Band excitation method applicable to scanning probe microscopy
Methods and apparatus are described for scanning probe microscopy. A method includes generating a band excitation (BE) signal having finite and predefined amplitude and phase spectrum in at least a first predefined frequency band; exciting a probe using the band excitation signal; obtaining data by measuring a response of the probe in at least a second predefined frequency band; and extracting at least one relevant dynamic parameter of the response of the probe in a predefined range including analyzing the obtained data. The BE signal can be synthesized prior to imaging (static band excitation), or adjusted at each pixel or spectroscopy step to accommodate changes in sample properties (adaptive band excitation). An apparatus includes a band excitation signal generator; a probe coupled to the band excitation signal generator; a detector coupled to the probe; and a relevant dynamic parameter extractor component coupled to the detector, the relevant dynamic parameter extractor including a processor that performs a mathematical transform selected from the group consisting of an integral transform and a discrete transform.
1. A method, comprising:
generating a band excitation signal;
simultaneously exciting a probe at a plurality of frequencies within a predetermined frequency band using the band excitation signal; and
measuring a response of the probe across a subset of frequencies of the predetermined frequency band.
2. The method of claim 1 , further comprising scanning a sample held in an apparatus and measuring the response of the probe at each position crossed during the scan.
3. The method of claim 2 , further comprising performing a mathematical transform, by a processor of a relevant dynamic parameter extractor, on the measured response and outputting amplitude-frequency data and phase-frequency data at each scanned position of the sample.
4. The method of claim 3 , wherein the mathematical function is selected from the group consisting of an integral transform and a discrete transform.
5. The method of claim 3 , further comprising extracting resonant frequency, maximum amplitude, and Q factor parameters for each position of the sample based on an analysis of the amplitude frequency data and the phase-frequency data.
6. The method of claim 5 , wherein the relevant dynamic parameter extracts resonant frequency, the maximum amplitude, and Q factor parameters independently for each position.
7. The method of claim 1 , further comprising adjusting the excitation signal based on the measured response.
8. The method of claim 1 , wherein the subset of frequencies of the predetermined frequency band includes a selected frequency and associated resonance frequencies.
9. The method of claim 8 , wherein the subset of frequencies is substantially the same as the predetermined frequency band.
10. The method of claim 1 , wherein the excitation signal includes a controlled amplitude and phase density within the predetermined frequency band.
11. A method, comprising:
generating an excitation signal;
simultaneously exciting a probe at a plurality of frequencies within a predetermined frequency band based on the excitation signal;
measuring a response of the probe across a subset of frequencies of the predetermined frequency band; and
adjusting the excitation signal based on the measured response.
12. The method of claim 11 , further comprising performing, by a processor of a relevant dynamic parameter extractor, a mathematical transform on the measured response and outputting an amplitude-frequency data and phase-frequency data at each scanned position of the sample.
13. The method of claim 12 , wherein the mathematical function is selected from the group consisting of an integral transform and a discrete transform.
14. The method of claim 12 , wherein the relevant dynamic parameter extractor extracts resonant frequency, maximum amplitude, and Q factor parameters for each position of the sample based on an analysis of the amplitude frequency data and the phase-frequency data.
15. The method of claim 14 , wherein the relevant dynamic parameter extractor extracts the resonant frequency, the maximum amplitude, and the Q factor parameters independently for each position.
16. The method of claim 11 , wherein the subset of frequencies of the predetermined frequency band includes a selected frequency and associated resonance frequencies.
17. The method of claim 11 , wherein the subset of frequencies is substantially the same as the predetermined frequency band.
18. The method of claim 11 , wherein the excitation signal includes a controlled amplitude and phase density within the predetermined frequency band.
19. A method, comprising:
generating an excitation signal;
simultaneously exciting a probe at a plurality of frequencies within a predetermined frequency band based on the excitation signal;
scanning a sample held in an apparatus to measure a response of the probe across a subset of frequencies of the predetermined frequency band; and
separately extracting, by a processor of a relevant dynamic parameter extractor, resonant frequency, maximum amplitude, and Q factor parameters associated with each position crossed during the scan.
20. The method of claim 19 , further comprising performing a mathematical transform on the measured response of the probe and outputting an amplitude-frequency data and phase-frequency data at each scanned position of the sample.
21. The method of claim 20 , wherein the mathematical function is selected from the group consisting of an integral transform and a discrete transform.
22. The method of claim 20 , wherein the relevant dynamic parameter extractor extracts the resonant frequency, the maximum amplitude, and the Q factor parameters for each position of the sample based on an analysis of the amplitude frequency data and the phase-frequency data.
23. The method of claim 19 , wherein the relevant dynamic parameter extractor extracts the resonant frequency, the maximum amplitude, and the Q factor parameters independently for each position.
24. The method of claim 19 , wherein the subset of frequencies of the predetermined frequency band includes a selected frequency and associated resonance frequencies.
25. The method of claim 19 wherein the subset of frequencies is substantially the same as the predetermined frequency band.
26. The method of claim 19 , wherein the excitation signal includes a controlled amplitude and phase density within the predetermined frequency band.
27. The method of claim 19 further comprising adjusting the excitation signal based on the extracted resonant frequency, maximum amplitude, and Q factor parameters.