Apparatus and method for monitoring and controlling thickness of a crystalline layer

1. An apparatus to monitor thickness of a crystalline sheet grown from a melt, comprising:

a process chamber configured to house the melt and the crystalline sheet;

an x-ray source disposed on a first side of the crystalline sheet and configured to deliver a first x-ray beam that penetrates a thickness of the crystalline sheet from a first surface to a second surface opposite the first surface; and

an x-ray detector disposed on the first side of the crystalline sheet and configured to intercept a second x-ray beam that is generated by reflection of the first x-ray beam from a group of crystallographic planes that extend through the thickness of the crystalline sheet,

wherein λ=2d sin θ,

where λ is a wavelength of at least some x-rays of the first x-ray beam, d is a spacing between adjacent crystallographic planes of the group of crystallographic planes, and θ is an angle of incidence of the at least some x-rays with respect to the group of crystallographic planes.

2. The apparatus of claim 1 , further comprising:

a crucible configured to contain the melt;

a heating system to provide heating to the melt;

a crystallizer configured to generate a crystallization front of the crystalline sheet at a surface of the melt; and

a crystal puller configured to draw the crystalline sheet at a pull rate along the surface of the melt.

3. The apparatus of claim 2 , further comprising a controller configured to:

receive a measurement signal from the detector indicative of the thickness of the crystalline sheet between the first surface and the second surface; and

responsive to the measurement signal, send at least one control signal to adjust operation of at least one of: the heating system, crystallizer, and crystal puller.

4. The apparatus of claim 1 , wherein the melt is silicon, and wherein a thickness of the crystalline sheet is less than 2 mm.

5. The apparatus of claim 1 , wherein the x-ray source is configured to generate monochromatic radiation, wherein λ is less than 1 Å.

6. The apparatus of claim 1 , wherein the x-ray source is configured to generate polychromatic radiation.

7. The apparatus of claim 1 , wherein the group of crystallographic planes is oriented at a non-zero angle with respect to the first surface.

8. The apparatus of claim 1 , wherein the detector comprises a planar detector surface configured to form an x-ray image of the second x-ray beam, wherein a height of the x-ray image along a first direction of the planar detector surface is proportional to a thickness of the crystalline sheet between the first surface and second surface, and wherein a width of the x-ray image along a second direction of the planar detector surface is proportional to a width of the crystalline sheet.

9. The apparatus of claim 1 , further comprising:

an entrance enclosure configured to conduct the first x-ray beam from the x-ray source to the process chamber under vacuum; and

an exit enclosure configured to conduct the second x-ray beam from the process chamber to the detector under vacuum.

10. An apparatus to control crystalline sheet grown from a melt, comprising:

a process chamber configured to house the melt and crystalline sheet;

a thickness monitoring system, comprising:

an x-ray source configured to deliver a first x-ray beam that penetrates the crystalline sheet through a thickness of the crystalline sheet from a first surface to a second surface opposite the first surface;

an x-ray detector configured to intercept a second x-ray beam that is generated by Bragg diffraction of the first x-ray beam from a group of crystallographic planes that extend through the thickness of the crystalline sheet; and

a control system coupled to the detector and configured to:

receive a measurement signal from the detector indicative of a thickness of the crystalline sheet between the first surface and the second surface; and

responsive to the measurement signal, send at least one control signal to adjust at least one of: heating rate of the melt, cooling rate at a crystallization region of the melt, and pulling rate of the crystalline sheet.

11. The apparatus of claim 10 , further comprising:

a crucible configured to contain the melt;

a crystallizer configured to generate a crystallization front of the crystalline sheet at a surface of the melt, wherein the crystalline sheet has an initial thickness downstream of the crystallizer;

a melt back heater to melt back a fraction of the initial thickness; and

a crystal puller configured to draw the crystalline sheet at a pull rate along the surface of the melt, wherein the at least one control signal is operative to adjust operation of at least one of: the crystallizer, melt back heater, and crystal puller.

12. The apparatus of claim 10 , wherein the x-ray source is configured to generate monochromatic radiation, wherein λ is less than 1 Å.

13. The apparatus of claim 10 , wherein the x-ray source is configured to generate polychromatic radiation.

14. The apparatus of claim 10 , wherein the group of crystallographic planes is oriented at a non-zero angle with respect to the first surface.

15. The apparatus of claim 10 , wherein the detector comprises a planar detector surface configured to form an x-ray image of the second x-ray beam, wherein a height of the x-ray image along a first direction of the planar detector surface is proportional to the thickness of the crystalline sheet between the first surface and second surface, and wherein a width of the x-ray image along a second direction of the planar detector surface is proportional to a width of the crystalline sheet.

16. The apparatus of claim 10 , wherein the controller is configured to determine from the measurement signal at least one of: a single point thickness of the crystalline sheet, an average thickness of the crystalline sheet, a thickness profile of the crystalline sheet, and a thickness variation of the crystalline sheet.

17. The apparatus of claim 10 , further comprising:

an entrance enclosure configured to conduct the first x-ray beam from the x-ray source to the process chamber under vacuum; and

an exit enclosure configured to conduct the second x-ray beam from the process chamber to the detector under vacuum.

18. A method for controlling thickness of a crystalline sheet, comprising:

crystallizing the crystalline sheet on a surface of a melt using a crystallizer wherein the crystalline sheet has an initial thickness downstream of the crystallizer;

pulling the crystalline sheet away from the crystallizer along a pull direction;

directing a first x-ray beam to the crystalline sheet, wherein the first x-ray beam is configured to penetrate the crystalline sheet through a thickness of the crystalline sheet from a first surface to a second surface opposite the first surface; and

intercepting at an x-ray detector a second x-ray beam that is generated by Bragg diffraction of the first x-ray beam from a group of crystallographic planes that extend through the thickness of the crystalline sheet.

19. The method of claim 18 , further comprising:

forming an image of the second x-ray beam on the x-ray detector; and

determining a sheet thickness t of the crystalline sheet from a height h of the image, where h is proportional to t.

20. The method of claim 18 , further comprising;

receiving a measurement signal indicative of the thickness of the crystalline sheet; and

sending a control signal to adjust one or more of: the crystallizing, the pulling, and melting back of the crystalline sheet.