Electronic Package Surface Shape Quantification via Series Expansion
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Solution Overview
Problem
Conventional electronic component packaging metrology assumes spherically symmetric surface shapes, failing to accurately characterize complex surface shapes like axial symmetry, saddle symmetry, and twisted symmetries, which are critical for ensuring functionality and reliability in stacked components due to thermal expansion and mechanical stresses.
Innovation Solution
A method and apparatus for quantifying surface shapes using a series expansion fit with base functions to calculate shape coefficients, allowing for the description of non-spherical symmetries and providing intrinsic surface shape parameters like Xsag, Ysag, and Twist, enabling precise control and communication of surface shapes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional warpage measurement methods are used, then measurement simplicity is maintained, but measurement precision deteriorates for complex surface shapes
Solution Approach 1:
The patent transforms the surface shape description from a single warpage parameter to a set of shape coefficients (a11, a12, a22, etc.) derived from a quadratic polynomial fit. This parameter transformation enables precise characterization of complex surface shapes including axial symmetry, saddle symmetry, and twisted symmetries that cannot be described by conventional warpage measurements alone.
2Manufacturing precision
If spherical symmetry assumption is made, then measurement process is simplified, but manufacturing precision deteriorates for non-spherical surfaces
Solution Approach 1:
The patent explicitly addresses and measures asymmetric surface shapes by incorporating cross-terms (a12) and separate quadratic coefficients (a11, a22) in the polynomial fit. This enables accurate characterization of axial symmetry, saddle symmetry, and twisted symmetries, allowing manufacturing precision to be maintained for non-spherical surfaces that were previously undetectable or mischaracterized.
3Loss of information
If single warpage parameter is used, then data processing is simplified, but information loss occurs for complex surface shapes
Solution Approach 1:
The patent segments the surface shape information into distinct quadratic polynomial coefficients (a11, a12, a22, a1, a2, a0) that can be independently measured and analyzed. Each coefficient represents a specific aspect of the surface geometry, allowing complete information retention about complex surface shapes while enabling systematic data processing and interpretation.
Data Source
AI summary
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.