilever, for example a Pt coating on the front side of the probe. In the description given below, a voltage is applied to the tip, and the sample is grounded. One can equally well apply the voltage to the sample, and put the tip at at ground. Which method is more convenient to use depends on the host AFM. If you are using a Bruker NSV controller and Icon AFM, the voltage that is applied between the tip and the sample comes from the MLA™ via the composite cable connected to the IMP Signal Access Module (SAM). Make sure that all switches on the SAM are in the IMP position and that the Bruker software is configured to apply voltage to the tip. In the Bruker software, enable advanced parameters (click red puzzle icon) and choose the option tip bias, on the setting tip bias. This setting should be effected if the ImAFM workspace is chosen in the Bruker software.

For other host AFMs, you need to work through the signal path for the tip-sample voltage which is applied from BNC port OUT 2 on the front panel of the MLA™. It can be a good idea to use a BNC Tee and look at this voltage with an oscilloscope in parallel, so that you can actually see the applied signal. A general connection scheme is given below.


Setting up the measurement

Before you begin ImEFM™ you must first do the standard calibration procedure in the first two steps of the ImAFM™ Work Flow: Finding the cantilever resonance with a Frequency Sweep and calibrating the cantilever using non-invasive thermal noise Calibration.


Open the ImEFM™ panel by clicking on the ImEFM™ icon in the work flow, or by selecting ImEFM from the Advanced pull-down menu. The ImEFM™ panel has the following controls:

Settings group controls the following:

  • Osc. amplitude is the desired amplitude of cantilever oscillation. When Setup is executed, the piezo drive voltage will be adjusted to achieve this value. If you are using a standard EFM cantilever, for example the HQ:NSC15/Pt by micromash ( f_0 = 325 kHz, k = 40 N/m , Pt front-side coated) you may want to use about 40-60 nm oscillation amplitude.

  • Tip AC voltage sets the amplitude of the low-freqeucy AC voltage applied between the tip and sample. This voltage induces a small electrostatic force on the cantilever, which modulates of the cantilever oscillation. The larger this voltage, the larger the electrostatic force. A typical value here is between 1 and 6 Volts. The maximum voltage that the MLA™ can apply is 7 Volts ( 14 volts by changing an internal jumper).

  • Tip DC offset sets a DC offset voltage between the tip and sample. Often this can be set to zero, but a small offset is useful when the contact actual potential is close to zero, so that you measure some signal and not only noise. You can also test for a change of potential by changing this DC offset.

  • Set-point is the fraction of free oscillation amplitude (in %) used as the set-point for the scanning feedback. Setting this this to a smaller value will cause the probe to oscillate closer to the surface. To measure purely electrostatic force the tip should not come too close to the surface, where other surface forces are much stronger than the electrostatic force. A typical value for this parameter is 85% to 95%, however you may want to use a smaller set-point if the free oscillation is measured very far from the surface.

  • Pixel rate sets the measurement bandwidth, or inverse the measurement time at each image pixel. Making this smaller will improve the signal-to-noise ratio, but it will also slow down the scan rate for a given image resolution (number of pixels).

  • Setup executes an automatic routine to configure the MLA™ and software for the measurement. After setup is executed, the AC voltage will be applied to the tip.

  • ON/OFF check box controls the tip-sample voltage. Checked means ON. Uncheck and Check to see if anything changes in your image. If not, you may have a loose or incomplete electrical connection to the tip. If you are using and ImEFM™ with front-panel connections, the tip-sample voltage is applied from BNC port OUT 2. You can use a BNC T and oscilloscope in parallel to monitor this voltage.

  • LED toggle check box controls the LED illumination when measuring surface photo voltage. When unchecked, there will be no illumination on either trace or retrace. When checked the LED will be on during trace, and off during retrace. You can check that this is actually the case by storing the LED voltage as a axillary signal (image) of your host AFM has this capability. The LED voltage is applied from the MLA™ through port OUT B.

  • Scheme selector allows you to choose between:

    • ImEFM - the standard mode for measuring contact potential difference. In this mode the measurement bandwidth is equal to the frequency of the applied tip-sample AC voltage.
    • ImEFM_slow - scans slower, with better SNR. In this mode the measurement bandwidth is half the frequency of the applied tip-sample AC voltage.

After all settings have been adjusted, press Setup to configure measurement, press Start , and then use the host AFM software to engage the sample. The system will start to process triggers collect data and build an ImEFM™ image. You must manually set the Scan Rate on the host AFM to the value given by the ImEFM™ software, at the bottom of the panel. After you engage and get a stable scan, it is a good idea to press Measure Free to make a new measurement of the free oscillation, well above the sample. The electrostatic force is determined from the difference between the engaged oscillation and the free oscillation and accurate reconstruction requires a good measurement of the free oscillation.

The intermodulation spectral data will be processed in real time as you scan so that you can view images of various quantities. All raw intermodulation data and the processed image data will be stored in a the standard file type (e.g. scan01234.imp). You can view previous scans by pressing the Load .imp button and navigating to the file.

Analyzing and viewing the ImEFM data

View group controls how the intermodulaiton spectral data is analyzed and what data is plotted. You can select the following quantities to be shown in the image:

  • Vcpd [V] - the contact potential difference in Volts.
  • Cz [F/m] - the tip-surface capacitance gradient \frac{\partial C}{\partial z} in F/m.
  • Czs [F/m2] - the second derivative of the capacitance with respect to separation \frac{\partial^2C}{\partial z^2} in F/m^2.
  • Trace or Retrace controls which scan to view. The Difference between trace and retrace of Vcpd [V] gives the surface photo voltage, when the LED toggle is activated (i.e. change in contact potential between light and dark states).
  • Horiz. shift is the number of pixels to shift to compensate for offset between trace and retrace. This offset arises if the scan overshoot factor or scan speed is not exactly correct.
  • Vert. shift is the number of pixels to shift to compensate for offset between trace and retrace. This should always be zero, but there maybe something funny with the host AFM.
  • Swap diff. changes the sign of the difference, i.e from (trace-retrace), to (retace-trace).
  • Cz fit opens a dialog box Cz fit settings that allows you to control the intermodulation frequencies an polynomial order used for calculating the capacitance gradient \frac{\partial C(z)}{\partial z}, where a polynomial approximation of C(z) is assumed (see [Borgani-2014]). You can see the result of the calculation at any pixel by clicking the blue pixel inspector icon pixel_icon in the image tool bar. The red pixel inspector icon clears all selected pixels. This feature is in the experimental stage of development.
  • Load .imp will load a previous scan file with saved ImEFM™ data. If you load a file where ImEFM™ was not performed, you will get a warning, but your EFM images will show something that is not at all related to the electrostatic force.
  • Save .imp will save the currently analyzed raw data and EFM images. If Autosave is checked, each scan will automatically be saved upon completion.

Debug group contains some tools for trouble-shooting the measurement, checking to see if all connections are OK, and that you are really measuring an electrostatic force.

  • Set voltage When checked, the Setup routine will apply the AC voltage between tip and sample. When unchecked, the tip-sample voltage will not be applied and it will be held at ground. In this case, you are simply doing single-freqeuncy dynamic AFM.
  • Use Free When checked the free oscillation will be subtracted from the engaged oscillation to calculate the electrostatic force. The checked state is the normal and correct mode of operation. When unchecked, the free oscillation is not subtracted. You can un-check and check this box to test if something may be corrupt with your measurement of the free oscillation.
  • Down-sample will skip the given number of pixels in both X and Y directions, reducing the number of calculations for ImEFM. You may find the need to down-sample if you have a slow computer and you are scanning with high speed and high pixel density. In any case, all raw data will be saved to file and a full resolution image can be calculated offline.