Phase modulation mode of scanning ion conductance microscopy Available

Scanning Ion Conductance Microscopy (SICM) uses a nano pipette as the sensitive probe to image sample at nanoscale resolution without physical contact with the sample. It has been widely applied in electrochemistry,^1,2 physics,³ and biology fields.^4–6 SICM offers the opportunity to observe the cellular dynamic processes,⁴ such as cell growth and differentiation, at very high resolution without damaging the cell. There are several main scanning modes available for SICM including DC mode,^4,7 AC mode,^8,9 and hopping mode.¹⁰ In DC mode, the DC current is directly used as feedback to regulate the tip-sample distance during scanning. DC mode shows great advantage at scanning speed (less than 5 minutes/frame), but it suffers from current instability, the so called DC drift mainly due to slowly developed DC potentials at electrodes when scanning over long periods of time. In AC mode of SICM, either the tip or the stage oscillates up and down, which produces modulated AC current that can be used to control tip sample separation. The modulated frequency however is limited by the mechanical property of the piezo actuator. To date, the modulated frequency is in the range from 1 kHz to 2 kHz.¹¹ This low modulated frequency limits the band width of the overall feedback loop, therefore slows the scanning speed.¹² The time required to scan a full frame with the AC mode is between 15 and 40 min.^12,13 Hopping mode and its variant,¹⁴ a point by point approaching- and-retrieving approach to detect the tip-sample distance, can avoid tip sample collision when imaging complex samples. However, the hopping mode is considerably slow. Even with the adaptive hopping improvement, it takes more than 15 min to obtain a fine topography image.¹⁰ 

In this Letter, we introduce a phase modulation (PM) mode of SICM, which can eliminate the DC drift while also improve the scan speed. In this mode, an AC current is generated by an AC voltage applied between the tip electrode and the reference electrode, in contrary to the traditional AC mode that generates the AC current through mechanically oscillating the probe or the stage. Using only the AC current signal through the resistance path part that is in-phase with the AC voltage as the feedback input, the tip-sample distance can be regulated during scanning. The PM mode combines the advantages of both DC mode and AC mode including high scanning speed, no involvement of mechanical oscillation, and free of DC drift. The configuration of the PM mode of SICM is illustrated in Fig. 1. A sinusoidal voltage signal with frequency f, generated by a function generator (Tektronix, AFG3022B), is applied between the electrodes. The resulted AC current is amplified by a commercial patch clamp amplifier (Heka, EPC800USB), and then the AC current is detected and separated into two parts by a lock-in amplifier (Stanford research systems, SR830) through phase sensitive detection (PSD), one in phase with the driving voltage (resistance path) and the other one out of phase (capacitance path). Then the resistance path part of the AC current, which is the X output of the Lock in amplifier as shown in Fig. 1, is further used as the feedback input to control the movement of the tip by the controller.

The equivalent circuit of SICM in PM mode is illustrated in Fig. 2. The equivalent circuit includes a stray capacitance C_stray in parallel with a combination of pipette capacitance C_p, and three individual resistances including the bath electrolyte resistance R_b, the pipette resistance inside pipette R_p, and the resistance of tip opening region R_t. R_p depending on the geometric of tip region keeps constant, while R_t changes with tip-sample distance. C_p is in parallel with R_p and R_t, then in serial with R_b. C_stray accounts for the capacitance between the part of tip electrode not submerged into the bath solution and the adjacent ground, and the capacitance between the conductive wires. C_p increases with the immersion depth of the pipette tip, at about 1 pF/mm. Because R_b is at least three orders of magnitude less than R_p (usually R_b < 0.04 MΩ, and R_p > 40 MΩ in phosphate buffered saline solution), R_b can be neglected. So the equivalent circuit can be further simplified as shown in Fig. 2(c), in which a total capacitance C_total that accounts for both C_stray and C_p, is in parallel with the total resistance R_sol which is also called solution resistance. C_stray keeps constant (about 3 pF in our setup), and C_p remains unchanged due to relatively constant immersion depth during scanning, so C_total remains almost constant during scanning. C_total causes the AC current I_ac to lead the applied voltage U_ac by θ in phase. I_ac can be split into two parts: the current through solution resistance path I_sol (determined by the solution resistance R_sol) in phase with the applied AC voltage and the one through the capacitance path I_cap (determined by total capacitance C_total) leading the applied AC voltage 90° ahead (Fig. 3). The solution resistance R_sol can be approximated by¹⁵ 

where r_o is the outer radius of pipette tip; r_i is the internal radius of pipette tip; α is the pipette tip half cone angle, and z is tip-sample separation. According to Eq. (1), R_sol increases when the tip-sample separation reduces. Therefore, I_sol can be used as a feedback signal to control the tip-sample separation. When the amplitude and the phase of the total current are measurable, the two current paths can be calculated using the following equations:

The analysis above can be proved by the experimental approach curve as shown in Fig. 4, which is obtained when the pipette tip approaches a petri dish. Current I_dc is obtained in DC mode, while current I_ac and current I_sol are obtained in PM mode. Unlike the traditional AC mode, the amplitude of the AC current I_ac (blue line in Fig. 4) in PM mode is insensitive to the tip-sample separation because it is dominated by the current I_cap that keeps almost constant while scanning. For example, assuming that the capacitance C_total is 6 pF and the modulated frequency is 15 kHz, the impedance of the capacitance is about 2 MΩ, which is much less than the solution resistance R_sol (usually R_sol > 35 MΩ for tip with approximately 75 nm inner radius). Because R_sol is positively related to tip-sample separation, the current I_sol (black line in Fig. 4) is negatively associated with the tip-sample separation. The current I_sol can be obtained from Eq. (2), which is the X output of the lock in amplifier. The curve of the normalized current I_sol vs. tip-sample separation matches well with the normalized DC current I_dc (red line in Fig. 4). A slight difference between I_dc and I_sol may be due to the neglecting of R_b. According to the theoretical analysis and experimental results, the current I_sol is sensitive to tip-sample separation; therefore, it can be used to control the tip-sample separation during scanning.

To verify the effectiveness of the PM mode of SICM, we developed a home-built SICM system. The home-built SICM system is composed of a scan head, a scanning stage, a feedback control module, a host computer for interface. The scan head is mounted on an inverted fluorescence microscope (Chongqing Optical and Electrical Instrument Co., IBE2000). Sample is placed at a XY nano stage (Physik Instrumente, P517.3CD). The Z-axis piezo actuator (Physik Instrumente, P753.31C) is driven by a high voltage amplifier (Physik Instrumente, E504), while the XY nano stage was controlled by a digital piezo controller (Physik Instrumente, E710). The feedback control module is implemented on a computer (control PC) running a real time (RT) Linux operating system. And a host computer (host PC) provides a user interface for changing parameters, inputting commands, and displaying and storing data and images. Using the home-built SICM system, we have performed imaging on the surface of a polydimethylsiloxane (PDMS) micro-grid, which is prepared through soft lithographic approach¹⁶ using a silicon Calibration Gratings (Digital Instruments, P/N 498-000-026) with 10 μm pitch and 200 nm step depth as a master. Fig. 5 shows the image of PDMS micro-grid acquired through home-built SICM in PM mode. Figs. 5(a) and 5(b) are the topography and error images of the PDMS micro-grid, respectively. In the scanning, the modulated frequency is set at 15 kHz and the scan rate at 0.75 Hz. The time for a complete scan is approximately 7 min, which is much faster than 0.3 Hz scan rate with the similar sample in the traditional AC mode.¹⁷ And the topography shown in Fig. 6 also infers that the SICM with PM mode can provide fine image quality comparable to traditional AC mode.¹⁷ Moreover, with PM mode, continuous imaging of PDMS micro-grid can last several hours without losing control even with perturbation of bias DC voltage offset several times. These results indicate that we can greatly improve the efficiency and robustness of SICM with this PM mode.

The PM mode maintains the advantages of AC mode that is less prone to electronic noise and DC drift. In PM mode, only the AC component of the current is used to extract the phase and amplitude for controlling tip sample separation, therefore the PM mode is immune to DC drift. As shown in Fig. 7, when the applied DC voltage have slightly changes, the DC current exhibits significant changes (Fig. 7(a)); while the AC current shows very little variation (Fig. 7(b)).

An advantage of PM mode over traditional AC mode is that the modulated frequency in PM mode can reach several or even tens of kHz, which is much higher than that in AC mode that is limited by the pizeo actuator bandwidth. In our experiment, the modulation frequency can be set larger than 15 kHz. The modulated frequency determines the speed of the lock-in amplifier, and a higher modulated frequency will help to accelerate the response to change of tip-sample separation, improve the performance of feedback control, and reduce the scan time. Our current scanning speed is limited by the sampling rate of the PC based RT control system. A much faster scanning speed can be achieved when the control system has a higher sampling rate.

An apparent advantage of PM mode over other modes is that it does not have the electrode consuming problem. Traditionally, the chloride coating on the negative electrode can be consumed quickly due to large current in one direction with the bias DC voltage, thus greatly promotes the electrode drift, but with the alternative current method in PM mode, positive and negative electrodes is alternatively changed and so the electrodes are protected; then the issue of electrode consuming is completely solved.

In summary, we have developed a PM mode for SICM, which takes the advantages of both DC mode and AC mode by using AC component that is in phase with the applied AC voltage as the feedback control input. The principle of the PM mode is analyzed with equivalent circuit model and verified by experimental studies. The effectiveness of the PM mode has been proven by performing imaging on PDMS micro-grid. It has been demonstrated that fast and continuous scan can be achieved for a long period in PM mode with very good resolution and stability. The developed phase modulation mode is expected to greatly promote the wide applications of SICM.

This research work was partially supported by the National Natural Science Foundation of China (Project Nos. 61175103 and 61327014), the Instrument Developing Project of the Chinese Academy of Sciences (Project No. YZ201339), and the CAS FEA International Partnership Program for Creative Research Teams.