Determination of Lock-in Phase

A phase difference (–90° in the lower graph in Figure 1) is usually seen between tip oscillation signal and the AC bias driving signal. This phase lag varies from tip to tip, with operating frequency, and the potential difference between the tip and the spot on the sample.

Figure 1: Interleave Tuning Curve - Phase Lag

Figure 2 shows a Generic Sweep of Sample Bias while the potential feedback is turned off. Note that Input Igain and Input Pgain are 0.

Figure 2: Amplitude and Phase vs. Sample Bias (Feedback Off)

The amplitude, shown in the upper plot, dips to 0 when the sample is biased to match the tip potential; as the bias voltage moves away from that point, the amplitude increases. Potential feedback seeks that zero point. Because amplitude alone can not determine whether one is on the left side or right side of that zero amplitude point, the feedback relies on the phase to determine which direction to move the DC bias.

The bottom graph in Figure 2 shows the phase changing by 180° across “0” amplitude. Choose a Lock-In Phase to offset the oscillation phase so that the phase is negative when the tip voltage is positive relative to the sample. As you can see in Figure 2, when the sample bias is –2 V (tip is positive), the output Lock-In Phase is 90°. The Interleave Lock-In Phase then needs to be set to –180° to make it –90°.

It is logical to sweep the lock-in phase in a full circle to determine the phase range where feedback is working while the feedback is turned on (Input Igain and Input Pgain are non-zero).

Figure 3: Phase vs. Lock-in Phase (Feedback On)

The top plot in Figure 3 shows how the amplitude changes while lock-in phase is swept. In the mid-range of the phase sweep (approximately –100° to +100°), the amplitude stays non-zero, indicating that the phase is not correct for the feedback to work properly. On both ends, the amplitude remains around “0”, implying that feedback is working properly in “nulling” the amplitude. In principle, it is fine to choose any lock-in phase in these two regions 100° ~ 180° and –180° ~ –90° (equivalent to 180° ~ 270°); actually a combined region of 100° ~ 270°. It makes practical sense, however, to choose a value somewhere in the middle to have a good margin, e.g. –170°.

The lower plot in Figure 3 shows phase changing linearly in the middle of the sweep range, while jumping around when feedback is working on either end. This is explained above under Amplitude and Phase vs. Sample Bias—Feedback Off.

Figure 4 depicts a Generic Sweep of Lock-in phase while potential feedback is off and Input Igain and Input Pgain are “0”.

Figure 4: Alternative Phase vs. Lock-in Phase (Feedback Off)

The top plot in Figure 4 shows the amplitude remaining unchanged while the Lock-In Phase is swept.

The bottom plot shows the phase changing linearly as the lock-in phase is swept. There is one exception where the phase jumps from 180° to –180°, so-called phase wrapping.

In case the plots in the previous section were not obtained (due to software inconsistency), do the following:

• From the left bottom plot, choose a lock-in phase where oscillation phase falls within –180°~0° (or 0~180°), e.g. 10° (–170°)
• If this does not work, add/subtract 180°, e.g. –170° (10°)

Of course, you can simply pick any lock-in phase, if it works, fine. Otherwise, change the phase by 180°. The difference is that with the above outlined approach you know what kind of margin you have.