Methods for nondestructive measurements of thickness of underlying layers

1. A method, the method comprising:

irradiating a sample with a pump laser pulse to induce generation of an acoustic wave in the sample such that the acoustic wave propagates through the sample over time, the sample including a substrate, an underlying layer on the substrate, and an overlying layer on the underlying layer,

irradiating the sample with a probe laser pulse subsequent to irradiating the sample with the pump laser pulse;

determining a reflectance variation of the sample over time, based on monitoring a variation of a reflection of the probe laser pulse from the sample over time, to generate a first graph showing a variation of reflectance of the sample over time; and

determining a thickness of the underlying layer based on the first graph,

wherein the determining the thickness based on the first graph includes

determining the thickness based on magnitudes of the reflectance variation at highest points and lowest points of the first graph,

determining the thickness based on magnitudes of the reflectance variation at highest points and lowest points of a second graph, the second graph generated based on subtracting a saturation value from magnitudes of the reflectance variation in the first graph,

determining the thickness based on magnitudes of the reflectance variation at highest points and lowest points of a third graph, the third graph generated based on subtracting a background noise from magnitudes of the reflectance variation in the first graph, or

determining the thickness based on magnitudes of the reflectance variation at highest points and lowest points of a fourth graph, the fourth graph generated based on normalizing the third graph so that a magnitude of the reflectance variation at a first lowest point of the fourth is 0 and a magnitude of the reflectance variation at a first highest point of the fourth graph is 1.

2. The method of claim 1 , wherein

the determining the thickness includes

determining the thickness based on a difference between a magnitude of the reflectance variation at an nth highest point of the first graph and a magnitude of the reflectance variation at an nth lowest point of the first graph,

determining the thickness based on a difference between the magnitude of the reflectance variation at the nth highest point of the first graph and a magnitude of the reflectance variation at an n+1th lowest point of the first graph, or

any combination thereof, and

n is a natural number.

3. The method of claim 1 , wherein

the determining the thickness includes

determining the thickness based on a sum of (k+1) values, from a difference between a magnitude of the reflectance variation at an nth highest point of the first graph and a magnitude of the reflectance variation at an nth lowest point of the first graph to a difference between a magnitude of the reflectance variation at an n+kth highest point of the first graph and a magnitude of the reflectance variation at an n+kth lowest point of the first graph,

determining the thickness based on a sum of (k+1) values, from a difference between the magnitude of the reflectance variation at the nth highest point of the first graph and a magnitude of the reflectance variation at an n+1th lowest point of the first graph to a difference between the magnitude of the reflectance variation at the n+kth highest point of the first graph and a magnitude of the reflectance variation at an n+k+1th lowest point of the first graph, or

any combination thereof, and

each value of n and k is a natural number.

4. The method of claim 1 , wherein

the first graph converges to the saturation value over time.

5. The method of claim 4 , wherein

the determining the thickness based on the magnitude of the reflectance variation at highest points and lowest points of the second graph is based on a magnitude of the reflectance variation at an nth highest point of the second graph, and

n is a natural number.

6. The method of claim 4 , wherein

the determining the thickness based on the magnitudes of the reflectance variation at highest points aid lowest points of the second graph includes determining the thickness based on a sum of (k+1) values, from a magnitude of the reflectance variation at an nth highest point of the second graph to a magnitude of the reflectance variation at an n+kth highest point of the second graph, and

each value of n and k is a natural number.

7. The method of claim 1 , wherein the determining the thickness based on the magnitude of the reflectance variation at highest points and lowest points of the third graph includes determining the thickness based on a difference between a magnitude of the reflectance variation at an nth highest point of the third graph and a magnitude of the reflectance variation at an nth lowest point of the third graph,

determining the thickness based on a difference between the magnitude of the reflectance variation at the nth highest point of the third graph and a magnitude of the reflectance variation at an n+1th lowest point of the third graph, or

any combination thereof, and

n is a natural number.

8. The method of claim 1 , wherein the determining the thickness based on the magnitudes of the reflectance variation at highest points and lowest points of the third graph includes

determining the thickness based on a sum of (k+1) values, from a difference between a magnitude of the reflectance variation at an nth highest point of the third graph and a magnitude of the reflectance variation at an nth lowest point of the third graph to a difference between a magnitude of the reflectance variation at an n+kth highest point of the third graph and a magnitude of the reflectance variation at an n+kth lowest point of the third graph,

determining the thickness based on a sum of (k+1) values, from a difference between the magnitude of the reflectance variation at the nth highest point of the third graph and a magnitude of the reflectance variation at an n+1th lowest point of the third graph to a difference between the magnitude of the reflectance variation at the n+kth highest point of the third graph and a magnitude of the reflectance variation at an n+k+1th lowest point of the third graph, or

any combination thereof, and

wherein each value of n and k is a natural number.

9. The method of claim 1 , wherein

the determining the thickness based on the magnitudes of the reflectance variation at highest points and lowest points of the fourth graph is based on a magnitude of the reflectance variation at an n+1th highest point of the fourth graph, and

n is a natural number.

10. The method of claim 1 , wherein

the determining the thickness based on the magnitudes of the reflectance variation at highest points and lowest points of the fourth graph is based on a sum of (k+1) values, from a magnitude of the reflectance variation an n+1th highest point of the fourth graph to a magnitude of the reflectance variation at an n+k+1th highest point of the fourth graph, and

each value of n and k is a natural number.

11. The method of claim 1 , wherein a difference between a magnitude of the reflectance variation at a starting point of the first graph and a magnitude of the reflectance variation at a first lowest point of the first graph is constant regardless of the thickness of the underlying layer.

12. A method, the method comprising:

irradiating a sample with a pump laser pulse to induce generation of an acoustic wave in the sample such that the acoustic wave propagates through the sample over time, the sample including a substrate, an underlying layer on the substrate, an overlying layer on the underlying layer;

irradiating the sample with a probe laser pulse subsequent to irradiating the sample with the pump laser pulse;

determining an initial reflectance variation of the sample over time, based on monitoring a variation of a reflection of the probe laser pulse from the sample over time, to generate an initial graph showing an initial variation of reflectance of the sample over time;

controlling the pump laser pulse and the probe laser pulse based on the initial graph to

irradiate the sample with the controlled pump laser pulse, and

irradiate the sample with the controlled probe laser pulse;

determining a final reflectance variation of the sample over time, based on monitoring a variation of a reflection of the controlled probe laser pulse from the sample over time, to generate a final graph showing a final variation of reflectance of the sample over time based on the controlling; and

determining a thickness of the underlying layer based on the final graph.

13. The method of claim 12 , wherein the controlling the pump laser pulse and the probe laser pulse based on the initial graph includes controlling the pump laser pulse and the probe laser pulse based on a difference between a magnitude of the initial reflectance variation at a starting point of the initial graph and a magnitude of the initial reflectance variation at a first lowest point of the initial graph.

14. The method of claim 13 , wherein the difference between the magnitude of the final reflectance variation at the starting point of the final graph and the magnitude of the final reflectance variation at the first lowest point of the final graph is constant regardless of the thickness of the underlying layer.

15. A method, the method comprising:

generating an acoustic wave in a sample including a substrate, an underlying layer on the substrate, and an overlying layer on the underlying layer;

generating a first graph showing a reflectance variation of the sample as a function of time during propagation of the acoustic wave in the sample; and

determining a thickness of the underlying layer based on the first graph,

wherein the determining the thickness based on the first graph includes

determining the thickness based on magnitudes of the reflectance variation at highest points and lowest points of the first graph,

determining the thickness based on magnitudes of the reflectance variation at highest points and lowest points of a second graph, the second graph generated based on subtracting a saturation value from magnitudes of the reflectance variation in the first graph,

determining the thickness based on magnitudes of the reflectance variation at highest points and lowest points of a third graph, the third graph generated based on subtracting a background noise from magnitudes of the reflectance variation in the first graph, or

determining the thickness based on magnitudes of the reflectance variation at highest points and lowest points of a fourth graph, the fourth graph generated based on normalizing the third graph so that a magnitude of the reflectance variation at a first lowest point of the fourth graph is 0 and a magnitude of the reflectance variation at a first highest point of the fourth graph is 1.

16. The method of claim 15 , wherein the generating the acoustic wave in the sample includes irradiating the sample with a pump laser pulse.

17. The method of claim 15 , wherein the generating the first graph includes irradiating the sample with a probe laser pulse; and

detecting a reflection of the probe laser pulse from the sample.