Closed loop controller and method for fast scanning probe microscopy

1. A method of operating a metrology instrument, comprising:

generating relative motion between a probe and a sample at a scan frequency using an actuator having a fundamental resonance frequency;

detecting motion of the actuator using a position sensor, wherein the position sensor exhibits noise in the detected motion;

controlling the XY position of the actuator with a control signal, u, using both a feedback loop and a feed forward algorithm, wherein a feedback signal, u fb , associated with the feedback loop is updated during operation of the metrology instrument by combining a signal associated with a predetermined path defined by the feed forward algorithm therewith;

wherein the the scan frequency is greater than 1/100th of the fundamental resonant frequency; and

wherein the bandwidth of the feedback loop is different than a bandwidth associated with operation of the feedforward algorithm.

2. The method of claim 1 , wherein the controlling step includes operating the feedback loop at a bandwidth less than the scan frequency associated with the generating step thereby attenuating noise in the actuator position compared to the noise in the detected motion in the corresponding bandwidth, and wherein the feed forward algorithm substantially continuously updates the control signal so that the XY motion of the actuator substantially follows a reference thereby compensating for the non-linear response.

3. The method of claim 1 , wherein the feed forward algorithm includes using an inversion-based control algorithm.

4. The method of claim 3 , wherein the inversion-based control algorithm adaptively produces a correction that contributes to a control signal that compensates for at least one of the non-linearities and the dynamics of the actuator.

5. The method of claim 4 , wherein the control signal produces a peak position error of less than about 1% of the total scan range after no more than about 10 iterations of 10 scan lines per iteration.

6. The method of claim 5 , wherein the control signal produces a peak position error of less than about 1% of the total scan range after no more than about 5 seconds.

7. The method of claim 1 , wherein the fundamental resonant frequency of the actuator is greater than about 100 Hz and the scan frequency is at least about 100 Hz.

8. The method of claim 7 , wherein the scan frequency is at least about 300 Hz.

9. The method of claim 1 , wherein the bandwidth of the feedback loop is less than the scan frequency.

10. The method of claim 1 , wherein the bandwidth of the feedback loop is less than about 10 hz.

11. The method of claim 1 , wherein the controlling step attenuates the noise in the actuator position to less than about 1 Angstrom RMS within a noise bandwidth equal to about seven times the scan frequency.

12. The method of claim 11 , wherein the controlling step includes using a PI controller.

13. A method of operating a metrology instrument, comprising:

generating, with an actuator exhibiting a non-linear response, relative motion between a probe and a sample at a scan frequency over a scan size;

detecting motion of the actuator using a position sensor;

calibrating the actuator to generate an initial scan table;

controlling the XY position of the actuator with a control signal, u, using both a feedback loop and a feed forward algorithm, wherein a feedback signal, u fb , associated with the feedback loop is updated during operation of the metrology instrument by combining a signal, u ff , associated with a predetermined path defined by the teed forward algorithm therewith, wherein the scan table is updated repeatedly during operation to generate u ff thereby causing the feed forward algorithm to substantially continuously update the control signal so that the XY motion of the actuator substantially follows a reference thereby compensating for the non-linear response; and

wherein the bandwidth of the feedback loop is less than about 10 Hz, and the bandwidth of the feedforward algorithm is greater than about 300 Hz, and the scan frequency is greater than 100 Hz.

14. The method of claim 13 , wherein the feed forward algorithm is an adaptive feed forward algorithm that estimates a transfer faction of the actuator in response to the position error and adjusts the generating step based at least in part on the transfer function.

15. The method of claim 14 , wherein the response of the actuator is dependent on an operating condition, wherein the operation condition is at least one of scan frequency, size, angle, and offset.

16. The method of claim 13 , wherein the scan frequency is greater than about 300 Hz.

17. A scanning probe microscope (SPM) comprising:

an actuator exhibiting a non-linear response that generates relative motion between a probe and a sample at a scan frequency;

a sensor that detects motion of the actuator and generates noise;

a controller including a feedback loop that generates an XY position control signal, u, based on the detected motion;

wherein the actuator is calibrated to generate an initial scan table;

wherein a feedback signal, u fb , associated with the feedback loop is updated during operation of the metrology instrument by combining a signal, u ff , associated with the scan table, wherein the scan table is updated repeatedly during operation to generate u ff thereby causing the feed forward algorithm to substantially continuously update the control signal;

wherein the bandwidth of the feedback loop is less than the scan frequency thereby attenuating noise in the actuator position compared to the noise in the detected motion; and

wherein the bandwidth of the feedback loop is different than a bandwidth associated with operation of the feedforward algorithm.

18. The SPM of claim 17 , wherein the XY motion of the actuator substantially follows a reference thereby compensating for the non-linear response.