Surface shape metric and method to quantify the surface shape of electronic packages
A method of quantifying a shape of a surface includes measuring an elevation (z) of the surface at a plurality of locations in an x-y plane of the surface. The measurement data is fit to a series expansion in terms of one or more base functions that include a series expansion fit. A vector of shape coefficients are calculated from the series expansion fit. A vector of shape coefficients are output.
1. A computer-implemented method of quantifying a shape of a surface of a semiconductor die comprising:
measuring an elevation (z) of the surface of the semiconductor die at a plurality of locations in an x-y plane of the surface comprising measurement data;
performing a fit of the measurement data to a series expansion in terms of one or more base functions comprising a series expansion fit, wherein the base functions are generalized monomials;
calculating a vector of shape coefficients from the series expansion fit;
calculating, based on the vector of shape coefficients, intrinsic surface shape parameters X sag describing an effective bow along a x-axis, Y sag describing an effective bow along a v-axis, and Twist describing an elevation of a fourth corner with respect to a seating plane containing three other corners of a four corner surface; and
outputting the intrinsic surface shape parameters.
2. The computer-implemented method of claim 1 , wherein the surface of the semiconductor die is an electronic component, package, package substrate, PCB, bolster plate, lid also known as a heat spreader, heat sink, or connector also known as a socket.
3. The computer-implemented method of claim 1 , wherein the base functions are natural modes of a rectangular plate with unconstrained edges.
4. A non-transitory computer readable medium comprising computer executable software instructions which, when executed by a processor, performs a method comprising:
measuring an elevation (z) of a surface at a plurality of locations in an x-y plane of the surface comprising measurement data;
performing a fit of the measurement data to a series expansion in terms of one or more base functions comprising a series expansion fit, wherein the base functions are generalized monomials;
calculating a vector of shape coefficients from the series expansion fit;
calculating, based on the vector of shape coefficients, intrinsic surface shape parameters X sag describing an effective bow along a x-axis, Y sag describing an effective bow along a v-axis, and Twist describing an elevation of a fourth corner with respect to a seating plane containing three other corners of a four corner surface; and
outputting the intrinsic surface shape parameters.
5. The non-transitory computer readable medium of claim 4 , wherein the surface of the semiconductor die is an electronic component, package, package substrate, PCB, bolster plate, lid also known as a heat spreader, heat sink, or connector also known as a socket.
6. The non-transitory computer readable medium of claim 4 , wherein the base functions are natural modes of a rectangular plate with unconstrained edges.
7. A computer-implemented method of quantifying a shape of a surface of a semiconductor die comprising:
identifying a target shape for the surface;
measuring the elevation (z) of the surface of the semiconductor die at a plurality of locations in the x-y plane of the surface comprising measurement data;
defining a residual surface as the difference between the measurement data and the target surface;
performing a fit of the residual surface to a series expansion in terms of one or more base functions comprising a series expansion fit, wherein the base functions are generalized monomials;
calculating a vector of shape coefficients from the series expansion fit;
calculating, based on the vector of shape coefficients, intrinsic surface shape parameters X sag describing an effective bow along a x-axis, Y sag an effective bow along a v-axis, and Twist describing an elevation of a fourth corner with respect to a seating plane containing three other corners of a four corner surface; and
outputting the intrinsic surface shape parameters.
8. The computer-implemented method of claim 7 , wherein the surface of the semiconductor die is an electronic component, package, package substrate, PCB, bolster plate, lid also known as a heat spreader, heat sink, or connector also known as a socket.
9. The computer-implemented method of claim 7 , wherein the base functions natural modes of a rectangular plate with unconstrained edges.