Force, pressure, or stiffness measurement or calibration using graphene or other sheet membrane

1. An apparatus comprising:

a substrate, including a substantially circular well;

a deformable sheet membrane, suspended over the well, the membrane configured to include a specified integer number of one or more monolayers; and

a processor-readable storage medium comprising:

accompanying information about the suspended membrane or the substrate that, with a deflection displacement response of the suspended membrane to an applied force or pressure, provides a measurement of the applied force or pressure; and

instructions that, when performed by a processor, cause the processor to calibrate a transducer using the accompanying information about the deflection displacement response of the suspended membrane to the applied force or pressure.

2. The apparatus of claim 1 , wherein the storage medium comprises accompanying information about at least one of a dimension of the well or a tension of the membrane.

3. The apparatus of claim 1 , further comprising the transducer configured to transduce a deflection of the membrane, for use with the accompanying information, to provide the measurement of the applied force or pressure.

4. The apparatus of claim 3 , wherein the transducer comprises at least one of an atomic force microscope (AFM) or a nanoindenter.

5. The apparatus of claim 1 , comprising a plurality of wells, included on the substrate, and corresponding suspended membranes.

6. The apparatus of claim 1 , wherein the membrane comprises graphene.

7. The apparatus of claim 6 , wherein the membrane consists of graphene.

8. A method comprising:

using a substrate including a substantially circular well;

using a deformable sheet membrane that is suspended over the well, the membrane configured to include a specified integer number of monolayers; and

calibrating a device using a deflection displacement response of the suspended membrane to an applied force or pressure.

9. The method of claim 8 , comprising calibrating the device using (1) information about the suspended membrane or the substrate and (2) the deflection displacement response of the suspended membrane to an applied force or pressure.

10. The method of claim 8 , comprising using measured information about a diameter of the well in performing the calibrating.

11. The method of claim 8 , comprising using measured information about a tension of the membrane in performing the calibrating.

12. The method of claim 11 , comprising using measured information about the tension of the membrane in performing the calibrating, wherein the measured information is obtained using x-ray diffraction.

13. The method of claim 11 , comprising using measured information about the tension of the membrane in performing the calibrating, wherein the measured information is obtained using Raman spectroscopy.

14. The method of claim 8 , wherein using a deformable sheet membrane comprises using a material comprising graphene.

15. The method of claim 14 , wherein using a deformable sheet membrane comprises using a material consisting of graphene.

16. The method of claim 8 , wherein the calibrating comprises:

measuring a deflection of the membrane; and

providing information about the deflection to a user or automated process.

17. The method of claim 16 , wherein the measuring the deflection of the membrane comprises using the device being calibrated for measuring the deflection of the membrane.

18. The method of claim 8 , wherein the calibrating the device comprises calibrating an atomic force microscope (AFM).

19. The method of claim 8 , wherein the calibrating the device comprises calibrating a nanoindenter.

20. A method of claim 8 , comprising:

measuring at least one of a diameter of the well or a tension of the membrane; and

providing a user or automated process with information about at least one of the diameter of the well or a tension of the membrane.

21. A method comprising:

providing an apparatus comprising:

a substrate, including a substantially circular well;

a deformable sheet graphene membrane, suspended over the well, the membrane configured to include a specified integer number of one or more graphene monolayers; and

a storage medium comprising accompanying information about the suspended membrane or the substrate that, with a deflection displacement response of the suspended membrane to an applied force or pressure, provides a measurement of the applied force or pressure, wherein the storage medium comprises accompanying information about a dimension of the well and a tension of the membrane;

a transducer configured to transduce a deflection of the membrane, for use with the accompanying information, to provide the measurement of the applied force or pressure, wherein the transducer comprises at least one of an atomic force microscope (AFM) or a nanoindenter; and

calibrating at least one of an atomic force microscope (AFM) device or a nanoindenter device, using (1) information about the suspended membrane or the substrate, including using measured information about a diameter of the well and measured information about a tension of the membrane obtained using at least one of x-ray diffraction or Raman spectroscopy, and (2) the deflection displacement response of the suspended membrane to an applied force or pressure, wherein the calibrating comprises

measuring a deflection of the membrane; and

providing information about the deflection to a user or automated process.

22. The apparatus of claim 4 , wherein the processor-readable medium includes instruction to calibrate the transducer using measured information about a diameter of the well and measured information about a tension of the membrane.

23. The apparatus of claim 22 , wherein the measured information about the tension of the membrane is obtained using at least one of x-ray diffraction or Raman spectroscopy.