Apparatus and method for determining surface contour of piezoelectric wafers

Claim 1

An apparatus for determining the surface contour of a substantially flat wafer of piezoelectric material having a slight convexity in its opposing faces by measuring a frequency response of the wafer in a plurality of locations, comprising: a base for supporting the wafer, said base including means for coupling the wafer to ground; probe means for applying a localized electrical field to a plurality of locations on one face of the wafer; and means for measuring the frequency response of the wafer at each of said locations.

Claim 2

An apparatus for determining the surface contour of a substantially flat wafer of piezoelectric material having a slight convexity in its opposing faces by measuring a frequency response of the wafer in a plurality of locations, comprising: a base for supporting the wafer, said base including means for coupling the wafer to ground; probe means for applying a localized electrical field to a plurality of locations on one face of the wafer; and means for measuring the frequency response of the wafer at each of said locations.

Claim 14

An apparatus for determining the surface contour of a substantially flat wafer of piezoelectric material having a slight convexity in its opposing faces by measuring the response of the wafer in a plurality of locations, comprising: a base comprising an electrically conductive member having a flat bearing surface for supporting the wafer, said flat bearing surface extending beyond the edges of the wafer, said base further including means for coupling the wafer to ground; probe means for applying a localized electrical field to a plurality of locations on one face of the wafer, said probe means having an electrode with a forward end having lateral dimensions much smaller than the face of the wafer, said forward end being supported adjacent said base at a distance sufficient to permit the wafer to be placed therebetween without physical contact between said electrode and the face of the wafer, said probe means further including shielding means surrounding said electrode but insulated therefrom, for grounding out electrical field fringing at said electrode forward end; and means for measuring the response of the wafer at each of said locations.

Claim 15

An apparatus for determining the surface contour of a substantially flat wafer of piezoelectric material having a slight convexity in its opposing faces by measuring the response of the wafer in a plurality of locations, comprising: a base comprising an electrically conductive member having a flat bearing surface for supporting the wafer, said flat bearing surface extending beyond the edges of the wafer, said base further including means for coupling the wafer to ground; probe means for applying a localized electrical field to a plurality of locations on one face of the wafer, said probe means having an electrode with a forward end having lateral dimensions much smaller than the face of the wafer, said forward end being supported adjacent said base at a distance sufficient to permit the wafer to be placed therebetween without physical contact between said electrode and the face of the wafer, said probe means further including shielding means surrounding said electrode but insulated therefrom, for grounding out electrical field fringing at said electrode forward end; and means for measuring the response of the wafer at each of said locations.

Claim 18

A method of determining the radius of curvature, R, of the surface of a convex wafer of piezoelectric material comprising: applying a localized electrical field to an arbitrary location on a face of the wafer while monitoring the frequency response to determine the Oth order frequency of the wafer; traversing the face of the wafer with said localized electrical field while monitoring the amplitude of the response at said Oth order frequency until the location of maximum amplitude is found, said location corresponding to the point of maximum thickness of said wafer; scanning the frequency response of the wafer at said point of maximum thickness to determine the frequency separation between the Oth order mode and at least one succeeding even order mode; developing a plot of the radius of curvature of the wafer, R, as a function of frequency separation from the formula: ##EQU3## where ω is the resonant frequency in radians for the Nth y axis overtone, the Mth x axis overtone and the Pth z axis overtone, C 66 =C 66 +e 26 2 /ε 22 where C 66 is an elastic coefficient of the piezoelectric material, e 26 is a piezoelectric coupling coefficient and ε 22 is a dielectric constant of the piezoelectric material in the thickness direction of the wafer, and C 11 and C 55 are elastic coefficients of the piezoelectric material; and correlating said frequency separation between the Oth order mode and at least one succeeding even order mode with said plot to determine R.

Claim 19

A method of determining the radius of curvature, R, of the surface of a convex wafer of piezoelectric material comprising: applying a localized electrical field to an arbitrary location on a face of the wafer while monitoring the frequency response to determine the Oth order frequency of the wafer; traversing the face of the wafer with said localized electrical field while monitoring the amplitude of the response at said Oth order frequency until the location of maximum amplitude is found, said location corresponding to the point of maximum thickness of said wafer; scanning the frequency response of the wafer at said point of maximum thickness to determine the frequency separation between the Oth order mode and at least one succeeding even order mode; developing a plot of the radius of curvature of the wafer, R, as a function of frequency separation from the formula: ##EQU3## where ω is the resonant frequency in radians for the Nth y axis overtone, the Mth x axis overtone and the Pth z axis overtone, C 66 =C 66 +e 26 2 /ε 22 where C 66 is an elastic coefficient of the piezoelectric material, e 26 is a piezoelectric coupling coefficient and ε 22 is a dielectric constant of the piezoelectric material in the thickness direction of the wafer, and C 11 and C 55 are elastic coefficients of the piezoelectric material; and correlating said frequency separation between the Oth order mode and at least one succeeding even order mode with said plot to determine R.

Claim 21

A method of determining the maximum thickness, 2ho, of a convex wafer of piezoelectric material comprising: applying a localized electrical field to an arbitrary location on a face of the wafer while monitoring the frequency response to determine the Oth order frequency of the wafer; traversing the face of the wafer with said localized electrical field while monitoring the amplitude of the response at said Oth order frequency until the location of maximum amplitude is found, said location corresponding to the point of maximum thickness of the wafer; scanning the frequency response of the wafer at said point of maximum thickness to determine the frequency separation between the Oth order mode and at least one succeeding even order mode; developing a plot of the maximum thickness, 2h o , of the wafer as a function of frequency separation from the formula: ##EQU4## where ω is the resonant frequency in radians for the Nth y axis overtone, the Mth x axis overtone and the Pth z axis overtone, C 66 =C 66 +e 26 2 /ε 22 where C 66 is an elastic coefficient of the piezoelectric material, e 26 is a piezoelectric coupling coefficient and ε 22 is a dielectric constant of the piezoelectric material in the thickness direction of the wafer, and C 11 and C 55 are elastic coefficients of the piezoelectric material; and correlating said frequency separation between the Oth order mode and at least one succeeding even order mode with said plot to determine 2h o .

Claim 22

A method of determining the maximum thickness, 2ho, of a convex wafer of piezoelectric material comprising: applying a localized electrical field to an arbitrary location on a face of the wafer while monitoring the frequency response to determine the Oth order frequency of the wafer; traversing the face of the wafer with said localized electrical field while monitoring the amplitude of the response at said Oth order frequency until the location of maximum amplitude is found, said location corresponding to the point of maximum thickness of the wafer; scanning the frequency response of the wafer at said point of maximum thickness to determine the frequency separation between the Oth order mode and at least one succeeding even order mode; developing a plot of the maximum thickness, 2h o , of the wafer as a function of frequency separation from the formula: ##EQU4## where ω is the resonant frequency in radians for the Nth y axis overtone, the Mth x axis overtone and the Pth z axis overtone, C 66 =C 66 +e 26 2 /ε 22 where C 66 is an elastic coefficient of the piezoelectric material, e 26 is a piezoelectric coupling coefficient and ε 22 is a dielectric constant of the piezoelectric material in the thickness direction of the wafer, and C 11 and C 55 are elastic coefficients of the piezoelectric material; and correlating said frequency separation between the Oth order mode and at least one succeeding even order mode with said plot to determine 2h o .

Claim 23

A method of determining the location of the point of maximum thickness of a convex wafer of piezoelectric material comprising: applying a localized electrical field to an arbitrary location on a face of the wafer while monitoring the frequency response to determine the Oth order frequency of the wafer; traversing the face of the wafer with said localized electrical field while monitoring the amplitude of the response at said Oth order frequency until the location of maximum amplitude is found, said location corresponding to the location of the point of maximum thickness of the wafer.

Claim 24

A method of determining the location of the point of maximum thickness of a convex wafer of piezoelectric material comprising: applying a localized electrical field to an arbitrary location on a face of the wafer while monitoring the frequency response to determine the Oth order frequency of the wafer; traversing the face of the wafer with said localized electrical field while monitoring the amplitude of the response at said Oth order frequency until the location of maximum amplitude is found, said location corresponding to the location of the point of maximum thickness of the wafer.