Test surfaces useful for calibration of surface profilometers
The present invention provides for test surfaces and methods for calibration of surface profilometers, including interferometric and atomic force microscopes. Calibration is performed using a specially designed test surface, or the Binary Pseudo-random (BPR) grating (array). Utilizing the BPR grating (array) to measure the power spectral density (PSD) spectrum, the profilometer is calibrated by determining the instrumental modulation transfer function (IMTF).
1. A test surface comprising:
(a) a substrate; and
(b) a plurality of grooves, wherein the plurality of grooves are distributed in a pseudo-random pattern on the substrate and have an essentially uniform depth, and wherein each groove is essentially parallel to each other groove and has a depth of about 1 nm to 100 μm;
whereby the test surface is configured for calibration of a surface profilometer.
2. The test surface of claim 1 , wherein the pseudo-random pattern of the plurality of grooves is a binary pseudo-random distribution of the grooves generated using a maximum-length pseudorandom sequence (MLPRS).
3. The test surface of claim 2 , wherein the pseudo-random pattern is generated using a pseudo-random number generator.
4. The test surface of claim 2 , wherein the pseudo-random pattern is generated using a maximum-length pseudorandom sequence (MLPRS).
5. The test surface of claim 1 , wherein the grooves have an elementary pitch equal to a width of the groove.
6. The test surface of claim 1 , wherein the grooves have a width of about 1 nm to 10 mm.
7. The test surface of claim 6 , wherein the width of each groove is about 1 nm to 2.5 μm.
8. The test surface of claim 1 , wherein the grooves are distributed into the substrate by a technique selected from the group consisting of lithography, etching, machining, deposition, or other suitable means.
9. The test surface of claim 1 , wherein the substrate is has a smooth surface.
10. The test surface of claim 1 , wherein the substrate is selected from the group consisting of silicon, silicon carbide, silicon nitride, glass, metal, and plastic.
11. The test surface of claim 1 , wherein the surface profilometer is a stylus profilometer, optical microscope, interferometric microscope, atomic force microscope, scanning probe microscope, optical scatterometer, extreme ultraviolet (EUV) scatterometer, or x-ray scatterometer.
12. The test surface of claim 1 , wherein the depth of each groove is about 1 nm to 700 nm.
13. A method of calibrating surface profilometers using a test surface comprising:
(a) providing a test surface comprising
(i) a substrate, and
(ii) a plurality of grooves, wherein the plurality of grooves are distributed in a pseudo-random pattern on the substrate and have an essentially uniform depth, and wherein each groove is essentially parallel to each other groove; and
(b) experimentally measuring a power spectral density distribution using the test surface;
(c) theoretically simulating an ideal power spectral density distribution of the test surface; and
(d) taking the square root of the ratio of the experimentally measured power spectral density to the theoretically simulated power spectral density to find an instrumental modular transfer function (IMTF).
14. The method of claim 13 , wherein the IMTF is evaluated by comparing a power spectral density distribution measured using the test surface with a corresponding ideal numerically simulated power spectral density distribution of the test surface.
15. A method of determining instrumental modular transfer function (IMTF) of surface profilometers comprising:
(a) providing a test surface comprising
(i) a substrate, and
(ii) a plurality of grooves, wherein the plurality of grooves are distributed in a pseudo-random pattern on the substrate and have an essentially uniform depth, and wherein each groove is essentially parallel to each other groove;
(b) experimentally measuring a power spectral density distribution using the test surface;
(c) theoretically simulating an ideal power spectral density distribution of the test surface; and
(d) taking the square root of the ratio of the experimentally measured power spectral density to the theoretically simulated power spectral density to find an IMTF.
16. A test surface comprising:
(a) a substrate,
(b) a plurality of indentations, wherein the plurality of indentations are distributed in a pseudo-random pattern on the substrate and have an essentially uniform depth and each indentation has a depth of about 1 nm to 100 μm;
whereby the test surface is configured for calibration of a surface profilometer.
17. The test surface of claim 16 , wherein the pseudo-random pattern of the plurality of indentations is generated using a uniformly redundant array (URA).