Thermal property microscopy with frequency domain thermoreflectance and uses thereof
The present invention relates to frequency domain thermoreflectance (FDTR) imaging of a thermophysical property or a set of thermophysical properties of a sample. A method comprises measuring the amplitude and/or phase of a beam of radiation reflected from a sample surface, while a heat source applied to the sample is modulated at at least two modulation frequencies simultaneously. Such measurement can be reiterated as a probe beam is scanned across the sample surface or a portion thereof. A 2D image or map of a thermophysical property or a set of thermophysical properties can be generated from data processing. Also provided herein is an apparatus for performing FDTR imaging.
1. A method of performing a frequency domain thermoreflectance measurement, the method comprising:
(i) projecting a first beam of radiation onto a sample while a heat source is applied to the sample, wherein the heat source is modulated at a modulation frequency;
(ii) measuring reflected radiation from the first beam of radiation at at least two modulation frequencies simultaneously, wherein amplitude and/or phase data of the reflected radiation are obtained, and wherein the modulation frequencies are determined from sensitivity of amplitude and/or phase of the reflected radiation to a given thermophysical property;
(iii) repeating steps (i) and (ii) at a plurality of spots in the sample; and
(iv) producing a two-dimensional (2D) image of at least one thermophysical property of the sample based on the measurements.
2. The method of claim 1 , wherein the measurement is at six modulation frequencies simultaneously.
3. The method of claim 1 , wherein one modulation frequency is at or near maximum sensitivity to the given thermophysical property.
4. The method of claim 1 , wherein the modulation frequencies are spaced to fit a desired set of thermophysical properties using a sensitivity function.
5. The method of claim 1 , wherein the modulation frequencies are in the range of 1 kHz to 50 MHz.
6. The method of claim 1 , wherein the measurement is done using a lock-in amplifier.
7. The method of claim 1 , further comprising moving the sample relative to the first beam of radiation, thereby scanning the first beam of radiation across the sample.
8. The method of claim 1 , wherein the thermophysical property is determined through fitting of data obtained from the measurement.
9. The method of claim 1 , wherein the thermophysical property is selected from the group consisting of film thickness, density, heat capacity, thermal conductivity, in-plane thermal conductivity, cross-plane thermal conductivity, and thermal interface conductance.
10. The method of claim 1 , wherein the 2D image exhibits a maximum spatial resolution of about 200 nm.
11. The method of claim 1 , wherein the first beam of radiation is a laser beam.
12. The method of claim 1 , comprising producing a 2D image of two or more thermophysical properties of the sample.
13. The method of claim 12 , wherein the two or more thermophysical properties are in-plane thermal conductivity and cross-plane thermal conductivity.
14. The method of claim 1 , wherein the sample is a bulk sample or a multilayered sample.
15. The method of claim 14 , wherein the sample is coated with a layer of metal.
16. The method of claim 1 , wherein the heat source is produced by a second beam of radiation projected onto the sample.
17. The method of claim 3 , wherein the second beam of radiation is aligned coaxially with the first beam of radiation.
18. The method of claim 16 , wherein the second beam of radiation is modulated via a sine wave for each modulation frequency.
19. The method of claim 16 , wherein the second beam of radiation is a laser beam.
20. A method of performing a frequency domain thermoreflectance measurement, the method comprising:
(i) projecting a first beam of radiation onto a sample while a heat source is applied to the sample, wherein the heat source is modulated at a modulation frequency;
(ii) measuring reflected radiation from the first beam of radiation at at least two modulation frequencies simultaneously, wherein amplitude and/or phase data of the reflected radiation are obtained, and wherein the modulation frequencies are spaced to fit a desired set of thermophysical properties using a sensitivity function;
(iii) repeating steps (i) and (ii) at a plurality of spots in the sample; and
(iv) producing a two-dimentional (2D) image of at least one thermophysical property of the sample based on the measurements.